Effects of external pressures on the pressure-volume relation of the left ventricle

The effects of ventricular geometry, muscle mass, muscle elasticity and external pressures on the pressure-volume and muscle stiffness-stress relations have been quantitated on the basis of a theoretical model. Data taken from patients before and after interventions with nitroprusside and angiotensin were applied to the model in order to explain the possible causes for the marked shifts in the pressure-volume relations. The results indicate that (a) ventricular geometry does not markedly alter the pressure-volume and stiffness-stress relations unless there is a drastic change from a spherical shape to an ellipsoidal shape orvice versa, (b) increases in muscle mass and muscle elasticity of the order of 30% result in significant alterations in the P-V relations but are not the cause for the parallel shifts unless accompanied by substantial external pressures, (c) the parallel shifts in the pressure-volume relations can be accounted for entirely by the presence of external pressures without changes in muscle mass or muscle elasticity. Thus manipulation of right ventricular pressures or pericardial pressures by drug interventions may be useful in the treatment of left heart disease and the presence of such pressures must be considered in the analysis of ventricular function curves.     

Effect of age on passive elastic stiffness of rat heart muscle.

A thick-wall spherical model for the rat left ventricle was used to deduce passive wall stiffness from diastolic pressure-volume data. This was done for rats in three age classes: young (1 mo), adult (17 mo) and old (17 mo). The model was based on finite deformation elasticity theory consistent with the magnitude of observed deformation. A least-squares procedure was used to determine elastic constants in postulated nonlinear stress-stretch relations for the myocardium. It was found that at a given level of stress, wall stiffness for ventricles in the young age class was consistently greater than wall stiffness in the other two classes. In addition, the difference in wall stiffness between rats in the adult and old age classes was found to be approximately 10%.     

Ventricular and arterial wall stresses based on large deformation analyses

Assuming a spherical geometry for the left ventricle and a cylindrical geometry for arteries, wall stresses and elastic stiffnesses are evaluated on the basis of a large elastic deformation theory. On the basis of canine pressure-volume data, the numerical results indicate marked gradients of stress in the endocardial layers even for thin-walled vessels, a result not predicted by the classical theory of elasticity. These high gradients of stress are due to the fact that the elastic stiffness of the wall material increases with the stress which reaches maximum levels in the endocardial layers. The high stresses may be responsible for ischemia of the left ventricle and be a triggering mechanism for atherosclerosis.     

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.     

Dynamic myocardial contractile parameters from left ventricular pressure-volume measurements

A new dynamic model of left ventricular (LV) pressure-volume relationships in beating heart was developed by mathematically linking chamber pressure-volume dynamics with cardiac muscle force-length dynamics. The dynamic LV model accounted for >80% of the measured variation in pressure caused by small-amplitude volume perturbation in an otherwise isovolumically beating, isolated rat heart. The dynamic LV model produced good fits to pressure responses to volume perturbations, but there existed some systematic features in the residual errors of the fits. The issue was whether these residual errors would be damaging to an application where the dynamic LV model was used with LV pressure and volume measurements to estimate myocardial contractile parameters. Good agreement among myocardial parameters responsible for response magnitude was found between those derived by geometric transformations of parameters of the dynamic LV model estimated in beating heart and those found by direct measurement in constantly activated, isolated muscle fibers. Good agreement was also found among myocardial kinetic parameters estimated in each of the two preparations. Thus the small systematic residual errors from fitting the LV model to the dynamic pressure-volume measurements do not interfere with use of the dynamic LV model to estimate contractile parameters of myocardium. Dynamic contractile behavior of cardiac muscle can now be obtained from a beating heart by judicious application of the dynamic LV model to information-rich pressure and volume signals. This provides for the first time a bridge between the dynamics of cardiac muscle function and the dynamics of heart function and allows a beating heart to be used in studies where the relevance of myofilament contractile behavior to cardiovascular system function may be investigated.     

On a nonlinear theory for muscle shells: Part II--Application to the beating left ventricle

This paper specializes the nonlinear laminated-muscle-shell theory developed in Part I to cylindrical geometry and computes stresses in arteries and the beating left ventricle. The theory accounts for large strain, material nonlinearity, thick-shell effects, torsion, muscle activation, and residual strain. First, comparison with elasticity solutions for pressurized arteries shows that the accuracy of the shell theory increases as transmural stress gradients and the shell thickness decrease. Residual strain reduces the stress gradients, lowering the error in the predicted peak stress in thick-walled arteries (R/t = 2.8) from about 30 to 10 percent. Second, the canine left ventricle is modeled as a thick-walled laminated cylinder with an internal pressure. Each layer is composed of transversely isotropic muscle with a fiber orientation based on anatomical data. Using a single pseudostrain-energy density function (with time-varying coefficients) for passive and active myocardium, the model predicts strain distributions that agree fairly well with published experimental measurements. The results also show that the peak fiber stress occurs subendocardially near the beginning of ejection and that residual strains significantly alter stress gradients within each lamina, but the magnitude of the peak fiber stress changes by less than 20 percent.     

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 finite deformation theory for cartilage and other soft hydrated connective tissues--I. Equilibrium results

The determination of valid stress-strain relations for articular cartilage under finite deformation conditions is a prerequisite for constructing models for synovial joint lubrication. Under physiological conditions of high strain rates and/or high stresses in the joint, large strains occur in cartilage. A finite deformation theory valid for describing cartilage, as well as other soft hydrated connective tissues under large loads, has been developed. This theory is based on the choice of a specific Helmholtz energy function which satisfies the generalized Coleman-Noll (GCN0) condition and the Baker-Ericksen (B-E) inequalities established in finite elasticity theory. In addition, the finite deformation biphasic theory includes the effects of strain-dependent porosity and permeability. These nonlinear effects are essential for properly describing the biomechanical behavior of articular cartilage, even when strain rates are low and strains are infinitesimal. The finite deformation theory describes the large strain behavior of cartilage observed in one-dimensional confined compression experiments at equilibrium, and it reduces to the linear biphasic theory under infinitesimal strain and slow strain rate conditions. Using this theory, we have determined the material coefficients of both human and bovine articular cartilages under large strain conditions at equilibrium. The theory compares very well with experimental results.     

Left ventricular wall stress compendium

Left ventricular (LV) wall stress has intrigued scientists and cardiologists since the time of Lame and Laplace in 1800s. The left ventricle is an intriguing organ structure, whose intrinsic design enables it to fill and contract. The development of wall stress is intriguing to cardiologists and biomedical engineers. The role of left ventricle wall stress in cardiac perfusion and pumping as well as in cardiac pathophysiology is a relatively unexplored phenomenon. But even for us to assess this role, we first need accurate determination of in vivo wall stress. However, at this point, 150 years after Lame estimated left ventricle wall stress using the elasticity theory, we are still in the exploratory stage of (i) developing left ventricle models that properly represent left ventricle anatomy and physiology and (ii) obtaining data on left ventricle dynamics. In this paper, we are responding to the need for a comprehensive survey of left ventricle wall stress models, their mechanics, stress computation and results. We have provided herein a compendium of major type of wall stress models: thin-wall models based on the Laplace law, thick-wall shell models, elasticity theory model, thick-wall large deformation models and finite element models. We have compared the mean stress values of these models as well as the variation of stress across the wall. All of the thin-wall and thick-wall shell models are based on idealised ellipsoidal and spherical geometries. However, the elasticity model's shape can vary through the cycle, to simulate the more ellipsoidal shape of the left ventricle in the systolic phase. The finite element models have more representative geometries, but are generally based on animal data, which limits their medical relevance. This paper can enable readers to obtain a comprehensive perspective of left ventricle wall stress models, of how to employ them to determine wall stresses, and be cognizant of the assumptions involved in the use of specific models.     

Rodent Working Heart Model for the Study of Myocardial Performance and Oxygen Consumption

Isolated working heart models have been used to understand the effects of loading conditions, heart rate and medications on myocardial performance in ways that cannot be accomplished in vivo. For example, inotropic medications commonly also affect preload and afterload, precluding load-independent assessments of their myocardial effects in vivo. Additionally, this model allows for sampling of coronary sinus effluent without contamination from systemic venous return, permitting assessment of myocardial oxygen consumption. Further, the advent of miniaturized pressure-volume catheters has allowed for the precise quantification of markers of both systolic and diastolic performance. We describe a model in which the left ventricle can be studied while performing both volume and pressure work under controlled conditions. In this technique, the heart and lungs of a Sprague-Dawley rat (weight 300-500 g) are removed en bloc under general anesthesia. The aorta is dissected free and cannulated for retrograde perfusion with oxygenated Krebs buffer. The pulmonary arteries and veins are ligated and the lungs removed from the preparation. The left atrium is then incised and cannulated using a separate venous cannula, attached to a preload block. Once this is determined to be leak-free, the left heart is loaded and retrograde perfusion stopped, creating the working heart model. The pulmonary artery is incised and cannulated for collection of coronary effluent and determination of myocardial oxygen consumption. A pressure-volume catheter is placed into the left ventricle either retrograde or through apical puncture. If desired, atrial pacing wires can be placed for more precise control of heart rate. This model allows for precise control of preload (using a left atrial pressure block), afterload (using an afterload block), heart rate (using pacing wires) and oxygen tension (using oxygen mixtures within the perfusate).     

Some implications of a constant fiber stress hypothesis in the diastolic left ventricle

A thick-wall incompressible, elastic sphere was used as a model for the diastolic rat left ventricle. A model for myocardial nonhomogeneity was derived assuming that fiber (circumferential) stress was independent of position in the ventricular wall. The theoretical implications of the resulting constitutive relations together with the spherical model were analyzed in the context of large deformation elasticity theory. It was found that muscle stiffness at a given level of uniaxial stress increased monotonically from the endocardium to the epicardium. In addition, fiber stress was found to be essentially a linear function of transmural pressure above a pressure of 6 g/cm². It was also shown theoretically that neglecting the nonhomogeneity of the myocardium resulted in a state of stress which differed significantly from that predicted by the nonhomogeneous model. For example, at a transmural pressure of 14 g/cm², fiber stress in the nonhomogenous model was equal to 17 g/cm² while fiber stress in the homogeneous model varied between 100 g/cm² at the endocardial surface and 2 g/cm² at the epicardial surface. The change in muscle stiffness with position which characterized the nonhomogeneous model also tended to linearize the highly curvilinear radial stress distribution predicted by the homogeneous model at a given transmural pressure.     

Potential theory for gate adsorption on soft porous crystals

We demonstrate that an adsorption potential at the gate adsorption pressure of soft porous crystals (SPCs) based on the Polanyi's potential theory of adsorption shows a constancy to temperature. This was done using grand canonical Monte Carlo simulations and free energy analysis, which were carried out with a simplified stacked-layer SPC model. This finding implies that the characteristic curve obtained from an experimental gate adsorption isotherm on SPCs can be used to predict the temperature dependence of the gate-opening pressure, even though the potential theory of adsorption does not take into account the deformation of porous solids during the adsorption. We develop a modified potential theory for gate adsorption and show that the derived relation has a form that the Gibbs free energy change due to the host framework deformation per guest molecule, ? ΔG_host/N, and a correction term, C, are added to the expression of the original potential theory of adsorption. The term C is not an empirical correction factor but is the difference of intermolecular interaction potential and entropy between the bulk liquid phase at the saturated state and the adsorbed phase, originating from spatial constraint of adsorbed guest molecules in the host. By evaluating the modified expression for gate adsorption using the simulation results, we demonstrate that the constancy of the adsorption potential to temperature results from a compensation effect between three terms: guest–host interaction potential per guest molecule, ? ΔG_host/N and C, which have a temperature dependence.     

Mesenchymal stem cell injection after myocardial infarction improves myocardial compliance

Cellular therapy for myocardial injury has improved ventricular function in both animal and clinical studies, though the mechanism of benefit is unclear. This study was undertaken to examine the effects of cellular injection after infarction on myocardial elasticity. Coronary artery ligation of Lewis rats was followed by direct injection of human mesenchymal stem cells (MSCs) into the acutely ischemic myocardium. Two weeks postinfarct, myocardial elasticity was mapped by atomic force microscopy. MSC-injected hearts near the infarct region were twofold stiffer than myocardium from noninfarcted animals but softer than myocardium from vehicle-treated infarcted animals. After 8 wk, the following variables were evaluated: MSC engraftment and left ventricular geometry by histological methods, cardiac function with a pressure-volume conductance catheter, myocardial fibrosis by Masson Trichrome staining, vascularity by immunohistochemistry, and apoptosis by TdT-mediated dUTP nick-end labeling assay. The human cells engrafted and expressed a cardiomyocyte protein but stopped short of full differentiation and did not stimulate significant angiogenesis. MSC-injected hearts showed significantly less fibrosis than controls, as well as less left ventricular dilation, reduced apoptosis, increased myocardial thickness, and preservation of systolic and diastolic cardiac function. In summary, MSC injection after myocardial infarction did not regenerate contracting cardiomyocytes but reduced the stiffness of the subsequent scar and attenuated postinfarction remodeling, preserving some cardiac function. Improving scarred heart muscle compliance could be a functional benefit of cellular cardiomyoplasty.     

Prevention of adrenaline-induced heart damage using the antioxidant ionol

Experiments on an isolated papillary muscle of the rat heart left ventricle have demonstrated that pretreatment with the antioxidant ionol prevents the disturbances of myocardial contractility caused by administration of a large dose of adrenaline. The data obtained are in agreement with the concept that the prophylactic action of antioxidants during stress is determined by the fact that they prevent activation of lipid peroxidation in the heart under the action of excess catecholamines.     

Functional evaluation of the rat heart in situ.

We have developed methods for evaluating muscle function in the intact rat heart in situ using a contractility index (dP/dt)P-1, calculated from left ventricular pressure derivative-left ventricular pressure loop plots. Aortic flow measurements were also taken to further characterize in situ rat heart function. The preparation remained functionally stable and was within physiological blood gas and pH limits for at least 30 min following surgical procedures. The contractility index was not influenced by increased afterload, decreased preload or increased heart rate; however, appropriate changes were observed following isoproterenol and propranolol administration. Appropriate changes in aortic flow measurements were observed also with the above interventions. These studies demonstrate that the in situ rat heart is a stable physiological experimental preparation. It should be useful for evaluating heart function since a contractility index derived from pressure-velocity relationships and measurements necessary for pump function analysis can be obtained simultaneously.     

Developmental changes in inotropic actions of neurotoxins observed in ventricular muscle of rat heart.

Developmental changes in functions of myocardial sodium channels were examined from inotropic effects of several neurotoxins in ventricular muscle preparations obtained from prenatal (20-22 day gestation) or adult (3-4 months old) rat hearts. Tetrodotoxin caused a negative inotropic effect in low concentrations and a loss of muscle responsiveness to electrical stimulation in high concentrations in preparations obtained from either prenatal or adult rat heart. The tetrodotoxin concentration that caused a 50% decrease in developed tension was higher in prenatal rats. Anemonia sulcata toxin, Androctonus australis toxin, veratridine, and Centruroides sculpturatus toxin all produced positive inotropic effects in adult rat heart. The effects were largest with A. sulcata and A. australis toxins, intermediate with veratridine, and smallest with C. sculpturatus toxin. Prenatal heart required higher concentrations of either veratridine, or A. sulcata or A. australis toxins to produce comparable positive inotropic effects. With C. sculpturatus toxin, no significant positive inotropic effect was observed in prenatal heart muscle preparations. These results indicate that cardiac sodium channels undergo significant functional changes during development and that negative and positive inotropic effects of neurotoxins resulting from inhibition and enhancement of fast Na+ channels reflect developmental changes in the cardiac sodium channels.     

Implantation of Mouse Embryonic Stem Cell-Derived Cardiac Progenitor Cells Preserves Function of Infarcted Murine Hearts

Stem cell transplantation holds great promise for the treatment of myocardial infarction injury. We recently described the embryonic stem cell-derived cardiac progenitor cells (CPCs) capable of differentiating into cardiomyocytes, vascular endothelium, and smooth muscle. In this study, we hypothesized that transplanted CPCs will preserve function of the infarcted heart by participating in both muscle replacement and neovascularization. Differentiated CPCs formed functional electromechanical junctions with cardiomyocytes in vitro and conducted action potentials over cm-scale distances. When transplanted into infarcted mouse hearts, CPCs engrafted long-term in the infarct zone and surrounding myocardium without causing teratomas or arrhythmias. The grafted cells differentiated into cross-striated cardiomyocytes forming gap junctions with the host cells, while also contributing to neovascularization. Serial echocardiography and pressure-volume catheterization demonstrated attenuated ventricular dilatation and preserved left ventricular fractional shortening, systolic and diastolic function. Our results demonstrate that CPCs can engraft, differentiate, and preserve the functional output of the infarcted heart.     

Evaluation of energy metabolism on the myocardium analyzing of creatine kinase isoenzymes in rats]

The purpose of this study is to evaluate the efficiency of energy metabolism in the myocardium by means of the activities of creatine kinase (CK) and CK isoenzyme following age-related change in the heart and experimental heart failure. Wistar strain male rats aged from 3 weeks to 57 weeks after birth were used. The main experimental results obtained are as follows. (1) There were differences in the compositions of CK isoenzyme of the ventricular, atrial, and papillar muscles. No apparent variation, however, was noted among the basal portions of the left and right ventricular muscles, free wall of the left ventricle, and apex. (2) Compositions of CK isoenzyme analyzed from the ventricle and atrium were clearly different. The level of CK-B subunit activity of the ventricular muscle was highest level in the 5-week-old rat, and subsequently dropped significantly in the 24-week-old rat. Thereafter, the level gradually increased with aging. Dramatic change in the energy metabolism in the myocardium occurred in rats more than 3 weeks old. (3) Decrease in activity of m-CK but increase in activity of succinate dehydrogenase analyzed from the ventricular muscle of experimental heart failure induced by monocrotaline was recognized. From these results, the author assumed that the trend of the composition of CK isoenzyme is one of the indices in the determination of the regulation of energy metabolism of the myocardium.     

Effect of chronic streptozotocin-induced diabetes on [3H]ouabain binding in the rat left ventricle

Earlier results from our laboratory have revealed that the inotropic response to ouabain was depressed in chronically diabetic rat heart (1). In this study we examined the effect of chronic streptozotocin induced diabetes (3 months) on [3H]ouabain binding in the rat heart. Scatchard analysis of [3H]ouabain binding to membrane preparations of rat left ventricle revealed two classes of binding sites; a high affinity/low capacity and a low affinity/high capacity binding site. The maximum number of binding sites of the high and low affinity binding sites in membrane preparations obtained from the chronically diabetic rats was significantly (p less than 0.05) reduced to 60.4 and 48.8% of controls, respectively. The dissociation constant of the high and the low affinity binding/sites in the chronically diabetic rat heart, compared to controls, was significantly (p less than 0.05) increased and decreased, respectively. These results suggest that the decreased inotropic response of ouabain in the intact tissue obtained from chronically diabetic rats (1) may be related to a decreased number of ouabain binding sites.