A class of steady-state compartmental models of the circulation is examined and it is shown that the mathematical problem for this model class involves a single nonlinear equation. In an important subclass and with certain assumptions regarding the form of the Starling-type cardiac function curves, the single equation is of the form Z = μ + λ log[(1 − Z)/Z] where μ and λ are mathematical parameters related to the physiological parameters of the system and Z is proportional to the cardiac output. This result holds regardless of the number and arrangement of compartments within the model itself or of the number of physiological parameters the model contains. An example of this class with 25 physiological parameters is presented to illustrate this approach.
R.J. White. A Note Regarding the Mathematical Treatment of a Class of Steady-State Compartmental Models of the Circulation. Physiol. Reports 4(17):1-11, 2016 DOI - 10.14814/phy2.12945.