University of Southern California Dissertations and Theses

New methods for carotid MRI

(USC Thesis Other)

New methods for carotid MRI

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content NEW METHODS FOR CAROTID MRI
by
Mahender K. Makhijani
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 2012
Copyright 2012 Mahender K. Makhijani
Acknowledgements
I’m grateful for the relationships with many generous and inspiring people I have had
the pleasure of meeting since the beginning of the PhD course. I greatly cherish each
contribution to my development.
I owe my deepest gratitude to my mentor and advisor Prof. Krishna Nayak. He
convincingly conveyed a spirit of adventure with regards to research and an excitement
for mentoring. His wisdom, knowledge and commitment to the highest standards inspired
and motivated me. His invaluable advice has had an impact not only on my research but
also in my life. Without his guidance and persistent help this dissertation would not have
been possible.
I sincerely thank Prof. Antonio Ortega for giving me new insights and research ideas.
I would also like to thank my committee members Prof. Richard Leahy, Prof. Ronald
Bruck, Prof. JayKuo, Prof. TzungHsiaifortheirencouragingwords, thoughtfulcriticism,
time and attention during busy semesters.
The good advice and support of Harry Hu has been invaluable, for which I am ex-
tremely grateful. Also I would like to thank Jon-Fredrik Nielsen, Chia-Ying Liu and Marc
ii
Lebel for very fruitful discussions. I have also greatly benefitted from advice and collab-
orations with Dr. Gerald Pohost, Dr. Niranjan Balu, Dr Kevin DeMarco and, Samuel
Valencerina.
To my colleagues for sharing their enthusiasm and comments on my work and gladly
accepting to be subjects of MRI scans at the USC hospitals: Kyunghyun Sung, Taehoon
Shin, Wesley Zun, Hsu-Lei Lee, Joao Luiz Carvalho, Yoon-Chul Kim, Samir Sharma,
Travis Smith. I thank all members of MREL in promoting a stimulating and welcoming
academic and social environment that will stand as an example to all those that succeed
them. I would also like to thank all EE and SIPI staff members for their administrative
assistance. The lab facilities at campus have been indispensable.
Lastbutcertainlynottheleastmyfamilywhohavegivenmetheirunequivocalsupport
throughout, asalwaysandforwhichmymereexpressionofthankslikewisedoesnotsuffice.
Carrie, I can’t thank you enough. Mum and Dad I am very grateful for all the scarifies
you made for me and made this dream a reality.
iii
Table of Contents
Acknowledgements ii
List of Tables vi
List of Figures vii
Abstract xii
Chapter 1: Introduction 1
1.1 Motivation and Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2: MRI Background 5
2.1 Basic MRI Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Basic Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 Signal Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.4 Relaxation and Contrast . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Accelerated Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Standard Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1.1 Partial k-space . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1.2 Parallel Imaging . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Emerging Methods: Compressed Sensing . . . . . . . . . . . . . . . 18
2.2.2.1 Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2.2 Model-Based . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Carotid MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Clinical Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Tissue and Plaque Characterization . . . . . . . . . . . . . . . . . 26
Chapter 3: Improved Blood Suppression using Diffusion Sensitizing Gra-
dients 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
iv
3.2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1.1 Blood Suppression: DIR Preparation . . . . . . . . . . . . 32
3.2.1.2 Blood Suppression: DSG Preparation . . . . . . . . . . . 32
3.2.1.3 Imaging: 3D Inner Volume -Fast Spin Echo . . . . . . . . 33
3.2.2 Attempted Optimization of DSG Preparation . . . . . . . . . . . . 34
3.2.3 Comparison of Blood Suppression Techniques . . . . . . . . . . . . 35
3.2.4 Image Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Attempted Optimization of DSG Preparation . . . . . . . . . . . . 36
3.3.2 In Vivo Comparison of Blood Suppression Techniques . . . . . . . 39
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 4: Rapid Imaging using an Asymmetric FOV 3D Cones Trajectory
45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Chapter 5: Accelerated 3D MERGE Carotid Imaging using Compressed
Sensing with a Hidden Markov Tree Model 51
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.1 Compressed Sensing MRI . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.2 Model-Based CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.3 Wavelet Tree Model . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2.4 Hidden Markov Tree Model . . . . . . . . . . . . . . . . . . . . . . 58
5.2.5 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2.6 Image Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.7 Image Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Chapter 6: Summary 72
References 74
v
List of Tables
2.1 Imaging parameters for a standard carotid MRI protocol. . . . . . . . . . 26
3.1 P-valuesforpairedt-testscomparingSNRandCNR
eff
ofthethreemethods
based on all subjects and only slices containing the carotid bifurcation. . . 42
5.1 Paired differences between plaque morphologic measurements made on im-
ages reconstructed using HMT model-based CS (4.5x) and full sampling
(1x). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
vi
List of Figures
2.1 Illustration of polarization of magnetic spins. (a) Spinning charged Hydro-
gen atoms are randomly oriented in all directions and this results in zero
net magnetic moment. (b) In the presence of external field B
0
, spins are
aligned either with or against the direction of B
0
resulting in a non-zero
net magnetic moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Excitation of magnetization in the rotating frame. (a) The net magneti-
zation vector (in rotating frame) M
0
is in equilibrium and aligned with
B
0
. (b) In the presence of dynamic B
1
field, M
0
is deviated away from its
equilibrium state into the transverse plane. . . . . . . . . . . . . . . . . . 7
2.3 Illustration of slice-selective excitation. A windowed sinc shaped B
1
pulse
when applied in the presence of a linear gradient along the longitudinal
direction (G
z
), excites a fixed band of spins perpendicular to the z-axis.
The linear gradient induces resonance offsets, causing spins to precess at
different rates based on spatial position. . . . . . . . . . . . . . . . . . . . 8
2.4 Example of Fourier acquisition. (a) k-space data with 2DFT sampling
trajectory for two lines of k-space (phase encodes). (b) Corresponding
image after 2D inverse Fourier transform. . . . . . . . . . . . . . . . . . . 10
2.5 Basic pulse sequence for 2DFT imaging. TR is time required for acquiring a
single phase encoding line of data and DAQ represents the data acquisition
window. Data is acquired only during a small portion of TR and hence
2DFT imaging is inefficient . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 Axial brain images with different contrast. The image on the left is T
2
weighted and on the right is T
1
weighted. . . . . . . . . . . . . . . . . . . 13
2.7 Receivercoilarrays. (a)Pictureofcarotidreceivecoil(http://www.hellotrade.
com/machnet-bv/phased-array-carotid-coil.html). (b) Image recon-
structed using sum of squares. (c) Individual coil images. . . . . . . . . . 16
vii
2.8 Estimation of missing data in GRAPPA with 4 coils and 2 fold undersam-
pling. The black circles indicate acquired data and light circles indicate
missing data points. Missing data is synthesized from a linear combination
of acquired data utilizing estimated weights. . . . . . . . . . . . . . . . . . 17
2.9 Carotid images reconstructed using only a fraction of its most significant
wavelet (Daubechies-6) coefficients. . . . . . . . . . . . . . . . . . . . . . . 19
2.10 Wavelet coefficients of the carotid image from Figure 2.9 sorted by magni-
tude (in blue). The slope of sorted coefficient plot (in red) corresponds to
the exponent of the decay of the coefficient magnitudes r. . . . . . . . . . 20
2.11 Illustration of the tree structure utilized in model-based CS. (a) 2D axial
imageatthecarotidbifurcation, and(b)2DWaveletcoefficientsofatypical
carotid image. The most significant coefficients fall along a connected tree.
Solid line connects all the large coefficients (red dots) . . . . . . . . . . . . 23
2.12 Example of multi-contrast carotid MR imaging. Transverse images depict
fibrous cap rupture (arrows) in right common carotid artery [56]. Lipid
rich necrotic core is denoted by the chevron. Parts of remaining fibrous
cap (arrowheads) are also depicted. . . . . . . . . . . . . . . . . . . . . . . 26
2.13 Plaque composition. The image on the left shows the different components
of plaque: necrotic core (green), calcification (red), loose matrix (blue) and
fibrous tissue (gray) segmented manually or automatically. The image on
the right is the corresponding histology segment. . . . . . . . . . . . . . . 27
3.1 Timing of the proposed pulse sequence. Imaging is performed using a 3D
fat-saturated inner-volume fast spin-echo (IV-FSE) pulse sequence. Blood
suppressionisachievedbyacombinationofdoubleinversionrecovery(DIR)
and diffusion sensitizing gradient (DSG) preparations. FATSAT = Fat
Saturation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Scatter plots of the velocity (cm/s) of unsuppressed luminal blood. Each
color represents one volunteer. (a) Projection onto the YZ plane with
(

V
y
,

V
z
) = (-0.8,-1.4) and (
Vy
,
Vz
) = (2.96,1.41). (b) Projection onto
the XZ plane, with (

V
x
,

V
z
)= (-2.7,- 1.4) and (
Vx
,
Vz
) = (1.51,1.41).
(c) Projection onto the XY plane with (

V
x
,

V
y
) = ([-2.3 -2.2], [-3.9 3.6])
and (
Vx
,
Vy
) = (1.04,1.64), (2.09,1.34). Maximum likelihood was used
to estimate the mean and standard deviation of one or two component
Gaussian mixture distributions for each plot (gray ellipses). Note that

Vy
>
Vz
but
Vx

Vz
, hence stronger dephasing is required along the
imaging slab (XY or L/R-A/P) rather than perpendicular to the imaging
slab (Z or S/I). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
viii
3.3 Blood and vessel wall SNR from a single volunteer, when using 3D IV-FSE
DIR+DSG imaging with a range of b-values. Blood signal (solid) decreases
with higher b-value. Vessel wall signal (dashed) decreases significantly for
b-value > 1 s/mm
2
. This is due to increased DSG duration and therefore
significant T
2
weighting. A b-value of 0.1 s/mm
2
was used in subsequent
studies (black arrow). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 T
1
weighted images from a healthy volunteer at the bifurcation of carotid
artery using the proposed 3D IV-FSE DIR+DSG, 3D IV-FSE DIR and 2D
multislice FSE DIR acquisitions. (a) Full FOV single slice just above the
bifurcation. The DIR only methods suffer from artifacts due to incomplete
blood suppression at the bifurcation (arrow). (b) Zoomed in view from all
the slices around the right carotid artery, highlighting box indicates the
slices with significant residual blood signal when using DIR alone. The
arrow clearly indicates the presence of significant residual luminal blood
signal when using 3D IV-FSE DIR. . . . . . . . . . . . . . . . . . . . . . . 39
3.5 T
1
weighted images from five volunteers at the bifurcation of the left carotid
artery using the proposed 3D IV-FSE DIR+DSG, 3D IV-FSE DIR and 2D
multislice FSE DIR acquisitions. The highlighting box indicates studies
with significant residual blood signal when using DIR alone. The arrows
clearly indicate the presence of significant residual luminal blood signal
when using 3D IV-FSE DIR. . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.6 ScatterplotsshowinginvivomeasurementsofthewallandlumenSNR,and
wall to lumen CNR efficiency on a per subject basis. Each color represents
one volunteer. a) Measurements from carotid segments only corresponding
tothecentralslicesatthebifurcationareplotted. b)Measurementsfromall
carotid segments across all the acquired slices are averaged per subject and
then plotted. The proposed method provides improved blood suppression
and wall to lumen CNReff, for all subjects when compared to the 3D DIR
IV-FSE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 k-space sampling for 2 cones at different angles shown in k
z
k
xy
plane
view. a) The sampling density along each cone varies as function of cone
angle, if a no empty rectangle constraint is applied. b) Sampling spacing
along two cones with angle greater and less than the critical angle. . . . . 46
4.2 k-space sampling density for 3 cone trajectories showingk
z
k
xy
quadrant
view: a)TheisotropicFOVdesignplacessamplesuniformlyonapolargrid.
b) The angular spacing between cones is varied to obtain a cylindrical FOV
shape. c) The proposed method further reduces the sample density along
each cone by applying a weaker no empty rectangle constraint. d) Proposed
constraints for a cylindrical FOV. . . . . . . . . . . . . . . . . . . . . . . . 49
ix
4.3 Comparison of images reconstructed using the proposed anisotropic trajec-
tory with its isotropic counter-part. The dashed box indicates the bifurca-
tion of the left carotid artery and SNR was measured on the sternocleido-
mastoid muscle (triangle). Using the proposed method number of readouts
is reduced by approximately 73 % and SNR dropped from 48.7 to 24. . . . 50
4.4 Scan time reduction as a function of FOV anisotropicity (f
z
/f
xy
). As f
z
decreases in comparison with f
xy
the proposed method offers significant
reduction in scan time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.1 Illustration of the tree structure utilized in model-based CS. (a) 2D axial
imageatthecarotidbifurcation, and(b)itsDaubechies-6waveletdecompo-
sition. The most significant coefficients fall along a connected tree, marked
by yellow lines, with large coefficients shown in red. . . . . . . . . . . . . . 56
5.2 Distribution of wavelet coefficients. (a) Log-histogram and (b) Histogram
of wavelet coefficients in one subband of a representative carotid image.
The red line is a mixture of two-component Gaussians fitted to the data
and the blue line is the approximation from a mixture of two-component
generalized Gaussians. The generalized Gaussian mixture provides a better
fit than Gaussian mixture. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3 Illustration of the phase encode (ky,kz) locations for 4.5x undersampling. . 62
5.4 Normalized RMSE (NRMSE) for HMT model-based CS reconstructions us-
ingmixtureofGaussiansandmixtureofgeneralizedGaussiansasafunction
of acceleration rate, averaged across all subjects, for an ROI containing the
carotid bifurcation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.5 Comparison of L1 minimization and model-based CS reconstructions. a)
Fully sampled reference. b) Normalized RMSE (NRMSE) for CS recon-
structionsasafunctionofaccelerationrate, averagedacrossallsubjects, for
an ROI containing the carotid bifurcation. c) Model-based CS reconstruc-
tions. d) L1 minimization reconstructions. e) Absolute difference between
the model-based CS and fully sampled reference. f) Absolute difference
between the L1 minimization reconstructions and fully sampled reference.
The arrow indicates severe artifacts in the L1 minimization difference im-
age as compared to the model-based CS difference image. All images are
axial reformats. Difference images are scaled to emphasize results. . . . . 66
x
5.6 Representative sagittal and axial images from 5 carotid arteries included
in this study (out of 12). Atherosclerotic plaques are marked with white
arrows. (a,c) fully sampled reference. (b,d) model-based CS with data
undersampled by a factor of 4.5. The model-based CS reconstructions have
slightly lower noise level than the reference images (*), and show slight
blurring of the vessel wall (dashed arrow) . . . . . . . . . . . . . . . . . . 67
5.7 BlandAltmanplotscomparingmorphologicalmeasurementsbetweenmodel-
basedCSreconstructionandfullysampledreference. Boldanddashedlines
correspond to mean difference and limits of agreement respectively. LA, lu-
men area; WA, wall area; MWT, mean wall thickness; MaxWT, maximum
wall thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.8 Correlationoflumenarea(LA),wallarea(WA),meanwallthickness(MWT)
and max wall thickness (MaxWT) between reference and model-based CS
reconstruction. Solid and dashed lines correspond to linear regression line
and 95% confidence intervals respectively. . . . . . . . . . . . . . . . . . . 69
xi
Abstract
Magnetic resonance imaging (MRI) is a promising modality for assessment and analy-
sis of arterial plaque because of its inherent 3D nature, excellent soft tissue discrimination,
and lack of ionizing radiation. Recently, clinicians have used non-invasive MRI measure-
ments of carotid artery plaque for diagnosis and management of carotid atherosclerosis.
However, the development of vessel wall imaging (VWI) in MRI is currently restricted
due to low signal-to-noise ratio (SNR), limited resolution and motion artifacts due to long
scan times. In addition the standard VWI technique used in MRI relies on suppression of
signal from flowing blood in the artery lumen to provide necessary contrast between the
plaque and surrounding tissue/blood. In this thesis, I present new methods for imaging
of the carotid arteries to improve on some of the current limitations in carotid MRI.
First, I introduce a new technique for improving blood suppression in carotid MRI.
In standard carotid MRI approaches a preparatory sequence is used for suppression of
flowing blood in order to improve plaque contrast with respect to the lumen. However, the
complicated and cyclic flow patterns at the carotid bifurcation result in slow and stagnant
blood flow. MR carotid artery images frequently suffer from plaque mimicking artifacts,
which may result in incorrect diagnosis. In addition these artifacts are exacerbated in 3D
imaging, which might alleviate some SNR limitations. The proposed method utilizes a
xii
hybrid preparation for blood suppression that is more robust to stagnant or re-circulant
flow with 3D imaging.
Second, I present a new anisotropic 3D cones sampling trajectory for accelerating data
acquisition. In carotid MRI a highly anisotropic field-of-view (FOV) is sufficient to cover
the anatomy of interest (carotid bifurcation). The proposed trajectory is an extension of
Gurney’s design to anisotropic FOVs. The resulting FOV is shaped like a flat cylinder
while spatial resolution remains isotropic. 3D carotid imaging with a 73.2% reduction in
scan time compared to isotropic FOV cones is demonstrated.
Finally, I present a new method for image reconstruction from undersampled data
using compressed sensing (CS) theory. CS is a relatively new theory that allows for accel-
eration and de-noising, and is independent of the traditional MR acceleration techniques.
The proposed method utilizes a variant of CS known as model-based CS which allows
for higher and more robust acceleration. Preliminary studies have verified the feasibility
of CS for achieving modest acceleration rates (<3) in carotid imaging. The proposed
method improves on this rate by exploiting correlations and dependencies by imposing
a data-driven statistical model. The signal model is trained on an application/anatomy
specific training database. A modified recovery algorithm is used to encourage sparse
solutions that comply with the learnt model while maintaining robustness of recovery. 3D
carotid imaging with rate 4.5 fold acceleration was successfully demonstrated in patients
without compromising clinically relevant quantitative endpoints or image quality.
xiii
Chapter 1
Introduction
1.1 Motivation and Aims
Atherosclerosis is a chronic, progressive and systemic disease state, which leads to
heart attack, stroke and coronary artery disease. It is perhaps the single most deadly
disease in the US accounting for 50% of deaths and has a high fatal incidence rate. Early
detection and management of this disease will significantly reduce the fatal incidence
rate. Atherosclerosis of the carotid artery leads to stroke which accounted for more than
120,000 deaths in 2010. Each year 700,000 americans experience stroke, resulting in a
total cost of $64 billion. The use of MR modality for study and diagnosis of carotid
atherosclerosis in humans has recently gained momentum. MRI is an excellent modality
for such assessment since it provides the capability of characterizing plaque composition
and lacks ionizing radiation. MRI has the unique capability of non-invasively screening
patients for high risk plaque.
The use of MRI for carotid VWI has been successfully demonstrated [58,60,64,75].
However, thestandardimagingprotocolsuffersfromlongscantimes[32,34,72,75]affecting
1
reproducibility of the study due to motion artifacts and does not provide adequate spatial
resolution or SNR to image fine plaque components that are precursors of significant
disease. In addition the standard techniques are dependent on suppression of signal from
flowing blood in the lumen of the artery to provide necessary contrast between the plaque
and surrounding tissue/blood.
Precise delineation of the interface between the vessel wall and lumen essentially relies
on efficient blood suppression of flowing spins. Hence accurate blood suppression plays an
important role in assessing the morphology and tissue composition of the atherosclerotic
plaque [24,74,75]. However due to re-circulant and cyclic flow patterns at the carotid
bifurcationtheflowofblowisslowandstagnant. Thestandardbloodsuppressionmethods
rely on outflow of blood from the imaging slab. As a result of this MR carotid artery
images frequently suffer from plaque mimicking artifacts [63],which may result in incorrect
measurementsofthevesselwallandplaquesize. Inadditiontheseartifactsareexacerbated
in 3D imaging. 3D imaging has recently been used in carotid MRI to improve SNR
limitationsandisnecessaryforprovidingisotropiccoveragearoundthebifurcationwithout
slice gaps. In this thesis, I present techniques for mitigating some of the limitations in
current carotid MRI.
2
1.2 Outline
This dissertation is outlined as follows:
Chapter 2: MRI Background
This chapter presents an overview of basic MR pulse sequences, k-space sampling,
relaxation and contrast, partial k-space acquistion, parallel imaging, compressed sensing,
and a brief introduction to carotid imaging and its clinical perspective.
Chapter 3: Improved Blood Suppression using Diffusion Sensitizing Gra-
dients
Thischapterpresentsabloodsuppressiontechniqueinthree-dimensionalcarotidvessel
wall imaging by using a hybrid preparation consisting of double inversion-recovery (DIR)
and diffusion sensitizing gradients (DSG). The problem associated with standard DIR
approach are described and novel solution to incomplete blood suppression is proposed for
3D imaging. Effectiveness of this technique over the standard preparation is demonstrated
in healthy volunteers.
Chapter 4: Rapid Imaging using an Asymmetric FOV 3D Cones Trajectory
This chapter presents a method for designing time-optimal 3D cones trajectory with
anisotropic FOV (flat-cylinder) and isotropic spatial resolution. Three Dimensional cones
is the most time efficient 3D k-space sampling trajectory, and efficient algorithms are
available for readout gradient design when the imaging field of view (FOV) and desired
spatial resolution is isotropic. Often the anatomic FOV is highly anisotropic; and as such
there is an opportunity to further optimize the trajectory design. Scan time reduction
3
capability of anisotropic FOV cones trajectory is demonstrated in 3D carotidimaging with
a 73.2% reduction in scan-time compared to isotropic FOV cones.
Chapter 5: Accelerated 3D MERGE Carotid Imaging using Compressed
Sensing with a Hidden Markov Tree Model
This chapter presents accelerated 3D black-blood carotid magnetic resonance imaging
using model-based compressed sensing. Model-based CS and conventional CS are retro-
spectively applied o 3D black-blood carotid MRI data with 0.7 mm isotropic resolution,
from six subjects with known carotid stenosis (12 carotids). A wavelet-tree model learnt
from a training database of carotid images, as a potential way to reduce the degrees of
freedom during CS reconstruction. Quantitative endpoints such as lumen area, wall area,
mean and maximum wall thickness, plaque calicification, and necrotic core area, were
measured and compared using Bland-Altman analysis along with image quality. Rate-4.5
acceleration with model-based CS provided image quality comparable to that of rate-3
acceleration with conventional CS and fully sampled reference reconstructions. Morpho-
logical measurements made on rate-4.5 model-based CS reconstructions were in good
agreement with measurements made on fully sampled reference images. There was no sig-
nificant bias or correlation between mean and difference of measurements when comparing
rate 4.5 model-based CS with fully sampled reference images.
Chapter 6: Summary
This chapter summarizes the thesis and presents future research topics that are worth
of more investigation.
4
Chapter 2
MRI Background
2.1 Basic MRI Physics
MRI is an important tool for clinicians to non-invasively study the vast structures
and functionalities inside the human body since the 1970s [37,51]. The following sections
brieflyreviewtheunderlyingmagneticresonance(MR)phenomenathatenablesMRimag-
ing from a classical view point. Quantum mechanics is required for a exact description of
MR physics, however a classical description is sufficient to describe macroscopic behavior
that governs most of MR imaging.
2.1.1 Basic Physics
Spinning atoms with an odd number of protons and/or neutrons exhibit an intrinsic
spin angular momentum [5], typically referred to as spin. These spins can be treated as
classical charged spinning spheres that possess a small magnetic moment. Hydrogen (
1
H)
is the most abundant atom of this type in biological specimens.
In the absence of any external magnetic field, these spins are randomly oriented result-
ing in a zero net magnetic moment (Figure 2.1). However if an external magnet generates
5
z
y
x
B
0
a )
b )
Figure 2.1: Illustration of polarization of magnetic spins. (a) Spinning charged Hydrogen
atomsarerandomlyorientedinalldirectionsandthisresultsinzeronetmagneticmoment.
(b) In the presence of external field B
0
, spins are aligned either with or against the
direction of B
0
resulting in a non-zero net magnetic moment.
a field say B
0
, then spins align with direction of this B
0
field resulting in a nonzero net
magnetic moment. Approximately half of the spins are parallel to B
0
and the rest are
anti-parallel. However there is always an additional tiny fraction of spins (approximately 7
part per million at aB
0
of 1.5 Tesla) that are aligned in the parallel direction. The result-
ing net magnetic moment per unit volume is denoted byM
0
. Even though the individual
spins are oriented parallel or anti-parallel to B
0
, macroscopically M
0
can be considered
to be aligned parallel to B
0
. Also the B
0
field is considerably stronger than the earth’s
magnetic field and is both static and homogenous. Additionally, these spins are rotating
around the direction ofB
0
field at a specific frequency knows as Larmor frequency defined
below. Here
is the gyromagnetic ratio specific to the type of atom. For the
1
H atom
this frequency is 42.58 MHz per Tesla.
f =

2
B
0
(2.1)
6
a)
b)
z
y
x
M
0
z
y
x
M
xy
B
1
“In rotating frame”
Figure 2.2: Excitation of magnetization in the rotating frame. (a) The net magnetization
vector (in rotating frame) M
0
is in equilibrium and aligned with B
0
. (b) In the presence
of dynamic B
1
field, M
0
is deviated away from its equilibrium state into the transverse
plane.
2.1.2 Excitation
Then net magnetic moment M
0
can be perturbed from its equilibrium position (see
Figure 2.2), by using another dynamic magnetic field (sayB
1
) that is tuned to the Larmor
frequency and transmitted in the transverse plane orthogonal to the static field B
0
. The
B
1
field is typically applied only for a short duration (few milliseconds). As a result
of this dynamic field the equilibrium magnetization moment M
0
can be tipped into the
transverse plane that is perpendicular to the main B
0
field. This phenomenon is also
know as excitation and can be described precisely using the Bloch equations [47].
Theresultingtransversecomponentoftheexcitedmagnetizationistimevaryingandas
per Faradays laws of electromagnetism, it induces a voltage in appropriately oriented RF
receiver coils. This induced voltage can recorded or detected. After excitation due to the
B
1
field, theresultingtransversemagnetizationexponentiallydecaysatratescharacterized
by tissue relaxation time constants and reverts back to its equilibrium state aligned with
B
0
. The tissue time constants,T
1
andT
2
, represent the magnetization’s longitudinal and
7
z
f
f
0
xy
z
F.T.
B
1
(t)
∆ z
z
B=(B
0
+G
z
z)k
^
Figure 2.3: Illustration of slice-selective excitation. A windowed sinc shaped B
1
pulse
when applied in the presence of a linear gradient along the longitudinal direction (G
z
),
excites a fixed band of spins perpendicular to the z-axis. The linear gradient induces
resonance offsets, causing spins to precess at different rates based on spatial position.
transversal relaxation rates respectively. The time varying signal that is generated is know
as free induction decay (FID).
2.1.3 Signal Equation
As discussed in the previous section, application of time varying B
1
field in presence
of static fieldB
0
field tips the net magnetization vector into the transverse plane. All the
spins in the volume that are rotating at the Larmor frequency are excited, hence this is
called nonselective excitation. Instead, if only a certain 2D section of the volume needs to
be imaged then slice selective excitation is needed. Spatial localization can be achieved
by applying a linear gradient field say G, in addition to the B
1
and B
0
field.
8
If the B
1
field has a windowed sinc envelope and is applied in the presence of slice
selective gradient G
z
, then this combination results in a excitation of 2D slice instead of
a 3D volume (see Figure 2.3). The spins only within the passband of the slice profile
are tipped into transverse plane and produce signal in the receive coil while the spins
outside the slice profile have negligible contribution. The main utility of the gradient
field is to create resonance offsets that enables encoding of spatial position. Now after
slice selective excitation, if time-varying gradient fields say G
x
and G
y
are applied along
respective directions then contributions of individual spins within the slice can be spatially
resolved. The G
x
and G
y
gradient fields induce additional resonance offsets that linearly
vary in the transverse plane along the respective axes resulting in spins to accrue phase
instantaneously depending on its x or y spatial position. Ignoring relaxation effects,
the signal detected in the RF receive coil at any time instant is an integral of all spin
contributions over the entire excited plane and can be given as:
s(t) =
Z Z
m(x;y)e
j2(kx(t)x+ky(t)y)
dxdy (2.2)
where,
k
x
(t),

2
Z
t
0
G
x
()d
k
y
(t),

2
Z
t
0
G
y
()d
hence,
s(t) =M(k
x
(t);k
y
(t))
9
k
y
k
x
a)
b)
y
x
Figure 2.4: Example of Fourier acquisition. (a) k-space data with 2DFT sampling trajec-
tory for two lines of k-space (phase encodes). (b) Corresponding image after 2D inverse
Fourier transform.
ThusMRsignalequationcanbeexpressedasasimpleFouriertransform. Wheres(t)is
signal detected in the receive coil and M(k
x
(t);k
y
(t)) is a function of spatial frequencies
(k
x
(t);k
y
(t)) that are parameterized by a time variable t. Here m(x;y) represents the
transverse component of the excited magnetization, (k
x
;k
y
) is the spatial frequency (also
know as k-space) location, and (x;y) is the spatial position. Also k
x
(t) and k
y
(t) are
trajectories in time and are proportional to the integral of the gradient waveforms G
x
(t)
10
RF
G
z
G
x
G
y
Slice Select
Crusher
DAQ
Phase Encode
TR
=
=
=
=
time
Slice Select
Crusher
DAQ
Phase Encode
Figure 2.5: Basic pulse sequence for 2DFT imaging. TR is time required for acquiring a
single phase encoding line of data and DAQ represents the data acquisition window. Data
is acquired only during a small portion of TR and hence 2DFT imaging is inefficient
and G
y
(t) respectively. The underlying spin density or MR image is basically the inverse
Fourier transform of the acquired signal samples M(k
x
(t);k
y
(t)) in k-space.
Two-dimensional imaging requires sampling of 2D k-space. One of the most common
MRacquisitiontechniquesisknownas2DFT(2DFourierTransform)imagingandinvolves
sampling of k-space in a simple raster like fashion, acquiring a single line of k-space
data (also known as phase encoding lines) after each excitation (see Figure 2.4). The
reconstruction algorithm is very simple and images can be formed quickly via a 2D inverse
Fourier transform. In addition, 2DFT imaging is very robust to system imperfections
such as gradient or acquisition delays and magnetic field inhomogeneities. A basic pulse
sequence for 2DFT imaging is shown in Figure 2.5. However 2DFT data acquisition is
slow and severely constrains MR imaging speed.
11
2.1.4 Relaxation and Contrast
MR imaging capabilities are constrained by underlying tissue constants likeT
1
andT
2
.
However these same constraints can be used to gain valuable image contrast to distinguish
between different tissue species and disease. The signal equation, after accounting for T
2
relaxation can be rewritten as:
s(t) =
Z
m(r)e
t=T
2
(r)
e
j2k(t)r
dr (2.3)
This equation is the same signal equation defined in Eq. 2.2 except for the exponential
T
2
weighting and r represents the vector spatial variable and k(t) and is the frequency
variable parametrized by time t. If the tissue T
2
was constant over the entire object
being imaged then this would imply that each phase encoding line being acquired will
be damped by an exponential factor as the trajectory along the readout evolves with
time. This implies that the decay in the transverse component of magnetization due to
T
2
relaxation, limits the time window for which a particular phase encoding line can be
acquired. The exponential weighting during readout causes blurring in the image domain
along the readout direction. This blurring is by a Lorentzian function, as the weighting in
k-space is exponential. Also the blurring is spatially variant as shortT
2
regions experience
greater blurring than long T
2
.
T
2
relaxation times are usually in the millsecond range (40 ms to 200 ms) while T
1
recovery times are much longer(200 ms to 2000 ms). This fact can be exploited to gain
contrast between tissue species with markedly differentT
2
constants. Figure 2.6 is a good
example of flexibility in image contrast that is native to MRI when compared with other
12
Figure2.6: Axialbrainimageswithdifferentcontrast. TheimageontheleftisT
2
weighted
and on the right is T
1
weighted.
modalities like computerized tomography. The key MR signal parameters that affect
image contrast are underlying proton (spin) density, tissue relaxation constants, tissue
abnormality like cancer. So the MR imaging parameters can be strategically set to obtain
the best possible contrast for the specific diagnostic task for which the clinical scan is
being done.
2.2 Accelerated Imaging
2.2.1 Standard Methods
Long scan times pose a major hurdle for MR imaging. Improving scan time reduces
motionartifact, improvesthepatientthroughput, andmayreduceimagingcost. Scantime
reduction can be achieved by acquiring multiple image slices in a interleaved (pseudo-
simultaneous) order [32], acquiring partial k-space data [48], utilizing parallel imaging,
or some combination of these. Techniques that interleaving multiple slices together are
susceptible to artifacts. However, utilizing parallel imaging theory [26,50] is now a clinical
13
routine [69]. Parallel imaging utilizes additional encoding provided by the varying spatial
sensitivity profile of the receiver coils in conjunction with gradient encoding to reduce the
minimum number of samples for reconstruction. However the acceleration rate achievable
by this method is dependent on coil design and number of receiver elements and their
geometrywithrespecttotheregionofinterest.Techniquesthatreducethenumberofphase
encoding steps suffer an SNR penalty proportional to the square root of the reduction
factor. However the primary concern with the conventional MR techniques is that the
acceleration rate is limited by gradient, coil and pulse sequence technology. For instance
in carotid imaging, the established MR techniques can achieve only modest acceleration
rates of the order of 3. This provides the opportunity to explore other generic acceleration
approaches in information theory.
2.2.1.1 Partial k-space
Partial k-space acquisitions take advantage of symmetry in frequency spectrum of real
images and data is collected completely only from half of k-space frequencies. Acquir-
ing only half the frequencies is feasible because of the property of Fourier transforms of
real objects known as Hermitian symmetry. This property implies that k-space data is
symmetric around the zero frequency (center of k-space) i.e. real part is symmetric and
imaginary part is anti-symmetric and is given in 2.4. Hence by acquiring only one half of
k-space, the other un-acquired half can be estimated by exploiting this symmetry.
s(

k) =s

(

k) (2.4)
14
MR reconstructed images are very susceptible to phase errors resulting from field
inhomogeneity, eddy currents, hardware delays and limitations, and motion etc. Hence
the reconstructed image in MRI is usually complex rather than only real. This problem
can be overcome by acquiring additional data from the other half of k-space to estimate
the image phase provided the phase varies smoothly. Partial k-space acquisitions can be
used along the readout direction to reduce the echo time or along the phase encoding
direction to reduce number of acquired phase encoding lines.
Partial k-space data can be reconstructed using zero filling or iterative procedures like
homodyne processing. Zero filling unmeasured data results in an accurate low resolu-
tion image only. Loss of high frequency phase information is a disadvantage of the zero
filled reconstruction. Iterative procedure like homodyne can be used in the presence of
more rapid phase variations. The homodyne algorithm uses the zero filled image along
with the low frequency phase map to form a complex image. The complex image is it-
eratively updated with more accurate phase estimates while maintaing data consistency.
The algorithm is halted when successive image estimates only differ marginally.
2.2.1.2 Parallel Imaging
Parallelimagingutilizesadditionalencodingprovidedbythevaryingspatialsensitivity
profile of the receiver coils in conjunction with gradient encoding to reduce the minimum
number of samples for reconstruction. Phased array coils are used to generate varying
spatial sensitivity profiles, that enables spatial encoding due to coils and not gradients
as shown in 2.7. The basis of all parallel imaging is to increase the distance between
phase encoding lines, i.e. acquire fewer phase encoding lines while maintaining the same
15
a b
c
Figure 2.7: Receiver coil arrays. (a) Picture of carotid receive coil (http://www.
hellotrade.com/machnet-bv/phased-array-carotid-coil.html). (b) Image recon-
structed using sum of squares. (c) Individual coil images.
maximal coverage in k-space. Increase the distance between phase encoding lines results
in aliasing artifacts, however these artifacts can be "unwrapped" by including information
about spatial dependence of receive coil arrays. However the acceleration rate achievable
by this method is dependent on coil design and number of receiver elements and their
geometry with respect to the region of interest.
The two dominant parallel imaging techniques are sensitivity encoding (SENSE) [50]
andgeneralizedautocalibratingpartiallyparallelacquisitions(GRAPPA)[26]. InGRAPPA
the spatial dependence of sensitivities is used to synthesize missing k-space lines by ap-
proximating the corresponding sinusoidal phase twists produced by encoding gradients. A
single k-space data set is reconstructed and Fourier transformed to give unaliased image.
In SENSE individual receive coil k-space data sets are separately Fourier transformed
16
C oil
1
C oil
2
C oil
3
C oil
4
k
y
k
y
+1 k
y
-1 k
y
-2 k
y
+2 k
y
-3 k
y
+3
Figure 2.8: Estimation of missing data in GRAPPA with 4 coils and 2 fold undersampling.
The black circles indicate acquired data and light circles indicate missing data points.
Missing data is synthesized from a linear combination of acquired data utilizing estimated
weights.
resulting in aliased images. The aliased images are then unwrapped using coil sensitivity
information that is acquired in a separate scan to give a single final image without aliasing
artifacts.
After the incorporation of the spatial coil sensitivity, the MR signal equation is given
as:
y
i
(t) =
Z
m(r)c
i
(r)e
j2k(t)r
dr (2.5)
wherey
i
is the signal received from thei
th
coil element,m is the transverse component
of the spin magnetization,c
i
is the coil sensitivity from the ith coil element,r is the spatial
position, and k(t) is the k-space location at time t. Coil sensitivity effect is modeled as a
multiplicative factor in the MR signal equation.
17
GRAPPA has emerged as a more robust alternative to SENSE as it avoids the need for
a separate coil sensitivity estimation scan [27]. The basic concept of GRAPPA is that an
appropriate linear combinations of acquired data across coils can directly generate missing
phase-encoding steps, which would normally be performed by using phase-encoding mag-
netic field gradients (see Figure 2.8). K-space data is synthesized from a neighborhood
group of measurements and this group is moved depending on which k-space data needs
to be synthesized. In general multiple choices for group size and location are possible
for any given missing k-space line. A small region of k-space is fully sampled and these
additional phase encoding lines also known as auto-calibration signal lines (ACS) are used
to estimate weights that are then used in synthesizing k-space data. The weights can be
estimated by performing a simple least squares fit. Once the weights are known, then
missing k-space can be synthesized by combining acquired neighborhood data using the
estimated weights.
2.2.2 Emerging Methods: Compressed Sensing
2.2.2.1 Standard
Compressed sensing (CS) [10,19] is a relatively new theory that allows for acceleration
and de-noising, and is independent of the native MR techniques. CS is utilized in Chapter
5 of this dissertation. To explain it, we must start with the continuous MR signal equation
shown in 2.5. The MR equation in the discrete form is given below, where represents the
Fourier encoding matrix, C
i
is the coil sensitivity matrix. Here m represents the discrete
image andy
i
is the data acquired from the i
th
coil in frequency domain. This continuous
to discrete mapping is an ill-posed problem.
18
5% 10%
25% 50%
R ef er enc e
Figure 2.9: Carotid images reconstructed using only a fraction of its most significant
wavelet (Daubechies-6) coefficients.
y
i
= C
i
m (2.6)
m = x (2.7)
Given N bases vectors
i
, we can represent every signal m2<
N
using N coefficients
x
i
. If we stack the vectors
i
into a N x N matrix then the sparse coding can be written
as a linear transform as shown in??. A signal is said to be K-sparse ifKN coefficients
out of N are nonzero. Set of all nonzero entries of a K-sparse signal will be called the
support ofx. The set of all K-sparse signals is the union ofC
N
K
, K-dimensional subspaces
aligned with the coordinate axes in<
N
. This will be denoted by
P
K
.
19
10
2
10
3
10
4
10
5
10
-6
10
-4
10
-2
10
0
10
2

Reference
r=3
i
|x
Si
|
Figure 2.10: Wavelet coefficients of the carotid image from Figure 2.9 sorted by magnitude
(in blue). The slope of sorted coefficient plot (in red) corresponds to the exponent of the
decay of the coefficient magnitudes r.
The MR images like many naturally occurring images are not strictly sparse but
compressible. A signal is compressible when its coefficients sorted in order of decreasing
magnitude x
S
i
decay at a rate comparable to the power law [2]:
jx
S
i
j const i
1=r
; i = 1;:::;N (2.8)
where S
i
represents the rank order which causes the magnitudes to decay monotoni-
cally. Due to the rapid coefficient decay rate, compressible signals are well approximated
by K-sparse signals. This approximation is the basis of transform coding algorithms like
JPEG2000 [55]. MR images, like most natural images, are also likely to be compressible
rather than strictly sparse as shown in Figures 2.9 and 2.10.
As per CS theory, if the image is compressible in a known sparsifying domain, then
with onlyO(Klog(N=K)) measurements, whereK is the sparsity level, andN is the size
20
of the image; a sparsity-seeking algorithm can recover the true image exactly with a high
probability provided certain additional requirements are satisfied [10]. Then the discrete
MR signal equation can be re-written in the CS framework as.
y
i
=A
M
i
x (2.9)
WhereA
M
i
represents the sensing matrix that maps the sparse coefficientsx of image
m to the acquired data y
i
via the MN undersampled (M N) Fourier matrix
M
and sparsifying matrix using the relation given below:
A
M
i
=
M
C
i
(2.10)
The CS recovery theorem holds provided the M N matrix A
M
i
satisfies a cer-
tain property known as Restricted Isometry Property (RIP) [10] in addition to the spar-
sity/compressibility requirement. The compressibility of the signal is exploited by reduc-
tion in the number of measurements. A matrix A has K-RIP with constant
k
if for all
x2
P
K
, the following inequality is satisfied:
(1
k
)jjxjj
2
jjAxjj
2
(1 +
k
)jjxjj
2
(2.11)
This property essentially guarantees that all submatrices of A with size MK are
near orthogonality. This is a very broad condition with no assumptions on the locations
of the sparse coefficients (support) hence puts excessive restrictions on the structure of
the sensing matrix [2]. Practical recovery algorithms require RIP of order 2K for unique
21
recovery. Once the problem has been formulated in this fashion with RIP and compress-
ibility satisfied, recovering x is just a matter of approximating the following L
0
norm
minimization problem (in the single coil case) [40,66].
arg minjjxjj
0
subject tojjyA
M
xjj
2
(2.12)
Hererepresentstheexpectednoiseinthemeasurements. Thisapproachisimpractical
since its solution is known to be NP-hard. However practical approximations include
relaxing theL
0
norm to theL
1
norm and a host of greedy algorithms. Basis pursuit (BP)
or L
1
norm minimization [6,10,11,19] offers best recovery guarantees and is more widely
used for MR applications but recent developments in greedy algorithm may change this
trend. Greedy algorithms include variants of matching pursuits [20,65], CoSaMP [46], and
iterative hard thresholding [7]. In the multi-coil case the, minimization can be formulated
as
arg min jjxjj
1
+
X
i
jjy
i
A
M
i
xjj
2
(2.13)
Here represents the regularization parameter that trades of data consistency with
sparsity. DatafromeachcoilcanalsobereconstructedindividuallyandcombinedafterCS
recovery. Our preliminary results have verified the feasibility of CS for achieving modest
acceleration rates (<3) in carotid imaging. Some of the assumptions in CS theory do not
apply to MR imaging, and therefore we should not expect the performance guarantees to
hold.
22
Figure 2.11: Illustration of the tree structure utilized in model-based CS. (a) 2D axial
image at the carotid bifurcation, and (b) 2D Wavelet coefficients of a typical carotid
image. The most significant coefficients fall along a connected tree. Solid line connects
all the large coefficients (red dots)
2.2.2.2 Model-Based
We can improve on this modest acceleration rate by incorporating the model based
CS framework developed by Baraniuk et al. [2] or by utilizing overcomplete trained rep-
resentations [23]. First, we must develop a more realistic signal model from an appli-
cation/anatomy specific training database and then modify the recovery algorithms to
encourage sparse solutions that comply with the learnt model while maintaining robust-
ness of recovery. CS theory provides a general framework for reconstructing arbitrary
sparse signals without making any assumptions about locations of the sparse coefficients.
However the sparse coefficients of most natural images exhibit some structure. For ex-
ample, the wavelet coefficients can be naturally organized into a tree structure, and large
23
coefficients of natural images will cluster along the branches of this tree [14,49,54,57].
Figure 2.11 shows an example of this tree structure in the wavelet expansion of a carotid
image. The correlations and dependencies that exist among sparse coefficient locations
and values for most natural images can be exploited by using a signal model. A signal
model M
K
, essentially restricts the K-sparse signal x that lives in the union of arbi-
trary K-dimensional cannonical subspaces to a much smaller subset i.e. M
K
subset of
C
N
K
=
P
K
. This provides a structured sparsity model that can be eventually used to
reduce the dimensionality of the sparse search space.
The signal model M
K
is the union of m
K
cannonical K-dimensional subspaces. If
it is known that the signal of interest is K-model sparse then overly-restrictive RIP can
be relaxed without sacrificing robustness or stability. A matrix A has M
K
-RIP with
constant
MK
if for all x2M
K
, the following inequality is satisfied:
(1
M
K
)jjxjj
2
jjAxjj
2
(1 +
M
K
)jjxjj
2
(2.14)
This condition only guarantees orthogonality of submatrices that comply with model.
In contrast to the standard RIP condition the model RIP does not require near orthogo-
nality of arbitraryMK submatrices. As per model based CS theory if this condition is
satisfied then the required number of measurements reduces to O(K). In standard RIP
other than simple sparsity no further assumptions are made in order to guarantee recovery
for a broad variety of natural and artificial signals. However as shown in the wavelet tree
model above, there are strong correlations between sparse coefficient locations and values
for carotid MR images. A signal model along with model RIP essentially endows us with
24
additional structure that only permits certain K-dimensional subspaces and disallows oth-
ers. This structure can be exploited by reducing the available degrees of freedom during
recovery and can provide for a flexible trade off with acceleration rate. Chapter 5 depicts
a direct comparison between standard and model based CS at different acceleration rates.
2.3 Carotid MRI
2.3.1 Clinical Needs
Atherosclerosis affects more than 18 million Americans. The fundamental processes
leadingtomyocardialinfarctionandthromboticstrokearetheformation, growth, andrup-
ture of intra-arterial atherosclerotic plaque. These deadly consequences of atherosclerosis
occur when there is a thrombosis associated with the plaque rupture. If thrombosis-prone
plaquecouldbedetectedandtreatedbeforerupture,theincidenceofatheroscleroticevents
could be significantly reduced. Clinicians can now turn to several invasive or non-invasive
modalities for diagnosis and management of this disease.
Magnetic resonance imaging (MRI) offers certain unique capabilities such as 1) char-
acterization of plaque composition, which is useful for detecting high risk plaque, 2) lack
of ionizing radiation, which is relevant for screening and longitudinal studies and, 3) 3D
depiction of plaque morphology, which is important for accurate plaque quantitation when
compared to other modalities. High-resolution MRI has been shown to identify atheroscle-
rotic carotid plaque [75], and optimized multi-spectral pulse sequences have been devel-
oped for vessel wall delineation and plaque characterization [74]. Imaging parameters for
the different sequences used in the typical carotid protocol [75] are summarized in Table
25
Parameters T
1
weighted T
2
weighted PD weighted TOF
FOV 16x16 cm
2
16x16 cm
2
16x16 cm
2
16x16 cm
2
Acquisition Matrix Size 256x256 256x256 256x256 256x256
TE (effective) 10 ms 40 ms 10 ms 3.8 ms
TR 1 R-R 3 R-R 3 R-R 23 ms
Table 2.1: Imaging parameters for a standard carotid MRI protocol.
Figure 2.12: Example of multi-contrast carotid MR imaging. Transverse images depict
fibrous cap rupture (arrows) in right common carotid artery [56]. Lipid rich necrotic core
is denoted by the chevron. Parts of remaining fibrous cap (arrowheads) are also depicted.
2.1. Atherosclerotic disease of the carotid arteries is estimated to cause 40 percent of
stroke producing thrombi.
2.3.2 Tissue and Plaque Characterization
The typical clinical carotid imaging sequence consists of two parts: (i) a preparatory
sequence that is used for blood suppression in order to improve vessel wall contrast with
respect to the lumen, and followed by (ii) rapid imaging sequences that are capable of
differentiating the various potential plaque components. Double inversion recovery (DIR)
is used for blood suppression since it’s an effective T
1
-based nulling technique [22], while
FSE is used for imaging due to its high SNR-efficiency and moderate intrinsic blood
suppression.
2D multislice fast spin-echo (FSE) with DIR preparation is the most widely used pulse
sequence for this application [75]. Four image sets ( proton density, T
1
, T
2
weighted FSE
26
Figure 2.13: Plaque composition. The image on the left shows the different components
of plaque: necrotic core (green), calcification (red), loose matrix (blue) and fibrous tissue
(gray) segmented manually or automatically. The image on the right is the corresponding
histology segment.
and time of flight) are typically acquired across a 2-3 cm segment around the bifurca-
tion. Figure 2.12 gives an example of multi-contrast images acquired using typical carotid
imaging protocol [56]. The main limitations of these 2D methods are low SNR, lack of
contiguous anatomic coverage, quantitation errors due to partial volume effects, and long
scan times. Multiple averages are required even at 3 Tesla [34,72], in order to achieve clin-
ically useful signal-to-noise ratio (SNR) and spatial resolution. This results in scan times
on the order of 5-7 minutes per slice for all three forms of FSE-based contrast [34,72,75].
The scan time needs to be shortened to avoid motion artifacts in general but this need is
especially relevant for patients that are unable to avoid swallowing during a long acqui-
sition. Scan time limitation also restricts the ability to achieve higher resolution (<300
microns) that is required for depicting fine features like thin caps. There is a need for
techniques that can image the vessel wall and plaque composition in a more time and
SNR-efficient manner.
27
Chapter 3
Improved Blood Suppression using Diffusion Sensitizing
Gradients
3.1 Introduction
High-resolution MRI has been shown to identify atherosclerotic carotid plaque [58,
60,64], and optimized multi-spectral pulse sequences have been developed for vessel wall
delineation and plaque characterization [75]. In several of these sequences, a preparatory
sequenceisusedforbloodsuppressioninordertoimprovevessel wallcontrastwithrespect
tothelumen, andisfollowedbyrapidimagingsequencesthatarecapableofdifferentiating
the various potential plaque components.
2D multislice fast spin-echo (FSE) with double inversion recovery (DIR) preparation
[75] is the most widely used pulse sequence for this application. Four image sets (proton-
density, T
1
, T
2
weighted FSE and time of flight [75]) are typically acquired across a 2-3
cm segment around the bifurcation. The main limitations of these 2D methods are low
SNR, lack of contiguous anatomic coverage, quantitation errors due to partial volume
effects, and long scan times. Multiple averages are required even at 3.0 T [34,72], in
28
order to achieve clinically useful signal-to-noise ratio (SNR) and spatial resolution. This
results in long scan times on the order of 5-7 minutes per slice for all three forms of
FSE-based contrast [34,72,75]. Scan time reduction can be achieved by interleaving
multiple slices [29,32,44,61,73] but at the cost of possible artifacts from incomplete blood
suppression due to imperfect T
1
-nulling in all but one of the slices.
Crowe et al. [16] utilized 3D inner volume (IV) [13,45] acquisitions to alleviate the
inherent SNR limitations of 2D methods along with DIR preparation for blood suppres-
sion. IV-FSE is a variant of standard FSE where the excitation and refocusing pulses are
applied on orthogonal spatial axes. This enables significant scan time reduction, since the
excited field of view (FOV) is reduced in one of the phase-encoding directions allowing for
lesser number of phase encoding steps. DIR preparation inverts all blood spins outside of
the imaging volume while static spins within the acquisition volume are realigned with the
equilibrium state. The acquisition window is delayed from DIR preparation to coincide
with null point of blood T
1
thus giving the effect of blood suppression. The efficacy of
DIR preparation depends on the outflow of unaffected blood spins within the imaging
volume. In some subjects, blood spins do not completely wash out of the imaging volume
by the time of data acquisition resulting in residual blood signal. Hence, directly applying
DIR preparation to 3D carotid imaging can lead to artifacts from unsuppressed blood
signal [17] near the bifurcation. Such artifacts may mimic the presence of plaque [63]
and/or lead to inaccurate vessel wall thickness measurements.
T
1
independent blood suppression techniques have been explored recently. One tech-
nique, calleddiffusionsensitizinggradients(DSG,alsoknownasdiffusion-prepareddriven-
equilibrium, diffusion-weighted-prep, and motion-sensitized driven-equilibrium), utilizes
29
three or more RF pulses: 90
x
(180
y
)
n
90
x
with symmetric flow sensitizing gradi-
ents pairs on a combination of all three axes. Flowing blood spins are suppressed due
to phase dispersion induced by the gradients [59]. Carotid blood suppression using DSG
preparation was first demonstrated by Koktzoglou et al. [35] with 3D SSFP acquisitions,
and later by Wang et al. [71] with 2D multislice FSE acquisitions. The main design pa-
rameter for this preparation is the amount of sensitization (gradient duration, amplitude
and direction). The gradients should ideally be applied at the maximum hardware limits
for the shortest duration that causes sufficient intravoxel dephasing of flowing spins. Ap-
plying gradients at peak strength can introduce eddy current related artifacts. This can
be avoided by derating the gradient amplitude but at the cost of further increasing the
DSG duration. This tradeoff eventually leads to loss of critical vessel wall signal due to
T
2
decay and true diffusion effects.
In this chapter, we utilize 3D IV-FSE sequence for imaging and hybrid DIR+DSG
preparation for blood suppression. The simultaneous application of DIR and DSG prepa-
ration has potential advantages when compared to DSG alone or DIR alone. The hybrid
DIR+DSG preparation reduces the duration of the DSG component to 11.0 ms from
18.2 ms that is required for the standalone DSG preparation. Hence this hybrid prepa-
ration reduces T
2
related signal loss in the vessel wall, which potentially improves vessel
wall SNR. The hybrid preparation provides improved blood suppression compared to DIR
preparation alone. We demonstrate this hybrid preparation with 3D IV-FSE imaging that
captures a 2 cm slab across the carotid bifurcation with 0.5 x 0.5 x 2.5 mm
3
resolution in
a single 80 second acquisition, with blood-lumen CNR > 20 throughout the bifurcation.
30

Figure 3.1: Timing of the proposed pulse sequence. Imaging is performed using a 3D
fat-saturated inner-volume fast spin-echo (IV-FSE) pulse sequence. Blood suppression is
achieved by a combination of double inversion recovery (DIR) and diffusion sensitizing
gradient (DSG) preparations. FATSAT = Fat Saturation.
3.2 Materials and Methods
3.2.1 Experimental Setup
Experiments were performed on two commercial 3.0 T systems (one Signa HD and
one Signa HDx, GE Healthcare, Waukesha, WI), with gradients capable of 40 mT/m
amplitude and 150 T/m/s slew rate, and receiver capable of 4 ms sampling. The body
coil was used for RF transmission. A four-channel bilateral carotid array coil (Pathway
MRI, Seattle, WA) was used for signal reception in the HD system. A six-channel bilateral
carotid array coil (NeoCoil, Waukesha, WI) was used for signal reception in the HDx
system. Volunteers were asked to avoid swallowing during the scan, and scans were
repeated if they were unable to do so. The study population consisted of 5 healthy
volunteers. Informed consent was obtained prior to scanning. The study was performed
31
with approval and in compliance with the guidelines set forth by our local Institutional
Review Board.
The proposed pulse sequence consists of three modules shown in Figure 3.1: DIR
preparation and DSG preparation (both for blood suppression), and 3D IV-FSE (for
image acquisition).
3.2.1.1 Blood Suppression: DIR Preparation
DIR preparation consists of two inversion pulses followed by a crusher gradient. One
non-selective hard inversion pulse (1.0 ms) is followed by one selective adiabatic inversion
pulse (8.6 ms) that restores the magnetization within the imaging volume. Imaging takes
place at the null point of blood T
1
, given by the inversion time below, adapted from
Ref. [22].
TI =T
1
log

(1 +e

TR
T
1
)
2

(3.1)
The inversion recovery time was computed based on the subjects heart rate at the
start of the scan using eqn, and assuming TI =1550 ms [39]. The thickness of the selective
inversion is made 1.5 times larger than the imaging slab [24].
3.2.1.2 Blood Suppression: DSG Preparation
The DSG block shown in Figure 3.1 is similar in structure to a T
2
preparation mod-
ule [8] and consists of 3 hard pulses: 90
x
(180
y
)
n
90
x
followed by spoiler gradients.
The first pulse (duration 0.5 ms, amplitude 0.12 G) tips all the spins into the transverse
plane, the second pulse (duration 1.0 ms, amplitude 0.12 G) refocuses the magnetization
and the third tip-up pulse (duration 0.5 ms, amplitude 0.12 G) realigns the spins along
32
the equilibrium direction. The refocusing pulse is sandwiched by a symmetric pair of
sensitizing gradients that are applied along a combination of the three axes for a duration
of 5.2 ms. The gradients and RF pulses are separated by a period of 0.4 ms in order to
mitigate eddy current effects. The DSG gradients along the imaging slab (A/P and R/L)
are set to 4 G/cm while the DSG gradient orthogonal to the imaging slab (S/I) is set to
2 G/cm. These amplitudes were determined from phase contrast (PC) velocity measure-
ments discussed later. The total duration of DSG block without the spoiler gradients was
8.8 ms (i.e. the amount of T
2
weighting).
3.2.1.3 Imaging: 3D Inner Volume -Fast Spin Echo
Imaging is preceded by a fat saturation (FATSAT) sequence, which consists of spec-
trally selective excitation followed by a crusher gradient. FATSAT improves vessel wall
delineation by suppressing perivascular fat [24]. The imaging sequence is a variant of
FSE, with excitation and all refocusing pulses applied on orthogonal axes. The initial 90

excitation pulse is selective in the A-P direction while the subsequent refocusing pulses
are selective in the S-I direction. The refocusing pulses were delivered at a flip angle of
150

due to SAR constraints. Each refocusing pulse is sandwiched by a pair of symmetric
crusher gradients to eliminate newly excited signal due to imperfect refocusing and signal
from outside the volume of interest. The excitation pulse is applied along the phase encod-
ing axis while the refocusing pulse is applied along the slab selection axis to minimize echo
spacing and maximize readout duty cycle. For the imaging parameters used in this study,
the echo spacing would have increased by 0.5 ms if the orientation had been swapped (ex-
citation along the slab direction (S/I), and refocusing along the phase encoding direction
33
(A/P)) A centric phase encoding order was chosen to mitigate ghosting artifacts arising
due to phase errors induced by sensitivity to eddy current. Sequential ordering was used
in the slice encoding direction. An echo spacing of 6.1 ms was used on HD system while
an echo spacing of 10.2 ms was using on the HDx system. Cardiac gatedT
1
weighted data
sets were acquired with scan parameters: TR = 1 RR, ETL=10, Resolution=0.5 x 0.5 x
2.5 mm
3
, acquired FOV for 2D acquisitions was 16 x 3.2 cm
2
and for 3D acquisitions was
16 x 3.2 x 2 cm
3
.
3.2.2 Attempted Optimization of DSG Preparation
In five healthy volunteers, we measured the contrast between the vessel wall and
luminal blood as a function of the b-value and orientation of the diffusion vector. This
procedure involved two experiments. First, the appropriate orientation of the diffusion
vector was determined from phase contrast derived luminal blood velocity measurements.
Second, the contrast between vessel wall and lumen was directly measured for several
b-values.
The goal of the first experiment was to determine the optimal orientation of diffusion
sensitizing gradients in DIR+DSG preparation. For this purpose two datasets were ac-
quired, one with information about the carotid anatomy and the other with luminal blood
velocity measurements. Images of the carotid anatomy at the bifurcation were acquired
using 3D IV-FSE with the proposed DIR+DSG preparation with diffusion sensitizing gra-
dients turned off. These images were used to identify locations which suffer from residual
luminal blood signal. Luminal blood signal is attenuated due to various aspects of the
proposed DIR+DSG preparation including: intra-voxel dephasing caused by the diffusion
34
sensitizing bipolar gradient, T
2
weighting caused by the non-zero duration of the prepa-
ration and, other system imperfections such as sensitivity to eddy current. In order to
isolate the effect of just the bipolar gradient, the anatomical images were acquired using
the proposed preparation with only the diffusion sensitizing bipolar gradient turned off.
Time resolved velocity maps were obtained using a 3D phase contrast (PC) sequence
with a resolution of 1.0 x 1.0 x 2.5 mm
3
. The anatomic images and velocity maps were
registered to obtain velocity vector profiles of the residual luminal blood. These velocity
profiles were then used to determine the ratio of in-plane and through-plane velocity com-
ponents of the unsuppressed blood. This ratio is indicative of the directional preference
of the residual blood and was used to determine the relative amplitudes of the sensitizing
gradients parallel and orthogonal to the imaging slab. After the relative strengths of all
three sensitizing gradients were established, we performed an experiment to determine
the most appropriate gradient area and duration (hence b-value). DIR+DSG prepared
carotid vessel wall image sets were acquired with various b-values. The vessel wall and
lumen regions of interest (ROIs) were manually segmented and the corresponding SNR in
the ROI for each acquired image was measured. Vessel wall and lumen SNR was plotted
as a function of b-value and an acceptable trade-off was determined.
3.2.3 Comparison of Blood Suppression Techniques
T
1
weighted axial datasets were acquired with 3D IV-FSE DIR+DSG, 3D IV-FSE DIR
and conventional 2D multislice FSE DIR scans in five healthy volunteers across the carotid
bifurcation. This was done to facilitate a fair comparison and evaluate blood suppression
levels using the proposed technique. All the relevant scan parameters including in-plane
35
spatial resolution, FOV and slice thickness were identical for all three methods. For the
3D methods the DIR slab thickness was set to 3 cm, while for the 2D methods it was set
to 7.5 mm. The inversion recovery time was computed based on the subject’s heart rate
at the start of the scan using eqn, and assuming T
1
=1550 ms [39]. For example, TI =
350 ms for a heart rate of 75 bpm.
3.2.4 Image Analysis
SNR measurements were based on manually drawn ROIs from the vessel wall and
lumen. Noise standard deviation (
n
) was measured by choosing a representative ROI
in the air space that did not contain any structure. SNR was computed for the vessel
wall (SNR
W
) and lumen (SNR
L
) from the magnitude images by using the relation
0:695S
n
where S represents the average signal intensity in the aforementioned ROIs. Contrast to
noise ratio (CNR) was computed by the relation
0:695(S
W
S
L
)
n
from the magnitude images.
CNR efficiency (CNR
eff
) was calculated using the relation where T
scan
represents the per
slice acquisition time in minutes [63]. A two-tailed paired t-test was used to determine
the statistical significance of the difference in vessel wall SNR, lumen SNR, and wall to
lumen CNR
eff
measured using the various techniques. Statistical significance was defined
at P < 0:01, in all tests.
3.3 Results
3.3.1 Attempted Optimization of DSG Preparation
Figure 3.2 contains scatter plots representing the velocities of residual luminal blood
from five volunteers. The spread of the velocity component along A/P (Y-axis) was
36
-6 -4 -2 0 2 4 6
-6
-4
-2
0
2
4
6
V y
Vz
a)
Vz
b)
-6 -4 -2 0 2 4 6
-6
-4
-2
0
2
4
6
Vx
-6 -4 -2 0 2 4 6
-6
-4
-2
0
2
4
6
Vx
V y
c)
L ef t
Sup er ior
A n t er ior
Sup er ior
L ef t
A n t er ior
Figure 3.2: Scatter plots of the velocity (cm/s) of unsuppressed luminal blood. Each color
represents one volunteer. (a) Projection onto the YZ plane with (

V
y
,

V
z
) = (-0.8,-1.4)
and (
Vy
,
Vz
) = (2.96,1.41). (b) Projection onto the XZ plane, with (

V
x
,

V
z
)= (-2.7,- 1.4)
and (
Vx
,
Vz
) = (1.51,1.41). (c) Projection onto the XY plane with (

V
x
,

V
y
) = ([-2.3
-2.2], [-3.9 3.6]) and (
Vx
,
Vy
) = (1.04,1.64), (2.09,1.34). Maximum likelihood was used
to estimate the mean and standard deviation of one or two component Gaussian mixture
distributions for each plot (gray ellipses). Note that
Vy
>
Vz
but
Vx

Vz
,
hence stronger dephasing is required along the imaging slab (XY or L/R-A/P) rather
than perpendicular to the imaging slab (Z or S/I).
greater than the spread of the through plane velocity component in every volunteer by
40% to 100%. The amplitude ratio of in plane to through plane sensitizing gradients in
the proposed DIR+DSG method was set to two, based on directional preference of the
unsuppressed blood. In other words, the orientation of the diffusion vector was tilted
towards the imaging plane.
37

Figure 3.3: Blood and vessel wall SNR from a single volunteer, when using 3D IV-FSE
DIR+DSG imaging with a range of b-values. Blood signal (solid) decreases with higher
b-value. Vessel wall signal (dashed) decreases significantly for b-value > 1 s/mm
2
. This
is due to increased DSG duration and therefore significantT
2
weighting. A b-value of 0.1
s/mm
2
was used in subsequent studies (black arrow).
Figure 3.3 demonstrates the trade-off between vessel wall and luminal SNR as a func-
tionofb-valuefromasinglevolunteer. Forasmallb-value(< 0.01 s/mm
2
)thevesselwall
signal experienced moderate attenuation consistent withT
2
decay but significant residual
blood signal persisted, presumably due to slow or cyclical flow. As the b-value increased
beyond 1 s/mm
2
, the residual blood signal approached the noise floor but the vessel wall
signal was also severely attenuated, presumably due to sensitivity to eddy current and
diffusion effects. The b-value of 0.1 s/mm
2
appeared to be a reasonable compromise be-
tween blood suppression and maintenance of high contrast between vessel wall and lumen,
and was used in the remaining studies. Note that a 3-fold increase from the suggested
b-value of 0.1 s/mm
2
carries a less than 10% penalty in contrast between wall and lumen.
38

Figure 3.4: T
1
weighted images from a healthy volunteer at the bifurcation of carotid
artery using the proposed 3D IV-FSE DIR+DSG, 3D IV-FSE DIR and 2D multislice
FSE DIR acquisitions. (a) Full FOV single slice just above the bifurcation. The DIR
only methods suffer from artifacts due to incomplete blood suppression at the bifurcation
(arrow). (b)Zoomedinviewfromalltheslicesaroundtherightcarotidartery,highlighting
box indicates the slices with significant residual blood signal when using DIR alone. The
arrow clearly indicates the presence of significant residual luminal blood signal when using
3D IV-FSE DIR.
3.3.2 In Vivo Comparison of Blood Suppression Techniques
Figure3.4containsrepresentativeimagesfromonevolunteeratmultipleaxiallocations
acquired using all three methods. Images acquired using the 3D IV-FSE DIR method
suffer from significant artifacts related to inadequate blood suppression in the carotid
lumen. The images acquired using 2D multislice FSE DIR and 3D IV-FSE DIR+DSG
exhibit comparable blood suppression across all the slices. Figure 3.5 shows the critical
central slice near the carotid bifurcation from all five volunteers. This slice has the highest
39

Figure 3.5: T
1
weighted images from five volunteers at the bifurcation of the left carotid
artery using the proposed 3D IV-FSE DIR+DSG, 3D IV-FSE DIR and 2D multislice FSE
DIR acquisitions. The highlighting box indicates studies with significant residual blood
signal when using DIR alone. The arrows clearly indicate the presence of significant
residual luminal blood signal when using 3D IV-FSE DIR.
likelihood of residual blood signal. Unsuppressed blood signal is visible in images acquired
fromthreeofthefivesubjectsusingthe3DIV-FSEDIRmethodwhiletheimagesacquired
using the 2D FSE and 3D IV-FSE DIR+DSG method remain relatively artifact free.
Figure 3.6 shows scatter plots of the measured SNRs and CNR
eff
from one central slice
in each subject that contained the bifurcation. Luminal SNR using the proposed method
was significantly lower than 3D IV-FSE DIR. Vessel wall SNR using the proposed method
was comparable to 3D IV-FSE DIR. Vessel wall to lumen CNR
eff
using proposed method
was statistically better than both 2D multi-slice FSE DIR and 3D IV-FSE DIR. Since
sequence timing was same for the two 3D methods, the improvement in CNR is identical
to the improvement in CNR
eff
when comparing the proposed method to 3D IV-FSE DIR.
Table 3.1 summarizes the corresponding p-value comparisons across all three methods for
the central slices that contain the bifurcation. The lumen SNR and wall to lumen CNR
eff
for the proposed 3D IV-FSE DIR+DSG technique were both statistically different from
40

Figure 3.6: Scatter plots showing in vivo measurements of the wall and lumen SNR, and
wall to lumen CNR efficiency on a per subject basis. Each color represents one volunteer.
a) Measurements from carotid segments only corresponding to the central slices at the
bifurcation are plotted. b) Measurements from all carotid segments across all the acquired
slices are averaged per subject and then plotted. The proposed method provides improved
blood suppression and wall to lumen CNReff, for all subjects when compared to the 3D
DIR IV-FSE.
3D IV-FSE DIR with P < 0.001 (6.96 vs. 14.15 for lumen SNR and 20.25 vs. 15.12 for
CNR
eff
). The wall SNR for the proposed method was not statistically different from 3D
IV-FSE DIR with P= 0.26 (28.9 vs. 29.8). Figure 3.6 shows scatter plot of the measured
SNRs and CNR
eff
averaged across all slices per subject, demonstrating similar trends.
41
3D IV-FSE
DIR+DSGvs.
3D IV-FSE
DIR
3D IV-FSE
DIR vs. 2D
Multislice
FSE DIR
3D IV-FSE
DIR+DSGvs.
2D Multi-
slice FSE
DIR
SNR – lumen <0.001 <0.001 0.06
SNR – wall 0.26 <0.001 <0.001
CNReff – wall-lumen <0.001 <0.001 <0.001
Table 3.1: P-values for paired t-tests comparing SNR and CNR
eff
of the three methods
based on all subjects and only slices containing the carotid bifurcation.
3.4 Discussion
DIR becomes a less effective method for blood suppression as the S/I thickness of the
imaging slab increases. This is due to inadequate inflow of inverted blood spins into the
imaging slab and diminished outflow of unaffected blood spins from the imaging slab.
Subjects with stagnant flow are more likely to suffer from artifacts due to residual blood
signal. In this study, significant residual blood signal was found in three of five subjects
when data was acquired with the 3D IV-FSE DIR method. Here it is worthwhile to note
that healthy volunteers are more likely to have stagnant flow than patients with steno-
sis. The proposed 3D IV-FSE DIR+DSG method produced complete blood suppression,
comparable to that of 2D multislice technique.
The typical implementation of DSG preparation involves applying gradients on all
three axes with equal gradient strength [35,71]. This is essentially done to maximally
dephase the flowing spins but without accounting for the directional preference of flow.
In the proposed DIR+DSG implementation, DIR preparation suppresses most of the
flowing spins that have a directional preference along the carotid axis or orthogonal to
the imaging slab. Blood spins that do not flow out of the imaging slab have a directional
preference orthogonal to the vessel axis and may be suppressed by aligning the diffusion
42
vector towards the imaging slab. Hence the area of the diffusion gradients aligned with
the imaging slab is set higher than component perpendicular to the imaging slab.
The proposed DIR+DSG preparation inherits some drawbacks of DSG alone prepara-
tion, including potential vessel wall signal loss due to true diffusion effect, T
2
, weighting
and, sensitivity to eddy current. However, these drawbacks are mitigated when using
the proposed hybrid preparation due to shortened duration of the DSG module and the
smaller b-value of flow dephasing bipolar gradients. This is evidenced by the fact that
there was no significant difference in vessel wall SNR when comparing DIR+DSG with
DIR alone.
There has been some debate on how to parameterize the blood suppression capability
of DSG preparation. In Ref. [35] b-value was used for quantifying various amounts of
sensitization, while in Ref. [71] the gradient first moment was used. This is because sup-
pression may result from flow induced phase rather than an actual diffusion effect. Here,
we prefer the b-value parameterization since the hemodynamics at the carotid bifurcation
are relatively complex and the blood spins within a voxel may have a distribution of ac-
celerations in addition to a distribution of velocities. There is no clear evidence to date
that indicates that the phase dispersion is resulting only from the gradient first moment
and not the higher moments.
The proposed 3D IV-FSE DIR+DSG scheme achieved comparable image quality with
respect to the various protocols but with a 40% reduction from the conventional 2D
multislice FSE DIR scan time. The expected SNR improvement with the 3D techniques
compared to the 2D technique is approximately 78% but the measured gain in SNR was
43
approximately 68%. This is presumably due to the poor slice profile of the refocusing
pulses, which causes a slight loss of signal in slices further from the slab center.
Mani et al. reported that gating did not affect image quality in black-blood multislice
studies [43]. However in our experience the repeatability of ungated 3D IV-FSE is poor.
We speculate that this was due to cumulative effect of vessel wall pulsation during the
3D scan which is of the order of 0.4 mm and is comparable with the in-plane resolution
used in our study. Also this study was performed in healthy volunteers that are more
likely to have compliant carotid vessel walls. Images obtained during this study were free
of artifact related to swallowing or motion, presumably due to the short scan times. In
patients unable to avoid swallowing, even during short scans, swallowing navigators may
be necessary.
3.5 Summary
In conclusion, 3D IV-FSE acquisitions were combined with both DIR and DSG prepa-
rations for blood suppression, which proved to be more effective than DIR alone. Data
acquired after the proposed hybrid DIR+DSG preparation was devoid of significant blood
signal and blood related artifacts. The reconstructed image quality was comparable to
that of conventional 2D multislice FSE DIR method and vessel wall to lumen CNR
eff
was
better than all competing methods. Furthermore, we demonstrate an 80 second acqui-
sition of 3D carotid vessel wall data with 0.5 x 0.5 x 2.5 mm
3
resolution, and a vessel
wall to lumen CNR 20 throughout the bifurcation. This approach can be applied to
proton-density, T
1
, and T
2
weighted FSE vessel wall imaging for accurate multi-spectral
plaque quantitation within a reasonable examination time.
44
Chapter 4
Rapid Imaging using an Asymmetric FOV 3D Cones
Trajectory
4.1 Introduction
Three dimensional cones [3,53,62] is the most time and SNR efficient k-space sampling
trajectory for 3D imaging. Gurney et al. [28] recently provided a highly efficient algorithm
forreadoutgradientdesignwhentheimagingfieldofview(FOV)andspatialresolutionare
both isotropic. In this chapter, we extend Gurneys design to anisotopic FOVs. We utilize
the method of Larson et al [36] to determine the appropriate cone angles, and propose a
new method for optimizing the sampling density along each cone. The resulting FOV is
shaped like a flattened cylinder and spatial resolution remains isotropic. We demonstrate
3D carotid imaging with a 73.2% reduction in scan-time compared to isotropic FOV cones
with comparable image quality.
45
a
b
K
z
K
xy
ø
n
ø
m
ø
critical
1/f
r
(ø
n
)
1/f
r
(ø
m
)
1/f
xy
1/f
z
1/f
r
(ø) = 1/(f
xy
* cos(ø)) if ø < ø
critical
1/f
r
(ø) = 1/(f
z
* sin(ø)) if ø > ø
critical

ø
critical
= arctan(f
xy
/f
z
)
Figure 4.1: k-space sampling for 2 cones at different angles shown in k
z
k
xy
plane view.
a) The sampling density along each cone varies as function of cone angle, if a no empty
rectangle constraint is applied. b) Sampling spacing along two cones with angle greater
and less than the critical angle.
4.2 Methods
Design of time-optimal anisotropic cones involves two essential steps: 1) finding the
minimum number of 3D conical surfaces along with the inter-cone spacing and 2) deter-
mining the minimum sampling requirement along each conical surface. In this chapter
we focus on the second step of optimizing the intra-cone sampling. Since the FOV is
symmetric about the z-axis, we can determine these requirements by projecting the cones
onto any (k
z
- k
xy
) quadrant where they can be viewed as radial spokes as shown in
46
Figure 4.1. Figure 4.2 illustrates the optimal sampling requirement for 3D cones with
isotropic (Figure 4.2a) and anisotropic FOV coverage (Figure 4.2b,c). The spacing be-
tween adjacent conical surfaces can be optimized for anisotropic FOV coverage by varying
the conical angles using the method developed by Larson et al [36]. The next step is to
reduce the radial sampling density along each cone by applying a geometrical constraint
ink
z
-k
xy
plane which ensures that every rectangle with dimensions 1/f
z
an 1/f
xy
in this
plane contains at least one sample point. The dimensions of this rectangle are related to
the degree of FOV anisotropy. The cones in k
z
- k
xy
plane are still oversampled near the
k-space origin. The near origin sample spacing can be increased by shifting the samples
on adjacent cones appropriately in a hexagonal fashion. Experiments were performed on
a Signa Excite 3T scanner (GE Healthcare, Waukesha, WI), first in a resolution phantom
using a birdcage head coil (results not shown), and then in human volunteers using a
4-channel carotid array coil (Pathway MRI, Seattle, WA). The carotid imaging sequence
consisted of 3 modules: DSG+DIR preparation, fat saturation and 3D-cones imaging. An
FOV of 15 x 15 x 3.75 cm
3
was used with a resolution of 1 x 1 x 1 mm
3
.
4.3 Results and Discussion
Plot containing the scan time reduction as a function of the anisotropy is shown
in Figure 4.3. The non-uniformly sampled data was reconstructed iteratively using the
conjugate algorithm (CG). Quadratic penalty is used for conditioning the non-Cartesian
system matrix. NUFFT [25] is used for interpolating the non-uniformly acquired k-space
data. Figure 4.4 compares images reconstructed from anisotropic and isotropic FOV
47
coverage. The image reconstructed using proposed trajectory is comparable to isotropic
counterparts with minimal artifacts.
4.4 Conclusion
We describe a method for generating 3D cones trajectories for anisotropic fields of
view. Relative to isotropic-FOV cones, a 4 fold reduction in the Z-FOV will result in
73.2% reduction in scan time without any perceptual loss in reconstructed image quality
except for SNR loss.
48
f
z
f
xy
Cylindrical FOV
No Empty
Rectangle in k
xy
- k
z
plane
f
z
1
a) Isoptropic b) Larson’s Anisoptropic
c) Proposed Anisoptropic
f
xy
1
d) Proposed Constraints
Figure4.2: k-spacesamplingdensityfor3conetrajectoriesshowingk
z
k
xy
quadrantview:
a) The isotropic FOV design places samples uniformly on a polar grid. b) The angular
spacing between cones is varied to obtain a cylindrical FOV shape. c) The proposed
method further reduces the sample density along each cone by applying a weaker no
empty rectangle constraint. d) Proposed constraints for a cylindrical FOV.
49
a)
Proposed
b)
Isotropic
Figure 4.3: Comparison of images reconstructed using the proposed anisotropic trajectory
with its isotropic counter-part. The dashed box indicates the bifurcation of the left carotid
artery and SNR was measured on the sternocleidomastoid muscle (triangle). Using the
proposed method number of readouts is reduced by approximately 73 % and SNR dropped
from 48.7 to 24.
0.2 0.4 0.6 0.8
0.2
0.4
0.6
0.8
f
z
/f
xy
Scan Time (%)
Variable Cone Angle
Proposed
Figure 4.4: Scan time reduction as a function of FOV anisotropicity (f
z
/f
xy
). As f
z
decreases in comparison with f
xy
the proposed method offers significant reduction in scan
time.
50
Chapter 5
Accelerated 3D MERGE Carotid Imaging using Compressed
Sensing with a Hidden Markov Tree Model
5.1 Introduction
High-resolution black-blood MRI has been used for quantifying carotid plaque mor-
phology [58,60,64] and multi-contrast pulse sequences have been used to delineate the
vessel wall and characterize plaque components [75]. Recently, non-invasive MRI mea-
surements of plaque burden are used as quantitative endpoints in clinical trials related to
atherosclerosis [67].
High signal-to-noise ratio (SNR) and high spatial resolution are important for quan-
titative measurements from plaque imaging. Several 2D and 3D imaging techniques have
been successfully applied for carotid plaque imaging. The typical carotid protocol acquires
multiple 2D multislice image sets (proton-density, T
1
andT
2
weighted fast spin echo, and
time of flight) across a 2-3 cm segment spanning the carotid bifurcation [75] and requires
about 30 minutes of scan time. Additional acceleration of imaging can be used to im-
prove SNR or resolution of carotid MR sequences and reduce motion artifacts. Scan time
51
reduction can be achieved by interleaving multiple image slices [29,32,61], employing
inner volume (IV) imaging [16], utilizing parallel imaging [26,50], or some combination
of these. Limitations exist to each of these methods of reducing scan time. Techniques
that interleave multiple slices together are susceptible to artifacts from incomplete blood
suppression [17,63] whereas both IV and parallel imaging sacrifice image SNR. Such tech-
niques may also be subject to limitations by gradient performance, RF coil geometry,
and may not be applicable to all pulse sequences. Additional complementary acceleration
methods that are not subject to such limitations are needed.
Compressed sensing (CS) is a relatively new technique that allows for acceleration
and denoising [10,19], and is independent of the native MR techniques. CS theory in-
dicates that if the image is compressible in a known sparsifying domain, then with only
O(Klog(N=K)) measurements, where K is the sparsity level, and N is the size of the
image, a sparsity-seeking algorithm can almost exactly recover the true image. Several
recent studies have demonstrated the feasibility of CS in MRI [40,41,69]. The application
of CS to carotid imaging has yielded only modest (3) acceleration rates thus far (ref
makhijanics), and is more fully explored in this work.
We demonstrate high acceleration by adapting the model-based CS framework devel-
oped by Baraniuk et al. [2]. The proposed method leverages an anatomy specific signal
model that is trained on a carotid image database. A modified recovery algorithm is
used to encourage sparse solutions that comply with the learnt model while maintaining
robustness of recovery. For instance, the wavelet coefficients naturally organize into a tree
structure, and large coefficients of natural images will cluster along the branches of this
52
tree [21,54]. Figure 5.1 illustrates this tree structure in the wavelet expansion of a 2D
axial carotid image.
5.2 Materials and Methods
5.2.1 Compressed Sensing MRI
CSallowsforacceleratedMRIbyconstrainingtheimagetoconformtoaknownmodel.
Classically, the MR signal can be expressed as:
s(t) =
Z
m(r)e
j2k(t)r
dr (5.1)
wherey
i
(t)representsthedataacquiredfromthei
th
coil,m(r)representtheunderlying
image and c
i
(r) is the receive coil sensitivity roll off for the i
th
coil, with r and k(t)
representing the spatial position and frequency dual variables. In discrete form, the signal
equation is:
y
i
= C
i
m (5.2)
where represents the Fourier encoding matrix,C
i
is the coil sensitivity matrix. Here
m represents the discrete image and y
i
is the data acquired from the i
th
coil in frequency
domain (k-space) Given N bases vectors
i
, we can represent every signal m2<
N
using
N coefficients x
i
. If we stack the vectors
i
into a NN matrix then the sparse coding
can be written as a linear transform as shown as:
53
m = x (5.3)
In this sense, the image is said to be K-sparse if K < N coefficients out of N are
nonzero. MR images, like most natural images, are likely to be compressible (many near-
zero coefficients) but not strictly sparse. Compressible images are well approximated
by K-sparse images. CS theory indicates that if the image is compressible by a known
transform and if certain conditions, described below, are satisfied, then O(Klog(N=K))
measurements are sufficient to recover the true image with very high accuracy and prob-
ability [10]. Assuming the MR image is compressible, the discrete MR signal equation
(eqn) can be re-written as:
y
i
=A
M
i
x (5.4)
where
A
M
i
=
M
C
i
(5.5)
represents the composite sensing matrix (of size MN, where M N) that maps
the sparse transform coefficients to the acquired data. The CS recovery theorems hold
provided thatA
M
i
satisfies the Restricted Isometry Property (RIP) [10] in addition to the
sparsity/compressibility requirement. If these criteria are satisfied then the underlying
image can be recovered by solving the following optimization problem:
54
^ x = arg min
x
jjxjj
1
subject to
X
i
jjy
i
A
M
i
xjj
2
(5.6)
where is a parameter that balances data consistency with transform sparsity. Data
from each coil can also be reconstructed individually and combined after CS recovery.
5.2.2 Model-Based CS
Conventional CS does not make any assumptions regarding the underlying support
(location) of the sparse coefficients in order to guarantee recovery for a broad variety of
natural as well as artificial signals. In reality these assumptions are too general and lead to
the requirement of unnecessarily inhibitive properties like the RIP. The correlations and
dependencies that exist among sparse coefficient locations and values for most natural im-
ages can be exploited by using a signal model. A signal modelM
K
, essentially restricts the
K-sparse signal x that lives in the union of arbitrary K-dimensional canonical subspaces
to a much smaller subset i.e. M
K
subset of C
NK
. This provides a structured sparsity
model that can be eventually used to reduce the dimensionality of the sparse search space.
Correlations among sparse coefficient locations and values enable us to learn statistics of
significant coefficients from a training database. Then these statistics are incorporated
in the recovery algorithm as a prior to effectively reduce the dimensionality of the search
space without sacrificing algorithm robustness. If an appropriate model is utilized, then
the required number of measurements reduces from O(Klog(N=K)) to O(K).
55
Figure 5.1: Illustration of the tree structure utilized in model-based CS. (a) 2D axial
image at the carotid bifurcation, and (b) its Daubechies-6 wavelet decomposition. The
most significant coefficients fall along a connected tree, marked by yellow lines, with large
coefficients shown in red.
5.2.3 Wavelet Tree Model
Wavelet transforms have been used for generating sparse representations in a wide va-
riety of applications including image compression and CS-MRI [2]. The wavelet transform
decomposes an image into coarse approximation coefficients, essentially a low-resolution
image, and detail coefficients, which are highly sparse. This corresponds to a one-scale
decomposition. The approximation coefficients can further be recursively decomposed
with subsequent wavelet transforms at coarse scales, forming a tree structure. For natural
56
Figure 5.2: Distribution of wavelet coefficients. (a) Log-histogram and (b) Histogram
of wavelet coefficients in one subband of a representative carotid image. The red line
is a mixture of two-component Gaussians fitted to the data and the blue line is the
approximation from a mixture of two-component generalized Gaussians. The generalized
Gaussian mixture provides a better fit than Gaussian mixture.
images, significant wavelet coefficients do not occur at arbitrary locations but exhibit a
characteristic structure [21,54]. If these statistics of significant coefficients can be learnt
from a training database then the resulting signal model can be incorporated at the recon-
struction stage. The CS recovery algorithms can be modified to encourage solutions that
comport with the learnt signal model. This provides an opportunity to flexibly trade off
thesearchcomplexityduringrecoverywithahigheraccelerationrateduringmeasurement.
In standard wavelet representation of images, nested sets of coefficients are generated
at every scale of the decomposition. All coefficients at every scale (except the last) will
have 4 children (in 2D image) or 8 children (in 3D image) coefficients at the next finer
scale. Similarly all children coefficients will have a parent at the previous coarser scale
(exceptthefirst). Coefficientmagnitudesusuallypersistthroughscalesduetotheanalysis
properties of wavelet basis functions. The presence of an edge in the original image will
manifest as a large wavelet coefficient while smooth regions will generally result in small
57
wavelet coefficients. Edges will usually create a chain of large coefficients linked across
scales. This phenomenon is known in the literature as the persistence property. Also
the magnitudes of wavelet coefficients exponentially decay at finer scales. This causes
the significant wavelet coefficients of piecewise smooth signals to concentrate within a
connected subtree of the wavelet tree.
In practice, coefficients of most real images will not form perfectly connected trees [21].
There are primarily three reasons for this break in structure. 1) The expected sparsity of
wavelet coefficients decreases at coarser scales, since carotid MR images are superpositions
of large smooth regions with contour singularities of varying sizes. 2) Since wavelet bases
are frequency band filters, its coefficients close to the edges oscillate around the zero
value. 3) The linearity of the wavelet transform may cause two or more edges to cancel out
coefficientsatcoarserscalesduetodestructiveinterference. Inotherwords, thepersistence
of the wavelets across scale is weaker at coarser scales. This yields a non-connected set
of meaningful wavelet coefficients. Hence we must develop a carotid specific model that
allows for such variations and embodies this statistical structure. These properties in spite
of problems of loose connectivity of the tree induce a joint statistical structure that is still
far stronger than simple sparsity or compressibility [2,21].
5.2.4 Hidden Markov Tree Model
Hidden Markov Tree (HMT) models succinctly and accurately represent this joint sta-
tistical structure. The key properties of wavelets that include persistence and exponential
decay across scales are captured by a tree-based Markov model that correlates the states
of parent and children coefficients. HMT modeling has been used successfully to improve
58
performance of denoising [54], classification, and even reconstruction from undersampled
data [21]. In this work we closely follow the framework developed in [21,54] and apply it
to MR image reconstruction. HMT models the non-Gaussian probability density function
of each wavelet coefficient as a mixture of two hidden binary states. The two states are
used to determine whether a particular coefficient is large or small in magnitude.
Atwo-componentmixtureofgeneralizedGaussianscanbeusedtostochasticallymodel
the distribution of sparse coefficients with large and small magnitudes. In previous works
[21,54] a two-component mixture of Gaussians was sufficient to model signal statistics.
However, we observed that a mixture of generalized Gaussians provide a better statistical
fit for wavelet coefficients of 3D MERGE carotid images (see Figure 5.2). Since the MR
images are generally complex, we must model statistics of real and imaginary component
separately. The generalized Gaussian reduces to the standard Gaussian and Laplacian
[18] distribution in special cases. The component corresponding to the small state has
a relatively small variance, capturing the peakiness around zero, while the component
corresponding to the large state has a relatively large variance, capturing the heavy tails.
The persistence of wavelet coefficient magnitudes across scale is modeled by linking
these hidden states across scale in a Markov tree. A state transition matrix for each link
quantifies statistically the degree of persistence of large or small coefficients. The other
properties of loosely connected wavelet trees can be also incorporated in the HMT model.
The decay in coefficient magnitude across scales will imply that variances associated with
generalized Gaussian mixture model will decay exponentially as the scale becomes finer
[21,54]. The weakening in persistence across scales can be modeled by appropriately
changingthestatetransitionweightsforfinerscales. TheMarkovmodelisthencompletely
59
determined by the set of state transition weights for linking the different coefficients at
different wavelet scales.
If fully sampled training images are available then maximum likelihood estimates of
the mixture variances and transition matrices can be calculated using the Expectation-
Maximization (EM) algorithm [52]. These parameter estimates yield a good approxima-
tion of the joint density function of the wavelet coefficients and hence the actual images.
Two sets of HMT parameter estimates are learnt, one for the real component and the other
for the imaginary component. With the knowledge of carotid specific HMT parameters
and hidden state probabilities at the coarsest wavelet scale, we can generate a distribution
for any coefficient’s hidden state by the Viterbi algorithm [15].
The iterative reweighted L
1
minimization (IRWL1) algorithm [12] enables a flexible
implementation that allows for specific signal penalizations while retaining the favorable
computationalcomplexityofL
1
normminimizations. TheIRWL1algorithmsolvesaseries
of L
1
minimization problems with an additional weighting matrix W
k
which is updated
after each minimization. In the traditional IRWL1 algorithm these weights are inversely
proportional to sparse coefficient magnitude. Here we utilize a weight rule proposed in 23
for the IRWL1 algorithm that integrates the HMT model to enforce the wavelet coefficient
structure during CS reconstruction. Weights are applied separately to real and imaginary
components.
^ x
k
= arg min jjW
k
xjj
1
+jjyA
M
xjj
2
(5.7)
60
The weighting can be summarized as: for each wavelet coefficient in the current es-
timate we obtain the probability that the coefficient’s hidden state is large; in the next
iteration, we apply to that coefficient a weight that is inversely proportional to that prob-
ability. The goal of this weighting scheme is to penalize coefficients with large magnitudes
that have low likelihood of being generated by a wavelet sparse signal; these coefficients
are often the largest contributors to the reconstruction error. The first step of proposed
algorithmconsistsof aninitialtrainingstage inwhich anEMalgorithm isusedto estimate
the values of the parameters for a representative signal; additionally, the solution for the
standard L
1
minimization is obtained. Subsequently, we proceed iteratively with two al-
ternating steps: a weight update step in which the Viterbi algorithm for state probability
calculations is executed for the previous solution, and a reconstruction step in which the
obtained weights are used in 5.7 to obtain an updated solution. The convergence criterion
for this algorithm is the same as for the IRWL1 algortihm.
5.2.5 Data Acquisition
All date were collected on a Philips Achieva 3T scanner with bilateral four channel
carotid phased array coils. Data were collected from 6 subjects with 16-79% carotid
stenosis by ultrasound. Informed consent was obtained prior to scanning under a protocol
approved by our Institutional Review Boards. Subjects were asked to avoid swallowing
during the scan, and scans were repeated if they were unable to do so. 3D Motion
Sensitized Driven Equilibrium prepared Rapid Gradient Echo (3D-MERGE) [1] images
were acquired in the coronal plane with scan parameters that provided coverage of the
full extent of carotid artery visible to the coil. One hundred coronal slices with isotropic
61
Figure 5.3: Illustration of the phase encode (ky,kz) locations for 4.5x undersampling.
resolution of 0.7x0.7x0.7 mm
3
(zero padded to 0.35x0.35x0.35 mm
3
) covering a 25x16 cm
2
FOV were acquired in a 2 minute scan. Other sequence parameters were TR-10ms, TE-
5ms, flip angle 6 degrees, Turbo factor 30, MSDE first gradient moment 1500 mTms
2
/m.
5.2.6 Image Reconstruction
Data were retrospectively undersampled using a region of full-sampling and a region
of variable density random undersampling. The sampling pattern for rate-4.5 is shown
in Figure 5.3. Acquired data from all subjects was randomly subdivided in two disjoints
sets, one for training and the other for evaluation. This process was repeated for each
dataset. CS was applied to each 2D slice oriented perpendicular to the readout direction
(i.e. along the two phase encoding directions, yz-plane). Three sets of images were
reconstructed from each undersampled dataset, two using HMT model-based CS [2] and
one using conventional L
1
-minimzation [40]. Two statistical models were used in HMT
model-based CS reconstructions, one using a mixture of Gaussians and the other using
62
mixture of generalized Gaussians. Reference images were also reconstructed from the fully
sampleddatausingconventionalFourierreconstruction. Greedyapproacheswerenotused
because they require more data samples for equivalent image quality [46]. Daubechies-6
wavelets (3-scale decomposition) are used to sparsify the images. The CS regularization
parameters were chosen empirically. Computation time for training model parameters
was 114 seconds using Matlab on a Linux workstation equiped with two 6-core 2.93 GHz
CPUs and 48 GB of RAM. Reconstruction time for the proposed HMT model-based CS
was 1900 seconds and for the standard L1 minimization was 392 seconds.
5.2.7 Image Analysis
Coronal images with isotropic resolution were reformatted to the axial plane with a
2 mm slice thickness for qualitative and quantitative measurements. Image quality was
visually assessed with respect to the presence of artifacts and aliasing, the conspicuity
of lumen and outer wall boundaries, and conspicuity of plaque components and rated on
a 4-point scale. The 12 carotids were randomized and stripped of patient information
prior to evaluation. A radiologist viewed the reference images and images reconstructed
using HMT model-based CS side by side on standard clinical picture archiving and com-
munication system (PACS) and assigned image quality scores, on the 4-point scale [68].
Lumen and outer wall boundaries were drawn using semiautomated plaque measurement
software [31] on all slices. Morphological measurements were derived from the contours
and compared between HMT model-based CS and reference images. Plaque burden mea-
surements, SNRL, SNRW, and CNR were compared using paired Student s t-test. Plaque
63
HMT CS (4.5x) Reference (1x) Difference P-value
Lumen area
(mm
2
)
19.6 20.81 18.98 20.54 0.17 0.45 0.25
Wall area (mm
2
) 15.27 10.76 15.54 10.62 -0.27 1.47 0.56
Mean wall
thickness (mm)
0.86 0.26 0.87 0.25 -0.035 0.096 0.27
Mean wall
thickness (mm)
1.37 0.49 1.41 0.51 -0.016 0.030 0.12
Necrotic core
area (mm
2
)
0.44 0.75 0.46 0.36 0.13 0.27 0.16
Calicification
area (mm
2
)
048 0.34 0.46 0.36 0.13 0.27 0.16
Table 5.1: Paired differences between plaque morphologic measurements made on images
reconstructed using HMT model-based CS (4.5x) and full sampling (1x).
burden measurements were also compared using Bland Altman plots. A 95% confidence
interval was used for all statistical tests and P-value <0.05 was considered significant.
5.3 Results
Normalized RMSE (NRMSE) plots for HMT model-based CS reconstructions using
mixture of Gaussians and mixture of generalized Gaussians are shown in Figure 5.4.
NRMSE is calculated for the region of interest the includes the carotid bifurcation is
averaged across all subjects and slices.
Figure 5.5 compares HMT model-based CS with standardL
1
minimization reconstruc-
tions. The images from L
1
minimization are corrupted with both aliasing and wavelet
basis artifacts at acceleration rates >3. At rate-4 acceleration the images from the stan-
dard approach shows significant aliasing artifacts along the undersampling direction while
the HMT model-based CS reconstruction does not show any substantive artifact. The
images reconstructed using HMT model-based CS suffer aliasing artifacts at rate-5. The
64
2 2.5 3 3.5 4 4.5 5
2
3
4
5
6
7
8
x 10
-3
Mixture of Generalized Gaussians
Mixture of Gaussians
Acceleration Rate
NRMSE
Figure 5.4: Normalized RMSE (NRMSE) for HMT model-based CS reconstructions using
mixture of Gaussians and mixture of generalized Gaussians as a function of acceleration
rate, averaged across all subjects, for an ROI containing the carotid bifurcation.
NRMSE plots correspond to error computed only in the region covering the carotid bi-
furcation across all 12 carotids. HMT model-based CS reconstructions consistently yield
a lower NRMSE at all acceleration rates.
Figure 5.6 shows reformatted sagittal and axials slices from 5 subjects. Vessel wall
imageswerevisualizedwellinthesagittalplane. Axialreformatsclearlydepictpresenceof
plaqueandshowsmalllesioncomponentssuchhascalicifications. Theimagereconstructed
from the proposed method at 4.5 fold undersampling is almost identical to the fully
sampled reference.
The average qualitative score for reference images was 2.1 0.57 while for HMT
model-based CS images was 2.3 0.67. Morphological measurements are summarized
in Table 5.1. Bland-Altman plots (Figure 5.7) showed no significant bias or correlation
65

Figure 5.5: Comparison of L1 minimization and model-based CS reconstructions. a) Fully
sampled reference. b) Normalized RMSE (NRMSE) for CS reconstructions as a function
of acceleration rate, averaged across all subjects, for an ROI containing the carotid bi-
furcation. c) Model-based CS reconstructions. d) L1 minimization reconstructions. e)
Absolute difference between the model-based CS and fully sampled reference. f) Absolute
difference between the L1 minimization reconstructions and fully sampled reference. The
arrow indicates severe artifacts in the L1 minimization difference image as compared to
the model-based CS difference image. All images are axial reformats. Difference images
are scaled to emphasize results.
between mean and difference of measurements. The absence of bias in plaque burden mea-
surements (Figure 5.7) was confirmed by a paired t-test. Figure 5.8 shows the correlation
of plaque burden measurements between reference and HMT model-based CS reconstruc-
tions. There was no significant correlation between mean values and mean differences
of any plaque burden measurement for both HMT model-based CS and fully sampled
reference images.
66

Figure 5.6: Representative sagittal and axial images from 5 carotid arteries included in
this study (out of 12). Atherosclerotic plaques are marked with white arrows. (a,c) fully
sampled reference. (b,d) model-based CS with data undersampled by a factor of 4.5. The
model-based CS reconstructions have slightly lower noise level than the reference images
(*), and show slight blurring of the vessel wall (dashed arrow)
5.4 Discussion
We have demonstrated the feasibility of accelerated 3D MERGE carotid MRI using
HMT model-based CS. This method exploits correlations and dependencies among trans-
form domain coefficients in addition to the basic sparsity and compressibility required
in CS. Rate-4.5 acceleration was achieved without any significant degradation in image
quality or fidelity of the most informative quantitative endpoints. In addition, this work
demonstrates that delineation of anatomic features that are routinely evaluated in carotid
MR scans is maintained in HMT model-based CS reconstructions. The proposed method-
ology is general and can be used for all forms of vessel wall imaging (VWI). VWI of
thoracic aorta and peripheral arteries also yield a similar challenge of distinguishing sharp
features embedded in a dull or suppressed background. However the number of fully
sampled images required for model parameter estimation and the sampling densities will
need to be tuned for the different anatomies. Recently several hybrid methods have been
proposed for combing parallel imaging and CS. HMT model-based CS does not utilize coil
67

Figure 5.7: Bland Altman plots comparing morphological measurements between model-
based CS reconstruction and fully sampled reference. Bold and dashed lines correspond
to mean difference and limits of agreement respectively. LA, lumen area; WA, wall area;
MWT, mean wall thickness; MaxWT, maximum wall thickness.
correlations and parallel imaging theory. The proposed method can be used to replace
the standardL
1
minimization step in these hybrid algorithms, or multi-coil reconstruction
can be directly incorporated in the proposed algorithm. However the sampling require-
ments for CS and parallel imaging are quite different and a new sampling density scheme
will be required to maximally exploit the combination of CS and parallel imaging based
acceleration. The computational complexity of HMT model-based CS is greater than
standard L
1
minimization, since the proposed method solves a series of L
1
minimization
68

Figure 5.8: Correlation of lumen area (LA), wall area (WA), mean wall thickness (MWT)
and max wall thickness (MaxWT) between reference and model-based CS reconstruction.
Solid and dashed lines correspond to linear regression line and 95% confidence intervals
respectively.
problems. We observed that the proposed method requires approximately 5 to 10 addi-
tional L
1
minimization steps. The model parameters can be estimated efficiently using
the EM algorithm and do not add significant computation cost to the reconstruction.
Reconstruction stability is impacted by fidelity of the model to the data. In this work,
initial parameter training was done using the EM algorithm, which is guaranteed to con-
verge only to a local minimum. Nevertheless we obtained reasonable estimates as long as
69
the training data was not excessively noisy. We also found that initializing the EM algo-
rithm with K-Means improved its convergence rate. The strength of the model mismatch
penalty is controlled by a regularization parameter. We set the penalty below its optimal
performance level to improve robustness. The proposed reconstruction was stable and
converged to visually acceptable estimate even with noisy data. We utilized a basic two
state HMT model to capture the correlations among wavelet coefficients. Other statistical
models such as Gaussian scale mixtures [70] or hierarchial Dirichlet processes [33] may
better capture these dependencies and potentially allow for higher acceleration. Since the
proposed method solves successive L
1
minimizations to form an estimate of sparse coeffi-
cients, the algorithm is not guaranteed to find a global minimum. Therefore, the choice
of an initial guess is critical. There are several possibilities, one is to use the solution
from L
1
minimization. The regularization used in the initial L
1
minimization problem
affects the final reconstruction. If a weak is used then the images will have ringing and
aliasing artifacts. If a strong is used then the images will be over sparse with wavelet
basis artifacts. However if the Haar wavelet is used rather than a long tap filter in the
initial L
1
minimization, the resultant images tend to have a benign blocking artifact.
Empirically, initializations using the Haar wavelet with a strong produced superior re-
constructions. This study has several limitations. For instance, data from only 6 patients
(12 carotids) were included. Morphological measurements were restricted to estimating
area and thickness. Inclusion of a larger number subjects, and a larger number of quan-
titative endpoints will be important next steps. Secondly, SNR and CNR measurements
were reported based on ROIs, however there is no established technique for quantifying
noise statistics in CS based MRI. SNR measurements are useful for comparison of imaging
70
techniques and were included for completeness. Finally, this work has only demonstrated
retrospective acceleration. Prospective studies are required to establish the full potential
of this approach, including any reduction of motion artifacts, improvements in patient
comfort and workflow, and potential improvements in spatial resolution.
5.5 Summary
In conclusion, we have demonstrated the application of HMT model-based CS recon-
struction to 3D MERGE carotid MRI. This method leverages the reduction in degrees of
freedom due to model imposition to achieve higher acceleration rates. This method ex-
ploits the connected tree structure that exists in wavelet coefficients of carotid images by
permitting only certain configuration of significant coefficients and support. The proposed
method provides superior reconstruction at higher acceleration factors when compared to
the standard CS-MRI approach. Rate-4.5 acceleration with 3D data sets was successfully
demonstrated without compromising image quality. This proposed method can be utilized
for reducing scan time, improving resolution, and/or improving SNR.
71
Chapter 6
Summary
Carotid MRI has recently gained popularity for diagnosis and management of carotid
atherosclerosis. This is primarily due to hardware developments that have lead to custom
receive coils for the imaging the carotids and also due to improvement in multi-spectral
pulse sequences that provide necessary contrast for analyzing plaque components. How-
ever the current state of the art carotid MRI has several limitations and unmet challenges.
These include unreliable contrast between plaque and surrounding tissue due to inaccu-
rate blood suppression, limited SNR or resolution and, long scan times which result in
motion or swallowing artifacts. In this thesis I present different methods for alleviating
some of these limitations. Primarily this thesis is focussed on accelerating data acquisi-
tion for reducing scan times and improving the contrast between plaque and lumen. The
proposed methods provide superior blood suppression and allow for higher acceleration
factors when compared to conventional approaches.
Improved Blood Suppression using Diffusion Sensitizing Gradients. 3D
IV-FSE acquisitions were combined with both DIR and DSG preparations for blood
suppression, which proved to be more effective than DIR alone. Data acquired after
72
the proposed hybrid DIR+DSG preparation was devoid of significant blood signal
andbloodrelatedartifacts. Thereconstructedimagequalitywascomparabletothat
of conventional 2D multislice FSE DIR method and vessel wall to lumen CNR
eff
was better than all competing methods. Furthermore, I demonstrate an 80 second
acquisition of 3D carotid vessel wall data with 0.5 x 0.5 x 2.5 mm
3
resolution, and
a vessel wall to lumen CNR 20 throughout the bifurcation. This approach can be
applied to proton-density,T
1
, andT
2
weighted FSE vessel wall imaging for accurate
multi-spectral plaque quantitation within a reasonable examination time.
Rapid Imaging using an Asymmetric FOV 3D Cones Trajectory. We de-
scribe a method for generating 3D cones trajectories for anisotropic fields of view.
Relative to isotropic-FOV cones, a 4 fold reduction in the the through plane FOV
will result in 73.2% reduction in scan time without any perceptual loss in recon-
structed image quality except for SNR loss.
Accelerated3DMERGECarotidImagingusingCompressedSensingwith
a Hidden Markov Tree Model. I have demonstrated application of model-based
CS reconstruction to black-blood carotid MRI. This method leverages the reduction
in degrees of freedom due to model imposition to achieve higher acceleration rates.
The proposed method provides superior reconstruction at higher acceleration fac-
tors when compared to the standard CS-MRI approach. Rate-4.5 acceleration with
3D data sets was successfully demonstrated without compromising image quality.
This proposed method can be utilized for reducing scan time, improving resolution,
and/or improving SNR.
73
References
[1] Niranjan Balu, Vasily L Yarnykh, Baocheng Chu, Jinnan Wang, Thomas Hatsukami,
and Chun Yuan. Carotid plaque assessment using fast 3D isotropic resolution black-
blood MRI. Magnetic Resonance in Medicine, 65(3):627–637, March 2011.
[2] R. G Baraniuk, V. Cevher, M. F Duarte, and C. Hegde. Model-Based compressive
sensing. IEEE Transactions on Information Theory, 56(4):1982–2001, April 2010.
[3] Andrew V Barger, Walter F Block, Yuriy Toropov, Thomas M Grist, and Charles A
Mistretta. Time-resolved contrast-enhanced imaging with isotropic resolution and
broadcoverageusinganundersampled3Dprojectiontrajectory. MagneticResonance
in Medicine, 48(2):297–305, August 2002.
[4] BerkinBilgic,VivekKGoyal,andElfarAdalsteinsson. MultiâĂŘcontrastreconstruc-
tionwithbayesiancompressedsensing. MagneticResonanceinMedicine, 66(6):1601–
1615, December 2011.
[5] F. Bloch, W. W. Hansen, and M. E. Packard. Nuclear induction. Phys. Rev., 69:127,
1946.
[6] T. Blumensath and M. E Davies. Sampling theorems for signals from the union
of Finite-Dimensional linear subspaces. IEEE Transactions on Information Theory,
55(4):1872–1882, April 2009.
[7] Thomas Blumensath and Mike E Davies. Iterative hard thresholding for compressed
sensing. Applied and Computational Harmonic Analysis, 27(3):265–274, November
2009.
[8] Jean H Brittain, Bob S Hu, Graham A Wright, Craig H Meyer, Albert Macovski,
and Dwight G Nishimura. Coronary angiography with Magnetization-Prepared T2
contrast. Magnetic Resonance in Medicine, 33(5):689–696, May 1995.
[9] E. J Candes, J. Romberg, and T. Tao. Robust uncertainty principles: exact signal
reconstruction from highly incomplete frequency information. IEEE Transactions on
Information Theory, 52(2):489– 509, February 2006.
[10] E.JCandesandT.Tao. Near-Optimalsignalrecoveryfromrandomprojections: Uni-
versal encoding strategies? IEEE Transactions on Information Theory, 52(12):5406–
5425, December 2006.
74
[11] Emmanuel Candes. The Dantzig selector: Statistical estimation when p is much
larger than n. The Annals of Statistics, 35(6):2313–2351, December 2007.
[12] Emmanuel J. Candes, Michael B. Wakin, and Stephen P. Boyd. Enhancing sparsity
by reweighted âL1 minimization. Journal of Fourier Analysis and Applications, 14(5-
6):877–905, October 2008.
[13] T. E. Conturo, R. R. Price, and A. H. Beth. Rapid local rectangular views and
magnifications: reduced phase encoding of orthogonally excited spin echoes. Magn.
Reson. Med., 6:418–429, 1988.
[14] M. S Crouse, R. D Nowak, and R. G Baraniuk. Wavelet-based statistical signal
processing using hidden markov models. IEEE Transactions on Signal Processing,
46(4):886–902, April 1998.
[15] M.S. Crouse, R.D. Nowak, and R.G. Baraniuk. Wavelet-based statistical signal
processing using hidden markov models. Signal Processing, IEEE Transactions on,
46(4):886 –902, April 1998.
[16] L. A. Crowe, P. Gatehouse, and G. Z. Yang. Volume-selective 3d turbo spin echo
imaging for vascular wall imaging and distensibility measurement. J. Magn. Reson.
Imaging, 17:572–580, 2003.
[17] Lindsey A Crowe, Anitha Varghese, Raad H Mohiaddin, Guang Zhong Yang, and
David N Firmin. Elimination of residual blood flow-related signal in 3D volume-
selective TSE arterial wall imaging using velocity-sensitive phase reconstruction.
Journal of Magnetic Resonance Imaging, 23(3):416–421, March 2006.
[18] M. N Do and M. Vetterli. Wavelet-based texture retrieval using generalized gaus-
sian density and Kullback-Leibler distance. IEEE Transactions on Image Processing,
11(2):146–158, February 2002.
[19] D. L Donoho. Compressed sensing. IEEE Transactions on Information Theory,
52(4):1289–1306, April 2006.
[20] David L. Donoho, Yaakov Tsaig, Iddo Drori, and Jean-luc Starck. Sparse solution of
underdetermined linear equations by stagewise orthogonal matching pursuit. Tech-
nical report, CiteSeerX, 2006.
[21] M. F Duarte, M. B Wakin, and R. G Baraniuk. Wavelet-domain compressive signal
reconstruction using a hidden markov tree model. In IEEE International Conference
on Acoustics, Speech and Signal Processing, 2008. ICASSP 2008, pages 5137–5140.
IEEE, April 2008.
[22] R R Edelman, D Chien, and D Kim. Fast selective black blood MR imaging. Radi-
ology, 181(3):655 –660, December 1991.
[23] M. Elad and M. Aharon. Image denoising via sparse and redundant representations
overlearneddictionaries. IEEETransactionsonImageProcessing, 15(12):3736–3745,
December 2006.
75
[24] Zahi A. Fayad, Valentin Fuster, John T. Fallon, Timothy Jayasundera, Stephen G.
Worthley, Gerard Helft, J. Gilberto Aguinaldo, Juan J. Badimon, and Samin K.
Sharma. Noninvasive in vivo human coronary artery lumen and wall imaging using
Black-Blood magnetic resonance imaging. Circulation, 102(5):506 –510, 2000.
[25] Jeffrey A. Fessler. On NUFFT-based gridding for non-Cartesian MRI. Journal of
Magnetic Resonance, 188(2):191–195, October 2007.
[26] Mark A Griswold, Peter M Jakob, Robin M Heidemann, Mathias Nittka, Vladimir
Jellus, Jianmin Wang, Berthold Kiefer, and Axel Haase. Generalized autocalibrat-
ing partially parallel acquisitions (GRAPPA). Magnetic Resonance in Medicine,
47(6):1202–1210, June 2002.
[27] Mark A Griswold, Stephan Kannengiesser, Robin M Heidemann, Jianmin Wang, and
Peter M Jakob. Field of view limitations in parallel imaging. Magnetic Resonance
in Medicine, 52(5):1118–1126, November 2004.
[28] Paul T Gurney, Brian A Hargreaves, and Dwight G Nishimura. Design and analysis
of a practical 3D cones trajectory. Magnetic Resonance in Medicine, 55(3):575–582,
March 2006.
[29] V. V. Itskovich, V. Mani, and G. Mizsei. Parallel and nonparallel simultaneous
multislice black-blood double inversion recovery techniques for vessel wall imaging.
J. Magn. Reson. Imaging, 19:459–467, 2004.
[30] Listerud J, Einstein S, Outwater E, and Kressel HY. First principles of fast spin
echo. Magnetic resonance quarterly, 8(4):199, December 1992.
[31] William Kerwin, Dongxiang Xu, Fei Liu, Tobias Saam, Hunter Underhill, Nori-
hide Takaya, Baocheng Chu, Thomas Hatsukami, and Chun Yuan. Magnetic res-
onance imaging of carotid atherosclerosis. Topics in Magnetic Resonance Imaging,
18(5):371–378, October 2007.
[32] S. E. Kim, E. K. Jeong, and D. L. Parker. Triple contrast technique for black blood
imaging with double inversion preparation. Magn. Reson. Med., 52:1379, 2004.
[33] J. J Kivinen, E. B Sudderth, and M. I Jordan. Image denoising with nonparametric
hidden markov trees. In IEEE International Conference on Image Processing, 2007.
ICIP 2007, volume 3, pages 121–124. IEEE, October 2007.
[34] I. Koktzoglou, Y. C. Chung, V. M. Mani, and et al. Multislice dark-blood carotid
artery wall imaging: a 1.5T and 3.0T comparison. J. Magn. Reson. Imaging, 23:699–
705, 2006.
[35] I. Koktzoglou and L. Debiao. Diffusion prepared segmented steady state free preces-
sion: application to 3D black-blood cardiovascular magnetic resonance of the thoracic
aorta and carotid artery walls. J. Cardiovasc. Magn. Reson., 9:33–42, 2007.
[36] P Z Larson, P T Gurney, and D G Nishimura. Anisotropic field-of-views in radial
imaging. IEEE Transactions on Medical Imaging, 27(1):47–57, January 2008.
76
[37] P. C. Lauterbur. Image formation by induced local interactions: Examples employing
nuclear magnetic resonance. Nature, 242:190–191, March 1973.
[38] Dong Liang, Bo Liu, JiunJie Wang, and Leslie Ying. Accelerating SENSE using
compressed sensing. Magnetic Resonance in Medicine, 62(6):1574–1584, December
2009.
[39] HanzhangLu, ChekeshaClingman, XavierGolay, andPeterC.MvanZijl. Determin-
ing the longitudinal relaxation time (T1) of blood at 3.0 Tesla. Magnetic Resonance
in Medicine, 52(3):679–682, September 2004.
[40] Michael Lustig, David Donoho, and John M Pauly. Sparse MRI: the application
of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine,
58(6):1182–1195, December 2007.
[41] Michael Lustig and John M Pauly. SPIRiT: iterative self-consistent parallel imaging
reconstruction from arbitrary k- space. Magnetic Resonance in Medicine, 64(2):457–
471, August 2010.
[42] Mahender K Makhijani, Houchun H Hu, Gerry M Pohost, and Krishna S Nayak.
Improved blood suppression in three-dimensional (3D) fast spin-echo (FSE) vessel
wall imaging using a combination of double inversion-recovery (DIR) and diffusion
sensitizing gradient (DSG) preparations. Journal of Magnetic Resonance Imaging,
31(2):398–405, February 2010.
[43] V. Mani, V. V. Itskovich, and S. H. Aguiar. Comparison of gated and nongated
fast multislice black-blood carotid imaging using rapid extended coverage and in-
flow/outflow saturation techniques. J. Magn. Reson. Imaging, 22:628–633, 2005.
[44] V.Mani, V.V.Itskovich, andM.Szimtenings. Rapidextendedcoveragesimultaneous
multisection black-blood double inversion recovery techniques for vessel wall imaging.
Radiology, 232:281–288, 2004.
[45] Dimitris Mitsouras, Robert V. Mulkern, and Frank J. Rybicki. Strategies for inner
volume 3D fast spin echo magnetic resonance imaging using nonselective refocusing
radio frequency pulses. Medical Physics, 33(1):173, 2006.
[46] D. Needell and J. A Tropp. CoSaMP: iterative signal recovery from incomplete and
inaccurate samples. Applied and Computational Harmonic Analysis, July 2008.
[47] D. G. Nishimura. Principles of magnetic resonance imaging. Stanford University
EE369B Course Notes, 1996.
[48] D. C Noll, D. G Nishimura, and A. Macovski. Homodyne detection in magnetic
resonance imaging. IEEE Transactions on Medical Imaging, 10(2):154–163, June
1991.
[49] J. Portilla, V. Strela, M. J Wainwright, and E. P Simoncelli. Image denoising using
scale mixtures of gaussians in the wavelet domain. IEEE Transactions on Image
Processing, 12(11):1338– 1351, November 2003.
77
[50] K.PPruessmann,M.Weiger,M.BScheidegger,andP.Boesiger. SENSE:Sensitivity
encoding for fast MRI. Magnetic resonance in medicine, 42(5):952–962, 1999.
[51] E. M. Purcell, H. C. Torrey, and R. V. Pound. Resonance absorption by nuclear
magnetic moments in a solid. Physical Review, 69(1-2):37–38, January 1946.
[52] L.R. Rabiner. A tutorial on hidden markov models and selected applications in
speech recognition. Proceedings of the IEEE, 77(2):257 –286, February 1989.
[53] Jorgen Rahmer, Peter Bornert, Jan Groen, and Clemens Bos. Three-dimensional
radial ultrashort echo-time imaging with T2 adapted sampling. Magnetic Resonance
in Medicine, 55(5):1075–1082, May 2006.
[54] J. K Romberg, Hyeokho Choi, and R. G Baraniuk. Bayesian tree-structured image
modeling using wavelet-domain hidden markov models. IEEE Transactions on Image
Processing, 10(7):1056–1068, July 2001.
[55] Mallat S. A wavelet tour of signal processing - Stephane G. Mallat.
[56] Tobias Saam, Thomas S. Hatsukami, Norihide Takaya, Baocheng Chu, Hunter Un-
derhill, William S. Kerwin, Jianming Cai, Marina S. Ferguson, and Chun Yuan.
The vulnerable, or High-Risk, atherosclerotic plaque: Noninvasive MR imaging for
characterization and assessment1. Radiology, 244(1):64–77, July 2007.
[57] J. M Shapiro. Embedded image coding using zerotrees of wavelet coefficients. IEEE
Transactions on Signal Processing, 41(12):3445–3462, December 1993.
[58] M. Shinnar, J. T. Fallon, S. Wehrli, and et al. The diagnostic accuracy of ex vivo
mri for human atherosclerotic plaque characterization. Arterioscler. Thromb. Vasc.
Biol., 19:2756–2761, 1999.
[59] M. Sirol, V. V. Itskovich, and V. Mani. Lipid-rich atherosclerotic plaques detected by
gadofluorine-enhanced in vivo magnetic resonance imaging. Circulation, 109:2890–
2896, 2004.
[60] K. Soila, P. Nummi, T. Ekfors, and et al. Proton relaxation time in arterial wall and
atheromatous lesions in man. Invest. Radiol., 21:411–415, 1986.
[61] H. K. Song, A. C. Wright, and R. L. Wolf. Multislice double inversion pulse sequence
for efficient black-blood mri. Magn. Reson. Med., 47:616–620, 2002.
[62] C Stehning, P Bornert, K Nehrke, H Eggers, and O Dossel. Fast isotropic volumetric
coronary MR angiography using free-breathing 3D radial balanced FFE acquisition.
Magnetic Resonance in Medicine, 52(1):197–203, July 2004. PMID: 15236387.
[63] David A Steinman and Brian K Rutt. On the nature and reduction of plaque-
mimicking flow artifacts in black blood MRI of the carotid bifurcation. Magnetic
Resonance in Medicine, 39(4):635–641, April 1998.
78
[64] J. F. Toussaint, G. M. LaMuraglia, J. F. Southern, and et al. Magnetic resonance
images lipid, fibrous, calcified, hemorrhagic, and thrombotic components of hum
atherosclerosis in vivo. Circulation, 94:932–938, 1996.
[65] J. A Tropp and A. C Gilbert. Signal recovery from random measurements via or-
thogonal matching pursuit. IEEE Transactions on Information Theory, 53(12):4655–
4666, December 2007.
[66] J. Trzasko and A. Manduca. Highly undersampled magnetic resonance image re-
construction via homotopic -Minimization. IEEE Transactions on Medical Imaging,
28(1):106–121, January 2009.
[67] Hunter R. Underhill, Thomas S. Hatsukami, Zahi A. Fayad, Valentin Fuster, and
Chun Yuan. MRI of carotid atherosclerosis: clinical implications and future direc-
tions. Nat Rev Cardiol, 7(3):165–173, March 2010.
[68] Hunter R. Underhill, Vasily L. Yarnykh, Thomas S. Hatsukami, Jinnan Wang, Ni-
ranjan Balu, Cecil E. Hayes, Minako Oikawa, Wei Yu, Dongxiang Xu, Baocheng
Chu, Bradley T. Wyman, Nayak L. Polissar, and Chun Yuan. Carotid plaque mor-
phology and composition: Initial comparison between 1.5- and 3.0-T magnetic field
strengths1. Radiology, 248(2):550 –560, 2008.
[69] Shreyas S. Vasanawala, Marcus T. Alley, Brian A. Hargreaves, Richard A. Barth,
JohnM.Pauly, andMichaelLustig. ImprovedpediatricMRimagingwithcompressed
sensing1. Radiology, 256(2):607 –616, 2010.
[70] Martin J. Wainwright and Eero P. Simoncelli. Scale mixtures of gaussians and the
statistics of natural images. Technical report, CiteSeerX, 2000.
[71] J. Wang, V. Yarnykh, and T. Hatsukami. Efficient slow-flowing blood suppres-
sion technique in atherosclerosis imaging with motion sensitized driven equilibrium
(MSDE) TSE sequence at 3T. Proc., ISMRM, 15th Annual Meeting, 15:442, 2007.
[72] V. L. Yarnykh, M. Terashima, C. E. Hayes, and et al. Multicontrast black-blood mri
of carotid arteries: comparison between 1.5 and 3 Tesla magnetic field strengths. J.
Magn. Reson. Imaging, 23:691–698, 2006.
[73] V.L.YarnykhandC.Yuan. Multislicedoubleinversionrecoveryblack-bloodimaging
with simultaneous slice reinversion. J. Magn. Reson. Imaging, 17:478–483, 2003.
[74] C. Yuan, W. S. Kerwin, and M. S Ferguson. Contrast enhanced high resolution mri
for atherosclerotic carotid artery tissue characterization. J. Magn. Reson. Imaging,
15:62–67, 2002.
[75] C. Yuan, L. M. Mitsumori, M. S. Ferguson, and et al. In vivo accuracy of mul-
tispectral magnetic resonance imaging for identifying lipid-rich necrotic cores and
intraplaque hemorrhage in advanced human carotid plaques. Circulation, 104:2051–
2056, 2001.
79

Abstract (if available)

Abstract Magnetic resonance imaging (MRI) is a promising modality for assessment and analysis of arterial plaque because of its inherent 3D nature, excellent soft tissue discrimination, and lack of ionizing radiation. Recently, clinicians have used non-invasive MRI measurements of carotid artery plaque for diagnosis and management of carotid atherosclerosis. However, the development of vessel wall imaging (VWI) in MRI is currently restricted due to low signal-to-noise ratio (SNR), limited resolution and motion artifacts due to long scan times. In addition the standard VWI technique used in MRI relies on suppression of signal from flowing blood in the artery lumen to provide necessary contrast between the plaque and surrounding tissue/blood. In this thesis, I present new methods for imaging of the carotid arteries to improve on some of the current limitations in carotid MRI. ❧ First, I introduce a new technique for improving blood suppression in carotid MRI. In standard carotid MRI approaches a preparatory sequence is used for suppression of flowing blood in order to improve plaque contrast with respect to the lumen. However, the complicated and cyclic flow patterns at the carotid bifurcation result in slow and stagnant blood flow. MR carotid artery images frequently suffer from plaque mimicking artifacts, which may result in incorrect diagnosis. In addition these artifacts are exacerbated in 3D imaging, which might alleviate some SNR limitations. The proposed method utilizes a hybrid preparation for blood suppression that is more robust to stagnant or re-circulant flow with 3D imaging. ❧ Second, I present a new anisotropic 3D cones sampling trajectory for accelerating data acquisition. In carotid MRI a highly anisotropic field-of-view (FOV) is sufficient to cover the anatomy of interest (carotid bifurcation). The proposed trajectory is an extension of Gurney's design to anisotropic FOVs. The resulting FOV is shaped like a flat cylinder while spatial resolution remains isotropic. 3D carotid imaging with a 73.2% reduction in scan time compared to isotropic FOV cones is demonstrated. ❧ Finally, I present a new method for image reconstruction from undersampled data using compressed sensing (CS) theory. CS is a relatively new theory that allows for acceleration and de-noising, and is independent of the traditional MR acceleration techniques. The proposed method utilizes a variant of CS known as model-based CS which allows for higher and more robust acceleration. Preliminary studies have verified the feasibility of CS for achieving modest acceleration rates (<3) in carotid imaging. The proposed method improves on this rate by exploiting correlations and dependencies by imposing a data-driven statistical model. The signal model is trained on an application/anatomy specific training database. A modified recovery algorithm is used to encourage sparse solutions that comply with the learnt model while maintaining robustness of recovery. 3D carotid imaging with rate 4.5 fold acceleration was successfully demonstrated in patients without compromising clinically relevant quantitative endpoints or image quality.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Seeing sleep: real-time MRI methods for the evaluation of sleep apnea

PDF

Improved brain dynamic contrast enhanced MRI using model-based reconstruction

PDF

Fast flexible dynamic three-dimensional magnetic resonance imaging

PDF

Accelerated chemical shift encoded water-fat imaging

PDF

Functional real-time MRI of the upper airway

PDF

Assessment of myocardial blood flow in humans using arterial spin labeled MRI

PDF

Radiofrequency pulse performance for myocardial ASL

PDF

Fast upper airway MRI of speech

PDF

Shift-invariant autoregressive reconstruction for MRI

PDF

Toward understanding speech planning by observing its execution—representations, modeling and analysis

PDF

Methods for improving reliability and consistency in diffusion MRI analysis

PDF

Novel computational techniques for connectome analysis based on diffusion MRI

PDF

New theory and methods for accelerated MRI reconstruction

PDF

Contributions to structural and functional retinal imaging via Fourier domain optical coherence tomography

PDF

Velocity-encoded magnetic resonance imaging: acquisition, reconstruction and applications

PDF

Correction, coregistration and connectivity analysis of multi-contrast brain MRI

PDF

Optimization methods and algorithms for constrained magnetic resonance imaging

PDF

A logic partitioning framework and implementation optimizations for 3-dimensional integrated circuits

PDF

A computational framework for diversity in ensembles of humans and machine systems

PDF

High-dimensional magnetic resonance imaging of microstructure

Asset Metadata

Creator Makhijani, Mahender K. (author)

Core Title New methods for carotid MRI

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 08/02/2012

Defense Date 08/02/2012

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

Tag acceleration,carotid,CS,MRI,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nayak, Krishna S. (committee chair), Hsiai, Tzung K. (committee member), Ortega, Antonio K. (committee member)

Creator Email mahendermakhijani@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-84109

Unique identifier UC11288744

Identifier usctheses-c3-84109 (legacy record id)

Legacy Identifier etd-MakhijaniM-1116.pdf

Dmrecord 84109

Document Type Dissertation

Rights Makhijani, Mahender K.

Type texts

Source 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 a...

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