Pseudo bond graphs for generalized compartmental models in engineering and physiology

True bond graphs, which use effort and flow variables whose product is power, can in principle be used to describe all types of physical systems. However, many system models do not use power variables and yet can be represented usefully as pseudo bond graphs. Pseudo bond graphs have been used particularly for open systems in which it is convenient to consider control volumes or compartments with boundaries across which mass can flow. In this paper, we show how the bond graph methods used for conductive and convective heat transfer can be generalized to account for diffusion, convection, and accumulation of a variety of physical quantities and how pseudo bond graphs can aid in constructing and representing such models. These models are known in mathematical biology as “compartmental models” and it is a main contribution of this paper to show that the same pseudo bond graphs apply to thermofluid and physiological dynamic models. The bond graphs build in some conservation principles automatically and yet have the flexibility to incorporate general multiport laws when necessary. Thus the pseudo bond graphs can exhibit system structure as do other network graphs and are very general in nature.