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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...

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 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 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...

Modelling of Dynamic Problems in Biomechanics

I. Petrov, Y. Bolotskikh, A. Vasyukov (2011)

Mathematical Modelling of Natural Phenomena

This paper is devoted to solving of dynamic problems in biomechanics that require detailed study of fast processes. Numerical method of characteristics is used to model the temporal development of the processes with high accuracy.

Modelling of Plant Growth with Apical or Basal Meristem

N. Bessonov, F. Crauste, V. Volpert (2011)

Mathematical Modelling of Natural Phenomena

Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results...

Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments

J. Clairambault (2009)

Mathematical Modelling of Natural Phenomena

This review aims at presenting a synoptic, if not exhaustive, point of view on some of the problems encountered by biologists and physicians who deal with natural cell proliferation and disruptions of its physiological control in cancer disease. It also aims at suggesting how mathematicians are naturally challenged by these questions and how they might help, not only biologists to deal theoretically with biological complexity, but also physicians to optimise therapeutics, on which last point the...

Currently displaying 61 – 80 of 107