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.
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.
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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.