Global Sensitivity Analysis for Uncertain Parameters Applied to a Cardiac Mitochondrial Model

Cardiac mitochondria are intracellular organelles that have several important roles. For instance, they ensure energy metabolism and calcium regulation, thus are linked to the excitation-contraction cycle of the heart cell. Mathematical models are useful to better understand the complexity of mitochondrial dynamics within a cardiac cell, and we are specifically interested in the dynamics of calcium. Litterature models reflect this complexity, especially in terms of number of equations and parameters, which makes them impossible to calibrate to experimental data. In this paper, we apply a global sensitivity analysis on our previously discussed simple mitochondria model [1], in order to quantify the uncertainty of the parameters. This analysis is done in two steps. First we eliminate non-influential parameters of the internal fluxes governing the activity of the mitochondria. Then we perform this analysis on the outputs of our ODE (ordinary differential equation) model, which are the respiratory rates. Finally, we calibrate the remaining influential parameters using a genetic algorithm with respect to experimental respiratory data.