# Mathematical models for biomedicine PDF  Författare: Luca Mesin.

“Si tratta del libro di testo del corso di “Modelli Matematici per la Biomedicina” che il Prof. L. Preziosi e io teniamo al Politecnico di Torino.” Hence a multi-compartment model is a lumped parameters model. In systems theory, it involves the description of a network whose components are compartments that represent a population of elements that are equivalent with respect to the manner in which they process input signals to the compartment. Instant homogeneous distribution of materials or energies within a “compartment. The exchange rate of materials or energies among the compartments is related to the densities of these compartments. Usually, it is desirable that the materials do not undergo chemical reactions while transmitting among the compartments. When concentration of the cell is of interest, typically the volume is assumed to be constant over time, though this may not be totally true in reality.

Most commonly, the mathematics of multi-compartment models is simplified to provide only a single parameter—such as concentration—within a compartment. As the number of compartments increases, the model can be very complex and the solutions usually beyond ordinary calculation. Generally speaking, as the number of compartments increase, it is challenging both to find the algebraic and numerical solutions of the model. However, there are special cases of models, which rarely exist in nature, when the topologies exhibit certain regularities that the solutions become easier to find. Closed model: No sinks or source, lit. Catenary model: All compartments are arranged in a chain, with each pool connecting only to its neighbors.