This paper proposes a mathematical model for the volume of distribution and kinetics of tracer dilution in the mammalian extracellular fluid system. Analogy to certain simple mechanical and electrical physical systems suggests an exponential decay formulation for the time course of tracer distribution, y = A(1−e −Bt) + Ct. This hypothesis is supported by the successful optimal curve fitting of the model to experimental data on 35SO4 and thiocyanate distribution in the extracellular fluid. Nonlinear regression analysis is performed by computer, utilizing techniques devised for exponential functions. The parameters of the equation suggest a correspondence to and an interpretation of the descriptive physical properties of the extracellular fluid system as discerned by tracer dilution.
Finseth F, Mazur M, Baue A, Burke JF. The Extracellular Fluid SystemA Mathematical Model of Tracer Distribution. Arch Surg. 1973;106(1):68-71. doi:10.1001/archsurg.1973.01350130070015