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)

A model approach to the adaptation of cardiac structure by mechanical feedback in the environment of the cell

The uniformity of the mechanical load of the cardiac fibers in the wall is maintained by continuous remodeling. In this proposed model the myocyte changes direction in optimizing systolic sarcomere shortening. Early systolic stretch and contractility increases the mass of contractile proteins. Cyclic strain of the myocardial tissue diminishes passive stiffness, resulting in the control of ventricular end-diastolic volume. Utilizing these rules of remodeling in our mathematical model yields that the natural helical pathways of the myocardial fibers in the wall are formed automaticall

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. [Journal Article; In English; United States

Relation between torsion and cross-sectional area change in the human left ventricle

During the ejection phase, motion of the left ventricular (LV) wall is such that all myocardial fibers shorten to the same extent. In a mathematical model of LV mechanisms it was found that this condition could be satisfied only if torsion around the long axis followed a unique function of the ratio of cavity volume to wall volume. When fiber shortening becomes non-uniform due to cardiac pathology, this pathology may be reflected in aberration of the torsional motion pattern. In the present study we investigated whether the predicted regular motion pattern could be found in nine healthy volunteers, using Magnetic Resonance Tagging. In two parallel short-axis cross-sections, displacement, rotation, and area ejection were derived from the motion of tags, attached non-invasively to the myocardium. Information from both sections was combined to determine area ejection, quantified as the change in the logarithm of the ratio of cavity area to wall area, and torsion, represented by the shear angle on the epicardium. Linear regression was applied to torsion as a function of area ejection. The slope thus found (-0.173 +/- 0.024 rad, mean +/- S.D.) was similar to the slope as predicted by the model of LV mechanics (-0.194 +/- 0.026 rad). In conclusion, the relation between area ejection and torsion could be assessed noninvasively in humans. In healthy volunteers, the relation was close to what was predicted by a mathematical model of LV mechanics, and also close to what was found earlier in experiments on animals. [Journal Article; In English; United States