Mathematical Modeling of Substrates Fluxes and Tumor Growth in the Brain

Perrillat-Mercerot, Angélique; Bourmeyster, Nicolas; Guillevin, Carole; Miranville, Alain; Guillevin, Rémy

doi:10.1007/s10441-019-09343-1

Cited by 8 publications

(8 citation statements)

References 26 publications

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“…To be more realistic, the parameters α and β can depend on the oxygen concentration or other nutrient concentrations [83,104]. Other compartments can be considered such as necrotic phase coming from quiescent phase with a lower oxygen level or invasive phase with a diffusion term.…”

Section: Cell Heterogeneitymentioning

confidence: 99%

“…When a glioma forms, it first received nutrient from the existing vessels and capillaries changing the first distribution plan. To understand nutritive changes in the brain when a glioma grows, Aubert, Costalat, Jolivet, Guillevin and coworkers proposed systems based on nonlinear ODEs focused on glucose, lactate and oxygen dynamics [13,68,56,104]. Their models also take into account energy creation, mitochondrial respiration, calcium or potassium and the venous balloon.…”

Section: The Volume Occupied By Nutrients and Enzymes Is Boundedmentioning

confidence: 99%

“…In particular nuclear magnetic resonance spectroscopy (MRS) may help to know the glioma mixture evolution. Therefore, coupled with modeling, it can describe or predict glioma behavior evolution [56,104].…”

Section: 5mentioning

confidence: 99%

See 2 more Smart Citations

What mathematical models can or cannot do in glioma description and understanding

Perrillat-Mercerot¹,

Miranville²,

Bourmeyster³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

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Our aim in this article is not to provide a review of the existing literature but to make a critical analysis on glioma behavior mathematical modeling. We present here mathematical modeling history, interests, modalities and limitations on the study of glioma growth. We also make a point on model consideration according to glioma comportments. We finally introduce medical imaging coupled with in silico models as the next step in glioma research. We do not claim completeness of the bibliography but we tried to cover a large amount of mathematical considerations for glioma behavior illustrated with selected representative papers.

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Section: Cell Heterogeneitymentioning

confidence: 99%

Section: The Volume Occupied By Nutrients and Enzymes Is Boundedmentioning

confidence: 99%

See 1 more Smart Citation

What mathematical models can or cannot do in glioma description and understanding

Perrillat-Mercerot¹,

Miranville²,

Bourmeyster³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

Self Cite

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“…The tumor aggregate has simply no clear perimeters and it covers up region inside the cranial cavity [12]. Plenty of analysts analyzed heterogeneous malignancy cell relationships through the growth mass by using many game theoretic [13] strategies which includes traditional ordinary type games, replicator characteristics, as well as, spatial games.…”

Section: Introductionmentioning

confidence: 99%

Development and Porting Of Mathematical Model to Design a PixTra Algorithm for Detection of Brain Tumor

Khalate,

Basotia,

Ghule

2019

IJEAT

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The goal of applied mathematics is to develop and implement the automated systems, services and support to execute engineering goals. Game theory is always a domain of choice for development of strategy to enhance the usability of mathematical applications. Today, there is rarely any system which works without keeping mathematics behind the curtain. A recent trend in medical imaging leads via mathematical algorithmic development for brain tumor analysis. The deep learning technology is a mathematical strategic solution to identify the brain tumor from medical resonance imaging. The game theory strategic development is necessary for mathematical modeling of image technologies as pixel level calculations are required. Hence, this paper shows the newly developed mathematical modeling for efficient brain tumor detection using game theory and set theory. This paper also suggests the new algorithm which is ported from mathematical modeling for deep learning brain tumor image processing.

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“…In particular, among the nutrients, we focus here on the lactate production, consumption and transport in the brain when a glioma occurs. Therefore we address a model proposed by [1] and [6] (see also [8]) to describe at the same time the evolution of the tumor cell density u and the lactate concentrations in the intracellular and in the capillary domains, respectively, ϕ and ψ.…”

mentioning

confidence: 99%

Analysis of a model for tumor growth and lactate exchanges in a glioma

Cherfils¹,

Gatti²,

Miranville³

et al. 2021

DCDS-S

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Our aim in this paper is to study a mathematical model for tumor growth and lactate exchanges in a glioma. We prove the existence of nonnegative (i.e. biologically relevant) solutions and, under proper assumptions, the uniqueness of the solution. We also state the permanence of the tumor when necrosis is not taken into account in the model and obtain linear stability results. We end the paper with numerical simulations.

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Mathematical Modeling of Substrates Fluxes and Tumor Growth in the Brain

Cited by 8 publications

References 26 publications

What mathematical models can or cannot do in glioma description and understanding

What mathematical models can or cannot do in glioma description and understanding

Development and Porting Of Mathematical Model to Design a PixTra Algorithm for Detection of Brain Tumor

Analysis of a model for tumor growth and lactate exchanges in a glioma

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