Cardiac mechanics: Basic and clinical contemporary research

Annals of Biomedical Engineering, Vol. 20, pp. 3-17, 1992 Printed in the USA. All rights reserved.

0090-6964/92 $5.00 ~- .00 Copyright 9 1992 Pergamon Press plc

Cardiac Mechanics: Basic and Clinical Contemporary Research Ares Pasipoularides Departments of Biomedical Engineering and Medicine Duke University and Duke University Medical Center Durham, NC (Received 4/23/91)

This survey o f cardiac hemodynamics updates evolving concepts o f myocardial and ventricular systolic and diastolic loading and function. The pumping action o f the heart and its interactions with arterial and venous systems in health and disease provide an extremely rich and challenging field o f research, viewed from a fluid dynamic perspective. Many o f the more important problems in this field, even if the fluid dynamics in them are considered in isolation, are f o u n d to raise questions which have not been asked in the history of fluid dynamics research. Biomedical engineering will increasingly contribute to their solution. Keywords-Cardiac mechanics, Hemodynamics, Ventricular function, Myocardium, Systole, Ventricular ejection, Diastole.

INTRODUCTION Contemporary work in biomechanics calls for very close and intimate collaboration between specialists in applied mathematics and biomedical engineering on one hand, and specialists in physiological sciences and clinical medicine on the other. Effective progress through biomedical engineering research on relevant clinical problems requires real interdisciplinary communication and collaboration. As the editorial responsibility for the Section on Biomechanics moves to Duke University in Durham this year, we are making a commitment to foster interdisciplinary communication. This special issue on hemodynamics is the first expression of this commitment. The issue contains contributions by leading research groups, which highlight the often unrecognized heritage of cardiovascular mechanics in academic clinical cardiology. These papers develop analytical and computational approaches through which new cardiodynamic concepts are evolving on the intricate interactions between the main cardiac pumping chamber and its diastolic and systolic loads. To facilitate un-

Acknowledgments-I thank Mrs. Ann Davis for expert preparation of the manuscript. I also wish to thank my graduate research assistants, YoungtackShim, MS, and Tom G. Hampton, MS, for their assistance with the references. This work was supported in part by Grant CDR 8622201 from the NSF/Duke University Engineering Research Center for Emerging Cardiovascular Technologies, Durham, NC. Address correspondenceto Ares Pasipoularides, 136 Engineering Building, Duke University, Durham, NC 27706. 3

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derstanding for those readers who may not be currently familiar with cardiac physiology, I provide a simplified brief review of pertinent information in Appendix A. LOW- VS. HIGH-PRESSURE OPERATING REGIMES: THE

DISPARATE NEEDS OF DIASTOLE AND SYSTOLE The pumping left ventricle forms the central link between the low-pressure and the high-pressure systems of the circulatory ensemble. The low-pressure system begins with the postarteriolar microcirculatory beds and comprises systemic vascular, right cardiac, pulmonary vascular, and left atrial components (6,7,8,30,42). Their hemodynamic coupling to the left ventricle in diastole enters in the determination of its diastolic filling and loading (preload) (8,35). The extracardiac high-pressure system is represented by the systemic arterial ensemble from the aortic root through the arteriolar resistance vessels. Its input impedance (28,29,37,39,54) enters in the determination not only of left ventricular systolic loading (afterload), but of coronary perfusion patterns as well (58,68). Representative intraluminal pressure levels in the low-pressure system are of the order of 10 mm Hg; in the high-pressure system, they are higher by one order of magnitude. The left ventricle in diastole is functionally a part of the low-pressure system. Its filling patterns reflect the interplay of atrioventricular fluid (including valvular) and wall dynamics (17,35,40,49,65,70). In some degree, filling patterns are affected also by contiguous pericardial and right ventricular pressures (8,17,35,36,38,49). The left ventricle in systole becomes part of the high-pressure system and its contraction and ejection patterns reflect again the intimate interactions of ventricular wall and fluid dynamics (10,23,45,61). Accordingly, the left ventricle must be adapted to the widely disparate functional-structural requirements of both systole and diastole, states in which both the thickness and curvature of its walls drastically change within each beat (15,43). Moreover, almost all forms of heart disease alter ventricular topography and those changes in ventricular configuration may in themselves set the stage for cardiac dysfunction. For instance, excessive wall hypertrophy in response to systolic pressure overloading is associated with diminished ventricular distensibility and, not uncommonly, with increased muscle stiffness, both of which may then be responsible for impaired diastolic function (34,35,49). Clearly, a better conceptual grasp and a more quantitative understanding of the dynamics of the interaction of the ventricle with its diastolic and systolic loading patterns in health and disease are badly needed. Such understanding is necessary in delineating, and hopefully forestalling, the transition from gradually accumulating quantitative adaptive changes of the chronically overloaded ventricle to the qualitatively new reactions which transform normal adaptation into pathology with impaired performance. In the following sections, I provide a concise but comprehensive picture of current knowledge of diastolic and systolic ventricular and myocardial mechanics. It should set the stage for a better appreciation of the papers that follow, which were chosen to provide an indication of the range and depth of work that is being conducted in this area of biomechanics. DIASTOLIC LOADING DYNAMICS Over the past two decades, interest in diastolic filling dynamics and loading, the diastolic properties of the left ventricle and myocardial relaxation has led to the de-

Cardiac Mechanics

5

velopment of new cardiodynamic concepts and models. During the 1970s, studies of diastolic mechanics focused on passive properties of the fully relaxed left ventricle (i.e., chamber volume, wall mass and composition), physical constraints extrinsic to it (i.e., the pericardium and right ventricle), as well as on the dynamics of isovolumetric relaxation, an active process (18,33). It had been well known, since the classic studies of Wiggers on the cardiac cycle in the 1920s, that during the early rapid filling phase (i.e., from mitral opening to minimum diastolic pressure) the left ventricular dimensions are increasing while pressure is declining (69). Thus, the processes going on during this early period are neither purely passive nor purely active. This led me by 1980 (50) to postulate that total measured left ventricular diastolic pressure (PM) is determined by two overlapping processes, namely (a) the decay of actively developed pressure (PR) and (b) the buildup of passive filling pressure (P*), as shown in Fig. 1, and to develop a comprehensive mathematical model for diastolic dynamics (49). Further application of this model is currently allowing evaluation of the role of active and passive dynamic factors in diastolic mechanics in health and disease (15,35,44,48,49). The fluid dynamics of left ventricular filling have been studied extensively by various groups and, in particular, by Yellin et ak (70). Stimulated by such research, imaging and Doppler echocardiography are becoming established as useful noninvasive methods for assessing diastolic function (2,9,19,35,64,70). Information on diastolic ventricular function is based on Doppler flow measurements in the ventricular inflow tract. Such parameters are very sensitive, but not at all specific. The reason is that, as shown in Fig. 2, many diverse factors, intrinsic and extrinsic to the left ventricle, enter in the determination of its inflow patterns. The interplay between all these factors in determining the filling of the ventricle is complex and quite protean. The integrative simulation model developed by Thomas and his coworkers offers a powerful means for interpreting this interplay and visualizing its expression in the polymorphic Doppler patterns of mitral inflow (66). Drs. Thomas and Weyman have used hydrodynamic analysis and computer simulation to study how the early transmittal velocity profile, in particular, is affected by changes in ventricular compliance and relaxation, atrial pressure and compliance, and valvular morphology. Their paper in this issue provides considerable new insights on the complex interplay of these variables in shaping the diastolic filling patterns. Active and passive properties of the ventricle interact with its venous return, and other factors summarized in Fig. 2, to determine its end-diastolic pressure and volume, the preload that fills the chamber just prior to the onset of systolic contraction. Discovery of the role of end-diastolic volume in determining the work of the heart (the Frank-Starling mechanism or Starling's law of the heart [12]) is one of the historic cornerstones of hemodynamics. It was not until the 1950s that Sarnoff developed his concept of a "family of Starling curves," which integrated the role of the Frank-Starling mechanism and the contractile state of the ventricle as two major determinants of cardiac performance (57). The third major determinant is the afterload, the load driven by the ventricular myocardium during systolic ejection, to which I must now turn our attention. SYSTOLIC LOADING DYNAMICS Ventricular systolic load represents pressure against which the walls contract and is to be distinguished from myocardial systolic load or wall stress, to which it is related by complex cardiomorphometric and histoarchitectonic factors. The total ven-

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A. Pasipoularides

W ~C

p*--pM-PR W n"

.

p*

TIME FIGURE 1. Schematic representation of the instantaneous diastolic left ventricular measured pressure (PM) as the sum of the decaying relaxation pressure (PR) and the passive filling pressure (P*) which increases monotonically with filling, as required in a passive process. (Reprinted from Pasipoularides et al. [49] by permission of the American Heart Association, Inc.)

tricular systolic load, or afterload, determines the manner by which the mechanical energy generated by the actin-myosin interactions in the ventricular walls is converted to the work that pumps blood through the circulation. Under any given contractile state, increased afterload reduces ejection rate and stroke volume; conversely, when afterload decreases, a larger volume is ejected at higher ejection velocities (3,23,34,45). This reflects the inverse force-velocity relation of working muscle (14,45). In the 1980s my clinical coworkers and I undertook intensive analytical and fluid dynamic studies of ejection, combining multisensor micromanometric/velocimetric

Cardiac Mechanics

7

LV INFLOW PATTERN

mvt

AP(LA-LV)

MVA(t)

r~

!1

II LV Relaxation (rate + extent) LV Volume LV Compliance Nonuniformity of Load + (in)activation External Constraints Pericardium Restoring Forces

LA Volume LA Compliance P u l m o n a r y Venous Compliance LA Contractility External Constraints

r~

---

Respiration Preload Afterload Heart Rate Age

FIGURE 2. The determinants o f left ventricular i n f l o w patterns and diastolic filling are many and diverse and include f a c t o r s intrinsic and extrinsic t o the ventricle. Abbreviations: LA = left atrial; LV = left ventricular; M V A = mitral (inflow) valve area; P = pressure; t = time; V = linear velocity.

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catheterization, angiocardiography, and imaging and Doppler echocardiography, in patients evaluated for all kinds of heart disease, and others found to have normal ventricular function (45). These studies demonstrated the presence of intraventricular ejection gradients of substantial magnitude in the human left ventricle in the absence of any organic or dynamic outflow obstruction (45,47,51,53) and delineated characteristics distinguishing them from obstructive gradients and transvalvular pressure drops (45,46,60). Larger gradients can occur when blood is ejected rapidly from an enlarged chamber through a normal-sized aortic anulus (21,23,45) as may occur in aortic regurgitation, and may reach 80 mm Hg or more in the special case of ~avity obliteration without obstruction in hypertrophic cardiomyopathy (45,51). Ejection gradients of this magnitude are not uncommon in the presence of left ventricular (or, long standing right ventricular) outflow tract obstruction, including aortic (pulmonic) valvular stenosis (3,45,51,52). Through this work, I developed the view that total ventricular systolic load comprises both intrinsic (flow associated intraventricular pressure gradients) and extrinsic (the aortic root ejection pressure waveform) hemodynamic components (23,45, 47,53). More recently, I introduced the concept of complementarity and competitiveness (45) in the dynamic interaction of these two components of the total ventricular and myocardial systolic loads under any given set of preload and contractility levels. Figure 3 provides a framework for the study of systolic loading dynamics in the in situ heart.

Extrinsic LV load (Ao. r o o t ejection P) c~

~s)

T

~ntrinsic LV Load -~ (Intraven. ]kP's)

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...... MUSCLE LOAD (Wall S t r e s s e s )

\ I LV G e o m e t r y Shape, Size Ao, Root Flo~ Waveform

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Loop

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Velocity u Shortening FIGURE 3. Framework for the study of systolic loading in the in situ heart and complementarity and competitiveness in the dynamic interactions betwen the intrinsic and extrinsic left ventricular (LV) load components. AO = aortic; Intraven = intraventricular; P = pressure. C denotes the mathematical operation of convolution, S denotes summation, L denotes operation of the Laplace law, B and GA denote Bernoulli effects and geometric actions, respectively. (Reprinted from Pasipoularides [45] by permission of the American College of Cardiology.)

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9

In my view, it is the interaction of the ejection flow patterns generated by the left (right) ventricle at the aortic (pulmonary arterial) root with the systemic (pulmonary) input impedance that gives rise to the extrinsic component of the total ventricular systolic load. This view differs from the widely quoted formulation, by Milnor (32), of the arterial impedance as complete representation of the ventricular afterload. Firstly, Milnor's formulation neglects entirely the intrinsic component of systolic ventricular loading (i.e., the intraventricular flow-associated pressure gradient). Secondly, Milnor arrived at his conception that arterial impedance, per se, represents the systolic load on the heart, because he felt that it would be wrong to conclude that the ventricle plays a part in determining its own afterload. However, invoking a need to deprive the intact pumping ventricle from the ability to influence its afterload is somewhat arbitrary. It is tantamount to accepting that the load imposed on, e.g., the muscular system of a cross-country runner is embodied solely on conditions characterizing the terrain and not on the way in which he interacts with it, namely the speed and pattern of his racing performance. The interaction of the left ventricle with the extrinsic component of its total systolic load is the subject of the article by Drs. Kass and Kelly in this issue (26). They bring considerable new insights into ventricular-arterial coupling in their comprehensive examination of coupling frameworks and their assumptions. The pulsatile hemodynamic properties of the pulmonary circulation are quantitatively more important in the coupling of vascular hydraulic load and ventricular systolic function than their left-sided counterparts. The companion paper by Drs. Kussmaul, Noordergaaf and Laskey (27) focuses on the distinctive characteristics of the pulmonary circulation and right ventricle, which underlie important differences in their pulsatile interaction compared with the systemic side. The intrinsic component of the total left ventricular systolic load is the subject of the paper by Drs. Georgiadis, Wang and myself (16). We address the effects of simple geometric variations on intraventricular ejection gradients, by methods from computational fluid dynamics. It is an early step in incorporating more and more relevant characteristics of the ejection process, such as continuously changing irregular geometry, in numerical simulations of systolic dynamics. MEMORY PROPERTIES OF CONTRACTING MYOCARDIUM

The myocardium is an engine whose mechanical output is continuously regulated by the ongoing results of its activity. I look on it as a versatile, time-varying, nonlinear dynamic system which is capable of determining, to a large extent, as well asfiltering the past history of its inputs. It is easy to see on a macro scale ways in which the ventricular myocardium influences its own input. Because blood flows in a circle, stroke volume contributes to venous return and so affects (with a delay) the end-diastolic volume or preload of subsequent beats. Furthermore, the stroke volume ejected affects directly the endsystolic volume; this also contributes (immediately) to the preload of the next beat and so to myocardial work output (Frank-Starling mechanism). Filtering of the past history of its inputs takes the form of weighting, or remembering the recent past more heavily than the distant past, and perhaps more heavily than the immediate present. In a time-invariant, linear dynamic system this sort of behavior would be expressed mathematically by convolution integrals. As I discuss

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elsewhere (45), already at the turn of the century, Otto Frank alluded to effects of myocardial memory of history of contraction, which preclude any simple relation between length and tension (12). He was likely to have been influenced by the work of his contemporary, Boltzmann, who developed the general constitutive equation for a linear viscoelastic solid (13). Short-term myocardial memory phenomena are still ill-defined. We are far from characterizing them mathematically and we are particularly ignorant about subtle ways in which they modulate ventricular ejection dynamics in health and disease. Their actions are superimposed on the dynamics accruing from two primary ventricular properties, i.e., a time-varying elastance (31,63) and a nonlinear internal resistance (22,59,67). These actions involve both activation and inactivation phenomena. Ejection induced "deactivation" was noted in the early studies of the German school on ventricular pressure-volume relations (24). Edman and Nilsson later showed that the residual ability of myocardium to produce motion or tension during contraction is strongly influenced by the amount of active shortening that had occurred previously during the same contraction (11). Shortening induced deactivation, under normal circumstances, limits energy consumption and may create an inotropic reserve that may be available when a decrease in contractility or an increase in systolic load must be compensated. Thus, if the total ventricular load were suddenly augmented in the course of ejection, outflow would diminish and consequently the deactivation would become less prominent than in a beat with lower systolic load levels. Hemodynamically, this would be equivalent to an increase in contractility. The converse memory phenomenon, ejection induced "superactivation," was observed by Vaartjes and Boom and other investigators in the 1980s (67). Some aspects of it were noted by Otto Frank who, one century earlier, had stated that the maximum of the isotonic curve occurs later than that of the isometric (12). The primafacie puzzling superactivating effect of ejection may not be, in fact, attributable to the ejection process as such, but rather to the different initial conditions that must apply for an ejecting as compared to an isovolumic beat at the same (end-systolic) volume. Firstly, the longer initial sarcomere length in the ejecting contraction will be associated with increased myofibrillar activation (1,20,25). Indeed, according to current concepts, length-dependent force changes (Frank-Starling) and inotropic alterations (Sarnoff homeo-metric autoregulation) of contractile performance may have the same or related underlying mechanisms. In both cases, the increase in contractile force may be due to an increased extent of calcium activation of the contractile elements. It is important to appreciate, in this context, that the contractile force o f the ventricle can be modulated not only by altering the free calcium ion concentration in the myoplasm, but also by altering the calcium responsiveness of the myofilaments. Secondly, there is a considerable lag in the development of peak external tension following the peak contractile element activation (55), as is illustrated in Fig. 4 from my own earlier studies on papillary muscles. Because of this lag, the greater potential for contractile stress generation established during the isovolumic phase of an ejecting beat with higher end-diastolic volume (compared to a beat starting at a lower volume) would not dissipate instantaneously as sacomeres shorten during ejection. In other words, the myocardium behaves as a recursive system whose ongoing activity is influenced by its output during the earlier stages o f the cycle. Such short-term aspects of myocardial memory phenomena are the subject of the paper of Drs. Boom and Wijkstra (5) in this issue. Their elegant studies provide fur-

Cardiac Mechanics

11 HYPOTHERMIA + REOXYGENATION +--+ Riled Twitch ~ RecordedTwitch(To)

EUTHERMIA 2,~_/,~'~ p

I/\f\

2.0 TENS~ON (g)

/

1.5 1.0 O5

-0.

0.5

1,0

1.5

0.5

1.0

1.5

SECONDS FIGURE 4. Temporal concentration profile of activated cross bridges (namely, contractile element tension) and simultaneous course of external tension in isometric twitches of papillary muscle during euthermia (left panel) and hypothermia with reoxygenation (right panel). Recorded tension reaches its peak well after m a x i m u m of internally generated tension. Solid line, contractile element tension (Ti). Solid line with crosses, model curve fitted to digitized recordings of external tension (To). Circles, data from actual recorded twitches; for convenience only every lOth recorded data point is indicated by a circle. (Reprinted from Pasipoularides et al. [55] by permission of the American Physiological Society.)

ther information on length, load and time dependence of activation in ventricular myocardium. The resultant dependence of systolic patterns of myocardial force development on these factors is quite a provocative finding. As I have stated recently (45), the intensity, time course and relative preponderance of local (proportional to muscle fiber acceleration) and convective (proportional to fiber velocity squared) components of the intrinsic load during earlier stages of ejection could well influence the evolution of myocardial stresses and kinematics later on. This implies, of course, that the end-systolic pressure-volume relationship and all its variants may not be quite as load-independent indices of contractility as is generally believed. This brings me to the last paper of this special issue, by Drs. Stein and Sabbah, who consider ejection phase indices of myocardial contractility and ventricular performance. EJECTION PHASE INDICES OF MYOCARDIAL CONTRACTILITY AND HEART STRENGTH Because of obvious clinical and experimental needs, there has been, through the years, great interest in indices capable of quantifying myocardial contractility and heart strength. Thanks to relatively recent advances in instrumentation which allow high-fidelity measurements of intracardiac pressures and velocities (23,45), it is now possible to learn how a given patient's heart is raising the intraventricular pressure and setting the blood in motion in the course of ejection. This allows cardiologists and experimenters alike to identify both the conditions which impair ejection and the interventions which improve it, based on high-frequency information brought out by taking derivatives of pressure, flow velocity and work. In an early modern study (4), myocardial contractility was characterized using time

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A. Pasipoularides

derivatives of the left ventricular pressure signals. Power-density functions, energyaveraged power density and power-averaged rate of power-density generation were derived in order to relate the free energy in the myocardium to systolic pressure. The phase-plane functions were shown to reflect the myocardial inotropic state and to be insensitive to volume loading. Since the ventricle's function is to set the blood in motion, to full~ understand what the heart has accomplished one needs knowledge of stroke volume as well as of the velocities and accelerations in the course of ejection. Looked at from this viewpoint, a single ejection time index of ventricular function is almost inconceivable; any single index will give evidence of only one aspect of function related to either blood displacement, velocity or acceleration. Which of these aspects is most important will depend on the problem at hand and on how subtle the changes evaluated are. I think that the hemodynamic situation is best explained by an analogy. Suppose that one cylinder of an automobile engine is dead and the problem is to discover the resulting performance defect. Clearly, the information given by the odometer would be useless for this problem, since the car could still be driven over a long distance. Input from the speedometer would probably not reveal the weakness, since the car might still cruise at 65 mph on the freeway. But knowledge of acceleration will detect the weakness readily, because with one cylinder out, the pickup will certainly be impaired. From these simple considerations we can expect that ventricular dysfunction (or hyperfunction) will best be revealed by estimates of acceleration during ejection. Already in 1963, Rushmer et al. (56) reported that when conscious dogs chronically instrumented with an aortic flowmeter were subjected to coronary occlusion, acceleration levels during ejection decreased immediately although stroke volume was maintained. In similar experiments shortly thereafter, Noble et al. (41) measured up to 40% reduction in peak blood acceleration with no, or only minimal, stroke volume impairment. They also found that positive inotropic agents may increase peak acceleration by more than 60% from control without changing stroke volume. When assessing ejection time indices, one should bear in mind the implications of the inverse relation between shortening load and fiber shortening velocity and acceleration (14,45). In view of this, a negative feedback loop is constituted between the total systolic load and the ventricular muscle fiber shortening velocity and acceleration, through the velocity and the acceleration of blood flow (3,23,34,45,47,52,53). Figures 3 and 5 illustrate this concept, which holds great importance for the proper evaluation of impaired acceleration and velocity patterns during ejection. Returning to the automobile analogy, for any available motor power, the pickup will depend on variables such as the car's weight and the grade and condition of the road. We have recently shown (21,23), in fact, that decreased outflow acceleration and velocity in dilated cardiomyopathy result from augmented feedback loading functions, in addition to an impaired contractile state. Drs. Stein and Sabbah (62) describe several ejection phase indices of left ventricular performance and explore their meaning, derivation, advantages and shortcomings. CONCLUSION In summing up, this special issue on hemodynamics updates evolving concepts on myocardial dynamics and ventricular systolic and diastolic loading and function. Our

Cardiac Mechanics

13

[ LVEDkV]

I

Contractility I Velocity, Acceleration of Fiber Shortening

o

ekv, PkA

I ]

I I

e ~l Early Ejection Afterload I FIGURE 5. Diagrammatic representation of the interrelation between contractility, load on the ventricular myocardium and ejection variables. LVEDV = left ventricular end-diastolic volume; LVVpkv = left ventricular volume at the time of peak velocity; PkA = peak outflow acceleration; PkV = peak ejection velocity. (Reprinted from Isaaz and Pasipoularides [23] by permission of the American College of Cardiology.)

c o n t r i b u t o r s have enriched t h e A n n a l s t h r o u g h these special articles. T h e y have illum i n a t e d m u l t i p l e facets o f c o m p l e x q u e s t i o n s with cogent a n d concise m a t e r i a l . Its p r e s e n t a t i o n in a single issue should circumvent the f r a g m e n t a t i o n which u n a v o i d a b l y a c c o m p a n i e s p u b l i c a t i o n o f individual articles in different issues and j o u r n a l s . P r o m ising areas for future research are well delineated in the individual contributed papers. Despite the r e m a i n i n g u n c e r t a i n t i e s , one m u s t c o n c l u d e t h a t s o p h i s t i c a t e d m e a n s (analytical, i n s t r u m e n t a t i o n a l a n d c o m p u t a t i o n a l ) are n o w available to secure better answers to m a n y clinical questions c o n c e r n e d with a b n o r m a l i t i e s o f c a r d i a c function a n d their t r e a t m e n t . B i o m e d i c a l engineers will i n c r e a s i n g l y c o n t r i b u t e to the s o l u t i o n o f the m a n y p r o b l e m s which r e m a i n . W e h o p e t h a t o u r r e a d e r s find this special issue to be h e l p f u l . We t h a n k o u r c o n t r i b u t o r s f o r t h e i r o u t s t a n d i n g w o r k .

REFERENCES 1. Allen, D.G.; Kurihara, S. The effects of muscle length on intracellular calcium transients in mammalian cardiac muscle. J. Physiol. 327:79-94; 1982. 2. Appleton, C.P.; Hatle, L.K.; popp, R.L. Relation of transmitral flow velocity patterns to left ventricular diastolic function: New insights from a combined hemodynamic and Doppler echocardiographic study. J. Am. Coll. Cardiol. 12:426-440; 1988. 3. Bird, J.J.; Murgo, J.P.; Pasipoularides, A. Fluid dynamics of aortic stenosis: Subvalvular gradients without subvalvular obstruction. Circulation 66:835-840; 1982. 4. Bloomfield, M.E.; Gold, L.D.; Reddy, R.V.; Katz, A.I.; Moreno, A.H. Thermodynamic characterization of the contractile state of the myocardium. Circ. Res. 30:520-534; 1972.

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5. Boom, H.B.K.; Wijkstra, H. The step response of left ventricular pressure to ejection flow: A system oriented approach. Ann. Biomed. Eng. 20:99-126; 1992. 6. Caldini, P.; Permutt, S.; Waddell, J.A.; Riley, R.L. Effect of epinephrine on pressure, flow, and volume relationships in the systemic circulation of dogs. Circ. Res. 34:606-623; 1974. 7. Coleman, T.G.; Manning, R.D., Jr.; Norman, R.A., Jr.; Guyton, A.C. Control of cardiac output by regional blood flow distribution. Ann. Biomed. Eng. 2:149-163; 1974. 8. Condos, W.R., Jr.; Latham, R.D.; Hoadley, S.D.; Pasipoularides, A. Hemodynamics of the Mueller maneuver in man: Right and left heart micromanometry and Doppler echocardiography. Circulation 76:1020-1028; 1987. 9. DeMaria, A.N.; Wisenbaugh, T. Identification and treatment of diastolic dysfunction: Role of transmittal Doppler recordings. J. Am. Coll. Cardiol. 9:1106-1107; 1987. 10. Devereux, R.B. Toward a more complete understanding of left ventricular afterload. J. Am. Coll. Cardiol. 17:122-124; 1991. 11. Edman, K.A.P.; Nilsson, E. The mechanical parameters of myocardial contraction studied at a constant length of the contractile element. Acta Physiol. Scand. 72:205-219; 1968. 12. Frank, O. On the dynamics of cardiac muscle. Am. Heart J. 58:282-317, 467-478; 1959. 13. Fung, Y.C. Biomechanics: Mechanical properties of living tissues. New York: Springer-Verlag; 1981. 14. Gault, J.H.; Ross, J., Jr.; Braunwald, E. Contractile state of the left ventricle in man. Circ. Res. 22:451-463; 1968. 15. Gelpi, R.J.; Pasipoularides, A.; Lader, A.S.; Patric, T.A.; Chase, N.; Hittinger, L.; Shannon, R.P.; Bishop, S.P.; Vatner, S.F. Changes in diastolic cardiac function in developing and stable perinephritic hypertension in conscious dogs. Circ. Res. 68:555-567; 1991. 16. Georgiadis, J.G.; Wang, M.; Pasipoularides, A. Computational fluid dynamics of left ventricular ejection. Ann. Biomed. Eng. 20:81-97; 1992. 17. Gilbert, J.C.; Glantz, S.A. Determinants of left ventricular filling and of the diastolic pressure-volume relation. Circ. Res. 64:827-852; 1989. 18. Glantz, S.A.; Parmley, W.W. Factors which affect the diastolic pressure-volume curve. Circ. Res. 42:171-180; 1978. 19. Hatle, L.K.; Appleton, C.P.; Popp, R.L. Differentiation of constrictive pericarditis and restrictive cardiomyopathy by Doppler echocardiography. Circulation 79:357-370; 1989. 20. Hibberd, M.G.; Jewell, B.R. Calcium- and length-dependent force production in rat ventricular muscle. J. Physiol. 329:527-540; 1982. 21. Hoadley, S.D.; Pasipoularides, A. Are ejection phase Doppler/echo indices sensitive markers of contractile dysfunction in cardiomyopathy? Role of afterload mismatch. Circulation 76:Supplement IV404; 1987. 22. Hunter, W.C.; Janicki, J.S.; Weber, K.T.; Noordergraaf, A. Systolic mechanical properties of the left ventricle. Effects of volume and contractile state. Circ. Res. 52:319-327; 1983. 23. Isaaz, K.; Pasipoularides, A. Noninvasive assessment of intrinsic ventricular load dynamics in dilated cardiomopathy. J. Am. Coll. Cardiol. 17:112-121; 1991. 24. Jacob, R.; Weigand, K.H. Die endsystolischen Druck- Volumenbeziehungen als Grund-lage einer Beurteilung der Kontraktilitaet des linken Ventrikels in situ. Pfluegers Archly. 289:37-49; 1966. 25. Jewell, B.R. A reexamination of the influence of muscle length on myocardial performance. Circ. Res. 40:221-230; 1977. 26. Kass, D.A.; Kelly, R.P. Ventriculo-arterial coupling: Concepts, assumptions, and applications. Ann. Biomed. Eng. 20:41-62; 1992. 27. Kussmaul, W.G.; Noordergraaf, A.; Laskey, W.K. Right ventricular-pulmonary arterial interactions. Ann. Biomed. Eng. 20:63-80; 1992. 28. Latham, R.D.; Westerhof, N.; Sipkema, P.; Rubal, B.J.; Reuderink, P.; Murgo, J.P. Regional wave travel and reflections along the human aorta: A study with six simultaneous micromanometric pressures. Circulation 72:1257-1269; 1985. 29. Laxminarayan, S.; Sipkema, P.; Westerhof, N. Characterization of the arterial system in the time domain. IEEE Trans. on Biomed. Eng. 25:177-184; 1978. 30. Maughan, W.L.; Shoukas, A.A.; Sagawa, K.; Weisfeldt, M.L. Instantaneous pressure-volume relationship of the canine right ventricle. Circ. Res. 44:309-315; 1979. 31. McKay, R.G.; Aroesty, J.M.; Heller, G.V.; Royal, H.D.; Warren, S.E.; Grossman, W. Assessment of the end-systolic pressure-volume relationship in human beings with the use of a time-varying elastance model. Circulation 74:97-104; 1986. 32. Milnor, W.R. Arterial impedance as ventricular afterload. Circ. Res. 36:565-570; 1975.

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APPENDIX A The heart is a hollow organ weighing well under a pound and only a little larger than the fist, in absence of abnormal enlargement and hypertrophy. Its tough, muscular wall (myocardium) is surrounded by a fibrous bag (pericardium) and is lined by a thin membrane (endocardium). A wall (septum) divides the heart cavity down the middle into a "right heart" and a "left heart." Each side is divided again into an upper chamber (atrium or auricle) and a lower chamber (ventricle). Atrioventricular valves (the "mitral" on the left and "tricuspid" on the right) regulate the flow of blood through the heart and semilunar valves (aortic and pulmonic) to the root of the pulmonary artery and the aorta. Considering a representative cardiac cycle, the moment ventricular pressure falls below atrial, the atrioventricular valves open and blood enters each ventricle which is at its end systolic volume (ESV). Early diastolic filling is rapid because of continued ventricular relaxation. The rapid filling phase is followed by a slower phase (diastasis). Toward the end of the filling phase, atrial contraction suddenly reaccelerates the filling rate and increases ventricular end diastolic volume (EDV) and pressure (EDP). Shortly after the initiation of ventricular myocardial depolarization, identified by the Q wave of the electrocardiogram, the ventricle begins to contract, increasing intraventricular pressure and closing the inlet valves. The ventricles vigorously contract and develop systolic wall stresses, raising intracavitary pressure to the level of aortic or pulmonic diastolic pressure. Closure of the atrioventricular valves defines the onset of isovolumic contraction and opening of the semilunar valves its termination.

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With the onset of ventricular ejection, a sharp increase in pressure is produced in the great vessels (aorta and pulmonary artery). Peak systolic pressures may be reached in the latter part of the ejection phase because of pulse wave reflections. In late ejection, ventricular pressure falls below that in the outflow trunk, outflow stops shortly thereafter, and the semilunar valves close. Conventionally, the end of the ejection phase is signaled by an incisura in the pressure tracing from the root of the great vessels. Following semilunar valve closure, ventricular pressure falls sharply during the isovolumic relaxation phase. This phase is concluded when atrial exceeds ventricular pressure and the atrioventricular valves open. The cardiac output (CO) equals the product of stroke volume (SV) by heart rate (HR). In presence of valvular regurgitations, angiographic cardiac output exceeds forward output by a fraction depending on regurgitant volume. The ejection fraction (EF) is given by (EDV-ESV)/EDV. Conventionally, the maximal value of ventricular dP/dt during isovolumic contraction and the ejection fraction are taken as readily obtainable ventricular systolic performance indices. The minimal value of the negative dP/dt during isovolumic relaxation and the time constant of pressure decay during this phase are taken as indices of myocardial diastolic relaxation.