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The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology

H. G. Othmer, K. Painter, D. Umulis, C. Xue (2009)

Mathematical Modelling of Natural Phenomena

We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems – Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns – illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding...

The Language of Caring: Quantitating Medical Practice Patterns using Symbolic Dynamics

J. Paladino, A. M. Kaynar, P. S. Crooke, J. R. Hotchkiss (2010)

Mathematical Modelling of Natural Phenomena

Real-world medical decisions rarely involve binary Ðsole condition present or absent- patterns of patient pathophysiology. Similarly, provider interventions are rarely unitary in nature: the clinician often undertakes multiple interventions simultaneously. Conventional approaches towards complex physiologic derangements and their associated management focus on the frequencies of joint appearances, treating the individual derangements of physiology...

The onset of necrosis in a 3D cellular automaton model of EMT6 multi-cellular spheroids

Simon D. Angus, Monika J. Piotrowska (2010)

Applicationes Mathematicae

A 3-dimensional (3D) extension to a previously reported scaled 2-dimensional Cellular Automaton (CA) model of avascular multi-cellular spheroid growth is presented and analysed for the EMT6/Ro cell line. The model outputs are found to compare favourably with reported experimentally obtained data for in vitro spheroids of the same cell line. Necrosis (unprogrammed central cell death) is observed to be delayed when compared with the experimental data. Furthermore, it is found that necrosis arises...

The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts

A. Szabó, A. Czirók (2010)

Mathematical Modelling of Natural Phenomena

Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated analogy...

The role of Mechanics in Tumor growth : Modelling and Simulation

D. Ambrosi (2011)

ESAIM: Proceedings

A number of biological phenomena are interlaced with classical mechanics. In this review are illustrated two examples from tumor growth, namely the formation of primordial networks of vessels (vasculogenesis) and the avascular phase of solid tumors. In both cases the formalism of continuum mechanics, accompanied by accurate numerical simulations, are able to shed light on biological controversies. The converse is also true: non-standard mechanical problems suggest new challenging mathematical questions....

The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below

Tomasz Cieślak (2006)

Banach Center Publications

In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.

The Use of CFSE-like Dyes for Measuring Lymphocyte Proliferation : Experimental Considerations and Biological Variables

B.J.C. Quah, A.B. Lyons, C.R. Parish (2012)

Mathematical Modelling of Natural Phenomena

The measurement of CFSE dilution by flow cytometry is a powerful experimental tool to measure lymphocyte proliferation. CFSE fluorescence precisely halves after each cell division in a highly predictable manner and is thus highly amenable to mathematical modelling. However, there are several biological and experimental conditions that can affect the quality of the proliferation data generated, which may be important to consider when modelling dye...

Thermal ablation modeling via the bioheat equation and its numerical treatment

Agnieszka Bartłomiejczyk, Henryk Leszczyński, Artur Poliński (2015)

Applicationes Mathematicae

The phenomenon of thermal ablation is described by Pennes' bioheat equation. This model is based on Newton's law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.

Thermodynamics of DNA microarrays

Enrico Carlon (2008)

Banach Center Publications

DNA microarrays have been widely used in molecular biology laboratories. The main current application of these devices is the determination of the gene expression level for thousands of genes simultaneously. Here we review a recently introduced physical model for hybridization (i.e. the binding of complementary DNA strands) in Affymetrix arrays and compare it to experimental results. The experimental data follow rather well the microscopic model and the approach offers several advantages compared...

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