Multi-compartment model

Multi-compartment model is a lumped-parameter mathematical model for continuous systems to simulate the transmission of materials or energies among the units,ie. compartments, of that system.
Multi-compartment model finds most of its application in the Biomedicine and Pharmaceutical occasions. However, essentially, the circuits systems can be view as a multi-compartment model as well.

Assumptions

Multi-compartment model assumes adopts several assumptions such that systems in physical existence can be modeled mathematically:

Most of the time, multi-compartment model simulates only one substance, eg. the concentration of solutions, to simplify the mathematics.

Single Compartment Model

Possibly the simplest application of multi-compartment model is in the single cell concentration monitoring. If the volume of a cell is V, the mass of solute is q, the input is u(t) and the secretion of the solution is proportional to the density of it within the cell, then the concerntration of the solution C within the cell over time is given by:

       $C=q/V$

       $dq/dt=u(t)-kq$

where k is the proportionality.