title: On the transformation of compartmental systems and the indeterminacy of the volume of distribution.
abstract: A general compartmental system with multiple-point elimination is transformable to a single-point elimination system. Transformation is achieved by a similarity transformation of the rate constant matrix, A, with a diagonal matrix, D. The elements of D (1, d1, d2,...) are equivalent to the "first-pass" effect between compartments and compartment 1. Application of the derived transformation demonstrates that the volume of distribution as defined by the normalized first-moment function is a minimal volume of distribution when there is no "first-pass" effect between the drug input compartment and the observation compartment. In all other cases, the volume of distribution is a meaningless metric since it may be a minimal or maximal metric and the exact status is indeterminate. Theorems on the non-negativity of the elements of (-A)-1 are derived.
authors.affiliation: Department of Pharmaceutics, Faculty of Pharmaceutical Sciences, Sunderland Polytechnic, Tyne & Wear, U.K.
authors.forename: D P
authors.initials: DP
authors.lastname: Vaughan
mesh_terms: D002626:Chemistry, Pharmaceutical; D008954:Models, Biological; D010599:Pharmacokinetics