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

Authors

Hans Volkmer, University of Wisconsin - Milwaukee
Anne V. Clough, Marquette UniversityFollow
Gholamhossein G. Hamedani, Marquette UniversityFollow
Albert William Manuel S.J., Marquette UniversityFollow
Gary S. Krenz, Marquette UniversityFollow

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.

Recommended Citation

Volkmer, Hans; Clough, Anne V.; Hamedani, Gholamhossein G.; Manuel, Albert William S.J.; and Krenz, Gary S., "Complete Monotonicity of Flow and Cross-Sectional Impulse Response Functions for Rigid Right Circular Tubes" (2009). Mathematics, Statistics and Computer Science Faculty Research and Publications. 597.
https://epublications.marquette.edu/mscs_fac/597