Abstract
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.
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This work supported in part by PHS Grant Nos. HL-19153 (SCOR for Pulmonary Vascular Disease) and HL-19370 at Vanderbilt University.
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Bateman, J.M. Heterogeneous organ models. Bltn Mathcal Biology 48, 525–543 (1986). https://doi.org/10.1007/BF02462322
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DOI: https://doi.org/10.1007/BF02462322