Indicator dilution theory for convective dispersion in laminar flow through straight tubes

From an analysis of the dispersion of indicator in steady laminar fluid flow, expressions are derived for the determination of flow in a straight tube in circumstances in which the familiar Stewart-Hamilton relations for indicator dilution do not generally apply, namely when the method of detection of the tagged blood flow depends on the density of the indicator in the system, as with X-ray videodensitometry. The analysis assumes no diffusion of indicator, and is carried out for arbitrary profiles of fluid flow velocity and tube cross-section. Injections of finite width and finite duration are considered, whereby the indicator is distributed over the tube cross-section either uniformly or in proportion to velocity. Spatial resolution of the detector is considered. A new method is proposed to utilise a priori information when the type of flow is known beforehand. The application of the results is illustrated by several examples for cases with laminar flow. The study is theoretical and is intended only as a first step towards the measurement of blood flow in the human circulation.