Bulletin of Mathematical Biology

, Volume 48, Issue 5–6, pp 525–543 | Cite as

Heterogeneous organ models

  • J. M. Bateman


A theoretical study is made of three organ flow models with heterogeneity of capillary transit times. A new parametrization of Rose and Goresky's Model III facilitates in many cases a reduction to Goresky's Model II, accomplished by a special time shift. The shift parameter\(\tau _{c_z } = \tau _{c_m } - t_{APP} /b\) defined here is critical in this analysis of Model III. A new expression of the series for outflow concentration in Model III is given and proves useful in examining the model as an operator and in relating it to Models I and II. A result on parameter optimization is given: if\(\tau _{c_z } \geqslant 0\) then Model III cannot fit better than Model II. This is applied to some data from Rose and Goresky [Circulation Res. 39, 541–544 (1976)] and raises a new question about their model. A heart model of Levin and Bassingthwaighte based on regional flow measurement is shown to be a discretized generalization of Model II.


Transit Time Large Vessel Organ Model Axial Dispersion Appearance Time 
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Copyright information

© Society for Mathematical Biology 1986

Authors and Affiliations

  • J. M. Bateman
    • 1
  1. 1.Department of Mathematical SciencesLoyola UniversityNew OrleansU.S.A.

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