It is known that mitochondria play a crucial role in the handling of calcium by cardiac cells during the excitationcontraction cycle. However, the precise characterization of this role is still under debate.With this intent, a collection of mathematical models have been developed, but they generally show a level of complexity that is not compatible with inverse problem techniques required for calibration with experimental data. Their large number of equations and parameters can also lead to transcription mistakes that can be found in the literature. In this paper we apply a similar methodology as Bertram et al.in [1] to propose a simple model that is derived from the base equations that constitute the origin of most mitochondrial models [2].Our model describes the main features of the mitochondrial activity with 6 equations and ∼30 parameters, which we will eventually reduce in a forthcoming sensitivity analysis.

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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 noninfluential 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.