Diffusion of sucrose, sodium, and water in ventricular myocardium

Abstract

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 cm²/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.

FIG. 1

Diffusion cell. M, right ventricular sheet; P, sampling port; G, gas inlets; S, magnetic stirrer rod; CE, current electrode; VE, voltage electrode. Each half of diffusion cell is 2.9 cm long, 2.5 cm in internal diameter, and 14.5 ml in volume.

FIG. 2

Time course of specific resistance, R_MA_M/l, in 2 experiments. Upper curve shows a 200-min control period (95% O₂, 5% CO₂) followed by oxygen deprivation (100% N₂) which was accompanied by a prompt increase in resistance. Recommencement of O₂ was followed after a time lag by a slower decline of resistance toward control levels. Lower curve demonstrates resistance changes following 2 additions of 88 mM NaF to each chamber. (For details see text.)

FIG. 3

Block diagram of parallel-pathway model. C_D(t) is donor concentration of tracer and C_R(t) is recipient concentration corrected for sample replacement. w_i is weighting factor, which gives the fractional utilization of each path length, l_i.

FIG. 4

Dead-end pore model of Goodknight, Klikoff, and Fatt (14). Sequestered regions are schematized as dead-end pores which at steady state are in equilibrium across cell membrane with extracellular diffusion channel where net diffusion occurs. V_dep is dead-end pore volume and V_d is steady-state diffusion volume.

FIG. 5

Normalized accumulation of sucrose-¹⁴C (□), ²⁴Na (×), and THO (▲) on initially tracer-free side of myocardial sheet. Data were obtained simultaneously on a sheet of mean thickness 1.14 mm (SD = 0.16 mm), which was 2nd most uneven sheet used. C_R(t) is recipient concentration corrected for sampling replacement and C_D(o) is donor concentration at onset of the sampling period.

FIG. 6

Transient phase of normalized accumulation, ×, of sucrose-¹⁴C in a sheet of mean thickness, l = 1.48 mm (SD, σ = 0.14 mm). Continuous curves are a family calculated from multiple-pathway model. Each curve represents a single Gaussian distribution of path lengths characterized by its relative dispersion (σ/l). Seventeen curves are shown with σ/l varying between 0.00 and 0.32. Curves differ only in transient portion and are superimposed at steady state, a σ/l of 0.20 providing best fit to data.