Regular Article

Acta Biotheoretica

, Volume 60, Issue 1, pp 99-107

First online:

Mathematical Modeling of Metabolism and Hemodynamics

  • R. CostalatAffiliated withUPMC, UMI 209, UMMISCO, University of Paris-6IRD, UMI 209, UMMISCO
  • , J.-P. FrancoiseAffiliated withLaboratoire Jacques–Louis Lions, UMR 7598 CNRS, Université P.-M. Curie, Paris 6 Email author 
  • , C. MenuelAffiliated withInserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie
  • , M. LahutteAffiliated withHopital des Armées, Val-de-Grâce, Service de Radiologie
  • , J.-N. ValléeAffiliated withDepartment of Neuroradiology, Amiens University Medical Center, University of Picardie-Jules Vernes
  • , G. de MarcoAffiliated withLaboratoire contrôle moteur et mouvement, UFR STAPS
  • , J. ChirasAffiliated withInserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie
  • , R. GuillevinAffiliated withInserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie

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Abstract

We provide a mathematical study of a model of energy metabolism and hemodynamics of glioma allowing a better understanding of metabolic modifications leading to anaplastic transformation from low grade glioma.This mathematical analysis allows ultimately to unveil the solution to a viability problem which seems quite pertinent for applications to medecine.

Keywords

Magnetic resonance spectroscopy Multinuclear spectroscopy Regional cerebral blood flow Differential equation Viability Slow-fast dynamics

Mathematics Subject Classification

34C05 34A34 34C14