Multiscale Biomechanical Modeling of the Brain

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Contents
Contributors
Preface
Chapter 1 - The multiscale nature of the brain and traumatic brain injury
	1.1 Introduction
	1.2 The brain’s multiscale structure
		1.2.1 Gross anatomy
			1.2.1.1 Cerebrum
			1.2.1.2 Cerebellum
			1.2.1.3 Diencephalon
			1.2.1.4 Brainstem
		1.2.2 Microanatomy
			1.2.2.1 Neuroglia
			1.2.2.2 Neurons
	1.3 The multiscale nature of TBI
		1.3.1 Multiscale injury mechanisms
		1.3.2 Types of injury
		1.3.3 Examples of injuries
		1.3.4 Neurobehavioral sequelae
		1.3.5 TBI research methods
			1.3.5.1 Experiments
			1.3.5.2 Computational models (simulations)
	1.4 Summary
	References
Chapter 2 - Introduction to multiscale modeling of the human brain
	2.1 Introduction
	2.2 Constitutive modeling of the brain
	2.3 Brain tissue experiments used for constitutive modeling calibration
	2.4 Modeling summary of upcoming chapters in the book
	2.5 Summary
	References
Chapter 3 - Density functional theory and bridging to classical interatomic force fields
	3.1 Introduction
		3.1.1 Why quantum mechanics?
		3.1.2 Physical chemistry of biomechanical systems
	3.2 Density functional theory
	3.3 Downscaling requirements of classical force field atomistic models
		3.3.1 Upscaling properties
	3.4 Sample atomistic force fields formalism and development of an interatomic potential for hydrocarbons
		3.4.1 MEAMBO
		3.4.2 Calibration of the MEAMBO potential
		3.4.3 Parameterization of the interatomic potential
		3.4.4 Validation of the interatomic force fields
	3.5 Summary
	References
Chapter 4 - Modeling nanoscale cellular structures using molecular dynamics
	4.1 Introduction
	4.2 Methods
		4.2.1 Molecular dynamics simulation method
		4.2.2 Atomic force fields
		4.2.3 Simulation ensembles of atoms
		4.2.4 Boundary conditions
		4.2.5 Current simulation details
		4.2.6 Molecular dynamics analysis methods for the phospholipid bilayer (neuron membrane)
			4.2.6.1 Stress–strain behavior of the neuron membrane
			4.2.6.2 Image analysis for stereological quantification of neuron membrane damage
	4.3 Results and discussion for the phospholipid bilayer (neuron membrane)
		4.3.1 Stress–strain and damage response
		4.3.2 Membrane failure limit diagram
	4.4 Summary
	Acknowledgments
	References
Chapter 5 - Microscale mechanical modeling of brain neuron(s) and axon(s)
	5.1 Introduction
	5.2 Modeling microscale neurons
		5.2.1 Modeling neurons
		5.2.2 Modeling mechanical behavior of axons
	5.3 Summary and future
	References
Chapter 6 - Mesoscale finite element modeling of brain structural heterogeneities and geometrical complexities
	6.1 Introduction
		6.1.1 Modeling length scale
	6.2 Methods
		6.2.1 Computational methods for properties
		6.2.2 Model validation and boundary conditions
	6.3 Results and discussion
		6.3.1 Geometrical complexities
			6.3.1.1 The effects of the sulci
			6.3.1.2 Sulcus orientation
			6.3.1.3 Sulcus length
	6.4 Summary
	References
Chapter 7 - Modeling mesoscale anatomical structures in macroscale brain finite element models
	7.1 Introduction
	7.2 Macroscale brain finite element model
	7.3 Mesoscale anatomical structures and imaging techniques
	7.4 The importance of structural anisotropy in macroscale models of TBI
	7.5 Material-based method
	7.6 Structure-based method
	7.7 Summary and future perspectives
	References
Chapter 8 - A macroscale mechano-physiological internal state variable (MPISV) model for neuronal membrane damage with  ...
	8.1 Introduction
		8.1.1 Definitions
	8.2 Membrane disruption
	8.3 Development of damage evolution equation
		8.3.1 Pore number density rate
		8.3.2 Pore growth rate
		8.3.3 Pore resealing
	8.4 Garnering data from molecular dynamics simulations
	8.5 Calibration of the mechano-physiological internal state variable damage rate equations
	8.6 Sensitivity analysis of damage model at this length scale
	8.7 Comparison of model with cell culture studies
	8.8 Discussion
	8.9 Summary
	References
Chapter 9 - MRE-based modeling of head trauma
	9.1 Introduction
	9.2 Model formulation
		9.2.1 MRE acquisition and inversion
		9.2.2 Finite element mesh generation
		9.2.3 Material properties
		9.2.4 Experimental verification
	9.3 Results and discussion
	9.4 Conclusion
	References
Chapter 10 - Robust concept exploration of driver’s side vehicular impacts for human-centric crashworthiness
	10.1 Frame of reference
	10.2 Problem definition
	10.3 Adapted CEF for robust concept exploration
	10.4 Head and neck injury criteria-based robust design of vehicular impacts
		10.4.1 Clarification of design task—Step A
		10.4.2 Design of experiments—Step B
		10.4.3 Finite element car crash simulations for predicting injury response—Step C
			10.4.3.1 Finite element model
			10.4.3.2 Head injury metric analysis
			10.4.3.3 Neck injury metric analysis
		10.4.4 Building surrogate models—Step D
		10.4.5 Formulation of robust design cDSP—Step E
		10.4.6 Formulating the design scenarios, exercising the cDSP and exploration of solution space—Step E
	10.5 Future: correlate human brain injury to vehicular damage
	10.6 Summary
	References
Chapter 11 - Development of a coupled physical–computational methodology for the investigation of infant head injury
	11.1 Introduction
	11.2 Methods
		11.2.1 Pediatric head development
		11.2.2 Material properties
		11.2.3 Mesh convergence
		11.2.4 Boundary and loading conditions
		11.2.5 Global validation of the FE-head against PMHS
		11.2.6 Global, regional, and local validation of the FE-head against the physical model
		11.2.7 Statistical analysis
	11.3 Results and discussion
		11.3.1 Global validation of the FE-head versus the postmortem human surrogate
		11.3.2 Global validation of the FE-head versus the physical model
		11.3.3 FE-head regional and local validation versus the physical model
		11.3.4 Head deformation
	11.4 Summary
	References
Chapter 12 - Experimental data for validating the structural response of computational brain models
	12.1 Introduction
	12.2 Methods
		12.2.1 Experimental brain pressure measurements
		12.2.2 Experimental brain deformation measurements
			12.2.2.1 High-speed X-ray
			12.2.2.2 Dynamic ultrasound
			12.2.2.3 Sonomicrometry
			12.2.2.4 Tagged magnetic resonance imaging
			12.2.2.5 Magnetic resonance elastography
	12.3 Challenges and limitations
	12.4 Summary and future perspectives
	References
Chapter 13 - A review of fluid flow in and around the brain, modeling, and abnormalities
	13.1 Introduction
	13.2 Flow anatomy
		13.2.1 Ventricular system
		13.2.2 Ventricles and subarachnoid space
	13.3 Characteristic numbers
		13.3.1 Reynolds number
		13.3.2 Womersley number
		13.3.3 Péclet number
	13.4 Common brain flow abnormalities
		13.4.1 Misfolded proteins
		13.4.2 Injury
		13.4.3 Reduced arterial pulsatility
		13.4.4 Hydrocephalus
		13.4.5 Chiari malformation
		13.4.6 Syringomyelia and syringobulbia
	13.5 Boundary conditions for models
		13.5.1 General comments
		13.5.2 Cardiac flow
		13.5.3 Respiratory flow
		13.5.4 Circulatory flow
			13.5.4.1 Production—classical model
			13.5.4.2 Absorption—classical model
			13.5.4.3 New model
			13.5.4.4 Diffusive versus advective transport
		13.5.5 Intracranial pressure
	13.6 Brain measurement and imaging
		13.6.1 Magnetic resonance imaging
		13.6.2 Spin/field/gradient echo MRI
		13.6.3 Phase contrast MRI
		13.6.4 MRI limitations
		13.6.5 Pressure monitoring
		13.6.6 MRI segmentation
	13.7 Flow modeling
		13.7.1 CFD simplifications: rigid walls
		13.7.2 CFD simplifications: microstructures
			13.7.2.1 CFD simplifications: arachnoid granulations
			13.7.2.2 CFD simplifications: arachnoid trabeculae
			13.7.2.3 CFD simplifications: other structures
	13.8 Literature gap
	References
Chapter 14 - Resonant frequencies of a human brain, skull, and head
	14.1 Introduction
	14.2 Problem set-up for the finite element simulations
	14.3 Results
		14.3.1 Whole head: fundamental frequency and mode shapes
		14.3.2 Brain: fundamental frequency and mode shapes
	14.4 Discussion
	14.5 Conclusions
	References
Chapter 15 - State-of-the-art of multiscale modeling of mechanical impacts to the human brain
	15.1 Introduction
	15.2 Work to be completed
		15.2.1 Multiphysics aspects of the brain
		15.2.2 Multiscale structure–property relationships of the brain
		15.2.3 Different biological effects on the brain
		15.2.4 The liquid–solid aspects of the brain
		15.2.5 Different human ages
	15.3 Conclusions
	References
Index
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