​ Atherosclerosis is a pathological condition of the arteries in which plaque buildup and stiffening (hardening) can lead to stroke, myocardial infarction (heart attacks), and even death. Cholesterol in the blood is a key marker for atherosclerosis, with two forms: (1) LDL - low density lipoproteins and (2) HDL - high density lipoproteins. Low LDL and high HDL concentrations are generally considered essential for limited atherosclerosis and good health. This book pertains to a mathematical model for the spatiotemporal distribution of LDL and HDL in the arterial endothelial inner layer (EIL, intima). The model consists of a system of six partial differential equations (PDEs) with the dependent variables 1. (,): concentration of modified LDL 2. h(,): concentration of HDL 3. (,): concentration of chemoattractants 4. (,): concentration of ES cytokines 5. (,): density of monocytes/macrophages 6. (,): density of foam cells and independent variables 1. : distance from the inner arterial wall 2. : time The focus of this book is a discussion of the methodology for placing the model on modest computers for study of the numerical solutions. The foam cell density (,) as a function of the bloodstream LDL and HDL concentrations is of particular interest as a precursor for arterial plaque formation and stiffening. The numerical algorithm for the solution of the model PDEs is the method of lines (MOL), a general procedure for the computer-based numerical solution of PDEs. The MOL coding (programming) is in R, a quality, open-source scientific computing system that is readily available from the Internet. The R routines for the PDE model are discussed in detail, and are available from a download link so that the reader/analyst/researcher can execute the model to duplicate the solutions reported in the book, then experiment with the model, for example, by changing the parameters (constants) and extending the model with additional equations. /div

Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.

Introduction to Statistics Using R is organized into 13 major chapters. Each chapter is broken down into many digestible subsections in order to explore the objectives of the book. There are many real-life practical examples in this book and each of the examples is written in R codes to acquaint the readers with some statistical methods while simultaneously learning R scripts.

This book has a two-fold purpose: (1) An introduction to the computer-based modeling of influenza, a continuing major worldwide communicable disease. (2) The use of (1) as an illustration of a methodology for the computer-based modeling of communicable diseases. For the purposes of (1) and (2), a basic influenza model is formulated as a system of partial differential equations (PDEs) that define the spatiotemporal evolution of four populations: susceptibles, untreated and treated infecteds, and recovereds. The requirements of a well-posed PDE model are considered, including the initial and boundary conditions. The terms of the PDEs are explained. The computer implementation of the model is illustrated with a detailed line-by-line explanation of a system of routines in R (a quality, open-source scientific computing system that is readily available from the Internet). The R routines demonstrate the straightforward numerical solution of a system of nonlinear PDEs by the method of lines (MOL), an established general algorithm for PDEs. The presentation of the PDE modeling methodology is introductory with a minumum of formal mathematics (no theorems and proofs), and with emphasis on example applications. The intent of the book is to assist in the initial understanding and use of PDE mathematical modeling of communicable diseases, and the explanation and interpretation of the computed model solutions, as illustrated with the influenza model.

This is an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, the reader is introduced to techniques used to obtain exact solutions of NPDEs. The chapters include the following topics: Compatibility, Differential Substitutions, Point and Contact Transformations, First Integrals, and Functional Separability. The reader is guided through these chapters and is provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. The book can be used as a textbook for a second course in PDEs (typically found in both science and engineering programs) and has been used at the University of Central Arkansas for more than ten years.

Recently, immunomodulatory nanomaterials have gained immense attention due to their involvement in the modulation of the body’s immune response to cancer therapy. This book highlights various immunomodulatory nanomaterials (including organic, polymer, inorganic, liposomes, viral, and protein nanoparticles) and their role in cancer therapy. Additionally, the mechanism of immunomodulation is reviewed in detail. Finally, the challenges of these therapies and their future outlook are discussed. We believe this book will be helpful to a broad community including students, researchers, educators, and industrialists.

MicroRNAs (miRNAs) are a member of the family of non-coding RNA molecules, and consist of small conserved sequences between 19–25 nucleotides in length that are responsible for regulating many cellular functions by affecting a wide range of messenger RNAs in a sequence specific manner. Fundamental biological processes like cell proliferation and growth, stress resistance, tumorigenesis, fat metabolism, and neural development have all been shown to be governed by miRNAs. miRNAs carry out the post-transcriptional silencing of gene expression via targeting the 30-untranslated region (UTR) of the complementary mRNA sequence. The dysregulation of the expression levels of various miRNAs is typical of tumor cells, and has been associated with tumor progression and poor prognosis. Many miRNAs are up-regulated in cancer, where they can silence tumor suppressor genes such as apoptosis and immune response associated genes. Therefore, it is possible to profile the expression levels of miRNAs as biomarkers, in order to diagnose cancer and noncancerous diseases. Moreover, cancer detection in the early stages is crucial in clinical situations. Characterization of miRNAs in serum, plasma, and other bodily fluids, and understanding their stability against RNase degradation, is important to assess their suitability as biomarkers and diagnostic tools. Exosomes play an important role in inter-cellular communications, and these nanosized particles have various functions in diverse physiological pathways, in normal as well as abnormal cells. Exosomes can carry diverse cargos such as mRNAs, miRNAs, and proteins that transfer information between donor and recipient cells. Furthermore, uptake of exosomes and their cargos may promote or suppress various molecular and cellular pathways, which alter the cellular behavior. Many reports have discussed the role of exosomes released from cancer cells on the progression of cancer at various stages. Exosomes and their cargos may affect the growth of the tumor, metastasis, drug resistance, immune system function, as well as angiogenesis. Therefore, exosomes have been explored as diagnostic biomarkers in many cancers. Moreover, exosomes can be used as biological vehicles to deliver different drugs and agents like doxorubicin (DOX), miRNAs, and siRNAs. The present book covers the role of exosomes and micro-RNAs in the pathogenesis and treatment of various diseases.