Thymic presentation of autoantigens and the efficiency of negative selection.
Time delays in proliferation and apoptosis for solid avascular tumour
The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the...
Time domain computational modelling of 1D arterial networks in monochorionic placentas
In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/ element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance....
Time domain computational modelling of 1D arterial networks in monochorionic placentas
In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/hp element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance....
Towards a theory of mind.
Towards prediction of HCV therapy efficiency.
Towards Sub-cellular Modeling with Delaunay Triangulation
In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...
Transport Equation Reduction for a Mathematical Model in Plant Growth
In this article a variational reduction method, how to handle the case of heterogenous domains for the Transport equation, is presented. This method allows to get rid of the restrictions on the size of time steps due to the thin parts of the domain. In the thin part of the domain, only a differential problem, with respect to the space variable, is to be approximated numerically. Numerical results are presented with a simple example. The variational...
Transport equations in cell population dynamics. I.
Transport equations in cell population dynamics. II.
Transport in a molecular motor system
Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.
Transport in a molecular motor system
Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.
Tumour angiogenesis model with variable vessels' effectiveness
We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties...
Tumour-induced angiogenesis: a review.
Two periodic solutions of neutral difference equations modelling physiological processes.
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.
Two-fluid mathematical models for blood flow in stenosed arteries: a comparative study.
Typical Atherosclerotic Plaque Morphology
Atherosclerosis always develops in plaques, and the reasons are not clear. We test the hypothesis that plaque morphology results from a self-perpetuating propagating process driven by macrophages (Mphs). A computer model of atherogenesis was written in which the computer screen represents a surface view of a flattened area of an arterial wall on which greatly accelerated atherogenesis is depicted. Rate of Mph recruitment from blood monocytes is set as a steeply rising function of the number of...
Un lien entre réseaux de neurones et systèmes de particules : un modèle de rétinotopie
Unique positive almost periodic solution for discrete nonlinear delay survival red blood cells model.