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The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart.
However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features
of this system. For this reason, a simplification of this model, called Monodomain problem is quite often
adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in
the presence of applied currents...
The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness in...
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided...
This paper describes three cytological image segmentation methods. The analysis includes the watershed algorithm, active contouring and a cellular automata GrowCut method. One can also find here a description of image pre-processing, Hough transform based pre-segmentation and an automatic nuclei localization mechanism used in our approach. Preliminary experimental results collected on a benchmark database present the quality of the methods in the analyzed issue. The discussion of common errors and...
Blood rheology is completely determined by its major corpuscles which are erythrocytes,
or red blood cells (RBCs). That is why understanding and correct mathematical description
of RBCs behavior in blood is a critical step in modelling the blood dynamics. Various
phenomena provided by RBCs such as aggregation, deformation, shear-induced diffusion and
non-uniform radial distribution affect the passage of blood through the vessels. Hence,
they have...
A method for system matrix calculation in the case of iterative reconstruction algorithms in SPECT was implemented and tested. Due to a complex mathematical description of the geometry of the detector set-up, we developed a method for system matrix computation that is based on direct measurements of the detector response. In this approach, the influence of the acquisition equipment on the image formation is measured directly. The objective was to obtain the best quality of reconstructed images with...
Epidermal wound healing is a complex process that repairs injured tissue. The complexity
of this process increases when bacteria are present in a wound; the bacteria interaction
determines whether infection sets in. Because of underlying physiological problems
infected wounds do not follow the normal healing pattern. In this paper we present a
mathematical model of the healing of both infected and uninfected wounds. At the core of
our model is an...
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...
In this paper we build and analyze networks using the statistical and programming
environment R and the igraph package. We investigate random, small-world, and scale-free
networks and test a standard problem of connectivity on a random graph. We then develop a
method to study how vaccination can alter the structure of a disease transmission network.
We also discuss a variety of other uses for networks in biology.
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