[Mathematical modelling in medicine and biology. Theoretical basis and fundamentals]

Mathematical modelling is currently a common tool in the study of physiological and biochemical systems. Its basis and fundaments are not, however, well known by the non-specialist. Its aims are to describe, explain and predict physiological and biochemical phenomena. Mathematical models provide a concise and objective description of complex dynamic processes by defining, through mathematical equations, the relationships between quantitative measurements; they indicate, also, ways to improve experimental designs, and allow the testing of hypotheses about physiological or biochemical phenomena. Mathematical models can be developed from simple non-compartmental representations to large scale multi-compartmental models. The basic steps in the formulation of a model include conceptualization, realization and solution of the model. Each step has to be verified and validated. In the case of compartmental models, mass-balance equations are used to represent each compartment. A brief review of the theory of system's analysis and the general aims of mathematical modelling is presented here. The modelling process is usually started with a definition of the problem and a parameter identification followed by the setting up of a clear conceptual model of the system. The model consists of the description of the principal flows of material (in and out) and of the main components which store, convert or transmit these flows. A selection of the class of mathematical representation follows, i.e. linear or non-linear, in order to formulate the equations relating the input and output flows of material for each individual component of the system.(ABSTRACT TRUNCATED AT 250 WORDS)