Advanced Image Processing in Magnetic Resonance Imaging (Signal Processing and Communications)

✍ Scribed by Luigi Landini (editor), Vincenzo Positano (editor), Maria Santarelli (editor)

• Publisher: CRC Press
• Year: 2005
• Tongue: English
• Leaves: 601
• Edition: 1
• Category: Library

✦ Synopsis

The popularity of magnetic resonance (MR) imaging in medicine is no mystery: it is non-invasive, it produces high quality structural and functional image data, and it is very versatile and flexible. Research into MR technology is advancing at a blistering pace, and modern engineers must keep up with the latest developments. This is only possible with a firm grounding in the basic principles of MR, and Advanced Image Processing in Magnetic Resonance Imaging solidly integrates this foundational knowledge with the latest advances in the field.

Beginning with the basics of signal and image generation and reconstruction, the book covers in detail the signal processing techniques and algorithms, filtering techniques for MR images, quantitative analysis including image registration and integration of EEG and MEG techniques with MR, and MR spectroscopy techniques. The final section of the book explores functional MRI (fMRI) in detail, discussing fundamentals and advanced exploratory data analysis, Bayesian inference, and nonlinear analysis. Many of the results presented in the book are derived from the contributors' own work, imparting highly practical experience through experimental and numerical methods.

Contributed by international experts at the forefront of the field, Advanced Image Processing in Magnetic Resonance Imaging is an indispensable guide for anyone interested in further advancing the technology and capabilities of MR imaging.

✦ Table of Contents

Advanced Image Processing in Magnetic Resonance Imaging
Preface
Contributors
Contents
Part I: Signal and Image Generation and Reconstruction
Chapter 1: Basic Physics of MR Signal and Image Generation
CONTENTS
1.1 INTRODUCTION
1.2 NUCLEAR SPIN
1.3 NUCLEI IN A MAGNETIC FIELD
1.3.1 NOTES ON LARMOR FREQUENCY: CHANGES DUE TO DISHOMOGENEITIES
1.3.2 BULK MAGNETIZATION
1.4 RF EXCITATION FOR THE RESONANCE PHENOMENON GENERATION
1.5 MR SIGNAL GENERATION AND ACQUISITION
1.5.1 FREE INDUCTION DECAY AND THE FOURIER TRANSFORM
1.6 MR SIGNAL CHARACTERISTICS
1.6.1 RELAXATION
1.6.1.1 The Decay of Transverse Magnetization: T2
1.6.1.2 The Recovery of Longitudinal Magnetization: T1
1.6.1.3 Pseudo-Relaxation: T2*
1.6.2 PROTON DENSITY
1.6.3 THE BLOCH EQUATIONS
1.6.3.1 Rotating Frame of Reference
1.7 MULTIPLE RF PULSES
1.7.1 GRADIENT ECHO
1.7.2 INVERSION RECOVERY
1.7.3 SPIN ECHO
1.8 MAGNETIC FIELD GRADIENTS
1.9 SPATIAL LOCALIZATION OF MR SIGNALS
1.9.1 SLICE SELECTION
1.9.2 FREQUENCY ENCODING
1.9.3 PHASE ENCODING
1.9.4 PHASE HISTORY OF MAGNETIZATION VECTORS DURING PHASE ENCODING
1.9.5 TIMING DIAGRAM OF AN IMAGING SEQUENCE
1.10 ACQUIRING MR SIGNALS IN THE K-SPACE
1.10.1 K-SPACE TRAJECTORIES
1.11 IMAGING METHODS
ACRONYMS
REFERENCES
Chapter 2: Advanced Image Reconstruction Methods in MRI
CONTENTS
2.1 INTRODUCTION
2.2 FOURIER RECONSTRUCTION
2.3 CONSTRAINED IMAGE RECONSTRUCTION
2.3.1 NONPARAMETRIC METHODS
2.3.2 PARAMETRIC METHODS
2.3.3 APPLICATION EXAMPLES
Example 2.1: Partial Fourier Reconstruction
Example 2.2: Data-Sharing Dynamic Imaging
2.4 REGULARIZED IMAGE RECONSTRUCTION IN PARALLEL MRI
2.4.1 BASIC RECONSTRUCTION METHODS
2.4.2 REGULARIZED RECONSTRUCTION METHODS
2.4.2.1 Construction of…
2.4.2.2 Selection of lambda
2.4.2.3 Sensitivity Analysis
2.4.3 APPLICATION EXAMPLE
2.5 CONCLUSION
REFERENCES
Chapter 3: Parallel MRI: Concepts and Methods
CONTENTS
3.1 INTRODUCTION
3.2 HISTORY OF PARALLEL MRI
3.3 FORMULATION OF THE PROBLEM
3.3.1 FOURIER ENCODING
3.3.2 SAMPLING AT THE NYQUIST RATE AND EQUATION INDEPENDENCE
3.3.3 PARALLEL IMAGING METHODS
3.3.3.1 Coil-Sensitivity Estimation
3.3.3.1.1 Static Estimate
3.3.3.1.2 Dynamic Self-Calibrated Estimate
3.3.3.2 Parallel MR Image Reconstruction Techniques
3.3.3.3 K-Space Approaches
3.3.3.3.1 SMASH
3.3.3.3.2 AUTO-SMASH
3.3.3.3.3 GRAPPA
3.3.3.4 Image Domain Approaches
3.3.3.4.1 SENSE
3.3.3.4.2 SPACE RIP
3.4 EXAMPLES
3.4.1 EXAMPLE 1: UNIFORM SUBSAMPLING
3.4.2 EXAMPLE 2: VARIABLE SUBSAMPLING
3.4.3 EXAMPLE 3: IN VIVO APPLICATIONS
3.5 SUMMARY
REFERENCES
Part II: SNR Improvement and Inhomogeneities Correction
Chapter 4: Estimation of Signal and Noise Parameters from MR Data
CONTENTS
4.1 INTRODUCTION
4.2 PDFs IN MRI
4.2.1 GAUSSIAN PDF
4.2.1.1 Moments of the Gaussian PDF
4.2.1.2 Central Moments
4.2.2 RICIAN PDF
4.2.2.1 Asymptotic Approximation of the Rician Distribution
4.2.2.2 Moments of the Rician PDF
4.2.2.3 Moments of the Rayleigh PDF
4.2.2.4 Generalized Rician PDF
4.2.2.5 Moments of the Generalized Rician PDF
4.2.2.6 PDF of Squared Magnitude Data
4.2.3 PDF OF PHASE DATA
4.3 PARAMETER ESTIMATION
4.3.1 PERFORMANCE MEASURES OF ESTIMATORS
4.3.2 PRECISION
4.3.3 ACCURACY
4.3.4 MSE
4.3.5 CRLB
4.3.6 ML ESTIMATION
4.4 SIGNAL AMPLITUDE ESTIMATION
4.4.1 INTRODUCTION
4.4.2 SIGNAL AMPLITUDE ESTIMATION FROM COMPLEX DATA
4.4.2.1 Region of Constant Amplitude and Phase
4.4.2.1.1 CRLB
4.4.2.1.2 ML Estimation
4.4.2.1.3 MSE
4.4.2.2 Region of Constant Amplitude and Different Phases
4.4.2.2.1 CRLB
4.4.2.2.2 ML Estimation
4.4.2.2.3 MSE
4.4.3 SIGNAL AMPLITUDE ESTIMATION FROM MAGNITUDE DATA
4.4.3.1 Region of Constant Amplitude and Known Noise Variance
4.4.3.1.1 CRLB
4.4.3.1.2 Conventional Estimation
4.4.3.1.3 Discussion
4.4.3.1.4 ML Estimation
4.4.3.1.5 Discussion
4.4.3.2 Region of Constant Amplitude and Unknown Noise Variance
4.4.3.2.1 CRLB
4.4.3.2.2 Geometric Average
4.4.3.2.3 Discussion
4.4.3.2.4 ML Estimation
4.4.4 DISCUSSION
4.4.4.1 CRLB
4.4.4.2 MSE
4.4.5 SIGNAL AMPLITUDE ESTIMATION FROM PCMR DATA
4.4.5.1 Region of Constant Amplitude and Known Noise Variance
4.4.5.1.1 CRLB
4.4.5.1.2 Mean Estimator
4.4.5.1.3 Modified RMS Estimator
4.4.5.1.4 ML Estimator
4.4.5.2 Experiments and Discussion
4.5 NOISE VARIANCE ESTIMATION
4.5.1 INTRODUCTION
4.5.2 NOISE VARIANCE ESTIMATION FROM COMPLEX DATA
4.5.2.1 Region of Constant Amplitude and Phase
4.5.2.1.1 CRLB
4.5.2.1.2 ML Estimation
4.5.2.1.3 MSE
4.5.2.2 Region of Constant Amplitude and Different Phases
4.5.2.2.1 CRLB
4.5.2.2.2 ML Estimation
4.5.2.2.3 MSE
4.5.2.3 Background Region
4.5.2.3.1 CRLB
4.5.2.3.2 ML Estimation
4.5.2.3.3 MSE
4.5.3 NOISE VARIANCE ESTIMATION FROM MAGNITUDE DATA
4.5.3.1 Background Region
4.5.3.1.1 CRLB (Variance)
4.5.3.1.2 CRLB (Standard Deviation)
4.5.3.1.3 ML Estimation
4.5.3.1.4 Conventional Estimation
4.5.3.2 Region of Constant Amplitude
4.5.3.3 Double-Acquisition Method
4.5.4 DISCUSSION
4.5.4.1 CRLB
4.5.4.2 MSE
4.6 CONCLUSIONS
4.7 APPENDIX
4.7.1 TRANSFORMATIONS OF PDFS
4.7.1.1 Theorem
4.7.1.2 Example
4.7.2 GENERAL THEOREM
4.7.3 APPROXIMATION OF THE MEAN OF A RANDOM VARIABLE
4.7.3.1 Theorem
4.7.3.2 Example
ABBREVIATIONS
SYMBOLS
REFERENCES
Chapter 5: Retrospective Evaluation and Correction of Intensity Inhomogeneity
CONTENTS
5.1 INTRODUCTION
5.2 EARLY SOLUTIONS
5.3 COMBINED SEGMENTATION AND INHOMOGENEITY CORRECTION METHODS
5.4 CORRECTION BASED ON EVALUATION OF THE HISTOGRAM
5.4.1 PARAMETRIC BIAS CORRECTION
5.4.2 INFORMATION MINIMIZATION AND N3
5.5 DISCUSSION AND CONCLUSION
ACKNOWLEDGMENTS
REFERENCES
Chapter 6: Noise Filtering Methods in MRI
CONTENTS
6.1 INTRODUCTION
6.2 THE MR IMAGE MODEL
6.3 WAVELET-BASED FILTERING
6.4 ADAPTIVE TEMPLATE FILTERING
6.5 ANISOTROPIC DIFFUSION FILTERING
6.6 APPLICATION OF ANISOTROPIC DIFFUSION FILTERING
REFERENCES
Part III: Image Processing and Quantitative Analysis
Chapter 7: Image Registration Methods in MRI
CONTENTS
7.1 INTRODUCTION
7.2 THE REGISTRATION PROBLEM
7.3 SIMILARITY METRICS
7.3.1 MUTUAL INFORMATION
7.3.2 PHANTOM EXPERIMENTS
7.4 THE INTERPOLATION EFFECT IN THE REGISTRATION PROBLEM
7.5 OPTIMIZATION TECHNIQUES IN IMAGE REGISTRATION
7.5.1 NELDER–MEAD SIMPLEX ALGORITHM
7.5.2 GENETIC ALGORITHMS
7.6 REGISTRATION OF MULTIPLE DATA SETS
7.7 BRAIN IMAGES REGISTRATION
7.7.1 FMRI IMAGES REGISTRATION
7.7.2 MAPPING OF FMRI ON ANATOMICAL IMAGES AND BRAIN ATLAS
7.7.3 FMRI REGISTRATION EXPERIMENT
7.8 CARDIAC IMAGES REGISTRATION
REFERENCES
Chapter 8: Multimodal Integration: fMRI, MRI, EEG, and MEG
CONTENTS
OVERVIEW
8.1 INTRODUCTION
8.2 SOURCE LOCALIZATION IN EEG AND MEG
8.2.1 ASSUMPTIONS UNDERLYING INTEGRATION OF EEG AND MEG
8.2.2 FORWARD MODELING
8.2.3 THE INVERSE PROBLEM
8.2.3.1 Equivalent Current Dipole Models
8.2.3.2 Linear Inverse Methods: Distributed ECD
8.2.3.3 Beamforming
8.3 MULTIMODAL EXPERIMENTS
8.3.1 MEASURING EEG DURING MRI: CHALLENGES AND APPROACHES
8.3.2 EXPERIMENTAL DESIGN LIMITATIONS
8.4 MULTIMODAL ANALYSIS
8.4.1 USING ANATOMICAL MRI
8.4.1.1 Registration of EEG and MEG to MRI
8.4.1.2 Segmentation and Tessellation
8.4.1.3 Forward Modeling of EEG and MEG
8.4.2 FORWARD MODELING OF BOLD SIGNAL
8.4.2.1 Convolutional Model of BOLD Signal
8.4.2.2 Neurophysiologic Constraints
8.4.3 ANALYSIS METHODS
8.4.3.1 Correlative Analysis of EEG and MEG with fMRI
8.4.3.2 Decomposition Techniques
8.4.3.3 Equivalent Current Dipole Models
8.4.3.4 Linear Inverse Methods
8.4.3.5 Beamforming
8.4.3.6 Bayesian Inference
8.5 CONSIDERATIONS AND FUTURE DIRECTIONS
REFERENCES
Chapter 9: A Survey of Three-Dimensional Modeling Techniques for Quantitative Functional Analysis of Cardiac Images
CONTENTS
ABSTRACT
9.1 INTRODUCTION
9.2 IMAGING TECHNIQUES FOR CARDIAC EXAMINATION
9.2.1 ANGIOCARDIOGRAPHY
9.2.2 CARDIAC ULTRASOUND
9.2.3 ISOTOPE IMAGING
9.2.4 CARDIAC COMPUTED TOMOGRAPHY
9.2.5 MAGNETIC RESONANCE IMAGING
9.3 CLASSICAL DESCRIPTORS OF CARDIAC FUNCTION
9.3.1 GLOBAL FUNCTIONAL ANALYSIS
9.3.2 MOTION AND DEFORMATION ANALYSIS
9.3.2.1 Motion Analysis
9.3.2.2 Wall Thickening
9.3.2.3 Strain Analysis
9.4 OVERVIEW OF MODELING TECHNIQUES
9.4.1 SURFACE MODELS
9.4.1.1 Continuous Models
9.4.1.1.1 Global Approaches
9.4.1.1.2 Hierarchical Approaches
9.4.1.1.3 Local Approaches
9.4.1.2 Discrete Models
9.4.1.2.1 Physics-Based Models
9.4.1.2.2 Spatiotemporal Models
9.4.1.2.3 Polygonal Models
9.4.1.2.4 Statistical Shape and Appearance Models
9.4.1.3 Implicitly Defined Deformable Models
9.4.2 VOLUMETRIC MODELS
9.4.3 DEFORMATION MODELS
9.4.3.1 General Techniques
9.4.3.1.1 Continuous Models
9.4.3.1.2 Discrete Models
9.4.3.2 MR Tagging-Based Techniques
9.4.3.2.1 Continuous Models
9.4.3.2.2 Discrete Models
9.5 DISCUSSION
9.5.1 VALIDATION
9.5.2 PERFORMANCE CRITERIA
9.5.2.1 Model Complexity or Flexibility
9.5.2.2 Robustness and Effective Automation
9.6 CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH
NOMENCLATURE
APPENDIX A
NONTRADITIONAL SHAPE AND MOTION DESCRIPTORS
GENERIC DESCRIPTORS
Mean and Gaussian Curvature
Shape Index and Shape Spectrum
LOCAL STRETCHING
MODEL-SPECIFIC SHAPE DESCRIPTORS
Geometrical Cardiogram (GCG)
Deformable Superquadric and Related Models
Global Motion Analysis Based On Departure from an Affine Model
Motion Decomposition through Planispheric Transformation
Modal Analysis: Deformation Spectrum
APPENDIX B
MR TAG LOCALIZATION TECHNIQUES
REFERENCES
Chapter 10: MRI Measurement of Heart Wall Motion
CONTENTS
10.1 INTRODUCTION
10.2 TAGGING
10.2.1 SELECTIVE TAGGING
10.2.2 SPATIAL MODULATION OF MAGNETIZATION
10.2.3 COMPLEMENTARY SPAMM
10.3 SPAMM IMAGE ANALYSIS
10.3.1 STRIPE TRACKING
10.3.2 HOMOGENEOUS STRAIN
10.3.3 NONHOMOGENEOUS STRAIN
10.3.4 RECONSTRUCTION OF 3-D KINEMATICS
10.3.5 SLICE FOLLOWING
10.4 HARP
10.4.1 THEORY
10.4.2 KINEMATICS
10.4.3 CSPAMM HARP
10.5 PHASE-CONTRAST VELOCITY
10.6 DENSE
10.6.1 THEORY
10.6.2 CSPAMM DENSE (CINE-DENSE)
10.6.3 KINEMATICS
10.7 DIFFUSION
10.8 FUTURE DIRECTIONS
10.9 CONCLUSIONS
REFERENCES
Part IV: Spectroscopy, Diffusion, Elasticity: From Modeling to Parametric Image Generation
Chapter 11: Principles of MR Spectroscopy and Chemical Shift Imaging
CONTENTS
11.1 INTRODUCTION
11.2 SVS
11.2.1 PRESS AND STEAM
11.2.2 ARTIFACTS IN SVS
11.2.3 WATER SUPPRESSION
11.2.4 COUPLING EFFECTS IN SVS
11.3 PRINCIPLES OF CSI
11.3.1 BASIC PRINCIPLES
11.3.2 AVOIDING UNDESIRED EXCITATIONS
11.3.3 RECONSTRUCTION OF CSI DATA
11.3.4 K-SPACE WEIGHTING TECHNIQUES
11.3.5 CSI PREPROCESSING
11.3.6 DISPLAY OF THE CSI DATA
11.3.7 COMPARISON OF SVS AND CSI TECHNIQUES
11.4 DIFFERENCES IN SEQUENCES FOR MEASUREMENTS WITH NONPROTON NUCLEI
REFERENCES
Chapter 12: Data Processing Methods in MRS
CONTENTS
12.1 INTRODUCTION
12.2 EXTRACTING INFORMATION FOR THE FID SIGNAL
12.3 TIME-DOMAIN PREPROCESSING
12.3.1 ZERO FILLING
12.3.2 WINDOWING
12.3.3 REMOVAL OF UNDESIRED RESONANCE
12.4 FREQUENCY-DOMAIN METHODS
12.5 TIME-DOMAIN METHODS
12.6 CONCLUSIONS
REFERENCES
Chapter 13: Image Processing of Diffusion Tensor MRI Data
CONTENTS
13.1 INTRODUCTION
13.2 DIFFUSION AND DIFFUSION TENSOR CALCULATION
13.3 ANISOTROPY AND MACROSTRUCTURAL MEASURES
13.3.1 GEOMETRICAL MEASURES OF DIFFUSION
13.3.2 MACROSTRUCTURAL TENSOR AND DIFFUSIVE MEASURES
13.4 VISUALIZATION OF DIFFUSION TENSORS
13.5 CONNECTIVITY ANALYSIS
13.6 METHOD ONE: DIFFUSION-BASED CONNECTIVITY
13.6.1 EXPERIMENTS
13.7 METHOD TWO: DISTANCE-BASED CONNECTIVITY
13.7.1 MEASURING DISTANCES IN THE TENSOR-WARPED SPACE
13.7.2 EXPERIMENTS
13.8 CONCLUSION
ACKNOWLEDGMENTS
REFERENCES
Chapter 14: Analysis of Dynamic Magnetic Resonance Elastography Data
CONTENTS
14.1 INTRODUCTION
14.2 ELASTIC PROPERTIES OF SOFT TISSUE
14.3 MR ELASTICITY IMAGING TECHNIQUES
14.4 MRE
14.5 DATA PROCESSING
14.5.1 EQUATIONS OF MOTION
14.5.2 SHEAR MODULUS AND MECHANICAL FREQUENCY
14.5.3 PHASE GRADIENT
14.5.4 LOCAL FREQUENCY ESTIMATION (LFE)
14.5.5 DIRECT INVERSION
14.5.6 VARIATIONAL METHOD
14.5.7 MATCHED FILTER
14.5.8 REMOVING THE LOCAL HOMOGENEITY ASSUMPTION
14.5.9 FINITE ELEMENT ANALYSIS
14.5.10 ANISOTROPIC INVERSIONS
14.5.11 HYPERELASTIC PARAMETER DETERMINATION
14.5.12 SIGNAL-TO-NOISE CONSIDERATIONS
14.5.13 PHASE UNWRAPPING
14.5.14 DIRECTIONAL FILTERING
14.6 RESULTS
14.6.1 PHANTOM OBJECT
14.6.2 ANIMAL TISSUES
14.6.3 BREAST
14.6.4 BRAIN
14.6.5 MUSCLE
14.6.6 ULTRASOUND WAVE FIELD VISUALIZATION
14.6.7 CHARACTERIZATION OF THERMALLY ABLATED TISSUE
14.7 CONCLUSION
ACKNOWLEDGMENTS
REFERENCES
Part V: BOLD Contrast MR Imaging and fMRI Signal Analysis
Chapter 15: Fundamentals of Data Analysis Methods in Functional MRI
CONTENTS
15.1 INTRODUCTION
15.2 PREPROCESSING OF FUNCTIONAL TIME SERIES
15.2.1 SLICE TIMING CORRECTION
15.2.2 MOTION CORRECTION
15.2.3 SPATIAL AND TEMPORAL FILTERING
15.3 STATISTICAL LOCALIZATION OF BRAIN ACTIVATION
15.3.1 THE GLM
15.3.1.1 Overall Effects (R2 Maps, F Maps)
15.3.1.2 Relative Contribution (RC) Maps
15.3.1.3 Specific Effects, Contrasts (t Maps)
15.4 SELECTION OF SIGNIFICANCE THRESHOLDS IN FMRI STATISTICAL MAPS
15.5 DATA-DRIVEN ANALYSIS OF FUNCTIONAL TIME SERIES
15.6 COMBINING BRAIN FUNCTION AND ANATOMY
15.6.1 COREGISTRATION OF FUNCTIONAL AND ANATOMICAL DATA SETS
15.6.2 SPATIAL NORMALIZATION
15.7 SEGMENTATION, SURFACE RECONSTRUCTION, AND MORPHING
REFERENCES
Chapter 16: Exploratory Data Analysis Methods in Functional MRI
CONTENTS
16.1 INTRODUCTION
16.2 MULTIVARIATE APPROACHES
16.3 DATA CLUSTERING APPROACHES
16.3.1 SIMILARITY
16.3.2 CLUSTERING TECHNIQUES
16.3.2.1 Hierarchical Methods
16.3.2.2 Hard Partitioning Methods
16.3.2.3 Fuzzy Clustering
16.3.2.4 Artificial Neural Networks
16.4 PCA
16.4.1 SPATIAL AND TEMPORAL PCA
16.4.1.1 Preprocessing of fMRI Data before PCA
16.4.2 INTERPRETATION OF THE PCA DECOMPOSITION
16.5 ICA
16.5.1 SPATIAL AND TEMPORAL ICA
16.5.2 METHODS FOR ICA
16.5.2.1 Historical Background
16.5.2.2 Nonlinear Decorrelation
16.5.2.2.1 Whitening as a Preprocessing Step
16.5.2.3 Information Maximization and Maximum Likelihood Approaches
16.5.2.4 Non-Gaussianity and Negentropy
16.5.2.5 Ambiguities in the ICA Model
16.5.3 PREPROCESSING
16.5.4 MODEL VALIDATION
16.5.5 INTERPRETATION OF THE RESULTS
16.5.5.1 Thresholding the Maps
16.5.5.2 Task-Related Activations
16.5.6 SIMULATION AND ALGORITHM COMPARISON
REFERENCES
Chapter 17: Classical and Bayesian Inference in fMRI
CONTENTS
17.1 INTRODUCTION
17.2 SPATIAL TRANSFORMATIONS
17.2.1 REALIGNMENT
17.2.2 ADJUSTING FOR MOVEMENT-RELATED EFFECTS IN FMRI
17.2.3 NORMALIZATION
17.2.4 COREGISTRATION OF FUNCTIONAL AND ANATOMICAL DATA
17.2.5 SPATIAL SMOOTHING
17.3 GENERAL LINEAR MODEL
17.3.1 DESIGN MATRIX
17.3.2 CONTRASTS
17.3.3 TEMPORAL BASIS FUNCTIONS
17.4 STATISTICAL PARAMETRIC MAPPING
17.4.1 RANDOM FIELD THEORY
17.5 POSTERIOR PROBABILITY MAPPING
17.5.1 EMPIRICAL EXAMPLE
17.6 DYNAMIC CAUSAL MODELING
17.6.1 EMPIRICAL EXAMPLE
17.7 CONCLUSION
REFERENCES
Chapter 18: Modeling and Nonlinear Analysis in fMRI via Statistical Learning
CONTENTS
18.1 INTRODUCTION
18.2 BACKGROUND
18.2.1 NONLINEARITIES IN FMRI
18.2.2 FEATURES OF FMRI DATA
18.2.3 FMRI DATA MODELING
18.2.4 OVERVIEW
18.3 STATISTICAL LEARNING THEORY
18.4 FMRI DATA ANALYSIS AND MODELING THROUGH SVR
18.4.1 DATA REPRESENTATION
18.4.2 TEMPORAL MODELING
18.4.3 MULTIRESOLUTION SIGNAL ANALYSIS
18.4.4 MERGING MODEL-DRIVEN WITH DATA-DRIVEN METHODS
18.4.5 GENERALIZATION TO MULTISESSION STUDIES
18.4.6 TESTING ON REAL FMRI DATA
18.5 CONCLUSIONS AND DISCUSSIONS
ACKNOWLEDGMENTS
REFERENCES
Chapter 19: Assessment of Cerebral Blood Flow, Volume, and Mean Transit Time from Bolus-Tracking MRI Images: Theory and Practice
CONTENTS
19.1 INTRODUCTION
19.2 THEORY
19.2.1 TRANSPORT FUNCTION
19.2.2 RESIDUE FUNCTION
19.2.3 CEREBRAL BLOOD VOLUME
19.2.4 MEAN TRANSIT TIME
19.2.5 CEREBRAL BLOOD FLOW
19.3 PRACTICE
19.3.1 FROM DSC-MRI SIGNAL TO TRACER CONCENTRATION
19.3.2 ARTERIAL INPUT FUNCTION
19.3.3 DECONVOLUTION
19.3.4 ABSOLUTE QUANTIFICATION ISSUES
19.3.5 CONCLUSION
ACKNOWLEDGMENTS
REFERENCES