PDE Modeling of Tissue Engineering and Regenerative Medicine: Computer Analysis in R presents the formulation and computer implementation of mathematical models for the forefront research areas of tissue engineering and regenerative medicine. The mathematical model discussed in this book consists of a system of eight partial differential equations (PDEs) with dependent variables. The computer-based example models are presented through routines coded in R—a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Includes detailed examples that the reader can execute on modest computers. - Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models - Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms - Authored by a leading researcher and educator in PDE models

Arguably the first book of its kind, Computational Bioengineering explores the power of multidisciplinary computer modeling in bioengineering. Written by experts, the book examines the interplay of multiple governing principles underlying common biomedical devices and problems, bolstered by case studies. It shows you how to take advantage of the la

One of the major challenges in tissue engineering is the translation of biological knowledge on complex cell and tissue behavior into a predictive and robust engineering process. Mastering this complexity is an essential step towards clinical applications of tissue engineering. This volume discusses computational modeling tools that allow studying the biological complexity in a more quantitative way. More specifically, computational tools can help in: (i) quantifying and optimizing the tissue engineering product, e.g. by adapting scaffold design to optimize micro-environmental signals or by adapting selection criteria to improve homogeneity of the selected cell population; (ii) quantifying and optimizing the tissue engineering process, e.g. by adapting bioreactor design to improve quality and quantity of the final product; and (iii) assessing the influence of the in vivo environment on the behavior of the tissue engineering product, e.g. by investigating vascular ingrowth. The book presents examples of each of the above mentioned areas of computational modeling. The underlying tissue engineering applications will vary from blood vessels over trachea to cartilage and bone. For the chapters describing examples of the first two areas, the main focus is on (the optimization of) mechanical signals, mass transport and fluid flow encountered by the cells in scaffolds and bioreactors as well as on the optimization of the cell population itself. In the chapters describing modeling contributions in the third area, the focus will shift towards the biology, the complex interactions between biology and the micro-environmental signals and the ways in which modeling might be able to assist in investigating and mastering this complexity. The chapters cover issues related to (multiscale/multiphysics) model building, training and validation, but also discuss recent advances in scientific computing techniques that are needed to implement these models as well as new tools that can be used to experimentally validate the computational results.

A comprehensive overview of the latest achievements, trends, and the current state of the art of this important and rapidly expanding field. Clearly and logically structured, the first part of the book explores the fundamentals of tissue engineering, providing a separate chapter on each of the basic topics, including biomaterials stem cells, biosensors and bioreactors. The second part then follows a more applied approach, discussing various applications of tissue engineering, such as the replacement or repairing of skins, cartilages, livers and blood vessels, to trachea, lungs and cardiac tissues, to musculoskeletal tissue engineering used for bones and ligaments as well as pancreas, kidney and neural tissue engineering for the brain. The book concludes with a look at future technological advances. An invaluable reading for entrants to the field in biomedical engineering as well as expert researchers and developers in industry.

Numerical Modeling in Biomedical Engineering brings together the integrative set of computational problem solving tools important to biomedical engineers. Through the use of comprehensive homework exercises, relevant examples and extensive case studies, this book integrates principles and techniques of numerical analysis. Covering biomechanical phenomena and physiologic, cell and molecular systems, this is an essential tool for students and all those studying biomedical transport, biomedical thermodynamics & kinetics and biomechanics. - Supported by Whitaker Foundation Teaching Materials Program; ABET-oriented pedagogical layout - Extensive hands-on homework exercises

A Complex and Growing Field The study of vascularization in tissue engineering and regenerative medicine (TERM) and its applications is an emerging field that could revolutionize medical approaches for organ and tissue replacement, reconstruction, and regeneration. Designed specifically for researchers in TERM fields, Vascularization: Regenerative Medicine and Tissue Engineering provides a broad overview of vascularization in TERM applications. This text summarizes research in several areas, and includes contributions from leading experts in the field. It defines the difficulties associated with multicellular processes in vascularization and cell-source issues. It presents advanced biomaterial design strategies for control of vascular network formation and in silico models designed to provide insight not possible in experimental systems. It also examines imaging methods that are critical to understanding vascularization in engineered tissues, and addresses vascularization issues within the context of specific tissue applications. This text is divided into three parts; the first section focuses on the basics of vascularization. The second section provides general approaches for promoting vascularization. The final section presents tissue and organ-specific aspects of vascularization in regenerative medicine. Presents Areas of Substantial Clinical and Societal Impact The material contains research and science on the process of vessel assembly with an emphasis on methods for controlling the process for therapeutic applications. It describes the tissue and organ-specific aspects of vascularization in regenerative medicine, and refers to areas such as bone tissue engineering, vascularization of encapsulated cells, adipose tissue, bone and muscle engineering. It also provides a mechanistic understanding of the process and presentation of experimental and computational approaches that facilitate the study of vascular assembly, and includes enabling technologies such as nanotechnology, drug delivery, stem cells, microfluidics, and biomaterial design that are optimized for supporting the formation of extensive vascular networks in regenerative medicine. A guide for researchers developing new methods for modulating vessel assembly, this text can also be used by senior undergraduate and graduate students taking courses focused on TERM.

Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin.Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the forumulation and use of alternative DODE/DPDE models. • Introduces time delay ordinary and partial differential equations (DODE/DPDEs) and their numerical computer-based integration (solution) • Illustrates the computer implementation of DODE/DPDE models with coding (programming) in R, a quality, open-source scientific programming system readily available from the Internet • Applies DODE/DPDE models to biological/physiological systems through a series of examples • Provides the R routines for all of the illustrative applications through a download link • Facilitates the use of the models with reasonable time and effort on modest computers