Kinetic scheme for arterial and venous blood flow, and application to partial hepatectomy modeling

Chloe Audebert*, Petru Bucur, Mohamed Bekheit, Eric Vibert, Irene E. Vignon-Clementel, Jean Frédéric Gerbeau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


The article introduces a kinetic scheme to solve the 1D Euler equations of hemodynamics, and presents comparisons of a closed-loop 1D–0D model with real measurements obtained after the hepatectomy of four pigs. Several benchmark tests show that the kinetic scheme compares well with more standard schemes used in the literature, for both arterial and venous wall laws. In particular, it is shown that it has a good behavior when the section area of a vessel is close to zero, which is an important property for collapsible or clamped vessels. The application to liver surgery shows that a model of the global circulation, including 0D and 1D equations, is able to reproduce the change of waveforms observed after different levels of hepatectomy. This may contribute to a better understanding of the change of liver architecture induced by hepatectomy.

Original languageEnglish
Pages (from-to)102-125
Number of pages24
JournalComputer Methods in Applied Mechanics and Engineering
Early online date22 Jul 2016
Publication statusPublished - Feb 2017

Bibliographical note

This material is based upon work supported by the French National Agency for Research ANR-13-TECS-0006 iFLOW. The authors gratefully acknowledge Dr. Damiano Lombardi for assistance with implementation of the 1D models, and Dr. Jacques Sainte-Marie for his expertise in kinetic schemes. The authors are grateful to the INRA Plateforme CIRE (Nouzilly, France) staff for their technical assistance in surgeries and imaging, and to Mylène Wartenberg for assistance in taking measurements.


  • Arterial flow
  • Kinetic scheme
  • Surgery simulation
  • Venous flow
  • Vessel collapse


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