Estimation of the Moments of the Residence Time and First Passage Time from Experimentally Measurable Permeation Parameters via a New Formulation of the Transmission Matrix

Siegel's analysis on membrane transport in the Laplace domain [J. Phys. Chem. 95 (1991) 2556] in terms of transmission matrix, T(s), has been extended to a more useful formulation. This is achieved by combining uses of the matrix transport equations appropriate for void initial condition, or for saturated equilibrium, or of Dirac delta functional type and the theorem det[T(s)] = 1. This formulation enables us to expand T(s) in power series of the Laplace variable, s, with the expansion coefficients as the algebraic functions of the experimentally measurable transport parameters. Utility of the formulation is illustrated in the estimation of the experimentally inaccessible time moments for the first passage or residence times. It was also applied to the percutaneous drug delivery to obtain from the experimental data. The higher moments of the time lag or time lead using a graphic method.