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. Content Type Journal Article Category Regular Article Pages 1-9 DOI 10.1007/s10441-012-9157-1 Authors R. Costalat, UPMC, UMI 209, UMMISCO, University of Paris-6, 75005 Paris, France J.-P. Francoise, Laboratoire Jacques–Louis Lions, UMR (...) 7598 CNRS, Université P.-M. Curie, Paris 6, 4 Pl. Jussieu, 16-26, 75252 Paris, France C. Menuel, Inserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie, Paris 6, 4783, boulevard de l’Hôpital, 75651 Paris Cedex 13, France M. Lahutte, Hopital des Armées, Val-de-Grâce, Service de Radiologie, 74 Bd de Port-Royal, 75005 Paris, France J.-N. Vallée, Department of Neuroradiology, Amiens University Medical Center, University of Picardie-Jules Vernes, chemin du Thil, 80025 Amiens, France G. de Marco, Laboratoire contrôle moteur et mouvement, UFR STAPS, Paris X, 200, avenue de la République, 92001 Nanterre, France J. Chiras, Inserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie, Paris 6, 4783, boulevard de l’Hôpital, 75651 Paris Cedex 13, France R. Guillevin, Inserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie, Paris 6, 4783, boulevard de l’Hôpital, 75651 Paris Cedex 13, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)
Abstract This article revisits a reduced model of cardiac electro-physiology which was proposed to understand the genesis of unidirectional block pathology and of ectopic foci. We underline some specificities of the model from the viewpoint of dynamical systems and bifurcation theory. We point out that essentially the same properties are shared by a simpler system more accessible to analysis. With this simpler system, it becomes possible to give a new presentation of the phenomenon in a phase plane with time moving (...) slow manifolds. This presentation can be of interest both for cardiac electro-physiologists and for mathematicians. Content Type Journal Article Category Regular Article Pages 1-7 DOI 10.1007/s10441-012-9158-0 Authors L. El Alaoui, Université Paris 13, C.N.R.S., U.M.R. 7539, L.A.G.A, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France J.-P. Francoise, Laboratoire Jacques-Louis Lions, UMR 7598 CNRS, Université P.-M. Curie, Paris 6, 4 Place Jussieu, 75252 Paris, France M. Landau, Laboratoire Jacques-Louis Lions, UMR 7598 CNRS, Université P.-M. Curie, Paris 6, 4 Place Jussieu, 75252 Paris, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)
This article describes new aspects of hysteresis dynamics which have been uncovered through computer experiments. There are several motivations to be interested in fast-slow dynamics. For instance, many physiological or biological systems display different time scales. The bursting oscillations which can be observed in neurons, β-cells of the pancreas and population dynamics are essentially studied via bifurcation theory and analysis of fast-slow systems (Keener and Sneyd, 1998; Rinzel, 1987). Hysteresis is a possible mechanism to generate bursting oscillations. A first part (...) of this article presents the computer techniques (the dotted-phase portrait, the bifurcation of the fast dynamics and the wave form) we have used to represent several patterns specific to hysteresis dynamics. This framework yields a natural generalization to the notion of bursting oscillations where, for instance, the active phase is chaotic and alternates with a quiescent phase. In a second part of the article, we emphasize the evolution to chaos which is often associated with bursting oscillations on the specific example of the Hindmarsh–Rose system. This evolution to chaos has already been studied with classical tools of dynamical systems but we give here numerical evidence on hysteresis dynamics and on some aspects of the wave form. The analytical proofs will be given elsewhere. (shrink)
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 1 H/ 31 P. 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 equations bring to light the parameters that push glioma cells out of their domain of viability. Four fundamental factors are highlighted. The first two are cerebral blood flow and the rate of lactate transport through monocarboxylate transporters, which must be reduced in order to push glioma out of its domain of viability. Another factor is the intra arterial lactate, which must be increased. The last factor is pH, indeed a decrease of intra cellular pH could interfere with glioma growth. These reflections suggest that these four parameters could lead to new therapeutic strategies for the management of low grade gliomas. (shrink)
: Françoise Dastur describes her efforts to practice history of philosophy in a (paradoxically) non-historical fashion. She discusses her concept of the historical, and argues that the only true way to be of one's time is to be against one's time.
Françoise Dastur describes her efforts to practice history of philosophy in a (paradoxically) non-historical fashion. She discusses her concept of the historical, and argues that the only true way to be of one's time is to be against one's time.
Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with (...) its main contributors: Archimedes, Cavalieri, Wallis, Hobbes, Pascal, Huygens, Bernoulli, and Nieuwentijt. Many of us know and probably have used the Leibnizian formula: to .. (shrink)
Dans cet ouvrage de 430 pages – dont neuf consacrées à un index des auteurs anciens et modernes – Geneviève Clerico, Bernard Colombat et Jean Soubiran ont réuni 22 textes écrits par Françoise Desbordes de 1981 à 2000 et généralement publiés antérieurement dans des revues scientifiques ou actes de colloques. Ces études ne concernent pas la rhétorique, domaine privilégié de l’activité scientifique de F.D., ni les analyses textuelles, les contributions de F.D. à ces disciplines ayant fait l’obje..
Le livre de F. Doro-Mégy (ci-après FDM) se fonde sur ses travaux de doctorat. Il s’agit d’un numéro spécial de la collection Linguistique contrastive et traduction dirigée par J. Guillemin-Flescher aux éditions Ophrys. Il est dédié à la mémoire de C. Bernigaud. Dans l’introduction, FDM expose son sujet et les limites de ce dernier. Elle part de l’idée intuitive selon laquelle think serait l’équivalent du français penser tandis que believe correspondrait presque systématiquement à croire. San..