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Mathematical and Computational Models in Tumor Immunology

F. Pappalardo, A. Palladini, M. Pennisi, F. Castiglione, S. Motta (2012)

Mathematical Modelling of Natural Phenomena

The immune system is able to protect the host from tumor onset, and immune deficiencies are accompanied by an increased risk of cancer. Immunology is one of the fields in biology where the role of computational and mathematical modeling and analysis were recognized the earliest, beginning from 60s of the last century. We introduce the two most common methods in simulating the competition among the immune system, cancers and tumor immunology strategies:...

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

Sébastien Benzekry (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

Sébastien Benzekry (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

Sébastien Benzekry (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...

Mathematical and numerical modeling of early atherosclerotic lesions***

Vincent Calvez, Jean Gabriel Houot, Nicolas Meunier, Annie Raoult, Gabriela Rusnakova (2010)

ESAIM: Proceedings

This article is devoted to the construction of a mathematical model describing the early formation of atherosclerotic lesions. The early stage of atherosclerosis is an inflammatory process that starts with the penetration of low density lipoproteins in the intima and with their oxidation. This phenomenon is closely linked to the local blood flow dynamics. Extending a previous work [5] that was mainly restricted to a one-dimensional setting, we couple...

Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices

Jeehyun Lee, Jin Keun Seo, Eung Je Woo (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Electro-muscular disruption (EMD) devices such as TASER M26 and X26 have been used as a less-than-lethal weapon. Such EMD devices shoot a pair of darts toward an intended target to generate an incapacitating electrical shock. In the use of the EMD device, there have been controversial questions about its safety and effectiveness. To address these questions, we need to investigate the distribution of the current density J inside the target produced by the EMD device. One approach is to develop a computational...

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Sansuke M. Watanabe, Pablo J. Blanco, Raúl A. Feijóo (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model comprises 108 arterial segments, with 64 main arteries...

Mathematical model of mixing in Rumen

Wiesław Szlenk (1996)

Applicationes Mathematicae

A mathematical model of mixing food in rumen is presented. The model is based on the idea of the Baker Transformation, but exhibits some different phenomena: the transformation does not mix points at all in some parts of the phase space (and under some conditions mixes them strongly in other parts), as observed in ruminant animals.

Mathematical model of tumour cord growth along the source of nutrient

S. Astanin, A. Tosin (2010)

Mathematical Modelling of Natural Phenomena

A mathematical model of the tumour growth along a blood vessel is proposed. The model employs the mixture theory approach to describe a tissue which consists of cells, extracellular matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is paid to consistent description of oxygen consumption and growth processes based on the energy balance. A finite difference numerical...

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