7 found
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  1.  7
    Mathematical Modeling of Substrates Fluxes and Tumor Growth in the Brain.Angélique Perrillat-Mercerot, Nicolas Bourmeyster, Carole Guillevin, Alain Miranville & Rémy Guillevin - 2019 - Acta Biotheoretica 67 (2):149-175.
    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.
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  2.  15
    On a Minimal Model for Hemodynamics and Metabolism of Lactate: Application to Low Grade Glioma and Therapeutic Strategies.Marion Lahutte-Auboin, Rémy Guillevin, Jean-Pierre Françoise, Jean-Noël Vallée & Robert Costalat - 2013 - Acta Biotheoretica 61 (1):79-89.
    WHO II low grade glioma evolves inevitably to anaplastic transformation. Magnetic resonance imaging is a good non-invasive way to watch it, by hemodynamic and metabolic modifications, thanks to multinuclear spectroscopy 1H/31P. In this work we study a multi-scale minimal model of hemodynamics and metabolism applied to the study of gliomas. This mathematical analysis leads us to a fast-slow system. The control of the position of the stationary point brings to the concept of domain of viability. Starting from this system, the (...)
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  3.  6
    Interactions Between the Cross-Shore Structure of Small Pelagic Fish Population, Offshore Industrial Fisheries and Near Shore Artisanal Fisheries: A Mathematical Approach.Alain Miranville, Rémy Guillevin, Jean-Pierre Françoise & Hermine Biermé - 2016 - Acta Biotheoretica 64 (4):479-493.
    This work presents a mathematical model describing the interactions between the cross-shore structure of small pelagic fish population an their exploitation by coastal and offshore fisheries. The complete model is a system of seven ODE’s governing three stocks of small pelagic fish population moving and growing between three zones. Two types of fishing fleets are inter-acting with the fish population, industrial boats, constrained to offshore area, and artisanal boats, operating from the shore. Two time scales were considered and we use (...)
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  4.  4
    Effects of Behavioural Strategy on the Exploitative Competition Dynamics.Alain Miranville, Rémy Guillevin, Jean-Pierre Françoise & Hermine Biermé - 2016 - Acta Biotheoretica 64 (4):495-517.
    We investigate a system of two species exploiting a common resource. We consider both abiotic and biotic resources. We are interested in the asymmetric competition where a given consumer is the locally superior resource exploiter and the other is the locally inferior resource exploiter. They also interact directly via interference competition in the sense that LIE individuals can use two opposite strategies to compete with LSE individuals: we assume, in the first case, that LIE uses an avoiding strategy, i.e. LIE (...)
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  5.  4
    Influence of Antithrombin on the Regimes of Blood Coagulation: Insights From the Mathematical Model.Alain Miranville, Rémy Guillevin, Jean-Pierre Françoise & Hermine Biermé - 2016 - Acta Biotheoretica 64 (4):327-342.
    Blood coagulation is regulated through a complex network of biochemical reactions of blood factors. The main acting enzyme is thrombin whose propagation in blood plasma leads to fibrin clot formation. Spontaneous clot formation is normally controlled through the action of different plasma inhibitors, in particular, through the thrombin binding by antithrombin. In the current study we develop a mathematical model of clot formation both in quiescent plasma and in blood flow and determine the analytical conditions on the antithrombin concentration corresponding (...)
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  6.  4
    The Poitiers School of Mathematical and Theoretical Biology: Besson–Gavaudan–Schützenberger’s Conjectures on Genetic Code and RNA Structures.Alain Miranville, Rémy Guillevin, Jean-Pierre Françoise & Hermine Biermé - 2016 - Acta Biotheoretica 64 (4):403-426.
    The French school of theoretical biology has been mainly initiated in Poitiers during the sixties by scientists like J. Besson, G. Bouligand, P. Gavaudan, M. P. Schützenberger and R. Thom, launching many new research domains on the fractal dimension, the combinatorial properties of the genetic code and related amino-acids as well as on the genetic regulation of the biological processes. Presently, the biological science knows that RNA molecules are often involved in the regulation of complex genetic networks as effectors, e.g., (...)
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  7.  3
    Preface.Alain Miranville, Rémy Guillevin, Jean-Pierre Françoise & Hermine Biermé - 2016 - Acta Biotheoretica 64 (4):309-310.