Calculation of organ and whole-body uptake and production with the impulse response approach

A general theory for the calculation of uptake and production in the non-ready state in both a single organ and in the whole body is proposed. The theory is based on an extension of Zierler’s impulse response approach for organ kinetics and on its application to whole-body kinetics through circulatory models. It describes the accessible (inlet-outlet) and non-accessible (inlet-uptake, production-outlet, and production-uptake) metabolic paths of an organ with four impulse responses. The mathematical formalization gives the factors that must be known with sufficient accuracy to ensure a well-founded calculation of uptake and production, and provides a basis for the evaluation of the currently used approximate approaches. The theory shows that if uptake and production occur simultaneously in organs—e.g. for amino acids—the major problem, which cannot easily be overcome, is the lack of knowledge of the non-accessible impulse responses. If uptake and production do not occur simultaneously (e.g. for glucose), substitutes of uptake and production (denoted as inlet-equivalent uptake and outlet-equivalent production) can be calculated from the knowledge of the inlet-outlet impulse response only. Qualitatively, uptake is delayed inlet-equivalent uptake and outlet-equivalent production is delayed production. The delays are the mean transit times of the inlet-uptake and production-outlet paths. Inlet-equivalent uptake and outlet-equivalent production can be calculated without hypotheses on the organ (or whole-body) total mass, which is known to be indeterminable with classical tracer experiments. If independent information on the mass is available, a rigorous qualitative prediction of the fluxes can be attempted. For whole-body kinetics, this approach has better foundations than compartmental analysis that necessarily requires assumptions on the total mass. Whole-body glucose kinetics in a specific non-steady-state condition are discussed as a relevant application of the theory.