Notes on the inverse gaussian distribution and choice of boundary conditions for the dispersion model in the analysis of local pharmacokinetics

The dispersion model has been widely used to analyze local pharmacokinetics in the organs and the tissues since the 1980's. However, an ambiguity stil l remains in selecting the boundary conditions which are necessary to solve the basic equation of the model. In this note, theoretical considerations are given to this problem and we present here some deficiencies of the mixe d boundary conditions. It seems that theoretical confusion exists in the li terature for the mixed boundary conditions. It is well-known that the solut ion of the dispersion model with a bolus input is the inverse Gaussian dist ribution for the mixed boundary conditions. However, it is rarely recognize d that the inverse Gaussian distribution requires an open boundary at eithe r the inlet or the outlet. For the analysis of local pharmacokinetics, the use of the classical Danckwerts for closed). boundary conditions is recomme nded.