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Modeling Spatial Effects in Early Carcinogenesis : Stochastic Versus Deterministic Reaction-Diffusion Systems

R. Bertolusso, M. Kimmel (2012)

Mathematical Modelling of Natural Phenomena

We consider the early carcinogenesis model originally proposed as a deterministic reaction-diffusion system. The model has been conceived to explore the spatial effects stemming from growth regulation of pre-cancerous cells by diffusing growth factor molecules. The model exhibited Turing instability producing transient spatial spikes in cell density, which might be considered a model counterpart of emerging foci of malignant cells. However, the process...

Modeling the Cancer Stem Cell Hypothesis

C. Calmelet, A. Prokop, J. Mensah, L. J. McCawley, P. S. Crooke (2010)

Mathematical Modelling of Natural Phenomena

Solid tumors and hematological cancers contain small population of tumor cells that are believed to play a critical role in the development and progression of the disease. These cells, named Cancer Stem Cells (CSCs), have been found in leukemia, myeloma, breast, prostate, pancreas, colon, brain and lung cancers. It is also thought that CSCs drive the metastatic spread of cancer. The CSC compartment features a specific and phenotypically defined cell...

Modeling the Dynamics of the Cardiovascular-respiratory System (CVRS) in Humans, a Survey

F. Kappel (2012)

Mathematical Modelling of Natural Phenomena

In this paper we give a survey on modeling efforts concerning the CVRS. The material we discuss is organized in accordance with modeling goals and stresses control and transport issues. We also address basic modeling approaches and discuss some of the challenges for mathematical modeling methodologies in the context of parameter estimation and model validation.

Modeling the Impact of Anticancer Agents on Metastatic Spreading

S. Benzekry, N. André, A. Benabdallah, J. Ciccolini, C. Faivre, F. Hubert, D. Barbolosi (2012)

Mathematical Modelling of Natural Phenomena

Treating cancer patients with metastatic disease remains an ultimate challenge in clinical oncology. Because invasive cancer precludes or limits the use of surgery, metastatic setting is often associated with (poor) survival, rather than sustained remission, in patients with common cancers like lung, digestive or breast carcinomas. Mathematical modeling may help us better identify non detectable metastatic status to in turn optimize treatment for...

Modeling the role of constant and time varying recycling delay on an ecological food chain

Banibrata Mukhopadhyay, Rakhi Bhattacharyya (2010)

Applications of Mathematics

We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the...

Modelli matematici a sostegno della ricerca contro il cancro

L. Preziosi (2005)

Bollettino dell'Unione Matematica Italiana

Questo articolo, a prevalente carattere di rassegna, ha lo scopo di presentare gli ambiti matematici e gli approcci metodologici utilizzati nello sviluppo di modelli matematici a sostegno della ricerca contro il cancro. La necessità di un approccio interdisciplinare e multiscala è messo in evidenza. Infine, alcuni modelli operanti alla scala macroscopica e mesoscopica sono presentati a titolo di esempio.

Modelling and Mathematical Analysis of the Glass Eel Migration in the Adour River Estuary

M. Odunlami, G. Vallet (2012)

Mathematical Modelling of Natural Phenomena

In this paper we are interested in a mathematical model of migration of grass eels in an estuary. We first revisit a previous model proposed by O. Arino and based on a degenerate convection-diffusion equation of parabolic-hyperbolic type with time-varying subdomains. Then, we propose an adapted mathematical framework for this model, we prove a result of existence of a weak solution and we propose some numerical simulations.

Modelling Circadian Rhythms in Drosophila and Investigation of VRI and PDP1 Feedback Loops Using a New Mathematical Model

D. Kulasiri, Z. Xie (2008)

Mathematical Modelling of Natural Phenomena

We present a brief review of molecular biological basis and mathematical modelling of circadian rhythms in Drosophila. We discuss pertinent aspects of a new model that incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not used to describe the regulation of genes, instead the explicit reactions of binding and unbinding processes of transcription factors to promoters are probabilistically...

Modelling DNA and RNA secondary structures using matrix insertion-deletion systems

Lakshmanan Kuppusamy, Anand Mahendran (2016)

International Journal of Applied Mathematics and Computer Science

Insertion and deletion are operations that occur commonly in DNA processing and RNA editing. Since biological macromolecules can be viewed as symbols, gene sequences can be represented as strings and structures can be interpreted as languages. This suggests that the bio-molecular structures that occur at different levels can be theoretically studied by formal languages. In the literature, there is no unique grammar formalism that captures various bio-molecular structures. To overcome this deficiency,...

Modelling Evolution of Regulatory Networks in Artificial Bacteria

Y. Sanchez-Dehesa, D. Parsons, J. M. Peña, G. Beslon (2008)

Mathematical Modelling of Natural Phenomena

Studying the evolutive and adaptative machanisms of prokayotes is a complicated task. As these machanisms cannot be easily studied "in vivo", it is necessary to consider other methods. We have therefore developed the RAevol model, a model designed to study the evolution of bacteria and their adaptationto the environment. Our model simulates the evolution of a population of artificial bacteria in a changing environment, providing us with an insight into the strategies that digital organisms develop...

Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models

A. R.A. Anderson, K. A. Rejniak, P. Gerlee, V. Quaranta (2010)

Mathematical Modelling of Natural Phenomena

Since cancer is a complex phenomenon that incorporates events occurring on different length and time scales, therefore multiscale models are needed if we hope to adequately address cancer specific questions. In this paper we present three different multiscale individual-cell-based models, each motivated by cancer-related problems emerging from each of the spatial scales: extracellular, cellular or subcellular, but also incorporating relevant information from other levels. We apply these hybrid...

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