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3D vessel mapping techniques for retina and brain as an early imaging biomarker for small vessel diseases

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3D vessel mapping techniques for retina and brain as an early imaging biomarker for small vessel diseases

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Content 3D Vessel Mapping Techniques for Retina and Brain as an Early Imaging Biomarker for Small
Vessel Diseases
By
Mona Sharifi Sarabi
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 2022

© Copyright by
Mona Sharifi Sarabi
2022

iii

DEDICATION
This dissertation is dedicated…
To my family.

iv
ACKNOWLEDGEMENTS
The research presented in this dissertation was supported by various funding sources
including grants from the National Institutes of Health (UH2NS100614, UH3NS100614,
R21EY027879, U01EY025864, K08EY027006, P41EB015922, and R01EY030564) and
Research to Prevent Blindness. My graduate training was supported in part by grants from the
National Institutes of Health (UH2NS100614, UH3NS100614, P41EB015922) as well as multiple
travel grants from the USC Viterbi School of Engineering, and USC Women in Science and
Engineering (WiSE) program. I am grateful for all the participants and volunteers who contributed
their valuable time, patience, and effort in this research.
Chapter 2 is based on a portion of the work presented in Sarabi, M.S., Gahm, J.K.,
Khansari, M.M., Zhang, J., Kashani, A.H. and Shi, Y. (2019). An automated 3D analysis
framework for optical coherence tomography angiography. BioRxiv, p.655175; Sarabi, M.S.,
Khansari, M.M., Zhang, J., Kushner-Lenhoff, S., Gahm, J.K., Qiao, Y., Kashani, A.H. and Shi, Y.
(2020). 3D retinal vessel density mapping with oct-angiography. IEEE Journal of Biomedical and
Health Informatics, 24(12), pp.3466-3479; Khansari, M.M., Zhang, J., Qiao, Y., Gahm, J.K.,
Sarabi, M.S., Kashani, A.H. and Shi, Y. (2019). Automated deformation-based analysis of 3D
optical coherence tomography in diabetic retinopathy. IEEE transactions on medical
imaging, 39(1), pp.236-245; Zhang, J., Qiao, Y., Sarabi, M.S., Khansari, M.M., Gahm, J.K.,
Kashani, A.H. and Shi, Y., 2019. 3D shape modeling and analysis of retinal microvasculature in
OCT-angiography images. IEEE transactions on medical imaging, 39(5), pp.1335-1346; Sarabi,
M.S., Zhang, J., Gahm, J.K. and Kashani, A., 2019. Automatic 3D Vessel analysis framework for
Optical Coherence Tomography Angiography (OCTA). Investigative Ophthalmology & Visual
v
Science, 60(11), pp.006-006, Abstract presented at The Association for Research in Vision and
Ophthalmology (ARVO) Imaging in the Eye Conference, Vancouver, B.C.
Chapter 3 is based on a portion of the work presented in Ma, S.J., Sharifi Sarabi, M., Yan,
L., Shao, X., Chen, Y., Yang, Q., Jann, K., Toga, A.W., Shi, Y., Wang, D.J.J. (2019).
Characterization of lenticulostriate arteries with high resolution black-blood T1-weighted turbo
spin echo with variable flip angles at 3 and 7 Tesla. NeuroImage 199:184-193. Paper presented at
the International Society of Magnetic Resonance in Medicine (ISMRM) Annual Meeting, Paris,
France.
The material of Chapter 4 is based on the primary study presented at ISMRM Annual
Meeting in London, England, UK, Mona SharifiSarabi, Samantha J Ma, Danny JJ Wang, and
Yonggang Shi. (2022). Vessel Density Mapping of Brain Small Vessels on 3D High Resolution
Black Blood MRI; and the journal version of the study will be submitted to NeuroImage.
This work would not have been possible without the remarkable mentorship and support
from Dr. Yonggang Shi. You have shown me the prospects for being an outstanding scientist, and
I admire your abilities as a creative leader in our field. Thank you for always giving me the
guidance and gentle push toward the direction I need to succeed in my own scientific endeavors. I
am also immensely grateful for the expert insight and additional mentorship I have received from
my committee members throughout this journey: Drs. Raghu Raghavendra, Dany JJ Wang, and
Justin Haldar. Thank you for contributing your valuable time and energy toward my scientific
growth. In addition, I wish to thank Drs. Amir H. Kashani, Samantha J Ma, Jin Kyu Gahm, Maziyar
M. Khansari, and Yuchuan Qiao for sharing their knowledge and expertise and supporting my
work. A heartfelt thank you also goes to Diane Demetras for keeping me on track since the
beginning of my Trojan path in ECE.
vi
To the Neuroimage Computing Research (NICR) and USC Roski Eye Institute member
past and present, I am grateful to be a part of such an innovative and dynamic team of individuals.
Thank you to Anoush Shahidzadeh for the great support in data collection and organization and
Dr. Sam Kushner-Lenhoff for sharing your expertise and knowledge in everything from working
with the imaging devices, understanding data collection protocols, and designing clinical
experiments.
To my friends who are more like family, thank you for being in my life. I am grateful that
you were there to listen to me while I expressed my frustrations. Despite the geographical distance
and difference in time zones, you were always there for me through all the ups and downs, and I
cannot express how much that means to me.
Most importantly, to my dearest family, thank you from the greatest depths of my heart for
your limitless love and support. I would not be who I am and where I am without your
encouragement. Thank you for everything.

vii
Table of Contents
DEDICATION .............................................................................................................................. iii
ACKNOWLEDGEMENTS ......................................................................................................... iv
LIST OF TABLES .........................................................................................................................x
LIST OF FIGURES ..................................................................................................................... xi
ABBREVIATIONS ......................................................................................................................xx
ABSTRACT .............................................................................................................................. xxiv
1. CHAPTER 1: General Introduction to the Dissertation ....................................................1
1.1. Novelty and Main Contributions .................................................................................... 1
1.1.1. Novel 3D-OCTA Vessel Enhancement and Segmentation ............................ 1
1.1.2. Novel 3D-OCTA Vessel Density Mapping Method ....................................... 2
1.1.3. 3D Vessel Density Mapping of Brain Small Vessels on High Resolution
Black Blood MRI .................................................................................................... 3
1.2. Clinical Importance of Cerebral Small Vessel Disease .................................................. 5
1.3. Non-contrast In Vivo Neurovascular Imaging ............................................................... 6
1.4. Clinical Importance of Retinal Vascular Diseases ......................................................... 8
1.5. In Vivo Imaging of Retina ............................................................................................ 10
1.6. 3D Vessel Segmentation .............................................................................................. 12
1.6.1. Hessian-Based Methods for Vessel Enhancement ........................................ 14
1.6.2. Comparison of Hessian-Based Methods on Synthetic Data ......................... 17
1.7. 3D Image Registration and Tensor-based Morphometry ............................................. 19
1.8. Overview of Studies ..................................................................................................... 22
2. CHAPTER 2: 3D Retinal Vessel Density Mapping with OCT-Angiography .................25
2.1. Abstract ........................................................................................................................ 25
2.2. Introduction .................................................................................................................. 26
2.3. Related Work ................................................................................................................ 29
2.4. Materials and Methods ................................................................................................. 31
2.4.1. Dataset........................................................................................................... 31
2.4.2. OCTA Preprocessing .................................................................................... 32
2.4.2.1. 3D Volume of Interest .................................................................................. 32
2.4.2.2. OCTA Vessel Enhancement ......................................................................... 32
2.4.3. Vessel Density Calculation ........................................................................... 35
2.4.4. Mapping Vessel Density Across Subjects .................................................... 36
2.4.5. Capillary Dropout Simulation ....................................................................... 38
2.5. Results .......................................................................................................................... 39
2.5.1. Qualitative Results ........................................................................................ 39
2.5.1.1. Individual Examples ..................................................................................... 39
2.5.1.2. Longitudinal Example ................................................................................... 41
2.5.2. Quantitative Results ...................................................................................... 46
viii
2.5.2.1. Group-wise Comparison Between Synthetic Patient Data and NC .............. 47
2.5.2.2. Group-wise Analysis of Age-dependent Vessel Density Changes in the
Normal Eyes.......................................................................................................... 49
2.5.2.3. Group Study of NCs and DRs ....................................................................... 50
2.6. Discussion and Conclusion .......................................................................................... 51
3. CHAPTER 3: Shape-Reeb graph analysis method for LSA morphological
quantification ........................................................................................................................54
3.1. Abstract ........................................................................................................................ 54
3.2. Introduction .................................................................................................................. 55
3.3. Materials and Methods ................................................................................................. 56
3.3.1. Subjects ......................................................................................................... 56
3.3.2. MRI Experiment ........................................................................................... 57
3.3.3. LSA Delineation Rating Scale ...................................................................... 57
3.3.4. Image Analysis: Vessel Segmentation and Morphology Metrics Model
Development ......................................................................................................... 57
3.3.5. Statistical Analysis ........................................................................................ 59
3.4. Results .......................................................................................................................... 59
3.4.1. Evaluation of T1w TSE-VFA Manual Segmentation and Age .................... 59
3.5. Discussion .................................................................................................................... 60
3.5.1. Aging Effects on LSAs ................................................................................. 60
3.5.2. Manual Segmentation and Shape Quantification .......................................... 62
3.5.3. Limitations .................................................................................................... 63
3.6. Conclusion .................................................................................................................... 64
4. CHAPTER 4: Vessel Density Mapping of Brain Small Vessels on 3D High
Resolution Black Blood MRI ...............................................................................................65
4.1. Abstract ........................................................................................................................ 65
4.2. Introduction .................................................................................................................. 66
4.3. Methods ........................................................................................................................ 68
4.3.1. Subjects and Imaging .................................................................................... 68
4.3.2. Pre-Processing............................................................................................... 70
4.3.3. 3D Vessel Enhancement ............................................................................... 71
4.3.4. 3D Vessel Segmentation and Performance assessment ................................ 73
4.3.5. Vessel Classification using Anatomical Masking......................................... 75
4.3.6. Vessel Density Calculation ........................................................................... 76
4.3.7. Mapping Vessel Density Across Subjects .................................................... 77
4.4. Results .......................................................................................................................... 78
4.4.1. Validation Results of in vivo MRI ................................................................ 78
4.4.1.1. Scale and threshold parameters estimation ................................................... 78
4.4.1.2. Performance evaluation using vessel landmarks and LSAs ......................... 81
4.4.2. Qualitative Results in Young and Aged Subjects ......................................... 84
4.4.3. Quantitative Results in Young and Aged Subjects ....................................... 84
ix
4.4.3.1. Global Mean Vessel Density ........................................................................ 84
4.4.3.2. Localized Vessel Density Analysis ............................................................... 85
4.4.3.2.1. Group-wise Analysis of Age-dependent Vessel Density Changes in
the Normal Brains ................................................................................................. 85
4.4.3.2.2. Group-wise Analysis of Vessel Density Changes in the Brains with
Vascular Risk Factors ........................................................................................... 85
4.5. Discussion .................................................................................................................... 86
4.5.1. Clinical Value of Whole Brain Small Vessel Density Mapping................... 87
4.5.2. Segmentation and Quantification .................................................................. 88
4.5.3. Limitations of the Study................................................................................ 90
4.5.4. Conclusions ................................................................................................... 90
5. CHAPTER 5: Conclusion and Ongoing Work ..................................................................91
5.1. OCTA Projection Artifact Removal ............................................................................. 92
5.2. Statistical Atlas of Cerebral Small Vessels using High-resolution Black Blood
MRIs ............................................................................................................................. 93
5.3. Correlation Analysis between Retinal Capillaries and Cerebral Small Vessels .......... 94
References .....................................................................................................................................96

x
LIST OF TABLES
Chapter 3
Table 3.1 Summary of imaging parameters for sequences .......................................................... 56
Table 3.2 Criteria for 4-point LSA Delineation Rating Scale ...................................................... 56
Table 3.3 Summary of Reeb graph metrics for 3T and 7T VFA-TSE manual segmentations
of young and aged subjects (mean ± SD) ................................................................ 62
Chapter 4
Table 4.1 Summary of evaluation metrics for small vessel segmentation using vessel
landmarks of validation .......................................................................................... 82
Table 4.2 Summary of evaluation metrics for LSA segmentation using manual annotation of
young and aged subjects. ......................................................................................... 82

xi
LIST OF FIGURES
Chapter 1
Figure 1.1 Standards for reporting and imaging of SVD: example findings, schematic
representations, and descriptive imaging characteristics on MRI. Adapted from:
Shi, Y and Wardlaw, JM, Stroke and Vascular Neurology, 2016 ............................. 5
Figure 1.2 TOF MRA at 7T allows visualization of fine perforating arteries (A, 10 mm thin
maximum intensity projection); 3D T1w TSE with isotropic 0.5 mm resolution
at 3T comparably delineates the lenticulostriate arteries in a healthy subject (B,
10 mm thin minimum intensity projection). .............................................................. 6
Figure 1.3 T1-weighted TSE-VFA at 3T (top) and 7T (bottom). ............................................... 7
Figure 1.4 Optimized T1-weighted VFA TSE at 3T (A, C) and 7T-TOF MRA (B, D).
Imaging at 3T VFA TSE show more details and small vessels. ............................... 9
Figure 1.5 Possible mechanisms occurring at the lenticulostriate arteries that cause a lacunar
infarct. Adapted from: Shi, Y and Wardlaw, JM, Stroke and Vascular
Neurology, 2016. ....................................................................................................... 9
Figure 1.6 Fluorescence angiography (FA) and indocyanine green angiography (ICGA) of
the right eye. (A) Mid-phase FA showed patchy choroidal filling and multiple
punctate hyperfluorescent lesions. (B) Late-phase FA showed diffuse leakage
and unilobular fluorescence pooling. (C) Early-phase ICGA (35 sec) showed a
hypofluorescent choroidal filling defect in the macula. (D) Mid-phase ICGA (4
min) showed a larger area of macular hypofluorescence due to fluorescence
blockage in the areas of exudative retinal detachment. Adapted from: Yang,Hee
Kyung et al., Korean Journal of Ophthalmology, 2009. ......................................... 10
Figure 1.7 Illustration of OCTA scanning methodology and signal processing scheme. This
figure illustrates the theoretical difference in the behavior of OCT beams that
interact with retinal tissue depending on whether the beams strike blood vessels
or neurosensory retinal tissue. At time T1, two OCT beams are incident on the
retinal tissue. Beam A1 (red) strikes a retinal artery while beam A2 (blue) strikes
adjacent neurosensory retinal tissue that is static. Each beam is back-scattered
and generates an A-scan signal shown in the middle. Similarly, at time T2
another scan is performed and illustrated. The interaction of the incident light
from beam A1 with moving red blood cells causes more variability in the OCT
signal from beam A1 as illustrated in the A-scan signal traces. These signals are
then “averaged” as shown by the black arrows to generate a composite OCTA
signal that is illustrated in the far right of the panel. The increased variability of
the OCT signal from beam A1 is illustrated and is localized to the regions where
red blood cell movement occurred. A sample B-scan is illustrated in the lower
xii
right of the panel. Adapted from: A.H. Kashnai et al, Progress in Retinal and
Eye Research, 2017. ................................................................................................ 11
Figure 1.8 Demonstration of various field-of-views in OCTA. (A) 3 * 3mm2 (B) 6 * 6mm2
and (C) 8 * 8mm2 field-of-view pseudo-colored OCTA of a normal subject.
Red represents superficial retinal layer. Green represents deep retinal layer.
Yellow represents regions of overlay. Images are from an AngioPlex™ device
(Carl Zeiss Meditec). Adapted from: A.H. Kashnai et al, Progress in Retinal and
Eye Research, 2017. ................................................................................................ 12
Figure 1.9 3D vessel segmentation results and response profile of Hessian-based methods
on synthetic data. (a) Synthetic image with vessels of different sizes, (b-d) the
results of Jerman’s, Frangi’s and Sato’s filters, respectively. (e) The comparison
plots of the three methods using dice similarity metric on synthetic image with
additive Gaussian noise with variable SD. (f, g) Vesselness response profile of
all three-methods annotated by f and g lines in ....................................................... 18
Figure 1.10 Example 3D registration and Jacobian maps using non-linear registration of
OCT image volumes in 2 PDR subjects demonstrated by a cut through the
volume. (a) OCT volume of the first PDR subject with visible diabetic macular
edema and alterations in shape of foveal pit. (b) Cut through the atlas which
represents retinal structure of healthy OCT volumes. (c) Color-coded Jacobian
map demonstrating magnitude of localized contraction and expansion for the
first PDR subject. (d) OCT volume of the second PDR subject with visible tissue
loss. (e) Cut through the atlas which represent retinal structure of healthy
subjects. (f) Color-coded Jacobian map demonstrating magnitude of localized
contraction and expansion. Adapted from Kashani et al. Past, present and future
role of retinal imaging in neurodegenerative disease, 2021 .................................... 21
Chapter 2
Figure 2.1 Method overview. (a) Selected en face view of original OCTA. (b) OCTA
preprocessing steps: (b-1) En face view of 3D-Curvelet denoised OCTA from
(a), (b-2) En face view of 3D-Enhanced OCTA obtained by applying OOF
vessel enhancement to (b-1). (b-3) En face view of binary vessel mask (BVM)
obtained by applying Otsu’s global thresholding on (b-2). (c) OCTA vessel
density image (VDI) generated from the BVM in (b-3). (d) OCT non-linear
registration for finding transformation of each image to the atlas space. These
transformations are later applied to bring VDIs into the atlas space allowing
localized capillary quantification. (d-row1) An OCT representing the atlas and
(d-row2) example of a moving OCT that will be registered to the atlas space.
(e) Registered VDI to the atlas space (e-row1) obtained by applying the non-
linear warp computed in (d) to the VDI of the moving scan (e-row2). The dashed
xiii
red line in (d, e) is fixed in the atlas space and used to visualize the relative
position of the moving scan and associated VDI before and after registration. ...... 27
Figure 2.2 Retinal layer definitions on structural OCT images. An illustration of the OCT
layer segmentation definitions as achieved by the OCT-Explorer. ......................... 32
Figure 2.3 Example of OCTA vessel enhancement of a severe NPDR subject. (a) Original
3D-OCTA image volume. (b) OCTA after applying 3D curvelet denoising on
(a). (c) OCTA after applying 3D OOF vessel enhancement on (b). (d, e) Selected
en face view of (a), (d-1) magnified view of the denoted region in (d), (d-2)
vessel discontinuity enhancement of (d-1) via curvelet, (d-3) vessel
discontinuity enhancement of (d-2) via OOF. (e-1) magnified view of the
denoted region with closely located microvasculature in (e), (e-2) vessel
enhancement of (e-1) via curvelet, (e-3) vessel enhancement of (e-2) via OOF.
Red and green arrows point to the disconnected and the resolved discontinuity
regions of the vessel, respectively. Red and green dashed circles represent the
high and low efficiency of the enhancement method in separation of closely
located microvasculature, respectively.................................................................... 33
Figure 2.4 OCTA binary vessel mask (BVM) and vessel density image (VDI) of a PDR
and a NC eye. (a, d) Selected 2D en face from BVM of a PDR and a NC eye,
respectively. (b, e) VDI of (a, d) which are obtained by the convolution between
BVM and a 3D ellipsoidal kernel. (c, f) overlay of (a, d) on (b, e), respectively.
Red is associated with highest VDI (dense vascular regions), and blue is
associated with the lowest VDI (avascular region). ................................................ 35
Figure 2.5 Example of OCT and VDI registration of a PDR subject with edema. (a) The
overlay of OOF vesselness response on 3D OCT scan of the PDR subject. (b)
OCT atlas volume. (c), (d) OCT volume of the PDR subject before and after
registration, respectively. (e), (f) VDI of the PDR subject before and after
registration overlaid on the corresponding OCT images (c, d), respectively. ......... 36
Figure 2.6 Example OCT volume registration for a normal and PDR subject. Selected OCT
cross-sectional scan of (a) Atlas image. (b) A moving NC subject. (c) Same
image in (b) after the extraction of VOI and denoising. (d) Same image in (c)
after non-linear registration to the atlas. (e) A moving PDR subject with edema.
(f) Same image in (e) after VOI extraction and denoising. (g) Same image in (f)
after non-linear registration to the atlas. The horizontal red dashed lines in (a, c,
d, f, g) are fixed in the atlas space to visualize the relative position of the OCT
images before (c, f) and after registration (d, g). The vertical dotted white line
in (a, c, d, f, g) are also fixed in the atlas space to show the alignment of the
fovea center. ............................................................................................................ 40
xiv
Figure 2.7 Example vessel density image registration of a selected normal and PDR subject.
Selected cross-sectional scan of (a) BVM of a moving NC subject overlaid on
the corresponding OCT scan. (b) VDI generated by diffusing the content of (a).
(c) The VDI in (b) after registration to the atlas space. (d) BVM of a moving
PDR subject with edema overlaid on the corresponding OCT scan. (e) VDI
computed from the BVM in (d). (f) the VDI in (e) after registration to the atlas
space. The horizontal red dashed lines and vertical white dashed lines in (b, c,
e, f) are the same lines demonstrated in the corresponding OCT scans in Figure.6
(c, d, f, g). ................................................................................................................ 41
Figure 2.8 Visualization of OCT deformation caused by diabetic macular edema (DME) in
a diabetic subject during edema development and treatment periods. Row1 (a-
c) 3D-OCT scans of the DME subject at three time points (t1, t2, t3) in
chronological order. Row2 (d-f) selected OCT cross-sectional scans from
similar slabs (orange dashed lines) of the corresponding 3D-OCT in (a-c). Row3
(g-i) selected cross-sectional scans of automatic OCT layer segmentation by
OCT-Explorer overlaid on the corresponding OCT cross sections in (d-f). (t1-
t2) is the edema progression period, (t2-t3) is the edema treatment period.
Edema regions are annotated by red in (d) and (e). The regions inside dashed
white rectangular in (g, h, i) show areas with OCT layer segmentation errors. ...... 43
Figure 2.9 Visualization of OCT deformation caused by diabetic macular edema (DME) in
another diabetic subject during edema treatment and recurrence periods. Row1
(a-c) 3D-OCT scan of a DME subject at three time points (t1, t2, t3) in
chronological order. Row2 (d-f) selected OCT cross-sectional scans from
similar slabs (orange dashed lines) of the corresponding 3D-OCT in (a-c). Row3
(g-i) selected cross-sectional scans of automatic OCT layer segmentation by
OCT-Explorer overlaid on the corresponding OCT cross sections in (d-f). (t1-
t2) is the edema treatment period, (t2-t3) is the edema recurrence period. Edema
regions are annotated by red in (d) and (f). The regions inside dashed white
rectangular show areas with OCT layer segmentation errors. ................................ 43
Figure 2.10 Longitudinal example of tracking VDI changes of a diabetic subject with edema
during edema development and treatment periods. Row1 (a-c) OCT volume cut
of the same subject at three time points (t1, t2, t3) in chronological order before
registration. Row2 (d-f) selected VDI cross-section from similar slabs of the
corresponding 3D-OCT in (a-c) overlaid on the corresponding OCT cross-
sections before registration. Row3 (g-i) OCT volume cuts of the same subject
(row1 (a- c)) after non-linear registration to the atlas. Row4 (j-l) selected VDI
cross-section overlaid on the corresponding OCT cross-sections after non-linear
registration. The regions with noticeable VDI changes between consecutive
time points are denoted by dashed white circles. Edema regions at t1 and t2 time
points are delineated by dashed red lines. ............................................................... 45
xv
Figure 2.11 Longitudinal example of tracking VDI changes of a diabetic subject with edema
during edema treatment and recurrence periods. Row1 (a-c) OCT volume cut
of the same subject at three time points (t1, t2, t3) in chronological order before
registration. Row2 (d-f) selected VDI cross-section from similar slabs of the
corresponding 3D-OCT in (a-c) overlaid on the corresponding OCT cross-
sections before registration. Row3 (g-i) OCT volume cuts of the same subject
(row1 (a-c)) after non-linear registration to the atlas. Row4 (j-l) selected VDI
cross-sections overlaid on the corresponding OCT cross-sections after non-
linear registration. The regions with noticeable VDI changes between
consecutive time points are denoted by a dashed white circle in (k) and (l).
Edema regions at t1 and t3 time points are delineated by dashed red lines. The
areas of edema recurrence at t3 are pointed by yellow arrows in (l)....................... 45
Figure 2.12 Localization of significantly different voxels (p<0.01) overlaid on the p-value
map in comparison between NC-NC and NC-Synthetic patients. (a) Localized
comparison between retinal vessel densities of two normal groups (NC-
group1(N = 12), NC-group2 (N = 13)) without simulated capillary dropout. (b)
Localized comparison between retinal vessel densities of normal controls and
synthetic patient data with 5% simulated capillary dropout (NC-group1(N = 12)
and synthetic patient data (N = 13)). Red regions are the significant voxels with
higher vessel density in the first group and yellow regions are the significant
voxels with lower vessel density in the first group as compared to the second
group (window size for VDI calculation for all subjects is set to [28 28 4]). ......... 48
Figure 2.13 Robustness of localization result of the significantly different voxels (p<0.01)
with different window sizes. Localized comparison between retinal vessel
densities of NCs (N=12) and synthetic patient data (N=13) with 5% branch
removal rate and different window sizes: (a) w = [ 26 26 4], (b) w = [30 30 4],
(c) w = [28 28 5], (d) w = [28 28 6]. Red regions are the significant voxels with
higher vessel density in NCs and the yellow regions represent voxels with lower
vessel density in the NCs as compared to the synthetic patient data. ..................... 49
Figure 2.14 Effect of the branch removal rate on the capillary dropout detection performance.
Localized comparison between retinal vessel densities of NCs (N=12) and
synthetic patient data (N=13) with different branch removal rates as: (a) 10%,
(b) 5%, (c) 2% and (d) 1%. Window size in all experiments is set to [28 28 4]
and significant level is considered as 0.01 (p<0.01). Red regions are the
significant voxels with higher vessel density in NCs and the yellow regions
represent voxels with lower vessel density in the NCs as compared to the
synthetic patient data. .............................................................................................. 49
Figure 2.15 Localization of the significantly different voxels (p<10
-3
) in comparison between
two age groups of NC. (a) Localized comparison results in the RET overlaid on
the RET p-value map. (b) Localized comparison results in the SRL overlaid on
xvi
the SRL p-value map. (c) Localized comparison results in the DRL overlaid on
the DRL p-value map. Red region in (a), (b), (c) demonstrate the voxels with
lower vessel density in NC older group (age>50) compared to NC younger
group (age<50). ....................................................................................................... 50
Figure 2.16 Localization of the significantly different voxels (p<10
-5
) in comparison between
NC (N=25) and PDR subjects (N=25). (a) Localized comparison results in the
SRL overlaid on the SRL p-value map. (b) Localized comparison results in the
DRL overlaid on the DRL p-value map. Red region in (a), (b) demonstrate the
voxels with lower vessel density in PDR group compared to NCs. ........................ 50
Chapter 3
Figure 3.1 Lenticulostriate artery morphological quantification workflow begins with
manual vessel segmentation using ITK-SNAP on the raw TSE-VFA image (a).
The vessel volumes are reconstructed, and a mesh surface is created in
preparation for shape analysis (b). Quantitative measures such as vessel length
and tortuosity are calculated from the Reeb graph (c). ........................................... 58
Figure 3.2 Three-dimensional renderings of left LSAs from the manual segmentations of
an aged subject (A,C,E) and a young subject (B,D,F). VFA-TSE at both 3T and
7T enabled the identification of more vessels in aged subjects, especially in the
medial region. 7T VFA-TSE enabled the identification of more branches in
general in the younger subjects (i.e. orange and turquoise branch vessels in D).
Despite longer segmentation of vessels using 7T TOF images, fewer vessels
could be identified. As summarized by the box plot of vessel count, significantly
more vessels were detected in young subjects than in aged subjects (**, p<0.01),
and more vessels were detected using VFA-TSE compared to 7T TOF MRA (*,
p<0.05). ................................................................................................................... 61
Figure 3.3 Additional examples of the 3D renderings of the manual vessel segmentation
for two younger subjects with larger number of vessels and branches detected.
Despite the high vessel density, the resolution was sufficient to distinguish
secondary branches from primary stems. ................................................................ 62
Figure 3.4 Comparison of mean vessel length and tortuosity of lenticulostriate arteries in
young (age 19-35 years) and aged (age > 60 years) groups for each modality. *
Indicates significance p<0.05; ** indicates significance p<0.01. ........................... 63
Chapter 4
Figure 4.1 Method overview. 1) Vessel segmentation pipeline including: (a) Input high-
resolution black blood MRI to the pipeline, (b) Preprocessing steps such as
skull-stripping, bias correction and denoising by non-local means (NLM)
applied on (a), (c) 3D vessel enhancement, various multiscale Hessian-based
xvii
methods (Frangi et al., 1998, Sato et al., 2000, Jerman et al., 2016) have been
evaluated for enhancement of the small vessels; Jerman filter outperformed
other candidate methods. (d) Binarized vessel mask (BVM) was obtained by
thresholding Jerman’s vesselness map using the optimal threshold. (e) Spatial
masking was defined to construct region of interest (ROI) and classify small
cerebral vessels. (f) Vessel density image (VDI) was calculated by diffusing the
content of (e) to the entire image volume.2) Co-registration of partial view of
black-blood MRI (g) and full view of MPRAGE image (h) pairs using 12
landmark points and 3D affine registration. 3) VDI mapping to normalize VDI
of each subject (I) to MNI atlas (i), non-linear registration was obtained by
registration MPRAGE of each subject (k) to MNI atlas(i). The normalized VDI
(j) was transformed to MNI Atlas by combining deformation fields computed
in step 1 and step 2. ................................................................................................. 67
Figure 4.2 Example high-resolution black blood MRI preprocessing shown on a selected
sagittal scan. (a) Raw image of a young control subject. (b) preprocessed image
using skull-stripping, bias correction and NLM denoising. .................................... 70
Figure 4.3 Method validation dataset. (1) Vessel and background landmark annotation on
selected sagittal slice of three representative subjects, where (A-1) is a healthy
29-year-old male, (B-1) is a healthy 64-year-old female and (C-1) is a 62-year-
old female with diabetes and hypertension. Magnified view of vessel landmarks
(red voxels) and background points (green voxels) of the corresponding selected
subjects are shown in (A-2), (B-2) and (C-2), respectively. (2) Manual
Lenticulostriate artery (LSA) annotation by experts using ITK-SNAP on (a) 2D
slices from axial (a-Row1), coronal (a-Row2) and sagittal (a-Row3) views, and
(b) 3D rendering of LSA labels in (a). (c, d) Thin minimum intensity projections
of high-resolution 3T MRI of LSAs for (G-1) a healthy 25-year-old male, and
(G-2) a healthy 67-year-old female. Matching 3D LSA labels are shown in (H-
1) and (H-2), respectively. ....................................................................................... 73
Figure 4.4 Spatial distribution of arteries, veins, and dural sinuses in high-resolution black
blood MRI. (a) sagittal, coronal, and axial slices with overlayed vessel
annotations. (b) 3D-rendering results of vascular network in (a); in (B-1, B-2)
vessels are color coded to show vascular classification, where red-colored
vessels are small arteries and veins, green-colored vessels are dural sinuses, and
yellow-colored vessels are MCAs. To obtain final small vessels mask (B-3, B-
4), dural sinuses and regions pointed by (1) and (2) are excluded using
anatomical masking. ................................................................................................ 74
Figure 4.5 Vessel density image (VDI) representation. (a) 3D-rendering of BVM of a young
control subject (A-1, A-2). (A-3) Corresponding VDI of BVM in (A-1, A-2)
before (A-3) and after normalization (A-4). (b) 3D-rendering of BVM of an
xviii
aged control subject (B-1, B-2). (B-3) Corresponding VDI of the BVM in (B-1,
B-2) before (B-3) and after normalization (B-4). .................................................... 75
Figure 4.6 Flow chart of co-registration and VDI normalization. Step1: Co-registration of
high-resolution black-blood MRI (a) and MPRAGE (b) image pairs, using 3D-
Affine registration with 12 landmark points, where (a) is the fixed and (b) is the
moving image. Step2) Nonlinear warp between the MNI-152 Atlas (c) and
MPRAGE (e) image. VDI was first reversely transformed to MPRAGE space
using affine transformation (f), and then non-linearly transformed to the MNI
Atlas using a B-spline transformation (d). .............................................................. 76
Figure 4.7 Scale and threshold parameters optimization using vessel landmarks. ROC
curves of Jerman response (a) with variable upper-bound in the scale range to
find the optimal upper-bound, (b) with variable lower- bound in the scale range
to find the optimal lower-bound (c) with optimal scale range of [0.1-0.4] to find
the optimal threshold value. The threshold range in (a) and (b) is set to [0.001-
0.4], and in (b) is set to a tighter range of [0.001-0.2]. Overall, the optimal scale
range and threshold were estimates as [0.1-0.4] and 0.072, respectively................ 79
Figure 4.8 Performance comparison of Hessian-based methods for small cerebral vessel
segmentation. (Row-1) 3D-rendering result of a young control subject (Female,
25 years old) by (a) Jerman, (b) Frangi, (c) Sato filter with optimized
parameters. (Row-2) Magnified view of the annotated white box in Row-1.
(Row-3) 3D-rendering result of an aged control subject (Female, 70 years old)
by (a) Jerman, (b) Frangi, (c) Sato filter with optimized parameters. (Row-4)
Magnified view of the annotated white box in Row-2. Overall, Jerman filter has
more uniform and continuous vessel segmentation result for both young and
aged subjects. .......................................................................................................... 80
Figure 4.9 Performance comparison of Hessian-based methods for LSA segmentation of
the same subjects in Figure3. 3D-rendering of the LSA manual segmentation
(column-1), and the segmentation result of the young (Row-1) and aged (Row-
3) subject by (a) Jerman, (b) Frangi, (c) Sato filters with the same parameters as
in Figure3. (Row-2, Row-4) Corresponding error map of the segmentation
results in (Row-1) and (Row-3), respectively. ........................................................ 81
Figure 4.10 3D visualization of small vessels segmentation using Jerman method with
optimized parameters. (a) young control, (b) aged control, (c) aged group with
vascular risk factors (VRF), where VCID002 has hypertension and high
cholesterol, VCID008 is diagnosed with diabetes, hypertension, and high
cholesterol, VCID010 has only diabetes and VCID041 has high cholesterol.
Aged groups (bottom two rows) have sparser vessel network compared to young
group (first row). ..................................................................................................... 82
xix
Figure 4.11 Comparison of mean vessel density of small cerebral vessels in young (age 22-
33 years) and aged (age > 60 years) groups with and without vascular risk
factors. * indicates significance p<0.05; ** indicates significance p<0.01. ........... 84
Figure 4.12 Localization of significantly different voxels (p<0.05) in comparison between
YC (N=10) and AC (N=18) subjects. (a) P-value map overlaid on the MNI152
atlas; blue regions have lower p-value compared to red-regions. (b) Color-coded
localization map overlaid on the MNI152 atlas; green regions demonstrate the
voxels with significantly (p<0.05) higher vessel density in YC compared to AC,
and red regions show the voxels with significantly (p<0.05) lower vessel density
in YC compared to AC. ........................................................................................... 86
Figure 4.13 Localization of significantly different voxels (p<0.05) in comparison between
YC (N=10) and A-VRF (N=24) subjects. (a) P-value map overlaid on the
MNI152 atlas; blue regions have lower p-value compared to red-regions. (b)
Color-coded localization map overlaid on the MNI152 atlas; green regions
demonstrate the voxels with significantly (p<0.05) higher vessel density in YC
compared to AD, and red regions show the voxels with significantly (p<0.05)
lower vessel density in YC compared to A-VRF. ................................................... 87
Figure 4.14 Localization of significantly different voxels (p<0.05) in comparison between
AC (N=18) and A-VRF (N=24) subjects. (a) P-value map overlaid on the
MNI152 atlas; blue regions have lower p-value compared to red-regions. (b)
Color-coded localization map overlaid on the MNI152 atlas; green regions
demonstrate the voxels with significantly (p<0.05) higher vessel density in AC
compared to AD, and red regions show the voxels with significantly (p<0.05)
lower vessel density in AC compared to A-VRF. ................................................... 88
Chapter 5
Figure 5.1 Visualization of OCTA projection artifact. (A) Schematic view of decorrelation
tail pointed by arrow. (B) Example OCTA surface reconstruction of a healthy
subject, the projection artifact or decorrelation tail (yellow pointed arrows) is
included in the final vessel shape. ........................................................................... 92

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ABBREVIATIONS
2D . . . . . . . Two-dimensional
3D . . . . . . . Three-dimensional
3T . . . . . . . 3Tesla
7T . . . . . . . 7Tesla
95HD . . . . . . . 95% percentile Hausdorff distance
AC . . . . . . . Age Control
AD . . . . . . . Alzheimer’s Disease
AMD . . . . . . . Age-related Macular Degeneration
ASL . . . . . . . Arterial Spin Labeling
AUC . . . . . . . Area Under the Curve
AVD . . . . . . . Average Hausdorff Distance
BVM . . . . . . . Binary Vessel Mask
CBF . . . . . . . Cerebral Blood Flow
CSF . . . . . . . Cerebral Spinal Fluid
CT . . . . . . . Computerized Tomography
DL . . . . . . . Deep Learning
DM . . . . . . . Diabetes Mellitus
DME . . . . . . . Diabetic Macular Edema
DR . . . . . . . Diabetic Retinopathy
DRL . . . . . . . Deep Retina Layer
DSA . . . . . . . Digital Subtraction Angiography
EPG . . . . . . . Extended Phase Graph
ETL . . . . . . . Echo Train Length
FA . . . . . . . Fluorescein Angiography
FAZ . . . . . . . Fovea Avascular Zone
FDA . . . . . . . Food and Drug Administration
FDCT . . . . . . . Fast Discrete Curvelet Transform
xxi
FV . . . . . . . Frangi Vesselness
GM . . . . . . . Gray Matter
ICGA . . . . . . . Indocyanine Green Angiography
ILM . . . . . . . Internal Limiting Membrane
INL . . . . . . . Inner Nuclear Layer
IPL . . . . . . . Inner Plexiform Layer
IRB . . . . . . . Institutional Review Board
L1 . . . . . . . Layer1
L3 . . . . . . . Layer3
L4 . . . . . . . Layer4
L5 . . . . . . . Layer5
LB . . . . . . . Laplace Beltrami
LSA . . . . . . . Lenticulostriate Artery
LSAD . . . . . . . Lenticulostriate Artery Delineation
MCA . . . . . . . Middle Cerebral Artery
minIP . . . . . . . Minimum Intensity Projection
MIP . . . . . . . Maximum Intensity Projection
ML . . . . . . . Machine Learning
MNI . . . . . . . Montreal Neurological Institute
MPRAGE . . . . . . . Magnetization Prepared Rapid Acquisition Gradient Echo
MR . . . . . . . Magnetic Resonance
MRA . . . . . . . Magnetic Resonance Angiography
MRI . . . . . . . Magnetic Resonance Imaging
NC . . . . . . . Normal Control
NLM . . . . . . . Non-Local Means
NMI . . . . . . . Normalized Mutual Information
NPDR . . . . . . . Non-proliferative Diabetic Retinopathy
OCT . . . . . . . Optical Coherence Tomography
xxii
OCTA . . . . . . . Optical Coherence Tomography Angiography
OOF . . . . . . . Optimally Oriented Flux
OPL . . . . . . . Outer Plexiform Layer
PDR . . . . . . . Proliferative Diabetic Retinopathy
PET . . . . . . . Positron Emission Tomography
RBC . . . . . . . Red Blood Cells
RET . . . . . . . Retina
ROC . . . . . . . Receiver Operating Characteristic
ROI . . . . . . . Region Of Interest
RPE . . . . . . . Retinal Pigment Epithelium
SD . . . . . . . Standard Deviation
SE . . . . . . . Sensitivity
SNR . . . . . . . Signal-to-Noise Ratio
SPECT . . . . . . . Single-Photon Emission Computed Tomography
SRL . . . . . . . Superficial Retina Layer
SVD . . . . . . . Small Vessel Disease
TBM . . . . . . . Tensor Based Morphometry
TOF . . . . . . . Time of Flight
TSE . . . . . . . Turbo Spin Echo
UHF . . . . . . . Ultra-High Field
VCID . . . . . . . Vascular Cognitive Impairment and Dementia
VDI . . . . . . . Vessel Density Image
VFA . . . . . . . Variable Flip Angle
VOI . . . . . . . Volume Of Interest
VR . . . . . . . Volume Ratio
VRF . . . . . . . Vascular Risk Factors
WM . . . . . . . White Matter
WML . . . . . . . White Matter Lesion
xxiii
YC . . . . . . . Young Control

xxiv
ABSTRACT
Vascular diseases are among the most common public health problems worldwide.
Associated conditions include diabetes, arteriosclerosis, cardiovascular diseases, hypertension,
and cerebrovascular small vessel disease (cSVD) to name only the most widely occurring ones.
Diabetic retinopathy (DR) is a significant microvascular complication of diabetes mellitus (DM)
and a leading cause of visual impairment in the developed world (Stitt et al. 2016). DR-related
vision impairment is expected to remain a major health concern since the prevalence of diabetes
is projected to increase from 14% in 2010 to 21% in 2050 (Boyle et al. 2010), and the lifetime
prevalence of DR in subjects with DM is well over 50% (Stitt et al. 2016). CSVD is responsible
for approximately 25% of both ischemic and hemorrhagic strokes worldwide and is associated
with increased risk of recurrent stroke (Rensma et al. 2018). It is also a primary contributor to
cognitive decline, with up to 45% of dementia cases in the general population being associated
with cSVD. Still, the underlying mechanisms of SVD remain poorly understood, resulting in no
specific guidelines for its staging, treatment, and prevention.
The knowledge gap in SVD is partly because small vessels, including cerebral small
vessels (e.g., arterioles and capillaries) and retinal capillaries, are largely inaccessible to existing,
clinically available in vivo imaging technologies. Recent development in magnetic resonance
imaging (MRI) techniques has demonstrated the feasibility of non-invasively visualizing cerebral
small vessels, such as the lenticulostriate arteries (LSAs), by optimized 3D black-blood MRI
sequence using T1-weighted turbo spin echo with variable flip angles (T1w TSE-VFA) with sub-
millimeter spatial resolution. In retina imaging, optical coherence tomography angiography
(OCTA) has been introduced recently that can safely, quickly, and non-invasively demonstrate the
3D retinal microvasculature network with micron-level resolution. The advent of these high-
xxv
resolution angiography images can have a significant impact in studying early microvascular
changes in small vessel diseases (SVD) of retina and brain. However, due to technical limitations,
the accurate three-dimensional (3D) analyses of the small vascular structure including detection,
localization and robust quantification in OCTA and high-resolution black blood MRI remain as an
open and essential area of research and development.
In retina studies, although the 3D micron-level visualization of retina is provided by recent
imaging devices, most of the current methods still largely perform their analyses and quantification
on two-dimensional (2D) projection images, which results in an inevitable information loss and
alteration of morphological information due to the overlap of 3D vascular structures after their
projection onto a 2D plane. In brain studies, neuroimaging plays a key role in characterizing cSVD
by identifying various features linked to cSVD including recent small subcortical infarcts, lacunes,
white matter hyperintensities, enlarged perivascular spaces, microbleeds, and brain atrophy.
However, when these features become visible or detectable in structural imaging, they are already
manifestations of significant deterioration caused by cSVD. Therefore, currently there is an
increasing desire to detect the earliest features of cSVD in order to mitigate downstream disease-
related tissue changes.
This dissertation aims to bridge the technical gap in localized analysis of small vessels of
retina and brain using state-of-the-art high-resolution imaging technologies. To this end we
developed a novel and generalizable framework that incorporates vessel segmentation, artifact
resolution, registration, and localized vessel density mapping across subjects. To demonstrate the
clinical utility of our developed tools and validation of the proposed frameworks, we showed
successful applications in localized detection of vascular changes and characterization of
morphological differences caused with simulated capillary loss, aging and vascular risk factors.
xxvi
In this dissertation, Chapter 1 provides a general introduction to the research outlined in
the following chapters. It covers the novelty and main contributions, clinical significance of small
vessel disease in retina and brain, the current state of existing in vivo imaging and the advent of
novel and high-resolution imaging techniques, the review and comparison of common techniques
such as Hessian-based solutions for vessel segmentation problems, and the registration methods
for retina and brain. Chapter 2 describes a study in which a novel approach was developed by
adopting curvelet denoising, optimally oriented flux (OOF) and non-linear registration for
mapping retinal vessel density from three-dimensional (3D) OCT-Angiography images. To
demonstrate the clinical utility of our method, in our experimental results, we presented an
application for longitudinal localized qualitative analysis of pathological subjects with edema
during the course of clinical care. Additionally, we quantitatively validated our method on
synthetic data with simulated capillary dropout, a dataset obtained from a normal control (NC)
population divided into two age groups and a dataset obtained from patients with diabetic
retinopathy (DR). Our results show that we can successfully detect localized vascular changes
caused by simulated capillary loss, normal aging, and DR pathology even in presence of edema.
Chapter 3 presents the development of shape-reeb graph quantification method for morphological
differences of lenticulostriate arteries (LSAs) with age. Novel optimized high-resolution 3D T1w
TSE-VFA sequence was utilized as input to the framework. Automated Reeb graph shape analysis
was performed to extract features including vessel length and tortuosity. All quantitative metrics
were compared between the field strengths and two age groups using ANOVA. The mean vessel
length and tortuosity were found to be greater on TOF MRA compared to TSE-VFA. The number
of detected LSAs by both TSE-VFA and TOF MRA was significantly reduced in aged subjects,
while the mean vessel length measured on 7T TSE-VFA showed significant difference between
xxvii
the two age groups. Chapter 4 describes a novel 3D analysis method for localized 3D vessel density
mapping of small vessels of the near whole brain from 3D black-blood MRI at 3T, with sub-
millimeter spatial resolution (isotropic ∼0.5 mm). Using automated vessel segmentation and non-
linear registration, a multimodal method was proposed and comprehensively validated by vessel
landmarks and full annotation of LSAs for localized detection and quantification of small vessel
density changes across populations and brain regions. Voxel-level statistics was performed to
compare regional vessel density between two age groups as well as between aged subjects with
and without vascular risk factors, respectively. Our results indicated that mean vessel density
across the whole brain in available field of view was significantly higher in young subjects
compared to aged subjects with and without vascular risk factors. The aged subjects with vascular
risks showed a trend of reduced mean vessel density compared to the aged subjects without
vascular risk factors. Lastly, Chapter 5 provides the conclusion, some of the ongoing work and
future direction of this research.

xxviii

1
1. CHAPTER 1: General Introduction to the Dissertation
1.1. Novelty and Main Contributions
This dissertation aims to bridge the technical gap in localized analysis of small vessels of
retina and brain using novel in vivo high-resolution imaging technologies. Numerous vessel
enhancement and segmentation methods have been proposed previously (Agam et al. 2005,
Wiemker et al. 2013, Krissian et al. 2000, Frangi et al. 1998, Sato et al. 2000, Li et al. 2003, Erdt
et al. 2008, Zhou et al. 2007, Law and Chung 2010, Jiang et al. 2006, Zhang et al. 2010), however,
robust comparison of vascular changes among different individuals is still challenging due to the
lack of one-to-one correspondence in vessel features. To tackle this challenge, we developed a
novel framework that incorporates vessel segmentation, artifact resolution, registration, and
localized vessel density mapping across subjects. The proposed method is a generalizable
technique that can be applied to localized comparison of small vessels network of both retina and
brain. The technical contributions details of this dissertation are provided in the following sections.
1.1.1. Novel 3D-OCTA Vessel Enhancement and Segmentation
Optical Coherence Tomography Angiography (OCTA) is a novel three-dimensional (3D)
image modality of retinal capillaries at micron resolution. Various challenges including high noise
level, vessel discontinuity, and projection artifact, however, makes it difficult to accurately
reconstruct 3D representation of retinal vasculature from OCTA. Due to these challenges, existing
methods mainly rely on 2D en face images derived from the 3D-OCTA data by maximum intensity
projection ( Zana and Klein 2001, Reif et al. 2012, Zhang et al. 2014, Lee et al. 2014, Eladawi et
al. 2017, Li et al. 2017).

2
In this work, we developed a novel analysis framework to systematically address the
challenges for 3D-OCTA analysis and reconstruct a reliable 3D-OCTA vessel segmentation. To
resolve noise and vessel discontinuity artifact, we optimized a 3D-Curvelet denoising method
(Ying, Demanet and Candes 2005) because it provides a multi-scale representation that matches
well with curvilinear vessel structures of varying sizes in the OCTA data. For the robust application
of curvelet denoising for OCTA data, we developed an automated method for the estimation of
appropriate shrinking threshold of curvelet coefficients. We demonstrate that vessel discontinuity
is greatly reduced with the optimized curvelet denoising method.
Due to OCTA’s dense vessel network, closely located microvasculature, and projection
artifact, vessel enhancement in 3D-OCTA scans is another challenge. Conventional 3D vessel
enhancement and segmentation methods were typically developed for ideal tubular shape vessels
( Law and Chung 2008, Agam et al. 2005, Wiemker et al. 2013, Krissian et al. 2000, Frangi et al.
1998, Sato et al. 2000, Li et al. 2003, Erdt et al. 2008, Zhou et al. 2007, Law and Chung 2010,
Jiang et al. 2006, Zhang et al. 2010), but their direct application to 3D-OCTA images are impacted
by projection artifact, which results in highly deformed and non-tubular appearance of the vessels
in OCTA. To overcome this challenge, we developed a novel vessel enhancement method based
on the eigenvalues generated by the OOF filter. We demonstrate that our method can provide
robust 3D vessel segmentation on large-scale OCTA datasets for both healthy controls and patients
with retinal diseases.
1.1.2. Novel 3D-OCTA Vessel Density Mapping Method
For the comparison of vascular properties across subjects, existing methods primarily use
global or regional measures of vascular features such as vessel length, vessel numbers and
tortuosity (Makita, Fabritius and Yasuno 2008, Yousefi, Liu and Wang 2015, Breger et al. 2017,
3
Kang et al. 2009). Such global measures, however, cannot provide a localized analysis of vascular
changes, which could be more informative for the early detection of vascular pathology. To enable
3D and localized comparison of retinal vasculature between longitudinal scans and across
populations, we developed a new approach for mapping retinal vessel density from OCTA images.
The vessel density mapping is a novel technique not only for OCTA but also in the field of vascular
analysis.
To enable robust comparison of vascular changes among different individuals, one of the main
challenges is the lack of one-to-one correspondence in vessel features. Additionally, in the field of
retina imaging, there are additional challenges caused by pathological subjects such as diabetic
macular edema (DME) that can cause retinal anatomical shape deformation and impose a
significant barrier in localized vessel mapping across OCTA images. To overcome these
limitations, we developed a novel localized OCTA mapping method for the systematic
examination of microvascular changes. Our key developments in this framework include the
development of novel algorithms for vessel density calculation, nonlinear registration method for
OCT images, and the statistical comparison of vessel densities in a common OCT atlas. With this
method, we provide the novel techniques to compare localized vascular difference across patient
groups, and pinpoint retinal vessel changes in longitudinal scans of DME patients.
1.1.3. 3D Vessel Density Mapping of Brain Small Vessels on High Resolution Black Blood
MRI
This study is an extension of our work for 3D-OCTA mapping. Despite some similarities
between the two studies, there are still fundamental differences in the method development due to
the inherit challenges related to the new optimized high-resolution black-blood MRI (iso 0.5mm).
More precisely, 3D cerebral vascular mapping in high resolution black blood MRIs is more
4
challenging compared to retinal vessels mapping due to relatively poor vessel contrast mainly in
the cerebrospinal fluid (CSF) region, varying degrees of noise, and inhomogeneous background.
Additionally, the optimized MRI sequence with TSE-VFA method is only able to acquire near
whole brain coverage (or partial FOV) with high resolution (in less than 10 minutes), where this
partial FOV adds another challenge to the method development.
To tackle these challenges, we developed an automated segmentation and mapping method
for high-resolution black-blood MRI which enables both localized and holistic assessment of
cerebral small vessels. Because visible small vessels in the black-blood MRI are on the order of
single voxel, it is important to carefully examine how existing vessel enhancement filters perform
in this challenging scenario. In our work, we carefully optimized the scale and thresholding
parameters for popular Hessian-based methods (Frangi et al., 1998, Sato et al., 2000, Jerman et al.,
2016) using both synthetic and clinical data. Our evaluation results demonstrated that the Jerman
filter, with optimized parameters, was more robust to noise compared to other candidate methods
and had higher and more uniform response for the small vessels, not only at vessel center, but also
at the vessel periphery. To overcome the challenges that the MRI scans can have different FOVs
across subjects, we developed a novel co-registration method that aligns all vessel density images
in the atlas space with consistent FOVs. After that, we developed localized statistical mapping
method for the comparison of localized vessel density changes across subject. With the novel
method developed in our work, we provide the enabling technique for the non-invasive
quantification of small vessel changes in human brains at the unprecedented resolution, which is
difficult to achieve with previous methods based on digital subtraction angiography (DSA), x-ray
computed tomography angiography, and MR angiography with TOF (Gotoh et al. 2012, Kammerer
et al. 2017, Wardlaw et al. 2013b).
5
1.2. Clinical Importance of Cerebral Small Vessel Disease
With recent improvements in biotechnology and therapies, people are living longer, and the
burden of cognitive impairment in an increasingly aging population has become an important
issue. While Alzheimer’s disease (AD) is the most common cause of dementia, the contribution of
vascular factors to cognitive impairment and dementia is becoming increasingly recognized
(Gorelick et al. 2011). Cerebral small vessel disease (cSVD) is the most common vascular cause
of dementia, a major contributor to mixed dementia, and the cause of about one fifth of all strokes
worldwide (Norrving 2008, Pantoni 2010). The aging population worldwide and the increase in
vascular disease with age has led to projections of major growth in vascular cognitive impairment
and dementia (VCID) over the next 30 years (Gorelick et al. 2011).
The initial degenerative processes that occur in cSVD are poorly understood due to limitations
in clinically available in vivo imaging technology. As shown in Figure 1.1, the current clinical

Figure 1.1 Standards for reporting and imaging of SVD: example findings, schematic representations, and
descriptive imaging characteristics on MRI. Adapted from: Shi, Y and Wardlaw, JM, Stroke and Vascular
Neurology, 2016

6
diagnosis of SVD depend on conventional magnetic resonance imaging (MRI) findings including
lacunar infarcts, white matter lesions (WML), cerebral microbleeds, prominent perivascular
spaces, and secondary brain atrophy (Wardlaw et al. 2009, Shi and Wardlaw 2016). These
parenchymal lesions are the downstream effects of SVD after significant damage has already
appeared, thus these imaging markers may not be ideal surrogate markers of early microvascular
changes.
1.3. Non-contrast In Vivo Neurovascular Imaging
The microvasculature involved in SVD includes small arteries/arterioles (~10µm-1mm),
capillaries (<10µm), and venules (~10-50µm) (Charidimou, Pantoni and Love 2016). To date,
limited in vivo imaging techniques are available to directly assess cerebral small vessels across the
whole brain. Digital subtraction angiography (DSA), x-ray computed tomography angiography,
and MR angiography with TOF have been applied to observe large cerebral vessel remodeling in
clinical populations (Gotoh et al. 2012, Kammerer et al. 2017, Wardlaw et al. 2013b), but the
sensitivity to small vessels such as the perforating arteries is moderate at best and difficult to
characterize and quantify.
Although small vessels are generally supposed to be inaccessible to existing in vivo MRI,
recent development of high-resolution MRI with sub-millimeter spatial resolution has provided at

Figure 1.2 TOF MRA at 7T allows visualization of fine perforating arteries (A, 10 mm thin maximum intensity
projection); 3D T1w TSE with isotropic 0.5 mm resolution at 3T comparably delineates the lenticulostriate arteries
in a healthy subject (B, 10 mm thin minimum intensity projection).

7
least the visualization of the small artery/arteriole end of the microvascular spectrum. For example,
as displayed in Figure 1.2A, high resolution time of flight MR angiography (TOF MRA) at Ultra-
High Field (UHF) 7T allows the visualization of the fine perforating arteries (or arterioles on the
order of a few hundred microns) (Cho et al. 2008). TOF MRA is a non-contrast “bright blood”
imaging technique that is optimized for flow enhancement. However, TOF techniques are
somewhat insensitive to in-plane flow because maximal enhancement of flow can only occur when
the vessel is perpendicular to the plane of imaging (Saloner 1995). Furthermore, to translate the
MRA technique from 7T to 3T for clinical studies, prolonged scan time (> 10 minutes) is required
and/or resolution must be compromised.
A new high-resolution “black blood” MRI technique
developed in the last decade for intracranial vessel wall imaging
at 3T utilizing a 3D turbo spin-echo (TSE) sequence with a
variable flip angle (VFA) scheme (Qiao et al. 2011, Qiao et al.
2014). This method can attain isotropic 0.4-0.5mm spatial
resolution, and the “black blood” contrast is due to the inherent
flow suppression as demonstrated in Figure 1.2B. TSE-VFA is
also able to acquire near whole brain coverage with high
resolution in less than 10 minutes. Implementing this sequence
at 7T produces even greater performance in terms of delineating LSAs with the higher signal-to-
noise ratio (SNR) that can be attained with higher field strength (Figure 1.3).
For the purposes of this dissertation, near whole brain field of view (Figure 1.4C) was chosen
as the focus for imaging with high resolution and high fidelity at both ultra-high magnetic field
strength (UHF 7T) and clinically available field strength (3T) and can capture more details and

Figure 1.3 T1-weighted TSE-VFA
at 3T (top) and 7T (bottom).

8
small vessels compared to 7T-TOF MRA (Figure 1.4B, D). Initially, in Chapter3, we focused our
study on the lenticulostriate arteries (LSAs) (Figure1.4A) which play a significant role in SVD
because they supply the subcortical regions that are involved in executive function and memory
and in Chapter4, near-whole brain scans are utilized for small vessel analysis (Figure1.4C). As
shown in Figure 1.5, these perforating arterioles that are on the order of 500 microns branch off
in a nearly perpendicular manner directly from the high flow middle cerebral artery (MCA)
(Marinković et al. 2001). Consequently, the LSAs are susceptible to either form microaneurysms
that may rupture or become occluded by an embolus or atheroma that may cause a lacunar infarct,
both of which would result in severe negative functional effects (Shi and Wardlaw 2016).
1.4. Clinical Importance of Retinal Vascular Diseases
Retinal vascular diseases are the leading cause of visual impairment in the Western world and
require prompt and accurate diagnosis, monitoring, and treatment. Common retinal vascular
disorders are diabetic retinopathy (DR), hypertensive retinopathy, hypercholesterolemia and
clotting disorders (vein and artery occlusions), macular degeneration (both “wet” or neovascular,
and dry). DR remains as one of the most common complications of diabetes mellitus and the
leading cause of blindness in working age adults in the developed world (de Carlo et al. 2015b,
Kashani et al. 2017, Spaide et al. 2018). Around 285 million individuals world-wide are likely to
have diabetes mellitus. Approximately, 33% have indications of any DR and ~11% have vision-
threatening DR (Lee, Wong and Sabanayagam 2015). One of the major challenges in the diagnosis
and management of DR is that the clinical presentation of the disease appears many years after the
9
diagnosis of diabetes mellitus (Klein 2007). Consequently, it is possible that clinical grading
identifies the disease at a relatively advanced stage of microscopic vascular alterations. Therefore,
there is need for more accurate diagnostics tools that can identify early signs of disease and
visualize microvascular change s. This becomes feasible with the recent advancement in retina
imaging technologies.

Figure 1.4 Optimized T1-weighted VFA TSE at 3T (A, C) and 7T-TOF MRA
(B, D). Imaging at 3T VFA TSE show more details and small vessels.

Figure 1.5 Possible mechanisms occurring at the lenticulostriate arteries
that cause a lacunar infarct. Adapted from: Shi, Y and Wardlaw, JM, Stroke
and Vascular Neurology, 2016.

10
1.5. In Vivo Imaging of Retina
To date, various in vivo imaging
techniques are presented in the clinical
management of retinal vascular diseases.
Fluorescein angiography (FA), and
Indocyanine green angiography (ICG) have
been commonly utilized as a diagnostic tool
in previous studies (Kashani et al. 2017).
FA has been employed extensively to
identify normal and abnormal flow patterns
such as choroidal and retinal
neovascularization and to quantitative
measure blood flow (Bursell et al. 1996,
Kashani et al. 2017). Although FA has been an essential tool for diagnosis of retinal vascular
alteration and disease monitoring, but one of its main limitations is that it requires an invasive dye
injection with a limited “transit window”, which can make imaging challenging in subsequent
frames. More importantly, FA has limited resolution compared to histology and may have a
significant underestimation of retina vascular features. There are studies that showed that
appearance of “nonperfusion” or impaired capillary perfusion in humans is a relatively late finding
on FA, resulting in late diagnosis. ICG assisted in visualization of lesions with recurrent choroidal
neovascularization (Reichel et al. 1995), occult choroidal neovascularization (Guyer et al. 1994),
and choroidal neovascularization complicated with subretinal hemorrhage (Reichel et al. 1995). In
many ways, the limitations of ICG, compared to OCTA, are similar to FA, with the notable

Figure 1.6 Fluorescence angiography (FA) and
indocyanine green angiography (ICGA) of the right eye.
(A) Mid-phase FA showed patchy choroidal filling and
multiple punctate hyperfluorescent lesions. (B) Late-phase
FA showed diffuse leakage and unilobular fluorescence
pooling. (C) Early-phase ICGA (35 sec) showed a
hypofluorescent choroidal filling defect in the macula. (D)
Mid-phase ICGA (4 min) showed a larger area of macular
hypofluorescence due to fluorescence blockage in the areas
of exudative retinal detachment. Adapted from: Yang,Hee
Kyung et al., Korean Journal of Ophthalmology, 2009.

11
improvement in visualization of deeper retinal structures due to its longer emission wavelength.
Examples of FA and ICG images are demonstrated in Figure 1.6.
OCTA is a new imaging technique based on OCT that was FDA approved in 2015. It
provides the visualization of retinal capillaries with micron-level resolution. The principle of
OCTA is to use contrast mechanism in OCT, caused by moving particles, such as red blood cells
(RBC) to construct blood flow imaging (Wang et al. 2007). Figure 1.7 illustrates OCTA scanning
methodology and signal processing scheme. OCTA enables depth-resolved imaging of the retinal
vasculature that is far superior to existing invasive angiography imaging using fluorescein and
approaching histologic resolution (Matsunaga et al. 2014, Spaide et al. 2015). This provides the

Figure 1.7 Illustration of OCTA scanning methodology and signal processing scheme. This figure illustrates the
theoretical difference in the behavior of OCT beams that interact with retinal tissue depending on whether the
beams strike blood vessels or neurosensory retinal tissue. At time T1, two OCT beams are incident on the retinal
tissue. Beam A1 (red) strikes a retinal artery while beam A2 (blue) strikes adjacent neurosensory retinal tissue
that is static. Each beam is back-scattered and generates an A-scan signal shown in the middle. Similarly, at time
T2 another scan is performed and illustrated. The interaction of the incident light from beam A1 with moving red
blood cells causes more variability in the OCT signal from beam A1 as illustrated in the A-scan signal traces.
These signals are then “averaged” as shown by the black arrows to generate a composite OCTA signal that is
illustrated in the far right of the panel. The increased variability of the OCT signal from beam A1 is illustrated
and is localized to the regions where red blood cell movement occurred. A sample B-scan is illustrated in the
lower right of the panel. Adapted from: A.H. Kashnai et al, Progress in Retinal and Eye Research, 2017.

12
separation of the retinal capillaries into two (or more) capillary plexus usually referred to as the
superficial and deep retinal layers (Campbell et al. 2017, Matsunaga et al. 2014). Figure 1.8
demonstrates an example OCTA of a normal subject with three different field of views. In previous
studies (de Carlo et al. 2015a, Kashani et al. 2017, Spaide et al. 2018), OCTA has been successfully
applied to study various ophthalmic diseases such as age-related macular degeneration (AMD),
uveitis, vein occlusions, glaucoma, and diabetic retinopathy (DR).
1.6. 3D Vessel Segmentation
Different methods have been proposed in the literature for enhancement and segmentation of
vascular structures both in 2D and 3D. Conventional filtering methods have been widely used for
enhancement of vascular structures, among them image derivatives, mainly Hessian-based
methods are the most popular method which will be explained thoroughly in the following section.
Alternative to the Hessian matrix is the Weingarten matrix (Jiang, Ji and McEwen 2006), which
combines first and second order derivatives. Vessel enhancement diffusion (Manniesing,
Viergever and Niessen 2006) that integrates Hessian and diffusion filtering is also designed to
further reduce the impact of background noise. To better preserve vascular boundaries, methods
based on gradient vector flow (Bauer and Bischof 2008) or oriented flux (Lee et al. 2014, Law and

Figure 1.8 Demonstration of various field-of-views in OCTA. (A) 3 * 3mm2 (B) 6 * 6mm2 and (C) 8 * 8mm2 field-
of-view pseudo-colored OCTA of a normal subject. Red represents superficial retinal layer. Green represents deep
retinal layer. Yellow represents regions of overlay. Images are from an AngioPlex™ device (Carl Zeiss Meditec).
Adapted from: A.H. Kashnai et al, Progress in Retinal and Eye Research, 2017.

13
Chung 2008) were also employed. Also, matched filters are still widely utilized in 2D vessel
enhancement, however due to computational burden these techniques are less suitable for 3D
applications.
Given the recent rapid improvements in computing resources, machine learning (ML) and
deep learning (DL) models have emerged as a groundbreaking tool for medical image computing
(Zaharchuk et al. 2018). In particular, DL network architectures such as 3D U-Net and
HighRes3DNet and more recently attention networks have shown great potential in the application
of medical image segmentation. The 3D U-Net is one of the most popular neural network
architectures in segmentation of volumetric objects (Ronneberger, Fischer and Brox 2015, Çiçek
et al. 2016). It relies heavily on data augmentation to maximize the efficiency of the annotated
samples through a fully convolutional network and can potentially achieve a promising
segmentation result even for small training sample size. HighRes3DNet (Li et al. 2017) was
designed for the segmentation of fine structures in volumetric images, and it seems to be a great
fit for automatic small vessels segmentation.
The performance of learning-based methods highly depends on the training data which is
incredibly challenging and time consuming to obtain for small vessel segmentation task in high
resolution images with vascular scales in the order of a few hundred microns. Due to this limitation,
most of the developed DL based methods are currently limited to 2D images (e.g. Fundus, 2D
projection of OCTA or MRA) or 3D images for larger scale vessels (e.g. Circle of Willis from
TOF MRA) (Livne et al. 2019, Phellan et al. 2017). In this dissertation, we collected 3D OCTA
with micron level resolution for retina vascular modeling, and 3D High-resolution black blood
MRIs for LSA and near-whole brain small vessel analysis. Vessels of interest were segmented by
Hessian-based methods or their adaptation. The feasibility of performing segmentation was tested
14
to demonstrate that small vessels from high-resolution retina and brain images can be
automatically segmented with optimal performance for visualization ,morphological
quantification and density mapping.
1.6.1. Hessian-Based Methods for Vessel Enhancement
To overcome the undesired intensity variations of angiographic images and to suppress non-
vascular structures, numerous filter-based enhancement methods have been proposed (Agam,
Armato and Wu 2005, Wiemker et al. 2013, Krissian et al. 2000, Frangi et al. 1998, Sato et al.
2000, Li, Sone and Doi 2003, Erdt, Raspe and Suehling 2008, Zhou et al. 2007, Law and Chung
2010, Jiang et al. 2006, Zhang, Zhang and Karray 2010), and their performance have been
significantly improved recently. Among these filtering methods, first order (Agam et al. 2005,
Wiemker et al. 2013, Krissian et al. 2000) and second order (Frangi et al. 1998, Sato et al. 1998,
Sato et al. 2000, Li et al. 2003, Erdt et al. 2008, Zhou et al. 2007, Jerman et al. 2016) image
derivatives are widely used, which encode border/or boundary and shape information of the
underlying image structures, respectively. Methods based on first order derivatives are generally
more susceptible to presence of noise and non-uniform background. Therefore, this class of
methods is not the preferred approach for vascular enhancement in presence of inhomogeneous
background. A large group of methods employs the Hessian matrix analysis (Frangi et al. 1998,
Sato et al. 1998, Sato et al. 2000, Li et al. 2003, Erdt et al. 2008, Zhou et al. 2007) which is based
on second order image derivatives and enables distinction among rounded, tubular, and planar
structures. Generally, these filtering techniques employ the eigen analysis of the Hessian matrix,
which is based on the second order image derivatives, to differentiate among underlying local
image geometry such as rounded, tubular and planer structures. To enhance the local structures of
15
different sizes, a certain enhancement function is maximized across Gaussian scale space of the
image.
Let I(x) imply the intensity of a D-dimensional image at coordinate 𝑋 = [𝑥 1
,𝑥 2
,….,𝑥 𝐷 ]
𝑇 ,
then the Hessian of I(x) at scale s is defined by a 𝐷 ×𝐷 matrix as:
𝐻 𝑖𝑗
(𝑋 ,𝑠 )= 𝑠 2
𝐼 (𝑥 )∗
𝜕 2
𝜕𝑥
𝑖 𝜕𝑥
𝑗 𝐺 (𝑋 ,𝑠 ) 𝑓𝑜𝑟 𝑖 ,𝑗 =1,…,𝐷 (2)
Where, 𝐺 (𝑋 ,𝑠 )=(2𝜋 𝑠 2
)
−𝐷 /2
exp(−
𝑋 𝑇 𝑋 2𝑠 2
) is a D-variate Gaussian and * indicates convolution.
The eigenvalues of H can be computed analytically (Kopp 2008) through eigen decomposition of
the Hessian Matrix, i.e., 𝑒𝑖𝑔 𝐻 (𝑋 ,𝑠 )→ 𝜆 𝑖 ,𝑖 =1,…,𝐷 . Local image structures can be identified
by analyzing the signs and magnitudes of Hessian eigenvalues. For 3D image, there are three eigen
values. If we sort them based on their magnitudes: |𝜆 𝑖 |≤ |𝜆 𝑖 +1
| ;𝑖 =1,..,3, vessels ideally
resemble as tube-like or elongated structures, and their relationship of Hessian eigenvalues could
be indicated as: 𝜆 2
≈ 𝜆 3
∧ |𝜆 2,3
|≫0 ∧ 𝜆 1
≈ 0. Furthermore, the positive (negative) sign of
𝜆 2
and 𝜆 3
denotes a dark (bright) vessel on a bright (dark) background. Ultimately, a multiscale
filter response 𝐹 (𝑥 ) is acquired by maximizing the given enhancement function 𝑉 , at each image
point x, over the scale range s as:
𝐹 (𝑥 )=sup {𝑉 [𝑒𝑖𝑔 𝐻 (𝑥 ,𝑠 )]:𝑠 𝑚𝑖𝑛 ≤𝑠 ≤𝑠 𝑚𝑎𝑥
} (3)
Where, 𝑠 𝑚𝑖𝑛 ,𝑠 𝑚𝑎𝑥
are the minimum and maximum vessels’ radii in the vascular structure of
interest.
The core of Hessian-based filters is the enhancement function V, also referred to as vesselness
measure or response, which is a mathematical expression involving the eigenvalues of Hessian
matrix. The widely used Frangi’s filter, utilized all eigenvalues of the Hessian to define the
vesselness measure, 𝑉 (𝑠 )= (1−exp (−
𝑅 𝐴 2
2𝛼 2
)) exp (−
𝑅 𝛽 2
2𝛽 2
) ( 1−exp(
𝑆 2
2𝐶 2
)) , (4)
16
Where: 𝑅 𝐴 =
|𝜆 2
|
|𝜆 3
|
, 𝑅 𝐵 =
|𝜆 1
|
√|𝜆 2
𝜆 3
|
, 𝑆 = ‖𝐻 ‖
𝐹 = √∑ 𝜆 𝑗 2
𝑗 ≤3
. 𝑅 𝐴 , 𝑅 𝐵 are geometric ratios,
where the first ratio accounts for distinguishing between plate-like and line-like structure and the
second ratio accounts for deviation from blob-like pattern. “S” is the “second order structure” that
is defined by Frobenius Hessian-matrix norm and can discriminate structure versus background
voxels.
Sato’s more recent enhancement function (Sato et al. 2000), also incorporated all three
eigenvalues in defining 3D line (𝜆 3
≈𝜆 2
≪ 𝜆 1
≈ 0 ) structure. The proposed enhancement
function by Sato is: 𝑉 𝑠 = |𝜆 3
|(
𝜆 2
𝜆 3
)
𝛾 (1+
𝜆 1
|𝜆 2
|
)
𝛾 , the parameter 𝛾 controls the sensitivity to
elongated structures and usually set to 0.5 or 1.
More recent development, Jerman’s enhancement function(Jerman et al. 2016) , is inspired by
the volume ratio (𝑉𝑅 = 𝜆 1
𝜆 2
𝜆 3
[
3
𝜆 1
+ 𝜆 2
+ 𝜆 3
]
3
) measure for detection of nearly spherical diffusion
tensors (Peeters et al. 2009). To ensure the robustness of vesselness measure to low magnitudes
of 𝜆 2
and 𝜆 3
, the regularized value of 𝜆 3
was proposed at each scale s as:
𝜆 𝜌 (𝑠 )
= {
𝜆 3
𝑖𝑓 𝜆 3
>𝜏 𝑚𝑎𝑥 𝑋 𝜆 3
(𝑋 ,𝑠 )
𝜏 max
𝑥 𝜆 3
(𝑋 ,𝑠 ) 𝑖𝑓 0< 𝜆 3
≤𝜏 𝑚𝑎𝑥 𝑋 𝜆 3
(𝑋 ,𝑠 )
0 𝑜𝑡 ℎ𝑒𝑟𝑤𝑖 𝑠𝑒 .
(5)
Where, 𝜏 is a cutoff threshold between zero and one. Higher value of 𝜏 increases the difference
between 𝜆 2
and 𝜆 3
magnitudes for low contrast structures. By utilizing 𝜆 𝜌 and some
modifications to VR (introducing 𝜆 1
→(𝜆 2
−𝜆 1
) to indicate both spherical and elongated
structures, removing 𝜆 1
, introducing 𝜆 𝜌 →(𝜆 𝜌 −𝜆 2
) and 𝜆 2
≤ 𝜆 𝜌 /2 to account for elliptic
cross-sections), the ultimate enhancement function was computed as:
17
𝑉 𝑝 =
{

0 𝑖𝑓 𝜆 2
≤0 ⋀ 𝜆 𝜌 ≤0
1 𝑖𝑓 𝜆 2
≥
𝜆 𝜌 2
>0
𝜆 2
2
(𝜆 𝜌 − 𝜆 2
)(
3
𝜆 2
+ 𝜆 𝜌 )
3
𝑜𝑡 ℎ𝑒𝑟𝑤𝑖𝑠𝑒 .
(6)
The proposed enhancement function’s response values range from 0 to 1.
Comparison of the mentioned enhancement functions and the impact of important
parameters, mainly for Jerman filter, will be discussed further in the following sections.
1.6.2. Comparison of Hessian-Based Methods on Synthetic Data
To assess and compare the Hessian-based methods with respect to detection rate of vessels
with different sizes, robustness to noise, and response profile at different vessel scales, a synthetic
image (Figure 1.9 (a)) has been generated with resolution matching the MRI clinical data (iso
0.5mm). In the synthetic data, the largest vessel’ diameter is two voxels (1mm), and the smallest
vessels’ diameter is one voxel (0.5 mm). Therefore, the radius of vessels in the synthetic data,
which corresponds to the scale of the Hessian-based methods, is in the range of [0.25mm-0.5mm].
To verify the scale of the vessels that can be detected, initially multiple commonly used
Hessian-based methods such as Frangi’s, Sato’s and Jerman’s were applied to the synthetic data.
The scale range of the Hessian-based methods, which is correlated to vessels’ radius, was set to
[0.1-0.4] to achieve the best segmentation performance. This smaller scale-range (compared to
ground-truth) was defined in order to improve the inclusion of small vessels in the detection
response of continuous Hessian-based methods applied on digital synthetic data. The filter
responses or vesselness maps from Jerman’s, Frangi’s and Sato’s were scaled between 0 and 1 and
then thresholded to construct the corresponding binary vessel mask (BVM) (Figure 1.9 (b-d)). As
shown in Figure 1.9 (b-d), all three candidate methods can detect the vessels of the synthetic data
with the radius between 0.25mm and 0.5mm.
18
To assess the robustness to noise, a multi-scale vessel probability map (vesselness response)
was computed by the Jerman’s, Frangi’s and Sato’s filters from the synthetic image, where
Gaussian noise with varying standard deviations (SD) from 0.3 to 1 were added to the synthetic
image (Figure 1.9 (a)) to create the image to be analyzed. Dice similarity (𝐷 =2×
|𝐴 ∩𝐵 |
|𝐴 |+ |𝐵 |
), where
A is the ground truth from synthetic image and B is the segmentation result of the noisy image,
was calculated at varying Gaussian noise levels (SD = [0.3-1]). Dice unitless values range from
minimum of zero when there is no overlap between the image pairs and maximum of one for two
identical regions, better performance is indicated by higher Dice values. As shown in Figure 1.9
(e), Jerman filter is more robust to noise and has better Dice-similarity value compared to Frangi’s
and Sato’s methods.

Figure 1.9 3D vessel segmentation results and response profile of Hessian-based methods on synthetic data. (a)
Synthetic image with vessels of different sizes, (b-d) the results of Jerman’s, Frangi’s and Sato’s filters,
respectively. (e) The comparison plots of the three methods using dice similarity metric on synthetic image with
additive Gaussian noise with variable SD. (f, g) Vesselness response profile of all three-methods annotated by f
and g lines in (a). Overall, compared to Frangi’s and Sato’s methods, Jerman filter is more robust to noise and
has higher and close-to-uniform response profile inside all the vascular structures of different scales.

19
To compare the response of vesselness measure within vascular structures, cross-sectional
profile of two vessels with radius of 0.5mm and 0.25mm are demonstrated in Figure 1.9 (f) and
Figure 1.9 (g), respectively. Different from Frangi’s and Sato’s functions, Jerman’s response has
a high and close-to-uniform profile inside all the vessels of different radius (Figure 1.9 (f, g)).
This property of Jerman’s response is achieved by fine tuning the value of Ƭ (cutoff threshold) in
(5). Choosing a high value for Ƭ would increase the difference between the magnitudes of 𝜆 2
and
𝜆 3
which will result in better performance of vessel enhancement in low contrast regions and
increase the response uniformity.
1.7. 3D Image Registration and Tensor-based Morphometry
In this dissertation, our focus is on retina and brain vessel density mapping (or registration)
using novel 3D imaging technologies such as OCT, OCTA (that is derived from OCT by contrast
mechanism) for volumetric imaging of retina and high-resolution black blood MRI for 3D high-
resolution imaging of cerebral small vascular network in brain. In this section, we will first provide
a general introduction and overview of image registration methods mainly for medical images
using different image modalities for retina and brain. Since OCT and OCTA are novel imaging
techniques compared to MRI, we will provide more comprehensive review of the registration
literature for these modalities. Afterwards, we look at the tensor-based morphometry methods that
is extensively used in brain imaging and in this dissertation, the localized comparison of vessel
densities across population is inspired by the previous work in anatomical deformation analysis in
retina and brain using this category of methods.
Image registration is a computational technique for finding one-to-one correspondence
between two or more images. The purpose of image registration is to discover the optimal
transformation for aligning the structures of interest in the input images. This method has been
20
extensively employed in field of medical image processing (Toga and Thompson. 2001, Zitová
and Flusser. 2003, Oliveira and Tavares. 2014, Murphy et al. 2008, Teng, Shapiro and Kalet. 2010,
Gavaghan et al., 2011). Some example applications of image registration in the medical field
include fusion of anatomical images from computerized tomography (CT) or magnetic resonance
imaging (MRI) images with functional images from positron emission tomography (PET), single-
photon emission computed tomography (SPECT) or functional magnetic resonance imaging;
intervention and treatment planning (Gering et al. 2001, Staring et al. 2009); computer-aided
diagnosis and disease following-up (Huang et al. 2009); atlas building and comparison
(Freeborough and Fox 1998, Joshi et al. 2004, Leow et al. 2006, Gooya, Biros and Davatzikos
2011). Medical image registration methods have been proposed for almost all anatomic organs of
the human body including brain (Maes et al. 1997, Gering et al. 2001, Shen and Davatzikos 2002,
Hipwell et al. 2003, Xie and Farin 2004, Xu et al. 2009, Mayer et al. 2011), retina (Stewart, Tsai
and Roysam 2003, Matsopoulos et al. 2004, Lin and Medioni 2008, Tsai et al. 2009), and vascular
structures (Hipwell et al. 2003, Groher, Zikic and Navab 2009, Ruijters, ter Haar Romeny and
Suetens 2009).
Registration of OCT and OCTA images have been presented previously to assess treatment
efficiency (Lee et al., 2015), providing insight about retinal diseases (Antony et al., 2016)(Lee et
al., 2015)(Chen et al., 2014), correcting motion artifacts (Kraus et al., 2012) and assisting with
OCT layer segmentation (Niemeijer et al., 2012)(Duan et al., 2018). Within subject registration of
3D-OCTA has been performed to align vascular pattern of repeated scans of healthy subjects
(Zhang et al., 2019). However, between-subject OCTA registration, which is one of the focuses of
this dissertation, is not feasible due to lack of features that can be reliably used for guiding
registration. In fact, vascular patterns are the predominant features in OCTA which have a
21
stochastic distribution and are not expected to match across subjects. However, since OCTA is
constructed by subtracting several OCT images, the same registration for OCT volumes is
applicable to OCTA images. In OCT, retinal layer boundaries and foveal pit are considered as
distinctive features across subjects (Khansari et al., 2020). These features can be used for reliable
between and within subjects’ registration of OCT image volumes. In fact, several methods have
been developed for cross-subject OCT registration (Gibson et al., 2010, Lee et al., 2015, Chen et
al., 2014). In a recent work by our research group, (Khansari et al., 2020) developed an automated
3D registration technique for cross-subject OCT image registration in DR subjects. This technique
consisted of an initial restricted affine transformation to define anatomically consistent volume of
interest. Afterwards, an efficient B-spline transformation using stochastic gradient descent is
performed to align layers boundaries and foveal pit. By registering each OCT volume to the atlas
volume and computing the Jacobian determinant from the atlas for each subject, we can perform

Figure 1.10 Example 3D registration and Jacobian maps using non-linear registration of OCT image volumes in
2 PDR subjects demonstrated by a cut through the volume. (a) OCT volume of the first PDR subject with visible
diabetic macular edema and alterations in shape of foveal pit. (b) Cut through the atlas which represents retinal
structure of healthy OCT volumes. (c) Color-coded Jacobian map demonstrating magnitude of localized
contraction and expansion for the first PDR subject. (d) OCT volume of the second PDR subject with visible tissue
loss. (e) Cut through the atlas which represent retinal structure of healthy subjects. (f) Color-coded Jacobian map
demonstrating magnitude of localized contraction and expansion. Adapted from Kashani et al. Past, present and
future role of retinal imaging in neurodegenerative disease, 2021

22
tensor-based morphometry (TBM) for comparison of retinal structure in different DR stages. TBM
is an image analysis technique that can detect and quantify regional structural differences from the
gradients of the nonlinear deformation fields that ‘warp’ images to a common anatomical template
(Ashburner, Friston and Penny 2003). At each voxel, a Jacobian determinant value indicates local
volume expansion or deficit compared to the corresponding anatomical structures in the template
(Freeborough and Fox 1998, Chung et al. 2001, Fox et al. 2001, Riddle et al. 2004). TBM has been
extensively utilized in neuroimaging to detect and characterize disorders such as Alzheimer’s
disease (AD), and schizophrenia (Freeborough and Fox 1998, Chung et al. 2001, Fox et al. 2001,
Riddle et al. 2004).
In the proposed OCT registration framework by our group (Khansari et al. 2019), the Jacobian
determinant of the non-linear deformation was used to visualize tissue expansion and contraction
in DR subjects. Tensor-based morphometry (TBM) was performed for detection of group localized
structural changes in different stages of DR. Figure 1.10 shows example non-linear registration of
OCT of DR subjects with diabetic macular edema to the atlas which is generated from healthy
subjects. Color-coded Jacobian maps show magnitude of local expansion and constriction. Once
OCT of different subjects are registered, the transformation can be applied to the corresponding
OCTA image volume of each subject. The idea of OCTA vessel density mapping in this
dissertation is adopted from our previous work in OCT that allows meaningful layer-based analysis
of vascular morphology in OCTA (Sarabi et al., 2019).
1.8. Overview of Studies
This dissertation aims to bridge the technical gap in systematic analyses of small vessel
diseases using novel high-resolution imaging technologies of retina and brain. To this end we
developed 3D state-of-the-art generalizable techniques and automatic tools for small vessel
23
detection, localized vessel density mapping, and quantification of vascular morphological features
and demonstrate the utility of the developed frameworks in novel clinical applications.
3D Retinal Vessel Density Mapping with OCT-Angiography
In Chapter 2, a novel multimodal 3D framework is proposed by utilizing information from
OCT and OCTA to detect localized capillary changes at voxel-level between longitudinal scans
and across populations. We first obtain a high-quality 3D representation of OCTA-based vessel
networks via curvelet denoising and optimally oriented flux (OOF). Then, a vessel density image
(VDI) is constructed by diffusing the vessel mask derived from OOF-based analysis to the entire
image volume. Subsequently, we utilize a nonlinear, 3D OCT image registration method to provide
localized comparisons of retinal vasculature across subjects. In our experimental results, we
demonstrate an application of our method for longitudinal qualitative analysis of two pathological
subjects with edema during the course of clinical care. Additionally, we quantitatively validate our
method on synthetic data with simulated capillary dropout, a dataset obtained from a normal
control (NC) population divided into two age groups and a dataset obtained from patients with
diabetic retinopathy (DR). Our results show that we can successfully detect localized vascular
changes caused by simulated capillary loss, normal aging, and DR pathology even in presence of
edema.
Shape-Reeb graph analysis method for LSA morphological quantification
In Chapter 3, the feasibility of visualization, characterization and Shape-Reeb based
morphological quantification of LSAs at both 3 T and 7 T using optimized high-resolution 3D T1-
weighted turbo spin echo sequence with a variable flip angle (T1w TSE-VFA) scheme is presented.
Automated Reeb graph shape analysis was performed to extract features including vessel length
and tortuosity. All quantitative metrics are compared between the two field strengths and two age
24
groups using ANOVA. Using optimized 3D T1w TSE-VFA at 3T and 7T, a greater number of
LSA branches can be detected compared to those by time-of-flight MR angiography (TOF MRA)
at 7T. The mean vessel length and tortuosity are greater on TOF MRA compared to TSE-VFA.
The number of detected LSAs by both TSE-VFA and TOF MRA was significantly reduced in aged
subjects, while the mean vessel length measured on 7T TSE-VFA showed significant difference
between the two age groups.
Vessel Density Mapping of Brain Small Vessels on 3D High Resolution Black Blood MRI
Chapter 4 describes a novel 3D semiautomatic framework for segmenting, quantifying, and
regional vessel density mapping of brain small vessels in high resolution (isotropic ~0.5mm) black-
blood MRI with near whole-brain coverage of young and aged subjects at 3T. Skull-stripped high
resolution black-blood MRIs were first preprocessed via bias correction and non-local means
(NLM) denoising. Hessian-based vessel segmentation methods (Jerman, Frangi and Sato filter)
were evaluated by vessel landmarks and manual annotation of LSAs. Using optimized vessel
segmentation and non-linear registration, a semiautomatic pipeline was proposed for localized
detection of small vessel density changes across population and brain regions. Voxel-level
statistics was performed to compare regional vessel density between two age groups as well as
between aged subjects with and without vascular risk factors, respectively. According to the
results, Jerman filter showed better performance for vessel segmentation than Frangi and Sato
filter which was employed in our pipeline. Cerebral small vessels on the order of few hundred
microns can be delineated using the proposed pipeline on 3D black-blood MRI at 3T. The mean
vessel density across the whole brain was significantly higher in young subjects compared to aged
subjects with and without vascular risk factors. The aged subjects with vascular risks showed a
trend of reduced mean vessel density compared to the aged subjects without vascular risk factors.
25
2. CHAPTER 2: 3D Retinal Vessel Density Mapping with OCT-Angiography
2.1. Abstract
Optical Coherence Tomography Angiography (OCTA) is a novel, non-invasive imaging
modality of retinal capillaries at micron resolution. Recent studies have correlated macular OCTA
vascular measures with retinal disease severity and supported their use as a diagnostic tool.
However, these measurements mostly rely on a few summary statistics in retinal layers or regions
of interest in the two-dimensional (2D) en face projection images. To enable 3D and localized
comparisons of retinal vasculature between longitudinal scans and across populations, we develop
a novel approach for mapping retinal vessel density from OCTA images. We first obtain a high-
quality 3D representation of OCTA-based vessel networks via curvelet-based denoising and
optimally oriented flux (OOF). Then, an effective 3D retinal vessel density mapping method is
proposed. In this framework, a vessel density image (VDI) is constructed by diffusing the vessel
mask derived from OOF-based analysis to the entire image volume. Subsequently, we utilize a
non-linear, 3D OCT image registration method to provide localized comparisons of retinal
vasculature across subjects. In our experimental results, we demonstrate an application of our
method for longitudinal qualitative analysis of two pathological subjects with edema during the
course of clinical care. Additionally, we quantitatively validate our method on synthetic data with
simulated capillary dropout, a dataset obtained from a normal control (NC) population divided into
two age groups and a dataset obtained from patients with diabetic retinopathy (DR). Our results
show that we can successfully detect localized vascular changes caused by simulated capillary
loss, normal aging, and DR pathology even in presence of edema. These results demonstrate the
potential of the proposed framework in localized detection of microvascular changes and
monitoring retinal disease progression.
26
2.2. Introduction
Optical Coherence Tomography Angiography (OCTA) is a novel and non-invasive image
modality that is clinically approved to evaluate the retinal vasculature (Wang et al. 2007, Zhang et
al. 2015, Chen and Wang 2017, Spaide et al. 2018, Drexler and Fujimoto 2008). OCTA has been
successfully applied to study various ophthalmic diseases such as age-related macular
degeneration (AMD), uveitis, vein occlusions, glaucoma, and diabetic retinopathy (DR), which is
one of the most common complications of diabetes mellitus and the leading cause of visual
impairment in working age adults in the developed world (de Carlo et al. 2015b, Kashani et al.
2017, Spaide et al. 2018). In this work, we develop a novel 3D analysis method for OCTA based
on localized mapping of vessel density changes and demonstrate its application in clinical research.
One major advantage of OCTA is its ability to depth-resolve retinal vascular networks at
capillary level (where pathologic changes in many retinal vascular diseases occur first) (Alterman
and Henkind 1968, Ashton 1970, Daicker 1976, Sun and Smith 2018). While OCTA imaging
devices provide three-dimensional (3D) image volumes, current studies still largely perform their
analyses on two-dimensional (2D) en face projection images, which results in an inevitable
information loss because of the overlap of 3D vascular networks after their projection onto a 2D
plane. Although current OCTA 2D analytical methods have shown their clinical value (Chu et al.
2016, Durbin et al. 2017, Kim et al. 2016), 3D analysis of OCTA could better represent vasculature
structures and potentially enhance our understanding of retinal diseases. Moreover, existing
analytical methods primarily use global measures or summary statistics derived from 2D en face
projection images for retinal quantification. But global measures cannot provide a localized
analysis of vascular changes, which could be more informative from a clinical perspective and
potentially enable early diagnosis and treatment monitoring of retinal diseases. Additionally, some
27
pathologies such as diabetic macular edema (DME) cause retinal anatomical deformation and
impose a significant barrier in quantitative analysis across OCTA images. Due to technical
limitations and data availability, exploring the dynamics of localized capillary changes over time
also remains challenging in OCTA, especially for DME subjects. To overcome these limitations,
there is thus a need of 3D and localized analysis of OCTA for the systematic study of
microvascular changes in retina diseases.
Recent studies have demonstrated that 3D analysis of OCTA can improve visualization and
detection of retinal microvascular changes. Spaide et al. (Chen et al. 2016, Spaide 2016, Spaide et
al. 2017), demonstrated that 3D volume rendering analysis of OCTA data can reveal useful
information about the correlation of intraretinal fluid and retinal capillaries. Another recent study
showed that 3D vessel density in OCTA can more effectively quantify foveal ischemia in DR
compared to the 2D vessel density (Wang et al. 2019). An automated 3D shape representation
framework (Zhang et al. 2019b), which provides a new way for the analysis of the geometric and

Figure 2.1 Method overview. (a) Selected en face view of original OCTA. (b) OCTA preprocessing steps: (b-1) En
face view of 3D-Curvelet denoised OCTA from (a), (b-2) En face view of 3D-Enhanced OCTA obtained by applying
OOF vessel enhancement to (b-1). (b-3) En face view of binary vessel mask (BVM) obtained by applying Otsu’s
global thresholding on (b-2). (c) OCTA vessel density image (VDI) generated from the BVM in (b-3). (d) OCT non-
linear registration for finding transformation of each image to the atlas space. These transformations are later
applied to bring VDIs into the atlas space allowing localized capillary quantification. (d-row1) An OCT
representing the atlas and (d-row2) example of a moving OCT that will be registered to the atlas space. (e)
Registered VDI to the atlas space (e-row1) obtained by applying the non-linear warp computed in (d) to the VDI
of the moving scan (e-row2). The dashed red line in (d, e) is fixed in the atlas space and used to visualize the
relative position of the moving scan and associated VDI before and after registration.

28
topological information in OCTA, was proposed recently by our group and has been applied
successfully to detect vascular changes in DR (Zhang, Kashani and Shi 2019a).
In this work, we develop a novel analysis framework for OCTA to enable localized 3D vessel
density mapping (Figure 2.1). There are two main modules in this framework: 1) preprocessing
to generate binary vessel segmentation from original OCTA, and 2) 3D vessel density mapping to
enable localized comparison of retinal vasculature across subjects. In the first step, we employed
our previously validated 3D vessel enhancement module (Sarabi et al. 2019, Zhang et al. 2019c)
to resolve noise and vessel discontinuity in OCTA volume via curvelet transforms (Candes and
Donoho 2005, Ying, Demanet and Candes 2005) and optimally oriented flux (OOF) (Law and
Chung 2008). The binarized vessel mask is then obtained by applying Otsu’s global thresholding
(Otsu 1979) on the OOF vesselness response. For localized vessel density analysis between
longitudinal scans and across population, we first calculate a vessel density image (VDI) that
extends the information of the vessel mask to the whole image volume. After that, we implement
a non-linear, 3D OCT registration approach developed recently in our group (Khansari et al. 2019)
to pool the VDI from all subjects into a common space, which enables the localized mapping of
vessel density changes across different subjects and patient groups. The main contributions of this
work can be summarized as follows:
I. A novel multimodal 3D framework is proposed by utilizing information from OCT and
OCTA to detect localized capillary changes at voxel-level between longitudinal scans
and across populations.
II. Present a capillary dropout simulation algorithm to generate syntetic groud truth data and
verify the robustness and detection-rate of the proposed method in localizing capillary
dropout, and to validate current work with different parameter settings.
29
III. Show application of the proposed method in three clinical trends (vascular changes in
DME during the course of clinical care, capillary loss in DR, and capillary loss in normal
aging) to demonstrate the efficacy of our method in detecting a localized pattern of
capillary loss.
2.3. Related Work
OCTA microvasculature morphology is often compromised by high noise levels, vessel
discontinuities and low vessel visibility that mainly affect the appearance of the small capillaries.
To enable the reliable analysis of retinal microvasculature in OCTA, it is important to apply
appropriate preprocessing steps to extract vessel-related signals. In this section, we provide a
summary of related works adopted in our OCTA preprocessing steps as shown in Figure. 1 (b).
For the denoising of OCTA images, we adopt curvelet-based analysis (Candès et al. 2006).
Several properties of the curvelet model make it an appropriate tool for 3D OCTA denoising.
Curvelet is a multiscale transform with high directional sensitivity and anisotropic characteristics
due to its needle-shaped frame elements and provides an efficient representation of edges and other
singularities along curves (Candès et al. 2006). The anisotropic property of this transformation
matches well with retinal vessel geometry since OCTA voxels do not have cubic shape. Moreover,
curvelets can be effectively used for elongated feature recovery, making it a proper tool for
resolving OCTA vessel discontinuity. In retinal image processing, the 3D curvelet transform was
previously applied to OCT (Jian et al. 2010) and OCTA (Zhang et al. 2019c, Sarabi et al. 2019)
to reduce the speckle noise. For numerical implementation, 3D Fast Discrete Curvelet Transform
(FDCT) based on second-generation curvelet transform (Candes and Donoho 2005, Candès and
Donoho 2004) was used for OCTA denoising and vessel enhancement (Sarabi et al. 2019, Zhang
et al. 2019c).
30
Vessel enhancement is another critical component of OCTA preprocessing (Figure. 1 (b-2)).
Among the most popular vessel enhancement filters such as Frangi vesselness (FV) (Frangi et al.
1998), optimally orientated flux (OOF) (Law and Chung 2008) and its improvements (Law and
Chung 2009, Law and Chung 2010), OOF has been successfully employed and adapted to improve
the multi-scale and multi-orientation vessel network in OCTA (Sarabi et al. 2019, Zhang et al.
2019c). OOF is a localized multi-scale curvilinear structure detector that computes the vesselness
measure based on the projected image gradient at the boundary of a spherical region centered at
every image voxel. One of the main advantages of OOF is its ability in providing accurate and
stable detection responses in presence of closely located adjacent structures (Law and Chung
2008). This makes OOF a suitable choice to provide an enhanced vesselness map for OCTA with
dense microvasculature structure. The quadratic form of OOF function is defined as a symmetric
matrix 𝑄 (𝑥 ; 𝑟 ) that can be decomposed as 𝑄 (𝒙 ; 𝑟 )= ∑ 𝜆 𝑖 3
𝑖 =1
(𝒙 ,𝑟 )𝑣 𝑖 ⃗⃗⃗ (𝒙 ,𝑟 )𝑣 𝑖 ⃗⃗⃗ (𝒙 ,𝑟 )
𝑇 , where
𝜆 𝑖 (𝒙 ,𝑟 ) and 𝑣 𝑖 ⃗⃗⃗ (𝒙 ,𝑟 ) are eigenvalues and eigenvectors in a local 3D spherical region (𝑥 =
(𝑥 ; 𝑦 ; 𝑧 )) with radius 𝑟 . For 3D images, there are three sets of eigenvectors and eigenvalues. If
the vessels are ideally represented as tubular shapes in the image, the first two eigenvalues would
be much smaller than the third one, i.e., 𝜆 1
(.)≤𝜆 2
(.)≪𝜆 3
≈0. Correspondingly, the first two
eigenvectors span the vessel’s normal plane while the third one represents vessel orientation. These
eigenvalues thus provide valuable information about vessel geometry and can be used to define
vesselness maps in both 2D and 3D images (Law and Chung 2008).
In summary, the curvelet-based denoising and OOF-based vessel enhancement form the
backbone of our preprocessing steps for OCTA images.
31
2.4. Materials and Methods
2.4.1. Dataset
The data included in this study was obtained under IRB approval from the University of
Southern California (USC) and in accord with the principles of Declaration of Helsinki. All eyes
were scanned at the USC Roski Eye Institute or affiliated clinics using a commercially available
spectral-domain OCTA device (AngioPlex, Carl Zeiss Meditec, Dublin, CA, USA) with a scan
speed of 68,000 A-scans per second, central wavelength of 840 nm and 3mm × 3mm field of view.
A foveal centered scan was taken in each eye, resulting in OCT and OCTA image volumes of size
245×245×1024 (comprised of 245 B-scans with an A-scan depth of 1024). OCTA images were
included in the study if the signal strength was >= 7 (an empiric threshold based on the
commercially available software and manufacturer recommendations). All images were also
reviewed for common imaging artifacts that cause signal attenuation. Scans with floaters detected
on the structural image were discarded if the decorrelation signal in the corresponding flow signal
was also attenuated. Scans with more than 10 visible motion artifacts were also discarded. A total
of 81 OCT and OCTA images were included in the study. 75 scans were from the right eyes of
normal controls (NC, N=50, Age mean± SD (yrs) = 50±18) and proliferative diabetic retinopathy
patients (PDR, N=25, Age mean± SD (yrs) = 56 ±11). In addition, two series of longitudinal scans
from the left and right eyes of two different DR patients with DME are included to demonstrate
the application of our method in following the dynamic changes of retinal vasculature. DR severity
was graded based on clinical examination by board certified ophthalmologists with subspecialty
training in retina. Patients with other retina vascular diseases were not included in this study.
32
2.4.2. OCTA Preprocessing
2.4.2.1. 3D Volume of Interest
In this work, our main interest is
to quantify 3D features of retinal vessels
which may be significantly impacted in
retinal vascular diseases such as DR
(Kashani et al. 2017, Koulisis et al.
2017). To exclude the non- retinal regions in OCT scans, we first define a volume of interest (VOI)
by excluding regions below the outer plexiform layer (OPL) and above the internal limiting
membrane (ILM) since vessels outside this region are of less interest. This is achieved based on
structural layer segmentation of the OCT scan generated by the publicly available OCT-Explorer
software (Li et al. 2006, Garvin et al. 2009, Bogunovic et al. 2014). Using a graph-based approach,
the Iowa reference algorithm identifies 10 surfaces in the retinal OCT scan as shown in Figure
2.2. The VOI can be divided into superficial retinal layers (SRL) and deep retinal layers (DRL),
which is composed of L1-L3 (ILM to inner plexiform layer (IPL)) and L4-L5 (Inner nuclear layer
(INL)-OPL), respectively.
To define the coordinate system in each OCT volume, we denote the direction along the
A-scan as the z-axis, and the other two directions as the x- and y-axis. The horizontal axis (x-axis)
is the fast scan. In the rest of this paper, x-y plane is also referred to as en face scan and x-z plane
as the cross-section scan.
2.4.2.2. OCTA Vessel Enhancement
OCTA image volumes can visualize the dense and multi-directional retinal vessel network
from the large superficial vessels to small capillaries in the deep retinal layers with low signal-to-

Figure 2.2 Retinal layer definitions on structural OCT images.
An illustration of the OCT layer segmentation definitions as
achieved by the OCT-Explorer.

33
noise ratio (Kashani et al. 2017). Previous clinical studies (Gariano and Gardner 2005) showed
that retinal angiogenesis in development and disease conserve the continuity of the vascular
components. However, the high noise level in OCTA images can result in vessel discontinuity and
low vessel visibility especially in small capillaries. Moreover, clinical work reports that in many
retinal vascular diseases, pathologic changes first affect the small vessels and capillaries (Alterman
and Henkind 1968, Ashton 1970, Daicker 1976, Sun and Smith 2018). Therefore, to enable early
diagnosis, detection and enhancement of small capillaries is of great importance. For the reliable
analysis of capillaries in OCTA, we utilize the curvelet-based denoising and OOF-based vessel
enhancement techniques. By combining these two well-validated vessel analysis techniques, we
enhance the 3D multi-scale and multi-directional curvilinear vasculature captured by OCTA.

Figure 2.3 Example of OCTA vessel enhancement of a severe NPDR subject. (a) Original 3D-OCTA image
volume. (b) OCTA after applying 3D curvelet denoising on (a). (c) OCTA after applying 3D OOF vessel
enhancement on (b). (d, e) Selected en face view of (a), (d-1) magnified view of the denoted region in (d), (d-2)
vessel discontinuity enhancement of (d-1) via curvelet, (d-3) vessel discontinuity enhancement of (d-2) via OOF.
(e-1) magnified view of the denoted region with closely located microvasculature in (e), (e-2) vessel enhancement
of (e-1) via curvelet, (e-3) vessel enhancement of (e-2) via OOF. Red and green arrows point to the disconnected
and the resolved discontinuity regions of the vessel, respectively. Red and green dashed circles represent the high
and low efficiency of the enhancement method in separation of closely located microvasculature, respectively.

(a) Original OCTA (b) OCTA curvelet denoised (c) OCTA OOF enhanced
(d) Vessel discontinuity enhancement
(e) Closely located microvasculature
separation
34
The curvelet implementation used in our work is based on the wrapping method (Candès
et al. 2006) proposed by CurveLab (http://www.curvelet.org) with the parameters which are
carefully estimated for OCTA of normal and diabetic eyes. In all of our experiments, the number
of scales and orientations were empirically set to 6 and 16, respectively. To avoid excessive
denoising and preserve capillary details in OCTA, the threshold value (15±1.5) for truncating the
curvelet coefficients was estimated from the noise standard deviation in the fovea avascular zone
(FAZ) of ten representative OCTA images that were selected equally from the NC and DR
subjects.
Conventional OOF-based vesselness measures were defined with the product of the first
two eigenvalues (Law and Chung 2008). This, however, is not appropriate for OCTA data since
the vessels do not necessarily appear tubular. Due to the presence of projection or tailing artifacts
in OCTA data, large vessels instead appear as plane-like structures (Figure 2.3 (a)). In this case,
the first eigenvalue will be much smaller than the second and third ones, i.e., 𝜆 1
(.)≪𝜆 2
(.)≈
𝜆 3
≈0. The first eigenvector will be along the normal direction of the plane-like structure, and the
other two eigenvectors will span the plane. Based on these observations, we define the OOF-based
vesselness measure for OCTA at each voxel as 𝑉 (𝑥 )= 𝑚𝑎𝑥 𝑟 1
4𝜋 𝑟 2
|𝜆 1
|
2
. To handle the varying
scales of vessels, we follow the multi-scale approach of Law and Chung (Law and Chung 2008),
which normalizes the eigenvalues of the OOF matrix by the surface area of the sphere (
1
4𝜋𝑟
2
). In
this study, OOF-based vesselness enhancement is applied to the curvelet-denoised OCTA scans.
OCTA binary vessel mask (BVM) is then obtained by automatic thresholding the OOF vesselness
map using Otsu’s global thresholding (Otsu 1979).
To demonstrate the efficacy of the preprocessing steps, the vessel enhancement process of
a non-proliferative diabetic retinopathy (NPDR) subject is presented in Figure 2.3. By comparing
35
the original OCTA (Figure 2.3 (d) (1), Figure 2.3 (e) (1)) and curvelet enhanced image (Figure
2.3 (d) (2), Figure 2.3 (e) (2)), respectively, we can clearly see that the vessel discontinuity and
separation of closely located microvasculature are not completely resolved by curvelet denoising.
However, the OOF vesselness response of the curvelet-denoised image (Figure 2.3 (d) (3), Figure
2.3 (e) (3)) presents a clean separation of a connected vessel network and background even in
dense vessel areas with small capillaries.
2.4.3. Vessel Density Calculation
Vessel density image (VDI) will be
calculated to allow effective localized comparison
of vascular changes across subjects. This is
necessary since the macular vessel network has a
stochastic distribution (Yu et al. 2010), meaning
the spreading pattern of the vessels in OCTA
varies across individuals. This makes the direct
comparison of retinal vessels at the voxel-level a
challenging task. To overcome this difficulty, we
will compute VDI by propagating the content of
the BVM to the entire image volume. More precisely, VDI is a smooth vessel map that is obtained
by the convolution between the BVM of each subject and a 3D ellipsoidal average kernel
(Lindeberg 1994, Romeny 2013). The ellipsoidal kernel is employed since it is better matched
with the elongated shape of the vessels. The window size of the kernel was empirically set to [28
28 4]. To assess the robustness of the window size parameter, we demonstrate the results with
different window sizes in Section 2.5.2.1 (Figure 2.13).

Figure 2.4 OCTA binary vessel mask (BVM) and
vessel density image (VDI) of a PDR and a NC eye.
(a, d) Selected 2D en face from BVM of a PDR and
a NC eye, respectively. (b, e) VDI of (a, d) which
are obtained by the convolution between BVM and
a 3D ellipsoidal kernel. (c, f) overlay of (a, d) on (b,
e), respectively. Red is associated with highest VDI
(dense vascular regions), and blue is associated
with the lowest VDI (avascular region).

(a) (b)
(d) (e) (f)
(c)
36
Representative examples for the VDI of a PDR and a NC subject are shown in Figure 2.4. In
the VDI representation, red regions indicate highest vessel density associated with large scale
vessels or dense vessel distributions. Blue regions demonstrate the lowest vessel density, such as
fovea avascular zone, capillary free zone and areas with macular edema. According to the VDI
images, we can see the sparse vessel distribution in the PDR subject (Figure 2.4 (b)) and a dense
vessel network in the NC subject (Figure 2.4 (e)). Both subjects have the lowest vessel density in
the fovea region as expected.
2.4.4. Mapping Vessel Density Across Subjects
To allow the comparison of the cross-subject
vessel density images, we performed a non-linear
registration based on our previously established
automated 3D technique for OCT volumes
(Khansari et al. 2019). Prior to registration, we
applied non-local means (NLM) denoising
(Buades, Coll and Morel 2005a) to reduce the
speckle noise in OCT images and improve the
contrast of anatomical structures. Additionally, for each OCT scan, the volume of interest (VOI)
that includes the whole retinal layers from the internal limiting membrane (ILM) to retinal pigment
epithelium (RPE) was generated by OCT-Explorer and extracted. These two preprocessing steps
are necessary in order to improve the accuracy of registration by suppressing noise and excluding
regions with highly variable appearances across subjects such as the choroidal layer that could be
misleading for registration algorithm.

Figure 2.5 Example of OCT and VDI
registration of a PDR subject with edema. (a)
The overlay of OOF vesselness response on 3D
OCT scan of the PDR subject. (b) OCT atlas
volume. (c), (d) OCT volume of the PDR subject
before and after registration, respectively. (e),
(f) VDI of the PDR subject before and after
registration overlaid on the corresponding OCT
images (c, d), respectively.

37
The OCT atlas (Figure 2.5 (b), Figure 2.6 (b)) constructed in our previous work (Khansari et
al. 2019), was used as the fixed volume in registration. The atlas volume (Figure 2.5 (b)) is well
centered, not tilted and has clear representation of retinal layers. The OCT scans from the rest of
the subjects were considered as moving volumes and registered to the atlas space. Registration was
performed in two steps, initially an anatomical volume of interest (VOI) with consistent field of
view was obtained via carefully designed masking and affine registration for each OCT image.
Then, we computed a non-linear deformation between the fixed and affine-registered OCT
volumes within VOI in order to align anatomical details (layer boundaries and foveal pit). This is
achieved by minimizing a normalized mutual information (NMI) cost function using stochastic
gradient descent optimization (Khansari et al. 2019). NMI is robust to intensity inhomogeneity and
the combination of B-spline with stochastic gradient descent improves the efficiency of image
registration (Klein et al. 2010).
The non-linear registration provides transformation of each OCT volume to the atlas space.
Since each pair of OCT and OCTA volumes are aligned during the imaging, we use the
deformation field of each OCT to bring its corresponding VDI (calculated based on OCTA) to the
atlas space. This process allows meaningful localized comparison of vessel density with voxel-
level accuracy across subjects in the atlas space.
Figure 2.5 illustrates an example of OCT and VDI registration for a PDR subject with edema.
Figure 2.5 (c) and Figure 2.5 (d) illustrate the OCT volume of the PDR subject before and after
registration to the atlas space, respectively. As shown in Figure 2.5 (c), before registration the
edematous layers in the PDR subject are thicker than the segmentation slabs in OCT images
without shape deformation (Figure 2. 5(d)). The VDI of the edema subject (Figure 2.5 (e)) is also
brought to the atlas space (Figure 2.5 (f)) by applying the deformation field that was obtained by
38
registering the OCT volume of the PDR subject to the atlas. By resolving the shape deformation
in OCT of the PDR subject with edema and transforming the vessels to a standard atlas space, it is
now feasible to include such subjects with edema in group studies and quantitatively assess the
vascular density deviation in these subjects. This overcomes a significant barrier to quantitative
analysis of OCTA images with deformed retinal boundaries.
2.4.5. Capillary Dropout Simulation
One of the earliest anomalies in DR is the reduction of retinal perfusion. This is caused by
progressive damage to the retinal blood vessels, ultimately causing the retina to become ischemic.
This loss of microvasculature is sometimes referred to as “capillary dropout”, which is a critical
process in DR (Kowluru and Chan 2008). Previous clinical studies based on in-situ and OCTA
imaging showed that the capillary dropout due to DR generally occurs at branch points (Tam et al.
2012, Pinhas et al. 2014, Chui et al. 2016, Ashimatey et al. 2019). To simulate the capillary
dropout, we developed an automated algorithm to generate synthetic patient data by removing a
percentage of the branch points from a localized region of the retina (e.g., temporal region). We
call this percentage value as branch removal rate.
To detect the branch points, we first computed the 3D skeleton of the OCTA image from
the BVM and OOF vesselness map using the Hamilton-Jacobi skeletonization method (Siddiqi et
al. 2002). Using connected component analysis, the small, disconnected components were detected
and removed from the skeleton image and a fully connected 3D skeleton was obtained. Then, we
constructed a 3D look-up table for each voxel on the skeleton image and examined a local region
of size 3x3x3 (27 voxels). For a continuous line without any branch points, its 3D look-up table
will only contain 3 out of the 27 voxels. Anytime the number of voxels in the local region exceeds
39
3, a branch point is detected. Afterwards, a branch-point-mask was generated by dilating detected
branch points with a disk of size 1.
To remove a subset of the branch points from a localized region of BVM, we constructed
a list such that each list element is the number of voxels in each disconnected component of the
branch-point-mask. Some neighboring branch points on the skeleton might become connected
after branch point dilation. In this case, two branch points might be considered as one disconnected
component. To handle such cases, we sorted the disconnected component list in increasing order
and iteratively removed the smallest components until the cumulative voxel counts reached the
voxels-to-remove value that is equal to: (branch removal rate * number of voxels in the branch-
point-mask). After branch point removal, we perform a connected component analysis to the BVM
localized region and remove disconnected and small branches.
2.5. Results
The result section is divided into qualitative and quantitative parts. The qualitative results
will include examples of individual OCT and VDI registration in NC and DR subjects (Section
2.5.1.1). Also, results from longitudinal clinical data will be presented (Section Error! Reference
source not found.2.5.1.2). The quantitative section will show findings of group-wise, localized
comparison between vessel densities of NC and synthetic patient groups (Section 2.5.2.1), NC
subjects divided into two age groups (Section 2.5.2.1) and NC and clinical DR dataset (Section
2.5.2.3).
2.5.1. Qualitative Results
2.5.1.1. Individual Examples
Figure 2.6 shows two examples of OCT registration for a NC (Figure 2.6 (b-d)) and a
PDR subject with edema (Figure 2.6 (e-g)). The preprocessed OCT images (Figure 2.6 (c), (f))
40
are generated by applying NLM denoising to the VOI (ILM-RPE) of the corresponding input OCT
scans (Figure 2.6 (b), (e)). As demonstrated in Figure 2.6 (c), before registration, the moving NC
subject is tilted, and its fovea is deviated from the center compared to the atlas (Figure 2.6 (a)).
The moving PDR subject (Figure 2.6 (f)) is also slightly tilted from the atlas, and it has severe
anatomical shape deformation in the foveal region due to presence of edema pathology. However,
after non-linear registration, both moving subjects are brought to the atlas space and their
orientation and foveal pit are aligned with the atlas (Figure 2.6 (d, g)). Moreover, the foveal shape
deformation caused by edema in PDR subject (Figure 2.6 (f)) has been successfully resolved in
the registered OCT scan (Figure 2.6 (g)).
Figure 2.7 demonstrates the VDI registration of the same normal and PDR subjects that
are shown in Figure 2.6. The VDIs (Figure 2.7 (b), (e)) are obtained by diffusing the content of
BVMs (Figure 2.7 (a), (d)). The VDI registration results of the NC (Figure 2.7 (c)) and PDR
(Figure 2.7 (f)) moving subjects are obtained by transforming the corresponding non-linear warp

Figure 2.6 Example OCT volume registration for a normal and PDR subject. Selected OCT cross-sectional scan
of (a) Atlas image. (b) A moving NC subject. (c) Same image in (b) after the extraction of VOI and denoising. (d)
Same image in (c) after non-linear registration to the atlas. (e) A moving PDR subject with edema. (f) Same image
in (e) after VOI extraction and denoising. (g) Same image in (f) after non-linear registration to the atlas. The
horizontal red dashed lines in (a, c, d, f, g) are fixed in the atlas space to visualize the relative position of the OCT
images before (c, f) and after registration (d, g). The vertical dotted white line in (a, c, d, f, g) are also fixed in the
atlas space to show the alignment of the fovea center.

41
that was computed between each moving OCT (Figure 2.6 (c), (f)) and the atlas (Figure 2.6 (a)).
After non-linear registration of vessel densities, the VDIs of the moving subjects are in the atlas
space while their distinctive vessel distribution is preserved, allowing voxel-level comparison.
This analysis provides a relatively straight-forward localized comparison of the vessel density
between the PDR (Figure 2.7 (f)) and NC subject (Figure 2.7 (c)) that is not possible by
comparison of the raw images along. From this analysis, it is more clearly apparent that vascularity
of the eye with edema is increased as compared to control.
2.5.1.2. Longitudinal Example
Diabetic macular edema (DME) is a common complication of diabetic retinopathy (DR),
characterized by the abnormal accumulation of fluid and protein deposits in the macular region. If
left untreated, DME can cause serious vision loss. The correlation of the macular vessel density in
the superficial and deep plexuses with the progression of DR has been widely studied using OCTA
[50-52]. However, exploring the dynamics of microvasculature changes of DR patients specifically
in the presence of DME has been challenging. Indeed, DME pathology can cause retinal
anatomical deformation and introduce significant inaccuracy in OCT layer boundaries (Figure 2.8

Figure 2.7 Example vessel density image registration of a selected normal and PDR subject. Selected cross-
sectional scan of (a) BVM of a moving NC subject overlaid on the corresponding OCT scan. (b) VDI generated by
diffusing the content of (a). (c) The VDI in (b) after registration to the atlas space. (d) BVM of a moving PDR
subject with edema overlaid on the corresponding OCT scan. (e) VDI computed from the BVM in (d). (f) the VDI
in (e) after registration to the atlas space. The horizontal red dashed lines and vertical white dashed lines in (b, c,
e, f) are the same lines demonstrated in the corresponding OCT scans in Figure.6 (c, d, f, g).

42
(g, h), Figure 2.9 (g, i)). Due to this spatial variation in the retinal region of DME subjects, the
precise comparison of vessel density changes is not possible by comparing the raw images along.
Nevertheless, attempts have been made to study the correlation between cystoid spaces and
capillary nonperfusion in longitudinal DME subjects based on qualitative and quantitative
comparisons of en face OCT and OCTA scans in superficial and deep retinal layers [53]. Although
previous works have shown their clinical value, tracking localized changes in common space may
provide a more nuanced and informative clinical perspective on disease progression and treatment
planning. To demonstrate an automatic and 3D localized comparison of microvasculature changes
of subjects over the course of DME development, resolution and recurrence, we apply our
proposed 3D vessel mapping method to OCT and OCTA images of two DR patient at three time
points.
Figure 2.8 and Figure 2.9 demonstrate the longitudinal OCT scans of two patients with
edema during the course of clinical care. In Figure 2.8, the degree of the edema is qualitatively
labeled to compare between the scans as baseline (Figure 2.8 (column 1)), increased from baseline
(Figure 2.8 (column 2)) and improved from baseline (Figure 2.8 (column 3)). In Figure 2.9, we
label the images as baseline (Figure 2.9 (column 1)), decreased from baseline Figure 2.9 (column
2)) and partial return to baseline (Figure 2.9 (column 3)). These labels were derived using the
degree of 3D-OCT anatomical deformation (Figure 2.8 (row1), Figure 2.9 (row1)) and the size
of edema (Figure 2.8 (row2), Figure 2.9 (row2)).
Figure 2.10 shows the results after we applied the OCT and VDI registration methods to
the DME subject shown in Figure 2.8, during progression (t1-t2) and treatment (t2-t3) of edema.
Edema appears as dark regions close to the fovea in the OCT scans at two time points (t1, t2)
(Figure 2.10 (a, b, g, h)) and then it returned to baseline with resolved edema at the t3 time
43
point(Figure 2.10 (c, j)). As shown in this Figure, edema caused anatomical shape deformation
which is more severe at t2 (Figure 2.10 (b)) as compared to t1 (Figure 2.10 (a)). The OCT and

Figure 2.8 Visualization of OCT deformation caused by diabetic macular edema (DME) in a diabetic subject
during edema development and treatment periods. Row1 (a-c) 3D-OCT scans of the DME subject at three time
points (t1, t2, t3) in chronological order. Row2 (d-f) selected OCT cross-sectional scans from similar slabs (orange
dashed lines) of the corresponding 3D-OCT in (a-c). Row3 (g-i) selected cross-sectional scans of automatic OCT
layer segmentation by OCT-Explorer overlaid on the corresponding OCT cross sections in (d-f). (t1-t2) is the
edema progression period, (t2-t3) is the edema treatment period. Edema regions are annotated by red in (d) and
(e). The regions inside dashed white rectangular in (g, h, i) show areas with OCT layer segmentation errors.

Figure 2.9 Visualization of OCT deformation caused by diabetic macular edema (DME) in another diabetic subject
during edema treatment and recurrence periods. Row1 (a-c) 3D-OCT scan of a DME subject at three time points
(t1, t2, t3) in chronological order. Row2 (d-f) selected OCT cross-sectional scans from similar slabs (orange
dashed lines) of the corresponding 3D-OCT in (a-c). Row3 (g-i) selected cross-sectional scans of automatic OCT
layer segmentation by OCT-Explorer overlaid on the corresponding OCT cross sections in (d-f). (t1-t2) is the
edema treatment period, (t2-t3) is the edema recurrence period. Edema regions are annotated by red in (d) and
(f). The regions inside dashed white rectangular show areas with OCT layer segmentation errors.

44
VDI scans, which are demonstrated in Figure 2.10 (row1, row 2) at different time points (t1, t2,
t3), were selected from the similar slabs of the 3D-OCT and 3D-VDI images, but they may not be
perfectly matched due to different image orientations and anatomical shape deformations caused
by edema. After registration, the time series of the OCT (Figure 2.10 (row3)), and VDI images
(Figure 2.10 (row4)) are anatomically aligned to the atlas space ((Figure 2.5 (b)). Comparison of
the registered VDI images allows qualitative evaluation of relative changes in longitudinal vessel
densities which would otherwise be confounded by spatial differences in retinal location and
retinal shape. More precisely, in Figure 2.10 (j-l), the region-wise evaluation between registered
VDIs of different time points in the highlighted regions marked as 1 and 2 (Figure 2.10 (k)) show
higher VDI at t2 as compared to the corresponding locations at the time point t1(Figure 2.10 (j)).
This example illustrates that there may be an increase in capillary density in the perifoveal region
during the peak of edema. The highlighted region marked as 3 at the t3 time point (Figure 2.10
(l)) focuses on the region where we can observe lower VDI at t3 as compared to t2. This qualitative
finding supports the observation from Figure 7 discussed in the first experiment.
Figure 2.11 demonstrates the OCT and VDI registration of the second longitudinal DME
subject, that was shown in Figure 2.9 over the periods of edema treatment (t1-t2) and recurrence
(t2-t3). Edema appears as dark regions in the foveal and temporal regions of the OCT scans at time
points (t1, t3) (Figure 2.11 (a, g), Figure 2.11 (c, i)). The decreased stage of edema is shown at
the t2 time point (Figure 2.11 (b, h)). Compared to the previous examples (Figure 2.8, Figure
2.10), we can see more severe edema stages and consequently more anatomical deformations in
this subject. The registered OCT and VDI scans are illustrated in Figure 2.11 (row 3) and Figure
2.11 (row 4), correspondingly. Figure 2.11 (j-l) shows the qualitative comparison between the
consecutive timepoints for tracking vascular variations during edema treatment and recurrence.
45
More precisely, the region-wise evaluation between registered VDIs in the highlighted region

Figure 2.10 Longitudinal example of tracking VDI changes of a diabetic subject with edema during edema
development and treatment periods. Row1 (a-c) OCT volume cut of the same subject at three time points (t1, t2,
t3) in chronological order before registration. Row2 (d-f) selected VDI cross-section from similar slabs of the
corresponding 3D-OCT in (a-c) overlaid on the corresponding OCT cross-sections before registration. Row3 (g-
i) OCT volume cuts of the same subject (row1 (a- c)) after non-linear registration to the atlas. Row4 (j-l) selected
VDI cross-section overlaid on the corresponding OCT cross-sections after non-linear registration. The regions
with noticeable VDI changes between consecutive time points are denoted by dashed white circles. Edema regions
at t1 and t2 time points are delineated by dashed red lines.

Figure 2.11 Longitudinal example of tracking VDI changes of a diabetic subject with edema during edema
treatment and recurrence periods. Row1 (a-c) OCT volume cut of the same subject at three time points (t1, t2, t3)
in chronological order before registration. Row2 (d-f) selected VDI cross-section from similar slabs of the
corresponding 3D-OCT in (a-c) overlaid on the corresponding OCT cross-sections before registration. Row3 (g-
i) OCT volume cuts of the same subject (row1 (a-c)) after non-linear registration to the atlas. Row4 (j-l) selected
VDI cross-sections overlaid on the corresponding OCT cross-sections after non-linear registration. The regions
with noticeable VDI changes between consecutive time points are denoted by a dashed white circle in (k) and (l).
Edema regions at t1 and t3 time points are delineated by dashed red lines. The areas of edema recurrence at t3
are pointed by yellow arrows in (l).

46
marked as 1 (Figure 2.11 (k)) show higher VDI at t2 as compared to the corresponding locations
at the time point t1(Figure 2.11 (j)). This example demonstrates the possibility of an increase in
capillary perfusion in the vicinity of the edema void region after treatment. The highlighted region
marked as 2 at the t2 time point (Figure 2.11 (k)) focuses on the region where we can observe
lower VDI at t2 (decreased from baseline) as compared to t1 (baseline). At edema recurrence time
(t3), we observe that edema appears in foveal and temporal regions (Figure 2.11 (l)), which is
similar to corresponding regions of edema at t1(before treatment). Also, the region-wise
comparison of the VDI in the highlighted regions marked as 3 and 4, show lower capillary
perfusion at t3 (recurrence stage of edema) compared to t2 (decreased stage of edema).
2.5.2. Quantitative Results
For localized quantitative assessment of 3D vessel density analysis in OCTA, we performed
three sets of experiments. The goal of these experiments is to perform group-wise, localized
comparison between vessel densities of the NC and the target group to detect the regions with
vessel expansion or vessel loss due to normal aging or disease effect in the target group. In the first
experiment, to generate ground-truth data, a synthetic patient dataset of capillary dropout subjects
has been produced from OCTA of NC subjects. Then, the result of group-wise analysis is presented
for the comparison between synthetic patient and NC subjects. The details of experiment one is
presented in Section 2.5.2.1. In the second experiment (Section 2.5.2.2), we performed a group-
wise study to demonstrate the age-dependent macular vessel density changes in the NC eyes.
Finally, in Section 2.5.2.3 a group-wise localized vessel density analysis on the clinical DR data
is presented.
47
2.5.2.1. Group-wise Comparison Between Synthetic Patient Data and NC
For quantification and localization of capillary loss caused by DR pathology across
population, we performed a group- wise comparison between synthetic patients and NC. 25 NC
subjects were divided into two groups (12 NC, 13 synthetic patients) such that there was no
significant age difference between the two groups. Using the capillary dropout simulation
algorithm from Section 2.4.5, patient data was generated by removing 5% of the branch points
from the temporal area of each subject’s BVM. For group comparisons, initially all OCT volumes
included in this experiment were non-linearly registered to the atlas. Then the calculated
deformation field was applied to the VDIs of the corresponding moving subject. After registration,
all vessel densities were transformed to the atlas space and a localized comparison became feasible.
In our experiment, a p-value map was generated by comparing the registered VDIs of the two
groups at the voxel-level. For each voxel within the retina region of the atlas (ILM-OPL), a two-
tailed student t-test was applied to examine the group difference between the VDI values from the
NC and simulated patient groups, and the resulting p-value was stored in a p-value map. Regions
with significant vessel density differences were determined at the significance level of 0.01. In our
comparison we included both vessel expansion and vessel loss patterns for significant voxels.
Figure 2.12 demonstrates the localization of the significantly different (p<0.01) voxels
overlaid on the p-value map for comparison between two NC groups (Figure 2.12 (a)) and between
NC and synthetic patient data (Figure 2.12 (b)). The results show that the localized comparison
between the two groups of NC do not represent noticeable regional vessel density changes.
However, localized vessel density comparison between NC and a synthetic patient group (with 5%
branch removal in the temporal area) demonstrates the temporal region of the synthetic patient
group has lower vessel density as compared to the NC.
48
To show the robustness of our method, we
repeated the synthetic patient and NC
comparison experiment with different settings of
kernel sizes in VDI calculation (Figure 2.13).
Furthermore, to evaluate the capillary dropout
detection-rate, we generated multiple synthetic
patient dataset with different branch removal
rates and presented the result in Figure 2.14.
Figure 2.13 illustrates the results of
localized vessel density comparison between
NCs and synthetic patient data with different
settings of the window size parameter used in the VDI calculation (w = [ 26 26 4], w = [30 30 4],
w = [28 28 5], w = [28 28 6]). As shown in this Figure, the localization pattern of the significantly
different (p<0.01) voxels is very robust with respect to the window size settings. Figure 2.14
demonstrates the effect of the branch removal rate on the capillary dropout detection performance
of the proposed method. The voxel-level comparisons between NC and synthetic patient data with
different branch removal rate shows that higher branch removal rate will lead to larger areas with
significantly different voxels. The similarity between the localization pattern of the significant
voxels in Figure.14 (d) (1% removal rate) and Figure 2.12 (a) (voxel-level t-test between two
groups of NC) shows that our method is most reliable when the voxel removal rate is greater than
2% of the temporal branch points.

Figure 2.12 Localization of significantly different
voxels (p<0.01) overlaid on the p-value map in
comparison between NC-NC and NC-Synthetic
patients. (a) Localized comparison between retinal
vessel densities of two normal groups (NC-group1(N =
12), NC-group2 (N = 13)) without simulated capillary
dropout. (b) Localized comparison between retinal
vessel densities of normal controls and synthetic
patient data with 5% simulated capillary dropout (NC-
group1(N = 12) and synthetic patient data (N = 13)).
Red regions are the significant voxels with higher
vessel density in the first group and yellow regions are
the significant voxels with lower vessel density in the
first group as compared to the second group (window
size for VDI calculation for all subjects is set to [28 28
4]).

49
2.5.2.2. Group-wise Analysis of Age-dependent Vessel Density Changes in the Normal Eyes
Previous OCTA studies observed a negative correlation between age and the inner retinal
vessel densities in healthy individuals [54-56]. A large population-based OCTA study of 1631
subjects reported a significant decrease of mean global macular vessel density with normal aging
starting from age 50, in superficial and deep retina [56]. In order to show the potential application
of our proposed localized vessel density analysis with respect to age, in this section we present a
group-wise experiment between two age groups of NC. Fifty NC right eye OCTA images divided
into younger (N = 25, age range = 21- 49, Age mean±SD (yrs) = 33.2 ± 7.99) and older groups (N
= 25, age range = 52-86, Age mean±SD (yrs) = 66.27 ± 8.74). Registered VDI of 25 younger NCs
were compared to that of the 25 older NCs. Figure 2.15 demonstrates the quantitative results of

Figure 2.13 Robustness of localization result of the significantly different voxels (p<0.01) with different window
sizes. Localized comparison between retinal vessel densities of NCs (N=12) and synthetic patient data (N=13)
with 5% branch removal rate and different window sizes: (a) w = [ 26 26 4], (b) w = [30 30 4], (c) w = [28 28 5],
(d) w = [28 28 6]. Red regions are the significant voxels with higher vessel density in NCs and the yellow regions
represent voxels with lower vessel density in the NCs as compared to the synthetic patient data.

Figure 2.14 Effect of the branch removal rate on the capillary dropout detection performance. Localized
comparison between retinal vessel densities of NCs (N=12) and synthetic patient data (N=13) with different
branch removal rates as: (a) 10%, (b) 5%, (c) 2% and (d) 1%. Window size in all experiments is set to [28 28 4]
and significant level is considered as 0.01 (p<0.01). Red regions are the significant voxels with higher vessel
density in NCs and the yellow regions represent voxels with lower vessel density in the NCs as compared to the
synthetic patient data.

50
the group comparison between these groups in the full retinal layers (RET), SRL and DRL
separately. For all significant regions (P<0.001), the older group has consistently lower vessel
density than the younger group. Furthermore, the results show that deep vascular plexus (Figure
2. 15 (c)) appears to be more affected by aging.
2.5.2.3. Group Study of NCs and DRs
Diabetic retinopathy (DR) is one of the leading causes of visual impairment in the developed
world (Prokofyeva and Zrenner 2012, Stitt
et al. 2016). DR can cause retinal blood
vessels to leak and presents with pathologic
features such as microaneurysms, exudates,
venous beading and FAZ enlargement
(Nayak et al. 2008). Retinal nonperfusion,
capillary dropout, hemorrhages, and other
microvascular abnormalities progressively
worsen with DR severity (Hwang et al. 2015, Kashani et al. 2017). The main stages of DR are non-
proliferative diabetic retinopathy (NPDR) and proliferative diabetic retinopathy (PDR).
Previous studies demonstrated that OCTA could detect microvascular changes caused by DR at

Figure 2.16 Localization of the significantly different
voxels (p<10
-5
) in comparison between NC (N=25) and
PDR subjects (N=25). (a) Localized comparison results
in the SRL overlaid on the SRL p-value map. (b)
Localized comparison results in the DRL overlaid on the
DRL p-value map. Red region in (a), (b) demonstrate the
voxels with lower vessel density in PDR group compared
to NCs.

(b) (a)
(a) SRL (b) DRL

Figure 2.15 Localization of the significantly different voxels (p<10
-3
) in comparison between two age groups of
NC. (a) Localized comparison results in the RET overlaid on the RET p-value map. (b) Localized comparison
results in the SRL overlaid on the SRL p-value map. (c) Localized comparison results in the DRL overlaid on the
DRL p-value map. Red region in (a), (b), (c) demonstrate the voxels with lower vessel density in NC older group
(age>50) compared to NC younger group (age<50).

51
different stages (Hwang et al. 2015, Ishibazawa et al. 2015). However, the quantitative
comparisons between DR groups were mainly limited to a global measure of vessel density in all
retinal layers, superficial retinal layer (SRL) or deep retinal layer (DRL) (Chu et al. 2016, Durbin
et al. 2017). In this section, we provide the results of localized mapping of vessel density changes,
for the first time, between PDR and NC subjects. Registered VDIs of 25 NC subjects were
compared to that of 25 PDR subjects. Among the PDR subjects, 20% of the images have macular
edema based on OCT. Figure 2.16 presents the quantitative results of the group comparison
between the NC and PDR subjects in the superficial and deep retinal layers separately. Similar to
the previous section, two-tailed t-test was used for voxel-level statistical analysis. For all
significant regions (p<10
-5
), the PDR subjects has consistently lower vessel density than the NC
group. Our results show that deep vascular plexus (Figure 2.16 (b)) appears to be affected more
by DR than the superficial plexus (Figure 2.16 (a)) which is consistent with previous findings
(Kaizu et al. 2017, Kashani et al. 2017, Dimitrova et al. 2017, Scarinci et al. 2018, Carnevali et al.
2017, Simonett et al. 2017). In addition, the vascular density changes in SRL are more localized
in the temporal area of the retina. A similar result has been reported recently in NPDR subjects
where the temporal-perifoveal region was found to be the most sensitive region for early detection
of DR (Alam et al. 2020). This demonstrates the potential of our method in localizing vascular
changes in clinical DR studies which can open a new direction for volumetric quantification of
retinal capillary changes in OCTA with voxel-level accuracy.
2.6. Discussion and Conclusion
In this work, we presented a novel and robust analysis framework for localized 3D vessel density
mapping in OCTA. To enable OCTA-based vessel density comparisons across populations and
between longitudinal scans at voxel-level, we first calculated vessel density image (VDI) via
52
curvelet denoising and OOF-based analysis. Localized VDI mapping was then realized using a
non-linear 3D OCT image registration approach (Khansari et al. 2019).
In our method, processing each 3D OCT/OCTA scan typically takes less than 30 minutes on a
PC with a 4.5 GHz CPU and 64 GB RAM. This processing time includes the vessel enhancement
using curvelet and OOF, binary vessel mask generation and vessel density image construction
(total time < 20 minutes). Moreover, registering a pair of OCT volumes and applying the computed
non-linear deformation to the corresponding VDI took less than 10 minutes on the same PC.
In our experimental results, we comprehensively validated the robustness and performance of
our method on patient data with synthetic capillary dropout, and further investigated three clinical
applications using a longitudinal dataset of two DR subjects with DME, a dataset of normal
controls from two age groups, and a clinical DR dataset. Our results indicate that the proposed
method can successfully detect local vascular changes across populations caused by simulated
vessel loss (branch removal rate = 2%), normal aging (p<10-3) or DR pathology in the presence
of edema (p<10-5). Due to the more prominent effect of DR on retinal vessel loss than normal
aging, a smaller p-value threshold was used for the DR experiment to demonstrate the localization
of vessel loss caused by DR.
Previous DR studies have shown the great potential of OCTA in analyzing global vessel density
changes in different DR stages (Hwang et al. 2015). There is currently growing evidence in OCTA
analysis that shows the deep capillary plexus is more affected than the superficial capillary plexus
in DR (Dimitrova and Chihara 2019, Scarinci et al. 2018, Simonett et al. 2017). This is consistent
with our finding in comparing NC and PDR subjects. Moreover, in our localized vessel density
analysis of NC and PDR, we observed more capillary loss in the temporal region of the superficial
plexus as was also recently shown in another OCTA study comparing the SRL of NCs to NPDR
53
subjects (Alam et al. 2020). This localization pattern may be predictable and thus helpful in
determining the earliest microvascular changes in DR. Another challenge in previous studies is the
accurate and localized assessment of capillary changes over time, especially for subjects with
severe pathology such as diabetic macular edema (DME). This challenge has been successfully
addressed by our presented technique. We showed the feasibility of our method for tracking
localized vascular density changes on two diabetic patients over the period of edema progression
and treatment in 3D. These localized longitudinal analyses may have a great clinical impact in
guiding edema treatment and monitoring treatment responses. It can also advance our
understanding of vascular changes in presence and resolution of edema which may potentially
contribute to better disease management.
For future work, we will extend our experiments to OCTA scans of DR from different stages,
especially the early stages for detecting initial vascular changes due to this pathology. We will also
apply our method to quantitatively examine the longitudinal vascular changes in population studies
and to track changes during treatment of edema pathology. We also want to emphasize that the
clinical experiments presented in this study point to potential applications of the proposed
techniques, but more extensive validation will be needed for their wide use in clinical settings.

54
3. CHAPTER 3: Shape-Reeb graph analysis method for LSA morphological quantification
3.1. Abstract
Objectives
The lenticulostriate arteries (LSAs) with small diameters of a few hundred microns take origin
directly from the high flow middle cerebral artery (MCA), making them especially susceptible to
damage (e.g. by hypertension). This study aims to present the feasibility of visualization,
characterization and Shape-Reeb based morphological quantification of LSAs at both 3 T and 7 T
using recently developed high resolution (isotropic ~0.5 mm) black blood MRI.
Materials and Methods
Twenty healthy volunteers (15 under 35 years old, 5 over 60 years old) were imaged with the
previously optimized T1-weighted 3D turbo spin-echo with variable flip angles (T1w TSE-VFA)
at both 3T and 7T. LSAs were manually segmented using ITK-SNAP. Automated Reeb graph
shape analysis was performed to extract features including vessel length and tortuosity. All
quantitative metrics were compared between the two field strengths and two age groups using
ANOVA.
Results
LSAs can be clearly delineated using optimized 3D T1w TSE-VFA at 3T and 7T, and a greater
number of LSA branches can be detected compared to those by time-of-flight MR angiography
(TOF MRA) at 7T. The mean vessel length and tortuosity were greater on TOF MRA compared
to TSE-VFA. The number of detected LSAs by both TSE-VFA and TOF MRA was significantly
reduced in aged subjects, while the mean vessel length measured on 7T TSE-VFA showed
significant difference between the two age groups.
Conclusion
55
Using high-resolution black-blood 3D T1w TSE-VFA manual sequence, 3D segmentation and
shape analysis of LSAs is demonstrated to be feasible with relatively high performance and can
serve as a potentially effective tool to aid quantitative morphometric analyses in patients with
cerebral small vessel disease.
3.2. Introduction
Cerebral small vessels are largely inaccessible to existing clinical in vivo imaging
technologies. As such, early cerebral microvascular morphological changes in small vessel disease
(SVD) are difficult to evaluate. In previous studies, high resolution time-of-flight MR angiography
(TOF MRA) at ultrahigh magnetic field of 7T has been applied for the characterization of
lenticulostriate arteries (LSAs) (Cho et al. 2008, Hendrikse et al. 2008). The morphology of these
LSAs (e.g. branch number, radius, tortuosity) showed significant differences between subjects
with subcortical vascular dementia (SVaD) and healthy controls (Seo et al. 2012) as well as
between hypertensive and normotensive subjects (Kang et al. 2009b). These data demonstrate the
potential for quantifying the morphology of LSAs as imaging biomarkers of hypertensive small
vessel disease, which primarily affects subcortical regions.
Since ultra-high field MRI is not commonly available in the clinical setting, the purpose of
this study was to utilize our previously optimized high resolution (isotropic ~0.5mm) 3D T1-
weighted TSE-VFA acquired at 3 and 7T to segment the LSAs and characterize the morphological
changes that may occur with age. Quantitative metrics of LSA morphology were derived by Reeb
graph analysis of segmented LSA shapes which were compared between the two age groups and
two field strengths, respectively. Unlike previous morphology analyses of LSAs that used two
dimensional maximum intensity projections from TOF MRA at 7T (Kang et al. 2009a) or two
dimensional minimum intensity projections from TSE-VFA at 3T (Zhang et al. 2019d), we
56
implemented a novel three-dimensional shape analysis of LSAs derived from T1-weighted TSE-
VFA black-blood images to quantify the morphology of the vessels.
3.3. Materials and Methods
3.3.1. Subjects
To evaluate the ability to observe age-related differences, the volunteer cohort from the
previous study described in Chapter 2 was imaged with the previously optimized T1-weighted 3D
Table 3.1 Summary of imaging parameters for sequences

Table 3.2 Criteria for 4-point LSA Delineation Rating Scale

57
turbo spin-echo with variable flip angles (T1w TSE-VFA) at both 3T and 7T. This cohort included
a total of 17 healthy volunteers, with 12 participants (7 male, 27 ± 3.5 years) between 19- 35 years
old and 5 participants (2 male, 64.2 ± 1.9 years) more than 60 years of age, herein referred to as
the young and aged group, respectively. All participants provided written informed consent
following a protocol approved by the MNI (IRB) of the University of Southern California.
3.3.2.MRI Experiment
All MRI scans were performed on a Siemens 3T Prisma scanner with a product 32-channel
head receive coil and body transmit coil, and on a Siemens 7T Terra scanner (Erlangen, Germany)
with a single-channel transmit/32-channel receive (1Tx/32Rx) head coil (Nova Medical,
Wilmington, MA, USA). The scan protocol and sequence parameters are described in Table 3.1.
3.3.3. LSA Delineation Rating Scale
To evaluate the LSA quality in the T1w TSE-VFA black blood images, a 4-point LSA
delineation (LSAD) rating scale was utilized as described in Table 3.2 and evaluated by two
independent raters. The LSAD rating scale is based on the number and observable tortuosity on
10mm thin minimum intensity projection (minIP) images from T1w TSE-VFA.
3.3.4. Image Analysis: Vessel Segmentation and Morphology Metrics Model Development
We developed a three-step method to extract quantitative 3D measurements of LSAs for both
TSE-VFA and TOF MRA (Figure 3.1). As the first step, manual vessel segmentation was
performed by an experienced neuroradiologist (Y.C.) using ITK-SNAP (Yushkevich et al. 2006).
To increase the accuracy of vessel masks, raw images of all axial, coronal, and sagittal views were
used in ITK-SNAP as shown in Figure 3.1a. However, geometric, and topological outliers occur
frequently during manual segmentation due to limited image resolution or anatomical variability
across subjects. As the second step to perform quantitative shape analysis on these data, we applied
58
the surface reconstruction method (Shi et al. 2010) that uses the Laplace-Beltrami (LB) spectrum
for outlier removal without shrinkage (Figure 3.1b). The LB spectrum can be viewed as a
generalization of the Fourier basis onto general surfaces. Building upon this intuitive
understanding, the mesh reconstruction method (Shi et al. 2010) iteratively projects the mask
boundary onto a subspace of low frequency LB eigenfunctions and removes outliers with large
changes during the projection process. As shown in Figure 3.1, our method successfully obtained
a smooth surface for each vessel (Figure 3.1b, vessel surface reconstruction). This fully automatic
and iterative method allows the generation of a smooth surface representation of LSAs without
shrinking other parts of the mask, and it ensures that all surfaces have a consistent genus-zero
topology, which means all surfaces have no handle or hole in the reconstructed mesh (Xiao,
Chenyang and Prince 2003).
As the last step, the Reeb graph analysis method (Shi et al. 2008) was applied to model and
extract geometrical measurements of 3D vessel shapes such as vessel length and tortuosity for 3T
and 7T images, respectively (Figure 3.1c). The Reeb graph is an abstract graph describing the
neighboring relation of the level contours of a function defined on a surface. Following our work

Figure 3.1 Lenticulostriate artery morphological quantification workflow begins with manual vessel segmentation
using ITK-SNAP on the raw TSE-VFA image (a). The vessel volumes are reconstructed, and a mesh surface is
created in preparation for shape analysis (b). Quantitative measures such as vessel length and tortuosity are
calculated from the Reeb graph (c).

59
on brain surfaces (Shi et al. 2013), we used the first non-constant LB eigenfunction as the feature
function f for Reeb analysis. More specifically, we sampled 25 evenly spaced level contours of f
as plotted on the vessel surface in Figure 3.1c. The centroid of each contour was used to explicitly
represent the graph nodes. For the purpose of measuring the longest branch in each vessel, we
assumed that the Reeb graph followed a chain topology, where each node on the graph only had
up to two neighbors. To estimate the vessel length (Figure 3.1c), we extracted the center line or
medial core of the 3D vessel surface by connecting the centroids of level contours, then summed
up the distances of every two adjacent centroids. For vessel tortuosity, we used the common
distance metric measure, which provides a ratio of the estimated vessel length to the Euclidean
distance between the two end points of the curve. Vessel thickness could also be estimated;
however, we chose not to report the results due to potential errors of small vessel size on the order
of one voxel.
3.3.5. Statistical Analysis
Statistical analysis was performed with STATA 13.1 (College Station, Texas). Morphological
metrics (vessel length, tortuosity) were subject to Repeated-Measures ANOVA to evaluate the
effect of age group, gender, field strength, and hemisphere. The total branch number was also
compared across the three techniques (T1w TSE-VFA at 3T and 7T, and TOF MRA at 7T) using
within-subject ANOVA. A p-value ≤ 0.05 (two-sided) was considered statistically significant.
3.4. Results
3.4.1. Evaluation of T1w TSE-VFA Manual Segmentation and Age
Figure 3.2 shows 3D renderings of manually segmented left LSAs on T1w TSE-VFA images
at both 3T and 7T. Each primary vessel is assigned a different color label, with shorter secondary
branches being given separate labels from the primary vessel. The total bilateral number of primary
60
vessels counted using T1w TSE-VFA at 3T (mean ± SD: 11.00 ± 3.02) and 7T (11.65 ± 2.55) was
significantly higher than that by TOF MRA at 7T (6.47 ± 1.68, p=0.0001). Additionally,
significantly more secondary branches could be detected in 7T T1w TSE-VFA (3.75 ± 1.60,
p=0.0075) compared to that at 3T (2.25 ± 1.71). Figure 3.3 shows a few more examples of the 3D
renderings where more branching is detected with 7T imaging. Metrics of vessel morphology
including vessel length and tortuosity were quantified by Reeb graph analyses and subjected to
ANOVA (see Table 3.3 for mean ± SD values of the metrics at 3T and 7T in two age groups,
respectively). The effect of hemisphere and gender were not significant for both metrics. The effect
of age group was significant for mean vessel length (p=0.0257), which was reduced in aged
subjects for 7T TSE-VFA. The mean tortuosity was increased in aged subjects, but the effect was
not significant (p=0.25 for 7T TOF), as shown in the boxplots in Figure 3.4.
3.5. Discussion
3.5.1. Aging Effects on LSAs
In this study, the two age groups exhibited differences regarding the morphology of the
detected LSAs. In addition to finding significantly fewer LSAs in the aged group, there was a trend
of decreased mean vessel length and increased mean tortuosity in the aged group. Our data is
consistent with past studies quantifying the morphology of LSAs showing significant differences
between subjects with subcortical vascular dementia (SVaD) and healthy controls (Seo et al. 2012)
as well as between hypertensive and normotensive subjects (Kang et al. 2009b). With the presence
of vascular risk factors such as diabetes, hypertension, and hyperlipidemia, the LSA metrics such
as vessel number and length may further decrease compared to healthy controls. However,
increased LSA tortuosity has been reported in vascular dementia compared to age matched controls
61
(Seo et al. 2012). While this trend of increased tortuosity of LSAs in aged subjects was observed
in the 7T TOF scans of our study, there was no significant difference in tortuosity when evaluated
using TSE-VFA images at 3 or 7T. As the morphologic metrics in our study were derived from
manually segmented LSAs, it is possible that the distal portions of LSAs were not well-detected
by the human eye. As a result, tortuosity was mainly quantified in larger LSA stems, leading to
similar tortuosity in aged subjects (tortuosity is defined as the ratio between the actual path length
divided by the linear distance). It is also possible that tortuosity of LSAs may increase and
subsequently contribute to altered blood brain barrier permeability at the distal ends of these
perforators in aged subjects at risk of developing cerebral small vessel disease and dementia

Figure 3.2 Three-dimensional renderings of left LSAs from the manual segmentations of an aged subject (A,C,E)
and a young subject (B,D,F). VFA-TSE at both 3T and 7T enabled the identification of more vessels in aged
subjects, especially in the medial region. 7T VFA-TSE enabled the identification of more branches in general in
the younger subjects (i.e. orange and turquoise branch vessels in D). Despite longer segmentation of vessels using
7T TOF images, fewer vessels could be identified. As summarized by the box plot of vessel count, significantly
more vessels were detected in young subjects than in aged subjects (**, p<0.01), and more vessels were detected
using VFA-TSE compared to 7T TOF MRA (*, p<0.05).

62
compared to age matched controls (Shao et al. 2019). This hypothesis is being tested in our lab on
a cohort of aged subjects.
3.5.2. Manual Segmentation and Shape Quantification
Using manual segmentation and automated surface modeling, we performed fully 3D
analyses of the LSA morphometry in this study. The vessel counts observed for each modality
using manual segmentation in this study align with the findings of number of stems (two to ten)
and tortuosity observed in previous 7T TOF studies (Kang et al. 2009b, Kang et al. 2009a, Seo et

Figure 3.3 Additional examples of the 3D renderings of the manual vessel segmentation for two younger subjects
with larger number of vessels and branches detected. Despite the high vessel density, the resolution was
sufficient to distinguish secondary branches from primary stems.
Table 3.3 Summary of Reeb graph metrics for 3T and 7T VFA-TSE manual segmentations of young and aged
subjects (mean ± SD)

63
al. 2012). The surface reconstruction and Reeb graph analysis methods provided a consistent
representation for the comparison of vessel geometry across subjects and vessel branches.
Significant differences were detected between age groups based on the measures from Reeb graph
modeling. While we used manually delineated masks for our quantification, the 3D shape analysis
tools can be directly applied to automated segmentation results when they become available. This
will be a main direction for our future research. The manually segmented masks form a reasonable
training data for supervised learning algorithms if we consider that there are typically 10+ vessel
branches from each subject. For medical image segmentation, patch-based deep learning
segmentation algorithms have achieved success in various tasks (Wachinger, Reuter and Klein
2018, Kamnitsas et al. 2017). We will leverage these frameworks for our research on automated
LSA segmentation as they fit very well with the vessel segmentation problem, which is inherently
based on contrasts in a local neighborhood.
3.5.3. Limitations
There are several limitations in this study. The manual segmentation of LSAs is time
consuming and subjective. Depending on human observation and the limitation of the human eye,

Figure 3.4 Comparison of mean vessel length and tortuosity of lenticulostriate arteries in young (age 19-35 years)
and aged (age > 60 years) groups for each modality. * Indicates significance p<0.05; ** indicates significance
p<0.01.

64
some very distal portions of the vessels may be missed in the segmentation process. Additionally,
vessels may be over-painted in ITK-SNAP, resulting in vessels that appear thicker than their actual
morphology. Since the images likely exhibit some partial volume effects, the delineation of very
thin segments of the vessels may be difficult to the human eye. However, as there is no gold
standard for delineating the LSAs on T1w TSE-VFA images, manual segmentation is the best
possible label that could be used as supervision for deep learning model training. Another
limitation is the number of data samples with completed segmentations. In addition to manually
separating the two hemispheres into separate images, data augmentation was employed to increase
performance. In the future, with fine tuning of the application of OOF or Frangi vesselness filters,
a rough segmentation can be performed to possible pre-train the network with more samples. As
this is a prospective ongoing study, more data will be collected and included in the training dataset.
3.6. Conclusion
The segmentation of LSAs in high-resolution black-blood 3D T1w TSE-VFA may serve as a
new method for the direct visualization and quantification of small vessel morphological changes
with age. Considering that automatic segmentation is highly feasible, evaluating the shape and
number of LSAs can be a promising imaging marker of pathological conditions related to damaged
LSAs.

65
4. CHAPTER 4: Vessel Density Mapping of Brain Small Vessels on 3D High Resolution
Black Blood MRI
4.1. Abstract
Objectives
Cerebral small vessels are largely inaccessible to existing clinical in vivo imaging technologies.
This study aims to present a novel 3D analysis method for automatic segmentation and regional
3D vessel density mapping of brain small vessels from high-resolution 3D black-blood MRI at 3T.
Materials and Methods
Fifty-two subjects (10 under 35 years old, 42 over 60 years old) were imaged with the T1-weighted
turbo spin echo with variable flip angles (T1w TSE-VFA) sequence optimized for black-blood
small vessel imaging with iso-0.5mm spatial resolution on a 3T Siemens Prisma scanner. High
quality cerebral small vessel segmentation was obtained by the Jerman filter. Hessian-based vessel
segmentation methods (Jerman, Frangi and Sato filter) were evaluated by vessel landmarks and
manual annotation of lenticulostriate arteries (LSAs). Using optimized vessel segmentation and
non-linear registration, a semiautomatic pipeline was proposed for localized detection of small
vessels changes across populations and further quantification of small vessel density across brain
regions. Voxel-level statistics was performed to compare regional vessel density between two age
groups as well as between aged subjects with and without vascular risk factors, respectively.
Results
Jerman filter showed better performance for vessel segmentation than Frangi and Sato filter which
was employed in our pipeline. Cerebral small vessels on the order of few hundred microns can be
delineated using the proposed pipeline on 3D black-blood MRI at 3T. The mean vessel density
across the whole brain was significantly higher in young subjects compared to aged subjects with
66
and without vascular risk factors. The aged subjects with vascular risks showed a trend of reduced
mean vessel density compared to the aged subjects without vascular risk factors.
Conclusion
The proposed pipeline is able to segment, quantify, and detect regional differences in vessel
density of brain small vessels in the order of a few hundred microns based on 3D high-resolution
black-blood MRI. This framework may serve as a tool for localized detection of small vessel
density changes in aging and neurovascular diseases.
Keywords: High-resolution black blood MRI, Turbo spin echo with variable flip angles (TSE
VFA), vessel segmentation, vessel density, small vessel disease

4.2. Introduction
Cerebral small vessel disease (cSVD) is often associated with neurodegenerative disease, and
it can contribute to the progression of cognitive decline and physical disabilities (Wardlaw, Smith
and Dichgans 2013a, Mayda and DeCarli 2009, Rosenberg et al. 2016, Breteler et al. 1994, Debette
et al. 2010). Neuroimaging plays a key role in characterizing cSVD by identifying various features
linked to cSVD including recent small subcortical infarcts, lacunes, white matter hyperintensities,
enlarged perivascular spaces, microbleeds, and brain atrophy (Wardlaw et al. 2013b, Blair et al.
2017, Vemuri, Decarli and Duering 2022). However, when these features become visible or
detectable in structural imaging, they are already manifestations of significant deterioration caused
by cSVD. Recent advanced imaging techniques have facilitated the assessment of pathophysiology
by determining microstructural tissue integrity (Baykara et al. 2016) as well as vascular function
through the measurement of cerebral blood flow, arterial stiffness, cerebrovascular reactivity, and
blood brain barrier leakage (Jann et al. 2021, Yan et al. 2016, Sur et al. 2020, Shao et al. 2019).
67
Because the underlying mechanisms of early cerebral microvascular changes in conditions related
to cSVD remain poorly understood, there is an increasing desire to detect the earliest features of
cSVD in order to prevent or mitigate downstream disease-related tissue changes.
Considering all the features that are consequences of cSVD, it is essential to be able to directly
visualize and evaluate the cerebral small vessels themselves. To date, however, these small vessels
are largely inaccessible to existing clinical in vivo imaging technologies. We recently proposed
and optimized a high resolution 3D black-blood MRI with sub-millimeter (iso-0.5mm) spatial
resolution using T1-weighted turbo spin echo with variable flip angles (T1w-VFA-TSE) at field
strengths of 3 and 7 Tesla (Ma et al. 2019). Utilizing this optimized black-blood sequence for a
smaller focused field of view, we demonstrated that the 3D segmentation and quantification of
lenticulostriate arteries (LSAs) was feasible (Ma et al. 2019). The long echo train of the TSE

Figure 4.1 Method overview. 1) Vessel segmentation pipeline including: (a) Input high-resolution black blood MRI
to the pipeline, (b) Preprocessing steps such as skull-stripping, bias correction and denoising by non-local means
(NLM) applied on (a), (c) 3D vessel enhancement, various multiscale Hessian-based methods (Frangi et al., 1998,
Sato et al., 2000, Jerman et al., 2016) have been evaluated for enhancement of the small vessels; Jerman filter
outperformed other candidate methods. (d) Binarized vessel mask (BVM) was obtained by thresholding Jerman’s
vesselness map using the optimal threshold. (e) Spatial masking was defined to construct region of interest (ROI)
and classify small cerebral vessels. (f) Vessel density image (VDI) was calculated by diffusing the content of (e) to
the entire image volume.2) Co-registration of partial view of black-blood MRI (g) and full view of MPRAGE image
(h) pairs using 12 landmark points and 3D affine registration. 3) VDI mapping to normalize VDI of each subject
(I) to MNI atlas (i), non-linear registration was obtained by registration MPRAGE of each subject (k) to MNI
atlas(i). The normalized VDI (j) was transformed to MNI Atlas by combining deformation fields computed in step
1 and step 2.

68
technique offers two main advantages for visualizing small vessels: 1) satisfactory flow
suppression by inherent dephasing of flowing signals (black blood MRI); 2) sub-millimeter spatial
resolution (isotropic ~0.5–0.6 mm) and near whole-brain coverage in a clinically acceptable time
(<10min). We and others demonstrated that TSE-VFA is suitable for visualizing lenticulostriate
arteries (LSAs) on the order of a few hundred microns, which can be manually segmented for the
quantification of their branch number, length, and tortuosity (Ma et al. 2019, Kang et al. 2009b,
Cho et al. 2008).
The purpose of this study is to present a semiautomatic post-processing pipeline (Figure 4.1)
for segmenting, quantifying, and regional vessel density mapping of brain small vessels in high
resolution (isotropic ~0.5mm) black-blood MRI with near whole-brain coverage of young and
aged subjects at 3T. Skull-stripped high resolution black-blood MRIs were first preprocessed via
bias correction and non-local means (NLM) denoising. Hessian-based vessel segmentation
methods (Jerman, Frangi and Sato filter) were evaluated by vessel landmarks and manual
annotation of LSAs. Using optimized vessel segmentation and non-linear registration, a
semiautomatic pipeline was proposed for localized detection and segmentation of small vessels
and further quantification of small vessel density across brain regions. Voxel-level statistics was
performed to compare regional vessel density between two age groups as well as between aged
subjects with and without vascular risk factors, respectively.
4.3. Methods
4.3.1. Subjects and Imaging
The study was approved by the institutional review board of the University of Southern
California (USC) and in accordance with the principles of the Tents of Declaration of Helsinki.
Black-blood MRI and T1w structural images (MPRAGE) were collected from 52 participants and
69
divided into young control (N =10, 4 female, 27±3.5 years, age range [22,33]), aged control (N
=18, 14 female, 69.4±6 years, age range [60, 81]), and aged with vascular risk factors (N =24, 24
female, 67.4±7.2 years, age range [59, 82]) groups. In the last group, subjects have at least one of
the diagnoses for diabetes, hypertension, or high cholesterol. Images were acquired using a
Siemens 3T MAGNETOM Prisma scanner with a 32-channel head coil. The “black blood”
contrast was attained with an optimized T1w-VFA-TSE sequence (Ma et al. 2019) with the
following parameters: TR/TE = 1000/12ms, turbo factor = 44, matrix size = 756x896, resolution
= 0.51x0.51x0.64 mm
3
interpolated to 0.5x0.5x0.5 mm
3
, 160 sagittal slices and 10% oversampling,
GRAPPA factor = 2; total imaging time = 8:39 min. This sequence provided nearly whole brain
coverage except that the sagittal FOV was 80mm, and bilateral saturation bands were applied to
suppress the out-of-volume signals from temporal regions. Image quality grading of the high-
resolution 3D black-blood MRI was performed by two expert graders. Grading criteria was based
on a 4-point Likert scale, considering imaging artifacts such as motion, blurring, ringing, and
wraparound. MRI images included in this study had an image quality grade and vascular quality
grade of 3 or higher. This dataset that was used for group-studies will be referred to as high-
resolution black blood-3T-52 (HRBB-3T-52) in the rest of the manuscript. Additionally, for the
validation purpose of the vessel segmentation methods, 15 LSA images from the volunteer cohort
of our previous study (Ma et al. 2019) was also included. This cohort included a total of 15 healthy
volunteers, with 9 participants (7 male, 27.2 ± 3.5 years) between 22-33 years old and 6
participants (1 male, 64 ± 2.4 years) more than 61 years of age, herein referred to as the young and
aged group, respectively. LSAs separated by left and right hemispheres to avoid the ventricular
structures for all image volumes, this dataset will be referred to as LSA-30 in the rest of the
manuscript.
70
4.3.2. Pre-Processing
To prepare the images for vessel
segmentation, initially, high-resolution
black blood MRI and MPRAGE images
were skull-stripped using Statistical
Parametric Mapping (SPM) software. Due
to intensity inhomogeneity and relatively
low signal to noise ratio (SNR), skull-
stripped images of high-resolution black-blood MRI were further pre-processed by bias correction
and denoised via non-local means (NLM) filter (Buades et al. 2005a). The NLM denoising
algorithm’s idea is to take advantage of self-similarities across the whole image by comparing
local neighborhoods or image patches. It weights patches across the image based on their similarity
to the patch centered at the current voxel. The denoised image is then constructed by the weighted
average of these patches. Due to the high computation burden of NLM in 3D (Buades, Coll and
Morel 2005b), block-wise NLM was adopted in this study which allows computationally efficient
filtering without compromising the denoising result (Coupé et al. 2008). In previous works (Chen
et al. 2011, Zhang et al. 2014), it was shown that this process preserves anatomical detail while
suppressing the noise. For each voxel 𝑥 𝑗 with intensity value of 𝑈 (𝑥 𝑗 ), the weight of 𝜔 (𝑥 𝑖 ,𝑥 𝑗 ) is
assigned to 𝑈 (𝑥 𝑗 ) in the restoration of 𝑥 𝑖 voxel. The
weights here quantify the similarity based on the Euclidean distance of local neighborhoods
𝑁 𝑖 and 𝑁 𝑗 for voxels 𝑥 𝑖 and 𝑥 𝑗 , respectively. The calculation of NLM weights is shown in (1).
𝜔 (𝑥 𝑖 ,𝑥 𝑗 )=
1
𝑍 𝑖 𝑒 −
‖𝑢 (𝑁 𝑖 )−𝑢 (𝑁 𝑗 )‖
2𝑎 2
ℎ
2
(1)

Figure 4.2 Example high-resolution black blood MRI
preprocessing shown on a selected sagittal scan. (a) Raw
image of a young control subject. (b) preprocessed image
using skull-stripping, bias correction and NLM denoising.

71
Where ‖.‖
2𝑎 2
is Gaussian weighted Euclidean distance, 𝑍 𝑖 is a normalization constant to
guarantee that ∑ 𝜔 (𝑥 𝑖 ,𝑥 𝑗 )
𝑗 =1 , and ℎ is the wight smoothing parameter that controls the degree
of filtering. In this study, the search window size, which has an impact on computational time and
visual quality of the results, was experimentally set to 3×3×3 in a block of size 32×32×32
within each 3D black blood MRI volume. To avoid excessive denoising and preserve small vessel
details, the smoothing parameter ℎ, which depends on the noise level, was empirically estimated
as 0.03. Figures 4.2(a) and 4.2(b) show an example of sagittal view of high-resolution black block
MRI of a young control subject before and after pe-processing, respectively.
4.3.3. 3D Vessel Enhancement
Apart from noise that could negatively impact accurate segmentation and quantification of
vascular analyses, another challenge that is mainly caused during image acquisition, is varying
intensities of curvilinear structures within and across vessels. To overcome the undesired intensity
variations of vessel images and to suppress non-vascular structures, numerous filter-based
enhancement methods have been proposed (Agam et al. 2005, Wiemker et al. 2013, Krissian et al.
2000, Frangi et al. 1998, Sato et al. 2000, Li et al. 2003, Erdt et al. 2008, Zhou et al. 2007, Law
and Chung 2010, Jiang et al. 2006, Zhang et al. 2010), and their performances have been
significantly improved recently. Among these methods, Hessian-based filters which are based on
second order image derivatives have shown great success in various clinical applications such as
segmentation of liver vessels in abdominal CTA (Luu et al. 2015), lung vessels in thoracic CT
(Rudyanto et al. 2014), and computer-aided detection of cerebral aneurysms in 3D rotational
angiography, MRA and CTA (Hentschke et al. 2014). In this category of methods, recently Jerman
filter which is based on the ratio of Hessian matrix eigenvalues has been proposed for enhancement
of both 2D and 3D vasculatures (Jerman et al. 2016). The authors demonstrated that Jerman
72
method overcomes some of the deficiencies of previous Hessian-based functions such as poor and
non-uniform response for vessels with varying contrast and size, at bifurcations and aneurysms.
Jerman’s enhancement function is inspired by the volume ratio measure for detection of nearly
spherical diffusion tensors (Peeters et al. 2009) and is defined as:
𝑉 =
{

0 𝑖𝑓 𝜆 2
≤0 ⋀ 𝜆 𝜌 ≤0
1 𝑖𝑓 𝜆 2
≥
𝜆 𝜌 2
>0
𝜆 2
2
(𝜆 𝜌 − 𝜆 2
)(
3
𝜆 2
+ 𝜆 𝜌 )
3
𝑜𝑡 ℎ𝑒𝑟𝑤𝑖𝑠𝑒 .
(1)
Where, 𝜆 𝜌 is the regularized value of 𝜆 3
at each scale S and is defined as below to ensure the
robustness of vesselness measure to low magnitudes of 𝜆 2
and 𝜆 3
.
𝜆 𝜌 (𝑠 )
= {
𝜆 3
𝑖𝑓 𝜆 3
>𝜏 𝑚𝑎𝑥 𝑋 𝜆 3
(𝑋 ,𝑠 )
𝜏 max
𝑥 𝜆 3
(𝑋 ,𝑠 ) 𝑖𝑓 0< 𝜆 3
≤𝜏 𝑚𝑎𝑥 𝑋 𝜆 3
(𝑋 ,𝑠 )
0 𝑜𝑡 ℎ𝑒𝑟𝑤𝑖𝑠𝑒 .
(2)
Where, 𝜏 is a cutoff threshold between zero and one. Higher value of 𝜏 increases the difference
between 𝜆 2
and 𝜆 3
magnitudes for low contrast structures. The proposed enhancement function’s
response values range from 0 to 1.
In this study, according to the vascular anatomy of the brain and the study cohort that includes
aged control and aged with vascular risk factors subjects with thin, tortuous and low contrast
vessels, an ideal enhancement function should exhibit robust, uniform, and high response in the
presence of: i) varying noise and contrast, ii) varying vascular morphology (e.g., multiscale vessels
especially small vasculature, vessels with different cross-sections (circular-elliptical)), iii)
pathology (e.g., vessels thinning, high tortuosity or vessel bends).
Based on the criteria we defined for ideal cerebral small vessel enhancement, Jerman filter
appears to be a proper choice. However, to justify our preference, the performance of Jerman
method was compared with widely used enhancement functions proposed by Frangi’s (Frangi et
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al. 1998) and Sato’s (Sato et al. 2000) methods. We will provide the results of performance
assessment and comparison among the candidate methods using clinical 3D vessel data in Section
4.4.1.2.
4.3.4. 3D Vessel Segmentation and Performance assessment
Two levels of validation were presented using: 1) Vessel landmarks of cerebral small vessels
from high-resolution black blood MRIs, and 2) 3D annotation of LSAs from unilateral LSA images
from left and right hemispheres of 15 subjects from LSA-30 dataset (Figure 4.3 (2)). To evaluate
the segmentation accuracy of the candidate Hessian-based methods, the vessel segmentation was
obtained by thresholding the vesselness map, where the threshold value was carefully estimated
using vessel landmarks of validation dataset. Validation cohort for marking cerebral vessel

Figure 4.3 Method validation dataset. (1) Vessel and background landmark annotation on selected sagittal slice
of three representative subjects, where (A-1) is a healthy 29-year-old male, (B-1) is a healthy 64-year-old female
and (C-1) is a 62-year-old female with diabetes and hypertension. Magnified view of vessel landmarks (red voxels)
and background points (green voxels) of the corresponding selected subjects are shown in (A-2), (B-2) and (C-2),
respectively. (2) Manual Lenticulostriate artery (LSA) annotation by experts using ITK-SNAP on (a) 2D slices from
axial (a-Row1), coronal (a-Row2) and sagittal (a-Row3) views, and (b) 3D rendering of LSA labels in (a). (c, d)
Thin minimum intensity projections of high-resolution 3T MRI of LSAs for (G-1) a healthy 25-year-old male, and
(G-2) a healthy 67-year-old female. Matching 3D LSA labels are shown in (H-1) and (H-2), respectively.

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landmarks was a subset of HRBB-3T-52 dataset, which included 15 subjects comprised of 5 young
control, 5 aged control and 5 aged subjects with vascular risk factors (Figure 4.3 (1)).
For objective assessment of the segmentation performance of the candidate methods, the
following metrics were employed:
• Sensitivity (SEN) = TP/ (TP + FN).
• Specificity (SPE) = TN/ (TN + FP).
• Accuracy (ACC) = (TP + TN)/ (TP + TN + FP + FN).
• Average Hausdorff distance (AVD)
Where TP is true positive, FP is false positive, TN is true negative, and FN is false negative. The
AVD metric is resistant to outliers and denote the longest distances in voxels between ground-
truth and segmentation results, hence, smaller values indicate better performance. AVD metrics
will be calculated only for LSA segmentation validation since we have complete annotation of the
vessels. We did not report Dice for LSA segmentation assessment because distance-based metrics

Figure 4.4 Spatial distribution of arteries, veins, and dural sinuses in high-resolution black blood MRI. (a)
sagittal, coronal, and axial slices with overlayed vessel annotations. (b) 3D-rendering results of vascular network
in (a); in (B-1, B-2) vessels are color coded to show vascular classification, where red-colored vessels are small
arteries and veins, green-colored vessels are dural sinuses, and yellow-colored vessels are MCAs. To obtain final
small vessels mask (B-3, B-4), dural sinuses and regions pointed by (1) and (2) are excluded using anatomical
masking.

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are recommended when the segment size (e.g., LSA) is significantly smaller than background
(Taha and Hanbury 2015) .
4.3.5. Vessel Classification using Anatomical Masking
The vessels of interest in this study are small artery, arterioles, venules and small veins which
are detected by a Hessian-based method applied on skull-stripped high-resolution black block MRI
(0.5mm isotropic), with optimized scale (vessel radii) range for the study cohort which is equal to
[0.1-0.4]. To obtain small vessels’ mask, the resultant vascular structure (or BVM) of skull-
stripped high-resolution black-block MRI should be classified. More precisely, apart from
complete small cerebrovascular network, the final BVM includes full or partial detection of
superficial veins, dural sinuses (include superior sagittal sinus, straight sinus, transverse sinus, etc.)
and middle cerebral artery (MCA) (Figure 4.4(a)). To separate these vessels, a region of interest
(ROI) is defined via anatomical regions of MPRAGE images using Freesurfer ASEG map. As
shown in Figure 4.4, dural sinuses form the terminal of superficial venous system and distribute

Figure 4.5 Vessel density image (VDI) representation. (a) 3D-rendering of BVM of a young control subject (A-1,
A-2). (A-3) Corresponding VDI of BVM in (A-1, A-2) before (A-3) and after normalization (A-4). (b) 3D-rendering
of BVM of an aged control subject (B-1, B-2). (B-3) Corresponding VDI of the BVM in (B-1, B-2) before (B-3) and
after normalization (B-4).

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without closely accompanying arteries (Rhoton 2002). Therefore, to isolate dural sinuses and
superficial veins, a tentative mask (Vten) is generated by morphological erosion of the brain mask
(consist of WM, GM, and CSF). Afterwards, to exclude regions with larger arteries and highly
variable small vessel detection due to low SNR or imaging artifacts, the final ROI (Figure 4.1(e))
is made by eliminating cerebellum, brainstem, optic-chiasm and ventral regions from Vten. The
ROI mask is then reversely transformed to angiographic image space using previously obtained
affine transformation in Section 4.3.7.
4.3.6. Vessel Density Calculation
Vessel density image (VDI) calculated to allow efficient localized comparison of vascular
changes across individuals. This step is essential since the spreading pattern of small vessels in
high resolution black blood MRI varies among different subjects. This makes the direct
comparison of cerebral small vessels at voxel-level a challenging task. To overcome this challenge,

Figure 4.6 Flow chart of co-registration and VDI normalization. Step1: Co-registration of high-resolution black-
blood MRI (a) and MPRAGE (b) image pairs, using 3D-Affine registration with 12 landmark points, where (a) is
the fixed and (b) is the moving image. Step2) Nonlinear warp between the MNI-152 Atlas (c) and MPRAGE (e)
image. VDI was first reversely transformed to MPRAGE space using affine transformation (f), and then non-
linearly transformed to the MNI Atlas using a B-spline transformation (d).

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we computed VDI of each subject by diffusing the content of BVM to the entire image volume.
More precisely, VDI is a quantitative smooth vessel map that is obtained by a convolution between
the BVM and a 3D average kernel, where the window size of the kernel was empirically estimated
as [30 30 30] to maintain vascular distribution of individual subjects.
Representative examples for VDI of a young control and aged control subject are shown in
Figure 4.5. In the VDI representation, red regions denote highest vessel density associated with
large vessels or regions with dense vessel distribution. Blue regions indicate lowest vessel density,
such as avascular areas. According to the VDI representations, we can observe spars vessel
distribution in the aged subject (Figure 4.5(b)) and a dense vessel network in the young subject
(Figure 4.5(a)).
4.3.7. Mapping Vessel Density Across Subjects
Due to anatomical variation, different brain size and MRIs’ orientations among subjects, it is
required to normalize the subjects’ VDIs into common space to enable cross-subject comparison
at voxel-level. To this end, we proposed a two-step registration method (Figure 6). In the first
step, to robustly co-register skull-stripped black-blood MRI and MPRAGE image pairs, a 3D
affine registration with 12 landmark points was performed (Figure 6(a, b)) using the Elastix
software (Klein et al. 2010). The landmarks were manually selected from the cerebrum,
cerebellum, and brainstem regions to guide the co-registration between the two 3D volumes with
different field of views, where the black-blood MRI has near-whole brain coverage while the
MPRAGE scan has full brain coverage. In the second step, we compute the nonlinear warp
between the MNI152 Atlas (common space in this study) and the MPRAGE image (Figure 6(c,
e)). By combining the affine and nonlinear warp, we obtain the final transformation from the black-
blood MRI to the MNI152 space.
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To pool the VDIs from all subjects into the MNI152 space for statistical analysis, VDI was
first reversely transformed to MPRAGE space using previously computed affine transformation
(Figure 4.6(Step-1)), and then non-linearly transformed to the MNI Atlas using a B-spline
transformation (Figure 4.6 (Step-2)). After non-linear registration, all VDIs were normalized, and
a p-value map was generated by comparing the registered VDIs of the two groups at voxel-level.
For each voxel, a two-tailed student t-test was applied to examine the group difference between
the VDI values of comparing groups.
4.4. Results
4.4.1. Validation Results of in vivo MRI
The enhancement of small cerebrovascular network with the frequently used multiscale
Hessian filters was quantitatively and qualitatively evaluated on clinical data. To this end, we first
presented an effective approach based on receiver operating characteristic (ROC) curve and
bootstrapping to find the optimized scale range and threshold value for the enhancement functions.
For further assessment, we present the performance assessment of the comparing methods on LSA
segmentation using the optimal parameters. Afterwards, the qualitative and quantitative results of
the best performing method, Jerman, is presented.
4.4.1.1. Scale and threshold parameters estimation
In multiscale Hessian-based methods, vessels’ scale range and the threshold value for
binarizing the vesselness response are two important parameters to estimate. Inaccurate assessment
of these parameters will result in over or under segmentation of the vascular network of interest.
To quantitatively evaluate the choice of parameters, for each high-resolution black blood MRI we
annotated 2000 vascular and 2000 non-vascular landmarks (Figure 4.3). Vessel landmarks were
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mostly placed at the center and boundary of small and low contrast vasculature to increase the
sensitivity of our evaluation in small vessel detection. The non-vascular landmarks were placed
densely in the vicinity of the vessel’s boundary and CSF region where over segmentation and false
positive detection are most likely to occur.
To fine-tune the scale parameter, we employed Jerman filter as the reference model. Initially,
the scale range was estimated as [0.1-0.5] with a step-size of 0.1 based on the vascular anatomy
within ROI of the study cohort. After that, to find the optimized scale’s lower and upper bounds,
we performed a window search by first fixing the lower bound (s = 0.1) and increasing the upper
bound by 0.1 in [0.2-0.5] scale range (Figure 4.7(a)), and then by freezing the upper bound to 0.5
and increasing the lower bound by 0.1 in scale range of [0.1-0.4] (Figure 4.7(b)).
At each scale range, Jerman response of every subject in the validation dataset was binarized
by applying various thresholds from the range of [0.001-0.4]. At each point on the ROC plot, the
average of TPR and FPR rates were calculated by iteration over the mentioned threshold range

Figure 4.7 Scale and threshold parameters optimization using vessel landmarks. ROC curves of Jerman response
(a) with variable upper-bound in the scale range to find the optimal upper-bound, (b) with variable lower- bound
in the scale range to find the optimal lower-bound (c) with optimal scale range of [0.1-0.4] to find the optimal
threshold value. The threshold range in (a) and (b) is set to [0.001-0.4], and in (b) is set to a tighter range of
[0.001-0.2]. Overall, the optimal scale range and threshold were estimates as [0.1-0.4] and 0.072, respectively.

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with step-size of 0.005. Comparing the ROC curves in Figure 4.7(a, b), shows that scale range of
[0.1-0.4] is the preferred setting due to higher area under the curve (AUC).
The optimal threshold, which was determined by a point on the ROC curve closet to the
optimal classifier (i.e., upper left corner of ROC plot), has been estimated as 0.072 for Jerman
filter (Figure 4.7(c)). To robustly estimate this threshold, we used bootstrapped samples of the

Figure 4.8 Performance comparison of Hessian-based methods for small cerebral vessel segmentation. (Row-1)
3D-rendering result of a young control subject (Female, 25 years old) by (a) Jerman, (b) Frangi, (c) Sato filter
with optimized parameters. (Row-2) Magnified view of the annotated white box in Row-1. (Row-3) 3D-rendering
result of an aged control subject (Female, 70 years old) by (a) Jerman, (b) Frangi, (c) Sato filter with optimized
parameters. (Row-4) Magnified view of the annotated white box in Row-2. Overall, Jerman filter has more
uniform and continuous vessel segmentation result for both young and aged subjects.

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validation cohort with 1000 iteration and performed ROC analysis, where the scale range was fixed
to the optimal discovered value range of [0.1-0.4] and the search window for the threshold value
was defined as [0.001-0.2] with the step size of 0.001.
4.4.1.2. Performance evaluation using vessel landmarks and LSAs
Evaluation and comparison of the multiscale filters with three enhancement functions:
Frangi’s (Frangi et al. 1998), Sato’s (Sato et al. 2000) and Jerman’s (Jerman et al. 2016) was
performed based on the annotated vessel landmarks of High-resolution black-blood MRIs (Figure
4.8) and manual segmentation of LSAs respectively (Figure 4.9). For all the three methods, the

Figure 4.9 Performance comparison of Hessian-based methods for LSA segmentation of the same subjects in
Figure3. 3D-rendering of the LSA manual segmentation (column-1), and the segmentation result of the young
(Row-1) and aged (Row-3) subject by (a) Jerman, (b) Frangi, (c) Sato filters with the same parameters as in
Figure3. (Row-2, Row-4) Corresponding error map of the segmentation results in (Row-1) and (Row-3),
respectively.

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scale range of multiscale Hessian-based methods was set to the optimal value of [0.1-0.4]. Utilizing
the ROC analysis described in Section 4.4.1.1, the optimal threshold value was identified as 0.072,
0.005 and 0.15 for Jerman, Frangi and Sato’s filters, respectively. We expect the winning method
to generate more robust and generalizable vessel segmentation for all small vessels including LSAs
with the same parameter setting.
Table 4.1 Summary of evaluation metrics for small vessel segmentation using vessel landmarks of validation

Table 4.2 Summary of evaluation metrics for LSA segmentation using manual annotation of young and aged
subjects.

Figure 4.10 3D visualization of small vessels segmentation using Jerman method with optimized parameters. (a)
young control, (b) aged control, (c) aged group with vascular risk factors (VRF), where VCID002 has
hypertension and high cholesterol, VCID008 is diagnosed with diabetes, hypertension, and high cholesterol,
VCID010 has only diabetes and VCID041 has high cholesterol. Aged groups (bottom two rows) have sparser
vessel network compared to young group (first row).

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Qualitative comparison of ROI vessels using the candidate methods of a young and aged
subject is demonstrated in Figure 4.8. The results show that Jerman filter (Figure 4.8(a)) generates
more robust, uniform and continuous vessel segmentation results compared to the other methods.
Moreover, Frangi results has more small, disconnected components in the vascular network
segmentation of both young (Figure 4.8(b)(B-1) and aged (Figure 4.8(b)(B-2)) subjects. With
Sato’s method, the resultant BVM has more discontinuity compared to Jerman’s and Frangi’s
methods. For further assessment of the candidate methods, the output of LSA’s segmentation of
the same young and aged subjects are demonstrated in Figure 4.9. The ground-truth of LSA
delineation for both subjects are illustrated in Figure 4.9(Column-1).By visual inspection,
Jerman’s (Figure 4.9(a)) and Frangi’s (Figure 4.9(b)) methods have comparable results for LSA
segmentation. The error map visualization of both methods shows that most of the vessels are
detected correctly for the representative subjects (Figure 4.9(A-2, B-2, A-4, B-4). Jerman’s filter
demonstrate less discontinuity compared to Frangi’s method in the young subject (White arrows
in Figure 4.9(A-1, B-1)). Sato’s filter (Figure 4.9(c)) demonstrates lower detection rate compared
to the other two methods mainly at the distal portion of the LSAs (white arrows in Figure 4.9(C-
2, C-4)).
Quantitative results of the three methods based on vessel landmarks and LSA annotation
of LSA-30 dataset are provided in Table 1 and Table 2 respectively. According to Table1, in
vessel landmarks validation, sensitivity (SE) better matched with our qualitative assessment of the
segmentation results. Jerman’s method showed the best performance in all three metrics including
the AUC of ROC curves, sensitivity (SE) and specificity (SP). Table 2 of LSA validation results
also shows that Jerman’s method outperformed the other two methods in all four metrics including
AUC, SE, SP and AVD.
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4.4.2. Qualitative Results in Young and Aged Subjects
Representative examples of 3D small vessel segmentation of High-resolution black blood
MRI using Jerman filter with optimized parameters are demonstrated in Figure 4.10. Four cases
are selected from each of the three groups in our study cohort, namely as young control (Figure
4.10(a)), aged control (Figure 4.10(b)), and aged with vascular risk factors (Figure 4.10(c)).
Overall, by qualitative comparison we can see that young control subjects have significantly higher
vessel density compared to the aged groups (Figure 4.10(b, c)). However, the vessel density
difference between the aged control and aged with vascular risk factors is not considerably
different.
4.4.3. Quantitative Results in Young and Aged Subjects
4.4.3.1. Global Mean Vessel Density
Figure 12 illustrates the comparison
among vessel density measures of the YC, AC
and aged with vascular risk factors (A-VRF)
groups. To account for variation of brain size
across different individuals, vessel density is
normalized by the ROI size of small vessels.
More precisely, normalized vessel density
measure of each subject equals to (small vessels
volume/ ROI volume), where ROI is defined in
Section 4.3.5. As shown in Figure 12, YC has
significantly higher vessel density compared to both aged groups, the result of two-way student t-
test demonstrates more significant difference between vessel densities of YC and A-VRF (p<0.01)

Figure 4.11 Comparison of mean vessel density of small
cerebral vessels in young (age 22-33 years) and aged
(age > 60 years) groups with and without vascular risk
factors. * indicates significance p<0.05; ** indicates
significance p<0.01.

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compared to YC and AC (p<0.05). Furthermore, A-VRF has lower vessel density than AC,
however the change of vascularity measure is not considerable between these two groups.
4.4.3.2. Localized Vessel Density Analysis
4.4.3.2.1. Group-wise Analysis of Age-dependent Vessel Density Changes in the Normal Brains
In order to demonstrate the potential application of our proposed localized vessel density
analysis with respect to aging, in this section we perform a group-wise experiment between two
age groups. Twenty-eight control subjects are divided into young control (N=10, age range =
[22,33], Age mean±SD (yrs) = 27±3.5) and aged control (N =18, age range = [60, 81], Age
mean±SD (yrs) = 69.4±6). Registered VDI of 10 YCs were compared to that of the 18 ACs. Figure
4.12 demonstrates the quantitative results of the group comparison between these groups in the
near-whole brain volume. For the large cluster of significant regions (P<0.05), the older group has
consistently lower vessel density than the younger group. Furthermore, the results show that larger
clusters (top 3) with higher vessel density in the younger group are located in Superior Frontal
Gyrus, Middle Frontal Gyrus, and Precentral Gyrus regions (Figure 4.12 (b)).
4.4.3.2.2. Group-wise Analysis of Vessel Density Changes in the Brains with Vascular Risk
Factors
For further assessment of our proposed localized vessel density mapping technique and to
compare the vascular changes in normal aging versus aging in the presence of any combination of
vascular risk factors, we conduct group-wise experiment between YC and A-VRF and between
AC and A-VRF groups. In the first experiment (Figure 4.13), registered VDI of 10 YCs (Age
range = [22,33], Age mean±SD (yrs) = 27±3.5) were compared to that of the 24 A-VRFs (Age
range = [59, 82], Age mean±SD (yrs) = 67.4±7.2) subjects. Similar to YC versus AC comparison,
in the right hemisphere, the older group has significantly (P<0.05) lower vessel density than the
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younger group with a similar localization pattern as YC-AC (Figure 4.12 (b) (left column)).
However, in the left hemisphere, compared to YC-AC experiment a larger cluster is observed with
vessel expansion in evaluating AC and A-VRF vessel densities. In the second experiment (Figure
4.14), the registered VDIs of the two aged groups (AC, A-VRF) were evaluated and the
localization result is presented in Figure 4.14(b). As shown in Figure 4.14(b)(B-1), there isn’t a
considerable localized clusters with vessel loss or expansion. However, in the left hemisphere
larger cluster is noted with significant (P<0.05) increased vascularity in aged subjects with
vascular risk factors compared to aged controls.
4.5. Discussion
In this study, we implemented and validated a comprehensive 3D analysis framework for
localized mapping of small vessel density changes in high resolution (isotropic ~0.5mm) black

Figure 4.12 Localization of significantly different voxels (p<0.05) in comparison between YC (N=10) and AC
(N=18) subjects. (a) P-value map overlaid on the MNI152 atlas; blue regions have lower p-value compared to
red-regions. (b) Color-coded localization map overlaid on the MNI152 atlas; green regions demonstrate the voxels
with significantly (p<0.05) higher vessel density in YC compared to AC, and red regions show the voxels with
significantly (p<0.05) lower vessel density in YC compared to AC.

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blood MRI with near whole-brain coverage of young and aged subjects at standard clinical
magnetic field strength of 3T. In our experimental results, we evaluated the performance of the
proposed framework in studying the normal aging and aging with vascular risk factors on the brain
small vessels. Overall, we observed a decreasing pattern in the small vessel density by aging, with
more decline in the cerebral vascularity in aging with vascular risks compared to normal aging.
4.5.1. Clinical Value of Whole Brain Small Vessel Density Mapping
To date, limited in vivo techniques are available to directly assess cerebral small vessels
across the whole brain. Digital subtraction angiography (DSA), x-ray computed tomography
angiography, and MR angiography with TOF have been applied to observe large cerebral vessel
remodeling in clinical populations (Gotoh et al. 2012, Kammerer et al. 2017, Wardlaw et al.
2013b), but the sensitivity to small vessels such as the perforating arteries is moderate at best and
difficult to characterize and quantify. With the proposed 3D multimodal framework for analyzing

Figure 4.13 Localization of significantly different voxels (p<0.05) in comparison between YC (N=10) and A-VRF
(N=24) subjects. (a) P-value map overlaid on the MNI152 atlas; blue regions have lower p-value compared to
red-regions. (b) Color-coded localization map overlaid on the MNI152 atlas; green regions demonstrate the voxels
with significantly (p<0.05) higher vessel density in YC compared to AD, and red regions show the voxels with
significantly (p<0.05) lower vessel density in YC compared to A-VRF.
.

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high-resolution black blood MRI, the automated segmentation enables both localized and holistic
direct assessment of cerebral small vessels. Moreover, our approach to vessel density mapping
sheds light on how the small vessel organization in the brain may be altered with respect to aging
or any combination of vascular risk factors. This analysis framework may be useful as an early
screening tool for cSVD to gauge overall health of cerebral small vessels. Furthermore, it could
serve as a biomarker to monitor disease progression and/or response to interventions for vascular
dementia.
4.5.2. Segmentation and Quantification
This study is inspired by our previous work (Sarabi et al. 2020), where we developed a 3D
retinal vessel density mapping approach for OCT-Angiography and demonstrated its efficacy in
localized detection of microvascular changes and monitoring retinal disease progression in

Figure 4.14 Localization of significantly different voxels (p<0.05) in comparison between AC (N=18) and A-VRF
(N=24) subjects. (a) P-value map overlaid on the MNI152 atlas; blue regions have lower p-value compared to
red-regions. (b) Color-coded localization map overlaid on the MNI152 atlas; green regions demonstrate the voxels
with significantly (p<0.05) higher vessel density in AC compared to AD, and red regions show the voxels with
significantly (p<0.05) lower vessel density in AC compared to A-VRF.

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different clinical applications such as normal aging and diabetic retinopathy (DR). Despite some
similarities between the two studies, with respect to two-module framework design for fine-scale
vessel segmentation and non-linear registration, there is still some fundamental differences in the
method development. 3D cerebral vascular mapping in high resolution black blood MRI images
is more challenging compared to retinal vessels mapping due to relatively poor vessel contrast
mainly in cerebrospinal fluid (CSF) region, varying degrees of noise, inhomogeneous
backgrounds, anatomical variations, and availability of partial view of the brain in this study. To
tackle these challenges, initially high-resolution black blood MRIs underwent several
preprocessing steps such as skull-stripping, bias correction and denoising by non-local means
(NLM). NLM was selected for the denoising since previous works (Chen et al. 2011, Zhang et al.
2014) demonstrated that this process preserves anatomical detail while suppressing the noise.
Since the microvasculature involved in SVD includes small arteries/arterioles (~10µm-1mm),
capillaries (<10µm), and venules (~10-50µm) (Charidimou et al. 2016), we employed multi-scale
hessian based method for the purpose of vessel segmentation. More precisely, multiple popular
Hessian-based methods (Frangi et al., 1998, Sato et al., 2000, Jerman et al., 2016) have been
evaluated for enhancement of the small vessels using both synthetic and clinical data. Our
evaluation results demonstrated that the Jerman filter was more robust to noise compared to other
candidate methods, had higher and more uniform response for small vessels not only at vessel
center but also at vessel periphery. To robustly detect the small vessels, validation experiments
were designed to discover the optimal scale and threshold value via receiver operating curve
(ROC) analysis using validation dataset with annotated vessel landmarks. For localized small
vessel density analysis across population, first, a vessel density image (VDI) was calculated by
diffusing the content of the vessel mask to the entire image volume. After that, we implemented a
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non-linear registration framework to pool the VDIs from all subjects into the common space (MNI-
152 Atlas). To this end, initially skull-stripped black-blood MRI and MPRAGE image pairs were
robustly co-registered using a 3D-Affine registration with 12 landmark points. Subsequently, a
non-linear registration was performed between MPRAGE of each subject and MNI-152 Atlas
using B-Spline method. By utilizing these two deformation fields, all VDIs were normalized to
MNI-152 Atlas and localized mapping of vessel density changes across different subjects and
patient groups was enabled.
4.5.3. Limitations of the Study
Partial FOV caused wraparound of ear tissue signal into the image at the brainstem. Saturation
bands should be placed more carefully to saturate the signal of tissue outside the FOV. Such high-
resolution imaging is susceptible to motion artifacts that cause blurring or ghosting in the images.
Motion was minimized by padding the subjects in the head coil and applying paper tape across the
forehead skin for tactile feedback. Motion compensated 3D VFA TSE sequence may provide a
robust method for small vessel visualization and quantification (Freeborough and Fox 1998).
4.5.4. Conclusions
We presented and evaluated a novel framework for automated segmentation and mapping of
brain small vessels from high-resolution black blood images acquired at 3T. Using filter-based
segmentations and non-linear registration, 3D mapping, and quantification of brain small vessels
is demonstrated to be feasible. This framework may serve as a as a promising tool for localized
detection of vessel density changes in patients with neurovascular diseases.

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5. CHAPTER 5: Conclusion and Ongoing Work
This dissertation aims to bridge the technical gap in systematic analyses of small vessel
diseases using novel high-resolution imaging technologies of retina and brain. To this end we
developed state-of-the-art generalizable methods and automatic tools for 3D small vessels analysis
by adopting and systematically optimizing existing Hessian-based, non-linear registration and
shape and reeb-graph methods. The proposed methods provided the capability for robust small
vessel segmentation in 3D-OCTA and 3D-High-resolution black blood MRI, mapping vessel
densities across population for localization of vascular abnormality (e.g., vessel loss, vessel
expansion), extraction and quantification of vascular morphological and geometrical features. To
demonstrate the clinical utility of our developed automatic tools and validation of the proposed
frameworks, we presented successful applications in localized detection of vascular changes and
characterization of morphological differences caused with simulated capillary loss, aging and/or
vascular risk factors in retina and brain. Furthermore, With the development of quantitative shape
analyses method, we demonstrated the achievability of directly evaluating the morphology of small
perforating arteries. In future work, we aim to further improve the of 3D-OCTA vascular analysis
framework by including shape-based projection artifact removal method to optimally suppress tail
artifact and reconstructing tubular vessel shapes. We are also working on generating a statistical
atlas of cerebral small vessels based on our former work for cerebral small vessel segmentation
and nonlinear registration of vessel densities to MNI atlas. In addition, we will explore the
correlation between small vessels features in retina and brain using paired OCTA and black blood
MRI.
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5.1. OCTA Projection Artifact Removal
In chapter 2, a method for OCTA vessel
enhancement and segmentation by adopting from OOF
method and thresholding the resultant vesselness map
was developed. However, there are still distinct
challenges to address such as projection artifact
removal of both large scale and fine scale vessels.
More precisely, the proposed OCTA vesselness
function and its corresponding BVM include
projection artifact as part of the true vessel signal. To
tackle this artifact, different solutions has been
proposed previously by vendors using embedded
commercial software, also post-processing algorithmic methods have been proposed (Liu et al.
2019, Zhang et al. 2016). Some of the main challenges in the proposed techniques are their
validation, unknown impact of projection artifact on small vessels and potential elimination of
small capillaries under the large vessels by tail removal process. The effect of projection artifact
on retinal vascular network in pathological subjects with edema is even more indefinite and
debatable. Particularly in longitudinal studies, during edema progression and treatment, due to
varying degree of anatomical deformation at different stages, projection artifact might vary over
time and currently due to technical limitations, no comprehensive quantitative method has been
proposed for edematous subjects using 3D-OCTA.
In previous work by our group a 3D-OCTA shape modeling method has been developed for
analysis of retinal microvasculature (Zhang et al. 2019c). In this development, large vessels that

Figure 5.1 Visualization of OCTA
projection artifact. (A) Schematic view of
decorrelation tail pointed by arrow. (B)
Example OCTA surface reconstruction of a
healthy subject, the projection artifact or
decorrelation tail (yellow pointed arrows) is
included in the final vessel shape.

93
cause the dominant projection artifact have been excluded from the vascular quantification. As an
extension of our previous shape modeling tool and in order to minimize the overestimation of
perfusion density due to projection artifact in both small and large vessels, one can reconstruct the
tubular vessel shapes from the deformed and elongated vessels (Figure 5.1). Since the direction
of projection artifact is known, a directional smoothing can be performed to remove the
deformation caused by tail artifact and reconstruct tubular vascular shapes. To this end, we can
first obtain the OCTA binary vessel masks (BVM) of retinal region of interest (ROI) using our
previously developed framework (Sarabi et al. 2019), since the processing pipeline will be
employed for inter and intra subjects quantitative comparisons, initial restricted affine
transformation could be utilized to transform BVMs to common space (3D_OCT Atlas (Khansari
et al. 2019)) and to define anatomically consistent field of view. Afterwards, projection-resolved
3D-OCTA surface mesh representation will be constructed.
5.2. Statistical Atlas of Cerebral Small Vessels using High-resolution Black Blood MRIs
Cerebral networks are difficult to analyze due to their complex organization of branches and
cyclic connections that varies across individuals. Evaluating cerebral structures could have a
significant impact in diagnosis and understanding of multiple cerebrovascular diseases, such as
stenoses, aneurysms, arteriovenous malformations, or ischemic strokes (Mouches and Forkert
2019). Detecting changes in the cerebrovascular system, mainly the small arteries and veins, could
also prove valuable as an early biomarker for neurological diseases, such as Alzheimer’s disease
(Wardlaw et al. 2013b). However, finding small vessel abnormalities requires detailed knowledge
of the normal morphology and distribution of the cerebral small arteries and veins in the brain.
Cerebral small vessel atlas would assist in describing the normative vascular data of healthy
94
individuals and enable the detection of abnormalities in patients with diseases, potentially in an
early stage.
Currently there is no study that focused on generating statistical atlas of small vessels to
investigate the fine-scale inter-subject vascular variations using High-resolution black blood MRI.
Efforts have been made using TOF MRA to generate the statistical atlas of cerebral arteries
(Mouches and Forkert 2019), however as shown in our previous study of LSA morphological
quantification in Chapter 3, high-resolution black blood MRI could detect more vessel branches
and have higher-resolution for fine-scale vascular analysis. For the statistical atlas construction,
in chapter 4, we developed and comprehensively validated a method for cerebral small vessel
segmentation and demonstrated the normalization of vessel density images to the MNI atlas. Using
the binary vessel segmentation and non-linear warp to MNI, an atlas of the small vessels from
normal control subjects can be constructed. However, to account for all inter-subject vascular
morphological variation and density distribution we need to extend the dataset size of healthy
control subjects.
5.3. Correlation Analysis between Retinal Capillaries and Cerebral Small Vessels
In Chapter 2 and Chapter 4, 3D vascular analysis frameworks for retina microvasculature in
OCTA and small cerebral vessels available in high-resolution black blood MRIs (~ 0.5 mm
isotropic) have been provided and comprehensively validated, respectively. Several recent studies
have revealed correlations between capillary features and neurodegenerative disease, most
remarkably in AD (O'Bryhim et al. 2018, Querques et al. 2019). Vascular contributions to
cognitive impairment and dementia are widespread and their diagnosis and monitoring signifies a
substantial unmet medical need (Gorelick et al. 2011, Snyder et al. 2015). There is very recent
study (Geerling et al. 2022) that reveals the association between cSVD using white matter lesion
95
analysis with changes in the retinal vasculature which can be assessed non-invasively with much
higher resolution than the cerebral vasculature using swept source OCTA. These consensus
statements called for the development of novel, clinically feasible biomarkers of vascular cognitive
impairment and dementia by means of OCTA more rapidly and with lower cost. Our former
development for retina and brain small vessel analysis provides the foundation and tools for such
correlation studies. As part of the MarkVCID project, the paired OCTA and high-resolution black
blood MRI has been collected and the 3D vascular features can be extracted from both modalities
and their correlation could be assessed.

96
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Abstract (if available)

Abstract Vascular diseases are among the most common public health problems worldwide. Associated conditions include diabetes, arteriosclerosis, cardiovascular diseases, hypertension, and cerebrovascular small vessel disease (cSVD) to name only the most widely occurring ones. Diabetic retinopathy (DR) is a significant microvascular complication of diabetes mellitus (DM) and a leading cause of visual impairment in the developed world (Stitt et al. 2016). DR-related vision impairment is expected to remain a major health concern since the prevalence of diabetes is projected to increase from 14% in 2010 to 21% in 2050 (Boyle et al. 2010), and the lifetime prevalence of DR in subjects with DM is well over 50% (Stitt et al. 2016). CSVD is responsible for approximately 25% of both ischemic and hemorrhagic strokes worldwide and is associated with increased risk of recurrent stroke (Rensma et al. 2018). It is also a primary contributor to cognitive decline, with up to 45% of dementia cases in the general population being associated with cSVD. Still, the underlying mechanisms of SVD remain poorly understood, resulting in no specific guidelines for its staging, treatment, and prevention.
The knowledge gap in SVD is partly because small vessels, including cerebral small vessels (e.g., arterioles and capillaries) and retinal capillaries, are largely inaccessible to existing, clinically available in vivo imaging technologies. Recent development in magnetic resonance imaging (MRI) techniques has demonstrated the feasibility of non-invasively visualizing cerebral small vessels, such as the lenticulostriate arteries (LSAs), by optimized 3D black-blood MRI sequence using T1-weighted turbo spin echo with variable flip angles (T1w TSE-VFA) with sub-millimeter spatial resolution. In retina imaging, optical coherence tomography angiography (OCTA) has been introduced recently that can safely, quickly, and non-invasively demonstrate the 3D retinal microvasculature network with micron-level resolution. The advent of these high-resolution angiography images can have a significant impact in studying early microvascular changes in small vessel diseases (SVD) of retina and brain. However, due to technical limitations, the accurate three-dimensional (3D) analyses of the small vascular structure including detection, localization and robust quantification in OCTA and high-resolution black blood MRI remain as an open and essential area of research and development.
In retina studies, although the 3D micron-level visualization of retina is provided by recent imaging devices, most of the current methods still largely perform their analyses and quantification on two-dimensional (2D) projection images, which results in an inevitable information loss and alteration of morphological information due to the overlap of 3D vascular structures after their projection onto a 2D plane. In brain studies, neuroimaging plays a key role in characterizing cSVD by identifying various features linked to cSVD including recent small subcortical infarcts, lacunes, white matter hyperintensities, enlarged perivascular spaces, microbleeds, and brain atrophy. However, when these features become visible or detectable in structural imaging, they are already manifestations of significant deterioration caused by cSVD. Therefore, currently there is an increasing desire to detect the earliest features of cSVD in order to mitigate downstream disease-related tissue changes.
This dissertation aims to bridge the technical gap in localized analysis of small vessels of retina and brain using state-of-the-art high-resolution imaging technologies. To this end we developed a novel and generalizable framework that incorporates vessel segmentation, artifact resolution, registration, and localized vessel density mapping across subjects. To demonstrate the clinical utility of our developed tools and validation of the proposed frameworks, we showed successful applications in localized detection of vascular changes and characterization of morphological differences caused with simulated capillary loss, aging and vascular risk factors.
In this dissertation, Chapter 1 provides a general introduction to the research outlined in the following chapters. It covers the novelty and main contributions, clinical significance of small vessel disease in retina and brain, the current state of existing in vivo imaging and the advent of novel and high-resolution imaging techniques, the review and comparison of common techniques such as Hessian-based solutions for vessel segmentation problems, and the registration methods for retina and brain. Chapter 2 describes a study in which a novel approach was developed by adopting curvelet denoising, optimally oriented flux (OOF) and non-linear registration for mapping retinal vessel density from three-dimensional (3D) OCT-Angiography images. To demonstrate the clinical utility of our method, in our experimental results, we presented an application for longitudinal localized qualitative analysis of pathological subjects with edema during the course of clinical care. Additionally, we quantitatively validated our method on synthetic data with simulated capillary dropout, a dataset obtained from a normal control (NC) population divided into two age groups and a dataset obtained from patients with diabetic retinopathy (DR). Our results show that we can successfully detect localized vascular changes caused by simulated capillary loss, normal aging, and DR pathology even in presence of edema. Chapter 3 presents the development of shape-reeb graph quantification method for morphological differences of lenticulostriate arteries (LSAs) with age. Novel optimized high-resolution 3D T1w TSE-VFA sequence was utilized as input to the framework. Automated Reeb graph shape analysis was performed to extract features including vessel length and tortuosity. All quantitative metrics were compared between the field strengths and two age groups using ANOVA. The mean vessel length and tortuosity were found to be greater on TOF MRA compared to TSE-VFA. The number of detected LSAs by both TSE-VFA and TOF MRA was significantly reduced in aged subjects, while the mean vessel length measured on 7T TSE-VFA showed significant difference between the two age groups. Chapter 4 describes a novel 3D analysis method for localized 3D vessel density mapping of small vessels of the near whole brain from 3D black-blood MRI at 3T, with sub-millimeter spatial resolution (isotropic ∼0.5 mm). Using automated vessel segmentation and non-linear registration, a multimodal method was proposed and comprehensively validated by vessel landmarks and full annotation of LSAs for localized detection and quantification of small vessel density changes across populations and brain regions. Voxel-level statistics was performed to compare regional vessel density between two age groups as well as between aged subjects with and without vascular risk factors, respectively. Our results indicated that mean vessel density across the whole brain in available field of view was significantly higher in young subjects compared to aged subjects with and without vascular risk factors. The aged subjects with vascular risks showed a trend of reduced mean vessel density compared to the aged subjects without vascular risk factors. Lastly, Chapter 5 provides the conclusion, some of the ongoing work and future direction of this research.

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Asset Metadata

Creator Sharifi Sarabi, Mona (author)

Core Title 3D vessel mapping techniques for retina and brain as an early imaging biomarker for small vessel diseases

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2022-08

Publication Date 07/25/2022

Defense Date 06/14/2022

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

Tag 3D medical image registration,brain,high-resolution black blood MRI,OAI-PMH Harvest,optical coherence tomography angiography,retina,vessel density mapping,vessel quantification,vessel segmentation

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Shi, Yonggang (committee chair), Haldar, Justin (committee member), Raghavendra, Raghu (committee member), Wang, Dany J.J. (committee member)

Creator Email mona.sharifi.sarabi@gmail.com,sharifis@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111375401

Unique identifier UC111375401

Legacy Identifier etd-SharifiSar-10960

Document Type Dissertation

Format application/pdf (imt)

Rights Sharifi Sarabi, Mona

Type texts

Source 20220728-usctheses-batch-962 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu