Construction, mathematical study and numerical simulation of a calcium turnover model during skeletal muscle...

Starting from recent physiological data we establish a first order non-linear differential system which models the calcium turnover during skeletal muscular contraction. We describe the methods allowing one to calculate with a computer the non-experimentally directly-measured initial conditions. In order to ensure the consistency of the system with physiology we prove the positivity, a priori inequalities and both the existence and the uniqueness of the solutions. To obtain a complete knowledge of the system during a twitch, the aim is to identify, using the experimental data the calcium, two re-uptake constants and the function describing its ejection rate. We demonstrate the uniqueness of the identification problem, we establish an original algorithm for the identification of the two constants, and we show that the function to be identified is the solution of an integral equation for the resolution of which we give an algorithm whose convergence is proved. According to this mathematical study the model is numerically simulated on a computer; this allows us thus to find again experimental data in a consistent frame, and to predict the values of some non-measured constants and functions.