Mathematical modelling of an ischemic stroke: an integrative approach

Understanding the mechanisms and the time and spatial evolution of penumbra following an ischemic stroke is crucially important for developing therapeutics aimed at preventing this area from evolving towards infarction. To help in integrating the available data, we decided to build a formal model. We first collected and categorised the major available evidence from animal models and human observations and summarized this knowledge in a flow-chart with the potential key components of an evolving stroke. Components were grouped in ten sub-models that could be modelled and tested independently: the sub-models of tissue reactions, ionic movements, oedema development, glutamate excitotoxicity, spreading depression, NO synthesis, inflammation, necrosis, apoptosis, and reperfusion. Then, we figured out markers, identified mediators and chose the level of complexity to model these sub-models. We first applied this integrative approach to build a model based on cytotoxic oedema development following a stroke. Although this model includes only three sub-models and would need to integrate more mechanisms in each of these sub-models, the characteristics and the time and spatial evolution of penumbra obtained by simulation are qualitatively and, to some extent, quantitatively consistent with those observed using medical imaging after a permanent occlusion or after an occlusion followed by a reperfusion.