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The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannose receptor, without knowing it a priori the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without it...
A nonlinear mathematical model with distributed delay is proposed to describe the reaction of a human organism to a pathogen agent. The stability of the disease free state is analyzed, showing that there exists a large set of initial conditions in the attraction basin of the disease-free state whose border is defined as the immunological barrier.
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
Magnetic Resonance Diffusion Tensor Imaging (MR–DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR–DTI, this paper describes the steps of the proposed neural tract visualization technique based on the DTI data. The cornerstone of the algorithm is a texture diffusion procedure modeled mathematically by the problem for the Allen–Cahn...
Neutropenia is a significant dose-limiting toxicity of cancer
chemotherapy, especially in dose-intensified regimens. It is
widely treated by injections of Granulocyte Colony-Stimulating
Factor (G-CSF). However, optimal schedules of G-CSF administration
are still not determined. In order to aid in identifying more
efficacious and less neutropenic treatment protocols, we studied a
detailed physiologically-based computer model of granulopoiesis,
as affected by different treatment schedules of doxorubicin...
The circulatory system is one of the
first to function during development. The earliest event in the
system's development is vasculogenesis, whereby vascular
progeniter cells form clusters called blood islands, which later
fuse to form capillary networks. There exists a very good
in vitro system that mimics this process. When HUVECs
(Human Umbilical Vein Endothelial Cells) are cultured on Matrigel,
they spontaneously form a capillary network structure. Two
theoretical models have been proposed...
Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition....
In vitro transmesothelial migration assays of ovarian cancer cells, isolated or
aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts
Models (CPM). We show that the simulations are in good agreement with the experimental
evidence and that the overall process is regulated by the activity of matrix
metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells
with the extracellular matrix and...
We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due...
Epidemiologic data suggest that schools and daycare facilities likely play a major role
in the dissemination of influenza. Pathogen transmission within such small, inhomogenously
mixed populations is difficult to model using traditional approaches. We developed
simulation based mathematical tool to investigate the effects of social contact networks
on pathogen dissemination in a setting analogous to a daycare center or grade school. Here
we show...
Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators...
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