A steady-state transfer function analysis of portions of the circulatory system using indicator dilution techniques.

A digital computer program has been developed whereby the distribution of dye-particle transit times across circulatory pathways can be found from recordings of upstream and downstream indicator-dilution curves. This distribution or transfer function is computed from Fourier-series representations of the upstream and downstream indicator curves and makes possible, for the first time, the calculation of transit-time distributions independent of the effects of recirculating dye. Since a discontinuity is introduced into the tails of the upstream and downstream curves at the end of sampling, the method requires an iterative approach in the termination of the upstream and downstream curves. The accuracy of the calculated distribution pattern is determined by comparison of the recorded downstream curve with the results of the convolution of the recorded upstream curve and computed transfer function. Effects of noise, bandwidth and sampling rate have been investigated through the use of analog computer models of the circulatory pathways. These studies show that the transfer-function description is limited by the bandwidth of the upstream (input) curve. Noise, or variations in magnitude and phase angle of input- and output-curve frequencies, tends to introduce oscillations into the time-domain representation of the transfer function as does the use of too few frequencies. This means that in biological systems the upstream sampling site must be relatively close to the dye injection site if the input and output sampling sites are close together. Circulatory transfer functions have been obtained from dogs across their lower extremity, renal and systemic circulations before, during and following moderate exercise (walking on treadmill at two miles per hour for four minutes).