Factors influencing left-ventricular stiffness

The aim of the study was to investigate the relative contributions of geometrical and material factors to overall left-ventricular cavity stiffness. Left-ventricular cavity shapes were reconstructed using a computer and the variation of myocardial elastic modulus was calculated, by the finite element method, through the passive phase of diastole when rising volume coincided with rising pressure. Geometric data were obtained from biplane cineangiography, with micromanometer pressure measurements, for ten patients with left ventricular disease. Dimensional analysis was applied to the initial and derived data from which the influences of myocardial compliance, wall thickness-to-long dimension ratio, and aspect ratio (long-to-short axes) were determined. The ratio between the volume elasticity and the myocardial modulus of elasticity, the normalized stiffness ratio (NSR), is proposed as a useful index of left ventricular mechanical behaviour in diastole. The volume elasticity of the chamber is dependent not only upon the myocardium elastic modulus and the wall thickness ratio, but also on the shape of the chambe. Changes in the thickness/radius ratio of the ventricle have less effect upon its distention than those in the long dimension/radius ratio. The left ventricle becomes more spherical in shpae through diastole and hence becomes stiffer by this geometric mechanism.     

Dynamics of left ventricular wall and mitral valve mechanics--a model study

The relation between global left ventricular pumping characteristics and local cardiac muscle fiber mechanics is represented by a mathematical model of left ventricular mechanics in which the mitral valve papillary muscle system is incorporated. The wall of the left ventricle is simulated by a thick-walled cylinder. Transmural differences in fiber orientation are incorporated by changing the direction of material anisotropy across the wall. The cylinder is free to twist. The upper end of the cylinder is covered by a thin, flexible sheet, representing the base of the left ventricle. The mitral valve is incorporated in this sheet. The tips of the mitral leaflets are connected by chordae tendineae to the papillary muscles which are attached to the bottom of the cylinder. Canine cardiac cycles were simulated for various end-diastolic values of left ventricular volume (25-120 ml, control 60 ml), left atrial pressure (0-2.7 kPa, control 0.22 kPa) and aortic pressure (5-11 kPa, control 11 kPa). In this wide range of preload and afterload mechanical loading of the muscle fibers appeared to be distributed quite evenly (SD: +/- 5% of control value) over all muscular structures of the left ventricle, including the papillary muscles.     

Myocardial blood flow regulation relative to left ventricle pressure and volume in anesthetized dogs

The influence of left ventricle pressure and volume changes on coronary blood flow was investigated in eight anesthetized dogs. Coronary artery pressure-flow relationships were determined at two levels of left ventricular pressure and volume. The distribution of blood flow within the myocardium was also determined when these relationships varied. Reducing left ventricle pressures and volumes increased heart rate. Rate-pressure product, diastolic coronary pressure, myocardial O2 consumption, total, subendocardial and subepicardial flow decreased. Hematocrit and blood gas data were unchanged. The pressure-flow relationships were shifted leftward (p = 0.001) but the range of autoregulation was not altered. At low left ventricle pressures and volumes, the lower coronary artery pressure limit was shifted leftward (from 75 to 45 mm Hg (1 mm Hg = 133.3 Pa)), while total, subendocardial, and subepicardial blood flow did not change compared with the control. Below the lower coronary artery pressure limit, subendocardial but not subepicardial flow decreased, resulting in maldistribution of flow across the left ventricular wall. When coronary pressure was reset between control and the lower coronary artery pressure limit, subendocardial flow was restored. These results show that the lower coronary artery pressure limit can be shifted leftward while the distribution of blood flow across the left ventricular wall is preserved.     

Regional passive ventricular stress-strain relations during development of altered loads in chick embryo

Mechanical load influences embryonic ventricular growth, morphogenesis, and function. However, little is known about changes in regional passive ventricular properties during the development of altered mechanical loading conditions in the embryo. We tested the hypothesis that regional mechanical loads are a critical determinant of embryonic ventricular passive properties. We measured biaxial passive right and left ventricular (RV and LV, respectively) stress-strain relations in chick embryos at Hamburger-Hamilton stages 21 and 27 after conotruncal banding (CTB) to increase biventricular pressure load or left atrial ligation (LAL) to reduce LV volume load and increase RV volume load. In the RV, wall strains at end-diastolic (ED) pressure normalized whereas ED stresses increased after either CTB or LAL during development. In the left ventricle, both ED strain and stress normalized after CTB, whereas both remained reduced with significantly increased myocardial stiffness after LAL. These results suggest that the embryonic ventricle adapts to chronically altered mechanical loading conditions by changing specific RV and LV passive properties. Thus regional mechanical load has a critical role during cardiogenesis.     

Structural finite deformation model of the left ventricle during diastole and systole

A model of left ventricular function is developed based on morphological characteristics of the myocardial tissue. The passive response of the three-dimensional collagen network and the active contribution of the muscle fibers are integrated to yield the overall response of the left ventricle which is considered to be a thick wall cylinder. The deformation field and the distributions of stress and pressure are determined at each point in the cardiac cycle by numerically solving three equations of equilibrium. Simulated results in terms of the ventricular deformation during ejection and isovolumic cycles are shown to be in good qualitative agreement with experimental data. It is shown that the collagen network in the heart has considerable effect on the pressure-volume loops. The particular pattern of spatial orientation of the collagen determines the ventricular recoil properties in early diastole. The material properties (myocardial stiffness and contractility) are shown to affect both the pressure-volume loop and the deformation pattern of the ventricle. The results indicate that microstructural consideration offer a realistic representation of the left ventricle mechanics.     

Influence of left-ventricular shape on passive filling properties and end-diastolic fiber stress and strain

Passive filling is a major determinant for the pump performance of the left ventricle and is determined by the filling pressure and the ventricular compliance. In the quantification of the passive mechanical behaviour of the left ventricle and its compliance, focus has been mainly on fiber orientation and constitutive parameters. Although it has been shown that the left-ventricular shape plays an important role in cardiac (patho-)physiology, the dependency on left-ventricular shape has never been studied in detail. Therefore, we have quantified the influence of left-ventricular shape on the overall compliance and the intramyocardial distribution of passive fiber stress and strain during the passive filling period. Hereto, fiber stress and strain were calculated in a finite element analysis of passive inflation of left ventricles with different shapes, ranging from an elongated ellipsoid to a sphere, but keeping the initial cavity volume constant. For each shape, the wall volume was varied to obtain ventricles with different wall thickness. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry along the muscle fiber directions. A realistic transmural distribution in fiber orientation was assumed. We found that compliance was not altered substantially, but the transmural distribution of both passive fiber stress and strain was highly dependent on regional wall curvature and thickness. A low curvature wall was characterized by a maximum in the transmural fiber stress and strain in the mid-wall region, while a steep subendocardial transmural gradient was present in a high curvature wall. The transmural fiber stress and strain gradients in a low and high curvature wall were, respectively, flattened and steepened by an increase in wall thickness.     

Mechanical tension in different parts of the left ventricle of the heart exposed to inotropic factors

A study was made of the effects of different inotropic factors on mechanical tension in the left ventricular wall and in the apex of the heart and of the participation of these regions in the formation of hemodynamic characteristics. Adrenaline caused similar effects whereas CaCl2 exerted different inotropic effects on the left ventricular wall and the apex of the heart. Changes in mechanical tension of the wall correlated with variations in the pressure inside the left ventricle. Tension in the apex of the heart produced alterations in the stroke volume.     

Repolarization of canine ventricular myocardium under the supraventricular rhythm

The ventricular myocardium is characterized by heterogeneity of activation-recovery interval durations. The transmural ARI gradients are present in the right ventricular apex (ARIs monotonically decreased as one moved from the endocardium to the epicardium), and in the left ventricular base (repolarization in the subepicardial layers was significantly shorter than that in the midmyo cardial layers whereas subendocardial ARIs did not differ from the others). The repolarization pattern of these myocardial regions is governed by the distribution of ARIs. In the apical left ventricular and basal right ventricular areas, no significant transmural differences in the repolarization durations were found. The repolarization pattern of these myocardial regions is governed by the activation sequence. In the right ventricle, ARIs were significantly longer at the base and shorter at the apex. In contrast, in the left ventricle, the apical ARIs were prolonged whereas the basal ARIs were abbreviated. The apex-to-base sequence of myocardial repolarization seems to depend on apex-to-base gradient of activation-recovery intervals durations.     

Respective impacts of aortic stenosis and systemic hypertension on left ventricular hypertrophy

It has been reported that 30-40% of patients with aortic stenosis are hypertensive. In such patients, the left ventricle faces a double (i.e. valvular and vascular) pressure overload, which results in subsequent wall volume hypertrophy. From a clinical standpoint, it is difficult to separate the respective contributions of aortic stenosis and systemic hypertension to left ventricular burden and patient's symptoms and thus to predict whether valve replacement would be beneficial. The objective of this theoretical study was therefore to investigate the relative effects of valvular and vascular afterloads on left ventricular hypertrophy. We used a ventricular-valvular-vascular mathematical model in combination with the Arts' model describing the myofiber stress. Left ventricular wall volume was computed for different aortic blood pressure levels and different degrees of aortic stenosis severity. Our simulations show that the presence of concomitant systemic hypertension has a major influence on the development of left ventricular hypertrophy in patients with aortic stenosis. These results also suggest that mild-to-moderate aortic stenosis has a minor impact on left ventricular wall volume when compared with hypertension. On the other hand, when aortic stenosis is severe, wall volume increases exponentially with increasing aortic stenosis severity and the impact of aortic stenosis on left ventricular hypertrophy becomes highly significant.     

Postsystolic shortening of ischemic myocardium: a mechanism of abnormal intraventricular filling

Acute myocardial ischemia has been associated with abnormal filling patterns in the left ventricular (LV) apex. We hypothesized that this may in part be due to postsystolic shortening of ischemic apical segments, which leads to reversal of early diastolic apical flow. Fourteen open-chest anesthetized dogs were instrumented with micromanometers in the LV apex and left atrium and myocardial sonomicrometers in the anterior apical LV wall. Intraventricular filling by color Doppler and wall motion by strain Doppler echocardiography (SDE) were assessed from an apical view. Measurements were taken before and after 5 min of left anterior descending coronary artery (LAD) occlusion. In four dogs, we measured the pressure difference between the LV apex and outflow tract. At baseline, peak early diastolic flow velocities in the distal one-third of the LV were directed toward apex (9.2 +/- 1.6 cm/s). After LAD occlusion, the velocities reversed (-2.3 +/- 0.4 cm/s, P < 0.01), indicating that blood was ejected from the apex toward the base during early filling. This interpretation was confirmed by wall motion analysis, which showed postsystolic shortening of apical myocardial segments. The postsystolic shortening represented 9.7 +/- 1.7% (P < 0.01) and 14.2 +/- 2.4% (P < 0.01) of end-diastolic segment length by SDE and sonomicrometry, respectively. Consistent with the velocity changes, we found reversal of the early diastolic pressure gradient from the LV apex to outflow tract. In the present model, acute LAD occlusion resulted in reversal of early diastolic apical flow, and this was attributed to postsystolic shortening of dyskinetic apical segments. The clinical diagnostic importance of this finding remains to be determined.     

The effect of distension of the left ventricle of the heart on the length of the individual myocardial fibers

Based on the ellipsoid model of the left ventricle and the helicoidal course of the left ventricular myocardial fibers, a theory has been developed for calculating the length of the individual myocardial fibers. Numerical solutions of the final equation show that when the left ventricle is distended, the increase in length of the myocardial fibers is not uniform throughout the thickness of the myocardial wall. It was shown that with increasing dimensions of the left ventricle, the distension of the myocardial fibers becomes smaller as one advances from the endocardium to the middle layer of fibers, whereas it increases as one advances from the middle layer to the epicardial layer. The mechanism by which this effect is brought about as well as its physiological implications are discussed.     

Dynamic geometry of the intact left ventricle

Knowledge of left ventricular chamber dynamics is central to our understanding of cardiac physiology. The complicated changes in left ventricular geometry observed in the dog during various phases of the cardiac cycle can be represented as distinct linear relationships between chamber eccentricity and intracavitary volume during diastole and ejection, and probably represent structural properties of the ventricular wall. Chamber geometry of the left ventricle is a major determinant of overall myocardial function. The slope of the radius of curvature (r) to wall thickness (h) relationship is a geometric constant that determines the mural force at any given transmural pressure. Chronic pressure and volume overload produce changes in this geometric relationship as a result of increased mural force resisting ejection. The adaptive mechanism of ventricular hypertrophy in this setting alters the r/h ratio and returns systolic mural force toward normal. Coronary occlusion induces acute changes in regional geometry characterized by holosystolic wall bulging and systolic wall thinning, which shift the r/h relationship upward and to the left. The geometric alteration during ischemia probably increases systolic mural force and could adversely affect myocardial function. Recent studies with patients have shown the r/h ratio to be of value in distinguishing between reversible and irreversible impairment of myocardial performance. Because most myocardial diseases produce major alterations in the structure of the ventricular wall, analysis of dynamic chamber geometry may prove of prognostic value in assessing patients with cardiac disorders.     

The principle of laplace and scaling of ventricular wall stress and blood pressure in mammals and birds

Maximum left ventricular wall stress is calculated at end-diastolic volume and systemic arterial diastolic blood pressure, according to a thick-walled model for the principle of Laplace. Stress is independent of body mass and averages 13.9 kPa (+/-2.3; 95% confidence interval) in 24 species of mammals weighing 0.025-4,000 kg and 15.5 kPa (+/-4.7) in 12 birds weighing 0.014-110 kg. Birds have higher arterial blood pressures and larger hearts than mammals. Systolic and diastolic arterial blood pressures increase with body mass according to M(0.05) in mammals, and heart mass increases according to M(1.06) in the same species, further supporting the principle. However, blood pressure in birds is independent of body mass, and heart mass scales isometrically. End-diastolic stress values, calculated according to Laplace, are about one-third of peak stresses recorded in isolated mammalian myocardial preparations.     

Cardiac remodelling: concentric versus eccentric hypertrophy in strength and endurance athletes

Cardiac remodelling is commonly defined as a physiological or pathological state that may occur after conditions such as myocardial infarction, pressure overload, idiopathic dilated cardiomyopathy or volume overload. When training excessively, the heart develops several myocardial adaptations causing a physiological state of cardiac remodelling. These morphological changes depend on the kind of training and are clinically characterised by modifications in cardiac size and shape due to increased load. Several studies have investigated morphological differences in the athlete’s heart between athletes performing strength training and athletes performing endurance training. Endurance training is associated with an increased cardiac output and volume load on the left and right ventricles, causing the endurance-trained heart to generate a mild to moderate dilatation of the left ventricle combined with a mild to moderate increase in left ventricular wall thickness. Strength training is characterised by an elevation of both systolic and diastolic blood pressure. This pressure overload causes an increase in left ventricular wall thickness. This may or may not be accompanied by a slight raise in the left ventricular volume. However, the development of an endurancetrained heart and a strength-trained heart should not be considered an absolute concept. Both forms of training cause specific morphological changes in the heart, dependent on the type of sport. (Neth Heart J 2008;16:129-33.)     

Finite-element analysis of left ventricular myocardial stresses

A versatile method of finite-element analysis is presented for the determination of the stress distributions in the left ventricular myocardial wall. The instantaneous shapes of the left ventricular myocardial wall, measured at 0,5 mm intervals and at a rate 0f 60 images/sec during a cardiac cycle, are approximated by axisymmetric shells following the approach of Gould et al. and analysed by the method of incremental loadings to account for the changing transmural pressure. The ventricular wall is mathematically divided up into coaxial rings of triagular cross sections so that determination of the stresses at any point within the wall can be achieved by assigning increased number of nodes across the wall thickness in the regions of the left ventricular wall where particular attention is needed. Appropriate boundary conditions are defined at the base of the left ventricle so that it can be treated as a shell with an open end. The computer program, which implements all the stress calculations involved, depends on the dimensions of the left ventricular wall measured from an operator-interactive roengen videometry system. It carries out the sequential formation of the nodes and elements and includes a CALCOMP subroutine to plot the finite-element partitioning of the instantaneous shape. Illustrative results of the end-diastolic stress distributions within the myocardial wall of a metabolically-supported, isolated, working canine left ventricle are given. This technique predicts higher endocardial meridional and hoop wall stresses relative to the stresses in the middle and epicardial region than those obtained with previous models.     

Functional state of the left ventricle of the heart in cardiocytotoxic shock]

Changes in the cardiodynamics and the contractile myocardium function under experimental shock caused by intracoronary injection of the anticardial cytotoxic serum were studied on 20 anesthetized dogs. Along with the symptoms of disturbance of the left ventricle function (a decrease of the systolic index, stroke work index of the left ventricle, rate of the intraventricular pressure rise, indices of myocardial contractility, ejection fraction) a decrease of the end-diastolic volume and pressure in the left ventricle was observed. These data show that disturbances in the cardiodynamics were cause not only by the cytotoxic heart damage, but also by derangement of the blood flow to the left heart.     

A concentric layer model for estimating the energy expenditure of the left ventricle

The energy cost of the left ventricle is quantitatively analyzed on the basis of the following assumptions: (1) The left ventricle is assumed to be an isotropic, homogeneous elastic, thick, spherical shell. (2) The ventricular wall is made up of a finite number of thin concentric shells. (3) The energetics of the left ventricle is in accordance with the second law of thermodynamics. An expression for the work done during ventricular contraction is derived according to the definition of physical work. The energy liberation during isovolumic contraction is formulated parallel to the concepts of heat production in skeletal muscle during isometric contraction. This expression gives the total work done per stroke in terms of mean systolic pressure, end diastolic volume, stroke volume and wall thickness during diastolic phase. Supported by a research fellowship and research grant from the Canadian Heart Foundation.     

Mechanics of left ventricular relaxation, early diastolic lengthening, and suction investigated in a mathematical model

We investigated the determinants of ventricular early diastolic lengthening and mechanics of suction using a mathematical model of the left ventricle (LV). The model was based on a force balance between the force represented by LV pressure (LVP) and active and passive myocardial forces. The predicted lengthening velocity (e') from the model agreed well with measurements from 10 dogs during 5 different interventions (R = 0.69, P < 0.001). The model showed that e' was increased when relaxation rate and systolic shortening increased, when passive stiffness was decreased, and when the rate of fall of LVP during early filling was decreased relative to the rate of fall of active stress. We first defined suction as the work the myocardium performed to pull blood into the ventricle. This occurred when contractile active forces decayed below and became weaker than restoring forces, producing a negative LVP. An alternative definition of suction is filling during falling pressure, commonly believed to be caused by release of restoring forces. However, the model showed that this phenomenon also occurred when there had been no systolic compression below unstressed length and therefore in the absence of restoring forces. In conclusion, relaxation rate, LVP, systolic shortening, and passive stiffness were all independent determinants of e'. The model generated a suction effect seen as lengthening occurring during falling pressure. However, this was not equivalent with the myocardium performing pulling work on the blood, which was performed only when restoring forces were higher than remaining active fiber force, corresponding to a negative transmural pressure.     

In vivo porcine left atrial wall stress: Computational model

Most computational models of the heart have so far concentrated on the study of the left ventricle, mainly using simplified geometries. The same approach cannot be adopted to model the left atrium, whose irregular shape does not allow morphological simplifications. In addition, the deformation of the left atrium during the cardiac cycle strongly depends on the interaction with its surrounding structures. We present a procedure to generate a comprehensive computational model of the left atrium, including physiological loads (blood pressure), boundary conditions (pericardium, pulmonary veins and mitral valve annulus movement) and mechanical properties based on planar biaxial experiments. The model was able to accurately reproduce the in vivo dynamics of the left atrium during the passive portion of the cardiac cycle. A shift in time between the peak pressure and the maximum displacement of the mitral valve annulus allows the appendage to inflate and bend towards the ventricle before the pulling effect associated with the ventricle contraction takes place. The ventricular systole creates room for further expansion of the appendage, which gets in close contact with the pericardium. The temporal evolution of the volume in the atrial cavity as predicted by the finite element simulation matches the volume changes obtained from CT scans. The stress field computed at each time point shows remarkable spatial heterogeneity. In particular, high stress concentration occurs along the appendage rim and in the region surrounding the pulmonary veins.     

Cardiac assist with a twist: apical torsion as a means to improve failing heart function

Changes in muscle fiber orientation across the wall of the left ventricle (LV) cause the apex of the heart to turn 10-15 deg in opposition to its base during systole and are believed to increase stroke volume and lower wall stress in healthy hearts. Studies show that cardiac torsion is sensitive to various disease states, which suggests that it may be an important aspect of cardiac function. Modern imaging techniques have sparked renewed interest in cardiac torsion dynamics, but no work has been done to determine whether mechanically augmented apical torsion can be used to restore function to failing hearts. In this report, we discuss the potential advantages of this approach and present evidence that turning the cardiac apex by mechanical means can displace a clinically significant volume of blood from failing hearts. Computational models of normal and reduced-function LVs were created to predict the effects of applied apical torsion on ventricular stroke work and wall stress. These same conditions were reproduced in anesthetized pigs with drug-induced heart failure using a custom apical torsion device programmed to rotate over various angles during cardiac systole. Simulations of applied 90 deg torsion in a prolate spheroidal computational model of a reduced-function pig heart produced significant increases in stroke work (25%) and stroke volume with reduced fiber stress in the epicardial region. These calculations were in substantial agreement with corresponding in vivo measurements. Specifically, the computer model predicted torsion-induced stroke volume increases from 13.1 to 14.4 mL (9.9%) while actual stroke volume in a pig heart of similar size and degree of dysfunction increased from 11.1 to 13.0 mL (17.1%). Likewise, peak LV pressures in the computer model rose from 85 to 95 mm Hg (11.7%) with torsion while maximum ventricular pressures in vivo increased in similar proportion, from 55 to 61 mm Hg (10.9%). These data suggest that: (a) the computer model of apical torsion developed for this work is a fair and accurate predictor of experimental outcomes, and (b) supra-physiologic apical torsion may be a viable means to boost cardiac output while avoiding blood contact that occurs with other assist methods.