Biomechanics of the Brain

Foreword
Contents
1 Introduction
	References
2 Human Brain Anatomy in 3D
	2.1 Introduction
	2.2 Structural (Gross) Neuroanatomy
		2.2.1 Brain Parcellation
		2.2.2 Cortical Areas
			2.2.2.1 Lateral Cortical Surface
			2.2.2.2 Medial Cortical Surface
			2.2.2.3 Inferior Cortical Surface
		2.2.3 Deep Grey Nuclei
		2.2.4 Ventricular System
		2.2.5 Sectional Neuroanatomy
		2.2.6 Main Stereotactic Target Structures
		2.2.7 Functional Areas
	2.3 Vascular Neuroanatomy
		2.3.1 Arterial System
			2.3.1.1 Parcellation of Arterial System
			2.3.1.2 Anterior Cerebral Artery
			2.3.1.3 Middle Cerebral Artery
			2.3.1.4 Posterior Cerebral Artery
			2.3.1.5 Circle of Willis
		2.3.2 Venous System
			2.3.2.1 Parcellation of Venous System
			2.3.2.2 Dural Sinuses
			2.3.2.3 Cerebral Veins
		2.3.3 Vascular Variants
	2.4 Connectional Neuroanatomy
		2.4.1 Commissural Tracts
		2.4.2 Association Tracts
		2.4.3 Projection Tracts
	2.5 Recent Extensions and Future Brain Atlas Developments
	2.6 Summary
	References
		Neuroanatomy Textbooks
		Print Brain Atlases
		Electronic Brain Atlases
		Other Materials
		Recent Brain Atlases Created (Products)
		Recent Extensions and Future Directions in Brain Atlasing
3 Introduction to Brain Imaging
	3.1 Structural and Functional Brain Imaging: A Comparative Overview of Techniques
		3.1.1 Magnetic Resonance Imaging (MRI)-Based Brain Imaging Techniques
			3.1.1.1 Magnetic Resonance Imaging (MRI)
			3.1.1.2 Functional Magnetic Resonance Imaging (fMRI)
			3.1.1.3 Diffusion Tensor Imaging (DTI)
			3.1.1.4 Ultrahigh Magnetic Fields
		3.1.2 Electrophysiological Brain Imaging Techniques
			3.1.2.1 Electroencephalography (EEG) and Magnetoencephalography (MEG)
			3.1.2.2 Simultaneous fMRI and EEG
			3.1.2.3 Intracranial EEG (iEEG)
		3.1.3 Molecular Brain Imaging Techniques
			3.1.3.1 Positron Emission Tomography (PET)
	3.2 Clinical Applications of Brain Imaging for Image-Guided Neurosurgery in Epilepsy and Brain Tumour Patients
		3.2.1 Structural MRI
		3.2.2 Presurgical fMRI Mapping
			3.2.2.1 Language and Memory Hemispheric Lateralisation
			3.2.2.2 Functional Mapping in Patients with Malignant Brain Tumours
		3.2.3 Presurgical DTI Mapping
		3.2.4 Presurgical Electrophysiological Mapping
		3.2.5 Presurgical PET
	3.3 Summary and Conclusions
	References
4 Brain Tissue Mechanical Properties
	4.1 Introduction
	4.2 Shear Properties of Brain Tissue
		4.2.1 Linear Viscoelastic Properties
			4.2.1.1 Oscillatory Loading
			4.2.1.2 Relaxation
			4.2.1.3 Other Measurements
			4.2.1.4 Elastography Measurements
		4.2.2 Nonlinear Viscoelastic Properties
			4.2.2.1 Oscillatory Response
			4.2.2.2 Relaxation
			4.2.2.3 Constant Loading Rate
			4.2.2.4 Other Test Types
	4.3 Compressive Properties of Brain Tissue
	4.4 Tensile Properties of Brain Tissue
	4.5 Constitutive Models for Brain Tissue
	4.6 Discussion
		4.6.1 Mechanical Characteristics of Brain Tissue
		4.6.2 Methodological Considerations
	4.7 Future Directions
	4.8 Conclusions
	References
5 Modelling of the Brain for Injury Simulation and Prevention
	5.1 Introduction
		5.1.1 The Incidence and Prevalence of Traumatic Brain Injury
		5.1.2 Investigating the Mechanisms of TBI
		5.1.3 Finite Element Modelling of the Head and Brain
	5.2 Challenges of Investigating TBI Using FE Head Models
		5.2.1 Lack of Sufficient Biomechanical and Injury Data for Model Validations
		5.2.2 Lack of Proven Injury Mechanism
	5.3 Challenges of Developing a Biofidelic FE Head Model
		5.3.1 Selection of Anatomical Features
		5.3.2 Issues Related to Quality of Mesh
		5.3.3 Numerical Convergence and Hourglass Energy
		5.3.4 Boundary Conditions
		5.3.5 Types of Injury to Be Simulated
		5.3.6 Acquisition of Experimental Data Specifically Conducted for Model Validation
	5.4 Revamp FE Modelling of Human Head: A Look into the Future
	5.5 Conclusions
	References
6 Biomechanical Modelling of the Brain for Neurosurgical Simulation and Neuroimage Registration
	6.1 Introduction
		6.1.1 Neurosurgical Simulation for Operation Planning, Surgeon Training and Skills Assessment
		6.1.2 Image Registration in Image-Guided Neurosurgery
	6.2 Biomechanics of the Brain: Modelling Issues
		6.2.1 Geometry
		6.2.2 Boundary Conditions
		6.2.3 Loading
		6.2.4 Models of Mechanical Properties of Brain Tissue
		6.2.5 Model Validation
	6.3 Application Example: Computer Simulation of Brain Shift
		6.3.1 Generation of Computational Grids: From Medical Images to Finite Element Meshes
		6.3.2 Displacement Loading
		6.3.3 Boundary Conditions
		6.3.4 Mechanical Properties of the Intracranial Constituents
		6.3.5 Solution Algorithm
		6.3.6 Results and Validation
			6.3.6.1 Qualitative Evaluation
			6.3.6.2 Quantitative Evaluation
			6.3.6.3 Results
	6.4 Conclusions
	References
7 Biomechanical Modelling of the Brain for Neuronavigation in Epilepsy Surgery
	7.1 Introduction
		7.1.1 Background
		7.1.2 Modelling the Intra-operative Deformation
	7.2 Computing Brain Deformations Due to Insertion of Invasive Electrodes
		7.2.1 Geometry
		7.2.2 Finite Element Meshing
		7.2.3 Boundary Conditions
		7.2.4 Loading
		7.2.5 Material Properties
		7.2.6 Solution Algorithm and Software
	7.3 Results
	7.4 Conclusions
	References
8 Dynamics of Cerebrospinal Fluid: From Theoretical Models to Clinical Applications
	8.1 Introduction
	8.2 Physiology and Pathophysiology
	8.3 Model of CSF Circulation
	8.4 Infusion Test
	8.5 Long-Term ICP Monitoring
	8.6 Compensatory Parameters Derived from the Infusion Test and ICP Monitoring
		8.6.1 RCSF and Pb
		8.6.2 Pulsatility and Pulse Amplitude
		8.6.3 Elastance Coefficient (or Elasticity)
		8.6.4 Pressure-Volume Curve and Its Hysteresis
		8.6.5 ICP Waveform Components
		8.6.6 Derived Parameters, RAP Index
	8.7 Pulsatile Flow of CSF: Phase-Contrast MRI Perspective
	8.8 Pulsatile CSF Flow-Basic Models
	8.9 Methodology of Phase-Contrast MRI
	8.10 Clinical Applications
		8.10.1 Differentiation Between Brain Atrophy and Normal Pressure Hydrocephalus
		8.10.2 Noncommunicating and Acute Communicating Hydrocephalus
		8.10.3 Testing of CSF Dynamics in Shunted Patients
		8.10.4 Phase-Contrast MRI in Clinical Practice
	8.11 Conclusion
	References
9 Modelling of Cerebrospinal Fluid Flow by Computational Fluid Dynamics
	9.1 Introduction
	9.2 Procedural Steps in CFD Modelling of CSF Dynamics
		9.2.1 Obtaining the Model Domain
		9.2.2 Spatial Discretization
		9.2.3 Boundary and Initial Conditions
		9.2.4 Calculating the Flow
	9.3 Existing CFD Models
		9.3.1 Ventricular Space
		9.3.2 Subarachnoid Space
			9.3.2.1 Normal Physiologic Conditions
			9.3.2.2 Syringomyelia
			9.3.2.3 Chiari Malformation
			9.3.2.4 Intrathecal Drug Delivery and Solute Transport
		9.3.3 Perivascular Space
	9.4 Conclusion
	References
10 Finite Element Algorithms for Computational Biomechanics of the Brain
	10.1 Introduction
	10.2 Algorithms for Injury Biomechanics
	10.3 Algorithms for Surgery Simulation
	10.4 Algorithms for Neurosurgery Modelling
		10.4.1 Dynamic Relaxation Algorithm
			10.4.1.1 Dynamic Relaxation Algorithm: Maximum Eigenvalue Am and Mass Matrix
			10.4.1.2 Dynamic Relaxation Algorithm: Estimation of the Minimum Eigenvalue A0
			10.4.1.3 Dynamic Relaxation Algorithm: Termination Criteria
	10.5 Element Formulation for Finite Element Algorithms for Surgery Simulation and Neurosurgery Modelling
		10.5.1 Volumetric Locking
		10.5.2 Stability of Under-integrated Hexahedral Elements: Hourglassing
	10.6 Modelling of the Brain-Skull Interactions for Image-Guided Neurosurgery: Efficient Finite Sliding Contact Algorithm
	10.7 Real-Time Computations Without Supercomputers: Increasing Computation Speed Through Algorithm Implementation on Graphics Processing Unit (GPU)
	10.8 Verification of Finite Element Algorithms of Computational Biomechanics
		10.8.1 Hourglass Control
		10.8.2 Volumetric Locking
		10.8.3 Dynamic Relaxation: Steady State Computation
		10.8.4 Brain-Skull Interface: Contact Algorithm
	10.9 Conclusions
	References
11 Meshless Algorithms for Computational Biomechanicsof the Brain
	11.1 Introduction
	11.2 Shape Functions for Meshless Algorithms for Computing Soft Tissue Deformations
	11.3 Spatial Integration Schemes for Meshless Algorithms for Computing Soft Tissue Deformations
	11.4 Visibility Criterion for Modelling of Surgical Dissection and Soft Tissue Rupture
	11.5 Stability of Explicit Dynamics Meshless Algorithms
	11.6 Algorithm Verification
		11.6.1 Meshless Total Lagrangian Explicit Dynamics (MTLED) Framework
		11.6.2 Modified Moving Least Square (MMLS) Shape Functions for Computing Soft Tissue Deformation
		11.6.3 Visibility Criterion for Modelling of Surgical Dissection and Soft Tissue Rupture
	11.7 Conclusions
	References
12 Intra-operative Measurement of Brain Deformation
	12.1 Introduction
		12.1.1 Brain Shift
	12.2 Measuring Brain Shift
		12.2.1 Quantitative Results
		12.2.2 Qualitative Observations
		12.2.3 Neuronavigation with Brain Shift
			12.2.3.1 Replacing Pre-operative Images with Intra-operative Images
			12.2.3.2 Brain Shift Compensation
	12.3 Intra-operative Imaging Methods
		12.3.1 Intra-operative MRI and Computed Tomography
		12.3.2 Measuring Cortical Surface Displacement
		12.3.3 Intra-operative Ultrasound
	12.4 Conclusion
	References
13 Computational Biomechanics of the Brain in the OperatingTheatre
	13.1 Introduction
	13.2 Key Steps for Computational Modelling in the Operating Theatre
		13.2.1 Before Surgery: Generation of a Patient-Specific Model
			13.2.1.1 Geometry
			13.2.1.2 Constitutive Law
			13.2.1.3 Mechanical Properties
			13.2.1.4 Known Boundary Conditions
			13.2.1.5 Precomputations
		13.2.2 In the Operating Theatre
			13.2.2.1 Intra-operative Imaging
			13.2.2.2 Processing Intra-operative Images
			13.2.2.3 Intra-operative Boundary Conditions and Loads
			13.2.2.4 Efficient Computational Methods
			13.2.2.5 Modelling Tissue Resection
			13.2.2.6 Rendering the Information
		13.2.3 Validation and Clinical Studies
			13.2.3.1 Practicability and Integration in the Surgical Workflow
	13.3 Example of Clinical Application: Constraint-Based Simulation During Tumour Resection
		13.3.1 Before Surgery: Model Generation
			13.3.1.1 Geometries from MRI Images
			13.3.1.2 Segmentation of the Vascular Tree
			13.3.1.3 Mechanical Coupling
		13.3.2 Intra-operative Datasets
			13.3.2.1 Vascular Tree from Power Doppler Ultrasound Images
			13.3.2.2 Probe Footprint from B-Mode Ultrasound Images
		13.3.3 Biomechanical Model: Formulation
			13.3.3.1 Constitutive Law and Parameters
			13.3.3.2 Constraints
			13.3.3.3 Solving Process
		13.3.4 Constraint-Based Iterative Registration
			13.3.4.1 Computing Pairings
			13.3.4.2 Filtering Pairings
			13.3.4.3 Sliding Constraints
		13.3.5 Clinical Evaluation
			13.3.5.1 Quantitative and Qualitative Results After Dural Opening
			13.3.5.2 Experiments During Tumour Resection
			13.3.5.3 Practicability
	13.4 Conclusion
	References
Index