Title

Complete Monotonicity of Flow and Cross-Sectional Impulse Response Functions for Rigid Right Circular Tubes

Document Type

Article

Language

eng

Publication Date

4-15-2009

Publisher

Elsevier

Source Publication

Journal of Mathematical Analysis and Applications

Source ISSN

0022-247X

Abstract

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.

Comments

Journal of Mathematical Analysis and Applications, Vol. 352, No. 2 (April 15, 2009): 702-710. DOI.

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