This page will look better in a graphical browser that supports web standards, but is accessible to any browser or internet device.

Served by Samwise.

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

Suenson1974

Single and Multi-path models of diffusion of sucrose, sodium, and water across a sheet of ventricular myocardium. Suenson et al. 1974 paper. Variation on Crank, 1956, solution for diffusion in a plane sheet with constant surface concentrations.

Model number: 0193

Run Model: 
    Help running a JSim model.
Java runtime required. Web browser must support Java Applets.
(JSim model applet may take 10-20 seconds to load.)

Description

   The cumulative fluxes of radioactive sucrose, sodium, and water across a sheet of cat right
ventricle were studied simultaneously to obtain the apparent tissue diffusion coefficients for
extravascular diffusion at 37°C. The sucrose data fitted the equations for diffusion in tortuous
channels in a plane sheet with a tortuosity factor, λ, of 2.11 ± 0.11 (mean ± SE, n = 10). The fit of
the earliest data before attainment of steady state was improved by assuming a Gaussian
distribution of diffusion path lengths through the extracellular space, but λ was only changed by a
few percent. The sucrose diffusion channel contained 0.27 ± 0.03 ml of total tissue water, which is
more than measured by others but still less than the expected sucrose space. The steady-state data
for sodium agreed with the model for extracellular diffusion using λ and the area available for
diffusion for sucrose when sodium equilibration with a dead-end pore volume (presumed to be
intracellular) was taken into account. The cumulative flux data for water were monotonic and
lacked secondary inflections. Thus the apparent tissue diffusion coefficients for sucrose, sodium,
and water were (in 10−6 cm^2/s) 1.77 ± 0.23, 5.13 ± 0.68, and 7.39 ± 0.99, respectively,
representing a reduction to 23% of the free diffusion coefficient for sucrose and sodium and 22%
for water.

  Two separate models are shown here, a multi-path and a single path model, as noted in the paper,
the multi-path model is not necessary to get a reasonable fit to the data obtained in the experiment.


Suenson et al. 1974 paper (pdf)

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.

Download JSim model project file

Model Feedback

We welcome comments and feedback for this model. Please use the button below to send comments:

References

 Armstrong W, Lurie D, Burt MR, High JR. Extracellular volume and ionic content of frog ventricle.
 Am J Physiol 1969;217:1230–1235. [PubMed: 5824325]

 Bassingthwaighte, JB.; Knopp, TJ.; Hazelrig, JB. Alfred Benzon Symp Capillary Permeability. 2nd.
 Copenhagen: 1970. A concurrent flow model for capillary-tissue exchanges; p. 60-80.

 Bassingthwaighte, JB.; Reuter, H. Calcium movements and excitation-contraction coupling in
 cardiac cells. In: DeMello, WC., editor. Electrical Phenomena in the Heart. New York: Academic;
 1972. p. 353-395.

 Birks RI, Davey DF. Osmotic responses demonstrating the extracellular character of the
 sarcoplasmic reticulum. J Physiol, London 1969;202:171–188. [PubMed: 5770880]

 Coleman HN, Dempsey PJ, Cooper T. Myocardial oxygen consumption following chronic cardiac
 denervation. Am J Physiol 1970;218:475–478. [PubMed: 5412463]

 Crane EE, Davies RE. Electrical potential difference and resistance of isolated frog gastric mucosa
 and other secretory membranes. Trans Faraday Soc 1950;46:598–610.
 
 Crank, J. The Mathematics of Diffusion. London: Oxford Univ Press; 1956.

 Creese R. Measurement of cation fluxes in rat diaphragm. Proc Roy Soc, London, Ser B
 1954;142:497–513. [PubMed: 13215507]

 Dick DAT. The rate of diffusion of water in the protoplasm of living cells. Exptl Cell Res
 1959;17:5–12. [PubMed: 13653043]

 Dydynska M, Wilkie DR. The osmotic properties of striated muscle fibres in hypertonic solutions.
 J Physiol, London 1963;169:312–329. [PubMed: 14079669]

 Fenichel IR, Horowitz SB. The transport of nonelectrolytes in muscle as a diffusional process in
 cytoplasm. Acta Physiol Scand 1963;60 221:1–63.

 Fenn WO, Cobb DM, Manery JF, Bloor WR. Electrolyte changes in cat muscle during stimulation.
 Am J Physiol 1938;121:595–608.

 Goodknight RC, Fatt I. The diffusion time-lag in porous media with dead-end pore volume. J Phys
 Chem 1961;65:1709–1712.

 Goodknight RC, Klikoff WA, Fatt I. Non-steady-state fluid flow and diffusion in porous media
 containing dead-end pore volume. J Phys Chem 1960;64:1162–1168.

 Grote J. Die Sauerstoffdiffusionskonstanten im Lungengewebe und Wasser und ihre
 Temperaturabhängigkeit. Arch Ges Physiol 1967;295:245–254.

 Grote J, Thews G. Die Bedingungen für die Sauerstoff-versorgung des Herzmuskelgewebes. Arch
 Ges Physiol 1962;276:142–165.

 Harris EJ, Burn GP. The transfer of sodium and potassium ions between muscle and the
 surrounding medium. Trans Faraday Soc 1949;45:508–528.

 Johnson JA. Kinetics of release of radioactive sodium, sulfate and sucrose from the frog sartorius
 muscle. Am J Physiol 1955;181:263–268. [PubMed: 14376606]

 Johnson JA, Simonds MA. Chemical and histological space determinations in rabbit heart. Am J
 Physiol 1962;202:589–592. [PubMed: 14452051]

 Krogh A, Lindberg AL, Schmidt-Nielson B. The exchange of ions between cells and extracellular
 fluid. II. The exchange of potassium and calcium between the frog heart muscle and the bathing
 fluid. Acta Physiol Scand 1944;7:221–237.

 Kushmerick MJ, Podolsky RJ. Ionic mobility in muscle cells. Science 1969;166:1297–1298.
 [PubMed: 5350329]

 La Force RC. Device to measure the voltage-current relations in biological membranes. Rev Sci
 Instr 1967;38:1225–1228.

 Ling GN, Ochsenfeld MM, Karreman G. Is the cell membrane a universal rate-limiting barrier to
 the movement of water between the living cell and its surrounding medium? J Gen Physiol
 1967;50:1807–1820. [PubMed: 6034769]

 Longsworth LG. Diffusion measurements, at 25C, of aqueous solutions of amino acids, peptides
 and sugars. J Am Chem Soc 1953;75:5705–5709.

 Longsworth LG. Temperature dependence of diffusion in aqueous solutions. J Phys Chem
 1954;58:770–773.

 Page E, Bernstein RS. Cat heart muscle in vitro. V. Diffusion through a sheet of right ventricle. J
 Gen Physiol 1964;47:1129–1140. [PubMed: 14192550]

 Page E, McCallister LP, Power B. Stereological measurements of cardiac ultrastructures implicated
 in excitation-contraction coupling. Proc Natl Acad Sci, US 1971;68:1465–1466.

 Page E, Page EG. Distribution of ions and water between tissue compartments in the perfused left
 ventricle of the rat heart. Circulation Res 1968;22:435–446. [PubMed: 5639053]

 Page E, Solomon AK. Cat heart muscle in vitro. I. Cell volumes and intracellular concentrations in
 papillary muscle. J Gen Physiol 1960;44:327–344. [PubMed: 13732016]

 Perl W, Chinard FP. A convection-diffusion model of indicator transport through an organ.
 Circulation Res 1968;22:273–298. [PubMed: 4867209]

 Phillips RA, Van Slyke DD, Hamilton PB, Dole VP, Emerson K Jr, Archibald RM. Measurement
 of specific gravities of whole blood and plasma by standard copper sulfate solutions. J Biol Chem
 1950;183:305–330.

 Ussing HH, Zerahn K. Active transport of sodium as the source of electric current in the shortcircuited
 isolated frog skin. Acta Physiol Scand 1951;23:110–127. [PubMed: 14868510]

 Van Harreveld A, Biber MP. Conductivity changes in some organs after circulatory arrest. Am J
 Physiol 1962;203:609–614. [PubMed: 13996055]

 Van Harreveld A, Malhotra SK. Demonstration of extracellular space by freeze-drying in the
 cerebellar molecular layer. J Cell Sci 1966;1:223–228.

 Vitagliano V, Lyons PA. Diffusion coefficients for aqueous solutions of sodium chloride and
 barium chloride. J Am Chem Soc 1956;78:1549–1552.	

Related Models

Key Terms

tissue diffusion, cat ventricular myocardium, diffusion models, tracer washout, extracellular fluid, dead-end pores heterogeneous systems, solute transport, DATA, Publication, PMID4440753, PMCID:PMC3024886

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.
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, 2:42 pm.]

Model development and archiving support at physiome.org provided by the following grants: 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.