Linear bulk diffusion into heterogeneous tissue

In this paper an expression is derived which describes the transient overall uptake of an inert solute by a section of tissue excised with parallel faces and placed upon an impermeable base. The approach diverges from the conventional analyses for perfused tissue (Morales and Smith,Bull. Math. Biophysics,6, 125–141, 1944;7, 47–99, 1945) because the extravascular zone is regarded as a heterogeneous diffusion medium. Account for this is taken by regarding tissue as effectively composed of two phases—a continuous (extracellular) phase similar to water, and a dispersed phase comprising cells of irregular profile. In both phases the relevant mode of uptake is taken as bulk diffusion rather than surface permeation, thus emphasizing the influence of the internal geometry of the tissue upon its overall exchange response.