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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto


Parallel pathway, dead-end pore model that accounts for sequestration or binding of calcium within heart muscle sheet. From Safford and Bassingthwaighte, 1977. Also contains an implementation of Suenson et al. 1974 diffusion model to validate new model with sucrose data.

Model number: 0202

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  ABSTRACT: Rates of diffusion through the extracellular space of thin sheets of myocardium
from the right ventricular outflow tract of kittens were estimated at 23C
for [45Ca(2+)] and an inert reference tracer, [14C]sucrose. The myocardial sheets were
mounted in an Ussing chamber and equilibrated with Tyrode solution with varied
calcium concentrations, Ca0. The tracers were added to one side and their concentrations
on the other side measured at 5-15-min intervals for 6 h. The apparent
tracer diffusion coefficient for sucrose was 1.11 0.06 x 10^-6 cm^2*s^-1 (mean t
SEM, n = 74), 22% of the free diffusion coefficient; the lag time before reaching a
steady state provided estimates of the intratissue volume of distribution or diffusion
space of 0.41 +- 0.15 ml/ml tissue (n = 74), a value compatible with expectations for
extracellular fluid space. Over the range of Ca0 from 0.02 to 9.0 mM, the intratissue
apparent diffusion coefficient for Ca, Dca, averaged 1.65 0.10 x 10^-6cm^2*s^-1, n =
74, which is 21% of the free D0ca, and was not influenced by Ca0. Because transsarcolemmal
Ca permeation is slow, Dca is the diffusion coefficient in the extracellular
region. The paired ratios Dca/D. averaged 1.32 +- 0.05 (n = 67) for all
levels of Ca0 but at physiologic or higher Ca0 averaged 1.45 +- 0.07 (n = 39), close
to the ratio of free diffusion coefficients, 1.53. Equations distinguishing transient
from steady state diffusion were fitted to the data, showing that the apparent distribution
volume of "binding sites" external to the diffusion pathway diminished at higher
Cao in a fashion suggesting that at least two different Ca(2+) binding sites were

  There are two diffusion models presented here: the dead-end pore model ('saff77_Binding') 
to account for Ca binding, and one based on Suenson et al. 1974 ('saff77_MPcrank', based on Crank 1956) 
that is used to model sucrose diffusion across the myocardium. The dead-end pore model contains 
the single and multi-path solutions using the same parameters so that it is easy to see the 
effect of heterogeneous tissue on diffusion across tissue.

Safford et al. 1977 paper (pdf)


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 (Primary) Safford RE, Bassingthwaighte JB, Calcium diffusion in transient and steady states in muscle, 
 Biophysical Journal, 20(1), Oct 1977, 113-136, ISSN 0006-3495

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 Crank J. The Mathematics of Diffusion. Oxford: Clarendon Press, 1956.

 Crank J. The Mathematics of Diffusion, 2nd edition. Oxford: Clarendon Press, 1975.

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Related Models

Key Terms

tissue diffusion, plane sheet, binding, dead-end pore, ventricular myocardium, calcium, sucrose, tutorial, heterogeneous transport, Data, Publication, PMID901900, PMCID: PMC1473340

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Posted by: BEJ


Please cite in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to:
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 02Nov16, 2:41 pm.]

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