"This informative new book reviews the methods for functional brain imaging analysis. Written and edited by a researcher in the field, this book ... is a welcome contribution to the field. ... The targeted audience includes individuals with a background in computer programming, numerical analysis, statistics, and medical imaging analysis. ... Each chapter ends with timely and relevant citations of the scientific literature." (Michael Joel Schrift, Doody's Book Reviews, March, 2014)

Chapter 1: MRI perfusion weighted imaging analysis

1.1 Perfusion imaging. 2

1.1.1 Indicator-dilution theory for DSC-MRI 3

1.1.2 MTT and CBV calculation. 5

1.1.3 DSC-MRI time series analysis. 7

1.2 Gamma-variate fitting. 9

1.2.1 Linear regression method for Gamma-variate fitting. 10

1.2.2 Nonlinear regression method for Gamma-variate fitting. 11

1.2.3 Baseline elimination for gamma-variate fitting. 15

1.2.4 Linear method and nonlinear method for gamma-variate fitting. 18

1.3 AIF selection. 18

1.3.1 Robust method for AIF determination. 19

1.3.2 Deconvolution calculation and residual function estimation. 21

1.3.3 SVD method for deconvolution. 22

1.3.4 L2 norm regularization for PWI study. 24

1.3.5 Piecewise linear method for ridge regression parameter estimation. 25

1.3.6 CBF, MTT, CBV, arrive time, and T-max maps. 29

1.4 Dispersion effects in DSC-MRI 32

1.4.1 Local density random walk for concentration time course. 32

1.4.2 Convolution method to study disperse effect 33

1.5 Summary of the PWI algorithm.. 33

Chapter 2: First level fMRI data analysis for activation detection

2.1 fMRI experimental design. 2

2.1.1 Block design. 2

2.1.2 Random ER design. 3

2.1.3 Phase-encoded design. 6

2.2 fMRI data pre-processing. 9

2.2.1 fMRI data motion correction. 9

2.2.2 fMRI time series normalization. 10

2.3 Activation detection: model free and model based methods. 11

2.3.1 Model free method: two sample t test for activation detection. 11

2.3.2 Correlation analysis method. 12

2.4 Models for hemodynamic response function and drift 12

2.4.1 HRF models for activation detection. 12

2.4.2 Drift models for activation detection. 15

2.5 General linear model (GLM) for activation detect 16

2.5.1 Generalized linear model (GLM) for activation detection. 16

2.5.2 Ordinary least square for parameters estimation in GLM.. 17

2.5.3 FOS to solve the inverse problem.. 18

2.5.4 Weighted least square estimation. 20

2.5.5 AR(1) model 20

2.5.6 AR(q) model 21

2.6 Hypothesis test and threshold correction. 22

2.6.1 Hypothesis test for the activation detection. 22

2.6.2 Bonferroni and FDR/FWE threshold correction. 24

2.6.3 Number of independent tests. 27

2.6.4 Permutation/random test 27

2.7 Summary of algorithm for 1^st level fMRI data analysis. 28

Chapter 3: 2^nd level fMRI data analysis using mixed model

3.1 Mixed model for fMRI data analysis. 2

3.1.1 Fixed and random effects in fMRI analysis. 3

3.1.2 Generalized linear mixed model for fMRI study. 3

3.1.3 Mixed model and its numerical estimations. 4

3.2 Numerical analysis for mixed effect models. 5

3.2.1 Two stage model for 2^nd level fMRI analysis. 5

3.2.2 Maximum likelihood method for variance estimation. 6

3.2.3 Different runs combination. 6

3.2.4 Group comparison in the mixed model 8

3.3 Iterative trust region method for ML estimation. 10

3.3.1 Levenberg–Marquardt (LM) algorithm.. 10

3.3.2 LM algorithm implementation. 11

3.3.3 T and likelihood (LR) tests for the mixed model 12

3.3.4 Modified EM algorithm for group average. 12

3.3.5 One simulation example for the numerical processing. 13

3.3.6 Simulation to combine 2 runs. 17

3.3.7 Combination of 100 runs. 18

3.4 Exception trust region algorithm for second level fMRI data analysis. 20

3.4.1 Average runs within subject 21

3.4.2 Comparing fMRI response within subject 22

3.4.3 Compare group of subjects. 25

3.4.4 Numerical implementation details. 27

3.4.5 Further numerical improvement: BFGS method. 27

3.4.6 Potential applications and further development 28

3.5 Degree of freedom (DF) estimation. 29

3.5.1 Estimation of DF for T distribution. 29

3.5.2 ML estimation of mixture of t distributions for mixed model 30

3.5.3 Hessian matrix calculation for trust region algorithm.. 31

3.5.4 Trust region and expectation trust region algorithms for df estimation. 32

3.6 fMRI data analysis future directions. 33

3.7 Second level fMRI data processing algorithm summary. 33

Chapter 4 : fMRI effective connectivity study

4.1 Nonlinear system identification method for fMRI effective connectivity analysis. 2

4.1.1 Current methods for fMRI effective connectivity analysis. 2

4.1.2 Nonlinear system identification theory. 3

4.1.3 Granger causality (GC) tests. 6

4.1.4 Directionality indices. 7

4.1.5 Network structure and regional time series extraction. 7

4.1.6 Examples to apply NSIM to study effective connectivity. 9

4.2 Model selections for effective connectivity study. 11

4.2.1 Nonlinear model for fMRI effective connectivity study. 11

4.2.2 Model selection for NSIM in effective connectivity study. 12

4.2.3 AIC and AICc criteria for model selection. 13

4.2.4 MLARS algorithm for model selection. 13

4.2.5 Nonlinear interaction terms for the effective connectivity analysis. 16

4.2.6 Advantages and disadvantages of NSIM.. 16

4.3 Robust method for second level analysis. 17

4.3.1 Robust regression and breakdown-point 17

4.3.2 Least trimmed squares for second level effective connectivity analysis. 18

4.4 Effective connectivity for resting-state fMRI data. 20

4.4.1 Resting-state fMRI 20

4.4.2 Example of applying NSIM to RSN from rfMRI 21

4.5 Limitations for fMRI effective connectivity in this study. 22

4.6 Summary of the algorithm for fMRI effective connectivity study. 23

Chapter 5: Diffusion weighted imaging analysis

5.1 Basic principle of diffusion MRI and DTI data analysis. 2

5.1.1 Physical background of MRI diffusion equation. 2

5.1.2 Apparent diffusion coefficient (ADC) map and DTI calculation. 3

5.1.3 Invariant indices for DTI analysis. 5

5.1.4 High order DTI data analysis. 7

5.2 Fiber tracking. 8

5.2.1 Color encoding method to represent fiber 8

5.2.2 Fiber tracking and 3D representation. 9

5.3 High angular resolution diffusion imaging (HARDI) analysis. 11

5.3.1 Q-ball imaging (QBI) 11

5.3.2 ODF representation. 12

5.3.3 ODF reconstruction theory. 12

5.3.4 Spherical harmonics (SH) 13

5.3.5 Least square method with constraints. 15

5.3.6 Testing the algorithm on rat data. 16

5.4 Adaptive Q-ball imaging regularization. 18

5.4.1 Generalized cross validation (GCV) algorithm for regularization. 18

5.4.2 Regularization or not regularization?. 19

5.4.3 GFA and ODF maps from rat data. 21

5.4.4 GCV method for human QBI ODF regularization. 22

5.5 Diffusion spectrum imaging. 23

5.5.1 Difference between QBI and DSI acquisition. 24

5.5.2 DSI image analysis. 25

5.5.3 DSI GFA map using fixed and GCV regularization method. 26

5.5.4 ODF map for DSI using fixed method and GCV method. 27

5.6 Summary and future directions. 28

5.7 Summary of DTI, QBI and DSI image analysis methods. 28

Chapter 6: Voxel based morphometry and its application to Alzheimer’s disease study

6.1 Background for voxel based morphometry analysis. 2

6.1.1 MRI image segmentation. 2

6.1.2 MRI image registration. 3

6.1.3 Statistical methods for VBM analysis. 3

6.2 Enhanced VBM.. 3

6.2.1 Histogram match. 4

6.2.2 Apply to AD study. 5

6.3 Longitudinal VBM and its application to AD study. 8

6.3.1 Longitudinal VBM preprocessing steps. 8

6.3.2 Results of longitudinal VBM for AD study. 9

6.4 Effective connectivity for longitudinal data analysis. 11

6.4.1 AR model within subjects for effective connectivity study. 11

6.4.2 An example from longitudinal AD structural MRI 12

6.4.3 Advantage and disadvantages of this study. 13

6.5 Other type of sMRI data analysis. 14

6.5.1 AD classification. 14

6.5.2 Structural covariance. 14

6.6 Summary of (longitudinal) VBM analysis methods. 14

Appendixes

Question answers and hints

Dr. Xingfeng Li obtained his first degree in automation control, master degree of engineer in power system control, and Ph.D. degree in pattern recognition and machine intelligence in 1996, 2001, and 2004, respectively. Since then, he has been working in various research institutions in different countries on MRI and PET image analysis. He worked as postdoc research fellow from 2004-2009 at McGill University in Canada and INSERM, Paris 6th University in France. From 2009–2013, he has been a research fellow at the University of Ulster, UK. He is currently working on applying nonlinear system identification theory for studying nonlinear dynamic brain system. He conducts extensive research work using fMRI, diffusion weighted imaging, perfusion weighted imaging, structural MRI, and PET methods to investigate human brain system. His research interests include functional medical imaging analysis, numerical analysis, statistical analysis, nonlinear system identification, and optimization algorithms. He has published dozen of papers in the journals NeuroImage, IEEE Transaction on Medical Imaging, and Medical Image Analysis. He is also a member of the editorial board of Journal of Nonlinear Dynamics.

With strong numerical and computational focus, this book serves as an essential resource on the methods for functional neuroimaging analysis, diffusion weighted image analysis, and longitudinal VBM analysis. It includes four MRI image modalities analysis methods. The first covers the PWI methods, which is the basis for understanding cerebral flow in human brain. The second part, the book’s core, covers MRI methods in three specific domains: first level analysis, second level analysis, and effective connectivity study. The third part covers the analysis of Diffusion weighted image, i.e. DTI, QBI and DSI image analysis. Finally, the book covers (longitudinal) VBM methods and its application to Alzheimer’s disease study.

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