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While the tissue is formed or regenerated, cells migrate collectively and remained adherent. However, it is still unclear what are the roles of cell-substrate and intercellular interactions in regulating collective cell migration. In this chapter, we introduce our newly developed finite element cellular model to simulate the collective cell migration and explore the effects of mechanical feedback between cells and between cell and substrate. Our viscoelastic model represents one cell with many triangular elements. Intercellular adhesions between cells are represented as linear springs. Furthermore, we include a mechano-chemical feedback loop between cell-substrate mechanics and cell migration. Our results reproduce a set of experimental observation of patterns of collective cell migration during epithelial wound healing. In addition, we demonstrate that cell-substrate determined mechanics play an important role in regulating persistent and oriented collective cell migration. This chapter illustrates that our finite element cellular model can be applied to study a number of tissue related problems regarding cellular dynamic changes at subcellular level.
This book provides several applications of the finite element method (FEM) for solving real-world problems. FEM is a widely used technique for numerical simulations in many areas of physics and engineering. It has gained increased popularity over recent years for the solution of complex engineering and science problems. FEM is now a powerful and popular numerical method for solving differential equations, with flexibility in dealing with complex geometric domains and various boundary conditions. The method has a wide range of applications in various branches of engineering such as mechanical engineering, thermal and fluid flows, electromagnetics, business management, and many others. This book describes the development of FEM and discusses and illustrates its specific applications.
Nature encourages diversity in life forms (morphologies). The study of morphogenesis deals with understanding those processes that arise during the embryonic development of an organism. These processes control the organized spatial distribution of cells, which in turn gives rise to the characteristic form for the organism. Morphogenesis is a multi-scale modeling problem that can be studied at the molecular, cellular, and tissue levels. Here, we study the problem of morphogenesis at the cellular level by introducing an integrated biomechanical model of cells embedded in the extracellular matrix. The fundamental aspects of mechanobiology essential for studying morphogenesis at the cellular level are the cytoskeleton, extracellular matrix (ECM), and cell adhesion. Cells are modeled using tensegrity architecture. Our simulations demonstrate cellular events, such as differentiation, migration, and division using an extended tensegrity architecture that supports dynamic polymerization of the micro-filaments of the cell. Thus, our simulations add further support to the cellular tensegrity model. Viscoelastic behavior of extracellular matrix is modeled by extending one-dimensional mechanical models (by Maxwell and by Voigt) to three dimensions using finite element methods. The cell adhesion is modeled as a general Velcro-type model. We integrated the mechanics and dynamics of cell, ECM, and cell adhesion with a geometric model to create an integrated biomechanical model. In addition, the thesis discusses various computational issues, including generating the finite element mesh, mesh refinement, re-meshing, and solution mapping. As is known from a molecular level perspective, the genetic regulatory network of the organism controls this spatial distribution of cells along with some environmental factors modulating the process. The integrated biomechanical model presented here, besides generating interesting morphologies, can serve as a mesoscopic-scale platform upon which future work can correlate with the underlying genetic network.
This contributed volume comprises research articles and reviews on topics connected to the mathematical modeling of cellular systems. These contributions cover signaling pathways, stochastic effects, cell motility and mechanics, pattern formation processes, as well as multi-scale approaches. All authors attended the workshop on "Modeling Cellular Systems" which took place in Heidelberg in October 2014. The target audience primarily comprises researchers and experts in the field, but the book may also be beneficial for graduate students.
Engineering and Physical Approaches to Cancer addresses the newest research at this interface between cancer biology and the physical sciences. Several chapters address the mechanobiology of collective and individual cell migration, including experimental, theoretical, and computational perspectives. Other chapters consider the crosstalk of biological, chemical, and physical cues in the tumor microenvironment, including the role of senescence, polyploid giant cells, TGF-beta, metabolism, and immune cells. Further, chapters focus on circulating tumor cells and metastatic colonization, highlighting both bioengineered models as well as diagnostic technologies. Further, this book features the work of emerging and diverse investigators in this field, who have already made impressive cross-disciplinary scientific contributions. This book is designed for a general audience, particularly researchers conversant in cancer biology but less familiar with engineering (and vice-versa). Thus, we envision that this book will be suitable for faculty, postdoctoral fellows, and advanced graduate students across medicine, biological sciences, and engineering. We also anticipate this book will be of interest to medical professionals and trainees, as well as researchers in the pharmaceutical and biomedical device industry. Describes physical aspects of cancer, including collective cell migration, the aberrant tumor microenvironment, circulating tumor cells, and metastatic colonization. First volume available on the topic of physical aspects of cancer
Polymer and cell dynamics play an important role in processes like tumor growth, metastasis, embryogenesis, immune reactions and regeneration. Based on an international workshop on numerical simulations of polymer and cell dynamics in Bad Honnef (Germany) in 2000, this volume provides an overview of the relevant mathematical and numerical methods, their applications and limits. Polymer and Cell Dynamics will be of interest to scientists and advanced undergraduates.
This collection of selected chapters offers a comprehensive overview of state-of-the-art mathematical methods and tools for modeling and analyzing cancer phenomena. Topics covered include stochastic evolutionary models of cancer initiation and progression, tumor cords and their response to anticancer agents, and immune competition in tumor progression and prevention. The complexity of modeling living matter requires the development of new mathematical methods and ideas. This volume, written by first-rate researchers in the field of mathematical biology, is one of the first steps in that direction.
This book contains a collection of original research articles and review articles that describe novel mathematical modeling techniques and the application of those techniques to models of cell motility in a variety of contexts. The aim is to highlight some of the recent mathematical work geared at understanding the coordination of intracellular processes involved in the movement of cells. This collection will benefit researchers interested in cell motility as well graduate students taking a topics course in this area.
This book presents the proceedings of 5th International and 20th National Conference on Machines and Mechanisms (iNaCoMM 2021) held at PDPM IIITDM Jabalpur during 9-11 December 2021. The conference was held in collaboration with the Association of Machines and Mechanisms (AMM) India and International Federation for the Promotion of Mechanism and Machine sciences (IFToMM). Various topics covered in this book include kinematics and dynamics of machines, compliant mechanisms; gear, cams and power transmission systems; mechanisms and machines for rural, agricultural and industrial applications; mechanisms for space applications; mechanisms for energy harvesting; robotics and automation; human-centric robotics; soft robotics; man-machine system, mechatronics and micro–mechanisms; CAD and CAGD; control of machines; vibration of machines & rotor dynamics; acoustic and noise; tribology; condition monitoring and failure analysis; fault diagnosis and health monitoring; biomedical engineering; and composites and advanced materials. Given the contents, the book will be useful for researchers and professionals working in the various domains of mechanical engineering.
This edited volume discusses the complexity of tumor microenvironments during cancer development, progression and treatment. Each chapter presents a different mathematical model designed to investigate the interactions between tumor cells and the surrounding stroma and stromal cells. The topics covered in this book include the quantitative image analysis of a tumor microenvironment, the microenvironmental barriers in oxygen and drug delivery to tumors, the development of tumor microenvironmental niches and sanctuaries, intravenous transport of the circulating tumor cells, the role of the tumor microenvironment in chemotherapeutic interventions, the interactions between tumor cells, the extracellular matrix, the interstitial fluid, and the immune and stromal cells. Mathematical models discussed here embrace both continuous and agent-based approaches, as well as mathematical frameworks of solid mechanics, fluid dynamics and optimal control theory. The topics in each chapter will be of interest to a biological community wishing to apply the mathematical methods to interpret their experimental data, and to a biomathematical audience interested in exploring how mathematical models can be used to address complex questions in cancer biology.