Determination of the single-pass impulse response of the body tissues with circulatory models

Classical in vivo kinetics are based on the analysis of the blood disappearance curve of a substance. This curve is determined by the interplay of the substance transport in the circulatory system and the kinetics of the body tissues. The characteristic response of the body tissues, that is, their single-pass impulse response, is obscured in the disappearance curve by multiple recirculations in the heart-systemic loop. The single-pass impulse response can be appropriately determined with circulatory models. This paper investigates the theoretical aspects of the determination of the impulse response and proposes suitable algorithms for the analysis of experimental data with circulatory models. The problem of what information the most typical experimental configurations yield on the single-pass impulse response, and what assumptions are necessary for determining the impulse response in a given configuration is studied first. It is shown that assumptions are usually necessary, unless a proper experiment design is adopted. Two algorithms are then developed for the determination of the impulse response from experimental data, in the general case. The first calculates the response from an exponential description of the disappearance curve, while the second is based on a state space representation of circulatory models. The first method has the important limitation that it does not always ensure physiologically plausible results; the state space approach overcomes this limitation, and is the method of choice. With the state space approach, the determination of the single-pass impulse response is a standard parameter estimation problem with finite dimensional linear systems. The analysis of real data from a study on glucose kinetics illustrates the practical relevance of the results.