Pde Models For Atherosclerosis Computer Implementation In R

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PDE Models for Atherosclerosis Computer Implementation in R

Author : William E. Schiesser
Publisher : Springer Nature
ISBN 13 : 3031024141
Total Pages : 136 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis PDE Models for Atherosclerosis Computer Implementation in R by : William E. Schiesser

Download or read book PDE Models for Atherosclerosis Computer Implementation in R written by William E. Schiesser and published by Springer Nature. This book was released on 2022-06-01 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Introduction to Statistics Using R

Author : Mustapha Akinkunmi
Publisher : Springer Nature
ISBN 13 : 3031024192
Total Pages : 215 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Introduction to Statistics Using R by : Mustapha Akinkunmi

Download or read book Introduction to Statistics Using R written by Mustapha Akinkunmi and published by Springer Nature. This book was released on 2022-06-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spatiotemporal Modeling of Influenza

Author : William E. Schiesser
Publisher : Springer Nature
ISBN 13 : 3031016653
Total Pages : 97 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Spatiotemporal Modeling of Influenza by : William E. Schiesser

Download or read book Spatiotemporal Modeling of Influenza written by William E. Schiesser and published by Springer Nature. This book was released on 2022-05-31 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analytical Techniques for Solving Nonlinear Partial Differential Equations

Author : Daniel J. Arrigo
Publisher : Springer Nature
ISBN 13 : 3031024176
Total Pages : 151 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Analytical Techniques for Solving Nonlinear Partial Differential Equations by : Daniel J. Arrigo

Download or read book Analytical Techniques for Solving Nonlinear Partial Differential Equations written by Daniel J. Arrigo and published by Springer Nature. This book was released on 2022-06-01 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Emerging Trends in Immunomodulatory Nanomaterials Toward Cancer Therapy

Author : Anubhab Mukherjee
Publisher : Springer Nature
ISBN 13 : 3031016696
Total Pages : 84 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Emerging Trends in Immunomodulatory Nanomaterials Toward Cancer Therapy by : Anubhab Mukherjee

Download or read book Emerging Trends in Immunomodulatory Nanomaterials Toward Cancer Therapy written by Anubhab Mukherjee and published by Springer Nature. This book was released on 2022-05-31 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exosomes and MicroRNAs in Biomedical Science

Author : Hamed Mirzaei
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1636393489
Total Pages : 175 pages
Book Rating : 4.6/5 (363 download)

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Book Synopsis Exosomes and MicroRNAs in Biomedical Science by : Hamed Mirzaei

Download or read book Exosomes and MicroRNAs in Biomedical Science written by Hamed Mirzaei and published by Morgan & Claypool Publishers. This book was released on 2022-04-21 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Inverse Obstacle Scattering with Non-Over-Determined Scattering Data

Author : Alexander G. Ramm
Publisher : Springer Nature
ISBN 13 : 3031024184
Total Pages : 53 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Inverse Obstacle Scattering with Non-Over-Determined Scattering Data by : Alexander G. Ramm

Download or read book Inverse Obstacle Scattering with Non-Over-Determined Scattering Data written by Alexander G. Ramm and published by Springer Nature. This book was released on 2022-06-01 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering (;;), where (;;) is the scattering amplitude, ; 2 is the direction of the scattered, incident wave, respectively, 2 is the unit sphere in the R3 and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is () := (;0;0). By sub-index 0 a fixed value of a variable is denoted. It is proved in this book that the data (), known for all in an open subset of 2, determines uniquely the surface and the boundary condition on . This condition can be the Dirichlet, or the Neumann, or the impedance type. The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown . There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.

Symmetry Problems

Author : Alexander G. Ramm
Publisher : Springer Nature
ISBN 13 : 303102415X
Total Pages : 71 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Symmetry Problems by : Alexander G. Ramm

Download or read book Symmetry Problems written by Alexander G. Ramm and published by Springer Nature. This book was released on 2022-06-01 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.

Nanotechnology for Bioengineers

Author : Wujie Zhang
Publisher : Springer Nature
ISBN 13 : 3031016688
Total Pages : 95 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Nanotechnology for Bioengineers by : Wujie Zhang

Download or read book Nanotechnology for Bioengineers written by Wujie Zhang and published by Springer Nature. This book was released on 2022-05-31 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nanotechnology is an interdisciplinary field that is rapidly evolving and expanding. Significant advancements have been made in nanotechnology-related disciplines in the past few decades and continued growth and progression in the field are anticipated. Moreover, nanotechnology, omnipresent in innovation, has been applied to resolve critical challenges in nearly every field, especially those related to biological technologies and processes. This book, used as either a textbook for a short course or a reference book, provides state-of-the-art analysis of essential topics in nanotechnology for bioengineers studying and working in biotechnology, chemical/biochemical, pharmaceutical, biomedical, and other related fields. The book topics range from introduction to nanotechnology and nanofabrication to applications of nanotechnology in various biological fields. This book not only intends to introduce bioengineers to the amazing world of nanotechnology, but also inspires them to use nanotechnology to address some of the world's biggest challenges.

Fast Quantitative Magnetic Resonance Imaging

Author : Guido Buonincontri
Publisher : Springer Nature
ISBN 13 : 303101667X
Total Pages : 124 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fast Quantitative Magnetic Resonance Imaging by : Guido Buonincontri

Download or read book Fast Quantitative Magnetic Resonance Imaging written by Guido Buonincontri and published by Springer Nature. This book was released on 2022-05-31 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among medical imaging modalities, magnetic resonance imaging (MRI) stands out for its excellent soft-tissue contrast, anatomical detail, and high sensitivity for disease detection. However, as proven by the continuous and vast effort to develop new MRI techniques, limitations and open challenges remain. The primary source of contrast in MRI images are the various relaxation parameters associated with the nuclear magnetic resonance (NMR) phenomena upon which MRI is based. Although it is possible to quantify these relaxation parameters (qMRI) they are rarely used in the clinic, and radiological interpretation of images is primarily based upon images that are relaxation time weighted. The clinical adoption of qMRI is mainly limited by the long acquisition times required to quantify each relaxation parameter as well as questions around their accuracy and reliability. More specifically, the main limitations of qMRI methods have been the difficulty in dealing with the high inter-parameter correlations and a high sensitivity to MRI system imperfections. Recently, new methods for rapid qMRI have been proposed. The multi-parametric models at the heart of these techniques have the main advantage of accounting for the correlations between the parameters of interest as well as system imperfections. This holistic view on the MR signal makes it possible to regress many individual parameters at once, potentially with a higher accuracy. Novel, accurate techniques promise a fast estimation of relevant MRI quantities, including but not limited to longitudinal (T1) and transverse (T2) relaxation times. Among these emerging methods, MR Fingerprinting (MRF), synthetic MR (syMRI or MAGIC), and T1‒T2 Shuffling are making their way into the clinical world at a very fast pace. However, the main underlying assumptions and algorithms used are sometimes different from those found in the conventional MRI literature, and can be elusive at times. In this book, we take the opportunity to study and describe the main assumptions, theoretical background, and methods that are the basis of these emerging techniques. Quantitative transient state imaging provides an incredible, transformative opportunity for MRI. There is huge potential to further extend the physics, in conjunction with the underlying physiology, toward a better theoretical description of the underlying models, their application, and evaluation to improve the assessment of disease and treatment efficacy.

3D Electro-Rotation of Single Cells

Author : Liang Huang
Publisher : Springer Nature
ISBN 13 : 3031016661
Total Pages : 101 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis 3D Electro-Rotation of Single Cells by : Liang Huang

Download or read book 3D Electro-Rotation of Single Cells written by Liang Huang and published by Springer Nature. This book was released on 2022-05-31 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dielectrophoresis microfluidic chips have been widely used in various biological applications due to their advantages of convenient operation, high throughput, and low cost. However, most of the DEP microfluidic chips are based on 2D planar electrodes which have some limitations, such as electric field attenuation, small effective working regions, and weak DEP forces. In order to overcome the limitations of 2D planar electrodes, two kinds of thick-electrode DEP chips were designed to realize manipulation and multi-parameter measurement of single cells. Based on the multi-electrode structure of thick-electrode DEP, a single-cell 3D electro-rotation chip of "Armillary Sphere" was designed. The chip uses four thick electrodes and a bottom planar electrode to form an electric field chamber, which can control 3D rotation of single cells under different electric signal configurations. Electrical property measurement and 3D image reconstruction of single cells are achieved based on single-cell 3D rotation. This work overcomes the limitations of 2D planar electrodes and effectively solves the problem of unstable spatial position of single-cell samples, and provides a new platform for single-cell analysis. Based on multi-electrode structure of thick-electrode DEP, a microfluidic chip with optoelectronic integration was presented. A dual-fiber optical stretcher embedded in thick electrodes can trap and stretch a single cell while the thick electrodes are used for single-cell rotation. Stretching and rotation manipulation gives the chip the ability to simultaneously measure mechanical and electrical properties of single cells, providing a versatile platform for single-cell analysis, further extending the application of thick-electrode DEP in biological manipulation and analysis.

Aspects of Differential Geometry IV

Author : Esteban Calviño-Louzao
Publisher : Springer Nature
ISBN 13 : 3031024168
Total Pages : 149 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Aspects of Differential Geometry IV by : Esteban Calviño-Louzao

Download or read book Aspects of Differential Geometry IV written by Esteban Calviño-Louzao and published by Springer Nature. This book was released on 2022-06-01 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces {which} are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group R2 is Abelian and the + group\index{ax+b group} is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type surfaces. These are the left-invariant affine geometries on R2. Associating to each Type surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue =-1$ turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type surfaces; these are the left-invariant affine geometries on the + group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere 2. The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension.

Aspects of Differential Geometry III

Author : Esteban Calviño-Louzao
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1627058826
Total Pages : 169 pages
Book Rating : 4.6/5 (27 download)

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Book Synopsis Aspects of Differential Geometry III by : Esteban Calviño-Louzao

Download or read book Aspects of Differential Geometry III written by Esteban Calviño-Louzao and published by Morgan & Claypool Publishers. This book was released on 2017-05-25 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book III is aimed at the first-year graduate level but is certainly accessible to advanced undergraduates. It deals with invariance theory and discusses invariants both of Weyl and not of Weyl type; the Chern‒Gauss‒Bonnet formula is treated from this point of view. Homothety homogeneity, local homogeneity, stability theorems, and Walker geometry are discussed. Ricci solitons are presented in the contexts of Riemannian, Lorentzian, and affine geometry.

Moving Boundary Pde Analysis

Author : William Schiesser
Publisher : CRC Press
ISBN 13 : 9780367224837
Total Pages : 128 pages
Book Rating : 4.2/5 (248 download)

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Book Synopsis Moving Boundary Pde Analysis by : William Schiesser

Download or read book Moving Boundary Pde Analysis written by William Schiesser and published by CRC Press. This book was released on 2019 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 teacher/analyst/researcher can use MFPDE models without having to rst study numerical methods and computer programming P>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 teacher/analyst/researcher can use MFPDE models without having to rst study numerical methods and computer programming

Moving Boundary PDE Analysis

Author : William Schiesser
Publisher : CRC Press
ISBN 13 : 1000001040
Total Pages : 191 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Moving Boundary PDE Analysis by : William Schiesser

Download or read book Moving Boundary PDE Analysis written by William Schiesser and published by CRC Press. This book was released on 2019-05-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Moving Boundary PDE Analysis

Author : William Schiesser
Publisher : CRC Press
ISBN 13 : 100000788X
Total Pages : 195 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Moving Boundary PDE Analysis by : William Schiesser

Download or read book Moving Boundary PDE Analysis written by William Schiesser and published by CRC Press. This book was released on 2019-05-29 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modeling of Post-Myocardial Infarction

Author : William E. Schiesser
Publisher : Elsevier
ISBN 13 : 0443136122
Total Pages : 146 pages
Book Rating : 4.4/5 (431 download)

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Book Synopsis Modeling of Post-Myocardial Infarction by : William E. Schiesser

Download or read book Modeling of Post-Myocardial Infarction written by William E. Schiesser and published by Elsevier. This book was released on 2023-09-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R presents mathematical models for the dynamics of a post-myocardial (post-MI), aka, a heart attack. The mathematical models discussed consist of six ordinary differential equations (ODEs) with dependent variables Mun; M1; M2; IL10; Ta; IL1. The system variables are explained as follows: dependent variable Mun = cell density of unactivated macrophage; dependent variable M1 = cell density of M1 macrophage; dependent variable M2 = cell density of M2 macrophage; dependent variable IL10 = concentration of IL10, (interleuken-10); dependent variable Ta = concentration of TNF-a (tumor necrosis factor-a); dependent variable IL1 = concentration of IL1 (interleuken-1). The system of six ODEs does not include a spatial aspect of an MI in the cardiac tissue. Therefore, the ODE model is extended to include a spatial effect by the addition of diffusion terms. The resulting system of six diffusion PDEs, with x (space) and t (time) as independent variables, is integrated (solved) by the numerical method of lines (MOL), a general numerical algorithm for PDEs. 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