The Role of the Frank–Starling Law in the Transduction of Cellular Work to Whole Organ Pump Function: A Computational Modeling Analysis

Abstract

We have developed a multi-scale biophysical electromechanics model of the rat left ventricle at room temperature. This model has been applied to investigate the relative roles of cellular scale length dependent regulators of tension generation on the transduction of work from the cell to whole organ pump function. Specifically, the role of the length dependent Ca ²⁺ sensitivity of tension (Ca ₅₀), filament overlap tension dependence, velocity dependence of tension, and tension dependent binding of Ca ²⁺ to Troponin C on metrics of efficient transduction of work and stress and strain homogeneity were predicted by performing simulations in the absence of each of these feedback mechanisms. The length dependent Ca ₅₀ and the filament overlap, which make up the Frank-Starling Law, were found to be the two dominant regulators of the efficient transduction of work. Analyzing the fiber velocity field in the absence of the Frank-Starling mechanisms showed that the decreased efficiency in the transduction of work in the absence of filament overlap effects was caused by increased post systolic shortening, whereas the decreased efficiency in the absence of length dependent Ca ₅₀ was caused by an inversion in the regional distribution of strain.

Author Summary

The heart achieves an efficient coordinated contraction via a complex web of feedback loops that span multiple spatial and temporal scales. Advances in computational hardware and numerical techniques now allow us to begin to analyse this feedback system through the use of computational models. Applying this approach, we have integrated a wide range of experimental data into a common and consistent modelling framework representing the cardiac electrical and mechanical systems. We have used this model to investigate how feedback loops regulate heart contraction. These results show that feedback from muscle length on tension generation at the cellular level is an important control mechanism of the efficiency with which the heart muscle contracts at the whole organ level. In addition to testing this specific hypothesis, the model developed in this study provides a framework for extending this work to investigating important pathological conditions such as heart failure and ischemic heart disease.