Representative Sinusoids for Hepatic Four-Scale Pharmacokinetics Simulations

PLoS One. 2015 Jul 29;10(7):e0133653. doi: 10.1371/journal.pone.0133653. eCollection 2015.


The mammalian liver plays a key role for metabolism and detoxification of xenobiotics in the body. The corresponding biochemical processes are typically subject to spatial variations at different length scales. Zonal enzyme expression along sinusoids leads to zonated metabolization already in the healthy state. Pathological states of the liver may involve liver cells affected in a zonated manner or heterogeneously across the whole organ. This spatial heterogeneity, however, cannot be described by most computational models which usually consider the liver as a homogeneous, well-stirred organ. The goal of this article is to present a methodology to extend whole-body pharmacokinetics models by a detailed liver model, combining different modeling approaches from the literature. This approach results in an integrated four-scale model, from single cells via sinusoids and the organ to the whole organism, capable of mechanistically representing metabolization inhomogeneity in livers at different spatial scales. Moreover, the model shows circulatory mixing effects due to a delayed recirculation through the surrounding organism. To show that this approach is generally applicable for different physiological processes, we show three applications as proofs of concept, covering a range of species, compounds, and diseased states: clearance of midazolam in steatotic human livers, clearance of caffeine in mouse livers regenerating from necrosis, and a parameter study on the impact of different cell entities on insulin uptake in mouse livers. The examples illustrate how variations only discernible at the local scale influence substance distribution in the plasma at the whole-body level. In particular, our results show that simultaneously considering variations at all relevant spatial scales may be necessary to understand their impact on observations at the organism scale.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adult
  • Animals
  • Blood Circulation
  • Caffeine / pharmacokinetics
  • Fatty Liver / metabolism
  • Humans
  • Insulin / pharmacokinetics
  • Liver / blood supply
  • Liver / cytology
  • Liver / metabolism*
  • Liver / physiology
  • Male
  • Mice
  • Models, Biological*
  • Pharmacokinetics*
  • Regeneration


  • Insulin
  • Caffeine

Grant support

This work was supported by the German Ministry of Education and Research (BMBF) via the systems biology network Virtual Liver (, grant numbers 0315769 (LOS, TP), 0315747 (AS, LK), and 0315766 (CK, JT, MMBR). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Bayer Technology Services provided support in the form of salaries for authors AS and LK, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the “author contributions” section.