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Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 50X1 -HUM Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ARDC TECHNICAL REPORT TR 58-72 AVIA DOCUMENT No. 158301 ? PHYSICAL PRINCIPLES OF VECTOR BALLISTOCARDIOGRAPHIC MEASUREMENT STAT So A. Talbot The Johns Hopkins University June 1938 AIR RESEARCH AND DEVELOPMENT COMMAND Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R0024onn1nn1 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 STAT Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 a fr Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 Page 2 10 13 15 18 33 35 36 44 47 50 51 53 56 60 64 67 70 74 75 78 86 CONTENTS Preface: pattern of contract and report. Chapter 1: Introduction. Relation to medicine, physiology, biophysics. Theory, methodology and significance of BCG information, General aims of this program. Specific aims and procedures. History: force ballistocardiography. displacement ballistocardiography. II: Concepts - the quantitative basis of ballistocardiography. Dynamical assumptions. Other concepts and assumptions from biophysical view. III: Dynamics of the support-body system General analytical approach. Reduced equations in 6 dimensions. Relation of translation and rotation through line of resistance. Derivation of equations of motion in xzp plane. Experimental determination of coefficients: inertias. Determination of spring and damping coefficients. Solution of equations of motion: relation between planes. Equations in detail for xzp plane. Solution by Reeves computer. Solution by LCR analog. Critique of solutions. Chapter IV: Design of practical support systems for recumbent human subject - detailed analysis of structure. Analysis of suspension: stiffness and frequency in 6 dimensions. Damping in 6 dimensions (translatior) (Rotation) yaw, pitch and roll. V: Mercury bed dynamics. VI: Frequency analysis of the BCG. VII: Conclusions. Chapter Chapter 99 103 114 Chapter 127 Chapter 133 Chapter 137 References. 140 Appendices. ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-ninzr4pnnoAnnninn4c A Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 Preface: The purposes of this contract were stated: (1) To improve the technique of recording and measuring the internal force patterns of the heart and great vessels. (2) To establish relationships between ballistocardiographic data, and the normal and abnormal physiology of the cardiovascular system. It developed first that the technique of getting an external view of the internal forces generated by the moving heart and blood, was barred in every mode of motion by extraneous forces. These reaction artefacts on the body from its necessary supports to earth, had been recognized in part and remedies devised for the head-foot BCG, prior to our contract. We have deepened and extended the understanding of the nature and coupling of these extraneous forces, in all six dimensions (3 translation, 3 rotation) of body-ballistic motion. We also have devised and constructed practical means INF everceming them. This hes led to problems of designing structures with maximum rigidity and minimum weight, requiring the detailed application of aerodynamic and airframe principles, analysis and methods. It also led to devising and testing various solutions to the problem of six-dimensional seism support; taking account also of the special biophysics of the human physique. The final solutions employed are given in this report. The steps intermediate thereto were given in progress reports previously submitted. The study of relationships between BCG data and cardiovascular forces, was limited to the biophysical aspects of body dynamics. We did not reach the stage of investigating controlled hemodynamic alterations, as to their BCG manifestation. But we have investigated certain biological matters which underly the interpretation of all such physiological experiments. Such matters are the transmission of cardiovascular force information, from Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 11 H its diverse sources to the local transducer signals which define the BCG in practice. Without understanding this detailed coupling of the observa- tion to the biological activity, we cannot hope to realize detailed bio- logical meaning of BCG observations. These relationships are discussed in our first two chapteLs. This writing is therefore as much a Technical Report on Physical Prin- ciples of BCG Measurement, as it is a final report on our contract under- taking. As such, it is phrased to reach the understanding of those whose use it may best serve, namely the physiologists, biophysicists, engineers and mathematicians associated with scientifically advancing our understand- ing of hemodynamics in humans. The research reported herein is the result of extensive teamwork. Wolf W. vonWittern contributed much to the early conceptual basis and the study of low frequency suspensions. Sidney Roedel and James Harrison did the exploratory developmental work. After v.Wittern's departure to Karls- ruhe, Dr. Paul A. Crafton helped with the engineering analysis and on physical models. The detailed work on structural stress and the generalized analysis in Chap. III, IV and V, were carried out by Mr. Joseph M. Gwinn III, assouisted with the G. L. Martin Company. Fabrication of the rugged but lightweight structure was by them, as was assistance in the analog computa- tions. Thomas Englar and Robert Cramer explored the simpler LCR method of computing. To Mr. John G. Kummell the author owes much for detailing, supervision and development of successive structures, and to Mr. Stanley Przyborowsky for its execution. Joseph H. Condon contributed analytical in- sight to the differential pendulum, negative spring and other problems. Mr. Peter Hume devised the ingenious modification of Fourier Analysis presented; which was subsequently developed by Mr. G. N. Webb and Robert N. Glackin. Finally, the competent handling of this difficult typescript should be credited to Mrs. R. B. Garrett, 1 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 mow - I - Physical Principles of Vector Ballistocardiographic Measurement Introduction: A report under this title should interest two types of readers: those dealing with ballistocardiography (BCG) for clinical or physio- logical information, and those concerned with medical methodology or with the physics of biological systems. Unfortunately these groups A uu not tft IS idlrh 12141,??, a c---nn language : the principles and concepts of dynamics which describe multi-dimensional systems in several modes of motion, are central to engineering and physical training, but are absent from medical or biological training. Although these principles are widely applicable in biology, and essential to understanding the methods and rationale of BCG measurements, a survey of basic mechanics would be out of place in this report. We choose therefore to aim at the under- standing of engineers and physicists who may be called to work in this field; and of those biologists and clinicians whose special concern with ballistocardiography gives them some prior grasp(1)of the mechanics involved. We will include a review of these mechanical principles, but for readers untrained in biology, will first show from the physical point of view, why ballistocardiography is needed, what it consists of, justification of the physical assumptions (model) used, and what has been done so far. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043Rnn94nnn1nni Declassified in Part - Sanitized Copy Chap. 1. SETTING and PHILOsOPHY: 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 1. Perspectives of Ballistocardiography in relation to medicine, cardiovascular physiology, and biophysics. Present knowledge of the cardiovascular system rests on a rather limited range of information; we lack a whole area of data, which prevents our forming clear concepts of how the heart and vascular system performs as a whole, or of defects in that performance. This situation may be described in non-medical terms. .4.1Lc; F'.4" ga.tc,a4v vi znfnrmatinll hoc+ apvpioned, are those from electro cardiography (EKG) and from auscultation. The EKG gives information on what may be called the ignition, trigger or firing system. There are various ways in which firing can be faulty: parts of the musculature that cannot fire (infarcts), incorrect order of firing, irregularity, delayed timing, weak or overdeveloped firing. Insofar as the magnitude of the EKG reflects the thickness of the heart muscle, and its extent in the chest, the electrical information does tell something about the potential strength of the muscular pump. But in no way does the EKG foretell the mechanical performance, which only begins after firing: namely, the force, velocity pattern or volume of the stroke, nor the character of the systemic flow after ejection. Neither does the EKG give indication of impending failure, or of how far the mechanism is reaching into its reserve capacity just to satisfy the ordinary demands of the body. Though the pump's ignition may be operating, the EKG does not reveal that the conduits are clogged, or their walls strained to the limit; whether the gas lines (coronaries) are half closed, the motor idling or straining* *Small changes in the recovery wave of the "ignition system" between firing indicates but does not measure strain. 1.1111mommiiiiii Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R00240001nn1S-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 . 3 . under load or damage. The EKG measures cardiac status and performance very inadequately, and vascular not at all; and so must be supplemented by many other tests. Failing "ignition" is, of course, important. While some of the cellular electro-physiology is understood, much of the coordinated mechanism of the EKG is still controversial. The ambiguity is being at- tacked by several new analytical approaches(2,3,4i5) so that misfiring sequences should be more accurately described. Auscultation (stethoscopy) gives mechanical or performance in- formation to a limited and equivocal degree, about certain restricted parts of the system. The intake and output performance of all four heart valves can be characterized as normal, opening imperfectly, or closing imperfectly. The anatomical character of such defects can be inferred, but not accurately. Many other sounds (murmurs) are thought related to degree of defect, but with low reliability. As regards detailed physical bases of these sounds, it can be said they are completely unknown as yet. That is, the hydromechanical mechanisms by which turbulent blood produces murmur or clicks in this kind of an environment, are entirely unexplained: more is known about automobile valves and knocks by auscultation, than those of the heart. Although the basic problems are now being attacked, this source of cardiovascular information has progressed but little in two centuries; and at best is restricted in its purview, in relation to both capacity and performance of the normal or the subclinically weakened cardiovascular astern under load. Blood pressure data taken by catheter provides most of our current information on the dynamical or performance characteristics of the heart and vascular system. Experiments with dogs (and recently with humans) at rest or exercised, normal and diseased, have given much information of how Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-010431 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 this system which supplies all the others, responds to stress or demand. However, taking pressures is by no means a simple, non-dangerous procedure, especially near the left heart; nor does the information so gained, really determine the mechanical action desired. 0 00MenOWI f* .1 irm^fa AiWW ?????????????? ? ????? win+4^111 ra +hp b1.0014 MUclt, nhp.prviNit in order to characterize performance of a system primarily designed to provide blood flow. Completely knowing all the pressures in the system throughout the cardiac cycle, does not suffice to specify the flow. In principle, if also one knew all imsansstl flow would be known; but we do not yet know the nature of these impedances, nor can we measure them. Indeed other than the En22/11t1T1 relation there is no direct measure of impedance: just as in the case of electric current networks. Like active electrical networks and systems, these impedances change rapidly, to provide general and local control of the flow: so that the temporal behavior of the impedance pattern must be known also, to understand the rationale of cardiovascular performance. The problem of externally estimating cardiac and vascular status and performance, (at rest, under normal load, or sustained stress, or sickness) therefore reduces to find- ing and developing the interpretation of measurement of flow: the thing for which the cardiovascular system is designed. Flow is the main study of ballistocardiography, and ultimately of this research, Direct measures of flow are just now coming into existence, but until recently all flowmeters required procedures which either changed the flow or measured it erroneously. Among these the best were the orifice(6) and bristle mythods(7) a Preliminary models exist of flowmeters which can be sewn into animals, to measure flow correctly and without changing what they measure. But these (magnetic and supersonic) methods guimmin Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ??? ? ? Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 .5. cannot be used to study normal humans or patients without surgery. A catheter method of promise" has appeared. This may serve well for research in the hands of experts, and in a few locations, but is unsafe for routine or group studies f cardiovascular conditions; and too stringent for many subjects. The catheter method itself can psycho- somatically and by stimulation of the arterial inner wall, seriously alter the cardiovascular function. While this will not prevent eventually accumulating important and necessary data, it is a barrier ..^114-4na and general use, either as a scientific or a practical test. In sum, because of these defects of observation by EKG, stetho- scope and pulse pressure, we have now and in prospect no better methods of assessing the functional status of cardiac and vascular performance as to blood flow, than those of plethysmograph y and ballistics. Plethysmography (measurement of blood flow from swelling) gives information more local than general; i.e. best when related to limbs. It may give valuable information on the state AVIA function of the peripheral vascular system, if one can distinguish between deep and superficial flow (which have separate controls). The measurement of central flow by (43) electrical "impedance plethysmography" is still too unspecific to be successful. The ballistic method of evaluating cardiovascular function to which this report refers, has moved ahead considerably in the last fifteen years. The rather superficial method of correlations (which in early stages of medical science is alone available), has sustained medical interest by a few outstanding successes and a general positive relation- ship to heart and artery disease, and to the athletic heart. But through- out medical science, such statistics eventually give place to the study of functional relations in both the physiological and mathematical sense. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01n4nRnn9Annni A Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 -6 So in ballistocardiography (BCG) (the study of motions of the body during the cardiac cycle), the correlation of BCG wave-forms with normality vs. disease, is aow declining in importance. Emphasis has shifted to more scientific questions. To what degree do individual cardiac and vascular mechanisms, account for each detail of the observed body-motion? How do the observed displacement, velocity, acceleration of the body relate to those of the blood at rest and in specified stress? How do known alter- ations of the cardiac action, and of the (complex) impedance of the vas- cular network with age or drugs, alter the blood flow in detail? In particular, to what extent are these measurable externally,by measuring the vector components of the body motions? Clearly, to answer such questions is to acquire important practical information for medicine and for physical fitness, as well as basic undei:standing for physiology and biophysics. Modern methods of recording these body motions reveal such rich and characteristic detail, that such crude categories as "normal vs. abnormal" become too complex to have scientific or medical meaning. But scientists close to BCG development, find physiological relationships emerging v and measurement problems yielding steadily and rationally; so that this approach to external and objective specification of cardiovascular functions, offers increasing encouragement. In interpreting the BCG, it turns out that we must give mstrh stfpn tion to individual differences, and to distinguish vascular from cardiac dynamics. The statistical approach common in medicine, of correlating recorded details with normality and disease, worked poorly enough with the EKG, but is worse with the BCG. Instead of one, there are four major cycles of activity to interpret, all varying with the individual. Without the functional (mechanistic) approach to supplement the usual normal-abnormal Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043Rnn94nnninnig_A a ? Declassified in Part- Sanitized Copy Approved for Release @50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 . 7 . rubrics, the very richness of physiological information in the BCG defeats statistical methods. This has discouraged the correlational school of physicians. To compound the problem, vascular hemodynamics is still an infant science, and cardiac dynamics as well, lacking measurements of flew, is gt411 but little understood. So in this mid epoch, the demand for practical interpretation of the BCG finds scant satisfaction: much as was true with virus or allergies before their mechanisms became known. Indeed the present situation is self-defeating, (1) in that ex- ternal measurements of cardiovascular dynamics by this method are so poor technically, that only statistics instead of mechanisms are applicable. (2) Internal measurements on normal hemodynamics are not yet possible technically. (3) The low correlation of observations with individual cardiovascular status, caused by inhomogeneity of subjects,by artefact and by irrelevance of component information (arising from ignorance of mechanisms), has reduced the interest of the medical profession in this field. In this situation, we here attack the sector of reducing artefact and irrelevance in the record itself. The problem of cardiovascular dynamic mechanisms, is being attacked also by our laboratory. (8) To a considerable accuracy' the flow of blood in the body is actually measured by the body motion it produces. But the principles of measuring and interpreting the dynamic aspects of blood flow sensed through the body motion, are still being developed. At any instant the observations include multiple actions, and a vector summation of flow information in several directions at once. Were it not that the organization of this flow is quite different in the three major axes of the body, one might despair of separating the variables. Also, cardiovas- cular events are separated not only in direction but also in time, which encourages the hope that reliable and informative differential relations Declassified in Part- Sanitized Copy Approved for Release @50-Yr 2013/10/24: CIA-RDP81-01043Rnn94nnn1nn1g_A 3. Declassified in Part - Sanitized Copy A 13/10/24: CIA-RDP81-01043R002400010015-4 . 8 . can be found, from adequate multidimensional data showing phase relations. The principles and methods of getting these data are a main objective of this report. In interpreting body-ballistic measurements, one encounters strong individual differences among normals, such that the use of BCG wave ampli- tude ratios as in the rKa is inadequate as a criterion. The whole normal vs. abnormal view for the population as a whole, breaks down except in ex- treme or advanced cases. In this situation, an obvious remedy is to select sub-groups identified by other criteria, and to use dynamic as well as static descriptions: such groups are sex, age, relative size of heart, elastic status of vessels (phystoloeical age), constitutional type. All these may be used as starting areas for systematic work on dynamic (stress- strain) analysis, of the successive complexes in the BCG cycle: A second remedy is to separate the cardiac from the vascular factors in analysing cardiovascular function. This procedure is harder, involving as it does the selective use of short-acting drugs (both natural and synthetic) to create standard changes, and a clearer understanding of the typical ways in which the heart normally responds to standard changes in its hydro- mechanical load. It is encouraging to realize, however, that we now have an observing method which can ask and answer such questions on physiology and biophysics. Thirdly, in cardiovascular mechanics in contrast to the present EKG, there are three kinds of information, whose intercorrelation may be used. The moment, momentum and force of the heart and blood (displacement, velocity, acceleration of the body), -- though related as derivatives and by frequency content -- give quite diverse information about cardiovascular properties and behavior. This focuses the analysis on the physiology of the individual, by introducing mechanical principles which hold for all individuals. The Declassified in Part-Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-R npRi_flinAwnnnAnrs,-... e't Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 . 9 . validity of this attack has a of course, which has yet to be determined. In summarizing our perspective, we may say that contrasted with the information content of auscultation and the electrocardiogram, the ballistocardiogram intrinsically carries much more discriminable and significant data about the functional status and performance of the cardiovascular system. Physiologically and medically, the problems are to obtain reproducible data free of artefact and needless irrelevance; to establish bases of classifying and analysing these data; to relate them to other facts of physiology and pathology in a rational way. This whole program is progressing, but is still in an early stage of understanding. Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : OP Declassified in Part - Sanitized Cop Approved for Release ? 50-Yr 2913/10/24: CIA-RDP81-01043R002400010015-4 -10- 2. Theory, methodology and the significance of BCG information. The union of physics with biological science emphasizes that the way of observing things often decides the value of the observation. With the EKG the use of limb-leads for decades prevented the differential diagnosis of infarction. Reliance on the ear with the stethoscope, for generations prevented any detailed objective analysis of heart sounds. In the case of cardiovascular performance, restriction to blood-pressure data has misled and confused our understanding; the naive methods of recording the BCG now in clinical use, have obscured and discredited the information contained therein. In a new field, one should design methods of observation which minimize irrelevancies and artefacts. This implies foreknowledge and criteria of what is relevant and true: an absurd position. But the simpler problem of electrocardiography (another field of vector dynamics) showed that advances in 1119.21x, have each time brought advances in method. The planar analysis of EKG limb-leads followed the theories of Waller and Einthoven. The spherical approximation and potential theory introduced by Wilson, at once stimulated the clinical study of the newer chest and dorsal leads. Burger's theory of lead-space, extended by Frank, led in turn to new methods which reduce the artefact arising from heart-position and body-configuration, and so let us view the heart-vector more directly. Similarly in studying cardiovascular dynamics by the BCG, the theoreti- cal analysis of body motions by Curtis and Nickerson(10)(perceived by Gordon in 1877) was further explored and verified experimentally for acceleration by v.Wittern(12)and for displacement by Burger(9). Without expecting that treating the body as a rigid-mass in this way will ultimately provide . ? - Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-0104f1Pnn9Annninnig A ? ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 11 - basic understanding of the ballistic effects, this simple concept of the BCG* stands alongside Wilson's potential theory, in cutting away the ad hoc clinical methods which went before. The theoretical advances by Burger and v.Wittern generated new methods and revealed details which at once superseded the obscure criteria of normal vs. abnormal that clogged the clinical literature. So we may legitimately expect that this interplay of theory and method, which we extend in this report from the head-foot to the other vector components of the ,?.A.Ae,t1 ler111 Ovily to hat+pr ways of recording and further eliminate current obscurities. However, we are not entitled to expect that for three-dimensional body dynamics, the basic theory will be simple: any more than was Wilson's for the three-dimensional EKG. Luckily it happens that public interest in the dynamics of missies and planes, at least makes the technical vocabulary of our analysis familiar to many. Certainly the theory of rigid (as opposed to elastic) bodies in vibra- tion, is only a first approximation; so that as new aspects are revealed, the BCG recording methods which result from these rigid-body concepts likewise will become outmoded. (1) The modern methods'and lines of progress, result from asking certain physical questions about blood-flow in the body; but the answers given by these methods are colored by the rigid-body theory of the measurement. (2) Because of the questions asked, information arising from other forces (tissue vibration, action of joints, etc.) may rightly be regarded as irrelevant, artefactual, and to be avoided. (3) Scientific methodology is concerned with separating variables? to make information from various aspects as independent (orthogonal) as possible. Consequently *The name "Ballistocardiogram' given in 1940 to the record of whole-body motions under cardiovascular forces, has since proved almost a misnomer. Very little of the information recorded is attributable uniquely to the neaLL.,in the sense th2t the EKG is. 40.1111????????????????1110 Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 this whole physical approach differs basically from the biological approach. The latter presumes that the observations relate to the biological events, in an intrinsic way, which is not really determined either by the observer's method or his conceptual approach. However, we use here the more physical strategy which emphasizes dependence of observations on method, to attack the problem of determining the cardiovascular dynamics from body motion. Furthermore, this information is considered significant for our purposes, if it brings out various independent aspects of the displacement, ? "41-1rte.1 A7 V MA* acceleration of the blood flow, with a minimum of background or distortion from other factors. The ultimate test of this "significance" is indeed a cross-correlation, but not with other information of the same kind as in statistics, nor with disease symptoms or pathology; rather with direct in- ternal observation of blood flow in relation to controlled variables of cardiac function. Consequently, BCG methodology itself - our concern at the moment - cannot even be developed without intimate knowledge of the physics of blood-flow, seen in the detailed anatomical context of the human body, in a way specifically related to the particular BCG methods proposed. However, as a problem in biophysics, at each stage we design not for the actual com- plexities of the body, but for our abstraction: a reduced or simplified model which includes only as much at this stage as we choose to. The real art is to include enough features in the abstraction, to make the results useful as well as interesting. In summary, we may attribute the slow growth of understanding in ballisto- cardiography in the last fifteen years, to lack of an adequate theory, as with the EKG. The rigid-body theory of the body, plus conservation of momentum (as developed by Curtis, Burger and v.Wittern) admittedly does not conform to the bodily detail, but does separate the variables for clarity by introducing a model. When finally this must be related to details of blood flow, the model probably must be modified. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043111111111=1.0111 a Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 13 - B. GENERAL AIMS OP THIS THEORETICAL AND EXPERIMENTAL PROGRAM. The present program attempts (a) to clarify the physical problems aris- ing in vector ballistocardiography, and (b) to spotlight the kinds of in- formation available. With this information clearly in view, we attack (c) the practical problem of inventing devices and procedures to observe it correctly. We concentrate on the pla.s_ital_EET.plla.s_ of three-dimensional mechanics as the most important at this stage, for several reasons: (a) the rotational motion clearly affects the translational motion used to define cardiovascular force. This coupling must be reduced, before one can deal intelligently with the translational vector components of the cardiac hemodynamics. (b) In the anterior-posterior motion and in pitch-rotation, one should find unique views of the cardiac output (stroke volume); which in other directions of motion (e.g. head-foot) may be mixed with other information (e.g. arterial elasticity). Due to this mixing, the vector summation may not always be desirable. (c) The structural difference of the body along its three axes, raises new problems of passive body-mechanics. (d) The ultimate aim (stress-testing the cardiac per- formance) for hemodynamic reasons requires a sitting posture, which in turn requires solving similar problems of experimental design (e.g. a vertical suspension of "zero" frequency) mentioned in (b) above. The physical information we seek is of three kinds. (a) An effective record of the vector components of body motion, separated in such a way (orthogonal and informationally homogeneous) that vector composition becomes permissible*. (b) A study of this vector motion in its various dynamical aspects * Some BCG vector composition which is not permissiblein this sense, has $ been done for several years.(201 41) 22, 24, 15 55). Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 vs Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 - 14 - (displacement of c.g.1 momentum, and force); these have separate significance both physically and physiologically. (c) A study of each of the six motional components (3 translation, 3 rotation) with relation to its distinct physio- logical meaning; eliminating those data which are least useful. Besides clarifying and formulating the detailed physical observables to be recorded and the parameters involved, there is finally an equally demanding practical problem of creating a method to get this information. That is, even with improved understanding of what wain. " 'Velma from ballistocardiography in the head-foot axis, methods must be worked out in practice, de novo, for the five other axes of motion. The first two years of this "hardware" part.of the task, were spent in exploring various practical means that suggested them- selves, for (1) observing translation, free of rotational component (2) fabri- cating body-suspensions which did in fact fulfill dynamical requirements for frequency and stiffness not previously achieved in applied mechanisms. Null-frequency suspensions in three rotational dimensions were being worked on (secretly), under the name of inertial guidance systems. Our problem however, though dynamically similar, is in six dimensions, requiring isolation from the surround in translation as well as in rotation. This resembles in essence designing an artificial cloud or flying carpet, strong enough for the subject to lie or sit upon. A qualitative review of trial solutions rejected and accepted has been given in previous progress reports*, will be presented in this final report The quantitative results found practical Accompanying these trial solutions, of course, is the mass of detailed design, calculations, drawings, mechanical Investigation of the Unloaded Internal Ballistocardiogram: Its iophysica and Physiological Relation to Cardiac Performance. Contract #AF-18(600)-11n7 9/22/56. Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R0o24onn1nni Declassified in Part - Sanitized Copy A 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 work and and out-bugging which go with each proposition tested. These cannot (a) be detailed here. However, we will present/the precise dynamical basis and values which emerged as acceptable for this problem, and their limitations in general and in particular. We will present (b) experimental procedures which can be used to put this theory in action for: (1) determination of parameters, (2) interaction between degrees of freedom, (3) spectral range of fidelity and (4) evidence of practical validity of this approach, from records of humans. C. SPECIFIC AIMS AND PROCEDURES, To design dynamical measurements on a biological system one must start with designing specific hardware and experimental procedures, which intrinsical- ly determine what is observed. If one chooses to observe motions of the whole body, one must decide upon what set of concepts are to govern the design details. These concepts have already been subjected to discussion by the author(1) and others(9) and will be further criticized here. Furthermore, these basic con- cepts once adopted imply a physical model; which then invokes the corresponding physical theory and laws. Most of this theory is quite old, but has been re- developed in convenient form, for the motion of missiles and stress-testing aircraft. It is the theory of two rigid bodies, coupled in vector rotation and translation in free space. The range of validity of this theory for our purpose will be discussed. After arguing the conceptual basis, we will apply rigid body mechanics to the special interaxial couplings and body dimensional peculiarities of ballistocardiography, which differ somewhat for the various kinds of body supports used. The dynamical and physiological interpretation of the records in turn depend on these supports. A theoretical solution of the differential equations in certain planes (by analog computer) will be shown vs. frequenu the boundary conditions being certain intrinsic frequencies seen in BCG records. 1 Declassified in Part - Sanitized Copy A ?proved for Release @ 50-Yr 2013/10/24 ? CIA-RDP81-01043R002400010015-4 _ Declassified in Part- Sanitized Copy Approved for Release 50-Yr 2013/1 9/24: CIA-RDP81-01043R002400010015-4 a a - 16 - Our experience from head-foot recording is transferred to the five other modes of motion, to get order-of-magnitude values for the individual's body-parameters in these other axes. We aim to show a practical way how to record the translational motions in- dependently of the rotational, especially difficult as regards body roll, This way minimizes mechanical coupling between these basically independent aspects, without requiring routine use of complex computing equipment to separate the variables. This aim is specially important because the data of multidimensional or vector recording can easily get out of hand. Separating the rotation vector from the translation space-vector, enables us (for the first time) to display correctly the phase relations of the cardiovascular events in each plane of projection. While we have not yet carried this aim so far as to correct thor- oughly for orthogonality, standardization and directional transmission of the body (as has recently been done for the EKG) this elimination of (rot-trans) interaction, does take a step nearer to sensing the "intrinsic" or essential geometry of cardiovascular dynamics. Since observation of the cardiovascular system through body-dynamics, is only one of several important aspects, it is important to reduce it to essentials. The "space-vector" presentation probably better uses the synthetic powers of the observer's mind, and exhibits certain details in a form more striking than does the older BCG record against time; but both enhance understanding. In summary, for this aspect of the problem of cardiovascular dynamics, we aim 1. To establish a physical basis for data in several degrees of freedom, whose assumptions, range and degree of validity are clear. 2. To design rationally and to execute structures which produce such data, in a way which separates the variables. 3. To discuss the limitations and interpretation of these data, in each degree of freedom: Declassified in Part- Sanitized Copy Approved forlYr 2013/10/24: ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 17 m a) Graphically, in its aspects of frequency spectrum, the time axis, and phased vectors (Lissajous complexes) both in plane projection on the body axes and in space view (intrinsic axes). b) Physically, as to the meaning of the displacement moments, momentum and force, derivable from motions of the body. Our procedures have been: a) To improve the conceptual foundation of ballistocardiography as a vector problem. b) To formulate and carry out the six-dimensional analysis entailed by the conceptual basis chosen. c) To devise and construct mechanical means of taking the measurements required. d) To display in several forms, criticize and interpret these measure- ments as meaningful for the cardiovascular system. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? ? ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 D. HISTORY: Prior development of the theory and practice of the ballistic measurement of cardiovascular dynamics. Understanding of this problem has progressed in two parallel streams (11)(12) or dynamic views: the force aspect (expositions of Starr and v.Wittern) and the displacement aspect (Burger's exposition)(13)(9). Lying between is the momentum aspect (whose integral is the displacement, and whose derivative the force). This third aspect is best shown by the data of Nickerson(14) His method, by virtue of a suspension having broad mechanical resonance, records mainly t,,,Aly_vpinr4+v 7 7 - /4? proportional to cardiovascular MOMentUMkJ) and so exhibits the best correlation with cardiac output. However, the records of this method, like those of Starr and Dock, are shifted in phase, distorted and confused by resonance of the body-support coupling, which un- Airranm4,4 recognizedly intermixed the 01,11CL t.tylawm aCnar ts. W. v:Wittern resolved this confusion about force recording, by taking the acceleration record from pendular suspensions like Burger's [similar to those of Gordon (1877) and Henderson (1905)]. As a result, we now have available bodies of data based on two complementary views of the blood-body dynamics: the displacement(16) and the force in the head-foot direction. These two views conflict in no way, but supplement each other's information, and contribute to each other's under- standing. 1. Force ballistocardiography. Records of head-foot body-acceleration, insofar as the body accelerates as a unit, measure the forces exerted thereon by the cardiovascular system. For frequencies up to 8 cis or so, this unitary motion of the body in the head-foot (12,1,17) direction has been corroborated roughly by several workers - using an indirect method (external shakers). Firstly, the proof is rough, because it refers only to the impedance of the system as seen from the shaking position. Local recordings from the body Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? 19 4- itself resemble each other somewhat in displacement(12)up to 8 c/s, but poorly in acceleration. This results from local resonances (head, shoul- ders, etc.) and local forces (apex beat). Secondly, the shaker-table evidence of body unity is indirect. Shaking the body from without is by no means comparable to shaking it from within as is done by the cardiovascular system. Shaking by dorsal contact (v.Witternts method) actuates the coupling springs in a particular stiffness configuration and drives them in-phase Thus the constituent masses of the body are made to vibrate in a particular amplitude distribution at each frequency. This is not the same amplitude distribution with which these submasses vibrate,. when driven by the feet at various footboard pressures (Cunningham's method), or when driven by the heart and aorta via the skeleton. These differences of effective mass-distribution vs. frequency, are greatest in the vicinity of the natural frequency of the supine body (in response to a step displacement). As a result, the shape of the BCG record for frequency components above 4 c/s, depends appreciably on the use of foot-boards (Scarborough), ankle-supports (18) (12) (Smith) 1 shoulder braces, etc.' In sum, we can readily measure acceleration of support; but to multiply this by a unitary body-mass to arrive at "force" on body, we assume an ap- proximation which shows increasing error above about 8 c/s (Cunningham). Consequently we cannot regard wave details of the acceleration BCG in the 12-30 c/s band, as representing "forces" which are on the same scale, or in phase, with the slower force components. It is therefore better to scale such records frankly in acceleration units rather than force units(19); and not refer in any quantitative sense to the "force BCG". Qualitatively, how- ever, the "force" interpretation is legitimate and helpful for relating the observations to cardiovascular dynamics, in contrast to the "momentum" and Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 1 1 ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 "displacement" aspects which also operate on the same assumptions of body- unity. This report, concerned with improving the dynamical foundation of these cardiovascular measurements, must omit the growing body of literature on physiological interpretation, as to details of the "force" record and the evidence for it. We turn now to review the work done on recognition of the vector nature ,r OA Liitau forces. Lateral components of the BCG arise from the oblique pos- ture of the heart in ejection (and bilateral non-symmetry of vessels as well) which varies with individuals, body habitus, respiratory phase, and age. It is found that persons having quite disorderly head-foot records, may have quite regular lateral components, which increase systematically as the heart tilts with age.(20) In most cases the lateral (RL) record looks more oscillatory, especially in diastole. As with the head-foot "force" record, we must first scrutinize the method and its assumptions, before we accept such lateral records as valid or try to interpret them physiologically. (1) In the lateral mode the body-unity assumption rests on much shakier uounds. Transverse rigidity of the body is far less than head-foot; in fact, most of what transverse rigidity the supine body has, comes from the support or bed rather than the skeleton. Because of the smaller mass (thoracic cage) engaged in lateral motion, the smaller lateral forces give R,L. accelerations large enough to compare with the head-foot. This scale- factor needed for the vector sum has not been recognized in the literature. (2) The lateral record is more likely to contain "local BCG" aspects than the head-foot, because "averaging t'y support" transverse to the spine is poorer. The role of a platform in summing or averaging forces from the body is important in the head-foot direction but more so laterally. The HP force-pattern entering the platform varies with the subject's pressure on the footboard.(13) In this way, the contribution via spine + legs + pedal Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R0n74nnn1nni_a Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 21 . compression becomes more or less strong, compared with the contribution via shear-of-dorsal-tissues. The pattern of HF motion varies accordingly, mainly in smaller details. This factor has not been studied systematically, although v.Wittern has attempted to accentuate the HF forces of thoracic origin by coupling a foot-strap to the bed at hip-level. (3) As to method, the lateral motion is currently recorded by con- straining rotation (yaw) of the body-support, at the foot end. Thus, by moving the axis of rotation (yaw) from the body's e.g. to beyond the feet, the inertia seen by the driving force; innrp2sed, and the motion is re- duced. But it is simplified also, in that there is no phase-reversal of the lateral motion at the center of rotation. However, this yaw artifact introduces another scale-factor in the lateral (RL) record; partly deter- minable, but varying by twenty-five percent between individuals. In the lateral (RL) record it is plain that the motion observed depends strongly on where the body transmits force to the platform. The spine acts as a flexible shock-absorber, for lateral internal impacts originating be- tween shoulders and hips. Since the latter points lie on opposite sides of the c.g. of support, this factor may even reverse the phase of the out- put (for higher frequencies), depending simply on where the dorsal contacts are, which contribute to the lateral summation. In other words, there is local relative motion between the body and the support, which only forms the average observed. This averaging is inevitable to some degree, since even in head-foot the right and left sides of the body do not displace equally to the apex beat and the aorta is not strictly axial. Consequently, lateral chocking of the body must in some way be standardized(21). Clearly also, although the hips do contribute part of the HF drive to the platform, they do not assist the RL drive and so become mainly an inertial load in the cntoro lateral Declassified in Pad-- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015_4 ??? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 As a result of these three factors (flexure, rotation, local effects) the standardization of a method for lateral recording becomes especially important, if one is to speak of "the" lateral component of "the" cardio- vascular force cycle. Various workers have used several quite different methods. Braunstein(22) used a platform of considerable inertia mounted on stiff springs, which (like the Starr platform in the HP mode) follows the body in RL motion only below about 3 cis, above which it gets out of phase (both laterally and in yaw), at frequencies low in the BCG spectrum. Scar- borough and Talbot( 21) used a lighter platform mounted transversely to a . Starr bed (stiff to earth), with hip and shoulder boards to pick up the. .LIIC p Dock(2 3,24) L.uuLauit- a.44.L.ivA.m moves laterally lateral body-motion. against stiff metal springs, with respect to which (again like the Starr bed) the body oscillates on its own tissue-springs, both in translation and roll (independently). Both these oscillations appear in the record, often as dominating artefacts, v.Wittern(25) and Honig(20) used a quite light pendular platform pivoted at feet. Since this is constrained to move in a horizontal plane, the body rolls somewhat: which shows in the record. The mercury bed (Talbot and Deuchar)(26) is mechanically similar and produces the same artefact. Indeed it can be said that no lateral BCG record has been published so far, which is acceptable physically. The errors can probably not be characterized in detail until good records have been taken for comparison, but there are at least two and sometimes three basic artefacts in current (1) records, which prevent quantitative interpretation . With the high-frequency supports of Braunstein, S.carborough and Talbot, and Dock, there is firstly, a lateral resonance in translation, corresponding to the head-foot resonance at 4-5 c/s seen in the Dock and Starr head-foot BCG(2) With the ultra-low frequency IlLommisimaium Declassified in Part - Sanitized Copy Approved for Release _@ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Imsimismiw ? Sanitized Copy Approved for Release .23. 2013/10/24 : CIA-RDP81-01043R002400010015-4 supports of v.Wittern, Honig, Talbot and Deuchar, Scarborough and Soper(27) , the translational ..oftness of the suspension prevents such resonance in lateral translation. Secondly, because the body oscillates in roll (depending on the above-axis impact of the heart and roll constraint, e.g. flatness of back) a resonance in rotation also emerges.(3) Thirdly, there is the coupling in recording the transverse motion of platform, between roll and lateral motion: that is, the "true roll-BCG" (as distinguished from roll resonance) exerts its tangential forces on the bed. These forces combine with the true lateral ones, to give a mixed or composite RL record, contain- ing both translation and rotation (with the latter not proportionate to former) and two characteristic resonance frequencies. Both these latter errors in the BCG have been demonstrated by Scar- (28) borough ', by taking RI, records from n subject first prone, then supine. If roll artefact is absent, the record appears inverted. If excessive, the records look alike; all gradations between occur. It becomes clear that any body support which fails to follow the body freely in "roll" (i.e., is aperiodic in roll) provides the conditions for roll-resonance, and also for a mixed roll-lateral. BCG., Any relative motion between body and support then creates (torsional) restoring forces about the body's long axis (0, when the body rolls under the transverse off-axis impacts of the heart. This error occurs with all BCor's currently in use: they are all maintained horizontal, i.e., stiff about this p axis. Secondly, even if the platform were mounted in compliant gimbals about this axis, one must still devise a way to sense the lateral BCG alone, sans roll BCG. It results that a true "frontal-plane BCG" has not yet been published, either in components against time, or in vector form:. although many authors (cited above) have thought to do so. Research programs even exist here and abroad specifically for "vector" BCG studies, whose equipment is intrinsi- cally incapable of recording true lateral components (not to mention the Declassified in Part -Sanitized Copy Approved for Release 2013/10/24: CIA_Rnpp 1 1 1 1 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 24 - vertical). The nature of this error is clarified by considering how radically the shape and timiTof the HF record changed when its resonances were removed around 1955. A main activity of this contract has been to under- stand and remedy these defects of the frontal-plane BCG. Anterior-posterior (AP) or vertical component of the "force" BCG. It is possible to mount a platform on a set of springs which have high and equal stiffness in all three axes(29)(24). Here again the AP record is found to be distorted by translational resonance, as well as admixture of the resonance in roll. But although the RI, (x) and HP (y) motions are relatively easy to make so compliant as to be aperiodic(26), away to do this has not heretofore been found simultaneously for the vertical (z) motion. The literature of mechanics actually provides no ready solutions for this practical problem; althqugh suspensions of very low vertical frequency have been achieved by air springs for busses; and by coil springs and graVity for seismography(30)and for calibrating low-frequency accelerometers. Previous progress reports on this contract, have outlined our experience in using both these approaches. Later in this report we will describe a suc- cessful quantitative solution applicable for ballistocardiography by use of non-linear negative springs. There exists in principle(31), a different solution to the problem of recording the xyz components of body motion, unmixed with "roll" in- formation. This is to construct a suspension which provides a system of "torque rods" (as commonly used in automobiles) to prevent roll and pitch of the body. If the body is fastened down to such a table so stiffly that roll vibrations can occur only at very high frequency (15 to 20 c/s)1 with respect to the table, and the torque rods are coupled rigidly enough to prevent rotation of the table to the same degree, then the frequencies Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -25- unn below this in the records of xyz' and xyz, will have no rotational artefact. Such a table has been designed and constructed in this project. It results that to combine the practical requirements of extreme compliance in 3 trans- lations, with extreme stiffness in 3 rotations, with errors in the .0001" range, demands an extraordinary amount of fine machine work. We have con- cluded that such a suspension is impractical to advocate for general use, and that tying down the subject to this degree inflicts excessive discom- fort. This last has been shown to alter the HCG(32) FurthPrmore the use of tight body constraint to earth in roll produces an underdamped r?- snnnnrp condition which is still well within the upper BCG range of frequencies. In principle, again, one can construct a BCG to measure rotational components directly as?Ernsthausen has done( 33). Here the body rests on a tubular bar, whose rotation may be defined and measured about any single axis (vertical, horizontal or oblique) passing throup it. If then one records the rotations and determines the three inertias, one can in prin- ciple compute the forces (as well as torques) producing them. At the time this work was published, attention had not been focussed on the emergence in practice of a resonance between body and support, in the case that the latter is stiffly coupled to earth. The subsequent demonstration of this factor by Burger(13) and by v.Wittern(12), proved at once the practical impossibility of correctly recording cardiovascular forces by this "tor- sional BCG" approach. The reasons in rotation are precisely the same, as account for the large errors in phase and amplitude of the Starr and Dock methods in translation. This torsional BCG is also dynamically im- pure_ or "mixed", in the sense of the following paragraph. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043002400010015-4 ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Theory of "force BCG". Theoretical cevelopment in this field has proceeded along two lines. The first explored the consequences of considering the body a rigid mass for motion in the HF (y) axis. The analytical solution of this problem by the author(1), its graphical interpretation and practical limitations, were almost simultaneously confirmed by Burger, et al.(9). The author's further exposition(1) of the "mixed" dynamical content of existing BCG (9) "fnrro" ror.nrric ? urnc mlcn aA 1-1v, Dt74.rvess.0 ? LUC oi.aLL (and Dock) reco:ds can legitimately be interpreted as "force" only below the body resonance frequency. At and around this resonance (4-5 c/s) the (jerk) record becomes the'aerivative of force' and the finer details ( > 6 c/s) theusecond derivative of force". Secondly, the basis of this whole analysis was challenged by Cunning (17) ham (Griswold and Cunningham) as a result of their experiments. This ana- lytical approach showed that the motion of the body when shaken via the feet, followed a law (in amplitude and phase) resembling above 10 c/s that of acoustic vibrations propagated in an elastic medium. Below 10 c/s a number of separate damped-resonators showed; suggesting that at quite low frequency the body is uncoupled from its unity into separate oscillators, and above this to an acoustic continuum: This serious challenge to any use at all of the unified body-mass concept, requires rebuttal. Since these newer data and concepts conflict with the experimental results of Wittern and of Talbot and Harrison, they must be explained by the differ- ence in technique, and some reason suggested for a choice between the two views. We may suggest that the disagreement results from how the body is driven: In their case, by an external sinusoidal force acting through a series of leg joints designed for compression only. Such a force must Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? A Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -27- pass through tendons; which having the properties of collagen and elastin known to be viscoelastic(34) can be expected to show phase-lag increasing with frequency. However, when the actual ballistic drive is from inside the body, we suggest that the strong longitudinal tethering of arteries, and of the diaphragmatic foramina, respond better dynamically than do joints seen in pressure-release, transmitting via tendons in parallel. Further work is needed; clearly, on the colligative properties of the body in small scale vibrations. However, this should be done with due regard to pre-stressing: which is the normal relation of joints, and with us has proved a basic consideration in transferring body mn+4n.,c port, for dynamic measurement. Another analysis treating the body as a non-unitary structure, has been offered by 13urger(35). This differs less radically from our first- order approximation of body unity than Cunningham's. He evaluated v.Wittern's(12) suggestion that heart mass be regarded separately as mechanical element. The calculations show that the mass of the heart made less difference, than the spring and damper couplings from heart to body. That is, if underdamped, a strongly selective response at the frequency of the heart as a passive oscillator, should result. Since no such transient occurs, Burger concluded that the heart's coupling must be overdamped; which seems reasonable dynamically in the closed and inflated chest, and corresponds with direct x-ray observation, Burger's argument applies only insofar as the heart's suspension participates in the pattern of forces acting on the body. However, this participation is limited to the events at isometric contraction and early ejection, which cover only a interval of BC0. cycle; beyond this time the heart inertial reaction no small longer enters the driving force. Subsequently such forces come from changes Declassified in Part - Sanitized Copy Approved for 50-Yr 2013/10/24: CIA-RDP81-0104nRnn9Annni MI AA ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -28.. of blood momentum other than by the heart; so that Burger':, analysis refers only to features of the record in an initial ten percent of the cycle. That is to say, in his basic equation, mh xh It h(xh s -x) = m x = F * SC h = heart S = rest of subject c = center of gravity of rest of body the driving force on the right can indeed be identified with heart force. But this equation expresses the total driving force F* only during this short period. Immediately thereafter, one should insert in the equation also, the inertia-elastic reaction [due to "wave-guide" impedance (Van der Tweel)(36) ] of the aorta_ Snlif there occurs at all a heart-resonance as predicted by the values used in Burger's calculation, it should show up as differences in the HI segment of the BCG only. For this reason, the name BCG is not well-chosen. The nature of the body-driving force was considered qualitatively by Honig(37). He did not attempt to subdivide the body masses, nor to propose any dynamic model which is exact or simple enough to formulate mathematically. Honig focussed on the later events in systole and early diastole, rather than the motion of the heart itself, confined to early systole. His model emphasizes first the role of ejection in stretching arterial walls, whereby the cardiac work is progressively stored and then discharged as a wave of kinetic energy. While it is true that a relation exists between heart work and body motion, it is not the simple one Honig assumed, i.e., that energy of body motion is proportional to combined potential and kinetic energy of blood ejection. What is conserved between * The notation of this paper, is confusing. Contrary to this notation, the motion of the whole center of gravity (Mc)=0 at all times. The ex- pression NM refers to the driving force on the body or moving cardio- vascular mases. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 4116 S roved for Release4_2:f Z13/10/24 : CIA-RDP81-01043R002400010015-4 - 29 - the two is momentum, rather than energy; so that the energy of body motion is a minute fraction of the kinetic energy of the blood. This fraction varies continuously, according to the mass of blood instantaneously in motion. The true relation involves the time derivative of the energy, in Lagrange's equation, of which Newton's law of conserved momentum is a. special case. It results that Honig's conclusions as to the irrelevancy of the BOG to cardiac strength, are based on erroneous physics. Secondly, emphasis ;3 laid on reflection at vessel junctions, as gener- ating counter forces which give resonance used by physiologists nrIrl 15?./0 WP.vCoo 4- ? L. Tk4c Vs1n:4.1 4-1-11:1 eXpa.a.1.11 ie14%, is based on assumptions of pulse wave. This interpretation, (38) while still under discussion, loses force on quantitative examination, and as other explanations of the pulse-form come to light. The BCG record is indeed sensitive to limb position and limblessness, which suggests a reflection com- ponent under these special circumstances. However, the circulatory dynamics also changes, so that new changes of momentum enter even when arms or legs are bent. Several physiologists, like Honig, are interested in establishing the relation between changes in cardiovascular mechanisms and changes in the 11CG record. In the author's estimation this can only be done by further hemo- dynaMic understanding, based on actual measurement of local blood flow veloci- ties in chronic animals. The attempts to account for the force record dn the basis of simple localized action, like cardiac ejection pattern (Starr), heart energetics and vascular resonance (Honig), or mass displacements of blood, do not take account of the summations of local dynamic action involved. The ? concept of a series of discreteeventg'accounting for the separate waves (Starr, v.Wittern) is probably a good first approximation, but the theory of Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R00240nn1nn1 OS ? OP Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 30 - a hydrodynamic network (Noordergraaf) better admits the pertinent variables. Pending fuller development of this theory, the interpretation of the body- ballistic record, will rest on the deceptive ground of correlation. At pres- ent, such correlation in one dimension is possible when the heart is idling, as on a bed; but the other components of the force vector, and the action of the heart under normal and heavy loads, which is of greatest interest, cannot be studied without further advances in methodology such as those in this reporI. One may summarize the progress in understanding the "force" aspects of tile external ballistics of blood flow, as follows: (1) By making the rude approximation that the body moves as a whole, in response to the sequence of composite forces, one can more clearly spotlight certain other large factors in the force picture. These are: (a) the ex- traneous forces arising from spring-coupling to earth in translations and rotations; and (b) the role of the support, both as to its inertia, its coupling stiffness and damping, and as to its averaging action in defining what I& being measured. Better understanding and control of these factors, in turn helps one take better practical account of departures from the unitary-body as (2) Coupling the body ?to earth via stiff supports has been shown to produce several effects: (a) strong resonant oscillation of the body on its own (dorsal) tissues, which distorted and confused the record; (b) mechanical differentiation and integration of the record (on either side of the resonance frequency), which makes erroneous any interpretation of the record as one of "force"; (c) external reactions from the ground, which enter the body via various contacts, act on the body in ways dynamically different from internal forces of the cardiovascular system. Consequently it has proved(1) . impos- sible practically or theoretically, to simply subtract their resonance-pro- ducing effect from the record, to get the "undistorted" or true record. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part- Sanitized Copy Approved for Release 0/24: CIA-RDP81-01043R002400010015-4 -31 - (d) Interaction forces between the axes of translation and rotation are created by grounding, so that one cannot simply combine the components of translation. When the head-foot coupling to ground was removed (Burger, v.Wittern, Talbot) it then became clear that interaction attributable to remaining coupling to ground (e.g., RL, AP, roll, yaw), still remained to distort the other components of motion. (3) Once the stiffness of support to earth was so reduced that any resonant distortion from this cause was pushed downward out of the BCG (1) spectrum, then the weight of the platform was shown - to remain as an important source of error. Due to its inertia, a platform even as light as 1/10 the body weight, gets out of phase with the body-motion at BCG frequencies as low as 10 c/s. Although this relative motion never produces much resonance (since light platforms are overdamped by the viscosity of body-tissues) important phase and amplitude losses occur(1). In other words, these errors from poor coupling between body and support, formerly at 4 c/s with stiff supports, are now moved up to 10 c/s or so, but are still well within the spectrum. One may reduce this decoupling error appreciably by lightening the support(39) but its weight must be 7 lbs. or more (for an adult bed) to keep adequate flexural, lateral and torsional rigidity, as we will show. Further improvement was had by v.Wittern's procedure, of coupling the body better to its suspension. This has complications, if one forgets the averaging property of a bed. A shoulder-contact for instance, enhances the contribution of local vibrations frpm the loose shoulder-structures. v.Wittern(31) advocates a foot-pressure derived from a spring-rope (rather than a foottoard)in'effect; this restricts the 'high frequency BCG information (in HF direction), the thoracic region. In sum, by adopting temporarily this theory of the unitary body, we have beea (1) led to practical changes in method which have brought out a new characteristic form for the head-foot BCG record; and (2) we have dis. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-n1n4flRnn9Annninnl a A Declassified in Part - Sanitized Copy Approved 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? PO 32 covered similar errors to be overcome in the other components of BCG response. If then we pass to the theory of the non-unitary body (Burger, Cunningham), our attention focusses on stiffness of coupling between body parts, and the frequencies at which they "break loose" under shaking by the heart. This invalidates (a) the ascription of all resonance artefacts to the body-bed coupling alone and (b) the use of [platform acceleration x whole- body-mass] as a'measure of force on body, by which one can legitimately call the record a "force" BCG. One must therefore speak warily of the body-accel- erati on Bra record in the y direction as measuring a y-"force" in all its details; and must examine this usage even more carefully in the roll (0, lateral (x), and anterior-posterior (z) modes. In passing ultimately to using the body in the seated position (as we shall propose), these questions of local-resonance and of mass-unity vs. frequency must all be raised again. Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: A Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -33.. Displacement ballistocardiography. The simplest physical picture of ballistocardiography, is that of the dis- placement of blood in an isolated system: the body. With no external force, the center of gravity cannot move, so that at any instant, the sum of the moments (displacement x mass) of the moving blood volumes must equal the change in moment of the rest of the body (displacement x mass). The time derivatives of this express the conservation of momentum, and the second derivative, the Newton's law of action. This view emphasizing displacement, is easily con- ceived, and was the basis of physical interpretation by Gordon(44), Henderson(45), Burger and Noordergraaf. In contrast have been the force or impact interpre- ( tation developed by Starr 11), Curtis and Nickerson(14)1 v.Wittern(12), and Ta1bot(1). Physically, the latter is better suited to visualizing the case when other external forces (from earth or suspensions) act on the body. The "moment" (mass x displacement) and its derivatives (the relative momenta and accelerations) aid more in understanding the internal dynamics. acting internally on the body are very complex. Thus, at the J peak, there has developed a maximum flow velocity (not a head-on impact) around the aortic arch, yielding a maximum pressure on its outer circumference, a maximum tug on the tethering of the aorta, mainly to spine and secondarily on pleural mediastinum and pericardial membranes, (transmitting forces to sternum, diaphragm and ribs). To trace these forces requires better knowledge of structural connections and stiffness as well as blood acceleration patterns than we yet have. Starr has worked for years to identify the force pattern at the heart itself, in a situation overcomplicated by other forces. However, the summation of blood displacements in detail, has proved feas- ible, though laborious. Noordergraaf, taking account of the measured pulsatile propagation, has constructed the contribution of head-foot moments from all the great arteries, and shown(8) the sum to equal the displacement BCG. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 S Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 34 - If this is done accurately, the time derivatives should equal the velocity and acceleration BCG's taken on a light bed: which indeed they This displacement BCG (called "the BKG" in Europe) or "whole body plythysmogram" (Nyboer)(43) has great rational appeal, showing clearly how each of the vessels gives part of the record. However, the displacement record itself contains so little detail, that clinicians are hard put to associate it with local physiological or pathological changes. It has a range of forms associated with body habitus and other factors; ferential dynamical aspects of heart action are too small to I,. 4+ the ail- came. nrs 011R .waa record. Since these aspects are also faster, they are considerably enhanced in the derivative; so that the blood-velocity record really begins to ex- hibit alterations in cardiac physiology or function. In our problem, we have felt that the dynamical changes in the cardio- vascular system were of most interest, and so have centered the analysis on the accelerations of the body and how to observe them. The approach to the latter depends largely on the concepts used: next to be discussed. ? Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24: CIA-RDP81-01043R00240001nn1S-4. Declassified in Part - Sanitized Copy A proved for Release ? 50-Yr 2013/10/24 : CIA-R C.) ? dr DP81-01043R002400010015-4 - 35 - 211241Lt Conceptst IlitARELIELINe basis of balliqamolimmtly. Three physical principles have been invoked as the conceptual basis of studying the status and operation of the cardiovascular system thru body vibrations: (1) conservation of center of gravity, by which a body freely suspended is displaced equally and oppositely to the displacements of all cardiovascular material within, = 0 or 2: m x I c.v. c.v. raj, # (2) Conservation of momentum in a free system, by which the velocity of the body follows equally and oppositely the summed momentum of the blood and vascular masses, 46.1m1v1 x 0 (3) Equality of action and reaction, by which a body freely suspended accelerates equally and oppositely to the summed momentum champs. (forces) inside it, d :Fozmi = 0 or mv = 0 since m and v vary. dt These three types of information, although related mathematically, are not dimensionally the same, and have separate and distinct physical, physiological and clinical significance. Which is most "important" is not yet known; indeed importance may depend mainly on usefulness or intelligi- bility. But technically, the potential information is proportional to the frequency spectrum which is always greater in the acceleration record. However; the technical requirements for rer....in of the three aspects of motion, though the same in kind are not in degree. As with heart sounds: the high frequency components of the motions seen clearly in velocity and force records, are much smaller in the BCG than are the components of dis. placement at heart frequency or lower; so that to sense them well enough for low noise in the second derivative, the free suspension mentioned above must be designed primarily for the force record. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-0104:1Rnn94nnninnig A Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Consequently we we will confine our discussion and theory to the prob- :I lem of observing MB and9 as the component aspects of translation jk ijk and rotation to be made available in the respective axes. To apply analysis in force ballistocardiography, one must carefully define what masses and what accelerations are to be observed. This we will discuss under "assumptions". Dynamical assumptions. We will assume: 114? kJ/ .1.144.h4v% the hAdv are transmitted to the suspension. PrimN (2) The body moves as a unit, i.e. may be treated as rigid in all A4rections and about all axes, to a sufficient approximation. (3) The acceleration of the suspension in all axes measures the corresponding accelerations of body, and so gives thefirce on the body, taking its mass as a whole, i.e. PB ? (4) The suspension also moves esseatially as a. unit. The justification for such assumptions, as regards the head-foot (HP or y) directions has been described by the author( 1) in some detail. However, the introduction of the frontal planar and 3-D vector components, demands a second look; as well as recent papersC))4?on theory of body ballistic suspensions. We will examine these assumptions in order. 1. Transmission of body forctti.2221. In a. biophysical system, the coupling of information from the living Material to the measuring device becomes of utmost importance.. Several questions arise: (a) how quantitatively do forces from accelerating material in the cardiovascular system, reach the bed or suspension? (b) Over how wide a frequency range? (c) And to what degree is this transmission of force information alike for all subjects? Declassified in Part - Sanitized Copy Approved for Release @50-Yr 2013/10/24: CIA-RDP81-01043R00240001nn1 5-4 mimmommommimmummimiolIMMIIIIIIIIMEnmminiummummummommismomm.111 Lownowsi Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 203/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 37 - a. Outward transmission and couplim. Prom the softness of inner suspensory tissues and the relatively heavy body shell, one would expect most of the force to be shunted off into motion of internal parts at heart frequency, leaving little for the body. The fact remains, that the slower force components 14 HP do move the whole body with almost the exact 00 a) acceleration calculated from blood motion, and with frequency com- ponents measurable to 30 or 40 c/s '. (The amount of attenuation and shift of the faster components must await further knowledge of the internal dynamics.) Mechanistically it is reasonable for this to be true in the HF direction, from the stiffness of aortic tethering to the spine and the strong mediastinum dorsad. The transmission laterad should be pporer and more variable; nevertheless lateral ballistic force records do show low- frequency detail calculable to first order. But dorsad, the transmission of force information out to the support should again be good, though poorer ventrad, Consequently it is worthwhile to have the suspension sense forces in all three directions, provided one can couple the forces well through the body in the lateral (RL) direction. This transverse internal coupling in the chest, being weak, varies with respiration and organic differences more than in the HP or AP directions, Although we have little control of the transmission of forces inside the body, we can do jnuch to assure transmission from the outside to the platform. The HP (y) and AP (anteroposterior) (z) transmission can be made good to probably 20 c/s(1) (of support following body) by prestress. ing the dorsal tissuestwith the couplings now used.. This also applies to pitch (X axis). Yaw (l) and roll () coupling are related to the lateral fixation, and depend on chocking methods and strapping which will be dis- cussed, under the various supports. The lateral (RL or x) coupling from body to support is the most critical; variations in it can radically change ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 the higher frequency components of R.L. forces (accelerations) observed. With suitable methods, distinct 20 cis components of lateral motion may reasonably be expected in the record. It is fashionable now on theoretical grounds, to view dimly the possibility of sensing externally the distinguishable details of internal cardiovascular forces, momenta and displacement, just as of flying fifty years ago. But the few laboratories now working to improve methods and principles of observation, do not find this to be so. Every change toward better coupling of body and support has improved reliability, increased detail and intelligibility. It has become clear that we are moving toward reproducible and highly detailed BCG information. While this does not automatically give illIEEELtILLIal it is prerequisite. The assumption that cardiovascular forces can "get out" into the support with good fre- quency range and in a systematic way, is justified by experience. b. The fag.t.....yienc range for which provision must be made in a good vibration-measuring system, has two aspects; (1) The support must not evoke resonances (if undamped) - or phase distortion (if well damped) - which can be driven by any component of the emerging force. (2) motional coupling exists between the modes of a solid structure excited off its elastic center, so that the highest driving frequency in any one direction governs the design. Since in the HF direction body-driven frequencies up to 40 c/s (49) in the force record have been demonstrated, our design criterion will be this rigidity in all fundamental modes of support vibration. However, the high degree of damping from the body, suggests this is excessive. c. Transmission of force information to the support, differs be- tween individuals. It depends on tissue coupling, which varies in elas- ticity and stiffness; on the area of body contacts; and on their location 1 Immiummg Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part- Sanitized Copy A 3/10/24: CIA-RDP81-01043R002400010015-4 - 39 - referred to the main internal generators of cardiovascular force, i.e. the dorsal thorax. Other parts of the body probably act as passive dampers (e.g. buttocks) and may reduce faster components. Such questions are important in a detailed way; but can all be studied later on a clini- cal basis. This matter of positive and negative transmission of body forces must eventually be studied, as part of the examination of the "integrating function of the support". d. Definiteness of design-criteria would be improved by statistical analysis of individual variability in body conformation. For the present stage of exploring principles, we have designed on an average basis, with small safety-factors. The internal variability of individuals (size of heart, impedance of joints, bones, etc.) may affect ^4 An+a, but is not taken into account as the biophysical interpretation 1,0wwv.,.. yet in design of methods. a. Our assumption that the body moves as a unit (i.e. a rigid body) is the basis of the analysis and (analog) computation in this report. This should be taken as a first-order approximation, sufficiently valid at frequencies up to about 8 c/s in the head-foot HP (y) direction, and much less in the RL (x) and AP (z) directions. The strength and purpose of this assumption is that it lets us pro- ceed to calculations of body suspension systems, as to the rigidity (stiff- ness or high frequency response) which will be sufficient to avoid resonance artifacts. That is, if the body oscillates (a) is an assembly of coupled masses or (b) as a propagative continuum (or both) then the structural stiff- nesses in the support found sufficient to respond at high natural frequency to the body taken as a whole, will yield still higher frequency toward the body parts. This results from the lower masses of the parts and the higher Declassified in Part - Sanitized Copy 50-Yr 2013/10/24 : CIA-RDP81-ninLinPnn9Annnirmi A Declassified in Part Sanitized Copy A proved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 41 - 40 - vibrational modes of the suspension excited. Whether these stiffnesses are necessary will vary a great deal with the 2211121im between our sup- port and the body. If this were uniform (body "poured in") the damping of the structure by the body would be so great, that no resonances could occur, and phase shift with frequency would be very gradual. In essence, some definite assumption must be made about the rigidity of the body-mass, in order to calculate the inertia and damping terms of the support under design. The acoustic-vibration propagation theory [proposed by Cunninghamb while reasonable at first sight (but see be- low) for small vibrations in the longitudinal direction, cannot hold in the transverse, anterior-posterior, pitch, roll or yaw modes because of (a) the small dimensions of the body in relation to wave-length of such waves, and (b) the strong damping of propagated waves by tissues Nest- , reicher02) j. In general neither the all-rigid nor all-acoustic theories of force transmission probably holds through the BCG vibrational spectrum, but are superimposed along with more complex coupling of body parts at intermediate frequencies and in the several directions. More specifically, in the head-foot direction, the recent work of Noordergraaf in predicting the observed acceleration BCG of the whole body to over 10 c/s, is sufficient validation of our assumption for this axis alone. But the full implications of this assumption for the other axes, should be noted. Although we may be justified in assuming a rigidity in the head-foot direction somewhat exceeding that demonstrated (Chap.') the rigidities transverse to the spine (lateral and anterior-posterior) are clearly much less. The body below the hips, as well as the arms, contains no net component of blood motion away from the spine, and so is passive in this region. The masses in these portions of the body mass mB Declassified in Part - Sanitized Copy A proved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R0074nnninni Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 do not enter the equation2,111B2i -0or mB Elofrom which forces on the B body are to be calculated. Similarly in roll, tE IBOB does not contain 1611C roll-inertia of the hips, thighs, and legs; since these portions suf- fer no roll-torque from the cardiovascular drive. Finally, it must be admitted that the body-inertia in yaw and pitch) standsin similar relation to the confinement of driving torques to the thoracic cage, which comprises perhaps 1/3 of the average body mass. In the face of these elementary facts of anatomy, we propose simply to ignore (in thexznRvayec) the inertial AffPr+ of the nacc4ue (extra thoracic) parts of the body-mass in the calculations. To a first approximation, they load the driving forces indirectly (via the support), and may be interpreted as increasing in a complex way the effective mass of the support in these axes. It will be the task of future work in this field of "external ballistocardiography", to devise means of overcoming this crude approxima- tion as to body inertia. [We have made a beginning in this direction by constructing an ultra- low-frequency 3D suspension for the thorax alone (Chap. I). This, when modified for freedom of rotations this report shows necessary, should be a clear advance toward a BCG that is more quantitative in the xi z, a, and y axes,] We conclude that the strategy in this a2mo 4 c c4rc+ . 4*". SPV OnAmet... LUC problem in terms of the very low frequency BCG components (4( 6 c/s) com- prising the dominant features of the whole-body BCG pattern. The process of removing artefacts of earth-coupling and rotational admixture by developing suitable whole-body suspensions, results in methods modifyable in detail, which let us better evaluate the bodily sub-vibrations and so to reduce errors of rendering them. We would emphasize the need of suc- cessive approximations, and of carrying along simpler concepts like the MN unitarybody assumptions, to their acceptable limit. Linimismi. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-11 Declassified in Part - Sanitized Cop ? Approved for Relezaa.p-yr 2013/10/24: CIA-RDP81-01043R002400010015-4 3. The acceleration of the suspension measures that ol_1121.1.)2.ca. This third assumption implies not only that the whole body has unitary acceleration vectors (rotation and translation) as above, but that the support is so connected to it, that it executes the same motions: at low frequencies, anyhow. [Part of our task is to calculate, and measure just how, at higher frequency, the inertial properties of the support make 4t tost from the body motion in the various fundamental modes of motion: xo yo zoo(' l.If only the body were actually rigid but with a soft viscoelastic envelope, this assumption about the support would present small difficulty. In practice, the motion_of "the boodyslial mania apart from that measured on the support. If one attaches light ac- celerometers to various parts of the body surface to compare the motions or read "the" body motion, one encounters a biophysical tangle. Firstly, each accelerometer generates a spurious 1^nQi AWysibj, natural frequency due to its own inertia and stiffness of surface attachment. Secondly the different local parts of the body surface are differently attached (and under dif- fering prestress) to the spine and to other routes of momentum transmission. There is a "local surface BCG" for every square inch of the body, with large local differences over the thorax especially. The only way a body- volume BCG can be defined at all, is in terms of some "standard" system of body-contacts which summates and so smooths the local surface differ- ences, and minimizes local "bounces" like those of the chest and sides near the heart (and shoulders, neck, feet, etc.) which are loosely or flexibly coupled to the spine and in &quite variable way. Of logical necessity, in this way the support itself defines the turns out to have "body" motion; so that "relative motion of body and support" -VP- no highly Declassified in Part - Sanitized Cop Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043Rnn94nnnin11 g_A 1 Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 precise meaning. Piny engineer realizes this is also quite generally true, e.g. the "point of insertion of a beam", etc.]. We therefore assume here explicitly, that the body "has" an acceleration 'Which is that of the support (other forces being absent) as seen at low frequency, and that any concept of the 122111.2121i22 can only be had in terms of some integrating support (or observing platform) rendered weightless. It follows that the need for this kind of extrapolative definition of theumntinn of the bothras a whole, at once affects our interpretation of the high-frequency details or blood-motion in terms of body-motion via' the laws, of momentum. In addition, the operational meaning of such con- cepts as "propagative transmission" of heart impacts, is rendered vague. Real accelerometers (linear) put on the body are subject to transient local tilts and jigglesowhich can produce as large local artefactual dif- ferences in phase as those being verified. Only by large-area summation can reproducible high-frequency details be recorded usefully. So a clear measure of the degree of failure ot the "unitary body" theory, is hard to demonstrate -. though not impossible. 4. The suspension moves as a unit (is rigid). Clearly this fourth assumption is necessary, if accelerometers attached to the suspension are to define the BCG. In the head-foot (y) direction, any simple tubular (39) frame- - fulfils this criterion. But to record lateral (x) accelerations, such simple hammocks or even honeycomb sheets are not stiff enough. The former vibrates in lateral flexure, and both in vertical flexure. Trussing to kill the latter still leaves compliance in torsion toward the Strong forces in roll [rotation (p) about the body axis]. But because there exists x3 coupling (Chap. III) the suspension must also be sufficiently stiff (unitary) in torsion. When this requirement is filled, we can say the 111......11111111 Declassified in Part- Sanitized Copy Approved for Release @50-Yr 2013/10/24: CIA-RDP81-01043R00240001nn1 Declassified in Part - Sanitized Copy Approved for Release A' tv ? -44. 2013/10/24: CIA-RDP81-01043R002400010015-4 suspension moves as a unit for the purposes of this problem. It is a major problem in mechanical design, to satisfy this requirement for torsional rigidity along with the lightness (1/10 the body weight) needed, with a mechanical assembly of body size. Other concepts and assumptions needed for physical analysis of the BCG. Simply to treat the motion of the body under cardiovascular forces, as a problem of rigid body or even coupled-system dynamics, overlooks some dominating principles concerning information. Unlike the dynamic assumptions stated above, these additional simplifications are dictated by the viewpoint of medical physics, rather than by physics. This 1. An acceptable solution must result in separation of variables. is the conditional of orthogonality, implied in the use of the tetra- hedral lead system in electrocardiography. Applied to ballistocardiography, this requires not only that we seek natural axes of the system for trans. lation, but also that rotational data be not mixed with translational. This turns out to imply the assumption of small angular velocities, so that centrifugal gyroscopic and coriolis forces are negligible (which is true). In principle, if enough is known about the coupling between modes of motion, for a system of rigid bodies,' one can readily compute the pure axial motions, in spite of interaction. For two reasons, this possibility is excluded. (a) Unlike the ECG, where simple resistive networks are now often used for this very purpose', the BCG 3-D computation involves complex reactive terms, which require a rather large Declassified in Part- Sanitized Copy Approved for Release 50-Yr 2013/10/24 ? ? ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 45 - analog computer of forbidding cost. (b) A BCG design which does not succeed in separating (uncoupling) the translational and rotational modes, introduces body artefacts so large as to obscure, even reverse the appearance of some components. If the system were indeed a pair of coupled rigid bodies (body and support), these spurious resonances could readily be rejected by filters. But in the rotational modes, with a real body, this assumption proves too simple, and the filter remedy will not work. There appears no choice but to uncouple these modes from the beginning, and avoid computers. 2. With systems as complex as those in biology, one must choose what information is most valuable, and not simply record every mani- festation that can be measured. In the y axis (head-foot) alone, the displacement, velocity and acceleration BCG yield quite different bio- logical information. When we add X and '7df4tn to we must raise the whole question of the value of retaining all three derivatives in all axes: a total of nine traces (apart from the necessary BCG, respiration and phonogram). Clearly to record the three rotational components and their derivatives as well, would require strong biophysical justifica- tion on purely informational grounds, however equivalent these axes may be physically. For this reason, in the analysis given here, we will concentrate cation is dictated not only by the general intractibility of excess information, but also by the special relation of blood displacement to the physiology of the heart muscle and vascular structure. The on recording the translational motion, solving but not studying in de- tail the rotations or how to read them from supports, This simplifi- Declassified in Part - Sanitized Copy A ?proved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 11 1 Declassified in Part - Sanitized Copy A proved for Release ? 50-Yr 2013/10/24 : CIA-RDP81-01 043R002400010015-4 - 46 - body rotations depend on features of body architecture which contribute little added understanding of normal blood flow. If reasons should arise from pathology to study the body's rotations (e.g. pitch) these will ac- quire informational value. Thirdly, we mention a need of unity and adhering to a restricted field, to penetrate further in this research. 3. Errors. To distinguish between "true" and erroneous data, label- ing the latter "artefact" or "noise" is mainly an ex-post-facto art. Never- theless in biological measurements, there is generally some sk?'ine activity unrelated to the problem at hand. The measurement problel in biology often consists of so devising the method that only pertinent in- formation is seen, and other information rejected. For example in blood- flow measurement (magnetically) the ECG may come through to mix with the flow information, and must be rejected. So with the BCG we find both extraneous and internal "noise", quite apart from misinformation mentioned above, where one mode of mechanical motion leaks through into another mode. A very practical requirement of BCG design, is to reduce couplings to extraneous systems. Though no mechanical system (in a gravitational field) can be studied completely free of coupling to earth, this simplification will be as- sumed in our analysis. Actually, this coupling proves a major problem and source of error, both in practical BCG supports, and in the analog computers used to solve the dynamic equations. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-0104:1Rnn94nnninni 1 A Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 .-47- Chap. III. DYNAMICS OP THE SUPPORT SYSTEM In order to obtain a repeatable and meaningful record of accelera- tion, it is necessary to secure the subject to a rigid frame and measure the motions of the frame. It would be ideal if this frame would follow the body vibrations without distortion, at least up to 40 c/s, the band- width of interest for cardiovascular performance. However; the spring and damping of the body tissue between body and frame stand against this requirement. Consequently a knowledge of the phase shift and amplitude change as between body and frame is needed, to interpret the data taken from the frame. This knowledge is expressed to a first approximation in the equations of motion for the frame and body, regarded as a two-mass system in rela- tive motion both of translation and rotation. These equations are derived here, experimental means of getting numerical values of the coefficients are suggested, and the nature of the solutions computed and shown. The complexity of the equations (12 simultaneous second order differential equations) require the analogue computer for solutions. Passive (LCR) analogs gave fair solutions, but the difficulties of varying parameters in rotational modes led us to use active (operational mnplifier) com. puters (Reeves) for the larger networks. For this the Martin Company gave generously of time and assistance in their computer laboratory. Solving the equations of motion in this way simulates the actual problem in a simplified form, it stimulates and points up physical think- ing and observation with real subjects. The computer program has given a clearer physical understanding if the genesis sand interaction of forces producing translational and rotational motion. Its solutions to the equations of motion are needed to interpret the acceleration record for cardiovascular performance analysis, and to provide data fcr improving Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Cop A?proved for Release ? 50-Yr 2013/10/24 : CIA-R DP81-01043R002400010015-4 the design of the frame and suspension relations, by varying the parameters embedded in the coefficients. Apart from the practical problem of improving BCG methods, there is the biophysical problem of enunciating principles by which the BCG record may be rationally understood. The computer program here serves to evaluate the range of validity for the theories of the BCG that are under discussion. Experience accumulated in this way should lead to better solutions with live subjects and real instrumentation. AL. EQUATIONS OP MOTION The most general equations of motion for a two-mass system in 12 degrees of freedom with static coupling are excessively complicated, and were whittled down considerably before a solution was considered. To get an idea of the complication and the simplifications introduced, degrees(50) of consider the equations of motion of a Luis mass in six freedom Figure 1 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDPs1_n1n4qpnnoAnrm4,-,,,,,, A A Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 -49- Coriolis where m (m.41 +4) = X hx Act Ef m (y.ia.41 f) = Y h = - Di - Fa Y m -i) = h? h )1,+h p = L x y z hh f = m z x 117 h i+h a = N z gyroscopic and A, A, C are moments of inertial defined by A. = J11(y24.z2)dm while D E F are products of inertial defined by D = fh yz, dm The forces on the left are inertia forces; those on the right are external forces (and torques) such as the drive. If now a second mass is coupled to this mass, the forces arising from the stiffness and damping of this coupling would appear on the right-hand side as shown here, although these also would involve the dependent variables (relative dis- placements and velocities). Before considering these coupling forces, in our case we may simplify considerably the expression for the inertia forces. This follows from two observations regarding our system: (1) Displacements and velocities are assumed small enough so that their squares and products can be neglected; (see Appendix A). This allows us to set the Coriolis accelerations [consisting of products of a linear and an angular velocity] and the gyroscopic moments [consist- ing of the products of angular momentum and angular velocity] equal to zero. (2) The body exhibits a plane of LassIa, the YZ saggital plane. Hence, products of inertia DEF are zero except in this plane of sym- metry, i.e., D :# 0, E = F = 0. So in our case, the above equations reduce drastically and separate the forces and torques: Declassified in Part - Sanitized Copy Approved for Release c 50-Yr 2013/10/24 : CIA-RDP81-01043Rnn9annni nni g_A Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 X = mx Ym Z mz -50- = A CI L 0 4 M ? B P*1 Dy ? ? C y f.? pp However, we are still left with dynamic coupling of rotational reactions, introduced by the product-of-inertia D about the transverse body (X) axis. Because the summation in D (JII)m dm) does not contain a squarelthe t contributions on either side of the body's xy plane tend to cancel one another. So the product-of-inertia D will be an order of mag- nitude or so less than the moments of inertia, B and C. Hence, the terms containing D can also be dropped, and the equations become simply those of a completely symmetrical body for small motion: irdt =X my = Y (C) We turn our attention next to the right-hand sides of these equa- tions, which involve the motion of both frame and body$ because the stiffness and damping forces depend upon the relative motion of the frame with respect to the body. The plane of body symmetry helps here because with no dynamic coupling, motions in the plane of symmetry do not excite motions out Of that plane. Hence, the equations can be separated into symmetric and asymmetric as follows: In plane of saggital or YZ plane my = y, ria = Z', It'a = L (D) Out of plane of body's s mmetr transverse xz and frontal xy plane (E) B13 = MI Cy11 = N Declassified in Part -Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? ? This means that torques in pitch such as L create only y, 2, a motion; while torques in roll or yaw such as M or N create only xt and y motion. The asymmetric equation will be a little more involved because of static coupling between forces and moments in the transverse xv and frontal xy planes. While the derivation of detailed expressions for Y, Z will be left to specific designs' (the human bed, mercury bed and chair) the equations of motion in one plane (the transverse xz) will be derived here to demonstrate certain general features for all equations, and later to develop experimental methods of coefficient determination. 1. Assumptions and geometry Fig. 2 The above diagram is an abstract of the transverse plane of the body on a bed seen by an observer looking footward along the spine. The con- ventions of direction are standard in BCG usage49). The body and bed are treated here as rigid bodies coupled together through the damping and spring characteristics of the body tissue. This coupling is assured be- cause the forces from the heart are not great enough in size to separate the body from the bed or to slide the body with respect to the bed. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R0074nnninni c_zt 0, 1.? Sanitized Copy Approved for Release 0/24: CIA-RDP81-01043R002400010015-4 -52 - While dependent non-linearly with tissue stress, they are linear for the small motions (.001) we are concerned with. That is, in the equations that follow, spring and damping forces k and r are taken as linearly pro- portional to displacement and velocity. "Center-of-resistance" is defined by the axis of a static force whose application causes no rotation. By way of illustration, consider how the center-of-resistance is determined for the x-direction. Apply a force in the x-direction on the body; if the body rotates in addition to translating) change the point of application. Keep changipg until a point is found at which a force produces translation, without rotation. The axis through this point in the x-direction is the center of x-resis- tance. In the same way, the centers of y- and z..resistance can be obtained. The concept of center-of-resistance allows rotational moments due to translational displacements and velocities, to be distinguished from rotational moments due to angular displacements and velocities. The driving (heart and blood) forces and moments are noted by Fx, Fz and Mp, which cause the motion we are trying to measure. Since the xz plane is not one of symmetry: the equations of motion in this plane, as derived earlier, are mU = X, q = M for both support and body, yielding a total of 4 equations, Note that the equation for vertical motion (mz = Z) is not involved in this motion because it is in the (saggital) plane of symmetry which, in the figure, Is a plane perpendicular to the paper through the Z-axis. That is, z forces being symmetrical cause no roll motion. Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R0074nnninni F-4 Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 2. Derivation of Equations of Motion Substituting the equivalent of X and M in terms of the known physical properties of the body and support, we have from Fig. 2 for the equations of motion* of the pody, in translation: B s ss ,x B B. B s hSpS) = FX (1) and in rotation: I 4 BB + r (pn-p ) k (p ) BIB p D S ? fA 4- Lr fri B s"hs s x 0 x B B p)4-k(xhBpB-xs. and for the supports, in translation: ? in x +r (A 4.41 p -A 441 p )41 (x +h ssxsssBBB xss and in rotation: (* -h [r 4141 p A S x s ss S *PM +11 -F h z x F B013);= (2) (3) P )+k (x +11 p = (4) X S SS DD All distances have signs. A distance is positive when measured in the positive direction of the coordinate. For example, the distance to the center-of-resistance hn is negative because it is in the negative z-direc- tion from the body c.g., the origin of the body coordinate axes. The various forces or moments and their signs are derived by imagining a force or moment applied to produce a positive displacement. The reactions are summed up on the left-hand side, being opposite in direction and hence sign from the driving force. * Rewritten from III (D) in terms of displacemepts and for each mass. Declassified in Part- Sanitized Copy Approved for Release @50-Yr 2013/10/24': CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -54. Consider the terms of equations (1). Application of a force Fx is instantaneously reacted by the inertia force MBxB. As time passes, velocity is developed, giving rise to the damping force xBBBsss The damping force depends only on the relative motion between body and support. Owing to the coupling of body and support, angular and linear velocities are built up for both support and body. The expression for damping accounts for these various motions in developing a relative Eve.ntuailv the velocity leads to displacements, bringing in a reaction from the stiffness of body tissue, given by kx(xehA- s h p ). ss with damping, the spring force depends on relative motion only, hence the similarity between the damping and stiffness terms. Equation (2) expresses the equilibrium of moments acting on the body. The applied moment-FzFthFFx+m (M being a pure couple) is reacted first by the inertia moment,then by damping moments, followed by spring moments. These latter two moments are due to pure relative rotation expressed by t r,,(pu-pd for damping torque and kp(pB-0s) for stiffness. Additional F - rotational reactions are suffered if a relative linear motion exists, and is obtained by multiplying the force due to linear motion by the appro- priate distance to the center-of-resistance, as shown above. The signs on these last terms will be explained to illustrate our sign convention. Looking at equation (2) for body moment equilibriums note that application of a positive moment F xh is reacted by a positive linear displacement of the body greater than that of the support. The linear displacement of the Locji at the contact with the support is xB+h p Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01n4:1Rnn9annnlnn1g A Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 55 - The displacement of the support at the contact isx+hp,the positive s s s Sign being required because although hs is negative, p being positive counterclockwise, gives a negative displacement at the contact point. Taking the difference, assuming the body displacement larger, we have for the relative linear displacement between body and support k 1 4. BPB)- xs + h5 135 )) multiplication of which by kx gives the translational spring force. The damping force is obtained by replacing displacement by velocity, and multiplying' by rx. The ToTaltranslational force reacting the . 4 plied rotational moment is r [(x + h + ' '1 'kx[( +h p )-(x R )) x B B B? ?"s. B BB s s' s- s s This must be multiplied by 114 to obtain this reacting moment. nn= No term representing the coupling to ground has been included in the equations. It has been assumed that the very soft suspension, 1/3 c/s cutoff, will keep the influence of ground to an unobservable size. eclassified in Part-Sanitized Copy Approved for Release @50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? 4 - 56 - B. EXPERIMENTAL DETERMINATION .OF COEFFICIENTS Numerical values of the coefficients in the equations of motion are, of course, needed for applications involving these equations. Although estimates of certain coefficients are possible from theoretical consider- ations, much easier and more reliable are estimates based on experimental procedures. We shall describe here the procedures required to measure all coefficients excepting those associated with specific shapes of the support, leaving this information to those sections dealing with support design. 1. Moments of Inertia Moments of inertia are conveniently determined by oscillating the item In some kind of pendulum, or spring-mass combination. The period of oscil- lation is related to the radius of gyration by a relation depending on the type of restoring force. We shall next derive these relations for the pendulums and spring-mass combinations used here. A detailed description of procedures will be taken up in the sections on support design. In this analysis, since the subject and support are treated as rigid bodies, the inertias must be found at very low test frequencies: not higher than one cps or so. a. The Bifilar Pendulum To determine inertia about a vertical axis. (72) 11.1?????????? L ................_*......_ , --, 44.1as....,,n4....A.1.441./Ulor???*4 ??....................,............ r ...........,......?....._, .... ....?0?....- ,..z.,-,........?-------;__. mai Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-0104nRnn9annnl rInIgA ? Part - Sanitized Copy Approved for Release 0/24: CIA-RDP81-01043R002400010015-4 The bifilar pendulum is useful for determining moments of inertia when the swing must be about a vertical axis, such as a subject sitting in a chair. As seen in the figure, a bifilar pendulum is simply a two-strand pendulum with the restoring moment FL being provided by the angular displacementes of the strands. We shall derive the period of the bifilar with strands of equal length, because these are the most convenient to use. This requires that the cog, be midway between the strands if all the energy of the oscil- lation is to be confined to motion about the vertical a,ic. Unequal c.g. spacing would lead to oscillation about a horizontal axis too. From the expression for F, we see immediately that the torsion spring rate is .,2 FL = k a = a? = torque/unit angle a 4.e The frequency is computed from the usual relationship 1 lig L2 g = 2 n where t) is the radius of gyration in the expression I =mf Solving forr the required quantity TT in terms of T, L and A. (2 = 4n (5) The test procedure is simple. Choose the strand spacing L and strand length A , so as to get a period greater than one second but no greater than five seconds or friction will influence the results. (For a recumbent adult, if S = 6 ft., L 3: 40"). Adjustments after tests of the length,?( and spacing L may be necessary to get repeatable results. Set the pendulum in motion; making sure that the amplitude is small enough to insure a linear oscillation. Keeping 6/k < .2 during the timing will suffice. Also, make sure the oscillation is about an axis through the Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-0104f1Pnn94nnn1nnig A Declassified in Part- Sanitized Copy Approved for Release ?50-Yr 2013/10/24 : CIA-RDP81-01 043R002400010015-4 c.g., by making the initial rotation about this axis. Repeat until the resulting motion is the required one. Time the oscillation over five complete oscillations and obtain an average period T. Repeat several times and average again, The value of r is available from equation (5) knowing L, g and T. ? The inertiafkbout theaxis of the body is determined similarly, with Or 12" for a standing adult. b. Wheelbarrow rbre Moments of inertia about a horizontal axis)4 for long slender shapes such as a body on a bed, can readily be obtained by resting one end on a knife-edge0 and the other end on a vertical spring of stiffness lc, shown in the adjacent figure. The restoring moment about an axis through the knife-edge equals the force at the spring kee times the length 2 , from which is obtained the torque/unit angle k k,e 2 0 From the relation for frequency 1.-- ----- k. = .1._AwL. 2n 1 T ... follows the expression for radius of gyration 2n i fb2m p ,,)- T h l o ki x. = 10 in terms of period To: Applying the moment-of-inertia transfer equation, we obtain the moment of inertia about the horizontal axis through the center of gravity: Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDPR1-n1naqpnnoAnnninr,4 - Declassified in Part - Sanitized Copy A proved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? 41 1??????? ????? 1477,2.. IA, me' In the test, adjust k and ,(4' to obtain a period To of between one and five seconds for reasons already discussed. (For a recumbent adult, k = 2.5 lb/in). Make sure the oscillation is in the vertical plane only. Leakage of energy to other degrees of freedom will reduce the accuracy of estimating r by altering To. -59- s.1.0. 49,4 Z 431., Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 2. Determination of body spring and damping coefficients. As far as we know, no one has ever made a serious attempt to obtain complete information on the spring and damping characteristics of the body tissue in this kind of motion. Some time ago, a measurement of head/foot characteristics was obtained here by restraining the bed in this direction by a very stiff spring and then exciting the head/foot motion of the body by a blow on the bed. Decay rates and frequencies of the lightly damped oscillation of the semi-fixed bed provided the basic data from which body damping and spring characteristics were calculated. The schemes for obtaining these coefficients described below is based on the transient response of the bed referred to above. We do not know now that this technique will give consistent results; it is advanced here as theoretically feasible but not necessarily practical. For illustrative purposes, determination of the stiffness and damping coefficients by transient response of the bed will be discussed for motion in one degree of freedom. We shall then give a detailed account of how this method will be applied to estimating coefficients controlling the motion of I the bed in the sagittal plane. For free motion in one degree of freedom of the bed 1 4 + ri, + ky = 0 (1) 1 has for a characteristic equation m.) + a + k = 0 where X. may be regarded as a (complex) " frequency. 14- . whose roots Ai give the exponents in the general solution to (1): y II These roots are easily calculated as II - r +.r-f---'.7.... -,? 1 i IL02_y,2co2 (2) 1 2m m 2m Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 iMillid11111111111111 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 For a lightly damped oscillation, the record will look as in the sketch. The measurements to be made are shown. The time 6 is chosen large enough to make the ratiol02/y1, considerably less than one in order to be insensi- tive to error in measurements of yi and y2. Damping, r, and spring, k, are related the test data by 00.0 0 ? ?????????? ??? .? ? ? 0.0.. ? ? ? ? y1 2 ........... 2n OA. ???? lob (3) Knowing the mass (m) of the bed, k and r can be extracted from these relations. Sagittal coefficients First we introduce stiff springs K from bed to ground, so that the natural frequency of the bed relative to ground is high compared to that of the bed to body. In this case, the amplitude of the body oscillation will be small compared to the amplitude of the bed, so that the bed displace- ment is relative to ground, which we can measure, is nearly equal to the dis- placement of the bed relative to the body. The equations of bed motion for this configuration are: rsor)?./1 di::: 4 k f4A .4.1* r icRx // t' 77-3-7?-7-77;-7.94:7; {77-7---9..eu.,;_ / Ltrisx] r (,) (4) Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? - 62 - In n this analysis, spring and damping from shear have been neglected because it is expected that they will be small for sagittal motion. Putting in effective values of k' and r',? we have 2 141 *LI L * + (17 L + K)y = 0 (5) for the equation of vertical motion. Assuming the pick-offs are acceler- ometers of output a1 and a2, this equation becomes in terms of the sum of the output - I. m(a, + ao) + 7?L (a + a2) + (rOL + K)(a1 + a2) = 0 4 fa Observe that (6) is similar to (1).Mence. from (3) .1 r L(y ) -1 t 2m - 6 (6) (7) where the quantities yl, y2, 6 and T are to be taken from a decay record of the sum of the accelerometer outputs. How the bed is excited does not matter in general, but if the frequency spectrum is scanned for maximum response to sinusoidal drive, the period T is easily determined as the frequency of maxi- mum amplitude. Then by removing the drive, the decay over a time 6 yields the ratio y1/y2. What we have done to this point is to determine effective values of damping and stiffness. We have now to determine the position x where these effective values act. This is determined from the moment equation by replacing the integrals by effective values and expressing the equation in terms of the difference of accelerometer readings - thus: Declassified in Part - Sanitized Copy A ?proved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 a Declassified in Part - Sanitized roved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 .2 (a1 - a2)+ r L x (a1 -a2 ) + -63- 2 + c L R )(a1-a2) = 0 (8) I - From the decay record of al - a2, one measures yi and y2 and 6, giving x: 2 r L x Y1/Y2 (9) 21 - No frequency (period) measurement is necessary since only one quantity is unknown. The damping relation was chosen for its higher sensitivity. 2n However, a frequency (--) measurement might be needed as an aid to getting good accuracy in the measurement of 1-c because it appears in combination with a large term - the K spring. It may even be necessary to take several -1 readings in computing k and then apply the methods of statistics to get a _1 meaningful estimate of k Declassified in Part - Sanitized Co .y Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R00240001on1 5-4 Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? *. - 64 - C. SOLUTION OF THE EQUATIONS OF MOTION As mentioned in Chapter I, the equations of motion of the body- support system have been solved(1)(9) for the simple case of head-foot (y) motion, which is relatively free of coupling with rotation. However, the lateral (x) motion of the body couples strongly with rotation in both yaw and roll, because the cardiovascular driving forces do not pass through the body's center of gravity. In the case of yaw [motion about the y or AP axis in the xy plane] the cardiovascular y-forces are so nearly along the body axis, and the inertia is so large about an AP axis through the navel (approx. cg), that the contribution of y-forces to rotation in yaw, is small. However, trans- verse (x) forces in the body's frontal plane are large because of the tilt of the heart. Consequently the body tends to rotate counter-clockwise in yaw with a motion: A {where is the instantaneous distance of transverse force X from the cg, and M is the pure couple exerted by the blood in rounding the aortic arch] However, a pendular body support rotates at quite low frequency in yaw (see bifilar calculation above) so that the coupling of x and y is compliant enough to be negligible if the x motion is not constrained. Moreover in this xy plane the coupling between body and support may be made relatively stiff, so their relative motion about the y axis is negligible. Hence there is little need to examine the xyy system of equations for interaction between body and support. Moreover information-wise, we do not need to solve for M (in the above equation) because the cardio- vascular "news" so obtained would be trivial. The value of x (transverse Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? Declassified in Part - Sanitized 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 component of cardiovascular force) however, is so strongly involved in roll, that the xyy system of force equations alone, will not define it. In the case of roll (forces in xzp plane, transverse to the body), we find a major difficulty in decoupling rotation from translation. This is because (a) the roll inertia 10 is much less than are Ia and I ?[/A2 = (13/40)2= 1/10 for the radii of gyration] and (b) the cardio- vascular forces at beginning and end of ejection and of filling, act on the body quite ventrad (3"-6") to the body e.g.. As a result with this moment arm, a rightward forceX tends to roll a light platform under the body to- ward the left, the while it translates the body (and platform) to the right. If now there is spring coupling with resonance(111 in roll, a roll BCG not only adds to the lateral, but has a highly variable phase and amplitude relation. In sum, the yaw BOG does not interfere with the lateral BCG as does the roll response, because (1) the body inertia I is much larger; (2) the )(force js on the same side of the body c.g. (i.e. headward) as is the best coupling to the support; (3) the support can be free to rotate with the body, avoiding excitation of springs k ; (4) the stiffness of coupling k from body to support is naturally much higher than is kp. For these reasons we will confine our analysis of the interaction error due to rotatory coupling in measuring the BOG, to the motions seen in the transverse (xpl)jolin.s. We will show analytically, that for sup- ports which are not free to roll with the body, the coupling from body to support in roll acts as a high-cut filter to the lateral BCG: (both as to resonance and cutoff). Further, for deep-chested individuals (high rota- tional moment of lateral forces) a double-resonance occurs. This creates a frequency band in mid-spectrum, where support and body act in phase- Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 CIA-RDP81-01043R00240001nn1 ' Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 opposition, and so suppresses important details in the lateral BCG. These relations result when physiological values of body stiffness are inserted in the' xzp equations, as follows, Particular BCG Equations of Motion for the xzp Rlane and their solutions. Equations 1 - 6 (Table 1) show the relations between the forces and motions, as well as the torques and rotations defined in Pig. 2. Implicit are the assumptions that through the frequency spectrum, there exist con- stant coefficients (parameters) of stiffness and damping (k's and r's) for each mode when the other motions are zero. Thus, with locked support, a pure couple will excite a roll frequency 6p .11117p7i;:(rp/2I13)2 [where kp is the equivalent shear stiffness seen by a pure rotation] rm?dows- = toy and a damping factor rp [which governs the p motion of the body alone] Similarly c7ox is the natural frequency of x vibration when rotation is locked; although physically U ic A (.4 ei stiffness mcnmr44, ra: 4-1-tcz ;r1,1/tissuesr-il tiSSPS ex- (.4.wkik;.-.6 VA 11,As?. X cited in a different way than for kr. In practice one cannot measure the force coefficients k and r, but only (7) and the frequency and damping of the single (locked) modes of vibration. Experience shows that referred to the support, whole body fre- quencies are > 3 c/s or 1 18 with dam'ping so that the damping term amounts to; = 2m r factor < .25 where 2mm 't The complex frequency is: close to monotonic w2 The decrement en (y /y ) = 5/3 1 2 2m ... 5/3 shows damping Y2/Y1 ,..11 which is quite strong. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 or 5 ? = Mg r- W>50 lb. 1 = 2 in terms of 2 resonance ratio Declassified in Part -Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 In order order to solve these six equations, one must calculate the k and r from observed values C7) and assuming suitable masses or inertias. Table 1. Equations of Motion (x 'z' plane) rewriting with moment arms positive, and rearranging for computer connections Forces on body and support: (B) rx [(k144-10 + (hB13B+hsk)] [(X -Xs) 4 (hBPJ + Os)] = (S) mM ss rx [(XB-Xs) kx Fx (drive) sk)1 ri X' (ground) x s [(XEcXs) + (h0B+hsps)) kiX X S Torques on body and support: (B) IB + rp(134s) + hBrx kp(pB-Qs) + hBk, ril(3134s) - h rx ?0 (S) p s s k -p, s ) hkx p B [(xB-x) + ? ? [(xlit-xs) z, Forces on body and support: (B) mJ' + rz(1B-Zs) + kz(zB-zs) 416 O ($) mz -rz(zB-zs) kz(rrizs) s s where ** mB = .375 inch slugs ms = .025 inch slugs ** T= .833 assumed 8"x20" assumed 1"x20" (ground) = 0 (hBpB+hsps)I (b0B+hsps)] = -Fzwf (hBil3B+hjis)] (hBPB411sPs)) = (drive) 0 4 r z +k z (ground) zs zs Ph kx = 375 lb/in kz = 1500 lb/in rx = 5 lb.sec./in rz = 11 lb.sec./in k, = 21,600 lb.in/rad hB= 2" =4', = 200 lb.in.sec./rad hs= 2" wf = 2" rp Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 C 1. Solution_ty2atlE_EmIlt_EL(4yferential anal set). Discussion: We have seen that the forces and torques in the transverse (xzp) plane prove particularly interesting, because of (a) the small inertia (In) of the recumbent human body in roll, and (b) the application of cardiovascular force on the body, on the (anterior) side of the p axis (thru c.g.) away from the contact with support. Qualitatively, the resulting lateral (x) response of the body to such forces, is bucked out by the body's a...Ilia motion about its c.g.. This unfavorable situation does not exist for any other rotational axis, and so becomes the most important dynamical relation to solve for. In Table I are gathered the xzp equations for body and support, as previously developed. These equations show the following features, which stand out clearly in the analog connections (Fig. 213). (a) In every equation there occurs the term in square brackets [(xB-xs)+(hdB+hsps)] TU4q is a force in shear proportional to the relative motion of body and sup- port, whether displacement or velocity. Note that the translational term depends on the difference of the motions, but the rotational term on the sum, because of the body and support are tangent. (b) This composite force in shear operates on both body and support, to oppose the relative translation and rotation of both: the 1.14-4-01- in nrn? r-- portion to the distances of the c.g.'s from the interface of shear motion, hB and hs' [Since this interface is curved, one must establish experimentally an equivalent straight line of "resistance" to which h is measured]. while hs Is constant, the dimension hB varies considerably with a subject's "thickness"; so that the coupling between lateral and roll BCG will vary similarly. (c) There also occur spring and damping forces in "pure" relative roll Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDPRi_n1n4qpnnoArmr14,-,,,,,, A 6.? Declassified in Part - Sanitized Copy A proved for Release ? 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 69 - (1311-13s). For this to happen without relative motion in shear, i.e. [NB-xs).1.(hBilifhsps)] = 0 there must be a relative vibration of both bodies in pure roll (013-p5), so as to produce alternating ..._Nmpsss!tI!..aIILILL522sl on both sides of the midline. This compressional vibration thus sees mainly the compressional tissue stiffness in the z direction but partly also stiffness in shear. The natural frequency of this vibration if excited separately, should be higher than that of tissue in shear, due partly to greater stiffness in compression and to lower inertia in roll. (d) A theoretical dynamic system set up on an analog computer, actually needs light coupling to "earth" just like a real system. This is shown in Fig. 2B for both translation and rotation, using both "springs" k' and "dampers" r'. During operation the integrated amplIfier drifts will move the output off scale, if equivalent springs K' to earth are not added. With such springs, the output will slowly oscillate till damped out by the added coefficient r'. So the analog clearly parallels real Systems designed to have zero force to earth, such as the "ideal BCG". This is because such real systems also show drift with the least wind, so that practical suspensions must have some "ultra-low-frequency" springing rather than be completely (e.g., mercury bed). (e) The particular dynamical problem whose solution is shown in Fig. 2B involves locking the platform rotationally, without stiffening the translation. The analog then acts like current clinical BCG beds of ultra low frequency. One accomplishes this in the computer, by grounding at p and p. When these terms drop out of all the equations the "relative" rotations become simply I3B: body roll on the support, as a recumbent subject on a table. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R00240001nn1s-4 Declassified in Part - Sanitized Copy Approved for 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? 6. vvonowevasemoosomamaw, 1 ar . 1.r 0 WW.wM?ftlaftnio.dirmiegettej 1- R A \Ir.), 1-16. U %.? r OMPLYTag,PNAleCiroaral OFALp poomics Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Results of - 70 - Computer solution of motion in Xql_ptlne. The lateral motion ;s of the support when driven by a force on the body Fx, appears in figure 2C as a function of frequency. The roll p of the body IS shown in figure 2D. The dotted curves show the response when support is free to roll with the body; while the solid curves show the resonances generated when the support is not permitted to roll, as with current BCG practice. The line T = 0 would be the response were the heart forces directed thru the roll axis. The lines T show the change due to the torque resulting from the anterior position of the heart. 2T is for normal heart position. When platform is free to roll (dashed lines), the lateral amplitude xs decreases somewhat at all frequencies as the heart force moves forward, due to energy going into roll. This enhanced roll motion appears in Fig. 2D (line 2T). However, the body would roll somewhat even if the heart force passes through the roll axisl due to inertia reactions of platform. The freely rolling platform resonance shows translational resonance at the frequency Icx of the support on its coupling to the body. This resonance cor- responds exactly to the cutoff seen in the head-foot (ys) frequency-response curves of ULF support(/); it is caused by finite mass of support ms and its coupling kx to the body, and so inevitable. For convenience this cutoff was set at 10 c/s, corresponding to a platform 'heavy" in translation. With support not free to roll with the body (a) a strongly resonant peak len - 2.5) appears at a frequency co_ where body-roll-resonance is in phase , op with translation; (b) just beyond this is a sharp trough (attenuation t about 1/5 amplitude) where the roll goes out of phase with the lateral motion; and finally (c) an increase to the undistorted (dotted) amplitude, exceeded LAJI"...! because the body's roll inertia adds. to its trails- somewhat with zero 4.,.....nito. I . of. coupled resonant systems. lational inertia. The dual peaking from phase interference is characteristic ?..........ma 111_ ' Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 71 - Our analog also describes (fig. 21), solid lines) the roll-motion of the ? body itself on a platform that won't roll. Even without impressed torque from the heart (T = 0), the platform translation causes a strong body-roll. But with the normal anterior cardiac drive, the energy goes increasingly into roll at the higher BCG frequencies, and less into lateral motion of the platform. In net effect, the roll constraint on the platform introduces a lateral BCG resonance followed by cutoff at and beyond the natural frequency of body- roll on the support. Since the dorsum is rounded the ribs and shoulders are compliant when chocked, the stiffness in roll is intrinsically low; so with the low inertia about the p axis, the roll-resonance is hard to raise above c/s. Such a periodicity is indeed seen commonly in lateral BCG records, as well as the predicted absence of sharp wave-forms (containing higher frequencies). The analog computer, using the simple two-mass model of Fig. 2A, therefore has accounted for the major artefacts of the (lateral) RL-(ULF)BCG. It also predicts that these artefacts vanish when the support is free to roll. The case of the 0114)BCG is not shown here, but again exhibits complex resonance in the RL record, due to coupling between the resonances (7)13x and wq; this time with higher Q and lower frequency ((7)Bx = 6 c/s). The frequency at which body is resonant in roll can be shifted upward (on the computer) to imitate tethering-straps fastened across the chest, and I. a form-fitting support. Since these will also raise w (the lateral resonance) sx the BCG pass-band can be increased. If instead the support is free to roll, r the resistive torques between body and platform k[hpB+hsps) and k[peps] are not forced into action, and such tethering becomes unnecessary. Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 4. 11 x-J F\t ? ? ? i_or?tked- 411.% ???? 011? 0" ? U0144:Y?:. le A 000 oP Urtioc., ,e1.1*1 4 G , C 4 ...........r114**41/164MAWOR004~.. 4 Fre 4i.)1C'41 C/IS ftewarporom F u Exx Fig. 2C Reeves computer results: Lateral acceleration of support by lateral force in body. [solid lines] (0): force through ca. (platform not free to roll), showing resonances due to inertial reaction of support, tangential to body. (T) and (2T): lateral force more anterior (in position of heart), showing enhanced roll-resonance and cut- off resulting. (Dotted lines): (0) and (2T) lateral heart force acting through c.g., and anterior to it (platform free to roll); showing simpler cutoff, due only to translational body-coupling to support (of 1/10 body mass). Fig. 2D: Roll acceleration of body by lateral force in body [Solid lines]: Support not free to roll -- showing resonant body-roll so created. [Dotted lines]: Support free to roll -- curve (0) force thru c.g.; body roll ceases, above frequency of platform decoupling. Curve (2T) force in heart position; body-roll (driven) persists without transmission to support. 29 Declassified in Part - Sanitized Copy Approved for Release 0 50-Yr 2013/10/24 : CIA-RDIDsi-ninaqpnnoAnrminr" ? r ? IIIL.mimmmiDeclassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -72- C-2. Passive analog solution. IL C R circuit] Just as in pure y or z motion f a two-mass system, one can set up a simple mechanical analog whose forces are: ? X, e? Its fa, 13 re, i 1 m x + (x -x )+k (x -x )=F ti/P-41i4 BBBBS BBS 1, 111 13 ii $ , n1/4 equivalent electrically to: & oNdl E I \ .00 where where i = A -A B S Similarly there is a passive circuit equivalent to the xp equations of Table 1. This circuit can be realized by multiplying the rotational quantities by a dis- tance h, which makes them linear and so able to combine with the linear equations. [In fact the linear networks of the active analog, receive rotational couplings by this same process.] A peculiarity of the passive (LRC) model is that cLmponents required by certain electrical analogs (resulting from particular mechanical assumptions) are unobtainable, e.g. variable transformers. However, it was found(47)that a more cpPr4A14zed model than Pig. 2, with mechanical parameters lumped in a particu- lar way would express the same mechanics. This is shown in Pig. For the body: yn+(r,+r,$)(1/1-10+(k,+k,')(kn-x I 11 -fir Bs)+k (xB -xs )] h BB x x , ? $ +Irze(zB-zs)+kzqz8-zs)]ult -Pxh +P Y f Por the support, similarly: mS MS -(r xx +e)BS xx+10)B-(x )=0 i; +(r w(i )+r -X )] SS zBSxBS +[k' w(r )+kh(xB-xS)) =0 z B x where K = torque/angle px = force .h/dist/h force 2 .h dist = ke h2 SP Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 This particular mechanical hookup may be analyzed rather simply, electrically [at far less cost than pn active (opera- tional) analog computer] with passive (LCR) elements: Fig. 3B. -73- ? , tfrslEr ) Experimentally the values of the inductors* (the most costly elements) determine the impedances throughout the circuit. These are set at an arbitrary level. The frequency level (machine time) is chosen at 100 x real frequency, to put the performance spectrum in the range 5 - 5,000 r/s, where the inductors have least error from intrinsic R and C. This puts the real spectrum at the BCG range [.05-50 c/s]. The L and C = 1/K values are calculated (as for the active network) from the assumptions for real-time resonances and damping: , WPB = 5 cis.=IKP/1P Q13 = 2 p X -2 t"513x = 10 cis =1"6"1 Lw qBx =2 R +R ' X X To simulate constraining the roll of support (ps= 0), sever the circuit at (x) so that body rollpB is excited via lc( and k;. There results a lateral motion of the support Ms (lateral BCG spectrum) shown in Fig. 3C. It is clear that the body-roll strongly distorts the lateral BCG, especially when the cardiovascular driving force creates (as usual) a clockwise moment. This moment opposes platform motion Ms below wBp and assists above this roll resonance. There results a pair of system-frequencies f1f2 (displaced from the locked natural frequencies (Ifit) which dominate the lateral BCG spectrum seen with the usual horizontal (non-roll) platform. This agrees with the "active analog" analysis above, confirming the passive *Hycor type EM-6. oria1nrr Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 74 - Results of passive analog solution: response spectrum of the transverse BCG. A. Effect of body coupling and platform mass. Before investigating the offprt of adding BCG motion in the roll mode, the purely translatory solutions were reexamined. This was done to tie in with previous theory(1) , and to specify quantitatively the amount of coupling ("tethering") needed between body and support in any mode, in terms of the "hatural frequency" of that coupling referred to a "locked" support. This is the method of determining coefficients examined theoretically in Chap. III. In Pig. 3C the solid lines show the influence of relative mass of sup- port with very stiff body-coupling (77.)B= 10 c/s). In dotted lines are shown heavy and light supports, with very weak body-coupling (Wp= 2 c/s). It is clear that the support could indeed be rather heavy, provided the coupling is extremely tight [Klo as= 25 x 1( c/s]; but that if no particular strapping or stressing of the body is used, the mass or inertia of the sup- port must be very much less than that of the body, to obtain satisfactory responses to the sharp (20 c/s) components of the BCG. This is particularly pertinent in the roll mode. In Table I the ratio of body inertia about the roll axis to that of the support is IB /I S ]p = 17.5 According to Fig, 11) with such a ratio no fastening in roll should be required, even on a flat- surfaced support. Be Effect of body roll on lateral response. When the "rotational" meshes of the circuit (Fig. 3B) are added, the important region 3-10 c/s acquires a dual resonance, with striking effects on the 51s /P spectrum. x The circled line in Fig. 3D shows the response to a lateral driving force FBx acting directly through the axis (back alongside the dorsal Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 'PH" 1 iiljiiiiiiiiii0 I. 1 ill 'NilIl muokipppliscom NI pi poomlopupeo illi 1 iIiii 1 piiiiiiIiiii , I 4 1 1 ,-, -,--t t 1111 I 11'1 III 111111111111101E01111 III 1 1 111 1111111111111111111111111111 IMMill liunimummlimm minimillmi all I rialiirimiall Illuirmuurnila INEMINIMMINIIIIIIMH111111 FORM WNW' ern Mau= WM Iniml HIM NM MEMBEINII II PRIMMIIIIIIMMEN11111110111111111 OthiliNEMMINllilil IIIMMINUMMIN NEINIMMODI PrAINIM11611111111MMININI MI Nile IMMOU11111117 MinglIMMINI IIMMINIMMENIONIMENNIMPINHOMPIUMIREMMIN I'll' VINOMMIN iii momemousimpummollomillonnammon mmlommull _11111101111.11011111d11111111110111111111111111111111111111111111111101111101 mu 1 mu mile*Emeninnom I opumpou Illblihr NNE iniM au MENINERNEMEARESEINitEN 111" I i ifilINIPPONNIHNIMMiiihinifill 11111111111111011111 . 1111111101110111111111110 mmammuumnimirmillana )---. INKIMIUMIUMBEMEMINIMIBIUMMOMMUUL____ IMMIIIIMIMMI 1/1"Will'inumilruthummi I IlmiummunrimnimPFPFFigiuma inumullmmumpuRn 9 IMMINIIMINIMMIIINOIRMIIIIMILIN 111114hunimpur MOMMMENNiiiniiMUJIMARMEEMMORiMilatiiiniEringnignrnii6HIPRAyibsii IMPIMPOINNIIIIIMIMPROMMINIMPOIMINIMINIIHIMPINERINMEM 11111111111111111-1111111011MMIRMININENTIMMIPPININEM i 1 MiiiiiiniliffilliPIPIONINIMMINIIMININKU 111111111111110111111101101111111111111111101061k1 lifillii1111111111d1d101111111111111111011 liimpimilerimiiir iiiiiiiMMENIIIIIIMPEffiiiiiiikiliiiiiiiiiiiiTichg, 21:;:. . 1 .1 "fiiiiii ? 1 a hilium II Id II I 1.111 ill I illi I 1 "Mil 111010 111111111111111111bilmililll ' Will ofillimilliimu MIN r II I ili I 1. will I 11 AIN 10 8 7 6 5 4 3 109 87 6 5 4 2 2 4 5 6 7 8 910/ 2 3 4 6 6 7 8 9 1/0 2 3 4 687891 30 Fig. 3C: Computation on LCR analog. Effect of body-coupling comnliance compared with effect of heavy- platform on lateral BCG spectrum: relative mass (ms/mB) lateral stiffness (1b/in) A 1/4 75 1/20 45 1/4 3 1/20 3 Showing resonance with tight coupling and heavy support, and loose coupling sufficient with light support. 9?000 -"eseoweola?oowea OOOOO *wow* Following page: Fig, 3D: LCR analog computations. Effect of non-rolling support on lateral BCG. [Solid lines] resonance and absorption due to enforced body roll (Ti 2T, 3T increasing anterior heart position) [dotted lines) resonance artefact predicted for counter-clockwise torque (-2T) exerted by heart in dextrocardia. Fig. 3B: Roll effects on lateral BCG without torque on body from blood flow: A, Neither body nor support can roll, both move laterally. B. Support cannot roll, body can roll, both move laterally. C6 Both body and support can roll, and move laterally. (roll resonance absent; lateral response reduced) Declassified in Part- Sanitized Copy Approved for Release ? 50-Yr 2013/10/24: CIA-RDP8 -I 0 4 I a ii Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 75 . aorta). The roll resonance resembles that in Fig. 2C for the same case, except that here .(Sp is set at 3.5 cis: somewhat less tethering in roll. Now when the drive is moved anteriorly to the natural position of the heart (curve T in Fig. 3D) a torque T is produced by F . A similar Bx peaking and sharp attenuation result in the active analog (Fig. 2C, curve T). As this torque is increased (2T and 3T) (as with deep chests), resonance in roll so increases as to obliterate the trough by phase opposition: The dotted lines show the change in roll artefact which would occur, were the crnrn ^4^^441^11.1 ???? ? ?'jag j???? ?ty es ? counterclockwise (seen footward). LW WE-k,WAIIV- [This could happen with an upright aorta ordextrocardia.] In this case the S.-shaped distortion of response begins at lower frequency, suppressing the important 3 c/s BCG component; while a broad resonance 4-10 cis appears . a band-pass effect. Finally, the passive computer was caused to show the motion of the system when the support was free to roll with the body-forces. The spectrum Pig 3E (C:dot-dash) is the lateral motion of support reacting to body roll, but now free of roll resonance. Mechanically, the springs responsible for this resonance are not excited by such a support. This result agrees with Fig. 2C. (dotted lines) These response-spectrum studies of the transverse BCG have been mainly exploratory, to gain control of the analytical method and models used. The resonance phenomena shown are produced by these models, and from the parameters (stiffness and damping) selected for the various modes of motion. The damping factors were purposely cut down to exaggerate the amplitude (Q) of the resonan- ces, and to seek their physical basis. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Se V - 7-- ? __. Declassified in Part_- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 r????????.????????????????,????????????0?111WPMWS.W.N.I.Ve.01 ,rfro, 1(.001, ? .r. ? .0. ; r b.. ,rIS V.5' / ? ? ? ? on........es?NrIVIlervo.41.11.4"........0..../.4.001", %."..10.?....1. ? da,????110 00. ? ,; ? ,I?1?? ? jA, ,???5AI.V It ? , , I :40?? ? 4. el tr.1...rhorr* rew' Il ?o" - ? 5 .0 ?????????????????......., r. .V?iten ?de .?" " .0?"." .00.# v0? (( 9.0???????' ........; ..... Ir........? ?? ...k ? ? ? .....4 ...1...,4????? ,, t (1)\N-?4 u N. \ ?? olp 4. ? ta No' ? sjyno.6.46.11MOIMP fr5?L'? ? t ???? ?? ? e. ? ?? ? ?7???? 141 ? 11???.161 0,04114..00 ? . ???? ..1 0 ? 0. ? .? ? ? r? ? ? .11...A ? ? 6??????1??????41......? ????,?????????.??????? ????? wo?????????????g? ri) 111111111,LIMAIIHEIMNIONIMMill 1111111 1111111111111111111111111111111r ill11011091111111"m101PP"IiiI1111111 1114"11111 i.it0111 win hi! h muntommarannaniAmiumioipoinevaminunaniiiimmuniumnournall 111111111111111111ERIEROURIONEMENNEI miumphauguipmummommunimpoompumommijilamong 10111111111FIPPIIIIMMINillitilldill111111111111N01111111 IIIII!ii1IiIII1IIIIII1 01110!! odhiloilodimpohoura I El i N?1111 440 r ? VI INIIIMMEN ? loom maw _ a 111111111111Milhill IM I ? "1111111110F1 I I 11111111111111100111111111111011111011 1010111 Utra101111111111111 1111101M1111111111S11 11111111 111111111111111, UM 1111111111110w11111113111111111111111111111MMIIMMUI1111111111111911MIITIMUMIS ri I I 11101110011111111111111111111111111 Nil!! Millaqii1111111111111111111111111HIRINIMMUNIMMIN ? 1111111 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 / 0, ?1??????.- ? ? 1 Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 The rotational resonances clearly depended on certain rotatory moments exerted by the cardiovascular force and the dynamic reactions to it: (a) about the axis of the body (hf); (b) from the body-axis to the surface of the support ( B' )? and (c) from this surface to the axis (c.g.) of the support (hs). These important measures differ appreciably among individuals and for variously designed supports, and must be con- sidered in interpreting the usual lateral riCa. As in both BCG and ECG, one considers the heart-axis in interpret- ing the record, so in BCG, the effective thickness of chest (hf+hB) matters whenever a suspension ?is used where body-roll affects the lateral *.ar.nrri. This complication in BCG interpretation can be avoided, if one gimbals the support to exclude the admixture of roll. Our comparison of active computer and passive analog methods, in practice, shows that they serve different purposes. The LCR circuit is quite adequate to demonstrate the qualitative relations, and explore the frequency and damping aspects of the coupling between body and support. The differential analyzer lets one vary separate factors (such as the his) more readily, and study the phase relations among all the motions and their derivatives. This was helpful in understanding in detail the sharp slopes of the response curves. The analog computer has some disadvantages in practice. It is slower for getting simple response curves, because at each frequency several variables were recorded and later measured. With one-percent precision in the calculator one takes more careful settings. A large network (Fig. 28) runs into difficulties (not found on the LCR) as to Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 ? ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 signal level, and as to circuit instability from cumulative phase-shift. This slowed down the problem to 1/10 real time vs. 100 x real time in the passive analog. The connections are much more numerous and complex, and require frequent checking. The main advantage is that the computer imposes less limitation on the model. Thus the LCR model required in- troducing compression springs (capacitors) to simulate the "pure" roll or stiffness; while the computer executed the corresponding mathematical .1M.40.+ ....??????????????.f, operation K (013-ps) with a simple voltage divider (coefficient potenti- [ti aP-r-1 ile al. computers can avoid specifying a particular physical mechanism, when this is unknown or unnecessary. More complex mechanics (such as interacting rotations in our case) requiring three-dimensional networks, may involve couplings which can not be realized by practically feasible LCR models. Further study is needed of the dynamics of rotation-translation coupling. For example, the yaw BCG also participates in the lateral motion; and in a more complex way, since the body-mass is distributed less symmetrically about the yaw axis, than about the roll axis. It must be verified experimentally, that a support with low frequency in yaw, does not intermix the yaw BCG with the lateral BCG. In this case, due to the several moment-arms involved, the accompanying analysis re- quires an analog computer rather than an LCR model. 1 1 Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 t 1 L ? \ /-3 yray-46)"171-11-4?Ti4r11 T rbr Fig. 4; A. Light-weight, torsion and yibration-free support of max, strength- weight ratio. B, Housing for 3D ultra-low frequency suspension. C. Relation of positive and negative springs of vertical suspension to u.l.f. leg (see fig. 6). Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 ??? 1 Declassified in Part Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ^ft " 10 Nip IV. DESIGN OF PRACTICAL SUPPORT SYSTEMS: RECUMBENT HUMAN SUBJECT DETAILED ANALYSIS OF STRUCTURE Since a great deal of data has been obtained on a recumbent human subject, the bed was chosen as a support so that a comparison can be made between data obtained from our design and others. This comparison is expected to resolve much of the discussion concerning artefact since presumably our design has reduced artefacts of the suspension to an unobservable value. Even if it doesn't, the frequency response test of the support/patient combination will reveal any resonances present which might alter the ballisto records With this information, such artefacts can be eliminated from the record. Our objective here is to present the details of the analysis used to establish the design. Figure A shows the general arrangement of bed, sus- pension and housing. The bed consists of a sheet of aluminum (S) hung from two parallel side rails (R), held apart by a series of bulkheads (P). The bulkheads take very little of the patient's weight, most of it being diaphragmed to the rails. The rail loads are delivered to the truss panels T, from which the load is fed to earth at the ends via the two vertical legs L. Note the high torsional rigidity provided by the torque box consisting of the sheet and two side trusses. Vertical and pitch frequencies are controlled by the vertical coil springs S (Fig. 40) at each end. Alone, these springs produce a frequency of liDcps. Horizontal tension T on the leg in opposition to the A-frames (Fig.4C) produces a negative (toggle) spring effect, which reduces their stiffness sufficient to bring the vertical frequency down to 1/3 cps or so. Roll frequency is controlled by additional vertical Springs on either side of the leg (not shown) acting between bed and base of outer leg. Lateral frequencies (including head-foot, side and yaw motion) are controlled by the legs at each end, each equivalent to a 20' pendular suspension. As will be described in detail later, the leg contains a positive and negative pendulum, whose combined stiffness yields a 1/3 cps natural frequency in linear motion. Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043Rni74nnninnig_A ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 79 R The housing H is required to protect the bed from everyday abuse and to provide a loading platform frOm which the patient can transfer his weight to the bed with a minimum of concentrated and, dynamic loading on the bed itself. The extreme lightness of bed construction required to get the low mass makes it important to mount the patient without damage to the bed. . This housing must establish rigid references for :Settilag the vertical suspension (legs) plumb to high accuracy (.010). It must deflect little under loading, tominimize the technicians concern with mechanical adjustments, A, STRUCTURE OF BED ALONE To achieve a bed of very low mass required detailed attention to stress and 'rigidity. First, however, design criteria must be established. 1. Design criteria and loads* A design load of 300 lbs. was used for static deflection and stress cal- culations. Temporary pressures from this load of 30 iblin2 are possible from one hand. Test pressures are much lower for the recumbent patient, estimated at 1 lb/in2 To insure no artefacts in the record from the bed, the stiffness should be great enough to provide a minimum natural frequency of 40 cps. This is not an easily applied criterion because the mass entering into oscillation of this high a frequency is not that of the entire body, upon which the criterion is based, but something much less. Probably only 20 to 30 pounds mass - the tissue between the thorax and bed - are affected. To be definite. 25 lb. mass will be used in all stiffness calculations involving the 40 cps requirement* This natural frequency requirement will be applied to the first force- free mode of bending and of torsion. The bending axes will be chosen as vertical and horizontal* Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ? Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24: CIA- -80- RDP81-01043R002400010015-4 2. Vertical frequency. Vertical and lateral stiffness come from the tubular frames. The bulkheads and sheet serve only to maintain the geometry and to deliver load to the frames, as far as vertical frequency is concerned. The sheet, of course, completes the torque box, so necessary to torsional rigidity. Shown below is one of the truss frames, loaded by unit force, 1/2 lb at each bay: 0 Oteem????????....41011,........A.1110 The stiffn 01.? .011 60.1,61 eh, ? 14 0414.? J.', I. Mr.. .? ? ? 4, .'.Mt / 0 ? or.??????? ????????????????? ss is computed from the formula for deflection, 21, at the center: = LI12 AB L = A = = length of truss member area of truss member load in truss member deflection Young's modulus Horizontals are all lux.03" dural tubes. dural tubes. End diagonals are 3/8"x.030". Center diagonals are 5/.8 ix.030 From the above formula: EA . 2 (1.1)2 (29) 2 (.5)2(13) 4 (1.0)2(26) .625 (.03)n .625 (.03)n n (.03) Since this = 3300 lb/in is due to a one pound load, stiffness 1 3300 A = 3000 lb/in in the plane of the cr`AmP Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 The vertical vertical stiffness of the bed depends on the stiffness of both frames and the geometry. The dotted outline in the sketch shows the deflection of an imaginary center bulkhead under unit frame loads, from the zero load, the solid The vertical load on the bed = 2 sin 6; the vertical deflection of the bed under this load = 6 = A/sin 6. Hence, the stiffness of the bed, 2 sin2 0 2 = 2 (9/13) 3000 2900 lb/in in the vertical plane. The frequency of the bed referred to support is f= 1 k 1 2900 27t c 2n 12-5/386 = 34 c/s = 40 c/s 1 Horizontal Frequenci 1 the horizontal horizontal stiffness is ????? cos2 8 10 (--) 3000 12 = 3500 1h/in from which is computed the frequency 1 3500 2nJ 25/386 ? Side force = 2 cos 0 Horizontal deflection = 6 = 41/cos 0, Hence, = 37 c/s = 40 c/s Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 1 ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 immommft? -82- 4. Torsional frequency The torsional rigidity is determined by the torque box formed by the two trusses and the sheet. For convenience, the shear rigidity of the trusses are assumed at least equal to the sheet. The shear rigidity of the curved sheet is assumed equal to that of a flat sheet for low stress levels. In this case, we can use a simple formula to compute torsional rigidity: shear modulus 4G A2t A = area enclosed by tube = length of torque tube Substituting in numerical values . 4(4x106) (60)2( 015). kt = 48(78) = .23x106 t = sheet thickness U = perimeter of tube section from which is computed the torsional frequency rftabrimeirmal 1 kt 2n .23x10 25 (3Y/386 = 100 C/S > 40 c/s allowed Local Frequem The frequency of the truss members must themselves be above the critical frequency. The diagonals have the lowest frequency, being the longest and thinnest of the members. The expression for frequency of these tubes of diameter D and length L is: , f 11X106 ) 2 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R00240001001 5-4 Declassified in Part - Sanitized Copy Approved for 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 ?83e. For the diagonal of the truss under consideration here ? f = (11x106) 375 (29)2 = 49 c/s 40 c/s allowable 6. Truss stress 330:1k fuorrYstereave???????????10????????1?01111,????*1?4111.?????????????11.04.1 ? ijow044.Am... vimmilo*.mwo,Vmw The 330 lb truss load arises from assuming a 300 lb subject placing his entire weight at that station. Direct stress on diagonal members = 490/.375 (.03,0)n = 13,800 lb/in2 Z, 50,000 lb/in2 allowable Direct stress on longitudinal members = 2(440)/1 (.030)n = 9,400 lb/in2 e, 50,000 lb/in2 in the lower longitudinal member which carries load from both frames. Diagonal Euler Load P = 2n2 ku n 2 (10) (.3l)3(.03) L2 (29)2 tor 660 lb allowable ) 245 lb actual Horizontal Euler Load 2n2 e 2n2(102) n(.5)3 (.03) T2 (26)2 = 3500 lb 400 lb actual Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release 7. Bulkhead stress ? 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 41ht. 84? wlz. \\_,/yrz: The function of the bulkhead is to maintain the geometry of the bed. If the sheet stresses Fs were parallel (p=o) to the truss reactance FT, the loading in the plane of the bulkhead would be essentially zero, except for some direct loading on the top due to deflection of the sheet itself. Loading_LLIalmisj Static equilibrium requires FT sin 0 = Fs sin a W/2 since Fs is due to a load in the center directly above the bulkhead. This will be the critical loading for the bulkhead with W equal to the entire patient weight, taken here as 300 lb. The net squeezing load Fl? is the difference between the horizontal components of Fs and FT Fi3 For = Fs cos a ? FT cos 0 = (cos a ? cos 0) o and a = 30o 45 = 110 lb. Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 -85-- p . stress at section a-a perpendicular to center line (This section probably has the highest stress) L Bending moment M = 5(110)=550 in lb. Moment of inertia Lr ..otgb agkse? 9f2,' Bending stress is, therefore: ^ MC 550(2.5) = = - 4200 lb/in2 b I .326 Direct Stress 110 = p/A = 6 .(.02) 920 lb/in2 53 4. 2(l/2)(2.5)2)(.020) = .326 in4 Buckling of flange and web Stresses are low so that no buckling is expected. Total stress 0060 Direct bending = 5000 lb/in2 total which is well under allowable tensile stress, but is probably near ?the allowable buckling stress. 1 1 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Copy A 4 ? proved for Rele4THaS 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 114 SUSPENSION: STIFFNESS Considerable care was required in getting a suspension of the correct frequency and damping characteristics. Analysis establishing the design is contained in this section. he damping is to be very small so that frequency criteria are based on undamped natural frequencies. 1. Vertical stiffness. The design frequency of the vertical springs without negative compensa- tion is 1 c/s, being a practical lower limit. To keep the springs below the deck requires a length no greater than 20". spring extended to 20" is 10". Varying patient weights are accommodated by using several 25 lb. springs with one at each end being adjustable for leveling and positioning A practical solid height fora 1 LA tne oeu esi conditions: 1 f=l 2n from which - t-m_,m0.1r1m,%11.. ra rnavieQ0 ly %,LawoCui vA Z 25 k = (2n) 70 2.5 lb/in meet the frequency Extension of this spring to 10 inches requires 25 lb., showing that the spring does have the required frequency of 1 c/s. Spring Design From reference (40), The stress relation: nrirm(Hk The stiffness relation: HC3k d = 1 The surge frequency relation: fs = 14,000/HC2 we have the following relations for the coil sprin d = wire diameter r = coil radius H = solid height (10") k = spring stiffness (2.5 lb/in) P = spring max. load (25 lb) C m 2 rid index of curvature K = function of C'accounting for stress concentration due to curvature - 1.2 for C> 4.0 G m shear modulus (11x10 lb/in2) lc a working shear stress (75,000 lb/iti).. f m surge frequency Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R00240001nn1s-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -87- Substituting in the equation for C 25 (1.2) (11x10 ) n (75,000) (10) 2.5) = 7.5 The index C must be greater than this to satisfy the stress attainable. Choosing C to be this minimum value, we have for the wire diameter 8 (10) (7.5)32.5 11 x 106 d ? .0875" The coil radius r is determined from the definition of the index C C = 7.6 = 2 r/d Solving for coil radius, r = 7.5d/2 c 7.5 (.0875)/2 = .328" The surge frequency fs = 14,000/10 (7.5)2 = 25 c/s, a minimum value, so that C cannot be larger. This is needed also to determine the ratio of maximum surge-force on the support, to maximum BCG force on the support. From appendix C , this ratio is shown to be R = ,;Ic (7):171- = 2.5 1(2n25)(.5) = .032 negligible) Design conclusion: Use where w = 65" mean diameter coil with .0875" diameter wire heat-treated to 250,000 lb/in2. Declassified in Part - Sanitized Copy Approved for Release @50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 Declassified in Part - Sanitized Cop 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -88- Ne tive spring for vertical motion "re to s Ts, ????????.0.....~..4%,?......, ? Above Above is a sketch showing how the positive spring K is compensated to achieve the very low frequency If 1/3 c/s. The toggle tod i$ under com- pression by the wire E attached to the spring K' under initial tension To due to its initial deflection V. This arrangement produces a destabilizing force P which subtracts from the supporting force Kv, to yield a net force ?(1) P = K-, P Differentiating with respect to yields the net spring rate Y = Yo The equilibrium position yo due to the misalignment condition = 0 = K yo a, Unstable Force -%.? P Taking moments about (A) gives the relation P L cos $1 T (u sin 62 By geometry, for small angles sin e1 = y/L cos 0 = [2] s given by the [3) el.% a m 1.2.4? p L cos 02 1 1- ( Y 441 2 [4 Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01n4f1Rnn9Annninnig A with Sanitized Copy Approved for Release 2 -89- U = (p.m +./. 2L 2 p 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 Because of the sliding contact at the spring K', the tension is computed as 2 2 + (Y+ / 1 = IOW - y/21, 12 pv Combining equations 4, 5 and 6, we obtain for the unstable force - [6] x (p.m 427-1 [(L t Ieft OL2. 2 '`Iii (VIL)2) . 211 Li T2 rd)2. p 2 L?L I V td.2 p L p L 2 [7] In order to extend the linearity of P' with respect to vertical dis- placement x we may choose the initial displacement x.! of the K' spring so that for 4 = 0, the coefficients of y2 in the first curly bracket add to zero. This requires . where p = 2 L = 8" L [8] xf = L/3 = 2.7" This assumption resembles setting the curvature (second derivative) of K to zero at the origin, except the above includes the A an 1 earnatiii A which affects the curvature of K. Simplifying by putting [8) i [7): 2:1 (- p P- 2 K'I p . [(1.114) r +J. or ,} for the residual force about the zero position. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R0074nnn1nn1 F-et -4 ? ? Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 1.31_12E1111. The coefficient of y in [9] gives the first order spring rate of the unstable force. Combining this with the positive spring, gives the overall stiffness of the vertical spring system: k c, Equilibrium position- y Putting [9) into [3] with [10), we obtain the dependence of zero position on leveling: R T0/21, in this case [10) To W T.' pi) For all practical purposes k in the negative spring wire Is: T = K o?p?si 2(8) 10 = = 160 lb. max. [10 = stiffness of 4 vertical' springs] 1 more accurately, k = 1 at f = 1/3 cis for 150 lbs Hence, from [10] the tension ? To =(K .. k.) 36 = (104) 16 = 144 lbs. Substituting m [11) with W = 175 lb/2, we find for sensitivity to leveling: V A Of 1"4 where = 10 p 2 td = 2 rad/sec = 101, Second order forces The presence of out of-level ei, as just shown, very seriously affects equilibrium position. The question here Is how much out-of-level can the design tolerate without affecting the spring rate. The second order forces ????????????????ftslilliallar. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 40. Declassified in Part - Sanitized Cop Ap roved for Release ? -91- 50-Yr 2013/10/24 CIA-RDP81-01043R002400010015-4 ( 0%, y2) are small compared to either positive or negative forces (proportional to y), but not so small compared to their difference* If we could operate the leg in the displaced position, no difficulty would arise. However, the design requires that the equilibrium position be held at y=o by cranking the patient up and down with the positive spring. This subjects us to changes in spring rate due to second order forces. The condition for judging how much 4 can be tolerated is when the ratio (R) of the forces involved are greater than some design value, say 10 percent. From [lb [10] and [11], the relation between yo and this ratio RI is Yo 2BR ft'vd"1". where R s s 6K 0-1 For a 10 percent restriction, y0=10 2 (2)(.1) (2-1) [12] a 6.3 in, so A = .63 in, out of level to change spring rate by 10 percent or frequency by 5 percent. 5. Results. *.?????.wartor?Nry.ar.somOSNA Although the equilibrium position is quite sensitive to level of the tension wire, a given position can be maintained by cranking the positive spring without fear of changing stability. Hence the tension wire need not be releveled for practical operation of this suspension. Declassified in Part- Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RnPRi_nirtez prinnArInr,,, nn A ? Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 2. Horizontal stiffness. The legs, one at each end of the bed, provide horizontal restoration(Fig .6). As indicated earlier, these legs embody a differential (negative and posi- tive) pendulum which is equivalent to a pendulum adjustable from 8 to 20 ft. long. The frequency of linear motion in a horizontal plane is, according to the well-known relation: f = 1/2n fir. A pendulum restoring force is more convenient than springs because the frequency is independent of the subject weight, a widely varying quantity in this application. Geneal_t12sau. The essential features of the differential pendulum leg are illustrated in the accompanying sketch, where the displacements have been greatly exag- gerated for clarity. ?"..`? Fl C The outer tube T has a bridge at A from which is suspended the positive pendulum of length a. At its ex- tremity, the point B, is hung the inner tube (b+c), the negative pendulum, which is constrained to vertical motion only at C (by the outer tube). The bed weight rests on the upper end D of the inner tube, and is free to swing around in any horizontal direction (circular Pendulum). Actually, the wire a runs down the inner tube (b+c) via a slide clamp at B and receives the load at C. As will be seen later, the frequency is controlled by sliding the clamp at B along the inner tube (b+c). Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP8i_ni nLVIP nil') A nnni m-14 c A Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 - 93 - The, point C is supposed to be on a plumb line through A, but any looseness in the fit at C or rocking of the outer leg T can cause a departure from plumb, indicated by A, In the scale showniei and x would be so small that a and (b+c) would appear on a single line. A displacement x is restored by the force in the wire a, but is aided by the leverage of the inner tube against the side of the outer tube at C. ELITIETEX? The frequency of horizontal motions x, y, y (yaw) with this suspension depends mainly on the geometry (as with simple pendulums) and not on the load. If we neglect the stiffness of the wire it is shown (appendix D) the horizontal frequency is that of a simple pendulum, multiplied by a difference of two small quantities easil adjusted to near zero: . 1. gla c2-ab 2n , "172Ur when plumb (see below for "out of plumb") That is, instead of a simple pendulum of frequency OFT we have a differ- ential pendulum adjustable to zero frequency (infinite period when c2 = ab). Frequency control in this design, results from moving a slide at point B in the previous figure, a distance along the inner tube (c+b). (Set Pig. 6) If B is the center position of (b+c), we have b+y = c-y So that b With y replacing et:, the expression for frequency in Appendix D becomes ?1 4na when f = 0 ) 9: PY7i. 4 yo ?.187" when I 1/3 c/s: y = .96" where ri= b-a = .75" 0 which indicates substantial stability. It is concluded that if the wire loop is clamped to the outer leg, no special sensitivity to alignment is expected. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP8_mmilimmi1-01043R002400010015-4 Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 a - 99 *6 Ce SUSPENSION: DAMPING A small amount of damping is desirable to settle the system out follow- ing the many and varied external dlsturbances that will occur. Without some damping, the patient and support would be in a continual state of low fre- quency vibration. 1. Formulation of The damping coefficients in each axis of the system are related to the respective mass and spring characteristics as follows: for linear motion: = 2 in wit along any axis i for angular motion: ri = 2 Iiwit about any axis i where w. (with ittaia) denotes the natural frequency associated with this axis. (a) The inertial toefficients are determIned as fnllnwg! In = mass of bed plus patient = 175/384 = .45 slugs" = moment of inertia [(inch) slugs] For the transverse axes, considering the bed and patient as a long, uniform rod, the inertia would be I = in L2/12 where L is the length of the bed. Based on this Ia = 211L I = :AL, /16 = .45 07212/16 = 170 slug in2. [Division by 16 instead of 12 accounts for the un-uniformity of mass dis- tribution along the bed, it being denser near the c.g. than at the ends]. For roll axis, the inertia is more or less a guess at the radius of gyration '0.) in the basic formula, 2 rat) = .45 (5)2 = 11.3 slug in2 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R00240001nn1 5-4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400010015-4 1 - 100 - (b)The(undamped)naturalies(w.)are found as follows: 1 For the linear motions our design criterion was a linear natural frequency 2 rad/see, ixyz stiffness (k) giving this frequency was provided by the legs at each end of the bed. For angular motions, the natural frequencies may be found as followst The legs resist an angular displacement (a) of the bed about the pitch (x) axis by a torque kzL2 a/4. Substituting the general relation for angular natural frequency about any axis 0 (corresponding to k Then abo-7rt- 2 torque/8 w = 0 this axis 2 CA) = (K L2/4) (mL2/16) a z w 2w a z Thus, wa = wy since kz = mw, = 4 rad/sec. That is, the natural frequency in pitch and yaw are twice that in translation. The roll frequency wp is determined separately, by coil springs designed to give w = 2 rad/sec. (c) Damping coefficient assumed. The damping ratio is chosen as .25 for each axis to keep the phase shift low at 1 c/s when the cut-off frequency is 1/3 c/s = 2 rad/sec. Substituting these values in the relations for the linear damping coefficients required: ?? X - rz = 2 (.45) 2) .25) .45 lb/in/sec. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R00240001005-4 1 I 1 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400010015-4 -101- For the rotational damping coefficients required = r = 2 (170) (4) (.25) a = 340 in/lb/rad/sec. rp = 2 (11.3) (2) (.25) = 11.3 in/lb/rad/sec. Individual damping elements must be sized and positioned to meet these conditions on damping. 2. T pe of damping element used The greatest energy absorption per unit volume is obtained from Couette flow, characterized by two close plates separated by a thin viscous fluid. The resistance of one plate relative to another is given by the re- (52) lation, as per page 621 of Lamb. where / //t) //