Model Description

In this chapter we study a model of the description of mitochondria swelling based on experimental observations. This chapter consists of four subsections: Sect. 3.1 is devoted to existing models that are focused on the evolution in time of mitochondria and, as a consequence, are described by ordinary differential equations (ODE models); they do not take into account local effects and only work with mean values over the whole domain. Coming from an ODE model, it is natural to think about the necessity of including spatial effects by means of considering partial differential equations (PDE models). We consider spatial effects in Sect. 3.2. Moreover, we show how to take into account this spatial effect is dictated by experiments. Indeed, in this section it is shown that the same amount of mitochondria with different concentrations have an influence on the volume outcome, that is, lead to different mitochondria swelling scenarios. With the necessity of taking spatial effects into account, in Sect. 3.3 we deal with the mitochondria model in vitro. We assume that mitochondria in the test tube as well as within the cell do not move in any direction and hence the spatial effects are only introduced by the calcium evolution. As a consequence of this assumption our mathematical model of mitochondria swelling is described by PDE-ODE systems (the so-called PDE-ODE coupling) with Neumann boundary conditions. We emphasize that in this vitro model we choose the underlying domain to be the test tube.