Steady-state volume of distribution of two-compartment models with simultaneous linear and saturated elimination

The model-independent estimation of physiological steady-state volume of distribution ([Formula: see text]), often referred to non-compartmental analysis (NCA), is historically based on the linear compartment model structure with central elimination. However the NCA-based steady-state volume of distribution ([Formula: see text]) cannot be generalized to more complex models. In the current paper, two-compartment models with simultaneous first-order and Michaelis-Menten elimination are considered. In particular, two indistinguishable models [Formula: see text] and [Formula: see text], both having central Michaelis-Menten elimination, while first-order elimination exclusively either from central or peripheral compartment, are studied. The model-based expressions of the steady-state volumes of distribution [Formula: see text] and their relationships to NCA-based [Formula: see text] are derived. The impact of non-linearity and peripheral elimination is explicitly delineated in the formulas. Being concerned with model identifiability and indistinguishability issues, an interval estimate of [Formula: see text] is suggested.