Electrical Wave Propagation in an Anisotropic Model of the Left Ventricle Based on Analytical Description of Cardiac Architecture

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher–Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation.     

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.     

Increased myocardial stiffness with maintenance of length-dependent calcium activation by female sex hormones in diabetic rats

A decrease in peak early diastolic filling velocity in postmenopausal women implies a sex hormone-related diastolic dysfunction. The regulatory effect of female sex hormones on cardiac distensibility therefore was evaluated in ovariectomized rats by determining the sarcomere length-passive tension relationship of ventricular skinned fiber preparations. Diabetes also was induced in the rat to assess the protective significance of female sex hormones on diastolic function. While ovariectomy had no effect on myocardial stiffness, collagen content, or titin ratio, a significant increase in myocardial stiffness was observed in diabetic rat only when female sex hormones were intact. The increased stiffness in diabetic-sham rats was accompanied by an elevated collagen content resulting from increases in the levels of procollagen and Smad2. Surprisingly, the increased myocardial stiffness in diabetic-sham rats was accompanied by a shift toward a more compliant N2BA of cardiac titin isoforms. The pCa-active tension relationship was analyzed at fixed sarcomere lengths of 2.0 and 2.3 μm to determine the magnitude of changes in myofilament Ca(2+) sensitivity between the two sarcomere lengths. Interestingly, high expression of N2BA titin was associated with a suppressed magnitude of changes in myofilament Ca(2+) sensitivity only in the diabetic-ovariectomized condition. Estrogen supplementation in diabetic-ovariectomized rats partially increased myocardial stiffness but completely reversed the change in myofilament Ca(2+) sensitivity. These results indicate a restrictive adaptation of myocardium governed by female sex hormones to maintain myofilament activity in compensation to the pathophysiological induction of cardiac dilatation by the diabetic condition.     

慢性心力衰竭大鼠心肌毛细血管密度及血管内皮生长因子变化

目的观察慢性心力衰竭大鼠心肌毛细血管密度及血管内皮生长因子(VEGF)变化,探究冠脉微循环障碍的病理特点及病因机制.方法实验组(n=15)皮下注射异丙肾上腺素,对照组(n=10)皮下注射生理盐水,间隔24h,连续2次.12周后测定血液动力学;计算左心室重量/体重;HE染色、Masson染色分别观察左心室病理改变、胶原变化;西非单叶豆素组织化学染色结合图像分析确定心内膜下心肌毛细血管密度、心肌细胞密度、毛细血管密度与心肌细胞密度的比值(毛细血管/心肌细胞);观察心内膜下心肌VEGF免疫组织化学变化.结果同对照组比较,实验组左心室收缩、舒张功能下降(P<0.05);左心室重量/体重升高(P<0.001);心内膜下心肌散在坏死,胶原沉积;心内膜下心肌毛细血管密度、心肌细胞密度、毛细血管/心肌细胞下降(P<0.05);VEGF合成增加(P<0.001).结论慢性心力衰竭大鼠心内膜下心肌毛细血管分布稀疏;该区域毛细血管代偿性生成减少与心肌VEGF表达无关.     

Computational modeling of left heart diastolic function: examination of ventricular dysfunction

A computational model that accounts for blood-tissue interaction under physiological flow conditions was developed and applied to a thin-walled model of the left heart. This model consisted of the left ventricle, left atrium, and pulmonary vein flow. The input functions for the model included the pulmonary vein driving pressure and time-dependent relationship for changes in chamber tissue properties during the simulation. The Immersed Boundary Method was used for the interaction of the tissue and blood in response to fluid forces and changes in tissue pathophysiology, and the fluid mass and momentum conservation equations were solved using Patankar's Semi-Implicit Method for Pressure Linked Equations (SIMPLE). This model was used to examine the flow fields in the left heart under abnormal diastolic conditions of delayed ventricular relaxation, delayed ventricular relaxation with increased ventricular stiffness, and delayed ventricular relaxation with an increased atrial contraction. The results obtained from the left heart model were compared to clinically observed diastolic flow conditions, and to the results from simulations of normal diastolic function in this model [1]. Cases involving impairment of diastolic function were modeled with changes to the input functions for fiber relaxation/contraction of the chambers. The three cases of diastolic dysfunction investigated agreed with the changes in diastolic flow fields seen clinically. The effect of delayed relaxation was to decrease the early filling magnitude, and this decrease was larger when the stiffness of the ventricle was increased. Also, increasing the contraction of the atrium during atrial systole resulted in a higher late filling velocity and atrial pressure. The results show that dysfunction can be modeled by changing the relationships for fiber resting-length and/or stiffness. This provides confidence in future modeling of disease, especially changes to chamber properties to examine the effect of local dysfunction on global flow fields.     

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 effects of changes in heart rate and aortic systolic pressure on left ventricular myocardial oxygen consumption in lambs

To determine whether changes in heart rate and aortic systolic pressure contribute equally to the determination of left ventricular myocardial oxygen consumption, we independently varied heart rate and pressure and compared the resultant oxygen consumption for similar rate-pressure products. In 6 young lambs which underwent atrioventricular node ablation, we varied heart rate by ventricular pacing at 250 beats/min, 300 beats/min, and 120 beats/min while aortic pressure remained stable and varied aortic systolic pressure by infusion of phenylephrine (to 132 +/- 15 mm Hg and 155 +/- 14 mm Hg) and by infusion of sodium nitroprusside (to 79 +/- 6 mm Hg) while heart rate was maintained stable at 200 beats/min. The 3 levels of change in aortic systolic pressure were chosen so that the ratepressure product during the pressure changes matched the rate-pressure product during the heart rate changes. We found that left ventricular myocardial oxygen consumption was the same at all 3 levels of the rate-pressure product whether heart rate was changed and pressure remained stable or pressure was changed and heart rate remained stable. Also, the correlation between oxygen consumption and the rate-pressure product was similar for both heart rate and pressure changes. During nitroprusside infusion at a fixed heart rate, oxygen extraction was significantly lower than during pacing at a heart rate of 120 beats/min when the rate-pressure product was comparable because of the direct vasodilatory effects of nitroprusside. We conclude that heart rate and aortic systolic pressure contribute equally to left ventricular myocardial oxygen consumption at the same rate-pressure product, even though there may be differences in myocardial blood flow and oxygen extraction.     

Atrial natriuretic peptide levels during development of chronic heart failure after myocardial infarction in rats

Serum levels of atrial natriuretic peptide (ANP) are elevated in chronic heart failure presumably due to dilatation of the left atrium resulting from increases in intracardiac pressures. To define the time course of changes in serum ANP levels and to determine the relationship to left ventricular end-diastolic pressure, rats were subjected to coronary artery ligation to produce myocardial infarction and left ventricular failure. Atrial natriuretic peptide levels were measured weekly for four weeks thereafter. In rats with myocardial infarction and elevation of left ventricular end-diastolic pressure there was no change in ANP levels at 7 and 14 days. However, at day 21 and 28, ANP levels were elevated more than 3 fold. There was a correlation between ANP levels and left ventricular end-diastolic pressures. There was no correlation between ANP levels and right atrial pressures or serum sodium concentrations. We conclude that the chronic elevation of left ventricular end-diastolic pressure is required to produce an increase in ANP after myocardial infarction which results in chronic heart failure.     

Electromechanical and structural alterations in the aging rabbit heart and aorta

Aging increases the risk for arrhythmias and sudden cardiac death (SCD). We aimed at elucidating aging-related electrical, functional, and structural changes in the heart and vasculature that account for this heightened arrhythmogenic risk. Young (5-9 mo) and old (3.5-6 yr) female New Zealand White (NZW) rabbits were subjected to in vivo hemodynamic, electrophysiological, and echocardiographic studies as well as ex vivo optical mapping, high-field magnetic resonance imaging (MRI), and histochemical experiments. Aging increased aortic stiffness (baseline pulse wave velocity: young, 3.54 ± 0.36 vs. old, 4.35 ± 0.28 m/s, P < 0.002) and diastolic (end diastolic pressure-volume relations: 3.28 ± 0.5 vs. 4.95 ± 1.5 mmHg/ml, P < 0.05) and systolic (end systolic pressure-volume relations: 20.56 ± 4.2 vs. 33.14 ± 8.4 mmHg/ml, P < 0.01) myocardial elastances in old rabbits. Electrophysiological and optical mapping studies revealed age-related slowing of ventricular and His-Purkinje conduction (His-to-ventricle interval: 23 ± 2.5 vs. 31.9 ± 2.9 ms, P < 0.0001), altered conduction anisotropy, and a greater inducibility of ventricular fibrillation (VF, 3/12 vs. 7/9, P < 0.05) in old rabbits. Histochemical studies confirmed an aging-related increased fibrosis in the ventricles. MRI showed a deterioration of the free-running Purkinje fiber network in ventricular and septal walls in old hearts as well as aging-related alterations of the myofibrillar orientation and myocardial sheet structure that may account for this slowed conduction velocity. Aging leads to parallel stiffening of the aorta and the heart, including an increase in systolic stiffness and contractility and diastolic stiffness. Increasingly, anisotropic conduction velocity due to fibrosis and altered myofibrillar orientation and myocardial sheet structure may contribute to the pathogenesis of VF in old hearts. The aging rabbit model represents a useful tool for elucidating age-related changes that predispose the aging heart to arrhythmias and SCD.     

Changes in cell autophagy and apoptosis during age-related left ventricular remodeling in mice and their potential mechanisms

Cardiac structures and functions change with advanced age, but the underlying mechanisms are not well understood. Autophagy and apoptosis play important roles in the process of cardiac remodeling. This study was designed to explore changes in cell autophagy and apoptosis during age-related left ventricular remodeling and to determine whether the mitogen-activated protein kinase (MAPK) pathway is an underlying mechanism. Eight 5-month-old (adult group) and eight 24-month-old male C57bl/6 mice (aged group) were studied. The heart mass index, left ventricular mass index and hydroxyproline content of both groups were compared. Western Blotting was used to quantitate the protein expression of microtubule-associated protein 1 light chain 3 (LC3), Beclin-1, caspase-3, B-cell leukemia-2 (Bcl-2) and MAPKs in the left ventricles of adult and aged mice. Our results showed that the heart mass index, left ventricular mass index and hydroxyproline content in the left ventricles of the aged mice were increased significantly compared with the adult mice, indicating that left ventricular remodeling occurs with aging. The expression of LC3 and Beclin-1 in the left ventricles of aged mice were decreased significantly compared to adult mice. Meanwhile, the level of myocardial caspase-3 in adult mice remained the same in aged mice, and the level of myocardial Bcl-2 increased significantly in aged mice. There were no differences in the expression level of myocardial extracellular signal-regulated kinase 1/2 (ERK1/2), activated/phospho-ERK1/2, c-Jun N-terminal kinase 1/2 (JNK1/2) and p38 between aged and adult mice. However, the expression of myocardial activated/phospho-JNK1/2 increased significantly in aged mice, while activated/phospho-p38 decreased significantly. These findings indicate that autophagy decreases without a concurrent change in apoptosis during age-related left ventricular remodeling in mice. The MAPK pathway may be involved in the regulation of age-related left ventricular remodeling by modulating autophagy.     

Heart failure: mechanisms of cardiac and vascular dysfunction and the rationale for pharmacologic intervention

Congestive heart failure is a complex clinical syndrome that has its basis in an abnormality of myocardial cell function resulting in impaired ventricular performance, exercise intolerance, and ventricular arrhythmias. The functional defect in myocardial performance may be related to alterations in receptor function, in regulatory proteins, or in biochemical mechanisms. Remodeling of the left ventricle has been observed to play an important role in the natural course of heart failure. The complex interplay between cellular elongation, reactive hypertrophy, and the influence of the change from ellipsoid to spheroidal shape of the left ventricle after acute myocardial infarction are just beginning to be understood. Prevention of this remodeling effect by pharmacologic intervention is being widely explored, although the mechanisms are poorly defined. Impedance to left ventricular ejection is also an important determinant of cardiac performance in heart failure. Constriction of arteriolar resistance vessels and reduction in compliance of arterial conductance vessels is a common manifestation of heart failure and may be under the influence of neural, hormonal, endothelial, and local regulatory factors. Increased tone of venous capacitance vessels contributes to a shift of blood centrally and to an increase in ventricular preload. Vasodilator drugs by relaxing the arterial, arteriolar, and venous vasculature result in a reduction in impedance and left ventricular afterload and a decrease in cardiac filling pressure and preload. Structural changes of hypertrophy and remodeling apparently contribute to the changes in resistance, compliance, and capacitance in the vasculature. Treatment of heart failure is aimed at relieving symptoms and prolonging life. Interventions to improve left ventricular function are critical to symptom relief. Vasodilators have been most effective for this purpose, and new positive inotropic drugs are being tested for efficacy. Long-term benefit may require interference with the myocardial and peripheral vascular remodeling processes that lead to progressive depression of ventricular performance. New insights into the cellular and subcellular mechanisms of this progression are critical to the development of innovative therapeutic strategies.     

Mechanics of the left ventricular myocardial interstitium: effects of acute and chronic myocardial edema

Myocardial interstitial edema forms as a result of several disease states and clinical interventions. Acute myocardial interstitial edema is associated with compromised systolic and diastolic cardiac function and increased stiffness of the left ventricular chamber. Formation of chronic myocardial interstitial edema results in deposition of interstitial collagen, which causes interstitial fibrosis. To assess the effect of myocardial interstitial edema on the mechanical properties of the left ventricle and the myocardial interstitium, we induced acute and chronic interstitial edema in dogs. Acute myocardial edema was generated by coronary sinus pressure elevation, while chronic myocardial edema was generated by chronic pulmonary artery banding. The pressure-volume relationships of the left ventricular myocardial interstitium and left ventricular chamber for control animals were compared with acutely and chronically edematous animals. Collagen content of nonedematous and chronically edematous animals was also compared. Generating acute myocardial interstitial edema resulted in decreased left ventricular chamber compliance compared with nonedematous animals. With chronic edema, the primary form of collagen changed from type I to III. Left ventricular chamber compliance in animals made chronically edematous was significantly higher than nonedematous animals. The change in primary collagen type secondary to chronic left ventricular myocardial interstitial edema provides direct evidence for structural remodeling. The resulting functional adaptation allows the chronically edematous heart to maintain left ventricular chamber compliance when challenged with acute edema, thus preserving cardiac function over a wide range of interstitial fluid pressures.     

Transmural heterogeneity of diffusion anisotropy in the sheep myocardium characterized by MR diffusion tensor imaging

The orientation of MRI-measured diffusion tensor in the myocardium has been directly correlated to the tissue fiber direction and widely characterized. However, the scalar anisotropy indexes have mostly been assumed to be uniform throughout the myocardial wall. The present study examines the fractional anisotropy (FA) as a function of transmural depth and circumferential and longitudinal locations in the normal sheep cardiac left ventricle. Results indicate that FA remains relatively constant from the epicardium to the midwall and then decreases (25.7%) steadily toward the endocardium. The decrease of FA corresponds to 7.9% and 12.9% increases in the secondary and tertiary diffusion tensor diffusivities, respectively. The transmural location of the FA transition coincides with the location where myocardial fibers run exactly circumferentially. There is also a significant difference in the midwall-endocardium FA slope between the septum and the posterior or lateral left ventricular free wall. These findings are consistent with the cellular microstructure from histological studies of the myocardium and suggest a role for MR diffusion tensor imaging in characterization of not only fiber orientation but, also, other tissue parameters, such as the extracellular volume fraction.     

Comparative effects of dehydroepiandrosterone sulfate on ventricular diastolic function with young and aged female mice

The adrenal steroid hormone dehydroepiandrosterone (DHEA) and its sulfated derivative [DHEA(S)] have been extensively studied for their potential anti-aging effects. Associated with aging, DHEA levels decline in humans, whereas other adrenal hormones remain unchanged, suggesting that DHEA may be important in the aging process. However, the effect of DHEA(S) supplementation on cardiac function in the aged has not been investigated. Therefore, we administered to young and old female mice a 60-day treatment with exogenous DHEA(S) at a dose of 0.1 mg/ml in the drinking water and compared the effects on left ventricular diastolic function and the myocardial extracellular matrix composition. The left ventricular stiffness (beta) was 0.30 +/- 0.06 mmHg/mul in the older control mice compared with 0.17 +/- 0.02 mmHg/mul in young control mice. Treatment with DHEA(S) decreased left ventricular stiffness to 0.12 +/- 0.03 mmHg/mul in the older mice and increased left ventricular stiffness to 0.27 +/- 0.04 mmHg/mul in young mice. The mechanism for the DHEA(S)-induced changes in diastolic function appeared to be associated with altered matrix metalloproteinase activity and the percentage of collagen cross-linking. We conclude that exogenous DHEA(S) supplementation is capable of reversing the left ventricular stiffness and fibrosis that accompanies aging, with a paradoxical increased ventricular stiffness in young mice.     

Measurement of strain in the left ventricle during diastole with cine-MRI and deformable image registration

The assessment of regional heart wall motion (local strain) can localize ischemic myocardial disease, evaluate myocardial viability, and identify impaired cardiac function due to hypertrophic or dilated cardiomyopathies. The objectives of this research were to develop and validate a technique known as hyperelastic warping for the measurement of local strains in the left ventricle from clinical cine-magnetic resonance imaging (MRI) image datasets. The technique uses differences in image intensities between template (reference) and target (loaded) image datasets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target image. To validate the technique, MRI image datasets representing two deformation states of a left ventricle were created such that the deformation map between the states represented in the images was known. A beginning diastolic cine-MRI image dataset from a normal human subject was defined as the template. A second image dataset (target) was created by mapping the template image using the deformation results obtained from a forward FE model of diastolic filling. Fiber stretch and strain predictions from hyperelastic warping showed good agreement with those of the forward solution (R2=0.67 stretch, R2=0.76 circumferential strain, R2=0.75 radial strain, and R2=0.70 in-plane shear). The technique had low sensitivity to changes in material parameters (deltaR2= -0.023 fiber stretch, deltaR2=-0.020 circumferential strain, deltaR2=-0.005 radial strain, and deltaR2=0.0125 shear strain with little or no change in rms error), with the exception of changes in bulk modulus of the material. The use of an isotropic hyperelastic constitutive model in the warping analyses degraded the predictions of fiber stretch. Results were unaffected by simulated noise down to a signal-to-noise ratio (SNR) of 4.0 (deltaR2= -0.032 fiber stretch, deltaR2=-0.023 circumferential strain, deltaR2=-0.04 radial strain, and deltaAR2=0.0211 shear strain with little or no increase in rms error). This study demonstrates that warping in conjunction with cine-MRI imaging can be used to determine local ventricular strains during diastole.     

Ventricular remodeling and diastolic myocardial dysfunction in rats submitted to protein-calorie malnutrition

The effects of protein-calorie malnutrition (PCM) on heart structure and function are not completely understood. We studied heart morphometric, functional, and biochemical characteristics in undernourished young Wistar rats. They were submitted to PCM from birth (undernourished group, UG). After 10 wk, left ventricle function was studied using a Langendorff preparation. The results were compared with age-matched rats fed ad libitum (control group, CG). The UG rats achieved 47% of the body weight and 44% of the left ventricular weight (LVW) of the CG. LVW-to-ventricular volume ratio was smaller and myocardial hydroxyproline concentration was higher in the UG. Left ventricular systolic function was not affected by the PCM protocol. The myocardial stiffness constant was greater in the UG, whereas the end-diastolic pressure-volume relationship was not altered. In conclusion, the heart is not spared from the adverse effects of PCM. There is a geometric alteration in the left ventricle with preserved ventricular compliance despite the increased passive myocardial stiffness. The systolic function 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.     

Experimental studies on the mechanism of the nitroglycerin effect.

The regional decrease of the speed and extent of the contraction and the relaxation of the canine myocardium induced by coronary ligation was enhanced by intravenously administered nitroglycerin (GTN), simultaneously with the decrease of the left ventricular pressure, while the increase of myocardial fiber length caused by that procedure was partly abolished. The above changes could be reproduced by GTN applied directly onto the ischaemic myocardial surface even before the decrease of the left ventricular pressure. These changes induced by GTN might play a role in the decrease or abolishment of regional asynergic wall motion.     

Fiber stress profiles in the left ventricle of the heart during diastole: Effects of distension and hypertrophy

Pressure-volume and volume-dimensions relationships, obtained from excised dog left ventricles were used for calculating the stresses acting along the longitudinal axis of the individual myocardial fibers. The calculations were based on a set of empirical and theoretical equations. The pressure-volume relationship as well as the volume-dimensions relationships for the excised left ventricle were expressed in the form of empirical equations; the fiber orientation was written as a function of the fiber location within the left ventricular wall; finally, the fiber stress was determined by means of theoretically derived formulas. Simultaneous solutions for the fibers of a meridian cut through the left ventricular myocardial shell were obtained by means of a digital computer and presented in the form of diagrams. The results showed that at low degrees of distension of the left ventricle there are two zones of higher stresses at the equatorial area, one near the epicardium and one near the endocardium. As the distension proceeds under the effect of progressively increasing intraventricular pressure, these two zones become less well defined, whereas a new zone of higher stresses appears near the apex. At high degrees of distension, the ventricle assumes a more spherical shape and the equatorial zones of higher stresses are replaced by zones of lower stresses. Increase in the myocardial mass results in appearance of the equatorial lower stress zones at lower degrees of distension.