# Safford1978

Calculates the bulk diffusion coefficient, Db, for water through a matrix of cells surrounded by ECF, influenced by cell membrane permeability. This is contrasted with results obtained from homogeneous sheet and dead-end pore models. From Safford et al. 1978 paper.

Model number: 0205

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## Description

Diffusion of water through a slab of uniform thickness. Tracer water at side 1 diffuses through a matrix of cells evenly spaced throughout an extracellular space, ECF. Cells are square beams,L by L, on a rectangular lattice, separated by Lzero. Diffusion occurs through both ECF and cells in parallel. The cells have permeability P on all surfaces allowing exchange between cells and ECF. (The cell shape (square, hexagonal or cylindrical beams) has negligible effect.). Given fixed intracellular and extracellular Ds, P dominates the effective intratissue effective bulk diffusion coefficint Db. Using P as an independent variable allows one to show the bulk D as a function of P and to vary other parameters in the loops. Running the program from P=P,min -1e-6 to P.max = 0.4 gives the plot in Figure 7 of Safford 1978 for which the cell sizes and surface area matches that of cardiac tissue. See also Figures 5 and 6 for variation in dimensions and Table II, p527. This steady state Db was estimated experimentally by Safford from the slope of dCr/dt in an experiment in which the tissue lies between Compartment 1 (stirred) with fixed concentration and tracer diffuses into compartment 2 whose concentration Cr(t) is initally zero. (A type of Barrer time-lag study.) The two other models presented here (Sheet Diffusion and Dead-end Pore) were previously presented in papers Suenson et al., 1974 and Safford et al., 1977. These models predict higher hindrance of water in tissue (ratio of observed to free) compared to that of sucrose due to physiologically unrealistic values for water permeability and water space available for diffusion.

Safford et al. 1978 paper (Journal link)

Safford et al., 1978

## Equations

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## References

(primary): Safford RE, Bassingthwaighte EA, and Bassingthwaighte JB. Diffusion of water in cat ventricular myocardium. J Gen Physiol 72: 513-538, 1978. BARRER, R. M. 1953. A new approach to gas flow in capillary systems. J. Phys. Chem. 57:35-40. BASSINGTHWAIGHTE, J. B., and H. REUTER. 1972. Calcium movements and excitation-contraction coupling in cardiac cells. In Electrical Phenomena in the Heart. W. C. DeMello, editor. Academic Press, Inc., New York. 353-395. BASSINGTHWAIGHTE, J. B., T. YIPINTSOI, and R. B. HARVEY. 1974. Microvasculature of the dog left ventricular myocardium. Microvasc. Res. 7:229-249. BERGER, W. K. 1972. Correlation between the ultrastructure and function of intercellular contacts. In: Electrical Phenomena in the Heart. W. C. DeMello, editor. Academic Press, Inc., New York. 63-88. BIRD, R. B., W. E. STEWART, and E. N. LIGHTFOOT. 1960. Transport Phenomena. John Wiley & Sons, Inc., New York. 780 pp. BLINKS, J . R. 1965. Influence of osmotic strength on cross-section and volume of isolated single muscle fibres. J. Physiol. (London). 177:42-57. BOYLE, P. J., and E. J. CONWAY. 1941. Potassium accumulation in muscle and associated changes. J. Physiol. ( Lond. ). 100:1-63. CRANK, J. 1956. The Mathematics of Diffusion. Oxford University Press, London. 347 PP. GOODKNIGHT R. C., and I. FATT. 1961. The diffusion time-lag in porous media with dead-end pore volume.J. Phys. Chem. 65:1709-1712. PAGE, E., and R. S. BERNSTEIN. 1964. Cat heart muscle in vitro. V. Diffusion through a sheet of right ventricle.J. Gen. Physiol. 47:1129-1140. SAFFORD, R. E., and J. B. BASSINGTHWAIGHTE. 1977. Calcium diffusion in transient and steady states in muscle. Biophys. J. 20:113-136. SCHAFER, D. E., and J. A. JOHNSON. 1964. Permeability of mammalian heart capillaries to sucrose and inulin. Am. J. Physiol. 206:985-991. SUENSON, M., D. R. RICHMOND, and J. B. BASSINGTHWAIGHTE. 1974. Diffusion of sucrose, sodium and water in ventricular myocardium. Am. J. Physiol. 227:1116-1123.

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## Key Terms

Diffusion, barrer, sheet diffusion, dead-end pore, DEP, publication, data, water, sucrose, cell geometry, permeation, PMID722277

## Model History

Get Model history in CVS.Posted by: BEJ

## Acknowledgements

Please cite **www.physiome.org** 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: staff@physiome.org.

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The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 14Mar18, 3:17 pm.]

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