Acta Biotheoretica

, Volume 67, Issue 2, pp 149–175 | Cite as

Mathematical Modeling of Substrates Fluxes and Tumor Growth in the Brain

  • Angélique Perrillat-Mercerot
  • Nicolas Bourmeyster
  • Carole Guillevin
  • Alain MiranvilleEmail author
  • Rémy Guillevin
Regular Article


The aim of this article is to show how a tumor can modify energy substrates fluxes in the brain to support its own growth. To address this question we use a modeling approach to explain brain nutrient kinetics. In particular we set up a system of 17 equations for oxygen, lactate, glucose concentrations and cells number in the brain. We prove the existence and uniqueness of nonnegative solutions and give bounds on the solutions. We also provide numerical simulations.


Brain lactate kinetics Fast–slow system Well-posedness Regularity Simulations Glioma ANLS Lactate Brain energy substrates 

Mathematics Subject Classification

34A34 35B09 35Q92 



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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratoire Signalisation et Transports Ioniques Membranaires, ERL CNRS 7003, Equipe 4CSUniversité de PoitiersPoitiersFrance
  2. 2.Laboratoire de Mathématiques et Applications, UMR CNRS 7348, SP2MI, Equipe DACTIM-MISUniversité de PoitiersChasseneuil Futuroscope CedexFrance
  3. 3.CHU de PoitiersPoitiersFrance

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