The investigation of the role of mechanical and mechano-chemical interactions in cellular processes and tissue development is a rapidly growing research field in the life sciences and in biomedical engineering. Quantitative understanding of this important area in the study of biological systems requires the development of adequate mathematical models for the simulation of the evolution of these systems in space and time. Since expertise in various fields is necessary, this calls for a multidisciplinary approach.
This edited volume connects basic physical, biological, and physiological concepts to methods for the mathematical modeling of various materials by pursuing a multiscale approach, from subcellular to organ and system level. Written by active researchers, each chapter provides a detailed introduction to a given field, illustrates various approaches to creating models, and explores recent advances and future research perspectives. Topics covered include molecular dynamics simulations of lipid membranes, phenomenological continuum mechanics of tissue growth, and translational cardiovascular modeling.
Modeling Biomaterials will be a valuable resource for both non-specialists and experienced researchers from various domains of science, such as applied mathematics, biophysics, computational physiology, and medicine.
Author(s): Josef Málek, Endre Süli
Series: Nečas Center Series
Publisher: Birkhäuser
Year: 2022
Language: English
Pages: 285
City: Basel
Preface
Contents
A Beginner's Short Guide to Membrane Biophysics
1 Introduction
2 Thermodynamics
2.1 Everything in Biology Happens in Water
2.2 The Concepts of Hydrophobicity and Hydrophilicity
2.3 Amphiphilic Molecules
2.4 Membranes are Two-Dimensional Liquids
2.5 Biological Membranes are Heterogeneous
3 Elasticity
3.1 In-Plane Elasticity
3.2 Curvature Elasticity
3.3 Helfrich Hamiltonian for Membrane Elasticity
3.4 Statistical Mechanics of Membrane Fluctuations
3.5 Membranes Under Tension and Confinement
3.6 Helfrich Free Energy
3.7 Edge Energy
4 Computer Simulations
4.1 Molecular Dynamics
4.2 Langevin Dynamics
4.3 Multi-Scale Simulations
References
Self-Organization of Tissues Through Biochemical and Mechanical Signals
1 Introduction
1.1 Self-Organization in Biological Systems
2 The Hydra Model System
2.1 Biochemical Stimuli and Models of Patterning
2.2 Mechanical Stimuli During Patterning
3 The Presomitic Mesoderm
3.1 Spatial Organization of the Presomitic Mesoderm
3.2 Temporal Organization of the Presomitic Mesoderm
3.3 Self-Organization of the Presomitic Mesoderm
4 Conclusions
References
Foundations of Viscoelasticity and Application to Soft TissueMechanics
1 Introduction
2 Linear Viscoelastic Models
2.1 Bases Decomposition for the Tensor K(t)
2.2 Rheological Models for the Relaxation Function
Ramp Tests
3 QLV Model
4 Simple Torsion
5 Results
5.1 Small Deformations
5.2 Large Deformations
5.2.1 Torque
5.2.2 Normal Force
6 Conclusions
References
Modelling of Biomaterials as an Application of the Theoryof Mixtures
1 Introduction
2 General Framework: Single Continuum
3 General Framework: Multiple Continua, Theory of Mixtures
3.1 Coupling Phenomena, CIT
3.1.1 Congruent Dependence of Phenomenological Coefficients on State Variables
3.1.2 Coupling Phenomena, an Example: Extended Law of Mass Action
3.2 Other Approaches
3.3 Single or Multiple Continua: Which One to Choose?
4 Application: Biphasic Model
4.1 Swelling Pressure and the Effect of Fixed Charge
4.2 Initial and Boundary Conditions in 1D
5 Note on Boundary Conditions
5.1 Are BCs Derivable?
6 Summary
References
Modeling Biomechanics in the Healthy and Diseased Heart
1 Introduction
2 Structure and Mechanical Function in the Heart
2.1 Organ Structure
2.2 Cells in the Heart
2.3 Myocardial Tissue Structure
2.4 Whole-Heart Function and the Cardiac Cycle
2.4.1 Cardiac Cycle
2.4.2 Cardiac Functional Metrics
2.4.3 Cardiac Adaptation
3 Modeling Passive Cardiac Tissue Mechanics
3.1 Continuum Mechanics
3.1.1 Kinematics
3.1.2 Kinetics
3.1.3 Conservation Laws
3.2 Stress–Strain Behavior of Myocardial Tissues
3.3 Data-Model Integration
3.4 Hyperelastic Modeling Approaches
3.4.1 Phenomenological Models
3.4.2 Structural Models
3.4.3 Hybrid Models
3.5 Viscoelastic Modeling Approaches
3.5.1 Fractional Viscoelasticity
3.5.2 Cardiac Viscoelastic Models in the Literature
3.6 Applications of Cardiac Constitutive Modeling
4 Tissue Growth and Remodeling
4.1 Modeling Approaches in G & R
4.2 Kinematic Growth
4.2.1 Finite Strain Kinematics of Growth
4.2.2 Balance Equations of Growth
4.2.3 Constitutive Equations for Growth
4.3 Applications of G & R in the Heart
5 Hemodynamics and Blood Flow Modeling in the Heart
5.1 Kinetics of Blood Flow
5.1.1 Constitutive Behavior of Blood
5.1.2 Artificial Domain Problem
5.2 Hemodynamic Modeling in the Heart
5.2.1 Cardiovascular Modeling Approaches
5.2.2 Requirements for Cardiovascular Modeling
5.2.3 Quantifying Model Output
5.3 Fluid–Structure Interaction in the Heart
6 Applications of Biomechanical Modeling in the Heart
6.1 Dilated Cardiomyopathy
6.1.1 Pathological Changes
6.1.2 Diagnosis and Therapies
6.1.3 Modeling Approaches
6.1.4 Challenges and Future Directions
6.2 Hypertrophic Cardiomyopathy
6.2.1 Pathological Changes
6.2.2 Diagnosis and Therapies
6.2.3 Modeling Approaches
6.2.4 Challenges and Future Directions
6.3 Aortic Stenosis
6.3.1 Pathological Changes
6.3.2 Diagnosis and Therapies
6.3.3 Modeling Approaches
6.3.4 Challenges and Future Directions
6.4 Myocardial Infarction
6.4.1 Pathological Changes
6.4.2 Diagnosis and Therapies
6.4.3 Modeling Approaches
6.4.4 Challenges and Future Directions
7 Conclusions
References
Translational Cardiovascular Modeling: Tetralogy of Fallot and Modeling of Diseases
1 Introduction
1.1 Tetralogy of Fallot
2 Ventricular Mechanics and Its Biomechanical Modeling
2.1 Assessment of Right Ventricular Mechanics in rTOF Patients
2.2 Early-Stage Heart Failure Assessment
2.3 Model-Augmented Monitoring During the Perioperative Period or in the ICU
2.4 Assessment of a Long-Term Cardiac Performance
3 Pulmonary Right Ventricular Resynchronization in Congenital Heart Disease
3.1 Temporary RV-CRT
3.2 Permanent RV-CRT
3.3 Toward Electromechanical Modeling for RV-CRT
4 Model-Constrained Image Processing
4.1 Assessment of T1 Relaxation Time from MOLLI MRI Sequence
4.2 Motion Extraction from Image Data Using Mechanical Model Constraints
4.3 Motion Extraction from Image Data Using Model of Imaging Modality
4.4 Model–Data Fusion
4.5 Data-Driven Strategies for Image Analysis
5 Large Vessel Flow Modeling
5.1 Phantom Experiment
5.2 Computational Fluid Dynamic Model
6 Discussion
7 Conclusion
References
