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Analysis of the Growth Control Network Specific for Human Lung Adenocarcinoma Cells

G. Pinna, A. Zinovyev, N. Araujo, N. Morozova, A. Harel-Bellan (2012)

Mathematical Modelling of Natural Phenomena

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...

Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis

D.P. Moualeu, S. Bowong, J.J. Tewa, Y. Emvudu (2012)

Mathematical Modelling of Natural Phenomena

Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is diabetes (DM), which is predicted to increase dramatically over the next two decades, particularly in low and middle income countries, where TB is widespread. This study aimed to assess the strength of the association between TB and DM. We present a deterministic model for TB in a community in order to determine the impact of DM in the spread of the disease....

Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth

Jan Poleszczuk, Urszula Foryś (2009)

Applicationes Mathematicae

We propose two models of vessel impairment in the process of tumour angiogenesis and we consider three types of treatment: standard chemotherapy, antiangiogenic treatment and a combined treatment. The models are based on the idea of Hahnfeldt et al. that the carrying capacity for any solid tumour depends on its vessel density. In the models proposed the carrying capacity also depends on the process of vessel impairment. In the first model a logistic type equation is used to describe the neoplastic...

Application of coupled neural oscillators for image texture segmentation and modeling of biological rhythms

Paweł Strumiłło, Michał Strzelecki (2006)

International Journal of Applied Mathematics and Computer Science

The role of relaxation oscillator models in application fields such as modeling dynamic systems and image analysis is discussed. A short review of the Van der Pol, Wilson-Cowan and Terman-Wang relaxation oscillators is given. The key property of such nonlinear oscillators, i.e., the oscillator phase shift (called the Phase Response Curve) as a result of external pulse stimuli is indicated as a fundamental mechanism to achieve and sustain synchrony in networks of coupled oscillators. It is noted...

Atherosclerosis Initiation Modeled as an Inflammatory Process

N. El Khatib, S. Génieys, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

In this work we study the inflammatory process resulting in the development of atherosclerosis. We develop a one- and two-dimensional models based on reaction-diffusion systems to describe the set up of a chronic inflammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic inflammatory reaction. Intermediate ox-LDL concentrations...

ATP Production and Necrosis Formation in a Tumour Spheroid Model

A. Bertuzzi, A. Fasano, A. Gandolfi, C. Sinisgalli (2010)

Mathematical Modelling of Natural Phenomena

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...

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