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

  • Xiaotian Wu
  • Fahima NekkaEmail author
  • Jun Li
Original Paper


The model-independent estimation of physiological steady-state volume of distribution (\(V_{dss,p}\)), 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 (\(V_{dss,nca}\)) 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 \(\mathrm{M}_1\) and \(\mathrm{M}_2\), 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 \(V_{dss,\mathrm{M}_i}\,\,(i=1,2)\) and their relationships to NCA-based \(V_{dss,nca}\) 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 \(V_{dss,p}\) is suggested.


Steady-state volume of distribution Simultaneous first-order and Michaelis–Menten elimination Non-compartmental analysis Compartment analysis Indistinguishability 



The research in this work is supported by the NSERC-Industrial Chair in Pharmacometrics—Novartis, Pfizer and Inventiv Health Clinical (FN), NSERC (FN) as well as FRQNT (FN, JL). NSFC (No. 11501358) of P. R. China (XW and JL) and FRQNT (No. 193180) (XW) are also acknowledged for their support.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiPeople’s Republic of China
  2. 2.Faculté de pharmacieUniversité de MontréalMontréalCanada
  3. 3.Centre de recherches mathématiques Université de MontréalMontréalCanada

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