4,455 research outputs found
Mathematical modeling of the metastatic process
Mathematical modeling in cancer has been growing in popularity and impact
since its inception in 1932. The first theoretical mathematical modeling in
cancer research was focused on understanding tumor growth laws and has grown to
include the competition between healthy and normal tissue, carcinogenesis,
therapy and metastasis. It is the latter topic, metastasis, on which we will
focus this short review, specifically discussing various computational and
mathematical models of different portions of the metastatic process, including:
the emergence of the metastatic phenotype, the timing and size distribution of
metastases, the factors that influence the dormancy of micrometastases and
patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie
A Review of Mathematical Models for the Formation of\ud Vascular Networks
Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud
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A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features
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Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations
We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated
Mathematical models for chemotaxis and their applications in self-organisation phenomena
Chemotaxis is a fundamental guidance mechanism of cells and organisms,
responsible for attracting microbes to food, embryonic cells into developing
tissues, immune cells to infection sites, animals towards potential mates, and
mathematicians into biology. The Patlak-Keller-Segel (PKS) system forms part of
the bedrock of mathematical biology, a go-to-choice for modellers and analysts
alike. For the former it is simple yet recapitulates numerous phenomena; the
latter are attracted to these rich dynamics. Here I review the adoption of PKS
systems when explaining self-organisation processes. I consider their
foundation, returning to the initial efforts of Patlak and Keller and Segel,
and briefly describe their patterning properties. Applications of PKS systems
are considered in their diverse areas, including microbiology, development,
immunology, cancer, ecology and crime. In each case a historical perspective is
provided on the evidence for chemotactic behaviour, followed by a review of
modelling efforts; a compendium of the models is included as an Appendix.
Finally, a half-serious/half-tongue-in-cheek model is developed to explain how
cliques form in academia. Assumptions in which scholars alter their research
line according to available problems leads to clustering of academics and the
formation of "hot" research topics.Comment: 35 pages, 8 figures, Submitted to Journal of Theoretical Biolog
Mathematical modelling plant signalling networks
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This sub-cellular analysis paves the way for more comprehensive mathematical studies of hormonal transport and signalling in a multi-scale setting
On the foundations of cancer modelling: selected topics, speculations, & perspectives
This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution
A Half-Century Research Footpath in Statistical Physics
We give an abridged account of a continued string of studies in condensed
matter physics and in complex systems that span five decades. We provide links
to access abstracts and full texts of a selected list of publications. The
studies were carried out within a framework of methods and models, some
developed in situ, of stochastic processes, statistical mechanics and nonlinear
dynamics. The topics, techniques and outcomes reflect evolving interests of the
community but also show a particular character that privileges the use of
analogies or unusual viewpoints that unite the studies in distinctive ways. The
studies have been grouped into thirty sets and these, in turn, placed into
three collections according to the main underlying approach: stochastic
processes, density functional theory, and nonlinear dynamics. We discuss the
body of knowledge created by these research lines in relation to theoretical
foundations and spread of subjects. We indicate unsuspected connections
underlying different aspects of these investigations and also point out both
natural and unanticipated perspectives for future developments. Finally, we
refer to our most important and recent contribution: An answer with a firm
basis to the long standing question about the limit of validity of ordinary
statistical mechanics and the pertinence of Tsallis statistics
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