Numerical Methods of Modeling in Biomedical Applications

The almost daily introduction of numerical modeling techniques into medical practice dates back to the widespread use of microcomputers in hospitals and doctors' surgeries in the early 2000s. The first stage led to an accumulation of data (pathophysiological signals and medical images), which had to be organized in large databases. Then, to reduce these data to their most explanatory content in terms of knowledge about the biological mechanisms at work in the diseases observed, modeling was necessary. The second step consisted in naming the state variables of the models envisaged (organ position, temperature, pressure, concentrations of essential metabolites, etc.), then specifying them in the model.), then specifying them by means of attributes (systolic radial blood pressure), identifying them by a verb in mechanisms (a blood glucose concentration above 2g/l increases blood insulin levels) and placing them in an interaction network, first qualitative, then numerical with discrete values (Boolean in the case of gene expression) and finally with continuous values, within the framework of differential equations. The numerical nature of the final model enables it to be simulated on a computer and thus to predict the future of a pathological state, as a function of known initial conditions, resulting from observation of the model's state variables in an individual patient, in the case of personalized diagnosis and treatment, or in a population, in the case of forecasting the spread of an epidemic.

The applications of such an approach touch almost every area of medical clinical and surgical practice, so much so that medicine that uses models is sometimes referred to as 5P medicine, with each "P" having a precise meaning: predictive (if the model is used to make a prognosis), personalized (if the variables are acquired at the individual level, the model enabling personalized therapeutic decisions), participatory (models that can be explained, validated and simulated by/for many healthcare players, including the patient), preventive (models that enable causal variables to be extracted and controlled before the onset of a pathology) and multi-expert (the model enabling simulations and decisions to be shared between healthcare professionals). Examples of the chosen fields of application are: pandemic forecasting, cardiorespiratory physiology, medical gesture guidance, monitoring of dependent persons, gene expression and risk factor epidemiology.