MioLab: simulator for cardiac myocyte contractile force of rat based on the dynamics of calcium

The calcium ion (Ca(2+)) is essential in cardiac electrical activity since it is the direct activator of myofilaments, which cause contraction. For this reason, irregular Ca(2+) flow in the cardiac myocyte is one of the main causes of cardiac arrhythmias and contractile dysfunction. In this sense, the formulation of mathematical and computational models of the mammalian ventricular myocyte has played an important role in understanding cardiac physiology. This paper proposes a biophysical model for the rat cardiac myocyte in order to reduce the number of degrees of freedom and provides a mathematical framework that makes computation simpler for our understanding of the complex process of excitation-contraction-relaxation (ECR), uses low-order lumped parameter of the myofilaments and Ca(2+)handling. The model allows the calculation of contractile force mainly based on the dynamics of Ca(2+), provides data on transient Ca(2+)andenables the analysis of the effects of drugs used in the treatment of cardiac arrhythmias.

The mathematical model which describes the kinetics of cytosolic Ca(2+) and dynamic cross-bridges, was implemented through nine differential equations, auxiliary equations, three 47 biophysical parameters. Each was implemented using C(++) programming and its user-friendly interface in the programming language Delphi. The results of each simulation were stored in a text file and its analysis was shown in a graphical interface using executable programs in Matlab(®). Additionally, the validation model was performed by comparing both the experimental data of Ca(2+) transient and several drug tests.

The model satisfactorily reproduced the Ca(2+) transient, as well as the effects of drugs that cause beta-adrenergic stimulation and the inhibition of the Ca(2+) uptake mechanism (SERCA). Changes in the parameters regulating Ca(2+) entry through L-type channels produced the oscillation amplitude of the Ca(2+) transient known as the syndrome of pulses alternans. Changes in parameters related to the Na(+)-Ca(2+) exchange has already stabilized the transient Ca(2+) and produced a decrease in amplitude of the contractile force.

The simulator proved to be a tool to study and understand the mechanisms that involve the kinetics of Ca(2+) and the dynamics of cross-bridges in the unit heart muscle, as well as a tool to analyze the possible factors that may cause arrhythmias and study the effects of drugs that are used in the treatment of cardiovascular diseases in general.