Mathematical and numerical modelling of engineering problems in medicine is aimed at unveiling and understanding multidisciplinary interactions and processes and providing insights useful to clinical care and technology advances for better medical equipment and systems. When modelling medical problems, the engineer is confronted with multidisciplinary problems of electromagnetism, heat and mass transfer, and structural mechanics with, possibly, different time and space scales, which may raise concerns in formulating consistent, solvable mathematical models. Computational Medical Engineering presents a number of engineering for medicine problems that may be encountered in medical physics, procedures, diagnosis and monitoring techniques, including electrical activity of the heart, hemodynamic activity monitoring, magnetic drug targeting, bioheat models and thermography, RF and microwave hyperthermia, ablation, EMF dosimetry, and bioimpedance methods. The authors discuss the core approach methodology to pose and solve different problems of medical engineering, including essentials of mathematical modelling (e.g., criteria for well-posed problems); physics scaling (homogenization techniques); Constructal Law criteria in morphing shape and structure of systems with internal flows; computational domain construction (CAD and, or reconstruction techniques based on medical images); numerical modelling issues, and validation techniques used to ascertain numerical simulation results. In addition, new ideas and venues to investigate and understand finer scale models and merge them into continuous media medical physics are provided as case studies. Presents the fundamentals of mathematical and numerical modeling of engineering problems in medicine Discusses many of the most common modelling scenarios for Biomedical Engineering, including, electrical activity of the heart hemodynamic activity monitoring, magnetic drug targeting, bioheat models and thermography, RF and microwave hyperthermia, ablation, EMF dosimetry, and bioimpedance methods Includes discussion of the core approach methodology to pose and solve different problems of medical engineering, including essentials of mathematical modelling, physics scaling, Constructal Law criteria in morphing shape and structure of systems with internal flows, computational domain construction, numerical modelling issues, and validation techniques used to ascertain numerical simulation results
Author(s): Alexandru Morega; Mihaela Morega; Alin Dobre
Publisher: Academic Press
Year: 2020
Language: English
Pages: 314
City: London
Computational Modeling in Biomedical Engineering and Medical Physics
Copyright
Contents
Preface
Computational modeling for biomedical engineering
Solvable physical–mathematical models
Shape, structure, and rhythm
From the drawing to the numerical modeling—computational domains
Modeling multidisciplinary processes and interactions
Acknowledgments
1 Physical, mathematical, and numerical modeling
1.1 Experiments and numerical simulation
1.2 The system and its boundary
1.3 First law analysis: energy, heat, and work interactions
Electromagnetic power transferred through the boundary (at the electrical terminals)
1.4 Multidisciplinary (multiphysics) problems
1.5 Mathematical models
Complete and independent, coherent, and noncontradictory system of laws
Boundary conditions (external interactions) and initial conditions (initial state)
Initial values problems
Boundary and initial values problems
1.6 Numerical solutions to the mathematical models
1.7 Coupled (multiphysics) problems
1.8 Time and space scales
1.9 Properties of anatomic media
Electrical properties
Rheological properties of blood
1.9.3 Bioheat models, homogenization methods
1.10 The computational domain
Allometric laws, fractal geometry, and constructal law
Medical image-based construction, CAD and fused computational domains
1.11 Diffusion–convection problems: heatfunction and massfunction
1.12 A roadmap to a well-posed, direct problem and its solution
References
A.1 Scalar and Vector Fields
Scalar fields
Vector fields
2 Shape and structure morphing of systems with internal flows
2.1 Natural form and organization—quandary, observation, and rationale
2.2 Biomimetics, bionics, fractal geometry, constructal theory
2.3 Shape and structure
The fundamental problem of volume to point flow and the constructal growth
Fluid trees
Living trees
Counterflow convection trees
2.4 Structure in time: rhythm
Intermittent heat transfer
Respiration
Heart beating
Coupled rhythms in the cardio-pulmonary system
2.5 The effect of body size
References
3 Computational domains
3.1 Physical domains generated using computer-aided design techniques
A CAD construct for an intervertebral disc
A CAD abstraction of the kidney
3.2 Image-based reconstruction of anatomically accurate computational domains
Rigid and elastic arterial networks
The heart
A vertebral column segment
References
4 Electrical activity of the heart
4.1 Introduction
Electrophysiology insights
Bioelectric sources. The direct ECG problem
4.2 Coupled direct and inverse ECG problems for electrical imaging
Image-based construction of a human heart and thorax
4.3 The electrical activity of the cardiac strand
One-dimension action potential propagation
Two-dimensional action potential propagation
4.4 Coupling the action potential with the electric field diffusion in the thorax
4.5 Blood pressure pulse wave reflections
The blood pressure wave
The augmentation index
The generalized transfer function
Using small size data collections to process the arterial flow evaluation
4.6 Arterial function evaluation
The arterial hemodynamic
Structural analysis
Pressure transducers and their positioning
Arterial flow evaluation
A equivalent lumped parameters electric circuit
References
5 Bioimpedance methods
5.1 Introduction
5.2 The electrical impedance
5.3 The electrical impedance in noninvasive hemodynamic monitoring
The plethysmogram
Bioimpedance methods and models
5.4 Thoracic bioimpedance methods and models
The thoracic electrical bioimpedance
The electrical velocimetry model and the cardiometry method
5.5 The electrical cardiometry—electrical velocimetry
The electrical conductivity of the blood
Hemodynamic of larger vessels
The electromagnetic field
5.6 The ECM brachial bioimpedance
5.7 Some comments on numerical modeling results
References
6 Magnetic drug targeting
6.1 Introduction
6.2 Magnetic nanoparticles for magnetic drug targeting
Magnetic properties of materials used in designing the magnetic drug targeting medication
Superparamagnetic iron oxide nanoparticles
Superparamagnetic iron oxide nanoparticles synthesis, coating, and functionalization
6.3 Several modeling concerns in magnetic drug targeting
6.4 Magnetic drug mixing
6.5 Magnetic drug targeting, from the blood vessel to the targeted region
Hemodynamic and magnetic field driven mass transfer in larger vessels
The constructal optimization of the magnetic field source
Using electromagnets for magnetic drug targeting
From conceptual to more realistic models
6.6 The magnetic drug transfer from the larger blood vessel to the region of interest
Biorheological models in magnetic drug transfer
Magnetic drug transfer thorough larger vessels
Magnetic drug transfer through the membrane and tissue
References
7 Magnetic stimulation and therapy
7.1 Introduction
7.2 Magnetic stimulation of long cell fibers, a reduced mathematical model
Cable theory and the activating function
A computational model for the induced electric field and the activating function
The activating function produced by circular coils
Example of activation function distribution inside the body
7.3 Magnetic stimulation of the spinal cord
Modeling the lumbar magnetic stimulation
Numerical simulation results
7.4 Transcranial magnetic stimulation
Modeling the transcranial magnetic stimulation
Numerical simulation results
7.5 Magnetic therapy
Modeling the magnetic field therapy
Numerical simulation results
References
8 Hyperthermia and ablation
8.1 Thermotherapy methods
Hyperthermia
Ablation
8.2 Radiofrequency thermotherapy
Thermal ablation of a kidney tumor
Mathematical modeling
Numerical modeling
Some thermographic considerations
8.3 Pin interstitial applicators for microwave hyperthermia
Numerical analysis of heating when blood flow is taken into account
Thermal analysis in mild hyperthermia of soft tissue
Temperature-dependent dielectric properties
8.4 Magnetic hyperthermia
The magnetic field work interactions
Microwave magnetic thermal thermotherapy of a hepatic tumor
8.5 Ultrasound thermotherapy
The ultrasound work interactions
Ultrasound ablation of a breast tumor
References
Index
