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.     

An anatomic basis for fetal right ventricular dominance and arterial pressure sensitivity

Fetal right ventricular dominance of flow and arterial pressure sensitivity were recently recognized but controversial findings. We investigated ventricular volumes, weights and dimensions in order to understand if there were anatomic differences between the ventricles which might explain these differential functional findings in the fetal sheep. Forty-four near term lambs and their hearts were weighed. Right and left ventricular free wall weights were not different. Volumes were measured by generating in vitro pressure-volume relations and by casting the two ventricles after fixation at equal, physiologic pressures. Right ventricular volume was greater than left ventricular volume by both techniques. Ventricular interaction and a restraining effect of the pericardium were present. Measurements of the fixed ventricles and their casts revealed the following: left ventricular wall thickness was slightly greater than right ventricular wall thickness; lateral ventricular diameters were not different but anteroposterior ventricular diameters were much greater in the right than left ventricle. Because of these findings, the right ventricular circumferential radii of curvature were greater than for the left ventricle as was the radius to wall thickness ratio. Greater right ventricular volume and radius to wall thickness ratio may be important factors in right ventricular flow dominance and greater sensitivity to arterial pressure.     

The echocardiographic study of the rabbit heart left ventricle morpho-functional parameters

Morphometric and functional parameters of the heart left ventricle in rabbits during systole and diastole were investigated by the method of echocardiography. Morphometric parameters were studied on three levels: the mitral valve, the papillary muscles and the apical level. The internal dimension of the left ventricle uniformly decreases in three parallel planes during systole, its maximal reduction being observed on the apical level. During the contraction phase, the posterior wall thickness of the left ventricular and the interventricular septum thickness increases on the basal level to a greater extent than on the apical one. During systole, the interventricular septum movement is greater than the left ventricular posterior wall motion. During the heart cycle, the form of the left ventricular cavity changes from an ellipsoid in diastole to elliptic paraboloid in systole.     

Incremental elastic modulus for ventricles in diastole

Utilizing the formulation of so-called 'small deformations superimposed on a large initial deformation' the incremental pressure modulus of a ventricle in diastole is studied and the explicit expression of it is obtained as a function of intraventricular pressure. In the analysis the ventricular wall material is assumed to be homogeneous, incompressible, isotropic and the stress-strain relation is exponential. The numerical results for a dog left ventricle indicate that above a critical value of inner pressure the incremental pressure modulus increases with increasing intra-ventricular pressure. Furthermore, the relationship between the stiffness and pressure is seen to be curvilinear (particularly for low pressure level), but for large values of inner pressure the behavior of the curve may be approximated by a set of straight lines.     

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.     

Relationship between apexcardiogram,left ventricular pressure and wall stress

Simultaneous measurement of left ventricular dimension and wall thickness by M-mode echocardiography, of left ventricular pressure by a tip-transducer manometer, and of the calibrated apexcardiogram with a pixie beam transducer, were made during acute experiments on anaesthetized dogs. Instantaneo us values for chamber dimensions and wall thickness were obtained throughout the heart cycle by digitizing the echo-mechanocardigrams.From these data myocardial stresses, derived from a thick shell theory (meridional and circumferential components) and from Laplace's law, were computed. Laplace stress is shown to be an adequate expression for average wall stress. Its value was correlated with the calibrated apexcardiogram. The present investigation suggests that to a certain extent, the apexcardiogram not only reflects pressure changes but also dimensional changes of the left ventricle.     

Concentric adaptation of the left ventricle in response to controlled upper body exercise training.

Upper body exercise has many applications to the rehabilitation and maintenance of cardiovascular health of individuals who are unable to exercise their lower body. The hemodynamic loads of upper body aerobic exercise are characterized by relatively high blood pressure and relatively low venous return. It is not clear how the left ventricle adapts to the specific hemodynamic loads associated with this form of exercise training. The purpose of this study was to measure left ventricular structure and function in previously sedentary men by using echocardiography before and after 12 wk of aerobic arm-crank exercise training (n = 22) or a time control period (n = 22). Arm-crank peak oxygen consumption (in ml x kg(-1) x min(-1)) increased by 16% (P < 0.05) after training, and significant differences (P < 0.05) were found in wall thickness (from 0.86 to 0.99 cm) but not in left ventricular internal dimension in diastole or systole. This suggested a concentric pattern of left ventricular hypertrophy that persisted after scaling to changes in anthropometric characteristics. No differences (P < 0.05) were found for any measurements of resting left ventricular function. We conclude that upper body aerobic exercise training results in a specific left ventricular adaptation that is characterized by increased left ventricular wall thickness but no change in chamber dimension.     

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.     

Effect of right ventricular hypertrophy on cardiac performance and the relation between right ventricular systolic peak pressure and end-systolic volume

To investigate the role of hypertrophy of the right ventricle upon right heart performance and the significance of the peak systolic pressure/end-systolic volume (P/V) ratio in terms of right ventricular systolic performance, simultaneous measurements of radionuclide ventriculograms and central hemodynamics were done in 32 patients with chronic obstructive pulmonary disease. In 26 of the patients (80%) technically adequate two-dimensional echocardiograms could be performed. In the subset of patients with increased (greater than or equal to 6 mm) right ventricular end-diastolic wall thickness no relationship between pulmonary artery pressure and right ventricular ejection fraction (RVEF) existed in comparison with the remaining patients. P/V indices and cardiac output were not decreased. Considering the patients, whose P/V ratio did not increase from rest to exercise, RVEF decreased highly significantly more than in the remaining patients. The ratio of wall thickness and end-diastolic radius as determinant of peak systolic stress was significantly decreased in these patients compared with the remaining patients. In the patients with right ventricular hypertrophy despite significantly higher values of pulmonary artery pressures and resistances, the afterload in terms of systolic wall stress is markedly reduced. We conclude that in the hypertrophic state, right ventricular performance is not impaired despite decreased RVEF values. In the patients whose P/V ratio does not increase from rest to exercise, an inappropriate high peak systolic wall stress may exist both due to inadequate wall thickness and increased diameter of the right ventricle. The role of P/V in terms of prognosis and development of decompensated right heart failure remains undetermined.     

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.     

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.     

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.)     

Effect of timing and velocity of impact on ventricular myocardial rupture

The effects of impact timing during the cardiac cycle on the sensitivity of the heart to impact-induced rupture was investigated in an open-chest animal model. Direct mechanical impacts were applied to two adjacent sites on the exposed left ventricular surface at the end of systole or diastole. Impacts at 5 m/s and a contact stroke of 5 cm at the end of systole resulted in no cardiac rupture in seven animals, whereas similar impacts at the end of diastole resulted in six cardiac ruptures. Direct impact at 15 m/s and a contact stroke of 2 cm at the end of either systole or diastole resulted in perforationlike cardiac rupture in all attempts. At low-impact velocity the heart was observed in high-speed movie to bounce away from the impact interface during a systolic impact, but deform around the impactor during a diastolic impact. The heart generally remained motionless during the downward impact stroke at high-impact velocity in either a systolic or diastolic impact. The lower ventricular pressure, reduced muscle stiffness, thinner myocardial wall and larger mass of the filled ventricle probably contributed to a greater sensitivity of the heart to rupture in diastole at low-impact velocity. However, the same factors had no role at high-impact velocity.     

Deformation of the diastolic left ventricle—II. Nonlinear geometric effects

A finite element model for the rat left ventricle has been developed which is based on finite deformation elasticity theory: i.e. the model is not limited by assumptions relating to the magnitudes of extensions, shears and angles of rotation which are inherent in the classical theory of elasticity. This model represents the ventricle as a heterogeneous, nonlinearly elastic, isotropic thick-wall solid of revolution. For the representation of myocardial elasticity used in this study, the model predicts overall ventricular stiffnesses at physiological pressures which are 20–30 per cent lower than those obtained with a model based on the classical theory. However, extentions predicted by the two theories differ by as much as 100 per cent in certain portions of the ventricular wall.     

A two-phase finite element model of the diastolic left ventricle

A porous medium finite element model of the passive left ventricle is presented. The model is axisymmetric and allows for finite deformation, including torsion about the axis of symmetry. An anisotropic quasi-linear viscoelastic constitutive relation is implemented in the model. The model accounts for changing fibre orientation across the myocardial wall. During passive filling, the apex rotates in a clockwise direction relative to the base for an observer looking from apex to base. Within an intraventricular pressure range of 0-3 kPa the rotation angle of all nodes remained below 0.1 rad. Diastolic viscoelasticity of myocardial tissue is shown to reduce transmural differences of preload-induced sarcomere stretch and to generate residual stresses in an unloaded ventricular wall, consistent with the observation of opening angles seen when the heart is slit open. It is shown that the ventricular model stiffens following an increase of the intracoronary blood volume. At a given left ventricular volume, left ventricular pressure increases from 1.5 to 2.0 kPa when raising the intracoronary blood volume from 9 to 14 ml (100 g)-1 left ventricle.     

Deformation of the Diastolic Left Ventricle: I. Nonlinear Elastic Effects

A linear incremental finite element model is used to analyze the mechanical behavior of the left ventricle. The ventricle is treated as a heterogeneous, non-linearly elastic, isotropic, thick-walled solid of revolution. A new triaxial constitutive relation for the myocardium is presented which exhibits the observed exponential length-passive tension behavior of left ventricular papillary muscle in the limit of uniaxial tension. This triaxial relation contains three parameters: (a) a “small strain” Young's modulus, (b) a Poisson's ratio, and (c) a parameter which characterizes the nonlinear aspect of the elastic behavior of heart muscle. The inner third and outer two-thirds of the ventricular wall are assumed to have small strain Young's moduli of 30 and 60 g/cm², respectively. The Poisson's ratio is assumed to be equal to 0.49 throughout the ventricular wall. In general, the results of this study indicate that while a linearly elastic model for the ventricle may be adequate in terms of predicting pressure-volume relationships, a linear model may have serious limitations with regard to predicting fiber elongation within the ventricular wall. For example, volumes and midwall equatorial circumferential strains predicted by the linear and nonlinear models considered in this study differ by approximately 20 and 90%, respectively, at a transmural pressure of 12 cm H₂O.     

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.     

Quantitative relationships between left ventricular ejection and wall thickening and geometry.

The quantitative relationships that exist between left ventricular (LV) wall shortening, wall thickening, and geometry during LV ejection are not well defined. We used a mathematical model to measure these parameters in 40 patients with various LV geometries studied by echocardiography. As opposed to wall shortening, the percent contribution of wall thickening to LV ejection (% delta Vh) was 25 +/- 2% in normal subjects; in all the patients, it varied from 18 to 45% and was inversely correlated (r = 0.94) to the midwall radius-to-wall thickness ratio (R/h) of the ventricle at end diastole. On the other hand, the ratio of the quantity of blood ejected per unit of LV wall volume magnitude of delta V/V omega magnitude of varied from 0.20 to 1.20 (normal subjects 0.83 +/- 0.11) and was directly correlated (r = 0.94) to R/h; using independent data in the literature, we also found a similar relationship (r = 0.80) between the ratio of quantity of blood ejected per unit of LV mass (magnitude of delta V/M omega magnitude of) and R/h. Patients with presumably abnormal myocardial function did not satisfy the relationship between magnitude of delta V/V omega magnitude of or magnitude of delta V/M omega magnitude of and R/h.(ABSTRACT TRUNCATED AT 250 WORDS)     

Left ventricular hypertrophy in obese hypertensives: is it really eccentric? (An echocardiographic study)

In order to study left ventricular hypertrophy patterns in obese hypertensives, we examined 132 patients with essential hypertension by 2D, M-mode and Doppler echocardiography. The patients were classified in four comparable groups, corresponding to the values of Quetelet's body mass index (BMI) and grades of obesity. More obese hypertensives had on average larger left ventricles with thicker walls and larger left atria than less obese, or lean ones. Left ventricular mass increased significantly and progressively with advancing grades of obesity, but relative wall thickness (wall thickness/cavity size ratio) did not diminish. Doppler echocardiography revealed significantly higher prevalence of left ventricular diastolic dysfunction among obese than among lean hypertensives. In the second part of our study, we analyzed the subgroups defined by the severity of hypertension and the age of the patients. The correlation of the indices of left ventricular and left atrial hypertrophy with the BMI values was considerably better in the group of moderate than in the group of mild hypertension. The r values were 0.62 vs. 0.22 for left ventricular mass and 0.64 vs. 0.26 for left atrial dimension. The group of patients with severe hypertension was characterized by left ventricular cavity enlargement in correlation with increasing BMI values, but without corresponding left ventricular wall thickening. So called left ventricular "eccentricity index", as the reverse value of relative wall thickness, correlated well (r = 0.76) with the BMI values. The indices of left ventricular hypertrophy correlated with the BMI values slightly better in middle age groups than in the groups of the youngest (< or = 30 years) or the eldest (> or = 61 years) hypertensives. In conclusion, eccentric left ventricular hypertrophy does not seem to be a distinctive feature of hypertensive heart disease in obesity. There is only some tendency toward the "eccentricity" of left ventricular geometry which becomes more apparent in more severe forms of hypertension, especially in very obese persons.     

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.