Acta Biotheoretica

, Volume 60, Issue 1–2, pp 99–107 | Cite as

Mathematical Modeling of Metabolism and Hemodynamics

  • R. Costalat
  • J.-P. Francoise
  • C. Menuel
  • M. Lahutte
  • J.-N. Vallée
  • G. de Marco
  • J. Chiras
  • R. Guillevin
Regular Article

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 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • R. Costalat
    • 1
    • 2
  • J.-P. Francoise
    • 3
  • C. Menuel
    • 4
  • M. Lahutte
    • 5
  • J.-N. Vallée
    • 6
  • G. de Marco
    • 7
  • J. Chiras
    • 4
  • R. Guillevin
    • 4
  1. 1.UPMC, UMI 209, UMMISCOUniversity of Paris-6ParisFrance
  2. 2.IRD, UMI 209 UMMISCOBondy CedexFrance
  3. 3.Laboratoire Jacques–Louis Lions, UMR 7598 CNRSUniversité P.-M. Curie, Paris 6ParisFrance
  4. 4.Inserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière HospitalUniversité P.-M. CurieParis Cedex 13France
  5. 5.Hopital des Armées, Val-de-GrâceService de RadiologieParisFrance
  6. 6.Department of Neuroradiology, Amiens University Medical CenterUniversity of Picardie-Jules VernesAmiensFrance
  7. 7.Laboratoire contrôle moteur et mouvement UFR STAPSNanterreFrance

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