Annals of Biomedical Engineering

, Volume 26, Issue 6, pp 914–930 | Cite as

Accounting for the Heterogeneity of Capillary Transit Times in Modeling Multiple Indicator Dilution Data

  • S. H. Audi
  • J. H. Linehan
  • G. S. Krenz
  • C. A. Dawson
Article

Abstract

To mathematically model multiple indicator dilution (MID) data for the purpose of estimating parameters descriptive of indicator-tissue interactions, it is necessary to account for the effects of the distribution of capillary transit times, hc(t) In this paper, we present an efficient approach for incorporating hc(t) in the mathematical modeling of MID data. In this method, the solution of the model partial differential equations obtained at different locations along the model capillary having the longest transit time provides the outflow concentrations for all capillaries. When weighted by hc(t) these capillary outflow concentrations provide the outflow concentration versus time curve for the capillary bed. The method is appropriate whether the available data on capillary dispersion are in terms of capillary transit time or relative flow distributions, and whether the dispersion results from convection time differences among heterogeneous parallel pathways or axial diffusion along individual pathways. Finally, we show that the knowledge of a relationship among the moments of hc(t) rather than hc(t) per se, is sufficient information to account for the effect of hc(t) in the mathematical modeling interpretation of MID data. This relationship can be determined by including a flow-limited indicator in the injected bolus, thus providing an efficient means for obtaining the experimental data sufficient to account for capillary flow and transit time heterogeneity in MID modeling. © 1998 Biomedical Engineering Society.

PAC98: 8745Ft, 8710+e, 0230Jr

Flow distribution Axial diffusion Mathematical model Perfusion heterogeneity Relative dispersion Heterogeneity Capillary transit times Indicator dilution 

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Copyright information

© Biomedical Engineering Society 1998

Authors and Affiliations

  • S. H. Audi
    • 1
  • J. H. Linehan
    • 1
  • G. S. Krenz
    • 2
  • C. A. Dawson
    • 3
    • 4
  1. 1.Department of Biomedical EngineeringMarquette UniversityMilwaukee
  2. 2.Department of Mathematics Statistics and Computer ScienceMarquette UniversityMilwaukee
  3. 3.Department of PhysiologyMedical College of WisconsinMilwaukee
  4. 4.Department of Veterans AffairsZablocki VAMCMilwaukee

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