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A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours

M. Pons-Salort, B. van der Sanden, A. Juhem, A. Popov, A. Stéphanou (2012)

Mathematical Modelling of Natural Phenomena

A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs treatment....

A Hybrid Model Describing Different Morphologies of Tumor Invasion Fronts

M. Scianna, L. Preziosi (2012)

Mathematical Modelling of Natural Phenomena

The invasive capability is fundamental in determining the malignancy of a solid tumor. Revealing biomedical strategies that are able to partially decrease cancer invasiveness is therefore an important approach in the treatment of the disease and has given rise to multiple in vitro and in silico models. We here develop a hybrid computational framework, whose aim is to characterize the effects of the different cellular and subcellular mechanisms involved...

A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation

Banibrata Mukhopadhyay, Rakhi Bhattacharyya (2006)

Applications of Mathematics

In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The influence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability...

A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

Roman Cherniha, Joanna Stachowska-Piętka, Jacek Waniewski (2014)

International Journal of Applied Mathematics and Computer Science

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a threecomponent nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations...

A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies

G. Kapitanov (2012)

Mathematical Modelling of Natural Phenomena

There is evidence that cancer develops when cells acquire a sequence of mutations that alter normal cell characteristics. This sequence determines a hierarchy among the cells, based on how many more mutations they need to accumulate in order to become cancerous. When cells divide, they exhibit telomere loss and differentiate, which defines another cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model, which combines...

A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation

Mahiéddine Kouche, Bedr'eddine Ainseba (2010)

International Journal of Applied Mathematics and Computer Science

In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent with the existence...

A mathematical model of inflammation during ischemic stroke

Cristiana Di Russo, Jean-Baptiste Lagaert, Guillemette Chapuisat, Marie-Aimée Dronne (2010)

ESAIM: Proceedings

In this article we propose a model to describe the inflammatory process which occurs during ischemic stroke. First, an introduction to some basic concepts about the biological phenomenon is given. Then, a detailed derivation of the model and the numerical scheme used are presented. Finally, the studies of the model robustness and sensitivity are showed and some numerical results on the time and space evolution of the process are presented and discussed....

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