Approximate solution for capillary exchange models with and without axial mixing

Explicit expressions are obtained which give quite accurate values for the effluent blood concentration for the model with axial mixing in tissue for the cases in which the initial capillary concentration is either zero or one. These simple expressions are useful since the formal solutions of Gosselin and Gosselin (1987,Bull. math. Biol 49, 329–349) are cumbersome to use. Reasonably accurate expressions are also provided for the model without axial mixing since the formal solution for the case in which the initial capillary concentration is zero (Gosselin and Gosselin, 1987) and for the case in which the initial concentration equals that of the tissue, the solution for which is provided here, require numerical integration.