Mathematical modelling and computer simulations are playing a crucial role in the solution of the complex problems arising in the field of biomedical sciences and provide a support to clinical and experimental practices in an interdisciplinary framework. Indeed, the development of mathematical models and efficient numerical simulation tools is of key importance when dealing with such applications. Moreover, since the parameters in biomedical models have peculiar scientific interpretations and their values are often unknown, accurate estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In the light of the new challenges brought by the biomedical applications, computational mathematics paves the way for the validation of the mathematical models and the investigation of control problems. The volume hosts high-quality selected contributions containing original research results as well as comprehensive papers and survey articles including prospective discussion focusing on some topical biomedical problems. It is addressed, but not limited to: research institutes, academia, and pharmaceutical industries.

This book presents applications to several fluid dynamics problems in both the bounded and unbounded domains in the framework of the discrete velocity models of kinetic theory. The proposition of new models for dense gases, gases with multi-components, and gases with chemical reactions are also included. This is an up-to-date book on the applications of the discrete Boltzmann equation.

Ubiquitous and fundamental in cell mechanics, multiscale problems can arise in the growth of tumors, embryogenesis, tissue engineering, and more. Cell Mechanics From Single Scale-Based Models to Multiscale Modeling brings together new insight and research on mechanical, mathematical, physical, and biological approaches for simulating the behavior of cells, specifically tumor cells.

In the first part of the text, the book discusses the powerful tool of microrheology for investigating cell mechanical properties, multiphysics and multiscale approaches for studying intracellular mechanisms in cell motility, and the role of subcellular effects involving certain genes for inducing cell motility in cancer. Focusing on models based on physical, mathematical, and computational approaches, the second section develops tools for describing the complex interplay of cell adhesion molecules and the dynamic evolution of the cell cytoskeleton. The third part explores cell interactions with the environment, particularly the role of external mechanical forces and their effects on cell behavior. The final part presents innovative models of multicellular systems for developmental biology, cancer, and embryogenesis.

This book collects novel methods to apply to cells and tissues through a multiscale approach. It presents numerous existing tools while stimulating the discovery of new approaches that can lead to more effective and accurate predictions of pathologies.

This unique collection highlights the central role played by modeling in general, and the modeling of mechanical considerations that have an effect on living matter. The volume collects several survey papers by actively working specialists, dealing with some of the most important problems both theoretical and practical in biomechanics. Written in a user-friendly style, these papers clearly explain both the biomedical and mechanical backgrounds associated with complex phenomena. This book may be used in interdisciplinary introductory courses covering various biomechanical topics for graduate students in applied mathematics, engineering, and biomedicine.

Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa tions is a relevant, maybe the fundamental, aspect of the interactions be tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula tions to provide the description of the real system according to the model. Within this framework, one has an evolution equation and the re lated mathematical problems obtained by adding all necessary conditions for their solution. Then, a qualitative analysis should be developed: this means proof of existence of solutions and analysis of their qualitative be havior. Asymptotic analysis may include a detailed description of stability properties. Quantitative analysis, based upon the application ofsuitable methods and algorithms for the solution of problems, ends up with the simulation that is the representation of the dependent variable versus the independent one. The information obtained by the model has to be compared with those deriving from the experimental observation of the real system. This comparison may finally lead to the validation of the model followed by its application and, maybe, further generalization."

Tumour evolution is a complex process involving many different phenomena. Mathematical modelling and computer simulations can help us understand these phenomena, but their development requires a multidisciplinary background-one that includes an understanding of the biological phenomena involved and knowledge of the mathematical techniques used to obtain both qualitative and quantitative results.

Cancer Modelling and Simulation builds the requisite biological foundation and presents the mathematical models and methods most useful for understanding the dynamics of tumour development and growth. In chapters contributed by an interdisciplinary team of leading researchers, this book addresses the entire modelling process, from phenomenological observation to simulation and validation, through the development of mathematical models and their qualitative and quantitative study.

This treatment effectively links the analytical, mathematical, and biological aspects of tumour growth modelling to provide researchers from multiple disciplines with the common language and practical knowledge they need to break down the barriers that can hamper interdisciplinary research. Cancer Modelling and Simulation is an important contribution to the field that undoubtedly will stimulate and remain a valuable reference for continued research for many years.

Most materials used in contemporary life and industry are heterogeneous (composites) and multicomponent, possessing a rich and complex internal structure. This internal structure, or microstructure, plays a key role in understanding and controlling the continuum behavior, or macroscopic, of a wide variety of materials. The modeling process is a critical tool for scientists and engineers studying the analysis and experimentation for the micromechanics and behavior of these materials. "Heterogeneous Media" is a critical, in-depth edited survey of the major topics surrounding the modeling and analysis of problems in micromechanics of multicomponent systems, including conceptual and practical aspects. The goal of this extensive and comprehensive survey is to provide both specialists and nonspecialists with an authoritative and interdisciplinary perspective of current ideas and methods used for modeling heterogeneous materials behavior and their applications. Topics and Features: * all chapters use interdisciplinary modeling perspective for investigating heterogeneous media*Five chapters provide self-contained discussions, with background provided*Focuses only upon most important techniques and models, fully exploring micro-macro interconnections*extensive introductory survey chapter on micromechanics of heterogeneous media*microstructure characterization via statistical correlation functions*micro-scale deformation of pore space*wave fields and effective dynamical properties*modeling of the complex production technologies for composite materials The book is ideal for a general scientific and engineering audience needing an in-depth view and guide to current ideas, methods and

Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa tions is a relevant, maybe the fundamental, aspect of the interactions be tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula tions to provide the description of the real system according to the model. Within this framework, one has an evolution equation and the re lated mathematical problems obtained by adding all necessary conditions for their solution. Then, a qualitative analysis should be developed: this means proof of existence of solutions and analysis of their qualitative be havior. Asymptotic analysis may include a detailed description of stability properties. Quantitative analysis, based upon the application ofsuitable methods and algorithms for the solution of problems, ends up with the simulation that is the representation of the dependent variable versus the independent one. The information obtained by the model has to be compared with those deriving from the experimental observation of the real system. This comparison may finally lead to the validation of the model followed by its application and, maybe, further generalization."

Most materials used in contemporary life and industry are heterogeneous (composites) and multicomponent, possessing a rich and complex internal structure. This internal structure, or microstructure, plays a key role in understanding and controlling the continuum behavior, or macroscopic, of a wide variety of materials. The modeling process is a critical tool for scientists and engineers studying the analysis and experimentation for the micromechanics and behavior of these materials. "Heterogeneous Media" is a critical, in-depth edited survey of the major topics surrounding the modeling and analysis of problems in micromechanics of multicomponent systems, including conceptual and practical aspects. The goal of this extensive and comprehensive survey is to provide both specialists and nonspecialists with an authoritative and interdisciplinary perspective of current ideas and methods used for modeling heterogeneous materials behavior and their applications. Topics and Features: * all chapters use interdisciplinary modeling perspective for investigating heterogeneous media*Five chapters provide self-contained discussions, with background provided*Focuses only upon most important techniques and models, fully exploring micro-macro interconnections*extensive introductory survey chapter on micromechanics of heterogeneous media*microstructure characterization via statistical correlation functions*micro-scale deformation of pore space*wave fields and effective dynamical properties*modeling of the complex production technologies for composite materials The book is ideal for a general scientific and engineering audience needing an in-depth view and guide to current ideas, methods and

Ubiquitous and fundamental in cell mechanics, multiscale problems can arise in the growth of tumors, embryogenesis, tissue engineering, and more. Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling brings together new insight and research on mechanical, mathematical, physical, and biological approaches for simulating the behavior of cells, specifically tumor cells. In the first part of the text, the book discusses the powerful tool of microrheology for investigating cell mechanical properties, multiphysics and multiscale approaches for studying intracellular mechanisms in cell motility, and the role of subcellular effects involving certain genes for inducing cell motility in cancer. Focusing on models based on physical, mathematical, and computational approaches, the second section develops tools for describing the complex interplay of cell adhesion molecules and the dynamic evolution of the cell cytoskeleton. The third part explores cell interactions with the environment, particularly the role of external mechanical forces and their effects on cell behavior. The final part presents innovative models of multicellular systems for developmental biology, cancer, and embryogenesis. This book collects novel methods to apply to cells and tissues through a multiscale approach. It presents numerous existing tools while stimulating the discovery of new approaches that can lead to more effective and accurate predictions of pathologies.

The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods.Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.

La finalita del libro e quella di presentare i concetti di base della Meccanica dei Continui a studenti che frequentano sia corsi di laurea che corsi di dottorato in Matematica, Fisica e Ingegneria. Questo obiettivo e perseguito da una parte limitando per quanto possibile i prerequisiti culturali necessari per la comprensione della materia e dall'altra mantenendo un linguaggio si rigoroso, ma anche semplice e colloquiale. In questo modo il testo risulta adatto anche agli studenti che per la prima volta si interessano alla Meccanica dei Continui e che non hanno conoscenze pregresse specifiche. Nella presentazione di ogni argomento gli aspetti teorici sono corredati di esempi ed esercizi, tutti svolti. Inoltre, pur mantenendo la tradizionale e irrinunciabile struttura ipotetico-deduttiva, il libro presenta, soprattutto nei capitoli finali dedicati ai solidi e ai fluidi, una attenzione particolare alle applicazioni che gli studenti potrebbero incontrare in altri insegnamenti.