Complete monotonicity of flow and cross-sectional impulse response functions for rigid right circular tubes

Indicator dilution theory is the conceptual base for many flow measurement methods within living organisms; a whole animal, an organ, or an individual vessel. In this manuscript, we provide a characterization of the system impulse response function for flow- and cross-sectionally sampled indicator curves within a rigid right circular tube. The curves are measured downstream from the position of an injector, which labels uniformly the streamlines of a steady, laminar power law fluid flow. The system impulse response function is shown to be the weighted sum of a Dirac delta function and a completely monotonic function. A numerical example employing data from a physical experiment involving a vertically orientated, perfused glass tube is presented, illustrating the characterization of the impulse response function between cross-sectionally sampled upstream and downstream measurement sites.