By Alberto d'Onofrio, Alberto Gandolfi (eds.)
With chapters on loose barriers, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, dependent populations, and functions of optimum keep an eye on conception, this quantity provides the main major fresh leads to the sector of mathematical oncology. It highlights the paintings of world-class study groups, and explores how diversified researchers procedure a similar challenge in a variety of ways.
Tumors are complicated entities that current a number of demanding situations to the mathematical modeler. in the beginning, they develop. hence their spatial suggest box description comprises a unfastened boundary challenge. moment, their interiors can be modeled as nontrivial porous media utilizing constitutive equations. 3rd, on the finish of anti-cancer remedy, a small variety of malignant cells stay, making the post-treatment dynamics inherently stochastic. Fourth, the expansion parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor remedies. adjustments in those parameters may possibly set off phenomena which are mathematically reminiscent of section transitions. 5th, tumor vascular progress is random and self-similar. ultimately, the medicine utilized in chemotherapy diffuse and are taken up through the cells in nonlinear ways.
Mathematical Oncology 2013 will entice graduate scholars and researchers in biomathematics, computational and theoretical biology, biophysics, and bioengineering.
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Extra info for Mathematical Oncology 2013
Treated in the literature in the context of the optimal fractionation of radiation dose [16, 66]. , . 3 What Kind of a Fluid Can the “Cell Fluid” Be? A Model for Bingham-Like Spheroids We have mentioned the advantages of the two-fluid approach, which, despite all the internal contradictions, have been responsible for its success. It is quite evident that the choice of identifying cells with a Newtonian fluid, which is frequent in this context, is arbitrary. ” However, cells do not just slide one upon the other.
In the recent paper  a very complex analysis of the mechanics of the cellular component has been performed justifying the presence of a yield stress and therefore of a Bingham-like constitutive law. We will return to such a question in the next section. Here we are pursuing the aim of keeping the mechanics as simple as possible. For this reason we perform some operations that ultimately will circumvent the dynamical problem almost completely, exploiting symmetry to bypass the necessity of writing down the momentum balance equations.
L. Morandi, S. Asioli, A. Cavazza, A. Pession, S. Damiani, Genetic relationship among atypical adenomatous hyperplasia, bronchioloalveolar carcinoma and adenocarcinoma of the lung. Lung Cancer 56(1), 35–42 (2007) 28. J. G. Berg, M. Ehrenberg, Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. Proc. Natl. Acad. Sci. 97(13), 7148–7153 (2000) Stochastic and Deterministic Spatio-Temporal Carcinogenesis 25 29. P. W. M. R. G. J. Keely, Collagen reorganization at the tumor-stromal interface facilitates local invasion.