The effects of axial diffusion and permeability barriers on the transient response of tissue cylinders. II. Solution in time domain.
A mathematical description of transient mass transfer in a Krogh tissue cylinder, for which a solution in transform space was presented previously, is solved in the time domain. The solution is found in the form of an expansion in terms of the eigenfunctions of a non-self-adjoint differential operator, with the eigenvalues being found by way of a computational scheme which makes use of the known characteristics of the constitutive compartments of the system. The solution is compared with previous solutions of both a complete and an approximate nature, and two modifications of the single-phase axial dispersion model are found to be especially useful: the previously-used flow-limited approximation is satisfactory for highly permeable solutes, while the apparently novel barrier-limited approximation is accurate for poorly permeable solutes at the early times of most experimental interest. Although the neglect of axial diffusion does not affect the qualitative nature of the solution, e.g. in predicting a bimodal response curve, significant discrepancies shed doubt on this practice when truly impulsive inputs are used. The results obtained raise several questions regarding existing approaches to interpretation of indicator dilution experiments. These include the use of extraction ratios and of exponential extrapolation of the tails of response curves.