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This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.
During the days 14-18 of October 1991, we had the pleasure of attending a most interesting Conference on New Developments in Partial Differential Equations and Applications to Mathematical Physics in Ferrarra. The Conference was organized within the Scientific Program celebrating the six hundredth birthday of the University of Ferrarra and, after the many stimulating lectures and fruitful discussions, we may certainly conclude, together with the numerous participants, that it has represented a big success. The Conference would not have been possible without the financial support of several sources. In this respect, we are particularly grateful to the Comitato Organizzatore del VI Centenario,...
This contributed volume highlights two areas of fundamental interest in high-performance computing: core algorithms for important kernels and computationally demanding applications. The first few chapters explore algorithms, numerical techniques, and their parallel formulations for a variety of kernels that arise in applications. The rest of the volume focuses on state-of-the-art applications from diverse domains. By structuring the volume around these two areas, it presents a comprehensive view of the application landscape for high-performance computing, while also enabling readers to develop new applications using the kernels. Readers will learn how to choose the most suitable parallel alg...
With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how different researchers approach the same problem in various ways. Tumors are complex entities that present numerous challenges to the mathematical modeler. First and foremost, they grow. Thus their spatial mean field description involves a free boundary problem. Second, their interiors should be modeled as nontrivial porous media using constitutive e...
This book focuses on the spatio-temporal patterns generated by two classes of mathematical models (of hyperbolic and kinetic types) that have been increasingly used in the past several years to describe various biological and ecological communities. Here we combine an overview of various modelling approaches for collective behaviours displayed by individuals/cells/bacteria that interact locally and non-locally, with analytical and numerical mathematical techniques that can be used to investigate the spatio-temporal patterns produced by said individuals/cells/bacteria. Richly illustrated, the book offers a valuable guide for researchers new to the field, and is also suitable as a textbook for senior undergraduate or graduate students in mathematics or related disciplines.
Hemofiltration is now recognised as the optimal therapeutic solution for supplying renal function in patients with acute renal failure associated with poor hemodynamic conditions This situation is often observed in patients with severe impairment in the function of one or several other organs Since its introduction in the intensive care units in the 1970s, hemofiltration has been subject to some major improvements regarding the required material and devices such as catheters, lines, filters, or pumps This progress has been accompanied by a better knowledge of the management of patients undergoing the technique, especially concerning nutritional support, drug administration, control of body temperature, as well as fluid and electrolytes balance or cost control Moreover, some additional beneficial effects of hemofiltration have been recently pointed out, suggesting that this technique could provide more than an already efficient renal support by removing some substances responsible for an exagger
Acute kidney injury (AKI) is a serious and as yet incompletely understood disorder in which sudden impairment of kidney function occurs secondary to one or more of a variety of underlying conditions. This disorder is very common in (elderly) ICU patients and is associated with very high mortality. Many of those who survive suffer from permanent kidney failure and other long-term morbidities, which may include cardiovascular disease and immune dysfunction. Epidemiologic evidence suggests that AKI is not a single disease, but a syndrome comprised of multiple, often coexisting, etiologies. Being usually part of multiorgan failure syndrome, it calls for multiple organ support therapy.The publication at hand contains sections on prerenal azotemia syndromes, dying ‘of’ or ‘with’ AKI, pathophysiology of sepsis-induced acute kidney injury, developments in prevention / treatment / rehabilitation, and renal support. Reporting the latest recommendations from experts, it provides valuable information for those that are interested in understanding the disorder and its treatment options.
Acute organ damage and the ensuing multiple organ failure are the result of a pathophysiological process involving various cytokines. Once activated, these proteins cannot be eliminated even when the kidneys function at their maximum capacity. To counteract this mechanism, researchers in Japan have developed an innovative concept employing blood purification to remove the overwhelming cytokines.This book describes the use of hemodiafiltration to inhibit the cytokine storms which cause serious organ damage in patients with septic shock. Moreover, the technical construction of the blood purification system, which includes various machines, devices, membranes, fluids, etc., is explained in detail. Finally, leading experts discuss the concept of continuous renal replacement therapy as the standard care in critically ill patients with severe acute kidney injury.Describing the current state of acute blood purification, this publication provides new impulses and opens new avenues in the treatment of acute organ damage.
This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought t
Cancer is a complex disease process that spans multiple scales in space and time. Driven by cutting-edge mathematical and computational techniques, in silico biology provides powerful tools to investigate the mechanistic relationships of genes, cells, and tissues. It enables the creation of experimentally testable hypotheses, the integration of dat