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Immunotherapy with interleukin-2: A study based on mathematical modeling

Sandip Banerjee (2008)

International Journal of Applied Mathematics and Computer Science

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.

Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation

Pavel Strachota (2009)

Kybernetika

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...

Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis

V. Vainstein, Y. Ginosar, M. Shoham, A. Ianovski, A. Rabinovich, Y. Kogan, V. Selitser, Z. Agur (2010)

Mathematical Modelling of Natural Phenomena

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...

In vitro Vasculogenesis Models Revisited - Measurement of VEGF Diffusion in Matrigel

T. Miura, R. Tanaka (2009)

Mathematical Modelling of Natural Phenomena

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...

Indecision in Neural Decision Making Models

J. Milton, P. Naik, C. Chan, S. A. Campbell (2010)

Mathematical Modelling of Natural Phenomena

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....

Individual Cell-Based Model for In-Vitro Mesothelial Invasion of Ovarian Cancer

C. Giverso, M. Scianna, L. Preziosi, N. Lo Buono, A. Funaro (2010)

Mathematical Modelling of Natural Phenomena

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...

Influence of diffusion on interactions between malignant gliomas and immune system

Urszula Foryś (2010)

Applicationes Mathematicae

We analyse the influence of diffusion and space distribution of cells in a simple model of interactions between an activated immune system and malignant gliomas, among which the most aggressive one is GBM Glioblastoma Multiforme. It turns out that diffusion cannot affect stability of spatially homogeneous steady states. This suggests that there are two possible outcomes-the solution is either attracted by the positive steady state or by the semitrivial one. The semitrivial steady state describes...

Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics

Marek Bodnar, Urszula Foryś (2009)

Applicationes Mathematicae

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...

Influenza Transmission in Preschools: Modulation by contact landscapes and interventions

A.A. Adalja, P.S. Crooke, J.R. Hotchkiss (2010)

Mathematical Modelling of Natural Phenomena

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...

Input-output systems in Biology and Chemistry and a class of mathematical models describing them

Erich Bohl, Ivo Marek (2005)

Applications of Mathematics

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...

Integrating Photosynthesis, Respiration, Biomass Partitioning, and Plant Growth: Developing a Microsoft Excel®-based Simulation Model of Wisconsin Fast Plant (Brassica rapa, Brassicaceae) Growth with Undergraduate Students

Y. L. Grossman, A. B. Berdanier, M. L. Custic, L. R. Feeley, S. F. Peake, A. J. Saenz, K. S. Sitton (2011)

Mathematical Modelling of Natural Phenomena

This paper demonstrates the development of a simple model of carbon flow during plant growth. The model was developed by six undergraduate students and their instructor as a project in a plant ecophysiology course. The paper describes the structure of the model including the equations that were used to implement it in Excel®, the plant growth experiments that were conducted to obtain information for parameterizing and testing the model, model performance, student responses to the modeling project,...

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