### A closed form solution of convective mass transfer model for intracellular calcium response of endothelial cells.

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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....

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 model of tumor growth in a spatial environment is analyzed. The model includes proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes of increasingly proliferative aggressiveness. The model incorporates spatial dependence due to both random motility and directed movement haptotaxis. The model structures tumor cells by both cell age and cell size. The model consists of a system of nonlinear partial differential equations for the compartments of...

Recently, adult stem cells have become a focus of intensive biomedical research, but the complex regulation that allows a small population of stem cells to replenish depleted tissues is still unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that a feedback control of stem cells on their own proliferation and differentiation (denoted Quorum Sensing) suffices...

We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-time convergence. The main difficulty comes from natural degeneracy of birth terms that we overcome with a regularization technique. We then extend the results to the case with several parameters and recall the link between this...

Many cancer-associated genes and pathways remain to be identified in order to clarify the molecular mechanisms underlying cancer progression. In this area, genome-wide loss-of-function screens appear to be powerful biological tools, allowing the accumulation of large amounts of data. However, this approach currently lacks analytical tools to exploit the data with maximum efficiency, for which systems biology methods analyzing complex cellular networks...

A hybrid model of red blood cell production, where cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models, is proposed. Spatial organization and regulation of red blood cell production (erythropoiesis) are investigated. Normal erythropoiesis is simulated in two dimensions, and the influence on the output of the model of some parameters involved in cell...

We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takes into account a finite number of stages in blood production, characterized by cell maturity levels, which enhance the difference, in the hematopoiesis process, between dividing cells that differentiate (by going to the next stage) and dividing cells that keep the same maturity level (by staying in the same stage). It is described by a system of n nonlinear differential equations with n delays. We study...

Mathematical models of tumour spheroids, proposed since the early seventies, have been generally formulated in terms of a single diffusive nutrient which is critical for cell replication and cell viability. Only recently, attempts have been made to incorporate in the models the cell energy metabolism, by considering the interplay between glucose, oxygen and lactate (or pH). By assuming glucose and lactate as the only fuel substrates, we propose a simple model for the cell ATP production which takes...

Cancer has recently overtaken heart disease as the world’s biggest killer. Cancer is initiated by gene mutations that result in local proliferation of abnormal cells and their migration to other parts of the human body, a process called metastasis. The metastasized cancer cells then interfere with the normal functions of the body, eventually leading to death. There are two hundred types of cancer, classified by their point of origin. Most of them...