Continuous macroscopic limit of a discrete stochastic model for interaction of living cells

In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded volume is derived, describing cells moving in a medium and reacting to each other through both direct contact and long range chemotaxis. The continuous macroscopic model is obtained as a Fokker-Planck equation describing evolution of the cell probability density function. All coefficients of the general macroscopic model are derived from parameters of the CPM and a very good agreement is demonstrated between CPM Monte Carlo simulations and numerical solution of the macroscopic model. It is also shown that in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. General multiscale approach is demonstrated by simulating spongy bone formation from loosely packed mesenchyme via the intramembranous route suggesting that self-organizing physical mechanisms can account for this developmental process.Comment: 4 pages, 3 figure

Tsallis entropy approach to radiotherapy treatments

The biological effect of one single radiation dose on a living tissue has been described by several radiobiological models. However, the fractionated radiotherapy requires to account for a new magnitude: time. In this paper we explore the biological consequences posed by the mathematical prolongation of a model to fractionated treatment. Nonextensive composition rules are introduced to obtain the survival fraction and equivalent physical dose in terms of a time dependent factor describing the tissue trend towards recovering its radioresistance (a kind of repair coefficient). Interesting (known and new) behaviors are described regarding the effectiveness of the treatment which is shown to be fundamentally bound to this factor. The continuous limit, applicable to brachytherapy, is also analyzed in the framework of nonextensive calculus. Also here a coefficient arises that rules the time behavior. All the results are discussed in terms of the clinical evidence and their major implications are highlighted.Comment: 6 figures, accepted for publication to Physica

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Effect of Catalyst Layer and Fuel Utilization on the Durability of Direct Methane SOFC

International audienceSolid oxide fuels cells with and without anodic catalytic layer and specific anodic current collectors were developed in order to be fueled by dry methane. Due to the cell architecture integrating a 0.1wt% Ir-CGO catalyst layer onto the anode, platinum, gold and cupper screen-printed meshes were designed and optimized to ensure efficient current collection between the anode surface and the catalyst membrane. Current density and ageing in H2 and in pure dry CH4 respectively were compared to conventional pressed grid collecting systems. Similar performances were achieved using bulk grids or gold, platinum and copper screen-printed meshes. Operation in pure dry methane is compared with and without the catalytic layer as a function of the fuel utilization. It is demonstrated that long term operation is possible provided that sufficient faradic efficiency is achieved