Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.

The Encyclopedia of Medical Robotics combines contributions in four distinct areas of Medical robotics, namely: Minimally Invasive Surgical Robotics, Micro and Nano Robotics in Medicine, Image-guided Surgical Procedures and Interventions, and Rehabilitation Robotics. The volume on Minimally Invasive Surgical Robotics focuses on robotic technologies geared towards challenges and opportunities in minimally invasive surgery and the research, design, implementation and clinical use of minimally invasive robotic systems. The volume on Micro and Nano robotics in Medicine is dedicated to research activities in an area of emerging interdisciplinary technology that is raising new scientific challenges and promising revolutionary advancement in applications such as medicine and biology. The size and range of these systems are at or below the micrometer scale and comprise assemblies of micro and nanoscale components. The volume on Image-guided Surgical Procedures and Interventions focuses primarily on the use of image guidance during surgical procedures and the challenges posed by various imaging environments and how they related to the design and development of robotic systems as well as their clinical applications. This volume also has significant contributions from the clinical viewpoint on some of the challenges in the domain of image-guided interventions. Finally, the volume on Rehabilitation Robotics is dedicated to the state-of-the-art of an emerging interdisciplinary field where robotics, sensors, and feedback are used in novel ways to re-learn, improve, or restore functional movements in humans.Volume 1, Minimally Invasive Surgical Robotics, focuses on an area of robotic applications that was established in the late 1990s, after the first robotics-assisted minimally invasive surgical procedure. This area has since received significant attention from industry and researchers. The teleoperated and ergonomic features of these robotic systems for minimally invasive surgery (MIS) have been able to reduce or eliminate most of the drawbacks of conventional (laparoscopic) MIS. Robotics-assisted MIS procedures have been conducted on over 3 million patients to date — primarily in the areas of urology, gynecology and general surgery using the FDA approved da Vinci® surgical system. The significant commercial and clinical success of the da Vinci® system has resulted in substantial research activity in recent years to reduce invasiveness, increase dexterity, provide additional features such as image guidance and haptic feedback, reduce size and cost, increase portability, and address specific clinical procedures. The area of robotic MIS is therefore in a state of rapid growth fueled by new developments in technologies such as continuum robotics, smart materials, sensing and actuation, and haptics and teleoperation. An important need arising from the incorporation of robotic technology for surgery is that of training in the appropriate use of the technology, and in the assessment of acquired skills. This volume covers the topics mentioned above in four sections. The first section gives an overview of the evolution and current state the da Vinci® system and clinical perspectives from three groups who use it on a regular basis. The second focuses on the research, and describes a number of new developments in surgical robotics that are likely to be the basis for the next generation of robotic MIS systems. The third deals with two important aspects of surgical robotic systems — teleoperation and haptics (the sense of touch). Technology for implementing the latter in a clinical setting is still very much at the research stage. The fourth section focuses on surgical training and skills assessment necessitated by the novelty and complexity of the technologies involved and the need to provide reliable and efficient training and objective assessment in the use of robotic MIS systems.In Volume 2, Micro and Nano Robotics in Medicine, a brief historical overview of the field of medical nanorobotics as well as the state-of-the-art in the field is presented in the introductory chapter. It covers the various types of nanorobotic systems, their applications and future directions in this field. The volume is divided into three themes related to medical applications. The first theme describes the main challenges of microrobotic design for propulsion in vascular media. Such nanoscale robotic agents are envisioned to revolutionize medicine by enabling minimally invasive diagnostic and therapeutic procedures. To be useful, nanorobots must be operated in complex biological fluids and tissues, which are often difficult to penetrate. In this section, a collection of four papers review the potential medical applications of motile nanorobots, catalytic-based propelling agents, biologically-inspired microrobots and nanoscale bacteria-enabled autonomous drug delivery systems. The second theme relates to the use of micro and nanorobots inside the body for drug-delivery and surgical applications. A collection of six chapters is presented in this segment. The first chapter reviews the different robot structures for three different types of surgery, namely laparoscopy, catheterization, and ophthalmic surgery. It highlights the progress of surgical microrobotics toward intracorporeally navigated mechanisms for ultra-minimally invasive interventions. Then, the design of different magnetic actuation platforms used in micro and nanorobotics are described. An overview of magnetic actuation-based control methods for microrobots, with eventually biomedical applications, is also covered in this segment. The third theme discusses the various nanomanipulation strategies that are currently used in biomedicine for cell characterization, injection, fusion and engineering. In-vitro (3D) cell culture has received increasing attention since it has been discovered to provide a better simulation environment of in-vivo cell growth. Nowadays, the rapid progress of robotic technology paves a new path for the highly controllable and flexible 3D cell assembly. One chapter in this segment discusses the applications of micro-nano robotic techniques for 3D cell culture using engineering approaches. Because cell fusion is important in numerous biological events and applications, such as tissue regeneration and cell reprogramming, a chapter on robotic-tweezers cell manipulation system to achieve precise laser-induced cell fusion using optical trapping has been included in this volume. Finally, the segment ends with a chapter on the use of novel MEMS-based characterization of micro-scale tissues instead of mechanical characterization for cell lines studies.Volume 3, Image-guided Surgical Procedures and Interventions, focuses on several aspects ranging from understanding the challenges and opportunities in this domain, to imaging technologies, to image-guided robotic systems for clinical applications. The volume includes several contributions in the area of imaging in the areas of X-Ray fluoroscopy, CT, PET, MR Imaging, Ultrasound imaging, and optical coherence tomography. Ultrasound-based diagnostics and therapeutics as well as ultrasound-guided planning and navigation are also included in this volume in addition to multi-modal imaging techniques and its applications to surgery and various interventions. The application of multi-modal imaging and fusion in the area of prostate biopsy is also covered. Imaging modality compatible robotic systems, sensors and actuator technologies for use in the MRI environment are also included in this work., as is the development of the framework incorporating image-guided modeling for surgery and intervention. Finally, there are several chapters in the clinical applications domain covering cochlear implant surgery, neurosurgery, breast biopsy, prostate cancer treatment, endovascular interventions, neurovascular interventions, robotic capsule endoscopy, and MRI-guided neurosurgical procedures and interventions.Volume 4, Rehabilitation Robotics, is dedicated to the state-of-the-art of an emerging interdisciplinary field where robotics, sensors, and feedback are used in novel ways to relearn, improve, or restore functional movements in humans. This volume attempts to cover a number of topics relevant to the field. The first section addresses an important activity in our daily lives: walking, where the neuromuscular system orchestrates the gait, posture, and balance. Conditions such as stroke, vestibular deficits, or old age impair this important activity. Three chapters on robotic training, gait rehabilitation, and cooperative orthoses describe the current works in the field to address this issue. The second section covers the significant advances in and novel designs of soft actuators and wearable systems that have emerged in the area of prosthetic lower limbs and ankles in recent years, which offer potential for both rehabilitation and human augmentation. These are described in two chapters. The next section addresses an important emphasis in the field of medicine today that strives to bring rehabilitation out from the clinic into the home environment, so that these medical aids are more readily available to users. The current state-of-the-art in this field is described in a chapter. The last section focuses on rehab devices for the pediatric population. Their impairments are life-long and rehabilitation robotics can have an even bigger impact during their lifespan. In recent years, a number of new developments have been made to promote mobility, socialization, and rehabilitation among the very young: the infants and toddlers. These aspects are summarized in two chapters of this volume.

This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences.

Mathematical modelling in biomedicine is a rapidly developing scientific discipline at the intersection of medicine, biology, mathematics, physics, and computer science. Its progress is stimulated by fundamental scientific questions and by the applications to public health. This book represents a collection of papers devoted to mathematical modelling of various physiological problems in normal and pathological conditions. It covers a broad range of topics including cardiovascular system and diseases, heart and brain modelling, tumor growth, viral infections, and immune response. Computational models of blood circulation are used to study the influence of heart arrhythmias on coronary blood flow and on operating modes for left-ventricle-assisted devices. Wave propagation in the cardiac tissue is investigated in order to show the influence of tissue heterogeneity and fibrosis. The models of tumor growth are used to determine optimal protocols of antiangiogenic and radiotherapy. The models of viral hepatitis kinetics are considered for the parameter identification, and the evolution of viral quasi-species is investigated. The book presents the state-of-the-art in mathematical modelling in biomedicine and opens new perspectives in this passionate field of research.

The aim of the present volume was to give an overview over different available methodological approaches. The specialists may, perhaps, object that in their particular field the level of information is superficial. However, let them look at other chapters in which different approaches are discussed and which, surely, will appear less superficial from the more general point of view. We hope, at least, that crucial references can be traced throughout the book that would enable the readers to go in more detail when desired. It can be traced throughout the book that would enable the readers to go in more detail when desired. It was really one of our ideas to draw the survey of possibilities available. If this can stimulate the readers to use ideas to draw the survey of possibilities available. If this can stimulate the readers to use other methods that those they are routinely using the goals will be met.

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

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 equations. Third, at the end of anti-cancer therapy, a small number of malignant cells remain, making the post-treatment dynamics inherently stochastic. Fourth, the growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. Changes in these parameters may induce phenomena that are mathematically equivalent to phase transitions. Fifth, tumor vascular growth is random and self-similar. Finally, the drugs used in chemotherapy diffuse and are taken up by the cells in nonlinear ways. Mathematical Oncology 2013 will appeal to graduate students and researchers in biomathematics, computational and theoretical biology, biophysics, and bioengineering.

Mathematicalmodelingofhumanphysiopathologyisatremendouslyambitioustask. It encompasses the modeling of most diverse compartments such as the cardiovas- lar,respiratory,skeletalandnervoussystems,aswellasthemechanicalandbioch- ical interaction between blood ?ow and arterial walls, and electrocardiac processes and electric conduction in biological tissues. Mathematical models can be set up to simulate both vasculogenesis (the aggregation and organization of endothelial cells dispersed in a given environment) and angiogenesis (the formation of new vessels sprouting from an existing vessel) that are relevant to the formation of vascular networks, and in particular to the description of tumor growth. The integration of models aimed at simulating the cooperation and interrelation of different systems is an even more dif?cult task. It calls for the setting up of, for instance, interaction models for the integrated cardio-vascular system and the interplay between the central circulation and peripheral compartments, models for the mid-to-long range cardiovascular adjustments to pathological conditions (e.g., to account for surgical interventions, congenital malformations, or tumor growth), models for integration among circulation, tissue perfusion, biochemical and thermal regulation, models for parameter identi?cation and sensitivity analysis to parameter changes or data uncertainty – and many others.

Describes and analyzes recent breakthroughs in healthcare and biomedicine providing comprehensive coverage and definitions of important issues, concepts, new trends and advanced technologies.