Model number
0202

  

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.

Description

  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
present.

  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.

Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

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References
 (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

 ALDRICH BI. The effects of the hyaluronic acid complex on the distribution of ions. 
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 Beeler GW, Jr, Reuter H. Membrane calcium current in ventricular myocardial fibres. 
 J Physiol. 1970 Mar;207(1):191–209.  

 Birks RI, Davey DF. Osmotic responses demonstrating the extracellular character of the 
 sarcoplasmic reticulum. J Physiol. 1969 May;202(1):171–188.  

 BLINKS JR. INFLUENCE OF OSMOTIC STRENGTH ON CROSS-SECTION AND VOLUME OF ISOLATED SINGLE 
 MUSCLE FIBRES. J Physiol. 1965 Mar;177:42–57.  

 Caillé JP, Hinke JA. Evidence for Na sequestration in muscle from Na diffusion measurements. 
 Can J Physiol Pharmacol. 1972 Mar;50(3):228–237. 

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

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

 ENGEL MB, JOSEPH NR, CATCHPOLE HR. Homeostasis of connective tissues. I. Calcium-sodium equilibrium. 
 AMA Arch Pathol. 1954 Jul;58(1):26–39. 

 ENGEL MB, JOSEPH NR, LASKINDM, CATCHPOLE HR. Binding of anions by connective tissue: dermis 
 and cartilage. Am J Physiol. 1961 Oct;201:621–627. 

 Fawcett DW, McNutt NS. The ultrastructure of the cat myocardium. I. Ventricular papillary muscle. 
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 Connective tissues. Arch Biochem Biophys. 1959 Sep;84:224–242. 

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 its localization. J Cell Biol. 1972 Sep;54(3):441–455.  

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 cell membranes. Ultrastructural and electrophysiological evidence. J Cell Biol. 1973 Jul;58(1):1–10.  

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 J Physiol. 1957 Oct 30;138(3):506–515.  

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 Biophys J. 1976 Jan;16(1):43–57.  

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

Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.