University of Southern California Dissertations and Theses

Methods for improving reliability and consistency in diffusion MRI analysis

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Methods for improving reliability and consistency in diffusion MRI analysis

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Content METHODS FOR IMPROVING RELIABILITY AND CONSISTENCY IN DIFFUSION MRI
ANALYSIS
by
Yihao Xia
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2023
Copyright 2023 Yihao Xia
Dedication
To my family,
for always loving and supporting me.
Acknowledgements
I would like to thank my doctoral advisor, Prof. Yonggang Shi, whose expertise, patience, and guidance
throughout this process were invaluable. Despite the challenges posed by the pandemic, his dedication to
my project motivated me to stay focused, delve deeply into my work, and grasp the broader perspective.
I would also like to thank my committee members, Prof. Justin P. Haldar, Prof. Cauligi S. Raghavendra,
and Prof. Paul M. Thompson. Their insightful comments and constructive suggestions have elevated the
quality of my work, fostering its progression to a superior level.
My work has also benefited from Dr. Junyan Wang and Dr. Dogu Baran Aydogan, the postdoctoral
researchers in our group, for their continuous assistance and intellectual discussions were instrumental in
initiating my research in diffusion MRI and tractography. My thanks are also extended to my colleagues
and friends, Dr. Mona Sharifi Sarabi and Xinyu Nie. Their support and shared wisdom have provided a
stimulating and nurturing environment, fostering my intellectual growth.
I am indebted to my parents for instilling the values of integrity, diligence, and perseverance in me.
Your encouragement, understanding, and love have facilitated my journey through life, free from pressure.
Finally, I wish to convey my appreciation to my partner, Yifan Chen. Your presence enhances my existence
and perpetually inspires me to strive for the best within myself.
iii
TableofContents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Principal Focuses of the Doctoral Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 2: Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Diffusion Process and Diffusion MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Diffusion Tensor Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 High Angular Resolution Diffusion Imaging (HARDI) . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Spherical harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Tractography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 3: Groupwise Track Filtering via Iterative Message Passing and Pruning . . . . . . . . . . 16
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Algorithmic Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Fornix bundle reconstruction from ADNI2 data . . . . . . . . . . . . . . . . . . . . 27
3.3.2 Locus coeruleus pathway and atlas from HCP data . . . . . . . . . . . . . . . . . . 30
3.3.3 Quantitative comparison of corticospinal tract reconstruction from HCP data . . . 33
3.3.4 Computational cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Chapter 4: Personalized Diffusion MRI Harmonization . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
iv
4.2.1 Diffusion MRI harmonization in a common space . . . . . . . . . . . . . . . . . . . 49
4.2.2 Personalized template estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2.3 Personalized harmonization based on mapping spherical harmonics features . . . . 52
4.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.1 Dataset and implementation details . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.1.1 Subjects and dMRI data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.1.2 Implementation details of dMRI harmonization . . . . . . . . . . . . . . 55
4.3.2 Local reference selection and personalized template construction . . . . . . . . . . 56
4.3.3 Regularization parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.3.1 Across-reference regularization . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.3.2 Spatial smoothness regularization . . . . . . . . . . . . . . . . . . . . . . 59
4.3.4 Inter-site variation and harmonization . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.5 Number of available references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.6 Impact of personalized harmonization on DTI feature distribution in cortical gray
matter regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.7 Preservation of fiber orientation distribution (FOD) . . . . . . . . . . . . . . . . . . 66
4.3.8 Preservation of sex effects on DTI features . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Chapter 5: Personalized dMRI Harmonization on the Cortical Surface . . . . . . . . . . . . . . . . . 70
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2.1 Diffusion MRI harmonization and LinearRISH framework . . . . . . . . . . . . . . 74
5.2.2 Construction of personalized templates . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2.2.1 Inter-subject local correspondence detection on the cortical surface . . . 75
5.2.2.2 Construction of personalized reference sets . . . . . . . . . . . . . . . . . 76
5.2.2.3 Weighted pooling for site-effect estimation . . . . . . . . . . . . . . . . . 76
5.2.3 Elimination of confounding variables in dMRI harmonization . . . . . . . . . . . . 77
5.2.4 RISH based harmonization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.1 Subjects and Implementation details . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.1.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.1.2 dMRI data and preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.3.1.3 Diffusion weighted signal projection on the cortical surface . . . . . . . 81
5.3.1.4 Implementation details of RISH feature based harmonization . . . . . . . 82
5.3.2 Inter-subject local correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3.3 Personalized harmonization mapping on the cortical surface . . . . . . . . . . . . . 83
5.3.4 Parameter selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.5 Harmonization evaluation of DTI in the presence of age confounding . . . . . . . . 88
5.3.6 Preservation of the association between DTI features and age . . . . . . . . . . . . 90
5.3.7 Preservation of gender differences . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4 Discussion and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Chapter 6: Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.1 Groupwise Track Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.1.1 Accelerating groupwise fiber filtering via representation learning . . . . . . . . . . 97
6.2 Personalized Diffusion MRI Harmonization . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.1 Beyond the RISH feature based harmonization . . . . . . . . . . . . . . . . . . . . . 98
v
6.2.2 Mitigating multisite discrepancies in subjects with disease . . . . . . . . . . . . . . 99
6.2.3 Towards learning based dMRI harmonization . . . . . . . . . . . . . . . . . . . . . 99
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
vi
ListofTables
3.1 Hausdorff Distance of Fiber Bundles to Manually Delineated ROIs. . . . . . . . . . . . . . . 39
3.2 Size (num of tracks) of filtered fiber bundles. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Summary of the Computing Cost in Each Experiment . . . . . . . . . . . . . . . . . . . . . 41
4.1 Diffusion MRI parameters for the Siemens Prisma and GE 750 scanner in the ABCD study. 55
4.2 Inter-site coefficients of variation and negative rates ( r
N
) after harmonization for FA and
MD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Jensen-Shannon divergence of FA features across scanners before (Orig) and after
harmonization (LinearRISH and our method). Results from both the left and right
hemispheres are listed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4 Jensen-Shannon divergence of MD features across scanners before (Orig) and after
harmonization (LinearRISH and our method). Results from both the left and right
hemispheres are listed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 FOD peaks before and after harmonization. Row 1 and 2: harmonized GE toward
SIEMENS; row 3 and 4: harmonized SIEMENS toward GE. . . . . . . . . . . . . . . . . . . 67
5.1 Inter-site differences analysis on b=1000 s/mm
2
shell . . . . . . . . . . . . . . . . . . . . 90
5.2 Inter-site differences analysis on b=3000 s/mm
2
shell . . . . . . . . . . . . . . . . . . . . 91
vii
ListofFigures
2.1 Illustration of unit gradient directions in (a), a B0 image in (b), and multiple diffusion-
weighted images in (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 A axial view of fractional anisotropy image (a) and mean diffusivity image (b). . . . . . . . 12
2.3 Spherical sampling schemes of single-shell and multi-shell HARDI. . . . . . . . . . . . . . 13
2.4 RISH features at different spherical harmonics orders. The RISH features at order 0, 2, 4,
6, and 8 are shown from left to right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Whole brain tractography and reconstruction of fiber bundles. . . . . . . . . . . . . . . . . 15
3.1 An illustration of the proposed groupwise track filtering framework. All fiber bundles
from N subjects will first be nonlinearly warped to a common space such as the MNI152
atlas. Outlier points (colored in yellow) will be iteratively pruned based on the consistency
measure obtained via messages passed from tracks in a reference set, which is updated
dynamically. Once the pruning process is completed, the same pruning operations are
applied to points on the original tracks to obtain the filtered fiber bundles. . . . . . . . . . 19
3.2 Calculation of localized consistency measures on a track based on message passing. (a)
The points on the track under consideration (cyan) are plotted as gray dots. The points on
the three reference tracks are plotted in red, green, and blue, respectively. (b) Each point
on the track under consideration is color-coded according to the consistency measure
from messages they receive from neighboring tracks. The consistency measures range
from 0 to 3 as 3 reference tracks are used in this example. . . . . . . . . . . . . . . . . . . . 23
3.3 ROIs used for fornix bundle reconstruction are plotted against the MNI152 T1 image. (a)
A sagittal view of the manually drawn seed (green), inclusion (red), and exclusion (blue)
ROIs. (b) An axial view of the manually drawn exclusion ROIs. Note they do not overlap
with the seed and inclusion ROIs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 The iterative pruning results with different proximity requirements of the fornix bundle of
an EMCI subject. The original bundle and the filtering outcomes with proximity threshold
δ = 20 mm,7 mm,3 mm, and2 mm, corresponding to the results after 1, 2, 5, and 10
iterations of filtering, are displayed from left to right, respectively. . . . . . . . . . . . . . . 29
viii
3.5 Input and reconstructed fornix bundles from ADNI2 subjects. Each sub-figure from (a)
to (d) shows three input (top row) and filtered (bottom row) bundles from the AD, LMCI,
EMCI, and CN groups, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 The filtering results of the same EMCI subject in Fig. 3.4 with different choices of the
affinity parameter K. The input fiber bundle, and the filtered bundle with K = 8, 16, 24, 32,
and 39, are shown from left to right, respectively. . . . . . . . . . . . . . . . . . . . . . . . 30
3.7 The impact of the parameterL
max
on track filtering performance. (a) Input LC pathway of
an HCP subject. Spurious tracks were highlighted by the ellipsoid and arrow. (b) Filtered
LC pathways with varyingL
max
=0.05,0.1,0.3, and0.5, from left to right, respectively. . 32
3.8 Results of filtering the right LC bundle from five HCP subjects. Top row: input LC
pathways; Bottom row: filtered bundles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.9 A probabilistic atlas of the right LC bundle is plotted on eight coronal slices in the MNI152
space. (a) indicates the zoom-in region (within the red box) on one coronal slice. The
corresponding regions on different coronal slices are magnified and displayed in (b). . . . . 33
3.10 Groupwise track filtering results of the left CST from five representative HCP subjects.
Top row: input fiber bundles from FOD-based tractography. The white arrow and ellipse
highlight the main outliers removed during the filtering process. Middle row: filtered fiber
bundles generated by our groupwise filtering algorithm. Bottom row: filtering results
at the whole-streamline level by adding back pruned points for tracks retained after the
groupwise filtering process, i.e., tracks shown in the middle row. . . . . . . . . . . . . . . 35
3.11 A comparison of the filtering results from our method and other track filtering methods
and two tract reconstruction methods for the left CST of an HCP subject. (a) The input
bundle reconstructed with one inclusion ROI (the white disk). (b) The overlay of the
filtered bundle from our method and the five manually delineated ROIs (white disks). (c)
The overlay of the filtered bundle from QuickBundles and the five manually delineated
ROIs (white disks). (d) CCI-based result. The left CST bundle reconstructed by the
atlas-based method in RecoBundles and SlicerDMRI are displayed in panels (e) and
(f), respectively. The whole brain tractography, used as the input for both atlas-based
methods, is displayed in the top-right in (e). . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.12 The impact of proximity parameters on CST reconstruction with our groupwise method.
The mean and standard deviation of Hausdorff distances (y-axis on the left side) from the
reconstructed bundle to each ROI (2 - 5) are plotted in (a) and (b) as colored curves and
shaded regions with respect to the change of the parameters σ and δ , respectively. In
addition, the number of tracks (y-axis on the right side) in the reconstructed bundle are
plotted as black dots with respect to the change of parameters. . . . . . . . . . . . . . . . . 40
ix
4.1 Inter-subject anatomical variability and the resulting mismatch between individual
subjects and the sample mean template. (a) FA images of two ABCD subjects co-registered
to the template space. Top: NDARINV15MFU6UZ acquired from a GE MR750 scanner;
bottom: NDARINV1NW3HM13 scanned on a Siemens Prisma scanner. (b) A template
image constructed from the FA images of 100 ABCD subjects. Left column: axial slices
of the two ABCD subjects and the template. For each axial slice, zoomed views of the
ROIs highlighted by yellow and blue boxes are shown in the middle and right columns,
respectively, where the variations of the brain anatomy are noticeable. . . . . . . . . . . . 46
4.2 An overview of our personalized dMRI harmonization method. (a) The overall framework
for the estimation of personalized templates and inter-site mapping functions to achieve
the harmonization from the source to the target site. (b) Details about the estimation of
the personalized pooling tensors (W
src
andW
tar
) by computing a weight vector w at
each voxel as the solution of a convex optimization problem based on local similarity of
the anatomy between the query subject and reference subjects of each site. . . . . . . . . . 48
4.3 An illustration of selected and discarded references at two representative locations. In
each subfigure (a) and (b), the results are organized as follows. Left: the transverse
slice of the FA image indicating the location of the query patch in the common space
(highlighted in red); middle: a zoomed view of the query patch (in red box); right (top row):
top-4 reference patches ordered by their pooling weights; right (bottom row): discarded
reference patches with zero weights. The assigned weights and the query-reference
anatomical similarity are displayed above each reference patch in the form of "weight
(anatomical similarity)". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 A comparison of site-specific templates estimated by the LinearRISH method based on
sample mean and our personalized method for the zeroth-order RISH feature. Left: a
transverse slice of the zeroth-order RISH feature of a query subject (GE Subject ID:
NDARINV15MFU6UZ). Right (top row): the corresponding slice of templates estimated
from the GE and SIEMENS cohort by the LinearRISH method. Right (bottom row): the
corresponding slice of the templates estimated from the GE and SIEMENS cohort by our
personalized method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5 The spatial distribution of reference numbers in personalized and site-specific template
construction with different choices of the regularization parameter γ 1
. (a) Query subjects
from the GE cohort and Reference subjects from the SIEMENS cohort. (b) Query subjects
from the SIEMENS cohort and Reference subjects from the GE cohort. . . . . . . . . . . . . 60
4.6 Spatial consistency regularization by changing the parameter γ 2
. For query subjects
from the GE cohort and reference subjects from the SIEMENS cohort, the mean values of
the weight smoothness measure across all query subjects with respect to varyingγ 2
are
plotted in red. Similarly, the green curve shows the results under an alternative setting
(query subjects from the SIEMENS and reference set from the GE cohort). . . . . . . . . . . 61
x
4.7 Inter-site coefficients of variation of FA and MD before and after harmonization. The
results for original datasets before harmonization, SIEMENS + harmonized GE, and GE +
harmonized SIEMENS are shown in the left, middle, and right panels. In the second and
third panels, the results of LinearRISH, our method, and the improvement rate (IR
CoV
)
are displayed from left to right, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.8 Inter-site CoVs for FA and MD with varying numbers of available references. (a) and (b)
display the inter-site CoVs (in red line) and the negative rates of CoV (in blue line) of FA
and MD with SIEMENS + harmonized GE data. (c) and (d) show the corresponding results
for GE + harmonized SIEMENS data. The inter-site CoVs and the negative rates of CoV
for the results produced by LinearRISH with 100 references from each platform are in red
dashed-line and blue dashed-line, respectively, in each panel. . . . . . . . . . . . . . . . . . 64
4.9 FA distributions before and after harmonization. The density curves of FA within the
frontal, occipital, parietal, and temporal lobes of the left hemisphere are shown in (a), (b),
(c), and (d), respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.10 Preservation of sex differences during harmonization. The effect sizes of sex differences in
FA before (blue), after harmonization using LinearRISH (orange), and our method (green)
for the GE cohort. The quantitative values of effect sizes ( d) and the absolute differences
(∆ d) between the effect sizes before and after harmonization are annotated in the form of
"d(∆ d)". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.1 Comparison between the anatomy of the individual subjects after volumetric registration:
co-registered FA images of three HCP subjects are shown from left to right. Typical
misaligned regions are circled out. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 An overview of the proposed personalized dMRI harmonization on the cortical surface. (a)
shows the overall framework of personalized dMRI harmonization on the cortical surface
and (b) illustrates the detection of inter-subject local correspondence . . . . . . . . . . . . 73
5.3 Examples of inter-subject correspondence detection on the cortical surface at two typical
locations: (a) caudal middle frontal and (b) middle temporal. The query vertex (a red dot)
on a source cortical surface (left) and corresponding reference sets (dots in red) of two
reference subjects with better correspondence and another two references with relatively
larger distances are displayed. The multi-scale vertex-wise differences, annotated under
each panel, increase from left to right. The corresponding parcels of cortex in green
generated using Desikan-Killiany’s cortical atlas are used to demonstrate the anatomical
information of the vertex in each panel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4 Personalized inter-site mapping on the cortical surface for the HCP subject 103414 in (a)
and HCD0042420 from HCP-D dataset in (b) forb = 1000 s/mm
2
shell. The scale maps
for SH order of 0, 2, 4, 6, and 8 are arranged from left to right. . . . . . . . . . . . . . . . . 85
5.5 Personalized inter-site mapping on the cortical surface for the HCP subject 103414 in (a)
and HCD0042420 from HCP-D dataset in (b) forb = 3000 s/mm
2
shell. The scale maps
for SH order of 0, 2, 4, 6, and 8 are arranged from left to right. . . . . . . . . . . . . . . . . 85
xi
5.6 Parameter tuning of personalized dMRI harmonization on the cortical surface. . . . . . . . 87
5.7 The impact of harmonization on the relationship between FA and age in the left frontal
lobe (a) and left temporal lobe (b) on theb = 1000 s/mm
2
shell. Each dot represents the
FA and age relationship of a subject. The linear regression of the integration of data from
HCP with HCP-D, HCP-D harmonized by using LinearRISH, and HCP-D harmonized by
using our method, are shown in green, red, and orange dash lines, respectively. The blue
line represents the estimated linear relationship between age and FA for the HCP site. . . . 92
5.8 The impact of harmonization on the relationship between MD and age in the right frontal
lobe (a) and left temporal lobe (b) on theb = 1000 s/mm
2
shell. The linear regression of
pooled data from HCP with HCP-D, HCP-D harmonized using LinearRISH, and HCP-D
harmonized using our method are shown in green, red, and orange dash lines, respectively.
The blue line represents the linear relationship between age and MD for the HCP site. . . . 93
5.9 The effect size of gender difference for FA on the b = 1000 s/mm
2
shell. The effect size
(d
c
) and the modification ( ∆ d
c
) after harmonization are denoted in the form ofd
c
(∆ d
c
). . 94
xii
Abstract
Diffusion magnetic resonance imaging (dMRI), capable of quantifying the diffusion of water in vivo, allows
the probing of brain microstructure and connectivity non-invasively. Though widely used in neuroscience
and clinical research, dMRI still faces numerous technical challenges. To improve the reliability and con-
sistency in dMRI analysis, this thesis focuses on developing novel computational methods including track
filtering for the removal of artifacts in tractography and dMRI harmonization for the mitigation of inter-site
variability.
Tractography is an important tool for the in vivo analysis of brain connectivity based on diffusion
MRI data, but it has well-known limitations in false positives and negatives for the faithful reconstruc-
tion of neuroanatomy. These problems persist even in the presence of strong anatomical priors in the
form of multiple regions of interest (ROIs) to constrain the trajectories of fiber tractography. To improve
the reliability of fiber bundle reconstruction, we propose a novel track filtering method by leveraging the
groupwise consistency of fiber bundles that naturally exists across subjects. We first formalize our group-
wise concept with a flexible definition that characterizes the consistency of a track with respect to other
group members based on three important aspects: degree, affinity, and proximity. An iterative algorithm
is then developed to dynamically update the localized consistency measure of all streamlines via message
passing from a reference set, which then informs the pruning of outlier points from each streamline.
The inter-site variability of dMRI hinders the aggregation of dMRI data from multiple centers. This
necessitates dMRI harmonization for removing non-biological site-effects. One fundamental challenge in
xiii
dMRI harmonization is to disentangle the contributions of scanner-related effects from the variable brain
anatomy for the observed imaging signals. To account for the misalignment of neuroanatomy that still
widely persists even after registration, we propose a personalized framework to more effectively address
the confounding from the misalignment of neuroanatomy in dMRI harmonization. The main novelty of
our method is the adaptive computation of personalized templates for the estimation of site effects and
inter-site mapping.
The emergence of high-resolution dMRI data across various connectome imaging studies allows the
large-scale analysis of cortical microstructure. Existing harmonization methods, however, perform poorly
in the harmonization of dMRI data in cortical areas because they rely on image registration methods to
factor out anatomical variations, which have known difficulty in aligning cortical folding patterns. To
overcome this fundamental challenge in dMRI harmonization, we propose a framework of personalized
dMRI harmonization on the cortical surface to improve the dMRI harmonization of cortical gray matter by
adaptively estimating the inter-site harmonization mappings. This is the first work in the field for dMRI
harmonization on cortical surfaces.
In summary, our work advances the state-of-the-art in track filtering and dMRI harmonization by
devising novel algorithms to account for the impact of variable brain anatomy. Related software tools
have also been developed and will be distributed freely to the research community.
xiv
Chapter1
Introduction
1.1 Motivation
Diffusion magnetic resonance imaging (dMRI) [7], capable of quantifying the diffusion of water molecules
in vivo, allows the probing of brain microstructure non-invasively. Over the last decades, dMRI has been
employed extensively to investigate pathological alternations in brain microstructure [67, 141, 109, 65],
delineate white matter tracts for the guidance of neurosurgery [26, 118], advance our understanding of
brain development [92, 13, 24], and explore structural connectivity of the human brain [48, 122]. Despite its
extensive applications in neuroscience and clinical research, dMRI is still confronted with many technical
challenges in data acquisition, preprocessing, diffusion signal modeling, interpretation, and validation. The
focus of this thesis is on improving the reliability and consistency in dMRI analysis via 1) filtering artifacts
in tractography induced by the intrinsic uncertainty in microstructure estimation and 2) mitigating inter-
site discrepancies of dMRI data caused by the inter-site variations.
• Artifacts in Tractography. Tractography is the central technique for noninvasively revealing
white matter pathways/tracts in the brain. It provides valuable insights into brain connectivity
and facilitates the quantification of white matter integrity. However, tractography, a process that
1
generates fiber trajectories by successively inferring from local orientation fields, is subject to un-
certainty in the estimation of local orientations. With the potential error propagation in trajectory
proceeding, tractography has well-known limitations in false positives and negatives for the faithful
reconstruction of neuroanatomy. These limitations hinder the reproducibility and comparability of
dMRI studies across different populations, posing a significant limitation to tractography [5, 78].
To improve the reliability of tractography, it is thus desirable to develop automated track filtering
techniques for outlier removal and enhance the consistency in fiber bundle reconstruction.
• Inter-siteDiscrepanciesindMRIData. Diffusion MRI, with its unique capability of revealing the
diffusion process, offers significant potential for advancing our understanding of the human brain.
However, constrained by the expense of data collection, many dMRI based research studies, relying
only on small datasets, suffer from potential reproducibility problems. To mitigate this issue, there
is growing interest in data aggregation of targeted populations across multiple imaging centers [89,
13] and dataset expansion via incorporating cohorts from publicly available datasets [122], by which
sample size and statistical power would be increased. However, various non-biological effects in-
duced by inter-site variations in magnetic field strength, scanner vendor, and acquisition protocol,
impede the comparability of dMRI data across imaging sites [125, 143, 76]. These discrepancies in
dMRI across sites, which can contribute to diminished statistical power and biased findings, should
be taken into account in multisite studies. To enhance the consistency of dMRI data acquired from
multiple sites, it is essential to develop novel dMRI harmonization methods to alleviate the discrep-
ancies across sites.
2
1.2 PrincipalFocusesoftheDoctoralStudy
The uniqueness of each individual’s brain, attributed to variations in size, shape, and cortical folding pat-
terns, presents a fundamental challenge in neuroscience research. Image registration techniques play a piv-
otal role in establishing inter-subject correspondences, facilitating meaningful comparisons across subjects
both in volume [51, 44, 104, 4] and on surface [114, 121]. Image normalization via co-registering multiple
images into a common atlas space is conventionally performed to allow for comparisons across a group
of subjects. However, image normalization, inherently reliant on population averages, may inadequately
represent the brain structure of a specific individual and thus fail to fully account for the pervasive inter-
subject variability [75, 140]. With large-scale datasets encompassing a broad spectrum of individual varia-
tions, we can now investigate brain structures within an adaptively generated context of sub-populations
specific to each individual. Within this personalized context, we can more effectively model the complexity
and variability of the human brain. In the domain of dMRI analysis, the complexity of inter-subject vari-
ability intertwines with the reproducibility and reliability of dMRI data. Thus, it is essential to incorporate
the modeling of inter-subject anatomical differences to advance the state-of-the-art in dMRI analysis. This
forms the backbone of my Ph.D. research in devising methods to enhance the reliability and consistency
of dMRI data analysis. Specifically, my research objectives in this thesis cover 1) Groupwise track filtering,
2) Diffusion MRI harmonization via personalized template mapping, and 3) Personalized diffusion MRI
harmonization on the cortical surface.
GroupwiseTrackFiltering. In reconstructing white matter pathways, a set of constraints conveying
anatomical prior and geometric regularization is typically employed to improve the validity of fiber bundle
reconstruction by excluding spurious streamlines. The conventional approach uses anatomical priors in
the form of region-of-interests (ROIs) [14, 127, 131]. This method is most effective for regularizing path-
ways with clear anatomical definitions [111]. However, due to incomplete anatomical knowledge and/or
the high cost of delineating extensive anatomical labels, a small number of ROIs may not effectively and
3
reliably reveal anatomy. Then, outlier fiber tracks often still exist in the reconstructed fiber bundles [101].
To compensate for the insufficiency of anatomical constraints, current track filtering methods conduct
artifact removal based on geometric or topographic regularity [43, 6, 128, 59]. However, these methods as-
sume regularity at the individual level and overlook the geometric consistency that naturally exists across
subjects. In addition, these tract filtering approaches typically operate the filtering process at the level of
the whole streamline, ignoring the spatial heterogeneity of streamline consistency. To impose geometric
constraints at the sub-population/group level and perform filtering at the segment level of streamlines,
we focus on developing a novel track filtering method by incorporating regularity from the perspective of
groupwise consistency.
Diffusion MRI Harmonization via Personalized Template Mapping. The incompatibility of
dMRI data from multiple sites makes data harmonization essential in large-scale imaging studies. One
fundamental challenge in dMRI harmonization is disentangling the contributions of scanner-related ef-
fects from the variable brain anatomy for the observed imaging signals, as the site-effects are regional-
and/or spatial-specific [85]. In an unsupervised and retrospective dMRI harmonization setting, where no
traveling subjects are scanned at both sites for direct inter-site mapping estimation, inter-site mapping
estimation is learned from a group of representative subjects. To disentangle the site-effects from the vari-
able brain anatomy for the observed imaging signals, image co-registration [4], constructing anatomical
correspondence across subjects, plays an essential role in dMRI harmonization. Conventional harmoniza-
tion methods rely on establishing an atlas space to resolve anatomical variability and generate a unified
inter-site mapping function [60, 31, 54]. However, due to inter-subject variability in neuroanatomy, de-
tecting anatomical correspondence across individuals is not ubiquitously achievable via image registration.
Failure to account for the confounding of anatomical variability can lead to erroneous harmonization and
profound impacts on downstream analysis. To eliminate the confounding of anatomy in the estimation of
dMRI harmonization mapping, we develop a personalized dMRI harmonization approach in this work.
4
DiffusionMRIHarmonizationontheCorticalSurface. The emergence of high-resolution dMRI
data from connectome imaging research has enabled the examination of cortical microstructure based
on dMRI. For instance, anisotropic diffusion has been characterized in cortical areas in [81]. Leuze et al.
reconstructed fiber pathways within the cortex to unveil intracortical connectivity [72]. More recently,
Fukutomietal. analyzed neurite distribution patterns on the cortical surface [34]. Harmonization of high-
resolution dMRI data in cortical gray matter is thus becoming an increasingly urgent problem. Existing
dMRI harmonization methods, however, perform poorly in cortical gray matter areas [94] because they
rely on volumetric registration methods to factor out anatomical variations, which have known difficulty
in accounting for the heterogeneity of cortical folding patterns [115, 119]. Hence, our work focuses on
surface-based dMRI harmonization to fill the gap of reliable dMRI harmonization in cortical gray matter.
1.3 Contributions
First, we present a novel track filtering method for fiber bundles by incorporating regularity from the
perspective of groupwise consistency. Our method filters the fiber bundles from a group of subjects simul-
taneously and takes advantage of the regularity that naturally exists at the group level to remove randomly
occurring errors in each subject, thus compensating for the gaps in anatomical priors. We developed an in-
tuitive definition of groupwise consistency of fiber track which provides flexible controls over the desired
consistency level across sub-population. Based on this definition, we proposed a novel fiber track filtering
algorithm using iterative message passing for fiber bundles. With the groupwise consistency estimated at
each point on each streamline via an iterative message passing mechanism, our method performs track
filtering via iteratively pruning away inconsistent portions. This approach preserves streamline portions
reproducible across subjects instead of making a binary decision as in many previous works. The pro-
posed algorithm is validated by filtering three important bundles: fornix, locus coeruleus (LC) pathways,
5
and corticospinal tract (CST), generated from diffusion imaging data of varying resolutions. Both qualita-
tive evaluations and quantitative comparisons show that our method achieved significant improvement in
enhancing the anatomical fidelity of fiber bundles. We have released this algorithm as open source, which
can be found at https://github.com/Samothracesmile/GroupwiseTractFiltering.
Second, we proposed a personalized framework to more effectively address confounding due to mis-
alignment of neuroanatomy in dMRI harmonization. Instead of using a common template for represent-
ing site-effects for all reference subjects, the main novelty of our method is the adaptive computation of
personalized templates via uneven integration of feature representations from reference subjects. The es-
timation of pooling weights is formulated as a convex optimization problem accounting for consistency
in weight assignment across similar references and over spatial neighborhoods of affinity. We integrated
our method with the rotation invariant spherical harmonics (RISH) features to achieve harmonization of
dMRI signals. We applied our approach to harmonize the dMRI from the Adolescent Brain Cognitive De-
velopment (ABCD) dataset [13] acquired from two scanning platforms: Siemens Prisma and GE MR750.
We demonstrated that the proposed harmonization framework achieves superior performance in reducing
inter-site variations due to scanner differences and preserving sex-related biological variability in origi-
nal cohorts. Furthermore, we assessed the impact of harmonization on the estimation of fiber orientation
distributions (FOD) and demonstrated the robustness of the personalized harmonization procedure in pre-
serving the fiber orientation of original dMRI signals.
Third, we presented a surface-based dMRI harmonization to improve the dMRI harmonization in cor-
tical gray matter. Our approach addressed the issue of anatomical misalignment arising from the compli-
cated folding of the cortical surface in the estimation of site effects via detecting personalized reference
contexts on the cortical surface. The reference context is established without relying on image registra-
tion. To achieve this, we proposed a surface matching metric based on multi-scale Laplacian-Beltrami (LB)
6
embeddings for corresponding vertex detection across cortical surfaces. We applied the proposed frame-
work to harmonize dMRI data on two shells of the WU-Minn Human Connectome Project (HCP) [122] and
the Lifespan Human Connectome Project in Development (HCP-D) [107]. Our method was validated by
demonstrating superior performance in minimizing inter-site differences in DTI features on both shells.
Via reliably eliminating inter-site discrepancies, our approach better preserved the age-associated effect
size of the original data after harmonization. Additionally, we showed that our method could retain the
inherent sex-related biological variability present in the original cohort.
1.4 OrganizationoftheDissertation
Chapter 2 covers the background of diffusion MRI including the principle of the diffusion process, diffusion
tensor imaging, high angular resolution diffusion imaging, and tractography. Chapter 3 presents the work
on groupwise track filtering. We will present the definition of groupwise consistency, describe our iterative
track filtering algorithm, and demonstrate its performance in multiple validation experiments. Chapter 4
presents a personalized dMRI harmonization framework by accommodating inter-subject variability in
brain anatomy. We demonstrate its performance by harmonizing multi-site dMRI data from the ABCD
dataset. Chapter 5 covers our work on personalized dMRI harmonization on the cortical surface. We will
elaborate and validate our method by conducting harmonization across the HCP and HCP-D datasets on
two shells of different b-values. Finally, Chapter 6 provides conclusions and a brief discussion of the future
directions of our research.
The chapter 3, 4, and 5 incorporate materials from the publications and manuscripts enumerated below.
Chapter3
• Yihao Xia and Yonggang Shi. “Groupwise track filtering via iterative message passing and pruning”.
In: NeuroImage 221 (2020), p. 117147
7
Chapter4
• Yihao Xia and Yonggang Shi. “Diffusion MRI Harmonization via Personalized Template Mapping”.
In: bioRxiv (2023). doi: 10.1101/2023.05.12.540537
Chapter5
• Yihao Xia and Yonggang Shi. “Personalized dMRI Harmonization on Cortical Surface”. In: Medical
Image Computing and Computer Assisted Intervention–MICCAI 2022: 25th International Confer-
ence, Singapore, September 18–22, 2022, Proceedings, Part VI. Springer. 2022, pp. 717–725
• Yihao Xia and Yonggang Shi. “Personalized Multi-shell dMRI Harmonization on the Cortical Sur-
face.” (In Progress)
8
Chapter2
Background
2.1 DiffusionProcessandDiffusionMRI
The diffusion process of water molecules is fundamental to diffusion MRI. In an infinite and unconstrained
environment of three dimension space, the diffusion process for a group of water molecules after diffusion
time∆ t can be described by a Gaussian distribution:
p(r,∆ t)=
1
p
(4π ∆ t)
3
D
f
exp(− r
T
r
4∆ tD
f
) (2.1)
wherer is a displacement in 3D space, andD
f
(inmm
2
/s) denotes the free diffusion coefficient, quanti-
fying the diffusion rate.
In the human brain, where the tissue surroundings restrict the diffusion process of water, the diffusion
coefficient for water in brain tissue appears smaller than the free diffusion coefficient. It is referred to as
the apparent diffusion coefficient (ADC) [69]. Under the diffusion process, the displacement of molecules
results in the dephasing of spins in a magnetic resonance scan, ultimately leading to signal attenuation.
The signal attenuation due to the dispersion of phase can be approximated by the Stejskal-Tanner equation
[110], which is a mono-exponential function:
9
S(b)=S
0
exp(− bD) (2.2)
whereS
0
represents the B0 image, which a T2-weighted image without any diffusion weighting, D is the
apparent diffusion coefficient, and b is "b-factor". For the pulsed gradient spin echo (PGSE), the b-factor is
given by the Stejskal-Tanner expression [110]:
b=γ 2
G
2
δ 2
(∆ − δ 3
), (2.3)
whereγ is the gyromagnetic ratio,G is the amplitude of the magnetic field gradient pulses. The δ and∆ are their duration and temporal separation, respectively.
2.2 DiffusionTensorImaging
To reveal the apparent diffusion coefficient along various directions, multiple diffusion weighted images
are required to encompass the orientation information of the entire diffusion process. In 1994, Basser et
al. [7] introduced a multivariate Gaussian model to describe the anisotropic diffusion process:
p(r,∆ t)=
1
p
(4π ∆ t)
3
|D|
exp(− r
T
D
− 1
r
4∆ t
) (2.4)
where the diffusion tensor, a 3× 3 symmetric and positive definite matrix:
D=








D
xx
D
xy
D
xz
D
xy
D
yy
D
yz
D
xz
D
yz
D
zz








, (2.5)
is for the description of the anisotropic diffusion behavior in tissue.
10
(a) (b) (c)
Figure 2.1: Illustration of unit gradient directions in (a), a B0 image in (b), and multiple diffusion-weighted
images in (c).
There are six unknown coefficients in the symmetric diffusion tensor D, which include the diagonal
coefficients D
ii
, representing the diffusion variances along the x, y, and z axes, and the off-diagonal ele-
ments, representing the covariance terms. Given a unit gradient directiong in q-space, (illustrated in Fig.
2.1 (a)) the diffusion tensor is solved by the diffusion tensor equation:
S(g,b)=S
0
exp(− bg
T
Dg). (2.6)
To estimate six unknown coefficients, one B0 image (illustrated in Fig. 2.1 (b)) and at least six diffusion-
weighted images (illustrated in Fig. 2.1 (c)) are required to estimate six unknown coefficients in D.
By performing an eigenvalue decomposition, one can obtain principal diffusion directions and corre-
sponding three eigenvalues,λ 1
,λ 2
,λ 3
, and three corresponding eigenvectors,e
1
,e
2
,e
3
. The eigenvalue
magnitude reflects the local diffusivity along the corresponding principal diffusion direction, which im-
plies the local tissue microstructure. Given that λ 1
≥ λ 2
≥ λ 3
, the λ 1
assesses the axial diffusivity and
(λ 2
+ λ 3
)/2 measures the radial diffusivity. Besides, several prevailing DTI measures, including mean
diffusivity (MD) and fractional anisotropy (FA), have proven valuable for neurodevelopment studies [90,
11
123, 42], neurological disorders diagnosis [103, 82, 9], brain connectivity [120], and brain injure [133].
Specifically, the MD is a rotation invariant feature defined as
MD =
λ 1
+λ 2
+λ 3
3
. (2.7)
This metric represents the average magnitude of local diffusion. Fractional anisotropy (FA):
FA=
3
2
s
((λ 1
− λ 2
)
2
+(λ 1
− λ 3
)
2
+(λ 2
− λ 3
)
2
)
(λ 2
1
+λ 2
2
+λ 2
3
)
, (2.8)
which reflects the local anisotropy of water diffusion. The images of FA and MD are shown in Fig. 2.2.
(a) (b)
Figure 2.2: A axial view of fractional anisotropy image (a) and mean diffusivity image (b).
2.3 HighAngularResolutionDiffusionImaging(HARDI)
The Gaussian diffusion assumption of the diffusion tensor model, only allowing the modeling of a single
fiber orientation, can result in erroneous interpretations of underlying microstructure when white matter
fibers exhibit crossing, kissing, or fanning patterns. This limits the accurate reconstruction of white matter
pathways and the estimation of brain connectivity. To handle complex fiber configurations, alternative
models relying on the acquisition of more diffusion-weighted images are needed. This motivated the
12
development of High Angular Resolution Diffusion Imaging (HARDI) techniques, which sample q-space
spherically. When single-shell sampling is applied to a specific b-value in q-space, it is termed single-
shell HARDI. Conversely, multi-shell HARDI employs multiple b-shell schemes for a more comprehensive
analysis of diffusion properties. Fig. 2.3 shows the single-shell (in (a)) and two-shell (in (b)) spherical
sampling of HARDI. AlongN gradient directions at a single b-value, the sampled diffusion signal can be
represented by a vector: S(b) = [S(g
1
,b),...,S(g
N
,b)]
T
, where g
i
denotes the gradient direction in
q-space.
(a) (b)
Figure 2.3: Spherical sampling schemes of single-shell and multi-shell HARDI.
2.3.1 Sphericalharmonics
To describe the complex orientation information of the dMRI signal, the spherical harmonics are conven-
tionally used for representation:
S≃
X
lm
C
lm
Y
lm
, (2.9)
where Y
lm
and C
lm
are the spherical harmonics basis and corresponding coefficients of order l and de-
greem. As the diffusion signal is real and antipodal symmetric, only even-order spherical harmonics are
typically employed for representing the diffusion signal. The rotation invariant spherical harmonic (RISH)
13
features are a well-known representation derived from spherical harmonics. RISH features, reflecting the
energy of the dMRI signal at different frequencies, are rotation invariant. At each order l, the RISH fea-
ture is the L
2
norm of spherical harmonics coefficients: ∥C
l
∥
2
=
P
2l+1
m=1
(C
lm
)
2
. a set of RISH feature
R = [∥C
0
∥
2
,∥C
2
∥
2
,...] can be estimated for a given dMRI signal. In Fig. 2.4, RISH features at spherical
harmonics orders ranging from 0 to 8 are demonstrated.
(a) (b) (c) (d) (e)
Figure 2.4: RISH features at different spherical harmonics orders. The RISH features at order 0, 2, 4, 6, and
8 are shown from left to right.
2.4 Tractography
Tractography is the only technique allowing forinvivo reconstruction and analysis of white matter path-
ways. With the voxel-wise orientation of fibers estimated from the dMRI signal, tractography techniques
integrate the local directions into a track or streamline to approximate underlying trajectories. With trac-
tography, a biologically meaningful tractogram, a collection of streamlines, can be reconstructed for white
matter pathway visualization and analysis. Fig. 2.5 presents a whole brain tractogram and major fiber
bundles extract from it. Depending on whether accommodate the uncertainty in local fiber orientation
estimation, there are two main approaches to tractography: deterministic [8, 87] and probabilistic [10, 22,
116]. The deterministic methods, assuming no uncertainty along the trajectory, generate each streamline
by only propagating along the local optimum directions. Despite the low computational cost, this approach
is prone to local errors and potentially underestimates the fiber tracts [64]. On the other hand, probabilistic
14
methods account for the variability in fiber orientations. Instead of focusing only on the local optima at
each tracking step, probabilistic tractography algorithms integrate local fiber orientations via a random
walk guided by the local fiber orientation distribution. Though at a higher computation cost, probabilistic
tractography can better account for complex fiber configurations (e.g., crossing fibers).
Figure 2.5: Whole brain tractography and reconstruction of fiber bundles.
15
Chapter3
GroupwiseTrackFilteringviaIterativeMessagePassingandPruning
3.1 Introduction
The advent of diffusion magnetic resonance imaging (dMRI) [7] allows the study of structural connectivity
in the human brain in vivo. To noninvasively reveal and study the trajectories of white matter pathways
of the human brain based on dMRI, tractography is a central approach [8, 87] and has been successfully
applied in neuroimaging studies of various brain disorders. On the other hand, recent validation studies [5,
78] showed tractography techniques had critical limitations in the reliable reconstruction of neuroanatomy.
To this end, we propose a novel track filtering algorithm for the robust reconstruction of fiber bundles
with groupwise consistency. We will demonstrate that the groupwise consistency is able to compensate
for limited anatomical knowledge in tractography-based fiber bundle reconstruction.
Fiber bundles can be generated by either deterministic [8, 87] or probabilistic tractography techniques
[10, 22, 116]. To remove artifacts from tractography results, various approaches have been proposed for
the filtering of fiber tracks with the inclusion of different degrees of anatomical priors. For the filtering
of whole brain tractograms, several methods have been developed that examine how well the tractogram
fits the dMRI data or the fiber orientation models computed from the dMRI data and remove streamlines
with low data fidelity [19, 99, 106]. Clustering techniques [43, 96] for the reconstruction of major fiber
bundles are most related to our current work. By taking advantage of the geometric similarity of pathways,
16
clustering algorithms can be applied to fiber tracks from individual subjects or multiple subjects warped
into a common space. Recently, this approach was applied to the whole brain tractography of 100 HCP
subjects for the extraction of common clusters and construction of white matter atlases, which were then
applied to the whole brain tractogram of individual subjects for bundle reconstruction [139]. This approach
is still largely data-driven and anatomical labels were typically assigned after the generation of clusters
[96]. For fiber bundle reconstruction, the most conventional type of approach uses strong anatomical
priors in the form of region-of-interests (ROIs) to increase the validity of tractography-based solutions
[14, 127]. This method is most suitable for the reconstruction of fiber bundles with well-characterized
anatomy [111]. Based on this approach, a white matter query language (WMQL) was developed as an
automated framework for ROI-based bundle segmentation [131].
Even with the use of strong ROI-based anatomical priors, however, residual artifacts still frequently
occur in the reconstructed fiber bundles [100]. This is because we usually can only provide a small num-
ber of ROIs to constrain the fiber trajectories due to either incomplete anatomical knowledge or the high
cost of generating extensive anatomical labels. To remove outliers from ROI-based reconstruction of fiber
bundles, track filtering methods based on geometric distances [36] or topological analysis [6] were pro-
posed. More recently, topographic regularity was proposed as a novel criterion for the removal of outlier
streamlines [128]. A cluster confidence index (CCI) was introduced to model the geometric similarity of
neighboring tracks and remove outliers [59]. One common theme of these methods is that they assume
a certain level of geometric or topographic regularity at the individual level to compensate for the in-
sufficiency of anatomical constraints, but consistency across subjects is not considered. In addition, the
filtering process typically operates at the level of whole streamlines.
In this chapter, we present a novel track filtering method for fiber bundles by incorporating regularity
from the perspective of groupwise consistency. In essence, our method will filter the fiber bundles from
a group of subjects simultaneously and take advantage of the regularity that naturally exists at the group
17
level to remove randomly occurring errors in each subject, thus compensating for the gaps in anatomical
priors. Compared to previous track filtering methods for fiber bundles, there are several unique aspects in
our work. First, we develop an intuitive definition of groupwise consistency that provides flexible controls
over the level of desired consistency across the group from three different aspects: degree, affinity, and
proximity. Second, we measure the groupwise consistency at each point on a streamline via an iterative
message passing mechanism from a set of carefully constructed reference fibers. Third, we perform the
filtering at the local level by iteratively pruning away the inconsistent portion of each streamline instead
of making a binary decision as in many previous works. This is one of the unique aspects of our method
that allows not only the elimination of whole streamlines with defects but also the extraction of stream-
line segments reproducible across subjects, which can be highly valuable when precise end ROIs cannot
be properly defined for a fiber bundle. In our experiments, we will demonstrate this property enables the
reconstruction of anatomically meaningful and consistent sub-bundle structures from fiber bundles domi-
nated by highly spurious outliers. We will also show the proposed method can be easily applied to perform
conventional filtering tasks that either accept or reject a track from a bundle.
The rest of this chapter is organized as follows. In section 3.2, we propose our definition of groupwise
consistency and develop the numerical algorithm to implement this concept to achieve track filtering at
the group level. In section 3.3, we present experimental results on the reconstruction of three important
bundles: fornix, locus coeruleus (LC) pathways, and the corticospinal tract (CST) to demonstrate the effi-
cacy of our method over conventional filtering methods. Finally, discussions and conclusions are made in
section 3.4,.
3.2 Method
In this section, we develop the proposed track filtering algorithm based on a novel and flexible definition of
groupwise consistency across fiber bundles. The main steps of our method are illustrated in Fig. 3.1. After
18
Figure 3.1: An illustration of the proposed groupwise track filtering framework. All fiber bundles
from N subjects will first be nonlinearly warped to a common space such as the MNI152 atlas. Outlier
points (colored in yellow) will be iteratively pruned based on the consistency measure obtained via
messages passed from tracks in a reference set, which is updated dynamically. Once the pruning
process is completed, the same pruning operations are applied to points on the original tracks to
obtain the filtered fiber bundles.
nonlinearly warping all fiber bundles into a common space, we iteratively estimate the level of groupwise
consistency at each point on each streamline and conduct the pruning of outlier points to enhance the
overall consistency across subjects. Streamlines will be rejected or refined during the filtering process for
the generation of the final outputs.
19
3.2.1 Definition
We denote a set of input fiber bundles from N subjects as
˙
F = {
˙
F
1
,...,
˙
F
N
}, where
˙
F
n
is the input
bundle from the n-th subject. To perform the proposed groupwise filtering, these fiber bundles are first
co-registered into a common coordinate space as illustrated in Fig. 3.1 and denoted asF ={F
1
,...,F
N
}.
For practical implementation, we typically warp all fiber bundles into the common MNI152 space [30]
using the nonlinear registration computed by the ANTS software [4]. Each streamline inF is represented
as a poly-linef ={x(l)|l∈[1,S]} withS points inR
3
. For groupwise filtering, our goal is to estimate a
subset of the streamlinef, which we denote as
ˆ
f ={x(l)|l∈[l
a
,l
b
]}, that are consistent with streamlines
from other subjects. More specifically, we consider the streamline segment,
ˆ
f ⊆ f, as groupwise consistent
if all points in
ˆ
f are close to streamlines from a certain number of other subjects. Formally, we define the
conditionsG(L;K;ξ ) for
ˆ
f, a portion of a streamlinef, to have groupwise consistency as follows:
• Degree (L): the minimum length requirement of the sub-streamline structure
ˆ
f that is consistent
with streamlines from other subjects.
• Proximityξ : a distance parameter reflecting the extent of closeness between
ˆ
f and streamlines from
other subjects.
• Affinity ( K): the number of subjects in the group that contains streamlines to whichf shares con-
sistency.
This definition is flexible in several aspects. The first parameter L specifies the minimum length or
proportion of a streamline that needs to be consistent with tracks of other subjects. This will avoid the
inclusion of overly short segments that do not reflect the connectivity of the fiber bundle. For fiber bundles
with well-defined end ROIs, setting a relatively high degree parameter L will ensure a valid representation
of the overall bundle similar to conventional filtering approaches can be obtained. The second parameter K
can be considered as an affinity measure that controls the trade-off between inter-subject consistency and
20
individual variability. The distance parameterξ determines the closeness when evaluating the consistency
among fiber trajectories. Taken together, these conditions characterize groupwise consistency locally at
the sub-streamline level. On the contrary, previous filtering methods often first perform fiber clustering
and make a decision about each cluster. Thus, the proposed groupwise definition allows the development
of filtering algorithms that can measure groupwise consistency and perform the pruning/filtering at a
higher resolution than previous methods.
3.2.2 AlgorithmicDetails
To computationally realize this flexible definition of groupwise consistency for fiber bundles, we essen-
tially need to estimate a fraction
ˆ
f of each streamlinef that is consistent with streamlines fromK other
subjects in the group. Since this portion
ˆ
f is unknown, theK subjects contributing to its groupwise con-
sistency cannot be determined a priori. To tackle this challenge, we develop an iterative algorithm that is
composed of consistency estimation and pruning of inconsistent points. At each iteration, a reference set
is constructed and dynamically updated for each streamline and a message passing mechanism is devel-
oped to estimate the level of consistency at each point, which then guides the pruning process to remove
inconsistent portions from the streamline.
Reference Set: For any pruned or unpruned streamline f
t
at the t-th (t = 0,1,... ) iteration, which
equals the input streamline f at t = 0, we construct a subject specific reference set R
t
k
= {r
m
k
| m =
1,...,M} composed of the M most similar streamlines from the fiber bundle F
k
of the k-th subject. In
most scenarios, the fiber bundle F
k
is saturated with streamlines sharing similar trajectory, and a sub-
sampled one
˜
F
t
k
would be enough to be used for reference searching. Practically, we offer an optional
parameter, subsampling rater, to control the percentage of streamlines stochastically selected fromF
k
for
reference set construction. The parameterr provides a trade-off between accuracy and efficiency. A low
subsampling rate could effectively reduce the computational burden, while the overly subsampled fiber
21
bundle may underrepresent the original trajectories. We used the fast fiber k-NN algorithm proposed in
[129] to efficiently construct the reference set. Given a streamline f
t
and a searching scope, e.g.,F
k
or
˜
F
t
k
,
the fast fiber k-NN algorithm ranks each streamline in the scope according to its similarity to f
t
. Then the
top-M streamlines are extracted to form the subject specific reference set.
To meet the affinity criterion that K subjects will be needed to define the groupwise consistency, we
build the groupwise reference setG
t
of each trackf
t
at the t-th iteration as follows:
G
t
(f
t
)=arg min
R
′
⊆R
t
,|R
′
|=K
X
R
t
k
∈R
′
X
r
m
k
∈R
t
k
d
mc
(f
t
,r
m
k
), (3.1)
whereR
t
={R
t
k
| k = 1,...,N − 1} is the collection of all subject specific reference sets and d
mc
(·,·)
is the mean closest point distance [18] depicting the streamline-wise distance. Specifically, this distance
measure between two streamlinesf
t
andr
m
k
∈F
k
is defined as:
d
mc
(f
t
,r
m
k
)=
1
|f
t
|
X
x∈f
t
min
y∈r
m
k
∥x− y∥, (3.2)
where|f
t
| is the number of points onf
t
. The groupwise reference setG
t
(f
t
) consists of the topK subject
specific reference sets in terms of the total distance between f
t
and the reference tracks.
Message Passing: Using the groupwise reference setG
t
(f
t
) at the current iteration, we will define
a consistency measure at each point on f
t
to enable localized track filtering. Inspired by the message
passing mechanism in graph-based optimization [126], we will quantify the consistency level of each point
by measuring the messages that it received from the reference set.
Given any pointx∈ f
t
, we denote a neighborhood point setN ={n
i
| i = 1,...,|N|}, wheren
i
is
the closest point to the i-th streamline in the reference setG
t
(f
t
). Note that the total number of points in
N equals the number of reference streamlines inG
t
(f
t
), i.e.,M× K. The message the i-th neighborhood
point sends tox is defined as e
−∥ x− n
i
∥
2
/σ
2
, which decays exponentially as the distance between these two
22
(a) (b)
Figure 3.2: Calculation of localized consistency measures on a track based on message passing. (a) The
points on the track under consideration (cyan) are plotted as gray dots. The points on the three reference
tracks are plotted in red, green, and blue, respectively. (b) Each point on the track under consideration is
color-coded according to the consistency measure from messages they receive from neighboring tracks.
The consistency measures range from 0 to 3 as 3 reference tracks are used in this example.
points increases. Note the distance∥x− n
i
∥ is normalized with respect to the distance scale parameterσ which controls the quantitative conversion from point-wise distance to point-wise affinity. By summing
up the messages from all neighboring points, we obtain the consistency measure atx as:
p(x)=
|N|
X
i=1
e
−∥ x− n
i
∥
2
/σ
2
. (3.3)
This message passing process is carried out at all points onf
t
to define the localized consistency mea-
sure on the streamline. An illustration of the consistency measure calculation based on message passing is
shown in Fig. 3.2. From the final consistency measure plotted in Fig. 3.2 (b), we can see that the local vari-
ation of the consistency level has been successfully captured, which will then inform the pruning process
for the removal of outliers in fiber bundles.
Track Pruning: After the estimation of the groupwise consistency measure for all the tracks from
all subjects, we filter the fiber tracks via a pruning process. We denote the set of filtered bundles from all
subjects asF
t
at the t-th iteration andp(F
t
) as the distribution of the consistency measure of the points
23
on all the fiber bundles in F
t
. At the t-th iteration, we first calculate the mean µ t
p
and standard deviation
σ t
p
ofp(F
t
) to determine the filtering threshold at the group level:
th
tp
=µ t
p
+2σ t
p
. (3.4)
We consider any point on a streamline with its consistency measure below th
tp
as an outlier. To
preserve the continuity of each streamline during the filtering process, we filter them at each iteration by
pruning the outlier points at both ends. For a streamlinef
t
, we obtain the filtered one f
t+1
for the next
iteration after removing its outlier points.
A filtered track will be rejected if it fails to meet the minimum degree of consistency in G(L;K;ξ ),
i.e., a sufficient amount of points after the pruning. We thus employ a length constraint L
min
to realize
this condition on the minimum degree of consistency. In our algorithm, the L
min
is a ratio parameter,
indicating the minimum ratio of the length of the pruned track to the overall mean streamline length. The
mean streamline length, the average number of points on streamlines in input fiber bundles, characterizes
the streamline length able to reflect meaningful connectome. A higher L
min
requires the filtering result
to preserve more end-to-end interconnectivity. Besides, note that outlier points may exist in the interior
of the track, which could result in local inconsistency. We constrain such interior local inconsistency by
using another ratio parameterL
max
controlling the maximum number of outlier points that are tolerable
in the filtered track. The filtered track will be rejected if the ratio of outlier point number to the overall
mean streamline length exceedsL
max
. With a smallL
max
, the filtering process would be sensitive to the
interior local outliers. Together these two parameters will control the filtered track to have enough degree
of consistency while keeping the number of residual outlier points small.
Proximity Estimation and Termination Criterion: Consider that the proximity (ξ ) constraint lo-
cally requires that the filtering result
ˆ
f and its counterparts, white matter trajectories from other subjects,
24
have a certain extent of closeness. We use the average distance between the pruned streamline and its
references to quantitatively reflect the group-wise closeness as follows:
d
mean
(f
t
)=
1
K× M
X
r
m
k
∈R
t
k
,R
t
k
∈G
t
d
mc
(f
t
,r
m
k
). (3.5)
The iterative process would not terminate until all pruned streamlines reach the proximity require-
ment. Thus, the overall groupwise inconsistency,ξ t
= max
f∈F
i
,F
i
∈F
td
mean
(f
t
), is used as the stopping
indicator. The pruning process would terminate onceξ t
is below a certain thresholdδ .
The overall implementation of our groupwise filtering algorithm is summarized in Algorithm 1. The
operationsReferenceSet,MessagePassing,TrackPruning, andProximityEstimation implement the main steps
described above. Once the filtering process stops, the same pruning operations are applied to correspond-
ing points in the original fiber bundles in the last step of the algorithm, which produces the filtered fiber
bundles
ˆ
F for all the subjects in the original space. If filtering at the whole streamline level is desired
to have complete end-to-end connections, our method can also recover the pruned portion and generate
whole-streamline filtering results for tracks that are retained after the groupwise filtering process, i.e.,
tracks including a portion meeting the groupwise consistency criteria.
While there are multiple parameters in the proposed algorithm, many of the parameters can be set a
priori and performed robustly across different track filtering tasks. For all our experiments, we set r =0.2,
M =3,σ =8 mm, andδ =3 mm. The rest of the parameters about groupwise consistency such as affinity
K, anatomical length constraintL
min
, and local inconsistency toleranceL
max
can be adjusted in different
filtering scenarios. We will demonstrate the intuitive ways of parameter setting and corresponding filtering
results next in the experiments.
25
Algorithm1: Groupwise Track Filtering Algorithm
Input: Original fiber bundles of N subjects
˙
F ={
˙
F
1
,...,
˙
F
N
}, The corresponding warped
bundles in a common space:F ={F
1
,...,F
N
}.
Parameters: K: affinity parameter, L
min
: consistency parameter,L
max
: local inconsistency
tolerance parameter,δ : proximity parameter for termination. r: subsampling rate,
M: reference set size,σ : distance scale parameter
Output: Filtered fiber bundles in original space:
ˆ
F ={
ˆ
F
k
|k =1,...,N}
MainSteps:
F
0
←F ;
t← 0 ;
ξ t
←∞ ;
whileξ t
>δ do
for∀f
t
∈F
t
do
G
t
(f
t
)← ReferenceSet(f
t
,F,K,M,r) ;
p(f
t
)← MessagePassing(f
t
,G
t
(f
t
),σ ) ;
end
F
t+1
← TrackPruning(p(F
t
),L
min
,L
max
) ;
ξ t+1
← ProximityEstimation(F
t+1
) ;
t← t+1 ;
end
ˆ
F ←F
t
.
3.3 ExperimentalResults
In this section, we present experimental results to demonstrate the proposed algorithm for the groupwise
filtering and reconstruction of important fiber bundles in the human brain. We applied our method to
diffusion MRI (dMRI) data from both the second phase of Alzheimer’s Disease Neuroimaging Initiative
(ADNI2) [89] and Human Connectome Project (HCP) [122]. With the aim of developing biomarkers for
the early detection of Alzheimer’s disease (AD), the ADNI enrolls subjects ranging from 55 to 90 years
old. The study cohort consists of varying disease stages: cognitively normal (CN), early mild cognitive
impairment (EMCI), late mild cognitive impairment (LMCI), and AD. The ADNI2 dMRI data used in our
experiment were acquired on 3-Tesla GE Medical Systems scanners. Each diffusion MRI scan contains 59
axial slices reconstructed to256× 256 matrix with voxel size2.7× 2.7× 2.7 mm
3
. Each scan includes 46
separate image volumes: 5 T2-weighted b0 images and 41 diffusion-weighted images ( b = 1000 s/mm
2
).
26
The HCP enrolls healthy young adults in the age range of 22-35 years. The advanced multi-shell dif-
fusion MRI data of HCP was acquired on a 3T Siemens Connectome Skyra scanner. The dMRI data of
HCP has an isotropic spatial resolution of 1.25× 1.25× 1.25 mm
3
from 270 gradient directions over
three b-values (b = 1000,2000,3000 s/mm
2
) [108]. In our experiments, we used the preprocessed dMRI
data from the 500-Subject release of HCP. For both HCP and ADNI2 dMRI data, we first reconstructed
the fiber orientation distribution (FOD) [117] and then ran FOD-based tractography in MRtrix3 [116] for
ROI-based bundle reconstruction. We used the iFOD1 algorithm in MRtrix3 for FOD-based probabilistic
tractography. As shown in previous validation studies [5], key parameters including step_size, angle,
andcutoff_threshold of the FOD at each step of the tractography algorithm all contribute to the regu-
larity of the fiber streamlines. For each fiber bundle, we picked these tractography parameters to ensure
sufficiently complete representations of these bundles are reconstructed according to our experience.
3.3.1 FornixbundlereconstructionfromADNI2data
In the first experiment, we applied our method for the groupwise reconstruction of the fornix bundle of
40 subjects from ADNI2 including 10 subjects each from groups with Alzheimer’s disease (AD), early mild
cognitive impairment (EMCI), late mild cognitive impairment (LMCI), and cognitively normal (CN). As
an important white matter tract of the limbic system, the fornix bundle was shown to be sensitive to the
early neurodegeneration in the hippocampus [83]. While the fornix anatomy is relatively well described
in neuroanatomy [93], the limited resolution in clinical dMRI data does not provide sufficient information
to accurately identify small ROIs such as the mammillary body that receives fornix projection.
In our experiment, we first manually delineated several ROIs in the T1-weighted MRI of the MNI152
atlas and then registered them to the subject space as the anatomical constraints for fornix reconstruction.
As shown in Fig. 3.3, the seed ROI (in green) and inclusion ROI (in red) corresponding to the two ends
of the fornix body were depicted on the axial and coronal slices respectively. The exclusion ROIs (in
27
(a) (b)
Figure 3.3: ROIs used for fornix bundle reconstruction are plotted against the MNI152 T1 image. (a) A
sagittal view of the manually drawn seed (green), inclusion (red), and exclusion (blue) ROIs. (b) An axial
view of the manually drawn exclusion ROIs. Note they do not overlap with the seed and inclusion ROIs.
blue) were drawn on the sagittal slices to avoid the tracking artifacts resulting from the entanglement
of the fornix and neighboring tracts such as the anterior commissure. To further reduce false positives
in bundle reconstruction, the hippocampus masks and cortical regions produced by FreeSurfer [28] were
used as inclusion and exclusion ROIs for FOD-based tractography, respectively. Other related tractography
parameters are as follows: step_size = 0.2 mm,angle = 6
◦ , andcutoff_threshold = 0.025. For each
subject, we generated 1000 streamlines for the fornix bundle.
As shown in Fig. 3.5, the reconstructed fiber bundles contain a large number of outliers. With the
following key parameters in our method: K = 24,L
min
= 0.6, andL
max
= 0.05, our method successfully
removed the outlier portion of the tracks and produced a consistent reconstruction of the fornix body. Note
that the affinity K = 24 is 60% of the total number of subjects in the dataset. The pruning results with
different termination criteria are demonstrated in Fig. 3.4, where the filtered bundle of a representative
subject was plotted. The reconstructed fiber bundles were obtained at the algorithm’s convergence and
shown in Fig. 3.5. These results demonstrate that our method can extract anatomically meaningful and
consistent fiber bundles even from inputs dominated by highly spurious outliers in this experiment.
28
Figure 3.4: The iterative pruning results with different proximity requirements of the fornix bundle
of an EMCI subject. The original bundle and the filtering outcomes with proximity threshold δ =20
mm,7 mm,3 mm, and2 mm, corresponding to the results after 1, 2, 5, and 10 iterations of filtering,
are displayed from left to right, respectively.
(a) (b)
(c) (d)
Figure 3.5: Input and reconstructed fornix bundles from ADNI2 subjects. Each sub-figure from (a) to (d)
shows three input (top row) and filtered (bottom row) bundles from the AD, LMCI, EMCI, and CN groups,
respectively.
The subjects involved in this experiment are from multiple groups regarding clinical diagnosis of AD.
This results in the potential pathological heterogeneity in the dataset of the reconstructed fornix bundle.
29
The affinity parameter K, which controls the scope of groupwise consistency in population, would signif-
icantly impact the filtering results. We examined the impact of the affinity parameter K qualitatively. By
fixing other parameters, we varied the parameter K in groupwise filtering. The reconstruction results of
a representative subject are shown in Fig. 3.6. We can see residual outliers can still be seen at relatively
smaller values (K = 8 or 16 which is 20% and 40% of the total number of subjects). With the increase
ofK, results become more constrained and lead to a reconstruction that underrepresents the fornix. This
is especially obvious whenK was chosen as 39, which is the maximum value for a group of 40 subjects.
This example also demonstrates that the affinity parameter K is robust. AlternatingK in the range from
16 to 32 results in little geometrical differences in the final filtering results. The observations conform to
the expectation that varying the parameterK allows the trade-off between inter-subject consistency and
individual variability. It is also detectable in Fig. 3.5 that the general morphological characters of each
fornix bundle are preserved.
Figure 3.6: The filtering results of the same EMCI subject in Fig. 3.4 with different choices of the
affinity parameter K. The input fiber bundle, and the filtered bundle with K = 8, 16, 24, 32, and 39,
are shown from left to right, respectively.
3.3.2 LocuscoeruleuspathwayandatlasfromHCPdata
In the updated Braak staging of tau pathology [11], the locus coeruleus (LC) nuclei in the brainstem was
considered the earliest region with tau tangles, one of the defining hallmarks of AD. There is thus increas-
ing interest in studying the LC morphology and connectivity [16]. In vivo reconstruction of LC pathways
in human brains, however, has been relatively understudied. In this experiment, we applied our method
30
to obtain groupwise consistent reconstruction of LC pathways to the medial temporal lobe (MTL), which
corresponds to Braak stage I after the LC (Braak stage 0). Robust and consistent reconstruction of the LC
pathways could facilitate the investigation of the propagation of tau pathology along fiber pathways [39]
and improve our understanding of the early development of AD.
We used the dMRI data from 50 HCP subjects in this experiment to demonstrate the consistent re-
construction of LC pathways in the right hemisphere of these subjects. Two ROIs were used in the
tractography-based reconstruction. The first ROI was the right LC mask nonlinearly warped from an
atlas in the MNI152 space [63]. This ROI was used as the seed region in tractography. The second ROI
was the amygdala mask produced by FreeSurfer [28] and used as an inclusion ROI. Parameter settings for
FOD-based probabilistic tractography are listed as follows: step_size = 0.125 mm, angle = 4.5
◦ , and
cutoff_threshold=0.05. Each input LC bundle contains around 1000 streamlines.
As shown in Fig. 3.8, while the ROIs played an important role in constraining the trajectories of
the fiber pathways, the tractography results still tend to be contaminated by erroneous outliers varying
from subject to subject. Parameters used in our method were chosen as L
min
= 0.8, L
max
= 0.05,
and K = 49. Compared to the filtering implementation for the fornix bundle, we can choose stricter
constraints on affinity and consistency in this experiment because of the high anatomical homogeneity
across HCP subjects. Constrained only by the ROIs at the two ends, the original LC pathway contains
many streamlines with interior false positive portions (pointed and circled out in Fig. 3.7 (a)). We also
show how the maximum outlier length L
max
affects the filtering result. As shown in Fig. 3.7, a cleaner
reconstruction of the LC pathway can be obtained with the decrease of the L
max
. When the L
max
is
small enough, e.g., less than 0.1, its influence on filtering results almost vanishes. The final reconstruction
results are shown in Fig. 3.8, where clean and consistent LC pathway reconstruction has been successfully
obtained. These results match very well with the trajectories of the dorsal noradrenergic pathway of the
LC as described in previous literature [80].
31
(a) (b)
Figure 3.7: The impact of the parameterL
max
on track filtering performance. (a) Input LC pathway of an
HCP subject. Spurious tracks were highlighted by the ellipsoid and arrow. (b) Filtered LC pathways with
varyingL
max
=0.05,0.1,0.3, and0.5, from left to right, respectively.
Figure 3.8: Results of filtering the right LC bundle from five HCP subjects. Top row: input
LC pathways; Bottom row: filtered bundles.
Using the reconstructed LC pathway of the 50 HCP subjects, we created a probabilistic atlas in the
MNI152 space following the same approach in [111]. As shown in Fig. 3.8, this atlas shows that the support
of the non-zero regions is compact and well connected, which further confirms the consistent trajectories
of the reconstructed pathways.
32
(a)
(b)
Figure 3.9: A probabilistic atlas of the right LC bundle is plotted on eight coronal slices in the MNI152 space.
(a) indicates the zoom-in region (within the red box) on one coronal slice. The corresponding regions on
different coronal slices are magnified and displayed in (b).
3.3.3 QuantitativecomparisonofcorticospinaltractreconstructionfromHCPdata
In the third experiment, we applied our groupwise filtering method to the reconstruction of the corti-
cospinal tract (CST) and quantitatively compared its performance with two publicly available methods.
The data of 20 HCP subjects from a previous brainstem atlas project [111] was used in this experiment.
For each CST bundle, five ROIs in the brainstem region (Fig. 3.11 (b)) were manually delineated by an
experienced neuroanatomist in [111] to guide the accurate reconstruction of the CST. To evaluate the per-
formance of different track filtering methods, we used only one brainstem ROI (ROI 1 as shown in Fig.
3.11 (a)) in the tractography-based reconstruction of the left CST of each subject. The other four ROIs
were used as ground truth to quantitatively measure the accuracy of filtered tracks by different methods.
With the brainstem ROI as an inclusion ROI, we also used the left precentral gyrus from the FreeSurfer
Aseg labels [28] as the seed region. For FOD-based tractography, the parameter setting is as follows:
step_size = 0.125 mm,angle = 4
◦ , andcutoff_threshold = 0.025. Each reconstructed CST contains
around 500 streamlines.
From the input CST bundles, shown in the first row of Fig. 3.10, we can see some frequent outliers in
the brainstem area and the lateral projections to part of the precentral gyrus that do not contribute to the
CST. Following the similar parameter selection strategy presented in the LC pathway filtering experiment,
33
we used the following parameters: K = 19, L
min
= 0.8, and L
max
= 0.01 for our groupwise filtering
algorithm. We selected a small L
max
to remove streamlines with short false positive segments (pointed
out by arrow in Fig. 3.10). The high consistency requirement, L
min
= 0.8, leads the filtering process to
produce results with a high degree of consistency. As shown in the second row of Fig. 3.10, our method
successfully removed these outliers and generated consistent and clean bundles that follow the correct
anatomy. We also displayed the filtering results at the whole-stream level by adding back the pruned
points for tracks retained by the filtering algorithm, highlighting the end-to-end connectivity from the
motor cortex to the spinal cord, in the bottom row of Fig. 3.10. For the filtered bundle from all subjects,
we calculated the number of tracks and listed their distribution in Table 3.2, which will be used to guide
parameter tuning in the tools we will compare with.
The first publicly available method we compare with is the track filtering method in the QuickBundles
software tool [36], which was applied to the same input bundles as our method. More specifically, we chose
the threshold for the distance between curves as5 mm and cluster size as 70 streamlines in QuickBundles,
which means the maximum Minimum Average Direct-flip (MDF) distance between curves within a cluster
was limited to 5 mm, and all streamlines belonging to clusters with less than 70 curves were discarded.
With the increase of the threshold for cluster size, more outliers will be removed but also potentially valid
tracks. For all subjects, we counted the number of tracks in the filtered fiber bundles and fine-tuned the
threshold of cluster size such that the lower end of the track number distribution will be slightly below our
method as listed in Table 3.2. This suggests we have filtered comparable or more outlier tracks with the
QuickBundles method compared to ours. A comparison of the filtering results from QuickBundles and our
method on an HCP subject is shown in Fig. 3.11. While QuickBundles successfully filtered out the outlier
tracks projecting to the inferior and lateral portion of the precentral gyrus, it did not completely remove the
tracks with defects in the brainstem area, which our method could handle consistently across the group. We
also compared our method with the cluster confidence index (CCI) based streamline filtering [59]. Given
34
Figure 3.10: Groupwise track filtering results of the left CST from five representative HCP subjects.
Top row: input fiber bundles from FOD-based tractography. The white arrow and ellipse highlight
the main outliers removed during the filtering process. Middle row: filtered fiber bundles generated
by our groupwise filtering algorithm. Bottom row: filtering results at the whole-streamline level by
adding back pruned points for tracks retained after the groupwise filtering process, i.e., tracks shown
in the middle row.
a streamline, the streamlines within a certain MDF distance (θ cci
) are employed as references. The CCI
qualitatively reflects the reproducibility of individual streamline according to the overall similarity with
its reference, where the streamline-wise similarity is characterized by theK
cci
-th power of the reciprocal
of the MDF distance. We setK
cci
= 1,θ cci
= 5 mm and the CCI threshold was fine-tuned to be 30 based
on the same criteria used above for QuickBundles, i.e., the lower end of the track number distribution
will be slight compared our method to ensure a comparable number of outliers were removed (Table 3.2).
Qualitatively, a filtering result example from CCI based method was demonstrated in Fig. 3.11 (d), where
we can observe that inconsistent streamlines were removed properly at the cost of removing more valid
35
tracts in comparison with our method. Both QuickBundles and CCI based filtering method have high
computational efficiency by completing the processing of the 20 CST bundles in around 10 seconds.
(a) (b) (c)
(d) (e) (f)
Figure 3.11: A comparison of the filtering results from our method and other track filtering methods and
two tract reconstruction methods for the left CST of an HCP subject. (a) The input bundle reconstructed
with one inclusion ROI (the white disk). (b) The overlay of the filtered bundle from our method and the
five manually delineated ROIs (white disks). (c) The overlay of the filtered bundle from QuickBundles and
the five manually delineated ROIs (white disks). (d) CCI-based result. The left CST bundle reconstructed
by the atlas-based method in RecoBundles and SlicerDMRI are displayed in panels (e) and (f), respectively.
The whole brain tractography, used as the input for both atlas-based methods, is displayed in the top-right
in (e).
Two automatic bundle reconstruction approaches, introduced in [37] and [139] are tested for further
comparisons. These methods used whole-brain tractography as the input and extracted individual fiber
bundles based on the precomputed tractography atlases. To apply these methods to the 20 HCP subjects
used in our experiment, we first generated whole brain tractography containing 100k streamlines (top
right in Fig. 3.11 (e)) for each subject using the FOD-based probabilistic tractography of MRtrix3 [116].
36
The following parameter setting was used for the tractography: step_size=0.125 mm,angle=4
◦ , and
cutoff_threshold=0.025.
The first atlas based approach, which has been implemented as the RecoBundles tool in Dipy [35], was
applied for the left CST reconstruction. In this approach, the whole brain tractography of each subject was
first registered to a population-average tractography atlas [137] using the nonlinear registration computed
by the ANTS software [4]. Following the guidance of parameter setting in [37], we chose the following
parameters for RecoBundles: cluster_threshold = 15 mm, model_cluster_threshold = 5 mm, and
reduction_threshold=20 mm and fine-tuned the parameter pruning_threshold to be6 mm so that the
lower end of track number distribution will be slightly below out method (Table 3.2) because this method
also follows similar techniques from QuickBundles. As demonstrated in Fig. 3.11 (e), we can see that the
extracted fiber bundle generally follows the trajectory of CST. Still, many of the tracks extracted from the
whole brain tractography terminated prematurely before reaching the end of the medulla. The second
atlas-based approach [139] has been distributed as part of the whitematteranalysis tool in the SlicerDMRI
project [95]. Both affine and nonrigid registration [97] were computed to warp the tracts to the atlas
space using tools provided in SlicerDMRI. After that, the atlas-based method in SlicerDMRI was applied
to extract the left CST as shown in Fig. 3.11 (f). Compared to the manually delineated ROIs, we can see a
large number of false positives in the brainstem area were included in this reconstruction.
To quantitatively compare the performance of different methods, we calculated the distance between
the fiber bundles and the other four manually delineated ROIs (ROI 2 - 5) not used in bundle reconstruction.
Because all the ROIs were delineated on axial slices, we denote the set of points in the j-th ROI of the i-th
subject asU
j
i
. Given a fiber bundle of the i-th subject, we denote its intersection with the corresponding
axial slice of the j-th ROI as the point set V
j
i
. The Hausdorff distances d
H
(U
j
i
,V
j
i
) between these two-
point sets were computed for the original input bundles, filtered bundles from our method, QuickBundles,
and CCI based reconstruction. These Hausdorff distances indicate the mismatches between streamlines
37
and the underlying anatomy delineated by ROIs. Statistics of the Hausdorff distances for each method and
ROI were reported in Table 3.1. Our method, QuickBundles, and CCI based filtering used the same input
bundles (Original CST as listed in Table 3.1), and the results show that our algorithm achieved the best
performance while all three methods were able to enhance the fidelity to manually delineated ROIs. We
also estimated the Hausdorff distance between these four ROIs (ROI 2 - 5) and CSTs generated by the two
atlas-based tools in RecoBundles and SlicerDMRI. The results in Table 3.1 suggest much larger errors as
compared to the manually delineated labels in the brainstem. This is consistent with a large number of
outliers as illustrated in Fig. 3.11 (e) and (f). Because the results from SlicerDMRI contain a much larger
number of tracks than other methods, we applied manually delineated ROI 1 as an inclusion region to the
bundle reconstructed by SlicerDMRI for a fair comparison to other methods. This removed many of the
outliers and improved distance measure to other ROIs are listed in Table 3.1 as SlicerDMRI+ROI 1, which
are comparable to the performance of the input bundles listed as Original CST. Such anatomical constraints
were not imposed for CSTs generated by RecoBundles because it tends to extract tracks from the whole
brain tractography that terminate early and rarely reach ROI 1.
With the manually delineated ground truth labels for brainstem ROIs, we can also demonstrate the
impact of the parameters used in our method. Because the CST bundle has clear end ROIs on both the
cortical and brainstem area, we have selected very high degree related parameters (largeL
min
=0.8 and
smallerL
max
= 0.01). In addition, we have selected a high affinity parameter ( K = 19) according to the
prior knowledge that HCP subjects are young and healthy. Thus, we focused on the fine-tuning of param-
eters related to the proximity condition: σ andδ , and examined their impact on the Hausdorff distances
of the reconstructed bundle with respect to the ground truth labels. As shown in Fig. 3.12, the colored
curves and associated shaded regions demonstrate the mean and standard deviations of the Hausdorff dis-
tances from the reconstructed bundle to each ROI with respect to the change of these two parameters. The
black dots show the number of fiber tracks in the reconstructed bundle under each parameter value. With
38
Table 3.1: Hausdorff Distance of Fiber Bundles to Manually Delineated ROIs.
ROIs Approaches Hausdorff Distance (mean ± std mm)
ROI 5
Original CST 9.49± 2.20
QuickBundles 4.76± 1.92
CCI 3.10± 1.76
RecoBundles 11.81± 3.63
SlicerDMRI 16.25± 3.10
SlicerDMRI+ROI 1 9.34± 2.18
Proposedmethod 2.33±1.19
ROI 4
Original CST 9.74± 2.50
QuickBundles 5.89± 2.21
CCI 4.26± 2.10
RecoBundles 13.19± 4.02
SlicerDMRI 18.15± 2.79
SlicerDMRI+ROI 1 9.32± 2.20
Proposedmethod 3.10±1.56
ROI 3
Original CST 9.86± 1.86
QuickBundles 6.68± 2.65
CCI 5.41± 2.07
RecoBundles 13.14± 3.22
SlicerDMRI 18.75± 3.30
SlicerDMRI+ROI 1 9.76± 1.90
Proposedmethod 3.78±1.91
ROI 2
Original CST 7.46± 1.49
QuickBundles 4.92± 1.99
CCI 3.65± 1.76
RecoBundles 12.27± 4.23
SlicerDMRI 16.43± 3.00
SlicerDMRI+ROI 1 7.23± 1.23
Proposedmethod 2.48±1.20
Table 3.2: Size (num of tracks) of filtered fiber bundles.
Approaches Num of Tracks (mean± std; [min, max])
QuickBundles 197.70± 80.89; [84, 381]
CCI 229.45± 75.64; [80, 342]
RecoBundles 146.90± 51.08; [78, 269]
SlicerDMRI 381.10± 101.26; [220, 611]
SlicerDMRI+ROI 1 81.75± 43.17; [25, 210]
Proposed method 168.90± 45.37; [98, 253]
the increase of σ , the consistent measure computed from message passing becomes more insensitive to
proximity conditions and could result in the pruning of more tracks. From Fig. 3.12 (a), we can see that
39
σ = 6− 8 mm would be good trade-offs. For the δ parameter, its decrease will lead to stricter stopping
criteria and the elimination of more tracks. We thus set it asδ = 3 mm to ensure a sufficient number of
tracks can be retained (around or above 100 for the CST bundle) in the final reconstruction. Overall, the
fine-tuning of the parameters strikes a balance between applying the proximity condition and ensuring
enough number of tracks to effectively represent the geometry of the fiber bundle.
(a) (b)
Figure 3.12: The impact of proximity parameters on CST reconstruction with our groupwise method. The
mean and standard deviation of Hausdorff distances (y-axis on the left side) from the reconstructed bundle
to each ROI (2 - 5) are plotted in (a) and (b) as colored curves and shaded regions with respect to the change
of the parametersσ andδ , respectively. In addition, the number of tracks (y-axis on the right side) in the
reconstructed bundle are plotted as black dots with respect to the change of parameters.
3.3.4 Computationalcost
In all experiments, our method was implemented in Python on a desktop computer with 3.60GHz Intel
i7-6850K CPUs and 64GB RAM. We conducted each experiment ten times to obtain a robust estimation of
running times. The overall processing times of all subjects in the experiments are summarized in Table
3.3.
40
Table 3.3: Summary of the Computing Cost in Each Experiment
Filtering Task #Subjects Time (mean± std seconds)
Fornix 40 1087.99± 20.74
LC Pathway 50 991.24± 17.92
CST 20 535.19± 9.07
3.4 DiscussionandConclusion
In this work, we developed a novel groupwise track filtering algorithm for the consistent reconstruction
of fiber bundles from diffusion imaging data. Our method is based on a flexible definition of groupwise
consistency that controls the degree, affinity, and proximity of each track with respect to other group
members. A key element of our algorithm is the dynamic construction and update of a reference set for
each track that allows the efficient implementation of localized consistency evaluation based on message
passing and outlier pruning. In summary, the main contributions of our work are a) Proposed a general
conceptual framework for characterizing groupwise consistency of fiber tracks; b) Developed a novel nu-
merical algorithm that iteratively and locally prunes inconsistent portions of each track; c) Demonstrated
the general applicability of the proposed algorithm on fiber bundles with varying level of artifacts and
complexity; d) Performed quantitative comparisons based on ground truth from manually delineated la-
bels and showed that groupwise filtering can compensate for the gap in anatomical knowledge and achieve
the more faithful reconstruction of fiber bundles.
Accurate bundle reconstruction relies on intensive anatomical priors. Multiple automated bundle re-
construction methods such as TRACULA [138], whitematteranalysis [96, 139], Recobundles [37], TractSeg
[132], WMQL [131] taking advantages of the anatomical priors in the form of segmentations of reference
tracts, tractography atlas, and brain parcellation atlases to effectively and efficiently reconstruct various
fiber bundles. With these methods, the analysis of the white matter at the fiber bundle level becomes
very convenient. While limited attention was paid to considering whether each streamline in the fiber
bundles is reliable and reproducible. From [100]2020), we know that the reproducibility of streamlines is
41
much more sensitive than which of whole bundle volume. If we would like to leverage the information
at the streamline level, it is necessary to determine how reliable each streamline is. In [59], the cluster
confidence index is proposed to quantitatively indicate the reliability of individual streamline according
to its similarity with neighborhoods. In this work, we further generalize the reliability concept to be the
reproducibility across subjects (groupwise consistency) and construct a framework to extract the most
reproducible sub-bundle structures.
The underlying assumption for the success of the proposed method is the existence of a certain level
of commonness in the fiber bundles across subjects. This is commonly adopted in brain mapping research,
where image or surface registration was first applied to factor out variability across subpopulations before
group level analysis. In our experiments, we warp all fiber trajectories into a common space using non-
linear image registration [4] before the filtering process. This ensures that individual variability in white
matter anatomy is taken into account. Tractography registration methods proposed in [38, 97] could also
be useful to align the fiber bundles before the application of our groupwise filtering algorithm. Without
referring to the images, these registration methods have the potential advantage of handling the bundle
alignment task for patients with severe white matter atrophy, lesion, and tumor.
In the algorithmic implementation of the proposed groupwise filtering framework, the parameters
used for controlling the degree (L
min
andL
max
) and affinity measures ( K) are typically chosen accord-
ing to the prior knowledge with respect to individual fiber bundles. For fiber bundles without stringent
ROIs that determine the endpoints of the tracks, we demonstrate a proper choice of the degree parameter
can help prune away spurious portions on both ends of the fiber bundle and produce a consistent rep-
resentation of the fornix bundle. This strategy can be generally applicable to various fiber bundles that
project diffusively to broad cortical areas and therefore have high variability in their tractography based
reconstruction. For example, the anterior commissure projects to the broad areas including the middle
and inferior temporal gyrus would benefit from our method to achieve a consistent reconstruction for
42
comparison across subjects. For fiber bundles that can be defined with relatively precise end ROIs, we can
increase the degree requirement (largerL
min
and smallerL
max
). Similar to existing track filtering meth-
ods, this will achieve essentially a binary decision (accept/reject) on each streamline with the assistance
of groupwise consistency. For the affinity measure, our method allows its adjustment for fiber bundles or
cohorts with varying levels of heterogeneity across the group. For the fornix bundle reconstruction from
the ADNI data, we demonstrated the robustness of the results with respect to the change of the affinity ( K)
parameter and the preservation of subject level variability in the reconstructed fiber bundles. For young
and healthy subjects from the HCP, a higher affinity parameter, selected in our experiments, reflects the
prior knowledge about the higher degree of similarity in this cohort. For the proximity condition, the
strengthening of its requirement (smallerδ ) will result in the filtering of more artifacts and potentially the
removal of valid tracks from the reconstructed fiber bundles. As demonstrated in Fig. 3.12, we chose the
proximity parameter by balancing the removal of artifacts and the preservation of a sufficient number of
valid tracks in the CST bundle. Overall, the parameters for the degree, affinity, and proximity conditions
in our method can be selected intuitively because of the clear expectation as explained above about their
effects on the filtered filter bundles.
As a fiber bundle filtering tool, our method depends on the original inputs and could be affected by
the bias issue of tractography algorithms [78]. In our CST experiment, the fiber pathways emanating
from the lateral portion of the precentral gyrus are harder to reconstruct because of the crossing regions
with complicated fiber geometry and the dramatic turning angles as they join the descending portion of
the CST at the internal capsule. Fiber tracks from the lateral portion of the motor cortex thus tend to
be severely under-represented and highly variable across subjects. As a result, our method will filter out
these tracks due to their lack of groupwise consistency. Improvements in tractography algorithms will
help provide a more balanced representation of input fiber bundles to our algorithm and hence generate
better reconstruction results. For example, the Anatomically Constrained Tractography (ACT) [105] can
43
improve tractography quality and hence the downstream filtering algorithms. Recently, [101] proposed a
tractography algorithm to mitigate the bias in the fiber bundle reconstruction by introducing anatomical
and orientational prior knowledge for tractography. For future work, we will investigate such tractography
tools and examine their impact on our groupwise filtering method. In addition, it will be highly valuable
to perform validations against ground truth provided by tracer injection data in other anatomical regions
such as the internal capsule for the CST bundle [55].
In summary, we developed an iterative algorithm to prune away inconsistent artifacts of fiber tracks for
the reconstruction of fiber bundles with groupwise consistency. Results from our method can improve the
comparability of bundle-based representations of white matter connectivity and hence potentially provide
increased power in the detection of group differences. In future work, we will apply our method to perform
more extensive validations and study the impact of groupwise filtering on the detection of connectivity
changes of critical fiber bundles in brain disorders such as the Alzheimer’s disease.
44
Chapter4
PersonalizedDiffusionMRIHarmonization
4.1 Introduction
Diffusion magnetic resonance imaging (dMRI) [7] allows the probing of brain microstructure in vivo and
plays a key role in brain mapping research. With the widespread use of large-scale dMRI data from various
studies [89, 13, 122], the harmonization of dMRI data across acquisition protocols, sites, and vendors is a
critical yet challenging problem [125, 143, 76]. One fundamental difficulty in dMRI harmonization is dis-
entangling scanner-related effects from anatomical variations on the local appearance of imaging signals.
To this end, we propose a novel personalized framework that better resolves the impact of anatomical vari-
ability on the estimation of inter-site mapping and advances the state-of-the-art in dMRI harmonization.
With the goal of limiting the impact of anatomical variability on the estimation of scanner effects, pre-
vailing dMRI harmonization approaches rely on the co-registration of dMRI data across sites into a common
atlas space. Then, spatial/regional mapping for dMRI harmonization can be estimated as the confounding
of anatomy is expected to be removed. Following this registration-based framework, several statistical
normalization approaches including Removal of Artificial Voxel Effect by Linear regression (RAVEL) [32],
Surrogate Variable Analysis (SVA) [70], and ComBat [58] were examined in [31] for the harmonization of
diffusion tensor imaging (DTI) features, and the ComBat method has been shown to be highly effective for
multi-site DTI data pooling. For the direct harmonization of dMRI signals, the rotation invariant spherical
45
(a)
(b)
Figure 4.1: Inter-subject anatomical variability and the resulting mismatch between individual subjects
and the sample mean template. (a) FA images of two ABCD subjects co-registered to the template space.
Top: NDARINV15MFU6UZ acquired from a GE MR750 scanner; bottom: NDARINV1NW3HM13 scanned
on a Siemens Prisma scanner. (b) A template image constructed from the FA images of 100 ABCD subjects.
Left column: axial slices of the two ABCD subjects and the template. For each axial slice, zoomed views of
the ROIs highlighted by yellow and blue boxes are shown in the middle and right columns, respectively,
where the variations of the brain anatomy are noticeable.
harmonics (RISH) feature based method was proposed [86] and embedded in a registration framework to
achieve voxel-wise harmonization in a template space [85, 60]. Similarly, a method of moments (MoM)
was proposed [54] to achieve the harmonization of dMRI signals after registration to an atlas space by
comparing the spherical moments of dMRI signals across sites to estimate a linear mapping function.
Despite the essential role of co-registration in previous harmonization methods, little work has been
done to examine its reliability in building anatomical correspondences across subjects in dMRI harmoniza-
tion. In fact, the inter-subject variability in neuroanatomy and hence the possible lack of one-to-one cor-
respondences across subjects will inevitably complicate the construction of anatomical correspondences
46
essential for the validity of existing harmonization models. This difficulty will be especially evident in re-
gions surrounding the cortical boundaries, where the high variability across subjects has been well-known
[115, 119]. As illustrated in Fig. 4.1(a), there are obvious anatomical differences between the two Adoles-
cent Brain Cognitive Development (ABCD) [13] subjects even after they have been co-registered to the
template image in Fig. 4.1(b). Because harmonization algorithms rely on pooling data across subjects from
different sites at locations with corresponding anatomy, this type of mismatch, shown in Fig. 4.1, would
make the estimation of the inter-site mapping function much less reliable and lead to invalid harmonization
of the dMRI data at affected locations.
To overcome this fundamental problem in establishing anatomically consistent correspondences for
the estimation of inter-site mapping functions, we develop a personalized template estimation framework
In this chapter to abridge the anatomical gaps between population-based templates and individual sub-
jects to be harmonized. We also integrate this personalized analysis framework with RISH features [85,
60] to achieve voxel-wise harmonization of dMRI signals across scanners. Fig. 4.2(a) shows the overall
harmonization framework. To integrate the feature representations of reference subjects from both source
and target scanning sites for each query subject, we introduce a personalized pooling tensor for each site.
As illustrated in Fig. 4.2(b), the pooling tensor of a site consists of weight vectors computed via solving
a convex optimization problem at each voxel based on the similarity of the local anatomy between the
query subject and the reference subjects, which are representative of a site. Once the pooling tensors are
estimated, site-specific templates will be estimated in a personalized manner for computing the inter-site
mapping function for each feature representation. By combining the transferred feature representations,
we achieve personalized harmonization of the dMRI data from the source to the target site for the query
subject.
The rest of this paper is organized as follows. Section 4.2 introduces the personalized dMRI harmo-
nization framework and related numerical algorithms. Experimental results are presented in Section 4.3
47
(a)
(b)
Figure 4.2: An overview of our personalized dMRI harmonization method. (a) The overall framework for
the estimation of personalized templates and inter-site mapping functions to achieve the harmonization
from the source to the target site. (b) Details about the estimation of the personalized pooling tensors
(W
src
andW
tar
) by computing a weight vectorw at each voxel as the solution of a convex optimization
problem based on local similarity of the anatomy between the query subject and reference subjects of each
site.
to demonstrate that the proposed personalized method is able to achieve much-improved performance
in comparison with the state-of-the-art method based on RISH feature mapping. Finally, discussions and
conclusions are made in Section 4.4.
48
4.2 Methods
4.2.1 DiffusionMRIharmonizationinacommonspace
Given dMRI data from a source and target site, the goal of the harmonization task is to estimate a mapping
function:
ˆ
S = Ψ( S) for each subject in the source site, whereS denotes the diffusion signal of a subject
from the source site andΨ denotes the inter-site mapping function to the target site. For the estimation
of the inter-site mapping function, sets of reference subjects from the source and target sites are typi-
cally needed to represent the scanner-dependent variations. In addition, it is important to consider the
anatomical variations across subjects and the spatial heterogeneity of scanner differences.
To this end, nonlinear image registration has played a key role in minimizing the impact of anatomical
differences across subjects and allowing the pooling of information from representative reference subjects
for the characterization of site-effects. Within a common space constructed through nonlinear registration
of the anatomical images of subjects from both sites, the harmonization mapping function Ψ can be de-
termined by comparing the rotation invariant diffusion features, such as RISH features [60] and diffusion
moments [54], across sites. For each feature, a population-based templateE is first constructed for both
the source and target sites by evenly pooling the co-registered feature images of the reference subjects
from each site:
E=
1
N
N
X
i=1
R
i
, (4.1)
whereR
i
is the diffusion feature image of the i-th reference subject from a given site. Using the population-
based feature templates from both the source and target site, the harmonization mapping functionΨ can
be estimated at each location in the common space, which can then be applied to all source subjects for
their harmonization to the target site [60, 54].
49
4.2.2 Personalizedtemplateestimation
While the common space from nonlinear registration can greatly reduce inter-subject variations, signifi-
cant anatomical differences remain, especially around the cortical areas. For a given query subject from
the source site to be harmonized, this type of anatomical misalignment will no doubt introduce significant
bias to the estimation of feature templates and consequently affect the harmonization mapping function.
To avoid the confounding caused by the anatomical misalignment in harmonization, we develop a per-
sonalized approach for template estimation by adaptively integrating the feature representations from the
reference subjects of a given site in the common space according to localized anatomical similarity. For a
given query subjectQ from the source site, we compute a personalized pooling tensorW
Q
for the esti-
mation of a personalized templateE
Q
:
E
Q
=R⊙W
Q
, (4.2)
whereR=[R
1
...R
N
] denotes the feature images ofN reference subjects from a given site. At a location
x in the common space, the uneven pooling of references is performed by a weighted sum:
E
Q
(x)=W
Q
(x)
T
R(x), (4.3)
where W
Q
(x) = [w
1
(x),...,w
N
(x)]
T
is a weight vector, with w
i
(x) > 0 and
P
N
i
w
i
(x) = 1 and
R(x) = [R
1
(x),...,R
N
(x)]
T
is the local reference vector containing diffusion features sampled from
the reference subjects.
For the calculation of the weight tensorW
Q
, we compute the reference weight vectorW
Q
(x) adap-
tively at each location x in the common space by solving a convex optimization problem. Let’s denote
that the co-registered anatomical image of the source query subject in the common space asU and those
50
of the N reference subjects asV = {V
1
,V
2
,...,V
N
}. For numerical implementation, we use the frac-
tional anisotropy (FA) image as the anatomical image of each subject in this work. At each point x in
the common space, the local anatomical similarity measure between the query subject and a reference
subject is denoted assim(U(x),V(x)), which we define based on the cross-correlation of local patches:
sim(U(x),V(x)) =
P
y
j
∈P
(U(y
j
)− µ U
)(V(y
j
)− µ V
)
σ U
σ V
, whereP is a 3D patch of size3× 3× 3 centered at the
voxelx in bothU andV ,µ U
andµ V
are the mean FA value within the patch, andσ U
andσ V
are the stan-
dard deviations. To ensure that the personalized templates are representative of reference subjects with
similar anatomy at each point, we introduce a Laplacian regularizer across reference subjects in the cost
function. This regularizer can encourage the reference subjects with highly similar anatomy to be assigned
with similar weights. Furthermore, we include a spatial consistency term in the cost function to consider
the local spatial dependencies in adjacent locations. The weight vector estimation is then formulated as
the following convex optimization problem:
max
w
p
T
w− γ 1
w
T
Lw+γ 2
q
T
w
s.t.w≥ 0,1
T
w =1.
(4.4)
wherew =W
Q
(x) is the weight vector atx andp=[sim(U(x),V
1
(x)),...,sim(U(x),V
N
(x))]
T
is the
query-to-reference similarity vector atx. In the Laplacian regularization termw
T
Lw,L = D− A is a
Laplacian matrix, whereA is the inter-reference similarity matrix with entryA(i,j)=sim(V
i
(x),V
j
(x)),
andD is the degree matrix. We can trade off between the potential mismatch of brain anatomy and the
reliability in template estimation by tuning the parameterγ 1
. By increasing the parameterγ 1
, the weights
would be propagated to more reference subjects, which would enlarge the sample size and improve the
reliability of the personalized templates. On the other hand, an overly large parameterγ 1
could result in
assigning non-negligible weights to all reference subjects and bring the misregistration problem back to
51
template construction. The third term of the cost function is designed to encourage the spatial consistency
of the weight vectors, where the neighborhood similarity vector for the query locationx is defined as
q=
P
x
′
∈N(x)
sim(U(x),U(x
′
))p(x
′
)
P
x
′
∈N(x)
sim(U(x),U(x
′
))
. (4.5)
Here N(x) is the neighborhood centered at x and p(x
′
) =
[sim(U(x
′
),V
1
(x
′
)),...,sim(U(x
′
),V
N
(x
′
))]
T
is the query-to-reference similarity vector of the
neighboring voxel x
′
∈ N(x). Note that the contributions of spatial neighborhoods are proportional to
their anatomical similarity with the query location to accommodate the anatomical inconsistencies that
may arise in neighborhood patches located at tissue boundaries. The tuning parameter γ 2
controls the
involvement of neighborhood information in the estimation of weight assignment. Overall, this quadratic
programming problem is solved by using the ECOS solver [25, 23].
For dMRI harmonization, personalized templates will be computed for each query subject with respect
to the reference subjects from both the source and target site, respectively. This procedure will be per-
formed for all pertinent diffusion image features which characterize the scanner effects for the source and
target sites. Subsequently, the inter-site mapping function for harmonizing the dMRI signal to the target
site can be estimated, as we will describe below.
4.2.3 Personalizedharmonizationbasedonmappingsphericalharmonicsfeatures
To demonstrate the application of our personalized template estimation for dMRI harmonization, we inte-
grate it with the rotational invariant spherical harmonics (RISH) features from the LinearRISH harmoniza-
tion method [60]. To compute the RISH features, the dMRI signals at each voxel are first represented by
the spherical harmonics (SPHARM) asS≃
P
lm
C
lm
Y
lm
, whereY
lm
andC
lm
are the SPHARM basis and
corresponding coefficient of order l and degreem. The RISH features characterize the energy distribution
52
of the dMRI signal at each orderl and is defined as R
l
=
P
m
C
2
lm
. In a common space constructed by non-
linear registration, the LinearRISH method computes a template from the source and target site for each
RISH feature and calculates a scale factorΦ l
at each location, which is then applied to scale the SPHARM
coefficients at the same order l:
ˆ
C
lm
= Φ l
C
lm
to realize the harmonization. Note that the template and
scale factors are the same for all subjects from the source site.
For the personalized harmonization of dMRI data from a source site (src) to a target site (tar) in our pro-
posed method, the mapping functionΦ l
is estimated separately for each query subjectQ at each SPHARM
order:
Φ l
(x)=
s
E
tar
l
(x)
E
src
l
(x)
, (4.6)
whereE
tar
l
andE
src
l
are the personalized template of the RISH feature at the order l for the target and
source sites, respectively. Compared with the conventional LinearRISH method, the main novelty of our
method is that the RISH feature templates are estimated by solving (4.4) and hence emphasize reference
subjects with similar anatomy to boost consistency. The mapping imageΦ l
is then warped back to the
subject space of the query individual. At each voxel in the query space, the SPHARM coefficient C
Q
lm
of
the dMRI signal is scaled by the mapping function at the orderl as
ˆ
C
Q
lm
=Φ l
C
Q
lm
. Finally, the harmonized
dMRI signal
ˆ
S
Q
is generated by using the scaled SPHARM coefficients:
ˆ
S
Q
=
X
lm
ˆ
C
Q
lm
Y
lm
. (4.7)
By repeating this process for all voxels, we obtain the harmonization of the query subject from the source
to the target site.
53
4.3 ExperimentalResults
To demonstrate the efficacy of the proposed personalized dMRI harmonization framework, we apply the
proposed method to harmonize dMRI data acquired from two scanning systems: Siemens Prisma and GE
MR750 from the ABCD study [13] and compare the performance with the state-of-the-art LinearRISH
method [60]. The results are organized as follows. In Section 4.3.1, we describe the dMRI dataset and
the implementation details of harmonization experiments. An illustration of the weight assignment for
personalized template construction in our method and a comparison with the template from LinearRISH
are presented in Section 4.3.2. Next, we discuss the selection of regularization parameters for our method
in Section 4.3.3. In Section 4.3.4, we present a comprehensive comparison of the proposed harmonization
framework with LinearRISH in terms of reducing the inter-site variation of DTI features. Then, we assess
the impact of available reference subjects on the performance of our personalized harmonization frame-
work in Section 4.3.5. In Section 4.3.6, we focus on the regional distribution of DTI features in cortical
gray matter areas to further demonstrate the effectiveness of our personalized harmonization method in
disentangling site-effects from variable brain anatomy. In Section 4.3.7, we examine the impact of dMRI
harmonization on the estimation of fiber orientation distribution. Finally, we investigate the preservation
of sex-related biological variability after harmonization and compare the performance of both methods in
Section 4.3.8.
4.3.1 Datasetandimplementationdetails
4.3.1.1 SubjectsanddMRIdata
In our experiments, we used data acquired on two scanning systems: Siemens Prisma (SIEMENS) and
GE Discovery MR750 (GE) from the ABCD Study [13]. A total of 200 subjects at baseline were selected
from the ABCD study, with balanced sample sizes for each scanner, including 100 subjects scanned on
Siemens Prisma and another 100 subjects on GE Discovery MR750, which we denote as the SIEMENS
54
Table 4.1: Diffusion MRI parameters for the Siemens Prisma and GE 750 scanner in the ABCD study.
Scanner TR (ms) TE (ms) Flip Angle (
◦ )
Siemens 4100 88 90
GE 4100 81.9 77
and GE cohort in our experiments, respectively. To control for confounding effects of age and gender, all
selected participants are 9 years old and well-matched for gender, consisting of 50 females and 50 males in
each cohort. For both scanners, the ABCD dMRI data used in harmonization experiments were acquired
atb=3000 s/mm
2
from 60 gradient directions using multiband EPI [61]. All dMRI data have an isotropic
spatial resolution of 1.7 mm. The sequence parameters, repetition time (TR), time to echo (TE), and flip
angle, are scanner-specific. See Table 4.1 for detailed dMRI sequence parameters for the SIEMENS and GE
scanners.
Furthermore, all data used in our experiments are part of the ABCD Data Release 4.0 from the NIMH
Data Archive (NDA) and have been preprocessed by the ABCD study. Quality control and preprocessing
were performed to minimize the influence of poor image quality and artifacts prior to harmonization [47].
For eddy current correction, distortions on the diffusion gradients were estimated using the approach
in [144]. The echo-planar imaging distortions were corrected for each acquisition using the reversing
gradient method with FSL’s TOPUP [1, 2]. The head motion correction and diffusion gradient adjustment
were performed following procedures in [46]. Additionally, to minimize the impact of noise on the RISH
based harmonization [60, 85], the diffusion-weighted images were denoised via the over-complete local
PCA-based method [79].
4.3.1.2 ImplementationdetailsofdMRIharmonization
For both our method and the LinearRISH method for comparison, we calculated five RISH features for
SPHARM orders ofl ={0,2,4,6,8} for the harmonization of dMRI signals at each voxel. For the gener-
ation of the common space for computing the harmonization mapping function, we applied the template
55
construction tool from Advanced Normalization Tools (ANTs) [4] to the FA images of all subjects. The
generated deformation fields were used to perform inter-subject alignment of the RISH and DTI features
in all harmonization and evaluation experiments. For our method, all subjects from the source or target site
(SIEMENS or GE ) served as reference subjects for the construction of personalized RISH feature template
and the estimation of mapping functions.
4.3.2 Localreferenceselectionandpersonalizedtemplateconstruction
Personalized template construction is achieved by adaptively assigning pooling weights at each voxel ac-
cording to the anatomical similarities between the query subject and reference subjects from each site.
First, we illustrate how the weight assignment was conducted at two typical locations with parameters:
γ 1
=0.1 andγ 2
=2.0. Fig. 4.3(a) presents a location centered in a white matter region where the anatom-
ical mismatching problem is relatively mild. In this example, both the query subject and reference subjects
were from the GE cohort. As can be seen in the top row on the right of Fig. 4.3(a), reference patches with
high anatomical similarity were assigned high weights and included for template construction. On the
other hand, reference patches with low similarity (shown in the bottom row of Fig. 4.3(a)) were assigned
zero weights and excluded from template estimation at the current voxel. Fig. 4.3(b) shows another exam-
ple at the boundary of gray and white matter with higher inter-subject anatomical variability. Here, the
query subject was from the GE cohort and the reference subjects were from the SIEMENS cohort. The top
row on the right of Fig. 4.3(b) presents the instances of selected reference patches with non-zero weights.
Compared to the results shown in Fig. 4.3(a), it is observable that the pooling weights are more concen-
trated over well-aligned references because a more limited number of references share similar anatomy
to the query subject at the highlighted location on the cortical boundary. As shown in the bottom row
on the right of Fig. 4.3(b), noticeable dissimilarities exist between the query and reference patches. With
56
zero weights assigned to those references, our method effectively alleviates the confounding due to the
misalignment of brain anatomy in template construction.
(a)
(b)
Figure 4.3: An illustration of selected and discarded references at two representative locations. In each
subfigure (a) and (b), the results are organized as follows. Left: the transverse slice of the FA image in-
dicating the location of the query patch in the common space (highlighted in red); middle: a zoomed
view of the query patch (in red box); right (top row): top-4 reference patches ordered by their pooling
weights; right (bottom row): discarded reference patches with zero weights. The assigned weights and
the query-reference anatomical similarity are displayed above each reference patch in the form of "weight
(anatomical similarity)".
By performing the personalized weight assignment at each voxel for reference subjects from the source
or target site, personalized templates can be generated for a given query subject to characterize site effects
in dMRI signals. Fig. 4.4 displays the zeroth-order RISH feature of a query subject (Subject ID: NDAR-
INV15MFU6UZ) and the corresponding templates estimated by the LinearRISH method based on sample
mean and the proposed personalized method. In contrast to the conventional templates from LinearRISH
(first row on the right) for both the GE and SIEMENS cohort, we can see the personalized templates from
57
our method (second row on the right) capture much more cortical folding details (circled by red dashed
lines) that align very well with the query subject.
Figure 4.4: A comparison of site-specific templates estimated by the LinearRISH method based on sam-
ple mean and our personalized method for the zeroth-order RISH feature. Left: a transverse slice of the
zeroth-order RISH feature of a query subject (GE Subject ID: NDARINV15MFU6UZ). Right (top row): the
corresponding slice of templates estimated from the GE and SIEMENS cohort by the LinearRISH method.
Right (bottom row): the corresponding slice of the templates estimated from the GE and SIEMENS cohort
by our personalized method.
4.3.3 Regularizationparameters
4.3.3.1 Across-referenceregularization
In the proposed personalized harmonization framework, the number of selected references primarily de-
pends on the underlying query-to-reference anatomical similarity at each voxel and the choice ofγ 1
. We
investigated the spatial distribution of the average number of selected references per query subject with
varyingγ 1
while keepingγ 2
=2.0. Because anatomical similarity across subjects varies in different brain
regions, the average number of references used for personalized template estimation differs spatially. For
58
two harmonization experiments: GE toward SIEMENS and SIEMENS toward GE, the spatial distribution
of reference number for the estimation of site-specific templates are plotted in Fig. 4.5 (a) and (b) under
different parameter choices of γ 1
. From the results, we can observe that white matter areas consistently
have a higher reference number than cortical gray matter regions. This suggests that gray matter regions
with higher inter-subject variability tend to have fewer qualified references. Furthermore, an increase of
γ 1
enlarges the size of the reference set. By tuning γ 1
, we trade off between the potential mismatch to
references and the reliability achieved through the availability of a sufficient number of references to rep-
resent site-specific characteristics at each location. Upon examining the distribution of reference numbers
withγ 1
=0.1, the number of references typically exceeds 20 in white matter regions, which is more than
sufficient for a reliable representation of population characteristics in harmonization [60]. For gray matter
regions with more severe misalignment in brain anatomy, there are still on average at least 10-15 refer-
ences available for template construction. Based on these observations, we setγ 1
=0.1 for the rest of our
experiments.
4.3.3.2 Spatialsmoothnessregularization
We further examined the effect of the regularization parameter γ 2
on the spatial consistency of reference
selection. For each query subjectQ, the 4D personalized pooling tensorW
Q
is composed of multiple 3D
weight imagesW
Q
i
:W
Q
=[W
Q
1
,...,W
Q
N
], whereN is the size of the reference set from a site. For each
weight image, we used the magnitude of its Laplacian to quantify the smoothness of weight assignment
[136]. Overall, the spatial smoothness of reference selection for a query subject is computed as follows:
η Q
=
N
X
i
X
j∈Ω |∆ W
Q
(j)|, (4.8)
where∆ W
Q
=
∂
2
W
Q
∂x
2
+
∂
2
W
Q
∂y
2
+
∂
2
W
Q
∂z
2
is the Laplacian of a 3D weight image andΩ denotes the location
set of the whole brain region in the common space. In Fig. 4.6, we demonstrate the relationship between
59
(a)
(b)
Figure 4.5: The spatial distribution of reference numbers in personalized and site-specific template con-
struction with different choices of the regularization parameter γ 1
. (a) Query subjects from the GE cohort
and Reference subjects from the SIEMENS cohort. (b) Query subjects from the SIEMENS cohort and Ref-
erence subjects from the GE cohort.
the parameterγ 2
and the overall smoothness of weight assignment in situations where query and reference
subjects are from different sites while maintaining γ 1
=0.1. It can be observed that increasingγ 2
leads to
a noticeable improvement in the spatial smoothness of weight assignment. Afterγ 2
reaches1.0, its impact
on the smoothness reaches a region of relative stability. The turning point is atγ 2
=2.0 and larger values
ofγ 2
result in a tendency towards less spatial consistency. Thus, it is reasonable to chooseγ 2
around 2.0.
In the following experiments, we setγ 2
=2.0 for the regularization of spatial consistency.
4.3.4 Inter-sitevariationandharmonization
To quantitatively evaluate the performance of harmonization methods, we calculated the inter-site coeffi-
cients of variation (CoVs) for diffusion features, including fractional anisotropy (FA) and mean diffusivity
60
Figure 4.6: Spatial consistency regularization by changing the parameterγ 2
. For query subjects from the
GE cohort and reference subjects from the SIEMENS cohort, the mean values of the weight smoothness
measure across all query subjects with respect to varyingγ 2
are plotted in red. Similarly, the green curve
shows the results under an alternative setting (query subjects from the SIEMENS and reference set from
the GE cohort).
(MD), before and after harmonization. The coefficient of variation, defined as the ratio of the standard de-
viation to the mean of a feature, quantifies the dispersion of a distribution. The inter-site CoVs, reflecting
the discrepancy of integrated datasets, are expected to be reduced after harmonization. For a qualitative
evaluation, Fig. 4.7 presents the voxel-wise CoVs of merged dMRI data for the following combinations:
(1) original SIEMENS and GE data (SIEMENS + GE), (2) original SIEMENS and harmonized GE data using
SIEMENS as the target site (SIEMENS + harmonized GE), and (3) original GE and harmonized SIEMENS
data using GE as the target site (GE + harmonized SIEMENS).
To clearly demonstrate the improvement achieved by our proposed method, we calculated the local
improvement rate (IR
CoV
) defined as follows:
IR
CoV
=
CoV
org
− CoV
a
max(CoV
org
− CoV
b
,ϵ )
, (4.9)
whereCoV
org
,CoV
b
, andCoV
a
were the CoVs before harmonization, after harmonization using the base-
line method (LinearRISH), and using the proposed method. To ensure a positive denominator,ϵ was set to
61
Figure 4.7: Inter-site coefficients of variation of FA and MD before and after harmonization. The results
for original datasets before harmonization, SIEMENS + harmonized GE, and GE + harmonized SIEMENS
are shown in the left, middle, and right panels. In the second and third panels, the results of LinearRISH,
our method, and the improvement rate (IR
CoV
) are displayed from left to right, respectively.
be 0.001. A value ofIR
CoV
>1 indicates superior performance by our method in reducing the CoV of the
integrated data from the GE and SIEMENS cohort. The voxel-wiseIR
CoV
images for FA and MD are shown
in the fourth and last column in Fig. 4.7 for two harmonization tasks: harmonizing GE data to SIEMENS
(SIEMENS + harmonized GE) and harmonizing SIEMENS data to GE (GE + harmonized SIEMENS). We can
clearly see that our method achieved better performance than LinearRISH in most brain regions, especially
in areas close to cortical gray matter. In other white matter regions, the two methods achieve comparable
performance in both harmonization tasks.
Besides, we calculated the average CoV across the whole brain and the negative rate (r
N
) of CoV after
harmonization to quantify the overall performance of the two harmonization methods. The negative rate
(r
N
) of CoV is defined as the ratio of the number of voxels with increasing or equal CoV after harmonization
to the total number of voxels in the common space. It represents the failure rate in terms of reducing the
inter-site variability. Table 4.2 summarizes the quantitative results for both harmonization tasks: SIEMENS
+ harmonized GE and GE + harmonized SIEMENS using the proposed method and LinearRISH. This further
demonstrates the much improved performance by our personalized harmonization framework in reducing
the inter-site variation and the negative rate (r
N
) for both the FA and MD features.
62
Table 4.2: Inter-site coefficients of variation and negative rates ( r
N
) after harmonization for FA and MD.
Dataset FA CoV (r
N
) MD CoV (r
N
)
SIEMENS+GE 0.404± 0.160 (-) 0.090± 0.052 (-)
SIEMENS+harmonized GE (LinearRISH) 0.361± 0.132 (9.83%) 0.087± 0.047 (15.47%)
SIEMENS+harmonized GE (our method) 0.332± 0.121 (2.27%) 0.080± 0.043 (3.14%)
GE+harmonized SIEMENS (LinearRISH) 0.409± 0.172 (30.04%) 0.096± 0.064 (65.71%)
GE+harmonized SIEMENS (our method) 0.367± 0.150 (11.58%) 0.088± 0.055 (15.56%)
4.3.5 Numberofavailablereferences
When constructing personalized templates in our method, having an adequate number of reference sub-
jects from each site is beneficial to cover the variability of neuroanatomy, especially in regions where the
anatomical structures are not shared by the majority of the population. In this experiment, we assessed the
impact of the number of available references on harmonization performance. The same parameter settings
were used with γ 1
= 0.1 and γ 2
= 2.0. For both the GE and SIEMENS scanners, we randomly selected
subsets, varying in size from 20 to 100, of the GE and SIEMENS cohorts as references for personalized tem-
plate construction. For both the GE and SIEMENS scanners, the same number of references were used in
all experiments. Fig. 4.8 shows that the inter-site CoVs (in red) and the negative rates (r
N
) of CoV (in blue)
for both FA and MD decrease as the size of the reference set increases for both harmonization tasks. This
indicates that sufficient references ( ≥ 60) are crucial for adaptive template construction and the success
of dMRI harmonization.
4.3.6 Impact of personalized harmonization on DTI feature distribution in cortical
graymatterregions
In section 4.3.4, we presented the overall performance enhancement achieved by our method and qualita-
tively visualized the major improvement in cortical gray matter regions. To further assess the performance
of harmonization, we analyzed the distribution of DTI features in cortical lobes before and after harmo-
nization. As we noticed that the task of harmonizing GE toward SIEMENS data achieved lower inter-site
63
(a) (b)
(c) (d)
Figure 4.8: Inter-site CoVs for FA and MD with varying numbers of available references. (a) and (b) display
the inter-site CoVs (in red line) and the negative rates of CoV (in blue line) of FA and MD with SIEMENS +
harmonized GE data. (c) and (d) show the corresponding results for GE + harmonized SIEMENS data. The
inter-site CoVs and the negative rates of CoV for the results produced by LinearRISH with 100 references
from each platform are in red dashed-line and blue dashed-line, respectively, in each panel.
CoVs in section 4.3.4, we focused on DTI features computed from harmonized GE data toward SIEMENS
by our method and LinearRISH. As shown in Fig. 4.9, four histograms of the FA feature (SIEMENS, GE,
harmonized GE by our method, harmonized GE by LinearRISH) within the gray matter voxels of each
cortical lobe (frontal, pariental, temporal, and occipital) of the left hemisphere are plotted. The cortical
lobes were defined by merging parcellated ROIs from FreeSurfer [27]. By comparing the respective FA
feature distribution curves in Fig. 4.9, we observe that both our method and LinearRISH can reduce the
noticeable discrepancies between the original GE (blue curves) and SIEMENS (red curves) data before har-
monization. However, it is evident that our method achieves better performance as the FA histograms of
harmonized data using our method (purple curves) align more closely with the target histograms (red)
than those produced by LinearRISH (cyan curves).
We can quantify the difference of feature distributions across scanners using the Jensen–Shannon
divergence (JSD) [73]:
64
(a) (b)
(c) (d)
Figure 4.9: FA distributions before and after harmonization. The density curves of FA within the frontal,
occipital, parietal, and temporal lobes of the left hemisphere are shown in (a), (b), (c), and (d), respectively.
JSD(P∥Q)=
1
2
KLD(P∥M)+
1
2
KLD(Q∥M), (4.10)
where JSD(P∥Q) is the JSD of distributions P and Q, the average distribution M =
1
2
(P +Q), and
KLD(·∥· ) indicates the Kullback–Leibler divergence. The JSD is a symmetric measure for comparing two
distributions. A lower JSD value indicates a higher resemblance between the two distributions. To quantify
the harmonization performance from the perspective of feature distributions, we computed the JSD of FA
65
Table 4.3: Jensen-Shannon divergence of FA features across scanners before (Orig) and after harmonization
(LinearRISH and our method). Results from both the left and right hemispheres are listed.
Lobe Hemi Orig LinearRISH Our method
Frontal
Left 0.048 0.011 0.007
Right 0.050 0.011 0.006
Parietal
Left 0.062 0.014 0.008
Right 0.056 0.012 0.007
Temporal
Left 0.034 0.009 0.003
Right 0.033 0.010 0.004
Occipital
Left 0.037 0.008 0.004
Right 0.031 0.006 0.002
Table 4.4: Jensen-Shannon divergence of MD features across scanners before (Orig) and after harmoniza-
tion (LinearRISH and our method). Results from both the left and right hemispheres are listed.
Lobe Hemi Orig LinearRISH Our method
Frontal
Left 0.052 0.053 0.044
Right 0.046 0.049 0.043
Parietal
Left 0.038 0.039 0.032
Right 0.029 0.033 0.029
Temporal
Left 0.039 0.037 0.023
Right 0.039 0.044 0.024
Occipital
Left 0.024 0.014 0.014
Right 0.011 0.011 0.010
and MD distributions across scanners for all four major cortical lobes. The results were summarized in
Table 4.3 and 4.4 for FA and MD features. We note that our method achieves lower JSD values for both FA
and MD features in nearly all cortical regions as compared to results from the LinearRISH method. This
reaffirms the efficacy of our method in improving the performance of dMRI harmonization.
4.3.7 Preservationoffiberorientationdistribution(FOD)
To understand the impact of harmonization on the analysis of structural connectivity, we examined the
changes in fiber orientation distribution (FOD) before and after harmonization. First, we estimated the
FOD from the original and harmonized dMRI data[117] and extracted the largest FOD peak at each voxel
for quantitative comparison. To measure the impact of harmonization on FODs, we computed the cosine
similarity of corresponding FOD peak directions estimated from dMRI signals at each voxel before and
66
Table 4.5: FOD peaks before and after harmonization. Row 1 and 2: harmonized GE toward SIEMENS; row
3 and 4: harmonized SIEMENS toward GE.
Dataset Cosine Similarity
GE (LinearRISH) 0.995± 0.001
GE (Our Method) 0.996± 0.001
SIEMENS (LinearRISH) 0.996± 0.001
SIEMENS (Our Method) 0.996± 0.001
after harmonization. The average voxel-wise cosine similarity across the white matter was calculated for
each subject. For the GE and SIEMENS cohort, the mean and standard deviation of the cosine similarity
measure from different harmonization experiments are listed in Table 4.5. As can be observed from the
second row and the fourth row in Table 4.5, the proposed method induces minimal changes in the FOD
peaks for both cohorts. These results also closely align with those obtained by LinearRISH, shown in the
first and third row, which suggests that both our method and LinearRISH are able to preserve the fiber
orientations of the original dMRI.
4.3.8 PreservationofsexeffectsonDTIfeatures
Preserving the inter-subject biological variability in original data is essential during the harmonization
of data across scanners. To evaluate the impact of harmonization procedures on the preservation of bio-
logical variability, we examined sex differences in white matter microstructure properties as such group
differences have been found significant and replicable in the baseline cohort of the ABCD study [68]. More
specifically, we calculated the effect sizes of sex differences for the GE cohort before and after harmoniza-
tion toward the SIEMENS cohort. The effect sizes are quantified using Cohen’s d [17]:
d=
µ f
− µ m
s
pooled
, (4.11)
67
where µ f
and µ m
are the mean feature values for the female and male subjects, respectively. s
pooled
=
r
(N
f
− 1)σ 2
f
+(Nm− 1)σ 2
m
N
f
+Nm− 2
is the pooled standard deviation, where N and σ denote the number of subjects
and the standard deviation of a specific gender group.
Considering the sex differences are region-specific [53, 41, 74], we examined the effect sizes for all
major lobes. The ROIs were delineated by merging the subcortical white matter parcellations extracted by
FreeSurfer [27]. The mean values of FA in each ROI were computed to reflect the regional white matter
maturation. Fig. 4.10 displays the effect sizes of sex differences in FA across brain regions for the GE
cohort before and after they were harmonized to the SIEMENS cohort. Compared with LinearRISH, it is
evident that our method is more effective in preserving the sex differences after harmonization in most
brain regions. It is also notable that the proposed approach is able to preserve effect sizes in all regions
with absolute differences ( ∆ d) of effect sizes before and after harmonization no greater than 0.035.
Figure 4.10: Preservation of sex differences during harmonization. The effect sizes of sex differences in FA
before (blue), after harmonization using LinearRISH (orange), and our method (green) for the GE cohort.
The quantitative values of effect sizes ( d) and the absolute differences ( ∆ d) between the effect sizes before
and after harmonization are annotated in the form of "d(∆ d)".
68
4.4 DiscussionandConclusion
In this chapter, we introduced the personalized idea to dMRI harmonization and comprehensively ex-
amined the importance of establishing reliable anatomical correspondences for dMRI harmonization. To
mitigate the confounding effects due to the entanglement of inter-subject anatomical variability and site-
specific variations in dMRI signals, we presented a personalized template estimation framework and in-
tegrated it with RISH features to realize the personalized harmonization of dMRI data. By applying the
proposed framework to harmonize dMRI data acquired from Siemens Prisma and GE MR750 scanners in
the ABCD study, we demonstrated that our method achieved much improved performance in reducing
scanner differences in dMRI signals and preserving sex-related biological variability in original cohorts.
Although the personalized harmonization framework presented in this work employs RISH features
for inter-site mapping estimation, the proposed personalized template estimation method is general and
can be integrated with other dMRI harmonization techniques for the refinement of anatomical correspon-
dences in different harmonization scenarios. For instance, when there are large variations in the number of
gradient directions between the source and target site, the moment-based method [54] might be preferable
as it is independent of the matching of spherical harmonic coefficients. Investigating the effectiveness of
embedding the proposed approach in other dMRI harmonization frameworks such as the moment-based
method is a direction of our future work.
In the current framework, multiple healthy controls, carefully matched for confounding effects, e.g.,
age and gender, from each scanning platform, are required to avoid bias from confounding variables in the
reliable estimation of harmonization mapping functions. To harmonize dMRI data from different cohorts
with a limited overlap of related confounding variables such as age, our method can be extended to consider
these confounding variables as additive terms in a regression model. Similar to the ComBat method [31],
the reference features can be adjusted by regressing out the confounding variables to reveal site-specific
characteristics for harmonization. This possible extension will be another direction for our future work.
69
Chapter5
PersonalizeddMRIHarmonizationontheCorticalSurface
5.1 Introduction
Diffusion MRI (dMRI) [7] is a prevalent technique for the non-invasive investigation of brain microstruc-
ture and connectivity. In large-scale imaging studies, data from multiple sites are often combined to in-
crease statistical power while addressing the limited acquisition capacity of individual scanners [89, 13].
However, the integration of data is complicated by inter-site variations caused by the differences in the
magnetic field strength, scanner manufacturer, and acquisition protocol, which impede the comparability
of the multi-site dMRI data [125, 143, 76]. Therefore, with the aim to mitigate inter-site variations and
facilitate the integration of multi-site datasets, dMRI harmonization becomes a critical problem.
A common observation from previous dMRI harmonization studies [31, 85] is that the inter-site vari-
ability in dMRI is tissue- and region-specific. To control the impact of variable brain anatomy across
subjects in site-effect estimation and inter-site harmonization, prevalent dMRI harmonization methods
rely on volumetric registration [4] to establish voxel-wise inter-subject correspondences of anatomy. In
[31], the ComBat method was used to harmonize the diffusion tensor imaging (DTI) by regressing out the
site-specific factors voxel-wisely in a co-registered space. Mirzaalian etal. [85] conducted multi-site diffu-
sion weighted imaging (DWI) harmonization in a registration framework. The proposed method utilized
70
(a) (b) (c)
Figure 5.1: Comparison between the anatomy of the individual subjects after volumetric registration: co-
registered FA images of three HCP subjects are shown from left to right. Typical misaligned regions are
circled out.
rotation invariant spherical harmonics (RISH) features and harmonization was achieved by linearly scal-
ing spherical harmonic (SH) coefficients of the dMRI signal. Following a similar registration framework,
Huynh et al. proposed a method of moments based harmonization approach [54].
However, due to inter-subject variability and consequent imperfections in registration, these ap-
proaches suffer from the misalignment of brain anatomy, particularly in cortical gray matter areas. As
illustrated in Fig. 5.1, the co-registration in volume cannot correctly establish the anatomical correspon-
dence across subjects, especially in cortical gray matter regions. This misalignment problem undoubtedly
leads to failure in disentangling the anatomical variability from site-effects, which consequently confounds
the estimation of harmonization transformations. As shown in [94], the intrinsic heterogeneity of the cor-
tical gray matter due to its heterogeneous layered architecture [77] and high-convoluted structure [115]
at the population level poses significant challenges for achieving reliable dMRI harmonization.
The recent emergence of high resolution dMRI data from connectome imaging studies allows the anal-
ysis of cortical microstructure on the cortical surface. For example, cortical diffusion anisotropy charac-
terization on the cortical surface was presented in [81]. In [72], fiber tracks were reconstructed within the
cortex to reveal intracortical connectivity. More recently, neurite distribution patterns were analyzed to
71
reveal microstructural variations on the cortical surface in [34]. The dMRI harmonization of cortical gray
matter in high resolution has become an increasingly urgent problem.
Accurate alignment in cortical regions via spatial normalization of volumetric brain images is difficult,
due to the geometric complexity of the cortex and the inter-subject variability. Alternatively, surface-based
registration [114, 29, 20], which leverages the geometric information, has been shown to mitigate some
of the anatomy misalignment problems. However, surface-based registration, which establishes inter-
subject alignment on the cortical surface using a group averaging template, struggles to accurately align
uncommon cortical folding patterns in the population[75, 140]. This problem is especially prominent in
association cortices, where topographically distinct folding patterns are commonly present across subjects.
The disentanglement of the scanner-related effects from the variable brain anatomy remains a challenging
problem.
We present a personalized framework, devised to effectively address the issue of anatomical misalign-
ment, for reliable dMRI harmonization of the cortical gray matter in high-resolution. Our approach adap-
tively estimates inter-site harmonization mappings on the cortical surface for each individual, as illustrated
in the flowchart in Fig. 5.2 (a). Instead of relying on non-linear registration, we adaptively construct a local
reference set at each cortical location of each query subject from the source site. The reference set consists
of reference vertices with high geometric similarity to the query vertex, as shown in Fig. 5.2(b). The dMRI
features sampled from these reference vertices, representing site-effects on corresponding reference loca-
tions, are then unevenly integrated for the characterization of subject specific site-effect. Our personalized
scheme for estimating site-effects is combined with the RISH-based dMRI harmonization framework [60]
to perform effective dMRI harmonization.
The proposed framework is applied to harmonize both low (b = 1000 s/mm
2
) and high (b =
3000 s/mm
2
) b-shells of dMRI data across the Human Connectome Project (HCP) [122] and the Lifespan
Human Connectome Projects in Development (HCP-D) [107] studies. The experiment results demonstrate
72
(a)
(b)
Figure 5.2: An overview of the proposed personalized dMRI harmonization on the cortical surface. (a)
shows the overall framework of personalized dMRI harmonization on the cortical surface and (b) illustrates
the detection of inter-subject local correspondence
that: 1) With improved anatomical correspondence on the cortical surface, our framework outperforms
the state-of-the-art LinearRISH method in harmonizing DTI features on both b-shells. 2) The proposed
method better preserves the original biological variability of age in contrast to LinearRISH. 3) Our method
also effectively maintains gender distinctions before and after harmonization.
73
5.2 Methods
The core of the personalized dMRI harmonization on the cortical surface is the adaptive construction of
local reference sets and inferring the site-effects from the references at each query vertex. We investigate
the geometric correspondence across the cortical surface to pinpoint corresponding locations among a vast
array of candidates. Subsequently, personalized site-specific templates can be accurately determined and
employed for estimating site-wise harmonization mapping.
5.2.1 DiffusionMRIharmonizationandLinearRISHframework
The harmonization of dMRI data from a source site to a target site can be formulated as an inter-site
mapping:
ˆ
S =Ψ( S), (5.1)
where S denotes the diffusion signal acquired from the source site,
ˆ
S denotes the harmonized diffusion
signal, and Ψ represents the inter-site mapping function. In an unsupervised setting, where there is no
traveling subject scanned at both sites for direct inter-site mapping estimation, it is typically necessary to
have representative reference subjects from each site. With these reference subjects, site-specific templates
of diffusion features such as the RISH features [60] and diffusion moments [54] can be constructed for the
characterization of the site-effects and explicit determination of the harmonization mapping function Ψ ,
enabling effective data harmonization across sites.
To disentangle the intertwinement between the site-effect characterization and the underlying tissue
and spatial heterogeneity, we develop a personalized mechanism, which allows for adaptive construction
of the reference set for each query location on the cortical surface. The diffusion features sampled from
the reference locations are then integrated for the characterization of the subject specific site-effects:
74
E =G(F), (5.2)
whereE is the template reflecting the site-effects, F is the array of diffusion features sampled from ref-
erences, andG is the pooling function. Then the harmonization mapping function Ψ can be explicitly
determined by comparing estimated site-effects.
5.2.2 Constructionofpersonalizedtemplates
5.2.2.1 Inter-subjectlocalcorrespondencedetectiononthecorticalsurface
On the cortical surface of a query subject, the reference set, comprised of vertices with similar geom-
etry from cortical surfaces of a vast array of reference subjects, is constructed for each query vertex.
To detect corresponding reference locations on the cortical surface we propose a multi-scale LB em-
bedding based measurement. For a real-valued function f on a Riemannian manifold M, the Laplace-
Beltrami (LB) operator ∆ M
is defined as: ∆ M
f := div(grad f) with grad f the gradient of f and
div the divergence. At a vertex v on the manifold M, the LB embedding defined in [102] is a infinite-
dimensional vector: E
M
(v) = [
ϕ 1
(v)
√
λ 1
,
ϕ 2
(v)
√
λ 2
,
ϕ 3
(v)
√
λ 3
,...], where λ i
and ϕ i
represent eigenfunction and
eigenvalue of the LB operator. Given two surfaces M
1
and M
2
, we can construct the spectral distance:
d
g
(v,u) = ∥E
M
1
(v)−E
M
2
(u)∥
2
for the corresponding vertex detection, wherev andw are on surfaces
M
1
andM
2
respectively.
However, the spectral distance defined in the context of the whole surface only enables coarse screen-
ing of the corresponding vertices. To refine the search of corresponding vertices we examine the similarity
of local LB embedding. Within the LB framework, we construct the local LB embedding:
H
N(k)
(v)=[
ϕ N(k)
1
(v)
q
λ N(k)
1
,
X
i=2
ϕ N(k)
i
(v)
q
λ N(k)
i
], (5.3)
75
whereN(k) is the k-ring patch with the center point at the vertexv,ϕ N(k)
i
andλ N(k)
i
are the i-th eigen-
function and eigenvalue of the patch N(k). In this chapter, we calculate the local LB embedding for
k ={1,3,5,7,9} and rearrange them into three groupsK ={{1,3,5},{3,5,7},{5,7,9}} to represent
the geometric characteristics at different levels of locality. With the multi-scale LB embedding, the inter-
vertex distance is defined as follows:
d
l
(v,u)= min
K∈K
max
k∈K
∥H
N(k)
(v)−H
N(k)
(u)∥
1
. (5.4)
5.2.2.2 Constructionofpersonalizedreferencesets
Equipped with the vertex-wise similarity measure, at any vertexv, one can construct a reference setR(v)
consisting of vertices from the cortical surfaces of reference subjects according to geometric similarity:
R(v)= argmin
R(v)⊆M
ref
,|R(v)|=N
X
u∈M
ref
d
l
(v,u), (5.5)
whereM
ref
represents the union of the cortical surfaces of reference subjects. Note that the reconstruc-
tion of the reference set does not rely on the assumption of one-to-one correspondences across subjects.
5.2.2.3 Weightedpoolingforsite-effectestimation
With the reference set adaptively constructed at each vertex, we unevenly pool these references to reflect
the site-effects by weighted sum:
E(v)=
X
u∈R(v)
w
l
(v,u)f(u), (5.6)
where w
l
(v,u) = exp(− d
l
(v,u)
σ )/
P
u∈R(v)
exp(− d
l
(v,u)
σ ) is the weights of the references, which is the
normalized geometric similarity. Heref(u) is the diffusion feature at the reference location u. The template
76
estimation is a weighted sum of multi-locations. The distance scale parameterσ controls the quantitative
conversion from vertex-wise distance to affinity. Unevenly pooling is employed for reliable site-effect
estimation, as it can adapt to different regional complexities and provide more robust estimations across
the whole cortex. In regions with highly convoluted folding patterns, the availability of reliable references
is limited. The implementation of a weighted sum serves to mitigate the influence of less reliable references,
thereby ensuring a more accurate estimation. In areas where candidate references exhibit high similarity,
the weighted sum tends to converge toward the sample mean, as the distances between references become
more indistinguishable. This further supports the use of uneven pooling, as it can adapt to different regional
complexities and provide more robust estimations across the whole cortex.
5.2.3 EliminationofconfoundingvariablesindMRIharmonization
The inter-site mapping is estimated by comparing site-effects, inferred from representative reference sub-
jects, of both the source and target sites. To minimize the confounding induced by non-imaging variables,
e.g. age, gender, and ethnicity, in estimating the harmonization mapping functions, healthy controls with
well-matched confounding variables are intentionally selected to serve as the representative reference
subjects[60, 31]. For the harmonization of dMRI data from cohorts with the limited overlap of related con-
founding variables across sites, our framework, similar to the ComBat method [31], adjusts the reference
features by regressing out the confounding variables prior to harmonization:
f =f
′
− Xβ, (5.7)
wheref andf
′
represent the diffusion feature before and after regressing out the component of confound-
ing variable, theX is the matrix for the covariates of interest, β is the corresponding vector of regres-
sion coefficients. The adjusted reference features reveal canonical site-specific characteristics allowing the
preservation of variations in dMRI data associated with these confounding variables after harmonization.
77
5.2.4 RISHbasedharmonization
We integrate our adaptive site-effect estimation mechanism with the rotational invariant spherical har-
monics (RISH) features [86, 60] to demonstrate the efficacy of personalized harmonization on the cor-
tical surface. With the spherical harmonics (SPHARM), the diffusion signal can be represented as S ≃
P
lm
C
lm
Y
lm
, where Y
lm
and C
lm
are the SPHARM basis and corresponding coefficient of order l and
degreem. The RISH features characterize the energy distribution of the dMRI signal at each orderl and
are defined as r
l
=
P
m
C
2
lm
. The dMRI harmonization is conducted by scaling the spherical harmonic
coefficients of the source site dMRI:
ˆ
C
src
lm
=Φ l
C
src
lm
, whereΦ l
is the linear scale map.
For the personalized harmonization of dMRI data on the cortical surface from a source site (src) to
a target site (tar), we unevenly pool the RISH features sampled from reference vertices to estimate the
personalized templates for both target and source site using 5.6:
E
l
(v)=
X
u∈R(v)
w
l
(v,u)r
l
(u), (5.8)
wherer
l
(u) is the RISH feature at the orderl sampled from vertexu,R(v) is the reference set construct
adaptively for each query vertex v following 5.5. Consequently, on each query vertex v, the mapping
functionΦ l
of the query cortical surface is estimated adaptively at each SPHARM order:
Φ l
(v)=
s
E
tar
l
(v)
E
src
l
(v)+ϵ , (5.9)
whereE
tar
l
andE
src
l
are the personalized site-effects estimation of the RISH feature at the order l for the
target and source sites, respectively. Finally, with scaled SPHARM coefficient, the harmonized dMRI signal
ˆ
S is generated by using the scaled SPHARM coefficients:
78
ˆ
S =
X
lm
Φ l
C
lm
Y
lm
. (5.10)
By repeating this process for all vertex, we obtain the harmonization of the query subject from the
source to the target site.
5.3 ExperimentsandResults
Due to the inter-site variations in MRI scanner models and acquisition protocols, there are observable
discrepancies in the dMRI data across the WU-Minn Human Connectome Project (HCP) [122] and the
Lifespan Human Connectome Project in Development (HCP-D) [107]. These inter-site differences conse-
quently hinder the comparison and integration of data from these two high-quality neuroimaging datasets.
To reveal the effectiveness of our method in reducing the inter-site differences, we performed harmoniza-
tion across the HCP and HCP-D studies on dMRI with multiple b-shell schemes. Furthermore, we also
investigated the impact of the personalized harmonization framework on preserving biological variability.
5.3.1 SubjectsandImplementationdetails
5.3.1.1 Subjects
A cohort of 104 subjects (23.55± 1.07 years, 53 females) was selected from the HCP dataset. With a bal-
anced sample size, the harmonization dataset of HCP-D studies consisted of 104 subjects (20.22± 1.11
years, 53 females). The age and gender of the participants from the two studies were carefully matched
to mitigate the potential entanglement of these confounders with site-effects. To ensure biological inde-
pendence for evaluating the biological variability of the dataset and to maintain geometric independence
when establishing inter-subject references, twins were excluded from the harmonization experiments.
79
5.3.1.2 dMRIdataandpreprocessing
The dMRI acquisition of HCP was conducted on a customized 3T Siemens "Connectome Skyra" (100 mT/m).
The dMRI data was obtained with 270 diffusion-weighted scans distributed equally at three b-values: b =
1000, 2000, and 3000 s/mm
2
and 18 b = 0 s/mm
2
(b
0
) volumes. The repetition time (TR) was 5520
ms, and the echo time (TE) was 89.5 ms. The diffusion weighted image has an isotropic resolution of 1.25
mm. Two phase encoding directions (L/R and R/L) were applied for each scan for susceptibility correction.
A multiband approach was used for acceleration, and the multiband factor is 3. The diffusion weighted
data of HCP-D were acquired on a 3T Siemens Prisma (80 mT/m). With a reduced scanning time, whole-
brain diffusion MRI was performed with the multiband factor increased to 4, the voxel size increased to
1.5 mm isotropic, and a shorter TR = 3230 ms. The diffusion protocol samples 185 directions over two
shells:b=1500 and3000 s/mm
2
, along with 28b
0
images. Every scan acquired Opposite phase encoding
directions (A/P and P/A) to facilitate robust correction of distortions.
The dMRI images were minimally preprocessed [40]. The minimal preprocessing of dMRI data includes
the echo-planar imaging distortion estimation and correction using the "topup" and "eddy" tools [1, 2]. We
conduct dMRI harmonization on both low and high b-value shells. This multishell harmonization allows us
to thoroughly evaluate the effectiveness of the harmonization method. For the harmonization of relatively
low b-value dMRI data, we mapped the 1500 s/mm
2
shell from the HCP-D to match with 1000 s/mm
2
shell from the HCP, to eliminate the intrinsic discrepancy in dMRI data induced by different b-values. We
followed the b-value mapping procedure in [60] to adjust diffusion signals with differences in b-values. It
is a linear scaling of the signal in the log domain:
S
btar
=S
0
exp(
b
tar
b
src
log(
S
bsrc
S
0
), (5.11)
80
where S
0
is the b
0
image without diffusion attenuation, b
src
and b
tar
are the source and target b-value,
S
bsrc
andS
bsrc
represent the original diffusion signal and target diffusion signals. Specifically, we mapped
theb=1500 s/mm
2
shell of the HCP-D data tob=1000 s/mm
2
to match the HCP data. Without losing
the generalizability, the b = 1000 s/mm
2
shell after b-value mapping will serve as the unharmonized
dMRI data in the following experiments. As for harmonizing the high b-value shell, we employed the
b=3000 s/mm
2
shell from two datasets.
Next, to unify the resolution of diffusion weighted volume across two datasets, we downsampled the
HCP data to1.5 mm isotropic to match the HCP-D data. This choice, in spite of eliminating the advantage
of volume-to-surface projection achieved by higher resolution dMRI images of the HCP data, allows a fair
comparison across the volume-based harmonization and the surface-based harmonization. In addition, we
utilized the unringing method [62] to remove Gibbs ringing artifacts and performed the over-completed
local PCA-based method [79] for denoising of diffusion weighted image to mitigate the effects of noise on
RISH feature based harmonization [60].
5.3.1.3 Diffusionweightedsignalprojectiononthecorticalsurface
The mid-thickness surface of each subject was extracted to sample diffusion weighted signal in the cor-
tical gray matter regions. The cortical mid-thickness surface is generated with the middle points located
between the corresponding node pairs of the pial and white surfaces generated by using Freesurfer [27]
from T1 weighted (T1w) images. Though the dMRI data had been transformed to the T1w space via rigid
registration through the minimal preprocessing pipeline, the misalignment between the T1w and dMRI
volumes still existed owing to the distortion of dMRI data. To address the misalignment problem, we per-
formed the non-linear co-registration between the FA and T1 volumes using the Advanced Normalization
81
Tools [4] for further alignment. The deformation fields were applied to transform the mid-thickness sur-
face to the diffusion image space for reliable diffusion signal projection. Then, the dMRI data were mapped
to surface vertices using linear interpolation.
5.3.1.4 ImplementationdetailsofRISHfeaturebasedharmonization
For HCP-D subject, we used one section of the whole dMRI data for each shell with 47 distinctive directions
overb = 1500 s/mm
2
shell and 46 directions overb = 3000 s/mm
2
. The HCP dMRI data, with a higher
angular resolution, were acquired with 90 directions over each shell. With sufficient angular resolution
on each shell, we fitted the dMRI signal at each vertex using spherical harmonic up to 8 order spherical
harmonics [21] and calculated five RISH features for spherical harmonic orders of l = {0,2,4,6,8}, for
dMRI harmonization.
For comparison with volumetric dMRI harmonization, LinearRISH [60] was applied to harmonize the
preprocessed dMRI images with the resolution of 1.5 mm isotropic voxel-wisely. The harmonized dMRI
data were then projected onto the mid-thickness surface following the same procedures in Section 5.3.1.3
for evaluation on the cortical surface. Based on the Desikan-Killiany’ cortical atlas [21], we parcelled each
cortical hemisphere into 34 cortical regions of interest (ROIs) using Freesurfer [27] for regional compari-
son. The medial orbitofrontal, lateral orbitofrontal frontal, and temporal pole parcels, where the diffusion
signal often suffers more severe susceptibility-induced distortion [52, 98, 57] than other brain regions, are
excluded from dMRI harmonization evaluation due to the frequent presence of residual distortion even
after correction [112].
To leverage the diversity of neuroanatomy covered by a large population, for a given source subject, 103
subjects from each study served as reference subjects. We avoided self-reference to prevent bias towards
one individual in site-effect estimation. To remove the confounding of age in site-effect estimation, we
estimated associations between age and each RISH feature using linear regression for each cortical region
82
and regressed out the age effects from the reference images. Similar procedures of confounding removal
were conducted for the implementation of LinearRISH.
5.3.2 Inter-subjectlocalcorrespondence
The results of local correspondence detection of HCP subject 103141 are illustrated in Fig. 5.3. The first
query vertex (the red dot), shown in the first column in Fig. 5.3 (a), is located on the ridge of the caudal
middle frontal gyrus. Multiple reference vertices with geometric similarity were detected across subjects,
as seen in the second and third columns. Despite being located on gyri with notably different folding
patterns, these vertices all reside in the middle of the wide ridges. In contrast, vertices with less geometric
similarity were also detected (see the fourth and fifth columns), as they are located at the boundary of the
gyrus ridge. Another example of a query vertex on the middle temporal gyrus is presented in Fig. 5.3 (b),
with a very similar observation.
5.3.3 Personalizedharmonizationmappingonthecorticalsurface
Our method allows the adaptive estimation of inter-site mapping on the cortical surface for each query
subject to alleviate the bias induced by the anatomical misalignment problem. For the RISH feature based
harmonization, the inter-site mapping consists of multiple RISH maps corresponding to the transformation
of different frequency components of the diffusion signal. In Fig. 5.4, we present the personalized RISH
mapping functions of an HCP subject in (a) and an HCP-D subject in (b) on the cortical surface for b =
1000 s/mm
2
shell. First, it is evident that the inter-site mapping is regionally varying, suggesting that the
discrepancy across sites is region- and tissue-specific [84, 31]. For instance, the mapping scale of zeros-
order sphere harmonics for HCP subject 103414, the first panel in Fig. 5.4 (a), shows a larger mapping scale
in the frontal lobe in contrast to which in the temporal lobe. This indicates the energy lift of low frequency
component in the frontal lobe of the HCP subject is generally higher when harmonizing to HCP-D. This
83
(a)
(b)
Figure 5.3: Examples of inter-subject correspondence detection on the cortical surface at two typical loca-
tions: (a) caudal middle frontal and (b) middle temporal. The query vertex (a red dot) on a source cortical
surface (left) and corresponding reference sets (dots in red) of two reference subjects with better correspon-
dence and another two references with relatively larger distances are displayed. The multi-scale vertex-
wise differences, annotated under each panel, increase from left to right. The corresponding parcels of
cortex in green generated using Desikan-Killiany’s cortical atlas are used to demonstrate the anatomical
information of the vertex in each panel.
observation affirms the spatial complicity of the harmonization mapping. In addition, by comparing the
corresponding mappings across two subfigures, we can detect a roughly inverse relationship across the
mapping functions for different harmonization tasks (HCP → HCP-D and HCP-D→ HCP). This suggests
the consistency of energy modification in RISH harmonization. However, in detail, the correspondence is
not exact because of inter-subject variability in cortex folding.
Fig. 5.5 presents the personalized RISH mapping functions forb = 3000 s/mm
2
shell. Via comparing
the RISH mapping functions across shells, it is observable that the scale mappings are inconsistent across
shells on the cortical surface. For SH ordersl≥ 2, the scale maps of the HCP subject, with local scales much
larger than 1 in most cortical regions, suggest that the HCP data are with increased energy in the middle and
84
(a)
(b)
Figure 5.4: Personalized inter-site mapping on the cortical surface for the HCP subject 103414 in (a) and
HCD0042420 from HCP-D dataset in (b) forb=1000 s/mm
2
shell. The scale maps for SH order of 0, 2, 4,
6, and 8 are arranged from left to right.
(a)
(b)
Figure 5.5: Personalized inter-site mapping on the cortical surface for the HCP subject 103414 in (a) and
HCD0042420 from HCP-D dataset in (b) forb=3000 s/mm
2
shell. The scale maps for SH order of 0, 2, 4,
6, and 8 are arranged from left to right.
high orders of SH components after harmonization. While this is not observable for theb=1000 s/mm
2
shell.
85
5.3.4 Parameterselection
In this section, we examine the influence of parameter selection for personalized site-effect estimation. To
ensure the parameter choice would not over-fit the inter-site harmonization, we constructed a validation
set by randomly selecting 24 subjects from each of the HCP and HCP-D cohorts for parameter tuning. The
remaining 80 subjects from each dataset were used as a test set for subsequent harmonization performance
evaluation. To quantify the overall harmonization performance, we calculated the inter-site coefficients
of variations (CoVs) of DTI features, including fractional anisotropy (FA) and mean diffusivity (MD), after
harmonization. The coefficient of variation, defined as the ratio of the standard deviation to the mean,
quantifies the dispersion of the DTI feature in the integrated dataset. The vertex-wise average DTI feature
across the entire cortical surface is calculated to reveal the overall DTI measurements for each subject.
Parameterσ controls the distortion of the conversion from distance to affinity, which affects the pooling
weight of a sample. An overly smallσ will emphasize only a small portion of the references, introducing
bias from individual subjects to site-effect estimation. As σ increases, the pooling weight becomes more
evenly distributed among the references. However, an excessively largeσ equalizes the contribution of all
references in template construction, making the template estimation susceptible to bias from samples with
less anatomical similarity. In Fig. 5.6 (a), the relationships between theσ and the inter-site CoVs for both
FA and MD features are displayed while keeping N = 50. We can observe that for both harmonization
tasks, the inter-site CoVs become stable afterσ reaches2.0 for FA. For MD from theb=1000 s/mm
2
shell,
the impact ofσ is not significant. With N =50 for constraining the scope of reference, this indicates the
MD feature is not sensitive to the choice of σ . In contrast, for the b = 3000 s/mm
2
shell, increasing σ leads to a noticeable reduction in the inter-site CoV for MD. The turning point is at σ = 2.0 and larger
values ofσ result in a tendency towards worse harmonization performance.
The reference size N controls the scope of reference candidates. Fig. 5.6 (b) presents the impact of
reference sizeN on the overall harmonization performance for both FA and MD features, while keeping
86
(a) Parameter tuning ofσ .
(b) Parameter tuning of the reference sizeN.
Figure 5.6: Parameter tuning of personalized dMRI harmonization on the cortical surface.
σ = 2.0. For the b = 3000 s/mm
2
shell, the optimal parameter choice is N = 50. While for the
b = 1000 s/mm
2
shell, the CoVs keep decreasing even afterN reaches 50 but the tendency of significant
decrease slows down. For MD, the change of reference size does not significantly alter the harmonization
87
performance on theb = 1000 s/mm
2
shell. While on theb = 3000 s/mm
2
shell, the optimal parameter
choice isN =50 as the larger reference size increases the inter-site CoV.
By examining the impact of parameters on harmonization performance, we found that N = 50 and
σ = 2.0 is optimal for bothb = 1000 s/mm
2
andb = 3000 s/mm
2
shells. This parameter setting is used
in the following evaluation experiments on the testing set.
5.3.5 HarmonizationevaluationofDTIinthepresenceofageconfounding
Considering the differences in age range covered by the HCP and HCP-D sites, the potential differences in
DTI features associated with the confounding of age can contribute to the inter-site CoVs. This poses an
extra challenge for the rigorous evaluation of harmonization performance as the lower bound of CoVs can-
not be determined. To account for the biological variability induced by age and the site-induced variability
simultaneously, we use a dummy variable in regression analysis [45, 50] to compare the DTI features ac-
quired from two studies in the presence of the confounding of age. Regarding the narrow age range (18-24)
of the integrated cohort, in this experiment, a linear model is used to fit the DTI data:
y =α 0
+α s
x
s
+α a
x
a
, (5.12)
where y and α 0
denote the diffusion measurement and the intercept, α a
x
a
describes the linear associa-
tion between the age and diffusion measurement, the dummy variable x
s
(1 for HCP and 0 for HCP-D)
represents the site, andα s
is the differential intercept of two sites quantify the inter-site discrepancy after
controlling for the biological variability induced by age.
In Table 5.1 and Table 5.2, we summarize the estimated coefficient of the site dummy variable for DTI
features onb = 1000 s/mm
2
andb = 3000 s/mm
2
shells respectively. To improve the interpretation of
the quantity results, we normalize the differential intercept of two sites by dividing it by the average DTI
88
of integrated original data (HCP + HCP-D). This normalized value, denoted as ˆ α s
, can be interpreted as
the ratio of deviation from the average due to site-effects.
As shown in Table 5.1, the inter-site discrepancies are observable (FA:10∼ 15% and MD:16∼ 20%)
and statistically significant for all cortical lobes in original data (HCP + HCP-D). After harmonization, via
either LinearRISH or our method, the inter-site differences are mitigated for both harmonization tasks in
all regions. For the FA on the cortical surface, our method achieves better performance in comparison
with the LinearRISH approach as the inter-site discrepancies achieved by our method are evidently less
than LinearRISH in almost all ROIs. This observation is consistent for both harmonization tasks: HCP-D→
HCP and HCP→ HCP-D. By comparing across harmonization directions, both our method and LinearRISH
produce less discrepancy consistently in almost all ROIs when HCP is the target site and HCPD is the source
site. Along this direction, the inter-site differences in all ROIs are removed ( |ˆ α s
| < 0.02 and p> 0.05) by
using our method, while the LinearRISH cannot eliminate the inter-site difference.
For the MD feature on b = 1000 s/mm
2
shell, our method reduced the inter-site discrepancies to
a negligible level (|ˆ α s
| < 0.015 and p > 0.05) in both harmonization directions, suggesting the efficacy
of our method in dMRI harmonization. In contrast, the LinearRISH approach had an almost equivalent
performance (|ˆ α s
|<=0.03), while significant inter-site differences were still retained in the left temporal
lobe when harmonizing HCP data to HCP-D and in the right frontal lobe, right temporal lobe, and left
temporal lobe when harmonizing HCP-D data to HCP.
The harmonization results on theb = 3000 s/mm
2
shell, shown in Table 5.2, are generally consistent
with those on the b = 1000 s/mm
2
shell. Focusing on the FA feature, we found that our method and
LinearRISH effectively reduce inter-site differences. Notably, the direction of the harmonization plays a
more crucial role in the harmonization of the b = 3000 s/mm
2
shell. We observed that the inter-site
differences are considerably larger in almost all ROIs when harmonizing HCP data to the HCP-D study,
as opposed to the alternative direction of harmonization. In the case of harmonizing the HCP-D data to
89
Table 5.1: Inter-site differences analysis on b=1000 s/mm
2
shell
Dataset
Right hemisphere Left hemisphere
Frontal Parietal Temporal Occipital Frontal Parietal Temporal Occipital
FA
HCP + HCP-D -0.135 * -0.163 * -0.143 * -0.179 * -0.103 * -0.145 * -0.121 * -0.124 *
HCP + HCP-D (LinearRISH) 0.028 0.015 0.028 0.023 0.050 * 0.023 0.038 * 0.044 *
HCP + HCP-D (Our method) 0.001 0.002 0.014 -0.007 0.006 -0.003 0.010 -0.003
HCP-D + HCP (LinearRISH) 0.046 * 0.039 * 0.037 * 0.043 * 0.069 * 0.054 * 0.053 * 0.071 *
HCP-D + HCP (Our method) 0.022 0.029 0.036 0.016 0.026 0.018 0.035 * 0.020
MD
HCP + HCP-D 0.153 * 0.132 * 0.147 * 0.116 * 0.133 * 0.112 * 0.087 * 0.099 *
HCP + HCP-D (LinearRISH) 0.025 * 0.013 0.018 * -0.006 0.002 0.004 -0.030 * 0.005
HCP + HCP-D (Our method) 0.008 0.007 0.014 0.004 0.003 0.005 0.002 0.016
HCP-D + HCP (LinearRISH) 0.020 0.001 0.016 -0.009 -0.002 -0.010 -0.034 * -0.003
HCP-D + HCP (Our method) 0.006 0.005 0.007 0.001 0.001 0.003 -0.003 0.008
∗ indicates significant inter-site discrepancy according to the t-test (p <0.05).
HCP, our method successfully eliminate the inter-site differences, with |ˆ α s
|≤ 0.02 (p > 0.05), in all ROIs.
However, LinearRISH fails to eliminate the original inter-site differences in left and right frontal lobes.
Compared with the MD features generated from theb = 1000 s/mm
2
shell (see first row of MD sec-
tion in Table 5.1 and ), the inter-site discrepancies of the counterparts on theb = 3000 s/mm
2
shell (see
first row of MD section in Table 5.2) are obviously smaller. This observation suggests that MD obtained
at a high b-value, reflecting neurite properties [3, 33], is less sensitive to the inter-site differences. In both
harmonization tasks, the inter-site differences, after applying the LinearRISH approach, were found to in-
crease in almost all ROIs, which indicates that the harmonization was not successful. These findings align
with our previous results in [135] that the LinearRISH notably increases the CoVs of MD after harmoniza-
tion onb = 3000 s/mm
2
shell. In contrast, our method properly reduced the inter-site differences to or
maintained the negligible inter-site differences in all lobes ( |ˆ α s
|<0.015) in both harmonization tasks.
5.3.6 PreservationoftheassociationbetweenDTIfeaturesandage
To illustrate the impact of harmonization on preserving the original association between DTI feature and
age, we estimated the regression relationship between them using an integrated dataset comprising the
original HCP data and HCP-D data before and after harmonization. Note that as harmonizing HCP-D
90
Table 5.2: Inter-site differences analysis on b=3000 s/mm
2
shell
Dataset
Right hemisphere Left hemisphere
Frontal Parietal Temporal Occipital Frontal Parietal Temporal Occipital
FA
HCP + HCP-D -0.206 * -0.170 * -0.252 * -0.226 * -0.183 * -0.188 * -0.250 * -0.220 *
HCP + HCP-D (LinearRISH) 0.041 * -0.002 -0.003 0.001 0.038 * -0.010 -0.013 -0.005
HCP + HCP-D (Our method) 0.017 0.010 0.003 0.011 0.013 0.020 0.014 0.001
HCP-D + HCP (LinearRISH) 0.062 * 0.015 -0.002 0.018 0.054 * -0.002 -0.014 0.018
HCP-D + HCP (Our method) 0.051 * 0.048 * 0.031 0.043 * 0.042 0.055 * 0.048 * 0.038
MD
HCP + HCP-D -0.013 * -0.007 -0.002 -0.024 * -0.011 * -0.017 * -0.026 * -0.038 *
HCP + HCP-D (LinearRISH) -0.021 * -0.029 * -0.032 * -0.036 * -0.026 * -0.031 * -0.043 * -0.034 *
HCP + HCP-D (Our method) -0.011 -0.011 -0.005 -0.009 -0.014 * -0.010 -0.006 -0.005
HCP-D + HCP (LinearRISH) -0.041 * -0.062 * -0.053 * -0.045 * -0.044 * -0.065 * -0.063 * -0.043 *
HCP-D + HCP (Our method) -0.011 -0.012 -0.007 -0.010 -0.014 * -0.010 -0.006 -0.007
∗ indicates significant inter-site discrepancy according to the t-test (p <0.05).
data to the HCP consistently achieved better harmonization performance demonstrated in section 5.3.5,
we focus on this optimal harmonization direction in this experiment.
Fig. 5.7 displays the linear fitting results in left frontal and temporal lobes on the b = 1000 s/mm
2
shell. The slope of the linear regression line reflects the effect size of age in diffusion features. The blue
line reflects the FA and age association of the target site data. From the results, we can first observe that
both harmonization frameworks rectify the observable incorrect association (green dashes) learned from
unharmonized data. While, the LinearRISH results, hampered by noticeable inter-site discrepancies (as
demonstrated in Table 5.1), erroneously amplify the original effect sizes of ages in both ROIs. In contrast,
the regression lines produced by harmonized data by using our method align better with which of the orig-
inal target site data for both ROIs. This indicates that our method has superior harmonization performance
and better preserves the original DTI-age association.
We also examined the association between MD and age. In Fig. 5.8, we present the regression results in
the right frontal lobe and left temporal lobe, where LinearRISH retained a small amount of inter-site differ-
ences (|ˆ α s
|∼ 0.03) while our method mitigates the inter-site differences to a negligible level ( |ˆ α s
|<0.015
and p> 0.05). The results show that our method nearly perfectly preserved the MD and age association
of the target site data in both lobes, while LinearRISH failed.
91
(a) Left frontal lobe
(b) Left temporal lobe
Figure 5.7: The impact of harmonization on the relationship between FA and age in the left frontal lobe (a)
and left temporal lobe (b) on theb = 1000 s/mm
2
shell. Each dot represents the FA and age relationship
of a subject. The linear regression of the integration of data from HCP with HCP-D, HCP-D harmonized
by using LinearRISH, and HCP-D harmonized by using our method, are shown in green, red, and orange
dash lines, respectively. The blue line represents the estimated linear relationship between age and FA for
the HCP site.
92
(a) Right frontal lobe
(b) Left temporal lobe
Figure 5.8: The impact of harmonization on the relationship between MD and age in the right frontal lobe
(a) and left temporal lobe (b) on theb=1000 s/mm
2
shell. The linear regression of pooled data from HCP
with HCP-D, HCP-D harmonized using LinearRISH, and HCP-D harmonized using our method are shown
in green, red, and orange dash lines, respectively. The blue line represents the linear relationship between
age and MD for the HCP site.
5.3.7 Preservationofgenderdifferences
Besides the age-related biological variability, we also examined the impact of harmonization procedures
on the biological variability related to gender. Quantitatively, we calculated the effect size of gender dif-
ferences for the HCP-D cohort using Cohen’sd
c
[17], which is defined as:
93
Figure 5.9: The effect size of gender difference for FA on the b = 1000 s/mm
2
shell. The effect size ( d
c
)
and the modification ( ∆ d
c
) after harmonization are denoted in the form ofd
c
(∆ d
c
).
d
c
=
µ f
− µ m
s
pooled
, (5.13)
where µ f
and µ m
are the means for the female and male groups, respectively. s
pooled
=
r
(N
f
− 1)σ 2
f
+(Nm− 1)σ 2
m
N
f
+Nm− 2
is the pooled standard deviation, where N and σ denotes the number of partic-
ipants and the standard deviation of a gender group.
Fig. 5.9 displays the effect sizes of gender differences in regional FA features on b=1000 s/mm
2
shell.
It is observable that after harmonization using LinearRISH the modification in effect size ∆ d
c
does not
change the original small effect in gender differences ( |d
c
|∼ 0.2), which indicates that both harmonization
methods preserved the biological variability of age.
94
5.4 Discussionandconclusion
In this chapter, we presented a novel framework for personalized dMRI harmonization on the cortical sur-
face. Our personalized harmonization framework focuses on addressing the misalignment problem arising
from the complicated folding of the cortical surface by adaptively estimating the inter-site harmonization
mappings based on the underlying anatomy. We validated the effectiveness of our method by conducting
harmonization across the HCP and HCP-D datasets on both low and high b-shells. The experiment results
indicated that, compared to the LinearRISH approach, our method achieved superior performance in min-
imizing inter-site differences in dMRI data on both b-shells. In addition to mitigating inter-site differences,
we demonstrated that our approach can better preserve the age-associated effect sizes of the target dataset
after harmonization. Furthermore, our method was shown to retain the inherent sex-related biological
variability in the original source cohort.
95
Chapter6
ConclusionsandFutureWork
This thesis focuses on developing methods to improve the reliability and consistency in diffusion MRI
analysis while accounting for inter-subject variability. To improve the reliability of fiber bundle recon-
struction, we developed a novel method for track filtering by leveraging the groupwise consistency of
fiber bundles to compensate for incomplete anatomical knowledge. To improve the inter-site consistency
of dMRI data, we proposed a personalized dMRI harmonization framework accounting for the confound-
ing caused by the anatomical misalignment problem in estimating inter-site harmonization mapping. To
tackle the challenge of dMRI harmonization in cortical gray matter, we presented a method of personalized
dMRI harmonization on the cortical surface devised to account for the heterogeneous layered architecture
and high-convoluted folding of cortices.
6.1 GroupwiseTrackFiltering
Tractography is an established tool for the in vivo reconstruction of white matter pathways and brain con-
nectivity analysis. With the deficiency of error propagation in trajectory proceeding, it has well-known
limitations in generating valid streamlines for the reliable representation of complex neuroanatomy. These
problems persist even when the trajectories of fiber tractography are regularized by anatomical priors in
the form of multiple regions of interest due to incomplete anatomical knowledge and lack of precision in
96
anatomical labels. To compensate for the gap in anatomical knowledge, we approached the track filtering
problem by proposing a general conceptual framework for characterizing the groupwise consistency of
fiber bundles. Guided by this definition, we developed a novel track filtering method by incorporating
regularity of groupwise consistency across subjects. Instead of making a binary decision as in many pre-
vious works, the proposed approach is able to extract sub-bundle structures to maximally preserve the
comparable anatomy while enhancing the fidelity of fiber bundles.
6.1.1 Acceleratinggroupwisefiberfilteringviarepresentationlearning
The pruning of inconsistent portions from each streamline is achieved by an integrative algorithm that
dynamically updates the localized consistency measure via message passing. The estimation of localized
consistency, requiring intensive pair-wise comparisons and point correspondences across streamlines, is
computationally expensive. This restricts the application of our fiber filtering method to a limited number
of reference subjects that may inadequately represent the diversity in the whole population. Moreover,
the relatively high computation cost also hinders the application of our method on the filtering of whole
brain tractograms. An influx of research has focused on developing methods for efficient and effective
streamline-wise comparison and matching [96, 130]. Some recent works [71, 134, 142] demonstrated the
potential of efficient streamline-wise comparison by leveraging representation learning methods such as
dictionary learning and deep auto-encoders. These methods, performing the comparison across stream-
lines in a low dimensional embedding space, are of great potential to accelerate our groupwise filtering
algorithm. Thus, leveraging representation learning methods to improve the scalability of groupwise fil-
tering can be a promising extension of our current filtering method.
97
6.2 PersonalizedDiffusionMRIHarmonization
In multisite studies, it is crucial to accommodate the inter-site discrepancies in dMRI data attributed to
inter-site variations, e.g., in scanner vendor and acquisition protocol. Neglecting these discrepancies can
potentially bias the resultant findings and diminish the statistical power of the pooled dataset. Thus, the
harmonization of dMRI data is a critical preprocessing procedure in multi-site studies. However, one fun-
damental challenge in dMRI harmonization is the complex entanglement of site-effects and the underlying
biology and anatomy of the human brain [85, 31]. In this thesis, we focused on disentangling anatomical
variability from site-effects and devised personalized harmonization frameworks both in volume and on
the cortical surface.
6.2.1 BeyondtheRISHfeaturebasedharmonization
The RISH feature based dMRI harmonization, achieving non-linear transformation of dMRI signal via linear
mapping in spherical harmonics domain, efficiently allows dMRI harmonization of data with sophisticated
inter-site discrepancies. However, its reliance on the spherical harmonics poses a major limitation to its
application on the harmonization of dMRI data with low SNR, as the high frequency component of dMRI
data is vulnerable to the contamination of noise in inter-site mapping [85, 60]. In chapter 5, we also
have demonstrated the impact of low SNR on inter-site mapping in Fig. 5.5. It shows that the scales of
RISH mapping are notably large at high SH orders, affected by the relatively low SNR of HCP-D data
when harmonizing HCP data to HCP-D. This results in an observable asymmetry in the harmonization
performance on the b = 3000 s/mm
2
shell. Although when harmonizing the HCP-D data to HCP, the
energy of high frequency components, which were surpassed, did not impact the mitigation of inter-
site differences of DTI features, contamination of noise was not eliminated and can potentially affect the
harmonization performance. Further exploration of the replacement of the RISH feature is an important
direction of future research.
98
6.2.2 Mitigatingmultisitediscrepanciesinsubjectswithdisease
To avoid confounding variables, inter-site mapping estimation in dMRI harmonization is learned from a
group of healthy controls carefully matched for confounding effects, for example, age and gender. Con-
ceptually, the inter-site mapping learned from healthy controls is independent of disease effects and con-
sequently would not introduce extra confounding for the harmonization of diseased subjects [85, 60].
Practically, the efficacy of RISH harmonization has been validated to successfully remove the inter-site
discrepancies in schizophrenia cohorts [60] and elderly cohorts with cerebral small vessel disease [12].
Nonetheless, it is imperative to acknowledge that pathological changes, such as atrophy or lesion, can
alter micro-structural properties, anatomical structures, and brain organization [124]. The presence of
disease-specific attributes can markedly augment the heterogeneity of the dataset. Thus, the establish-
ment of inter-subject correspondences between the query and references is even more crucial for decou-
pling site-effects and disease characteristics in inter-site mapping estimation. The personalized frame-
work, accounting for the inter-subject variability, offers a potential advantage in the dMRI harmonization
of subjects with disease. For future work, we are interested in applying our method to handle inter-subject
variability induced by pathological changes for dMRI harmonization of disease subjects.
6.2.3 TowardslearningbaseddMRIharmonization
Besides the conventional frameworks [85, 32, 54] that explicitly estimate the harmonization mapping func-
tion, many learning based methods were developed recently. With scans of traveling subjects obtained
from multiple sites, the dMRI harmonization problem could be formulated as a paired image-to-image
translation problem [66, 15, 91, 49]. In addition, several unsupervised harmonization methods that do
not require explicitly paired scans were proposed for dMRI harmonization [56, 88]. While in principle,
sophisticated inter-site transformation, learned with deep neural architectures, is beneficial for dMRI har-
monization, the inter-subject variability and misalignment of brain anatomy still have a significant impact
99
on these methods as the heterogeneity in anatomy (e.g., in cortical gray matter regions) can complicate the
learning of inter-site transformation and potentially result in a mismatch of training and testing data [94,
113]. For our future work, we are also interested in extending our method by developing learning based
harmonization algorithms that consider the inter-subject variability of neuroanatomy.
100
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Abstract (if available)

Abstract Diffusion magnetic resonance imaging (dMRI), capable of quantifying the diffusion of water in vivo, allows the probing of brain microstructure and connectivity non-invasively. Though widely used in neuroscience and clinical research, dMRI still faces numerous technical challenges. To improve the reliability and consistency in dMRI analysis, this thesis focuses on developing novel computational methods including track filtering for the removal of artifacts in tractography and dMRI harmonization for the mitigation of inter-site variability.

Tractography is an important tool for the in vivo analysis of brain connectivity based on diffusion MRI data, but it has well-known limitations in false positives and negatives for the faithful reconstruction of neuroanatomy. These problems persist even in the presence of strong anatomical priors in the form of multiple regions of interest (ROIs) to constrain the trajectories of fiber tractography. To improve the reliability of fiber bundle reconstruction, we propose a novel track filtering method by leveraging the groupwise consistency of fiber bundles that naturally exists across subjects. We first formalize our groupwise concept with a flexible definition that characterizes the consistency of a track with respect to other group members based on three important aspects: degree, affinity, and proximity. An iterative algorithm is then developed to dynamically update the localized consistency measure of all streamlines via message passing from a reference set, which then informs the pruning of outlier points from each streamline.

The inter-site variability of dMRI hinders the aggregation of dMRI data from multiple centers. This necessitates dMRI harmonization for removing non-biological site-effects. One fundamental challenge in dMRI harmonization is to disentangle the contributions of scanner-related effects from the variable brain anatomy for the observed imaging signals. To account for the misalignment of neuroanatomy that still widely persists even after registration, we propose a personalized framework to more effectively address the confounding from the misalignment of neuroanatomy in dMRI harmonization. The main novelty of our method is the adaptive computation of personalized templates for the estimation of site effects and inter-site mapping.

The emergence of high-resolution dMRI data across various connectome imaging studies allows the large-scale analysis of cortical microstructure. Existing harmonization methods, however, perform poorly in the harmonization of dMRI data in cortical areas because they rely on image registration methods to factor out anatomical variations, which have known difficulty in aligning cortical folding patterns. To overcome this fundamental challenge in dMRI harmonization, we propose a framework of personalized dMRI harmonization on the cortical surface to improve the dMRI harmonization of cortical gray matter by adaptively estimating the inter-site harmonization mappings. This is the first work in the field for dMRI harmonization on cortical surfaces.

In summary, our work advances the state-of-the-art in track filtering and dMRI harmonization by devising novel algorithms to account for the impact of variable brain anatomy. Related software tools have also been developed and will be distributed freely to the research community.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Xia, Yihao (author)

Core Title Methods for improving reliability and consistency in diffusion MRI analysis

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2023-08

Publication Date 07/14/2023

Defense Date 05/24/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag diffusion MRI,dMRI harmonization,OAI-PMH Harvest,personalized template,tractography

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Shi, Yonggang (committee chair), Haldar, Justin (committee member), Raghavendra, Cauligi (committee member), Thompson, Paul (committee member)

Creator Email yihaoxia@outlook.com,yihaoxia@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113279233

Unique identifier UC113279233

Identifier etd-XiaYihao-12088.pdf (filename)

Legacy Identifier etd-XiaYihao-12088

Document Type Dissertation

Format theses (aat)

Rights Xia, Yihao

Internet Media Type application/pdf

Type texts

Source 20230717-usctheses-batch-1068 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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