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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...

Time delays in proliferation and apoptosis for solid avascular tumour

Urszula Foryś, Mikhail Kolev (2003)

Banach Center Publications

The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the...

Time domain computational modelling of 1D arterial networks in monochorionic placentas

Victoria E. Franke, Kim H. Parker, Ling Y. Wee, Nicholas M. Fisk, Spencer J. Sherwin (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/ h p element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance....

Time domain computational modelling of 1D arterial networks in monochorionic placentas

Victoria E. Franke, Kim H. Parker, Ling Y. Wee, Nicholas M. Fisk, Spencer J. Sherwin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/hp element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance....

Towards prediction of HCV therapy efficiency.

Wasik, Szymon, Jackowiak, Paulina, Krawczyk, Jacek B., Kedziora, Paweł, Formanowicz, Piotr, Figlerowicz, Marek, Błażewicz, Jacek (2010)

Computational & Mathematical Methods in Medicine

Towards Sub-cellular Modeling with Delaunay Triangulation

G. Grise, M. Meyer-Hermann (2010)

Mathematical Modelling of Natural Phenomena

In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...

Transport Equation Reduction for a Mathematical Model in Plant Growth

S. Boujena, A. Chiboub, J. Pousin (2011)

Mathematical Modelling of Natural Phenomena

In this article a variational reduction method, how to handle the case of heterogenous domains for the Transport equation, is presented. This method allows to get rid of the restrictions on the size of time steps due to the thin parts of the domain. In the thin part of the domain, only a differential problem, with respect to the space variable, is to be approximated numerically. Numerical results are presented with a simple example. The variational...

Transport in a molecular motor system

Michel Chipot, Stuart Hastings, David Kinderlehrer (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.

Transport in a molecular motor system

Michel Chipot, Stuart Hastings, David Kinderlehrer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.

Tumour angiogenesis model with variable vessels' effectiveness

Jan Poleszczuk, Iwona Skrzypczak (2011)

Applicationes Mathematicae

We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties...

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