T. Arts

Relation between left ventricular cavity pressure and volume and systolic fiber stress and strain in the wall.

Pumping power as delivered by the heart is generated by the cells in the myocardial wall. In the present model study global left-ventricular pump function as expressed in terms of cavity pressure and volume is related to local wall tissue function as expressed in terms of myocardial fiber stress and strain. On the basis of earlier studies in our laboratory, it may be concluded that in the normal left ventricle muscle fiber stress and strain are homogeneously distributed. So, fiber stress and strain may be approximated by single values, being valid for the whole wall. When assuming rotational symmetry and homogeneity of mechanical load in the wall, the dimensionless ratio of muscle fiber stress (sigma f) to left-ventricular pressure (Plv) appears to depend mainly on the dimensionless ratio of cavity volume (Vlv) to wall volume (Vw) and is quite independent of other geometric parameters. A good (+/- 10%) and simple approximation of this relation is sigma f/Plv = 1 + 3 Vlv/Vw. Natural fiber strain is defined by ef = In (lf/lf,ref), where lf,ref indicates fiber length (lf) in a reference situation. Using the principle of conservation of energy for a change in ef, it holds delta ef = (1/3)delta In (1 + 3Vlv/Vw).

Homogeneity of cardiac contraction despite physiological asynchrony of depolarization : a model study

AbstractThe use of mathematical models combining wave propagation and wall mechanics may provide new insights in the interpretation of cardiac deformation toward various forms of cardiac pathology. In the present study we investigated whether combining accepted mechanisms on propagation of the depolarization wave, time variant mechanical properties of cardiac tissue after depolarization, and hemodynamic load of the left ventricle (LV) by the aortic impedance in a three-dimensional finite element model results in a physiological pattern of cardiac contraction. We assumed that the delay between depolarization for all myocytes and the onset of crossbridge formation was constant. Two simulations were performed, one in which contraction was initiated according to the regular depolarization pattern (NORM simulation), and another in which contraction was initiated after synchronous depolarization (SYNC simulation). In the NORM simulation propagation of depolarization was physiological, but wall strain was unphysiologically inhomogeneous. When simulating LV mechanics with unphysiological synchronous depolarization (SYNC) myofiber strain was more homogeneous and more physiologic. Apparently, the assumption of a constant delay between depolarization and onset of crossbridge formation results in an unrealistic contraction pattern. The present finding may indicate that electromechanical delay times are heterogeneously distributed, such that a contraction in a normal heart is more synchronous than depolarization.

Adaptation of cardiac structure by mechanical feedback in the environment of the cell: a model study.

In the cardiac left ventricle during systole mechanical load of the myocardial fibers is distributed uniformly. A mechanism is proposed by which control of mechanical load is distributed over many individual control units acting in the environment of the cell. The mechanics of the equatorial region of the left ventricle was modeled by a thick-walled cylinder composed of 6-1500 shells of myocardial fiber material. In each shell a separate control unit was simulated. The direction of the cells was varied so that systolic fiber shortening approached a given optimum of 15%. End-diastolic sarcomere length was maintained at 2.1 microns. Regional early-systolic stretch and global contractility stimulated growth of cellular mass. If systolic shortening was more than normal the passive extracellular matrix stretched. The design of the load-controlling mechanism was derived from biological experiments showing that cellular processes are sensitive to mechanical deformation. After simulating a few hundred adaptation cycles, the macroscopic anatomical arrangement of helical pathways of the myocardial fibers formed automatically. If pump load of the ventricle was changed, wall thickness and cavity volume adapted physiologically. We propose that the cardiac anatomy may be defined and maintained by a multitude of control units for mechanical load, each acting in the cellular environment. Interestingly, feedback through fiber stress is not a compelling condition for such control.

Cardiac resynchronization: Insight from experimental and computational models

Cardiac resynchronization therapy (CRT) is a promising therapy for heart failure patients with a conduction disturbance, such as left bundle branch block. The aim of CRT is to resynchronize contraction between and within ventricles. However, about 30% of patients do not respond to this therapy. Therefore, a better understanding is needed for the relation between electrical and mechanical activation. In this paper, we focus on to what extent animal experiments and mathematical models can help in order to understand the pathophysiology of asynchrony to further improve CRT.

Towards patient specific models of cardiac mechanics: a sensitivity study

In the design of patient specific mathematical models of cardiac mechanics, the lack of patient specific input data leads to default settings of various model parameters. To estimate the potential errors thus introduced, we evaluated changes in predicted mechanics in a model of the left ventricle (LV) induced by changes in geometry, fiber orientation, heterogeneity of passive material behavior and triaxial active stress development. Incorporation of measured heterogeneity of passive stiffness did not affect systolic mechanics. Incorporation of triaxial active stress development did significantly affect systolic mechanics, but knowledge on this mechanism is too limited to draw conclusions. LV geometry variations covering the biological range changed the equatorial distribution of active myofiber stress and shortening by about 10 to 15%. Similar changes were found by variation of fiber orientation by 8° at maximum. Since this change in orientation is at the edge of the accuracy, with which myofiber orientation can be measured in vitro, and far below the accuracy, obtainable for in vivo measurements, we conclude that the benefit of accounting for patient specific geometry is questionable when using experimental data on fiber orientation. We propose to select myofiber orientation such, that myofiber load is distributed homogeneously across the cardiac wall.

Cardiac mechanoenergetics replicated by cross-bridge model

AbstractThe aim of this work is to reproduce the experimentally measured linear dependence of cardiac muscle oxygen consumption on stress–strain area using a model, composed of a three-state Huxley-type model for cross-bridge interaction and a phenomenological model of Ca2+-induced activation. By selecting particular cross-bridge cycling rate constants and modifying the cross-bridge activation model, we replicated the linear dependence between oxygen consumption and stress–strain area together with other important mechanical properties of cardiac muscle such as developed stress dependence on the sarcomere length and force-velocity relationship. The model predicts that (1) the amount of the “passenger” cross bridges, i.e., cross bridges that detach without hydrolyzing ATP molecule, is relatively small and (2) ATP consumption rate profile within a beat and the amount of the passenger cross bridges depend on the contraction protocol.

Left ventricular shear strain in model and experiment: the role of myofiber orientation

Mathematical modeling of cardiac mechanics could be a useful clinical tool, both in translating measured abnormalities in cardiac deformation into the underlying pathology, and in selecting a propertreatment. We investigated to what extent a previously published model of cardiac mechanics could predict deformation in the healthy left ventricle, as measured using MR tagging. The model adequately predicts circumferential strain, but fails to accurately predict shear strain. However, the time course of shear strain proves to be that sensitive tomyofiber orientation, that agreement between model predictions and experiment may be expected if fiber orientation is changed by only a few degrees.

Simulating cardiac mechanoenergetics in the left ventricle

Distribution of myocardial perfusion and oxygen consumption within the cardiac wall is spatially heterogeneous. The cause of this heterogeneity is still unclear, but it is expected to be in close relation with the heterogeneity in mechanical function in the heart. In order to study the mechanical contraction and energy consumption by the cardiac wall, we developed a finite element model of the left ventricle with active properties described by the Huxley-type cross-bridge model. Here we present an overview of the developed model and the following simulation results obtained by the model. First, an important property of energy transformation from biochemical form to mechanical work in the cardiac muscle, the linear relationship between the oxygen consumption and the stress-strain area, is replicated by a cross-bridge model. Second, by using the developed cross-bridge model, the correlation between ejection fraction of the left ventricle and heterogeneity of sarcomere strain, developed stress and ATP consumption in the left ventricular wall is established. Third, an experimentally observed linear relationship between oxygen consumption and the pressure-volume area can be predicted theoretically from a linear relationship between the oxygen consumption and the stress-strain area.