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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...
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,...
Despite recent advances, treatment of patients with aggressive Non-Hodgkin's
lymphoma (NHL2) has yet to be optimally designed. Notwithstanding the contribution of
molecular treatments, intensification of chemotherapeutic regimens may still be beneficial.
Hoping to aid in the design of intensified chemotherapy, we put forward a mathematical
and computational model that analyses the effect of Doxorubicin on NHL over a wide
range of patho-physiological conditions. The model represents tumour growth...
When invading the tissue, malignant tumour cells (i.e. cancer cells) need to detach from
neighbouring cells, degrade the basement membrane, and migrate through the extracellular
matrix. These processes require loss of cell-cell adhesion and enhancement of cell-matrix
adhesion. In this paper we present a mathematical model of an intracellular pathway for
the interactions between a cancer cell and the extracellular matrix. Cancer cells use
similar...
This paper presents a parametrization of a feed-forward control based on structures of subspaces for a non-interacting regulation. With advances in technological development, robotics is increasingly being used in many industrial sectors, including medical applications (e. g., micro-manipulation of internal tissues or laparoscopy). Typical problems in robotics and general mechanisms may be mathematically formalized and analyzed, resulting in outcomes so general that it is possible to speak of structural...
In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo...
Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous
cell proliferation and motility rates. The interplay of proliferation and migration
dynamics plays an important role in the invasion of these malignant tumors. We analyze the
regulation of proliferation and migration processes with a lattice-gas cellular automaton
(LGCA). We study and characterize the influence of the migration/proliferation dichotomy
(also known...
This article presents the principal results of the doctoral thesis “Isomerism as internal symmetry of molecules” by Valentin Vankov Iliev (Institute of Mathematics and Informatics), successfully defended before the Specialised Academic Council for Informatics and Mathematical
Modelling on 15 December, 2008.This paper is an extended review of our doctoral thesis “Isomerism as Intrinsic Symmetry of Molecules” in which we present, continue,
generalize, and trace out Lunn–Senior’s theory of isomerism...
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