Les équations différentielles du premier ordre simple et généralisé. Leur utilisation dans quelques domaines de la macrophysiologie

First order differential equations formulate the simplest physiological models and, therefore, are endowed with wide applicability. They owe this advantage to the principle of parcimony: according to Occam's razor, the most general explanations are a priori the best. First order equations express the essential properties of the system. However, they often are inappropriate for representing complementary facts characteristic of the real objects. Any refinement of the model requires the inclusion of higher order terms. Our goal is to arrive at a general method for addressing a variety of problems. Here, we chose the example of the Windkessel model to introduce the mathematical framework. The input was simplified without loss of generality. We also proposed a possible analytical approach and compared its results with those of the numerical methods. This led to the improvement of the latters. Finally, some prominent examples in the field of macrophysiology were discussed.