Computational Models in Biomedical Engineering

Computational Models in Biomedical Engineering

Finite Element Models Based on Smeared Physical Fields: Theory, Solutions, and Software

1st Edition - September 1, 2022

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  • Authors: Milos Kojic, Miljan Milosevic, Arturas Ziemys
  • Paperback ISBN: 9780323884723

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Computational Models in Biomedical Engineering: Finite Element Models Based on Smeared Physical Fields: Theory, Solutions, and Software discusses novel computational methodologies developed by the authors that address a variety of topics in biomedicine, with concepts that rely on the so-called smeared physical field built into the finite element method. A new and straightforward methodology is represented by their Kojic Transport Model (KTM), where a composite smeared finite element (CSFE) as a FE formulation contains different fields (e.g., drug concentration, electrical potential) in a composite medium, such as tissue, which includes the capillary and lymphatic system, different cell groups and organelles. The continuum domains participate in the overall model according to their volumetric fractions. The governing laws and material parameters are assigned to each of the domains. Furthermore, the continuum fields are coupled at each FE node by connectivity elements which take into account biological barriers such as vessel walls and cells.

Key Features

  • Provides a methodology based on the smeared concept within the finite element method which is simple, straightforward and easy to use
  • Enables the modeling of complex physical field problems and the mechanics of biological systems
  • Includes features that are illustrated in chapters devoted to applications surrounding tissue, heart and lung
  • Includes a methodology that can serve as a basis for further enhancements by including additional phenomena which can be described by relevant relationships, derived theoretically or experimentally observed in laboratories and clinics


Students, educators, and researchers in computational mechanics focusing on biomedical engineering problems, researchers and students in biomedical engineering, and researchers in labs and clinics who need easy-to-use computational models for various applications Clinicians and researchers interested in computational models and their applications

Table of Contents

    1.1 Introduction
    1.2 Basic physiology of cells
    1.3 Basic physiology of tissues
    1.4 Basic mass transport physiology of body

    2.1 Diffusion
    2.2 Heat conduction
    2.3 Electrostatics
    2.4 Flow through porous media
    2.5 Fluid flow
    2.6 Solid mechanics

    1.1 Formulation of finite element models for physical fields
    1.2 FE models for mechanics
    1.3 FE models for solid-fluid interaction
    1.4 Kojic Transport Model (KTM). Composite smeared finite element (CSFE) for gradient driven physical fields
    1.5 Composite smeared finite element for mechanics (CSFEM)

    2.1 Basic physiology of tissue
    2.2 Detailed modes for convective and diffusive transport within vessels and composite tissue
    2.3 Smeared models
    2.4 Ionic multiscale transport models
    2.5 Models of tissue with tumors
    2.6 Tumor growth models with including drug delivery
    2.7 Migration of immune cells with chemotaxis effects
    2.8 Drug delivery from implants 

    3.1 Heart physiology
    3.2 Detailed and smeared models of electric potential field within heart wall
    3.3 Mechanical models of heart tissue
    3.4 Coupling electrical field and mechanics
    3.5 Complete heart models – coupled electrophysiology wall mechanics and blood flow
    3.6 Drug delivery within the heart

    Chapter 6 LUNG MODELS
    4.1 Lung physiology
    4.2 Models of lung microstructure
    4.3 Formulation of a smeared FE for air flow within the lung
    4.4 Composite smeared FE for lung tissue
    4.5 Mechanical model of entire lung
    4.6 Drug delivery from air (inhalation) and from capillary system

    5.1 General structure of graphical user interface (GUI) software accompanying the book
    5.2 Description of software modules
    5.3 Procedures for running examples and visualization of results

Product details

  • No. of pages: 332
  • Language: English
  • Copyright: © Academic Press 2022
  • Published: September 1, 2022
  • Imprint: Academic Press
  • Paperback ISBN: 9780323884723

About the Authors

Milos Kojic

Dr. Milos Kojic is one of the leading scientists in the computational mechanics and finite element method and its application in engineering and biomedicine. He is currently Full Member and Professor of Nanomedicine, Department of Nanomedicine, The Methodist Hospital Research Institute, Houston, TX, USA, as well as the Director of the Bioengineering R&D Center, Kragujevac, Serbia. In his long professional carrier, Dr. Kojic has been Professor of Mechanics at University of Kragujevac, Serbia (retired), Visiting Scholar of MIT; Research and Development Engineer of ADINA R&D, Boston; Senior Research Scientist, Harvard School of Public Health; and Member of the Serbian Academy of Science and Arts, from 2009. Dr. Kojic’s research is primarily concerning the finite element method, implementation in engineering and biomedicine; and software development. He has formulated and implemented a number of original concepts and solutions, among which is the Governing Parameter Method for inelastic analysis of solids and structures, and recently the smeared finite element models for field problems and mechanics, also known as the Kojic Transport Model (KTM). He initiated and has been PI of the FE software package PAK for solids and fluids, field and coupled problems, and biomechanics. The PAK software has been developing over decades with participation of several generations; today, it is the basic tool for applications in industry and in research within various domestic and international grants. Dr. Kojic is the lead author of over 10 textbooks in Serbian and two books by world leading publishers: Inelastic Analysis of Solids and Structures, from Springer, and Computer Modeling in Bioengineering, from J. Wiley and Sons.

Affiliations and Expertise

Full Member, Professor, Nanomedicine, Department of Nanomedicine, The Methodist Hospital Research Institute, Houston, TX, USA; Director, Bioengineering R&D Center, Kragujevac, Serbia

Miljan Milosevic

Dr. Miljan Milosevic is a Senior Research Engineer at Bioengineering R&D Center, Kragujevac Serbia. He also serves as an Associate Professor at Metropolitan University, Belgrade, teaching courses in informatics and its applications. Dr. Milosevic received his Ph.D. in Mechanical Engineering from the Faculty of Engineering Sciences, University of Kragujevac. His research interests are centered primarily on the development of the finite element methodology in bioengineering and implementation to the software package PAK. He has been leading research related to the creation of interfaces for use of the software PAK, including connection to imaging data.

Affiliations and Expertise

Senior Research Engineer, Bioengineering R&D Center, Kragujevac Serbia; Associate Professor, Metropolitan University, Belgrade

Arturas Ziemys

Dr. Arturas Ziemys is an Assistant Professor in the Program of Mathematics in Medicine, Department of Nanomedicine, Radiation Oncology, at The Methodist Hospital Research Institute, Houston, TX, USA. His professional experience includes being a research Scientist at the Institute of Biochemistry, Vilnius, Lithuania; Lecturer in Molecular Biology and Bioinformatics at Vytautas Magnus University, Kaunas, Lithuania. His research focus includes enzymatic catalysis, biophysics of protein function and structure, mass transport in nanoporous materials, nanomedicine, bioengineering and drug delivery. This research integrates in silico, in vitro, in vivo, and clinical aspects. His most recent publications focus on drug delivery and therapeutic resistance involving small molecules and immunotherapies.

Affiliations and Expertise

Assistant Professor, Program of Mathematics in Medicine, Department of Nanomedicine, Radiation Oncology, The Methodist Hospital Research Institute, Houston, TX, USA

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