On indicator dilution and perfusion heterogeneity: A stochastic model

Thomas A. Bronikowski*, Christopher A. Dawson, John H. Linehan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Unidirectional extraction of a substrate S in the capillaries following the arterial injection of a bolus containing S and a reference tracer R is assumed to follow first-order kinetics. If CR and CS denote normalized venous effluent concentrations of R and S, respectively, let L(t)=ln[CR(t){plus 45 degree rule}CS(t)]. We derive a formula which expresses the experimental L(t) data in terms of the mean μ(t) and variance of the transit times of those capillaries which are contributing indicators at each sample time t. We examine the information thus contained in the L data about capillary and noncapillary transit times under several kinematic assumptions. We show that if the capillary and noncapillary transit times are stochastically independent with frequency functions hc(t) and hav(t), respectively, then the shapes of the graphs of L(t) and μ(t) depend on the variances and skewnesses of hc(t) and hav(t). Specifically, let r2 be the ratio of the variance of hc(t) to the variance of hav(t), and let r3 be the ratio of skewnesses in the same order. Then the graph of μ(t) is concave downward if r2{plus 45 degree rule}r3 > 1, concave upward if r2{plus 45 degree rule}r3< 1, and linear if r2{plus 45 degree rule}r3 = 1. If the fraction of S extracted is not too large, L(t) has nearly the same shape as μ(t), and therefore, L(t) contains information about hc(t) and hav(t).

Original languageEnglish (US)
Pages (from-to)199-225
Number of pages27
JournalMathematical Biosciences
Issue number2
StatePublished - Apr 1987

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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