Physiological significance of the rate constants in compartmental analysis

Transfer (rate) constants in compartmental analysis are generally considered solely in operational terms, and little attention has been paid to their physiological interpretation. In this study we have examined the significance of their roles in physiological terms and the implications of this interpretation. When freely diffusible tracers are introduced into the blood stream by bolus injection, the sum of the exit rate constants from the blood compartment gives the number of blood volumes turned over per unit time; when multiplied by the blood volume, this value is the cardiac output. When corrected for body weight, the product yields the cardiac index, a biological constant for large mammals. The ratio of the rate constant supplying an organ to the exit-constant sum gives fractional cardiac output, and when multiplied by the cardiac output the ratio gives organ blood flow, independent of diffusibility. For freely diffusible tracers, organ blood flow can be calculated directly from the product of the organ rate constant and blood volume. At equilibrium and at equal concentration, the ratio of rate constants between adjacent compartments gives their relative volumes; this interpretation is fundamental when partitioning compartments for detailed analysis. These considerations have been validated by testing in both animals and man. Multiple solution sets may occur in mammillary models. Knowledge of the physiological interpretation of intercompartmental rate constants is of importance not only in model interpretation but in model validation, where this information serves as an independent check on model structure and its realization.