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Analysis of a mathematical model for brain lactate kinetics

1. Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, Equipe DACTIM-MIS, CHU de Poitiers, 2 Rue de la Milétrie, F-86021 Poitiers, France
2. Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, Equipe DACTIM-MIS, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France

The aim of this article is to study the well-posedness and properties of a fast-slow system which is related with brain lactate kinetics. In particular, we prove the existence and uniqueness of nonnegative solutions and obtain linear stability results. We also give numerical simulations with different values of the small parameter $\varepsilon$ and compare them with experimental data.

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Keywords Brain lactate kinetics; fast-slow system; regularity; well-posedness; linear stability; limit system; simulations; in vivo data

Citation: Carole Guillevin, Rémy Guillevin, Alain Miranville, Angélique Perrillat-Mercerot. Analysis of a mathematical model for brain lactate kinetics. Mathematical Biosciences and Engineering, 2018, 15(5): 1225-1242. doi: 10.3934/mbe.2018056


  • [1] A. Aubert,R. Costalat, Interaction between astrocytes and neurons studied using a mathematical model of compartmentalized energy metabolism, Journal of Cerebral Blood Flow & Metabolism, 25 (2005): 1476-1490.
  • [2] A. Aubert,R. Costalat,P. Magistretti,J. Pierre,L. Pellerin, Brain lactate kinetics: modeling evidence for neuronal lactate uptake upon activation, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005): 16448-16453.
  • [3] M. Cloutier,F. B. Bolger,J. P. Lowry,P. Wellstead, An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements, Journal of Computational Neuroscience, 27 (2009): 391-414.
  • [4] R. Costalat,J.-P. Françoise,C. Menuel,M. Lahutte,J.-N. Vallée,G. De Marco,J. Chiras,R. Guillevin, Mathematical modeling of metabolism and hemodynamics, Acta Biotheoretica, 60 (2012): 99-107.
  • [5] C. E. Griguer,C. R. Oliva,G. Y. Gillespie, Glucose metabolism heterogeneity in human and mouse malignant glioma cell lines, Journal of Neuro-oncology, 74 (2005): 123-133.
  • [6] R. Guillevin,C. Menuel,J.-N. Vallée,J.-P. Françoise,L. Capelle,C. Habas,G. De Marco,J. Chiras,R. Costalat, Mathematical modeling of energy metabolism and hemodynamics of WHO grade Ⅱ gliomas using in vivo MR data, Comptes rendus biologies, 334 (2011): 31-38.
  • [7] M. Lahutte-Auboin, R. Costalat, J.-P. Françoise, R. Guillevin, Dip and Buffering in a fast-slow system associated to Brain Lactacte Kinetics, preprint, arXiv: 1308.0486.
  • [8] M. Lahutte-Auboin,R. Guillevin,J.-P. Françoise,J.-N. Vallée,R. Costalat, On a minimal model for hemodynamics and metabolism of lactate : application to low grade glioma and therapeutic strategies, Acta Biotheoretica, 61 (2013): 79-89.
  • [9] P. J. Magistretti,I. Allaman, A cellular perspective on brain energy metabolism and functional imaging, Neuron, 86 (2015): 883-901.
  • [10] S. Mangia,G. Garreffa,M. Bianciardi,F. Giove,F. Di Salle,B. Maraviglia, The aerobic brain: Lactate decrease at the onset of neural activity, Neuroscience, 118 (2003): 7-10.
  • [11] J. R. Mangiardi,P. Yodice, Metabolism of the malignant astrocytoma, Neurosurgery, 26 (1990): 1-19.


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  • 3. Angélique Perrillat-Mercerot, Nicolas Bourmeyster, Carole Guillevin, Alain Miranville, Rémy Guillevin, Mathematical Modeling of Substrates Fluxes and Tumor Growth in the Brain, Acta Biotheoretica, 2019, 10.1007/s10441-019-09343-1
  • 4. A. Perrillat-Mercerot, C. Guillevin, A. Miranville, R. Guillevin, Using mathematics in MRI data management for glioma assesment, Journal of Neuroradiology, 2019, 10.1016/j.neurad.2019.11.004
  • 5. Lu Li, Alain Miranville, Rémy Guillevin, Cahn–Hilliard Models for Glial Cells, Applied Mathematics & Optimization, 2020, 10.1007/s00245-020-09696-x

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