University of Southern California Dissertations and Theses

Estimating liver iron non-invasively with high-field MRI

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Estimating liver iron non-invasively with high-field MRI

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Content ESTIMATING LIVER IRON NON-INVASIVELY WITH HIGH-FIELD MRI
by
Eamon Doyle
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
(BIOMEDICAL ENGINEERING)
December 2017
Copyright 2017 Eamon Doyle
Dedication
To Meghan and my parents for very many things.
ii
Acknowledgments
I would not be here without the support, mentorship, companionship, and
patience of so many people throughout my growth as a researcher, scientist and
engineer.
I would like to first thank my advisor, John Wood. He taught me to think
critically about data, formulate and pursue questions, and wade through confusion
to find truth. He has shared his personal interests and time with me in spite of
the constant demands from the divergent worlds of research and clinical medicine.
In many ways, he is as much my friend as my advisor. I consider it one of the
pleasures and privileges of my life to have worked with him as an undergraduate
and throughout my PhD.
Second, I wish to thank my lab mate and friend, Adam Bush. From the day I
took over half of his office, he has been an boundless source of research ideas and
the kinds of rambling discussions that often lead to unexpected insights. I have
grown in my understanding of the world through him.
I also would like to thank everyone at Children’s Hospital of Los Angeles who
worked with me all these years. Dr. Jon Detterich was always willing to take time
out of his day to explain fundamentals of physiology and clinical medicine without
more than a moment’s notice. Dr. Roberta Kato mentored me through the grant
writing process and helped me to develop an unlikely idea into a winning grant.
iii
Dr. Thomas Coates provided research space and resources and gave balance and
perspective to my thesis committee. Dr. Marvin Nelson and Julia Castro gave me
more freedom to use the research magnet than I ever expected a grad student to
receive, helping me to develop my ideas quickly. I also benefitted from the hard
work of Nathan Smith, Heather Mnoian, Kristin Toy, Bertin Valdez, and Noel
Arugay, all of whom were critical to our studies running.
My degree was truly interdisciplinary, in part due to the resources I received
at USC. Krishna Nayak co-advised me throughout my PhD work and helped to
teach me a variety of technical and theoretical concepts that were invaluable to me.
He, and his then-graduate student Kyung Sung, introduced me to MRI research
in 2007 and fundamentally changed my path in life.
Through our MRI vendor, Philips Healthcare, I had the pleasure of working
with Jon Chia and Tom Perkins, who provided clinical science support to CHLA.
They helped start my projects off on the right foot and always helped me to find
the technical information I needed to create new things on the scanner.
Iwouldalsoliketothankafewpeoplewhodon’tfitintooneparticularcategory.
Sandra Meyers not only helped me to learn Philips pulse programming, she did it
with more fun and celebratory dancing than possibly any other pulse sequence has
ever received in the early developmental phase. She also welcomed me into her lab
at conferences, helping to grow my social and professional networks at the same
time. Nilesh Ghugre laid the foundational simulation work that I carried forward
and Sam Thornton helped me to extend the simulation framework to answer new
questions. There are too many people to thank exhaustively, but I appreciate the
help that everyone has given me throughout my time at USC and CHLA.
Finally, I would like to thank my family. My parents taught me the work ethic
and commitment that was required of me in my PhD. My sister, Lindsey, provides
iv
me a constant reminder to consider the broader implications of my work. Lastly,
to my (almost) wife, Meghan, there simply are not words to describe what you
have given me the past 7 years. You started walking this path with me when you
proofread my grad school applications in 2010, and what a long, strange trip it
has been. Let’s start the next one, shall we?
v
Contents
Dedication ii
Acknowledgments iii
List of Tables ix
List of Figures x
Glossary xviii
Acronyms xx
Abstract xxii
1 Introduction 1
1.1 Iron Overload Disorders . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Mechanisms of Iron Overload . . . . . . . . . . . . . . . . . 1
1.1.2 Iron Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 Treatment for Iron Overload . . . . . . . . . . . . . . . . . . 5
1.1.4 Diagnosis and Monitoring of Iron Overload . . . . . . . . . . 9
1.2 Magnetic Resonance and Iron . . . . . . . . . . . . . . . . . . . . . 12
1.2.1 Nuclear Magnetic Resonance . . . . . . . . . . . . . . . . . . 13
1.2.2 Excitation and Acquisition . . . . . . . . . . . . . . . . . . . 15
1.2.3 Proton Imaging . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.2.4 Spatial Encoding and Selective Excitation . . . . . . . . . . 21
1.2.5 Pulse Sequences . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.2.6 Interactions with Iron . . . . . . . . . . . . . . . . . . . . . 29
1.3 Monte-Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . 29
1.4 Specific Aims & Significance . . . . . . . . . . . . . . . . . . . . . . 33
1.4.1 Aim 1 - Translate R
∗
2
Imaging from 1.5T to 3T . . . . . . . . 33
1.4.2 Aim 2 - Assess Non-Idealities at 3T . . . . . . . . . . . . . . 34
1.4.3 Aim3-DevelopandTestNovelMR-basedIronQuantitation
Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
vi
1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 Improved Liver Iron Estimates using T
1
-Corrected Proton Den-
sity Estimator 37
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.1 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 Relaxivity-iron calibration in hepatic iron overload: Predictions
of a Monte Carlo model 56
3.0.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.0.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.0.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.0.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.5 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4 Spin Echo-Based Liver Iron Estimates Require B
1
+
Inhomogene-
ity 72
4.0.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.0.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.0.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.0.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.1 Patient Population . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.2 Patient Assessment . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2.4 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
vii
4.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5 Ultra-Short Echo Time Images Quantify High Liver Iron 87
5.0.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.0.2 Theory and Methods: . . . . . . . . . . . . . . . . . . . . . . 87
5.0.3 Results: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.0.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.1 Participant Population . . . . . . . . . . . . . . . . . . . . . 90
5.2.2 Participant . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6 Chemical Shift Imaging - A Spectroscopic Approach to Quantify-
ing Iron 109
6.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1.2 Theory and Methods . . . . . . . . . . . . . . . . . . . . . . 109
6.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7 Conclusion 129
7.1 Original contributions . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Reference List 135
viii
List of Tables
1.1 Comparison of common chelators
1
. . . . . . . . . . . . . . . . . . . 8
1.2 Common spin nuceli . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Relevant scan parameters for patient exam. . . . . . . . . . . . . . . 51
2.2 Ranges of demographic and laboratory data for the participant pop-
ulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1 B
+
1
mean scale values in the whole liver and right and left lobes show
that image series from both 1.5T and 3.0T MRI scanners demon-
strate significant spatial variation in B
+
1
scale. Further, 3.0T images
demonstrate significant mean underexcitation. The mean excitation
did not correlate with BMI or weight in 1.5T studies. Underexcita-
tion was weakly associated with weight and BMI at 3T. . . . . . . . 84
5.1 Relevant scan parameters . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 Ranges of demographic and laboratory data for the participant pop-
ulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.1 R
2
and R
∗
2
estimates in phantom . . . . . . . . . . . . . . . . . . . . 121
6.2 3T-CSI and 3T-equivalent R
∗
2
estimates in four human subjects.
Conversion to R
2
is included for reference. . . . . . . . . . . . . . . 121
ix
List of Figures
1.1 Demonstration of Fenton (Haber-Weiss) reaction, including reaction
coefficients showing the extreme reactivity of unbound iron
2
. . . . 4
1.2 Demonstration of lab and rotating frames used in MRI . . . . . . . 14
1.3 Demonstration of precession about a B field with a non-zero trans-
verse RF component . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 Demonstrationofcurrentinducedinacoilbytime-varyingmagnetic
fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5 Example of T
1
and T
2
relaxation
3
. . . . . . . . . . . . . . . . . . . 18
1.6 Demonstration of R
2
and R
∗
2
decay with respect to tissue iron con-
tent. Reproduced from Wood et al.
4
. . . . . . . . . . . . . . . . . 20
1.7 Illustration of approximations of different waveforms with Fourier
series. As the number of Fourier coefficients increases, the sum of
sine waves becomes a better fit for the waveform.
5
. . . . . . . . . . 22
1.8 Illustrationofsliceselectionproducingtransversemagnetizationina
single slice. The hard pulse with no slice selection gradient produces
uniform excitation in the sensitive area of the coil while the sinc
pulse with a z-gradient produces excitation of only part of the object. 24
1.9 Illustration of slice selection producing transverse magnetization in
a single slice
3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
x
1.10 Example of a common multiecho gradient echo pulse sequence. . . 27
1.11 Example of a common multiecho spin echo sequence. . . . . . . . . 28
1.12 Illustration of a train of 180
◦
pulses generating multiple spin echoes
that decay with T
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.13 A demonstration of simulated tissue in 3 dimensions (panels a,b,c)
for LIC values of 4.4, 30, and 57.8
mg
⁄g, respectively. Panels d-f
demonstrate 2D projections of 4 μm slices of the 3D geometries;
panels g-i show histology samples that demonstrate the similarity
with physiologic data that the simulation can achieve. Reproduced
from the thesis of Nilesh Ghugre.
6
. . . . . . . . . . . . . . . . . . . 31
2.1 Exampleofunconstrainedandconstrainedmono-exponentialfitsfor
different R
2
species. When the decay rate is comparable to the first
echo time (left), the proton density is underestimated by 8% and
the R
2
is overestimated by 10%. The same trend is seen to a more
extreme degree in the right pane where the R
2
is shorter. . . . . . . 52
2.2 Unconstrained fits of acquired CPMG data plotted against LIC
demonstrated that curves derived by Christoforidis show similar
fit to the data. The disagreement in slope of fit compared to the
Christoforidis-R
∗
2
curve likely results from the apparent saturation
of their protocol due to shorted TE of 2.24 ms in the gradient echo
protocol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3 Comparison of fitting techniques. Top pane demonstrated the weak
relationship between R
2
and LIC in the unconstrained fits. Lower
pane shows the approximate tripling of the calibration curve with
the addition of the PDE constraint. . . . . . . . . . . . . . . . . . . 54
xi
2.4 Constrained vs unconstrained fitting of Jensen curve demonstrates
that sensitivity of the RR
2
parameter (top pane) follows the behav-
ior of the unconstrained R
2
estimates. The unconstrained aggrega-
tion parameter (lower pane) was less correlated tissue iron content
but demonstrated large variation. In contrast, the constrained RR
2
saturates quickly; the aggregation parameter (lower pane) increases
withironfortheconstrainedfits. Thissuggeststhatthebackground
RR
2
may represent saturating ferritin stores while the a parameter
represents large iron particles. . . . . . . . . . . . . . . . . . . . . . 55
3.1 Comparison between simulated relaxivities (x) and clinical calibra-
tion curves at 1.5T for both R2* (a) and R2 (b). The clinical cali-
bration curves are reproduced from the literature
7,4
, and represent
the behavior of in vivo patient data from large clinical trials. Sim-
ulated relaxivities at 3T(o) are included for comparison, although
no corresponding clinical calibration curves exist. Note that the
model predictions for R2* are highly linear and in agreement with
the clinical calibration curves at 1.5T. . . . . . . . . . . . . . . . . . 68
3.2 Relationship between relaxation rates at 3T and 1.5T. For both R2*
(a) and R2 (b), model predictions (x) were highly linear (R>0.99)
across field strength, and in good agreement with in vivo patient
data (o). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Enhancement of R2* and R2 relaxivities with field strength, relative
to 1.5T. For R2*, the predicted enhancement varied linearly with
field strength, while it was curvilinear for R2. At 3T, the predicted
relaxivity enhancements agree well with the values calculated from
in vivo data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
xii
3.4 Bland-Altman plots between matched pairs of 3T simulated and
patient data. R2* (a) showed no significant bias and a standard
deviation of 3.6%. R2 (b) also showed no bias and a standard devi-
ation of 7.2%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1 Spatial maps of B
+
1
scale in patients demonstrate significantly dif-
ferent behavior at 1.5T and 3T. 1.5T maps demonstrate largely uni-
form excitation patterns and consistently complete excitation. 3T
maps demonstrate significant spatial variation in B
+
1
as well as a
mean achieved B
+
1
of only 69.6%. . . . . . . . . . . . . . . . . . . . 85
4.2 Single echo simulations over a wide range of iron loads and B
+
1
inhomogeneities demonstrate that iron is overestimated in the pres-
ence of B
+
1
inhomogeneity at 1.5T. Further, inaccuracies increase
with iron load for a given B
+
1
. Although 1.5T R
2
estimates tend to
increase with B
+
1
variation, 3T maps show the opposite effect due
the combination of fast initial decay and lengthened T
1
resulting in
artificially flat decay curves. (B
+
1
Fraction = B
+
1
Scale/100) . . . . . 86
4.3 CPMG simulations over a wide range of iron loads and B
+
1
inhomo-
geneities demonstrates that iron is overestimated in the presence of
B
+
1
inhomogeneity except with low iron loads at high B
+
1
inhomo-
geneities. (B
+
1
Fraction = B
+
1
Scale/100) . . . . . . . . . . . . . . . 86
xiii
5.1 Phantom results demonstrate linear correlation of MnCl
2
concentra-
tion and R
∗
2
. Regression analysis demonstrated the following rela-
tionships: R
∗
2
-UTE = 117×[mM MnCl
2
] + 1.6 (r
2
= 0.9955, r
2
adj
= 0.9951, p<0.0001); R
∗
2
-GRE = 120×[mM MnCl
2
] + 3.5 (r
2
=
0.9998,r
2
adj
= 0.9998, p<0.0001). The R
∗
2
-GRE regression excluded
thehighest-concentrationvialduetoexpectedfailureoffitting. 95%
confidence intervals are shown with dashed lines for each regression. 103
5.2 Example images demonstrating image quality of 3T-UTE (above)
and 3T-GRE(below) first echo images and associated R
∗
2
maps. The
image selected is from a subject with high LIC, causing the failure
of the 3T-GRE protocol to capture sufficient signal to perform R
∗
2
estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3 Scatter plot demonstrating LIC estimates made with 3T GRE and
3T UTE image series compared with clinical estimates. Catas-
trophic failure in LIC estimates is apparent in 3T GRE estimates
for participants with clinical iron loads over 25
mg
/g. Points in the
shaded region demonstrate 3T-UTE LIC estimates that exceed the
upper limit that 1.5T-GRE can quantify. . . . . . . . . . . . . . . . 105
xiv
5.4 Bland-Altman analysis of LIC estimates made with 1.5T-GRE and
3T-GRE series. Solid circles ( ) represent participants with clinical
LIC≤25
mg
⁄g (μ=3.0(not significant), σ=9.6). Unfilled circles ( )
represent participants with clinical LIC>25
mg
⁄g (μ=37.3, σ=9.8).
95% limits of agreement are shown as dashed lines. Insignificant
bias is demonstrated with a dash-and-dotted line. The bias demon-
strated in the low-LIC cohort is thought to be a result of a lack
of sufficiently long TEs in the UTE protocol; simulation results
(supplemental results) for the 3T-UTE protocol in low LIC loads
supports this conclusion. . . . . . . . . . . . . . . . . . . . . . . . . 106
5.5 Bland-Altman analysis of LIC estimates made with 1.5T-GRE and
3T-UTE series. Solid circles ( ) represent participants with clinical
LIC≤25
mg
⁄g (μ=-15.3, σ=21.9). Unfilled circles ( ) represent par-
ticipantswithclinicalLIC>25
mg
⁄g(μ=-2.6(notsignificant)σ=14.48).
95%limitsofagreementareshownasdashedlines. Insignificantbias
is demonstrated with a dash-and-dotted line. Points in the shaded
region demonstrate 3T-UTE LIC estimates that exceed the upper
limit that 1.5T-GRE can quantify. . . . . . . . . . . . . . . . . . . . 107
xv
5.6 Simulation of 3T-GRE and 3T-UTE echo times with 0, 5, 10, and
20%PDFFoveranLICrangeof0.5-45
mg
⁄gdemonstratethatincreas-
ing fat fraction has a greater effect on R
∗
2
for the UTE sequence than
the GRE sequence. In particular, the 3T-UTE overestimates LIC
more as PDFF increases for a given LIC. Further, at low LIC, the
simulations for PDFF=0% indicate that LIC is overestimated when
noise is present and the decay rate is slow. The magnitude of error
due to physiologically realistic PDFF may explain the increased
apparent measurement variation between GRE and UTE. . . . . . . 108
6.1 Comparison if sinc (blue), Dolph-Chebyshev (green), and Tukey
(red) excitation pulses for a given flip angle. . . . . . . . . . . . . . 122
6.2 Achieved slice profile for Sinc Pulse . . . . . . . . . . . . . . . . . . 122
6.3 Achieved slice profile for Dolph-Chebyshev pulse . . . . . . . . . . . 123
6.4 Layout of the phantom demonstrating, from top to botton, left to
right, bottles of Philips Solution 11, mineral oil, tap water, 1mM
MnCl
2
, tap water, and 3mM MnCl
2
. . . . . . . . . . . . . . . . . . 123
6.5 Regression of phantom R
∗
2
estimates. The water vial was excluded
due to inability to differentiate it from surrounding MnCl
2
vials in
the CSI R
∗
2
and S
0
images. The slope is notably steeper than the
expected relationship. However, the magnet reported an unreliable
shim for the CSI sequence, which can lead to accelerated R
∗
2
decay. 124
6.6 Comparison of standard image and R
∗
2
map with CSI S0 image and
R
∗
2
map. Slice location is not preserved between the images shown. . 125
6.7 Regression of clinically-obtained 3T R
∗
2
estimates and CSI R
∗
2
esti-
mates in four human subjects. . . . . . . . . . . . . . . . . . . . . 126
xvi
6.8 A demonstration of signal from a single voxel (blue curve) and
resulting fit (red curve). The ExpC model (left) displays reason-
ablerelaxationestimationbehavioreveninthepresenceofincreased
spectral content. The spectral fit (right) fails, likely due to the high
order of the model; this often leads to overestimating PDFF signif-
icantly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.9 B
1
+
map demonstrating the wide variety of flip angles achieved in
the phantom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
xvii
Glossary
1-hydrogen todo. 20
ferritin An iron storage molecule that can store significant quantities of iron,
found primarily in the liver. 9
flip angle The angle of excitation relative to the axis of B
0
achieved by an RF
pulse. 16
Fourier transform A set of forward and inverse mathematical transforms that
converts signals between the time domain in which they are acquired and the
frequency domain, representing the spectral content of the signal.. 21
gradient Time-varying magnetic fields that allow spatial localization of MRI sig-
nals. 21
gyromagnetic ratio todo. 14
magnetic flux magentic flux. 17
relaxation The thermodynamic process in which the net magnetization of a
cohort of spins returning to equilbrium after excitation, coninciding with
a loss in transverse magnetization and a recovery of longitudinal magnetiza-
tion. 17
xviii
signal-to-noise ratio todo. 28
xix
Acronyms
CT computed tomography. 10, 11
DC direct current. 10
FID free induction decay. 19
G6PD glucose-6-phosphate dehydrogenase deficiency. 2
IV intravenous. 3, 6, 8
milligrams per gram,
mg
/g milligrams of iron per gram of dry liver tissue. 4,
11, 12, 129
MRI magnetic resonance imaging. xxii, 11
MRI magnetic resonance spectroscopy. xxii
NMR nuclear magnetic resonance. 13, 20
PPM parts-per-million. 29
RF radio frequency. 10, 15, 16
SAR specific absorption rate. 111
xx
SCD sickle cell disease. 2
SQUID superconducting quantum interference device. 10, 11
T Tesla. xxii
xxi
Abstract
Magnetic resonance imaging (MRI) has facilitated important advancements in
the clinical diagnosis and longitudinal monitoring of tissue iron overload disorders.
MRI at 1.5 Tesla (T) has supplanted invasive approaches such as liver biopsy with
a non-invasive test and allows for iron assessment in organs including the heart,
pancreas, and spleen rather than solely relying on the liver as a surrogate for total-
body iron. Most MRI approaches depend on iron’s significant paramagnetic effects
which noticeably increase R
2
(
1
⁄T2) or R
∗
2
(
1
⁄T
∗
2
). However, the increasing popularity
of 3T MRI scanners, also known as magnets, is threatening the availability of clini-
cal iron overload diagnosis. The proliferation of 3T scanners has not coincided with
improvements in signal acquisition and analysis techniques for fast decay species,
leading to a reduction in the quantifiable range of tissue iron as field strength
grows. Imaging centers without a 1.5T magnet are therefore unable to quantify
the upper half of the clinically-relevant iron range. Though previous studies have
demonstrated enhancement of R
2
and R
∗
2
with field strength, a theoretical basis
for the relationship between decay rates and tissue iron at arbitrary field strengths
has not been developed. Overcoming these new limitations requires the develop-
ment of novel scan techniques, improvements to curve fitting approaches, valida-
tion of liver iron-relaxation calibration curves, and corrections for non-idealities
present at higher field strengths. I pursued these open questions by implementing
xxii
echo and gradient echo MRI and magnetic resonance spectroscopy (MRI) pulse
sequences with reduced echo times, developing and applying a Monte Carlo Bloch
simulation framework to conduct experiments in-silico, scanning humans and cali-
brated phantoms, and comparing results with clinically-obtained standard values.
Spin echo-based R
2
estimates were attractive due to the demonstrated sub-linear
enhancement with field strength while gradient echo-derived R
∗
2
was shown to grow
approximately linearly with field strength. However, I found that spin echoes were
more susceptible to imaging confounders at 3T than gradient echo approaches. I
significantly increased the sensitivity of R
2
to liver iron by deriving signal con-
straints from within the same image series without additional scan time. Further,
I demonstrated that excitation imperfections grew from 1.5T to 3T and quantified
the effects on estimated R
2
to demonstrate the need for correction. By develop-
ing a ultra-short echo time gradient echo protocol for use in humans, I achieved
R
∗
2
quantitation robust to 3T imaging confounders; this technique demonstrates
reliable LIC estimates exceeding 50
mg
⁄g, representing a 25% improvement over the
dynamic range of 1.5T techniques. Finally, I demonstrated that short TE spin
echo spectroscopy shows promise as a method to simultaneously estimate R
2
and
R
∗
2
with high SNR. Overall, these techniques and findings represent a significant
step toward the clinical application of 3T-MRI for monitoring tissue iron overload
and provide useful insight to extend the dynamic range of iron quantitation at all
field strengths.
xxiii
Chapter 1
Introduction
1.1 Iron Overload Disorders
1.1.1 Mechanisms of Iron Overload
Iron is a critical element in cells. It is necessary for oxygen transport and
plays an important role in a wide variety of biological reactions. However, iron is
also highly reactive and leads to cell damage if improperly stored. Iron storage
is therefore tightly regulated to ensure that cells have access to the necessary
quantities for survival without allowing iron to exist in an unbound, reactive state.
When a disease or genetic condition results in excessive iron storage in the body,
it is known as hemochromatosis or iron overload. Iron overload occurs because the
body is unable to substantially increase the rate of iron excretion in response to
elevated iron levels. When the origin of iron overload is genetic, the intestinal tract
over-absorbs dietary iron, a condition known as hereditary hemochromatosis. Iron
accumulation due to other diseases or their requisite treatments is called secondary
hemochromatosis.
Primary Hyperabsorption
Hereditary hemochromatosis results from a number of genetic mutations that
cause the body to overabsorb iron through the digestive tract. Common hereditary
hemochromatosis is the most common inherited genetic disorder in Americans of
1
Northern European descent, affecting 1 in 250-300 people; it is carried by approx-
imately 1 in 10 white Americans
8
.
Secondary Hemochromatosis
Secondary hemochromatosis can occur when any factor other than the genetic
predisposition to over-absorption leads to increases in total body iron. Iron can
accumulate in the body due to disorders causing the over-retention of iron, under-
utilization of iron by the bone marrow during erythropoiesis, or blood transfusion.
Certaincancers, chronicliverdisease, andalcoholismcancauseironoverload, often
through changes to regulatory proteins such as ferroportin
9
. However, the most
severe cases of iron overload are seen in severe anemias.
Though the term “anemia” often colloquially refers to insufficient iron intake,
or nutritional anemia, anemias represent a much larger group of disorders that
result in lower-than-normal red blood cell counts. Severe anemias that cause
insufficient erythropoiesis ultimately lead to hemochromatosis. Anemias have
many origins ranging from red blood cell production to individual cell longevity.
Hemoglobinopathies are genetic conditions in which a patient produces insuffi-
cient or abnormally-structured hemoglobin, which can alter the function of red
blood cells. Thalassemia, for example, is common in Italian, Greek, Middle East-
ern, South Asian, and African descendants
10
and leads severe anemia; oxygen
transport is compromised due to insufficient quantities of hemoglobin. Hemolytic
anemias, such as glucose-6-phosphate dehydrogenase deficiency (G6PD), result in
the premature death of red blood cells. In aplastic anemias like Blackfan-Diamond
syndrome, the bone marrow produces an insufficient quantity of red blood cells.
Even certain cancers, called myelodisplasias, prevent the maturation of red blood
cells in the bone marrow. The diseases vary widely in their origin and sometimes
2
demonstrate overlap. Sickle cell disease (SCD), a genetic disorder in the equatorial
regions around the globe, produces abnormal hemoglobin that polymerizes when
deoxygenated, drastically reducing red blood cell survival time — as such, SCD is
both a hemoglobinopathy and a hemolytic anemia. Despite their differences, all
anemias result in low red blood cell counts that require treatment to improve the
patient’s health or ensure survival.
Treatment for anemias is dependent on the origin of the disease. For nutri-
tional anemias, increasing dietary iron intake often resolves the problem, though
intravenous (IV) iron may be used as well. Transfusion-dependent anemias,
including many forms of aplastic and hemolytic anemias and hemoglobinopathies,
require patients to receive red blood cell transfusion therapy about once every 3-4
weeks. Iron overload resulting from transfusion is known as transfusional siderosis.
Although iron is normally absorbed through the digestive tract, transfusion cir-
cumvents physiologic mechanisms by introducing hemoglobin-bound iron directly
into the blood stream at a rate that overwhelms physiologic excretion pathways.
1.1.2 Iron Storage
Iron is both a critical element for the human body and a highly reactive ele-
mentthatcanseverelydamagecellswhennotappropriatelystored. Mosttissuesin
the body do not contain significant quantities of iron under normal circumstances.
Notable exceptions are macrophages in the liver, spleen, lymph nodes, and bone
marrow. The liver is responsible for excess iron storage and buffering, containing
special receptors that permit the uptake of larger-than-normal quantities of iron.
The bone marrow uses iron to create the hemoglobin found in circulating erythro-
cytes. When iron exists in an the Fe
2+
oxidation state, ions can enter cells through
3
calcium channels
11
, leading to the deposition of iron in tissues where intracellu-
lar ferritin buffers and converts it to Fe
3+
. The heart, for example, will not take
up iron under normal circumstances. However, cardiac iron overload can occur
in transfusion-dependent patients, leading to arrhythmias and high likelihood of
cardiogenic death
12
. Although iron can be toxic through multiple mechanisms,
unbound iron can create free radicals via the Fenton reaction (or Haber-Weiss)
which are highly reactive and will damage surrounding cells.
Figure 1.1: Demonstration of Fenton (Haber-Weiss) reaction, including reaction
coefficients showing the extreme reactivity of unbound iron
2
To prevent tissue damage, iron is tightly regulated in the body. The body’s first
line of defense against iron storage is transferrin, a circulatory iron-binding protein
that is responsible for capturing any unbound iron in the blood and safely shut-
tling it into the bone marrow for recycling or liver for longer-term storage. Cells
throughout the body express a receptor called transferrin receptor 1, TfR1, which
4
is down-regulated when intracellular Fe
2+
is present in sufficiently high concentra-
tions. The liver also possesses cells with a second transferrin receptor, TfR2, which
does not down-regulate the uptake of transferring in spite of high intracellular fer-
ric iron. When the liver receives transferrin-bound iron, the iron is transferred to
ferritin, a large iron storage molecule that can store about 4500 iron atoms dis-
tributed between its 24 identical protein subunits
13
. The liver has enough ferritin
to store about 3
mg
⁄g, about 6 times the normal liver iron load. Once the liver’s
ferritin stores are saturated, ferritin will begin to aggregate and break down into
small iron-rich granules up to about 800 nm in size called hemosiderin, complexes
of ferritin, products of ferritin breakdown, and iron. Hemosiderin can store iron in
a more concentrated form than ferritin; the iron is in the Fe
3+
oxidation state and
therefore is not accessible to take place in physiological reactions.
1.1.3 Treatment for Iron Overload
Iron has profound effects on a number of organs. Iron has been shown to
cause liver disease
14
, endocrine dysfunction, myocardial damage
15,12
, and cognitive
effects
16
. It is therefore critical to maintain healthy iron levels to prevent tissue
damage to many organs.
Phlebotomy
The treatment for iron overload resulting from hereditary hemochromatosis
is straight-forward, requiring only phlebotomy (blood-donation) to maintain safe
tissue iron levels. Patients will generally donate a unit of blood once every 2-
4 weeks to rapidly decrease total body iron and then maintain a safe level by
donating blood about 3-6 times per year
17
.
5
Chelation
Treatment of secondary hemochromatosis is more challenging. Because phle-
botomy would simply undo the transfusion treatment used for anemias, a phar-
macological approach called chelation therapy is used to remove iron. Chelation
therapy involves the use of intravenous, subcutaneous, or oral drugs that bind to
metals in the body and safely remove them through the kidneys or gastrointestinal
tract.
Careful monitoring of iron stores is important for clinical decision making
because chelation therapy is both disease-dependent and patient-dependent. Some
drugsaremoreeffectiveatbindingtoironinthebloodstreamtoreduceexposureto
free iron while others can penetrate cells to reduce iron stores. Physicians depend
on regular (generally, annually or semi-annually) iron estimates to assess the effec-
tiveness of a prescribed treatment at removing excess iron for at-risk organs. Fur-
ther, uncontrolled chelation therapy can be toxic: chelators have the potential to
remove physiologically necessary iron or other metals such as magnesium, lead-
ing to kidney damage, neurotoxicity, arthritis, bone development, and reductions
in platelet and neutrophil counts
18,19
. For these reasons, safe and accurate iron
monitoring techniques are key.
Despite the importance of chelation therapy, patient compliance is often chal-
lenging. Notably, chelators have a variety of negative side-effects including
headache, nausea, vomiting, and diarrhea. IV and subcutaneous treatment can
cause burning sensations at the injection site and skin irritation. Issues of practi-
cality also affect compliance. Oral chelators require the patient to remember their
medication regimen multiple times per day while IV requires proximity to equip-
ment, whether the treatment is in a clinical or home setting. Motivating a patient
to tolerate these effects is challenging in the absence of demonstrable short-term
6
benefit. Diagnostic tests for iron that are safe for both regular and long-term use
can motivate the patient by giving them a concrete improvement metric while also
providing valuable data for clinical decision making.
7
Table 1.1: Comparison of common chelators
1
Property Deferoxamine Deferiprone Deferasirox
Route Subcutaneous,IV Oral Oral suspension
Usual dose 20-40 mg/kg/day over 8-24 hours, 5
days/week
3 doses/day, 25-33 mg/kg 20-40 mg/kg/day
Excretion Urinary, faecal Mainly urinary Faecal
Half-life 20-30 min 3-4 hours 8-16 hours
Adverse effects Local skin reactions
Ophthalmological
Auditory
Allergic reactions
Growth retardation
Bone abnormalities
At high doses:
- Pulmonary
- Neurological
Gastrointestinal Agranulocytosis/ neutrope-
nia
Arthralgia
Elevated liver enzymes
Gastrointestinal
Rash
Rise in creatinine
Proteinuria
Ophthalmological
Auditory
Elevated liver enzymes
Challenges Adherence due to parenteral administration;
need for yearly ophthalmology and audio-
metric examination
Need for weekly blood count monitoring; not
commercially available in all countries; lim-
ited data in children; variable efficacy in
removal of hepatic iron
Need for weekly blood count monitoring; not
commercially available in all countries; lim-
ited data in children; variable efficacy in
removal of hepatic iron
Status Licensed Licensed in USA and Europe Licensed in USA and Europe
Indications Treatment of chronic iron overload due
to transfusion-dependent anaemias (and for
treatment of acute iron intoxication)
Treatment of iron overload in thalassemia
major when DFO is contraindicated or inad-
equate.
In USA licensed for the treatment of chronic
iron overload due to transfusion-dependent
anaemias in individuals aged 2 years and
older In Europe licensed for the treatment
of transfusional iron overload in betatha-
lassaemia major patients, 6 years and
older, and approved for use when DFO is
inadequate or contraindicated in patients
with other anaemias, patients 2-5 years,
andpatientswithnon-transfusion-dependent
thalassaemia
Age considera-
tions
Not recommended for children<3 years with
low transfusional burden
Limited or no data on children aged <6-10
years
Studied in children as young as 2 years old
8
1.1.4 Diagnosis and Monitoring of Iron Overload
Due to the importance of accurately assessing tissue iron quantity, a number of
quantitative tests were developed, each with widely varying invasiveness, measure-
ment variability, sensitivity, and cost. Further, the resolution of these tests ranges
from providing total-body iron to organ-specific estimates.
Biopsy
Early attempts to quantify liver iron used needle biopsy to assess hepatic iron
stores. This outpatient procedure, performed about once per year in cases of
chronic iron overload, requires a small sample of liver to be removed and desic-
cated; the resulting mass of iron versus sample weight is reported. Because the
spatial distribution of iron is known to vary based on the cause of iron overload
and even the primary indication for transfusion therapy, light microscopy is some-
times performed when the cellular distribution of iron is relevant to treatment
20
.
However, biopsy presents a variety of challenges, including risk of complications
21
and sampling error
22,23,24
. Iron quantitation in the heart is possible by biopsy but
increases complication rates when used over a prolonged period
25
. Furthermore,
cardiac iron is heterogeneously distributed and biopsies can only be safely obtained
from the right ventricular septal surface. Pancreas iron quantitation is also crucial
in transfusion-dependent patients and cannot be safely accomplished with biopsy
due to its high complication and mortality rate
26
. Despite the noted measure-
ment variability, biopsy is still often cited as the reference standard for liver iron
quantitation
27
.
9
Serum Ferritin
Serum ferritin is a measure of the ferritin concentration in a blood sample
obtained by phlebotomy. Because ferritin can store a large quantity of iron and
is critical to enabling iron transport by ferritin, may attempts have been made to
correlate its presence with total body iron. Overall, serum ferritin concentration
does correlate with liver iron
28,29
. However, most studies demonstrate significant
variability between patients, repeat measurements, and disease populations
30,21
.
Further, serum ferritin is discordant with LIC in certain studies, especially in
transfused populations
31
. Together, these limitations cause serum ferritin to be an
undesirable metric of iron in transfusion-dependent patients.
CT
Computed tomography (CT) is an X-ray imaging technique that can generate
cross-sectional images of anatomy. The signal intensity demonstrated by each
tissue is proportional to its X-ray absorption properties. Liver iron content has
been demonstrated to increase X-ray absorption compared to normal tissue with
both single and dual energy CT
32,33,34
. In addition to producing tighter correlation
to liver iron than serum ferritin, CT is widely available due to its use in a variety of
other clinical imaging contexts. Its speed and low cost make it attractive for iron
quantitation. However, CT suffers from poor sensitivity to low iron loads
35
and
there is little human validation data available
36
. Further, when fat is present in the
liver, a condition often occurring secondary to chronic iron overload, the inverse
correlation between x-ray signal attenuation and fat lead to underestimates tissue
iron
37
. CTalsoexposespatientstounnecessaryradiationincreasinglifetimecancer
risk, especially in pediatric populations
38
.
10
SQUID
Superconducting quantum interference device (SQUID) is a device that uses
radio frequency (RF) or direct current (DC) signals to make extremely sensitive
measurementsofmagneticfields. Duetoiron’sinfluenceonmagneticfields,SQUID
candetectitspresenceintissues. SQUIDistheearliestapproachtoassessingtissue
iron burden
39
that is completely non-invasive. Although SQUID is highly sensitive
to iron, it suffers from a number of impediments. The combination of its high
installation cost and relatively limited utility outside of iron content assessment in
the liver and spleen have limited the availability of SQUID significantly
40
. At the
time of writing, only three SQUID devices are operational in the US.
MRI
MRI is an imaging technique that forms cross-sectional images by applying
static and time-varying magnetic fields to subjects, relying on a Fourier-based
mathematical transform to create images from received signal. Due to MRI’s
dependence on magnetic fields, it showed promise for iron quantitation early as
1984basedoniron’smagneticeffectssimilartoSQUID
41,42,43
. MRI,unlikeSQUID,
received wide-spread adoption due to its imaging capabilities, which provided an
unparalleled set of capabilities and flexibility that permitted the emphasis of cer-
tain tissues based on the scan parameters. This made MRI a promising candidate
for a completely non-invasive approach to gathering sensitive, accurate iron mea-
surement in a variety of tissues. Although early attempts at iron quantitation
failed, MRI has become the clinical standard in iron quantitation due to its supe-
rior inter-measurement variability and noninvasiveness.
11
1.2 Magnetic Resonance and Iron
Magnetic resonance imaging is a complex technology that has strong applica-
tions throughout medicine. Due to iron’s magnetic properties, researchers have
tried to leverage its effects on MRI signals since the late 1980s. Nonetheless,
biopsy remained the dominant tissue iron detection method into the early 2000s.
In the early-to-mid 2000s, a number of techniques were developed using 1.5T MRI
scanners that allowed the successful quantification of tissue iron. Studies demon-
strated success quantifying tissue iron in the liver, heart, pancreas, spleen, brain,
and bone marrow
4,7,44,45,46
. Compared to biopsy and serum ferritin measurements,
MRI demonstrates tighter measurement variability of about 3-8%. Further, MRI
demonstrates strong correlation with iron even at low tissue iron content while its
dynamic range reaches up to 40
mg
⁄g, providing sufficient information to prescribe
chelators accurately and monitor their effectiveness. As methods to suppress or
quantify fat were developed, MRI became a more complete quantitative solution
than CT. Due to its clear superiority compared to other available diagnostic tech-
niques, MRI supplanted biopsy as the clinical standard for iron quantitation in all
organs and obviated the need for the other quantitative modalities.
Despite MRI’s success, a number of limitations in existing scan techniques
remain. First, the maximum tissue iron content that can be quantified at 1.5T
is presently limited to approximately 40
mg
⁄g. Clinical iron loads of at least 60
mg
⁄g
have been identified through histology, suggesting that MRI may fail to correctly
estimate iron in an important subset of patients. Above an LIC of 20
mg
⁄g, the
precise iron load does not change the clinical treatment. However, quantitation
that is safe for repeat use still provides value in assessing chelation efficacy —
which is dependent on patient, tissue, and chelator — and provides important
motivationforpatientstocontinuewithchelationtherapyinspiteofuncomfortable
12
side-effects. A second problem arose as MRI technology developed higher field
strength magnets such as 3T. Though higher field magnets improve many aspects
of clinical imaging, the effects of iron on the signal are directly proportional to the
field strength. Increasing field strength from 1.5T to 3T leads to a 50% reduction
in the dynamic range for iron quantitation in an otherwise identical test. Other
problems, such as increased spatial intensity variation in images, have further
confounded iron quantitation at 3T.
Understanding the underlying principles of MRI allows us to acquire and pro-
cess signals in a way that tell us about iron even though it cannot be directly
measured with MRI, allowing us to overcome the current limitations in imaging
technology.
1.2.1 Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is an atomic phenomenon that forms the
basis for MRI, though “nuclear” and “atomic” simply refer to the nucleus of an
atom rather than ionizing radiation. Atoms with an odd number of protons or
neutrons demonstrate NMR when an external magnetic field is applied to them.
Quantum mechanics describes such atoms as having a non-zero quantum spin
states, leading to these atomic nuclei being called “spins.” The interaction between
spins and the magnetic field ultimately allow a signal to be generated from them.
Magnetization and Precession
In one sense, spins are like tiny bar magnets because they align with external
using magnetic fields. When a powerful magnetic field, called the main field or
B
0
, is applied to a sample containing spins, they align with the magnetic field.
This means that the individual magnetic vector of each of the spins sum together
13
to form a magnetic vector pointing parallel to B
0
. This forms the basis for a
coordinate system that defines the spatial orientation of the magnetic vectors.
The two primary coordinate systems used in NMR, the lab frame and the rotating
frame,areboth3-dimensionalCartesiancoordinatesystemswhoseZ-axisisparallel
to the B
0
. Known as the longitudinal axis, the Z axis is orthogonal to a plane
known as the transverse plane. The transverse plane contains orthogonal X and
Y axes, which remain fixed in physical space in the lab frame. The axes X’ and
Y’ also lie in the transverse plane but rotate at the same frequency as the spins in
the rotating frame. At equilibrium, there is no net magnetization pointing in the
transverse plane, only along the longitudinal axis.
z
Y
B
0
Figure 1.2: Demonstration of lab and rotating frames used in MRI
In addition to aligning with this axis, the spins demonstrate a second behavior
called precession that is unlike a standard bar magnet. The magnetic vectors of
the nuclei precess, or spin, around the main field in a counter-clockwise or “left-
handed” rotation. The angular velocity of this rotation is specific to the type of
nucleusandisproportionaltothefieldstrength. Thefrequencyofprecessioncanbe
determinedwiththegyromagneticratio, whichisequalto42.58
MHz
⁄Tforhydrogen;
14
Element Spin Gyromagnetic Ratio (MHz/T)
1
H
1
⁄2 42.58
2
H 1 6.54
3
He
1
⁄2 -32.43
13
C
1
⁄2 10.71
14
N 1 -4.32
19
F
1
⁄2 40.05
23
Na
3
⁄2 11.26
31
P
1
⁄2 17.24
Table 1.2: Common spin nuceli
the gyromagnetic ratios of other relatively common nuclei are summarized in table
1.2.1. Although precession is taking place constantly, no signal can be acquired
from the longitudinal magnetization. Until the spins are perturbed by an external
force, their net magnetization will remain in pointed along the longitudinal axis.
The precession of spins around a magnetic field is described by the Bloch equa-
tion
47,48
:
∂M
dt
=γ(M(t)×B(t)) (1.1)
which demonstrates that the rotation of the magnetization is dependent on mag-
netic fields orthogonal to it. The change in the magnetization is non-zero only
when M and the external B field are not parallel.
1.2.2 Excitation and Acquisition
The Bloch equation demonstrates a key relationship between proton magne-
tization and an external, applied magnetic field that ultimately allows for the
generation of images. If the B field can be manipulated to include a component
in the transverse plane, the spins will begin to rotate around it, effectively turning
the net magnetization vector onto the transverse plane. This is accomplished using
15
electromagnetic pulses oscillating at the Larmor frequency (γ in equation 1.1) of
theprotons. Thisfrequencyisproportionaltofieldstrength, equalto63.87MHzat
1.5T and 127.7 MHz at 3T, placing the electromagnetic waves in the RF spectrum.
RF pulses are applied in the transverse plane rather than along the longitudinal
axis, creating an axis of rotation that is orthogonal to the magnetization of the
spins. As the spins rotate about the new magnetization vector, a portion of the
net magnetization will move from the longitudinal axis into the transverse plane
— this process is called excitation.
z
Y
B
Figure 1.3: Demonstration of precession about a B field with a non-zero transverse
RF component
The strength and duration of the RF pulse determines the amount of excita-
tion achieved. Because the magnetization is a vector and because excitation is a
disturbance from equilibrium, the excitation is normally measured with an angle
relative to the B
0
field. The flip angle demonstrates how far the magnetic vector
has rotated, so a 90
◦
flip angle would move the entire magnetization vector onto
the transverse plane while a 180
◦
flip angle would invert the magnetization entirely,
making it point anti-parallel to B
0
. Assuming an arbitrary excitation flip angle of
16
Θ, the resulting transverse (M
xy
) and longitudinal (M
z
) magnetization magnitudes
immediately after excitation (t = 0 seconds) will be:
M
xy
(0) = M
z,eq
cos(Θ)
M
z
(0) = M
z,eq
sin(Θ)
(1.2)
Oncethespinsareexcited,theywillcontinuerotatingaroundtheB
0
fieldaccording
to the Bloch equation. As the magnetization rotates, it will create a sinusoidally-
varying magnetic flux, a time-varying magnetic field, in the lab frame which can
induce a current in a properly oriented wire loop. By recording this current, we
can determine the magnitude of the spins’ magnetization. If we can add more coils
orthogonal to the transverse plane, we can gather information about phase, or the
angle of the magnetization.
N
N
Figure 1.4: Demonstration of current induced in a coil by time-varying magnetic
fields
17
Relaxation
Although the spins can be pushed into the transverse plane with RF pulses,
the net magnetization will eventually reorient to the original equilibrium state,
returning to parallel with the B
0
field. In a process called relaxation. This process
involves the loss of transverse magnetization as well as the increase in longitudinal
magnetization. Transverse decay and longitudinal recovery are normally modeled
as exponential processes as follows:
M
xy
(t) = M
xy
(0)e
−
t
/T2
M
z
(t) = M
z,eq
−M
z
(0)e
−
t
/T1
(1.3)
Theprocessesaredescribedbytwoseparatetimeconstants, T
1
andT
2
. T
1
specifies
how long longitudinal recovery to 63.9% (1−e
−1
) takes to occur while T
2
describes
how quickly transverse signal falls to 36.7% (e
−1
) of its original value. Because
transverse decay must happen no slower than longitudinal recovery, T
1
is always
greater than T
2
. However, it is possible to lose transverse magnetization without
experiencing longitudinal recovery at the same rate, so T
2
is often significantly
smaller than T
1
.
Figure 1.5: Example of T
1
and T
2
relaxation
3
18
The complete Bloch equation accounts for T
1
and T
2
relaxation as follows:
∂M
dt
=γ(M(t)×B(t))−
Mx(t)
ˆ
i+My (t)
ˆ
j
T
2
−
(Mz (t)−M
0
)
ˆ
k
T
1
(1.4)
Although relaxation that is intrinsic to a given nucleus in a certain magnetic
field is described by T
1
and T
2
, many factors influence the NMR signal. Spatial
magnetic heterogeneity leads to an apparent increase in the transverse decay rate.
This apparent decay following a time constant called T
∗
2
. It is common to write
T
∗
2
as it relates to T
2
:
1
T
∗
2
=
1
T
2
+
1
T
0
2
(1.5)
where the decay component, T
0
2
, introduced by field inhomogeneities is greater
than 0. Equation 1.5 demonstrates that T
∗
2
is never larger than T
2
and converges
to T
2
when the field is perfectly homogeneous. Molecular motion such as diffusion
interacts with magnetic field disturbances to accelerate T
2
decay as well.
When a sample is excited, it will produce a free induction decay (FID), or an
observable, decayingelectromagneticsignaldescribedbytheBlochequations. This
FIDwillappeartodecaywithT
∗
2
ratherthanT
2
unlessthemagneticenvironmentis
perfectly homogeneous. The spins rotate out of phase with each other, causing the
vector sum of their magnetizations to fall. However, the transverse magnetization,
which is merely “hidden”, still decays with T
2
.
When working with iron, it is convenient to consider quantities that are pro-
portional to iron rather than inversely proportional. Because T
2
and T
∗
2
fall with
iron, their reciprocals grows. These quantities are called “relaxation rates” and
are defined:
R
2
=
1
T
2
(1.6)
19
R
∗
2
=
1
T
∗
2
(1.7)
For most purposes, referring to “T” or “R” decay is functionally equivalent. How-
ever, some nuances appear. First, R
∗
2
was found to be linearly related to iron
quantity, making it a desirable diagnostic metric due to its strong dependence on
iron
4
. R
2
is also related to iron, but loses sensitivity as the iron load increases
7
.
Although this makes it a less effective metric for total iron quantitation, it can
uncover tissue iron distribution that cannot be differentiated with R
∗
2
alone
49
.
Figure 1.6: Demonstration of R
2
and R
∗
2
decay with respect to tissue iron content.
Reproduced from Wood et al.
4
1.2.3 Proton Imaging
Although any nucleus with a non-zero spin state demonstrates NMR, hydrogen
proton imaging, or the imaging of
1
H is almost exclusively used in medicine due
to the high proportion of hydrogen atoms in the human body, bound mostly to
water or fat. In addition to the abundance of hydrogen in the body, practical
matters such as hardware equipment design limit most MRI systems to
1
H. The
20
terms “proton,” “spin,” and “nucleus” henceforth refer to
1
H atoms in particular,
though the general principles apply to imaging other nuclei.
MRIs are like large NMR spectrometers with a few modifications. Shaped
like a car-sized doughnut, the center of the magnet is called the bore. The bore,
commonly on the order of 60 cm in diameter, is large enough to fit a person but is
kept as small as possible to keep the magnetic field inside very accurate. Although
othermagneticconfigurationsandfieldstrengthsexist,1.5Tand3Ttoroidmagnets
are most common in clinical settings. In fact, the field in the MRI only varies by
1 part per million (ppm), or 0.000001%. The field needs to be precise to enable
the techniques that lead to image formation.
1.2.4 Spatial Encoding and Selective Excitation
In order to create images rather than whole-body NMR measurements, the
signal must be encoded with position and transformed from an acquired set of
waveforms into an image. The encoding of spatial information simply extends the
relationshipbetweenmagneticfieldstrengthandLarmorfrequencybygivingdiffer-
ent spins slightly different resonant frequencies relative to their physical position.
This is accomplished using gradients, time-varying magnetic fields that linearly
relate their strength to a position along the X, Y, or Z axis in the lab frame. Spins
at different locations can be identified by their slightly different resonant frequen-
cies, which can be exploited to ensure that only certain portions of tissue produce
signal and that the received signal can be traced back to a particular location.
After the application of appropriately-designed gradient fields, the encoded
data can then be decoded using Fourier transform. The Fourier transform is a
deceptively simple mathematical concept with major ramifications. A transform
is based on the idea that a signal can be represented in a number of ways, much
21
like how we can describe all colors as combinations of a few colors. For example,
purple is red plus blue. Every shade of purple can be obtained by varying the
ratio of red and blue. Similarly, a Fourier transform converts an arbitrary, often
apparently complicated or random, function into a simple sum of sine waves. That
means that a function f(x) can be written like this:
f(x) =
∞
X
n=1
F (n)(cos Θ−i sin Θ) =
∞
X
n=1
F (n)e
−iΘ
(1.8)
Θ = 2π(
n
T
)x (1.9)
where F (n) is a set of weight coefficients for each nth out of a set of N total
samples, Θ is an oscillatory frequency in Hz, f(x) represents an infinitely long
signal in the time domain, and T is the is length along a time-domain sampling
dimension. By adding higher frequency waves, the approximation gets better.
Figure 1.7: Illustration of approximations of different waveforms with Fourier
series. As the number of Fourier coefficients increases, the sum of sine waves
becomes a better fit for the waveform.
5
22
Moving from discrete coefficients into the continuous time domain, the integral
form of the Fourier transform is as follows:
F (ξ) =
Z
∞
−∞
f(x)e
−2πixξ
dx (1.10)
with the inverse transform being:
f(x) =
Z
∞
−∞
F (ξ)e
2πixξ
dξ (1.11)
Thus, gradient fields relate a spin’s precession frequency to a point in space
and the Fourier transform to relates frequency and time. Using these principles,
we can create a set of equations with only one variable. We can apply RF pulses
or sample signals in the time domain and use a combination of gradients and the
Fourier transform to gain spatial knowledge about the signal. For excitation, this
means that we can excite only certain spins by shaping our RF pulse. Consider
the following two pulses and their respective Fourier transforms:
23
0 0.5 1 1.5 2 2.5 3
x 10
−3
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
B1 Waveform
Hard Pulse

B1+ Amplitude (Gauss)
−10 −5 0 5 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Magnetization
0 0.5 1 1.5 2 2.5 3
x 10
−3
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
Sinc Pulse

B1+ Amplitude (Gauss)
Time (s)
−10 −5 0 5 10
−0.5
0
0.5
1
Slice Distance (cm)

Mx
My
Mz
Total
Transverse
Magnetization
B1+ Wave
Figure 1.8: Illustration of slice selection producing transverse magnetization in
a single slice. The hard pulse with no slice selection gradient produces uniform
excitation in the sensitive area of the coil while the sinc pulse with a z-gradient
produces excitation of only part of the object.
The hard pulse has a nearly constant effect across all frequencies while the sinc
(
sin(x)
⁄x) pulse only operates over a central set of frequencies. This means that if
a magnetic gradient is active, only spins in the region of the “bandwidth” will be
24
excited when a sinc pulse is used and the resulting signal comes only from those
spins.
Figure 1.9: Illustration of slice selection producing transverse magnetization in a
single slice
3
Similarly, if we have a gradient active along the X direction during signal recep-
tion, we apply a spatial-spectral constraint to our signal. More simply, the signal’s
position can be known if its frequency can be known. It results in a signal, s(t
x
),
that has the following mathematical form:
s(t
x
) =
Z
x
m(x)e
−iγGxtxx
dx (1.12)
where m(x) is the projection of the object onto the x axis, G
x
is the gradient
amplitude, x is distance along the X-axis, and t
x
is time. Comparing equation
1.12 to equation 1.10 for a Fourier transform, we see that they are identical if
γG
x
t
x
≡ 2πiξ andm(x,y)≡f(x). By using a gradient amplitudeG
x
and duration
t
x
, we can encode signal from the magnetization in a way that can be decoded by
25
a Fourier transform: to get the image back, we just compute the inverse Fourier
transform of our signal. By adding another gradient, we can expose the Y-axis as
well rather than projecting the object onto the X axis, giving us a signal, s(t
x
,t
y
)
of the form:
s(t
x
,t
y
) =
Z
x
Z
y
m(x)e
−iγGxtxx
e
−iγGytyy
dydx (1.13)
whereG
y
is the Y-gradient amplitude andt
y
is the length the Y gradient is turned
on. After acquiring signal for all relevant combinations oft
x
andt
y
, we can simply
invert the Fourier transform alongt
x
and alongt
y
to give us an image inx andy.
1.2.5 Pulse Sequences
When RF pulses, gradients, and acquisition parameters are combined to gen-
erate images, the combination is called a pulse sequence. Though many pulse
sequences exist, they share some common features. For iron quantitation, the most
important parameter in a pulse sequence is echo time, or TE. An echo occurs when
spins rephase after losing transverse magnetization, leading to a sudden increase
in signal. This is true for all classes of pulse sequences but the precise meaning
of echo time changes depending on the pulse sequence. Two types of sequences,
spin echo and gradient echo, are useful in iron overload because they demonstrate
different contrast mechanisms.
Gradient Echo
A gradient echo is the simplest type of pulse sequence, requiring only a single
RF pulse and encoding gradients to make an image. Because signal decays away,
gradient echoes actually accelerate the decay and then reverse the decay using a
gradient. For this reason, gradient echo signals decay with T
∗
2
. Many gradient
26
echo sequences use a “Cartesian” encoding scheme, which acquires lines of k-space
sequentially. They are popular due to the ease of image reconstruction but suffer
from echo time limitations related to gradient strength. Other sampling schemes,
such as center-out radial, can achieve shorter TEs but increase the complexity of
reconstruction. Further, “multi-echo” gradient echoes can play a series of gradients
that generate multiple echoes for a single excitation, with each echo showing more
T
∗
2
decay than the preceding echo.
RF
GrZ
GrX
GrY
Acq
T
Figure 1.10: Example of a common multiecho gradient echo pulse sequence.
Spin Echo
A spin echo is like a gradient echo, but with a second RF pulse called an inver-
sion pulse that is played half-way between the excitation pulse and the intended
TE. The inversion causes the phase accrued due to magnetic inhomogeneities to
be reversed, so the natural rotation of the spins rewinds the phase accrual. This
meansthatspinechoescanbeformedwithouttheapplicationofagradient, though
the readout gradient is necessary for spatial encoding. By naturally reversing the
effects of magnetic inhomogeneities, spin echo signals decay with T
2
rather than
T
∗
2
. Just as gradient echoes can create multiple echoes for a single excitation, spin
27
echoes can play an “RF train,” or a series of RF pulses, to generate many echoes
with compounding T
2
decay.
Figure 1.11: Example of a common multiecho spin echo sequence.
S(t)
0
RF
90
o
180
o
180
o
180
o
180
o
T
2
decay
Figure 1.12: Illustration of a train of 180
◦
pulses generating multiple spin echoes
that decay with T
2
28
1.2.6 Interactions with Iron
Iron demonstrates a profound effect on MR signals. Its paramagnetic behavior
causes the local magnetic field to be amplified, leading to more rapid T
∗
2
and
T
2
decay. In practice, tissues with even mild iron loading can appear dark or
completely black, reducing the signal-to-noise ratio, SNR, to nearly 0. But the
effect is predictable. As iron load increases, T
2
and T
∗
2
decrease.
Intheabsenceofnoise,therapiddecaycausedbyironwouldbeeasytoestimate
usingcommoncurvefittingtechniques. However, thermalnoisecausesunavoidable
error in the sampled signal. As the signal nears zero, the noise complicates the
iron estimates. What’s more, the complex signal is often reduced to its absolute
value for analysis purposes, leads a more complicated relationship between noise
and signal. This means that both the decay rate and the SNR are iron dependent,
which makes accurate fitting a challenge.
The presence of iron leads to increased dephasing along with the rapid decay
rates. Suchunanticipateddephasingcancausephase-basedquantitativetechniques
tofailbecausetheassumptionof1-parts-per-million(PPM)B
0
fieldhomogeneityis
no longer true. In a spectroscopic sense, the rapid decay of the water protons cause
the water peak to spread, enveloping fat peaks, making accurate fat quantitation
challenging.
1.3 Monte-Carlo Simulation
Although magnetic resonance imaging is an extremely popular research tech-
nique, conducting studies can be expensive and time-consuming. In response to
these limitations, many attempts have been made to simulate MRI signals com-
putationally to reduce protocol development time and magnet use. In the context
29
of iron, such a simulation must perform a series of tasks to accurately capture the
nuances of physiologic iron: simulate liver’s cellular tissue structure, simulate iron
distribution within the tissue, calculate the magnetic effects of the iron, track sim-
ulated proton paths as water diffuses in the tissue, excite the simulated protons,
and apply the iron-based magnetic disturbances to the protons. Hoping to extend
simulationstoironimaging, NileshGhugredevelopedamodular, iron-orientedsim-
ulationframeworkfromtissuehistologytoaccomplishthesetasks
6
. Theframework
generated signals demonstrating R
2
- and R
∗
2
-LIC estimates with the same variabil-
ity seen in patient populations, effectively allowing nearly-unlimited virtual patient
studies. To accomplish this life-like variability, Ghugre used light microscopy of
tissue histology to estimate Gamma probability distributions describing the spatial
statistical properties of iron particles in the liver.
Tissue is modeled in the simulation by an 80 μm cube of liver tissue containing
64 cuboidal hepatocytes measuring 20 μm and 18 cylindrical sinusoidal regions
measuring 10 μm diameter and 20 μm height, ignoring portal structures. The
model includes the ability to distribute iron-containing spheres with varying size,
frequency, and spacing in the hepatocytes and/or sinusoid based on the proba-
bilistic Gamma distributions for each iron overload phenotype. The tissue model
is complete with boundaries to represent cell membranes, which is necessary to
restrict diffusion. Within the tissue model, iron stores are placed in the tissue
according to gamma probability distributions, a two-parameter function that is
commonly used to model probability events. From the sphere placements, a spa-
tial magnetic disturbance map can be computed as follows:
ΔB(r, Θ)
B
0
=
1
3
χ
L
(
R
r
)
3
(3 cos
2
Θ− 1) (1.14)
30
where B
0
is the main magnetic field, R is sphere radius, r is the sphere’s radial
distance from the center of the sampling volume, Θ is the azimuthal angle relative
to the magnetic axis, χ
L
is the magnetic susceptibility
(LIC/WDR)∗χ
F
v
where v is
the sphere volume fraction,HIC is the tissue iron content andWDR is the tissue
wet to dry weight ratio (set to 4.1
50
).
Figure 1.13: A demonstration of simulated tissue in 3 dimensions (panels a,b,c) for
LIC values of 4.4, 30, and 57.8
mg
⁄g, respectively. Panels d-f demonstrate 2D pro-
jections of 4μm slices of the 3D geometries; panels g-i show histology samples that
demonstrate the similarity with physiologic data that the simulation can achieve.
Reproduced from the thesis of Nilesh Ghugre.
6
31
Simulating signal from water protons in a heterogeneous magnetic environment
requires the ability generate realistic motion so that the magnetic disturbances
from iron can be experienced. This is accomplished using a Monte Carlo simula-
tion, which uses repeated random sampling of probabilistic functions that describe
the motion of water molecules. In this framework, water motion can be free or
restricted to cell boundaries. Proton paths were computed by sampling a proton’s
displacement change at each timestep from a Gaussian distribution. The mean
absolute displacement, σ, is given by:
σ =
√
2Dδ (1.15)
where D is the diffusion coefficient (0.76
μm
2
⁄ms for human liver
51
) and δ is the
simulation time step (0.5 μs). At each timestep, the next position is randomly
selected; cell boundaries are tested according to the chosen rules before accepting
a new position. Once the random walk of the proton is known, the magnetic
disturbances can be calculated from the previously-generated field map.
MR signal can be estimated in a variety of ways. The first revisions of the
simulation assumed perfect RF pulses, achieving exact, instantaneous excitation
— perfect inversion was simulated by reversing the accrued phase for each pro-
ton at
TE
⁄2. The behavior of the resulting signal showed strong agreement with
experimental data.
Despite the strong correlation between simulated and acquired data, the frame-
work did not allow for certain phenomenon such as pulse bandwidth to be mod-
eled. Further, the amplitude effects and non-idealities in RF transmit systems
could not be simulated using phase-based signal calculations alone. To create a
more complete simulation, a 3D Bloch simulator was added to the framework,
32
allowing for the computation of a proton’s magnetization vector in X, Y, and Z.
This also allowed RF pulse waveforms to be used for excitation and allowed for
pulse non-idealities that occur due to imperfect flip angles. This approach added
critical functionality to the simulation framework for addressing many practical
questions.
1.4 Specific Aims & Significance
Though 1.5T MRI is now the clinical standard for iron overload diagnosis,
a variety of challenges have arisen. Most notably, the extreme loss of dynamic
measurement range of liver iron 3T is hindering iron overload quantitation. It is
estimated that over 50% of new MRI installations are 3T, leaving some imaging
centers without a 1.5T magnet for diagnosis and monitoring of iron overload. This
research focused on one primary unifying goal: make 3T MRI a reliable diagnostic
tool for all clinically-relevant tissue iron loads. To accomplish this goal, a variety
of practical and theoretical challenges needed to be overcome relating to lack of
human validation, pulse sequence limitations, and increasing non-idealities at 3T.
The results will help to remove barriers to the use of 3T MRI while providing
valuable insight into resolving limitations at 1.5T and permitting the use of even
higher-field magnets should them become available clinically.
1.4.1 Aim 1 - Translate R
∗
2
Imaging from 1.5T to 3T
Develop and implement imaging protocols and quantitative evaluation tech-
niques to enable iron quantitation at 3T.
Hypothesis 1a) Clinical R
∗
2
estimates will exhibit field-dependent relaxation
enhancement in humans.
33
Hypothesis 1b) Ultra-short echo time imaging will extend the dynamic range of
LIC estimates at 3T further than Cartesian gradient echo can
achieve.
Hypothesis 1c) Relaxometry of ultra-fast decay species can be improved with
information from a patient’s iron-free tissues without the need for
additional imaging series.
1.4.2 Aim 2 - Assess Non-Idealities at 3T
Understand and correct for known imaging confounds that are present or more
pronounced at 3T.
Hypothesis 2a) B
+
1
inhomogeneitymustbecorrectedat3Twhenspinechoimaging
is used for R
2
quantitation.
Hypothesis 2b) B
+
1
inhomogeneity will not appreciably affect R
∗
2
quantitation.
1.4.3 Aim 3 - Develop and Test Novel MR-based Iron
Quantitation Techniques
Determine the feasibility of using novel pulse sequences to robustly perform
iron quantitation.
Hypothesis 3a) A spectroscopic approach using chemical shift imaging can simul-
taneously quantify R
2
and R
∗
2
with high robustness.
Hypothesis 3b) Short TE spin echo sequences can quantify R
2
at 3T.
34
1.5 Outline
Chapter 2 demonstrates the benefit of fitting CPMG spin echo data with a
proton density estimator to improve sensitivity to tissue iron content. This retro-
spective study showed that using only data derived from within an imaging series,
the relationship between R
2
and LIC becomes stronger than estimates made with-
out the constraint. This study validates this effect by replicating another cen-
ter’s imaging study parameters and demonstrating nearly identical relationships
between LIC and unconstrained or constrained R
2
.
Chapter 3 examines the relationship between relaxation estimates made with
1.5T and 3T MRI systems. This study uses simulation data to demonstrates
a closed-form solution for converting liver R
2
and R
∗
2
estimates acquired at an
arbitrary field strength to any other field strength. It also presents human imaging
data from 1.5T and 3T to validate the predictions of the model.
Chapter 4 assesses the effect of B
+
1
inhomogeneity, a common imaging con-
founder at 3T, on R
2
and R
∗
2
estimates. Simulation results demonstrate the impor-
tance of correcting single spin echo and CPMG-based R
2
estimates in the presence
of B
+
1
inhomogeneity. Human imaging results demonstrate the magnitude of B
+
1
inhomogeneity in a patient population at both 1.5T and 3T. Correction at 1.5T
was found to be beneficial while correction at 3T was critical.
Chapter 5 demonstrates a new imaging protocol to assess liver iron at 3T
using ultra-short echo time imaging in conjunction with existing clinical processing
pipelines. A 23-patient study found that UTE imaging could assess moderate-
to-high liver iron with similar variability seen with clinical techniques at 1.5T.
Comparison by Bland-Altman and regression analysis are provided. Further, the
effects of tissue fat are assessed for each imaging protocol to explain disagreement
between clinical LIC estimates and UTE estimates.
35
Chapter 6 describes a novel approach to iron imaging through a modified chem-
ical shift imaging spectroscopy sequence. Through the application of custom RF
pulses and a decreased minimum echo time, the sequence successfully quantifies
R
∗
2
in a small patient cohort. Phantom data provide a proof of concept for simul-
taneous R
2
/R
∗
2
imaging using CSI.
36
Chapter 2
Improved Liver Iron Estimates
using T
1
-Corrected Proton
Density Estimator
Abstract
Purpose: CPMG spin echo series are attractive due to their time efficiency and
potential to reveal unique information about tissue iron distribution. Clinical
adoption remains low due to the traditionally flat relationship between CPMG-
based R
2
estimates and LIC. In this work, we demonstrate that the inclusion of
a proton density estimator from within acquired image datasets can increase the
sensitivity of CPMG R
2
estimates to iron in both human and simulated data.
Theory and Methods: A retrospective data analysis of 50 patient records was
performed, fitting CPMG spin echo data with and without a muscle-based proton
density estimator segmented from within each image series. Data was compared
to R
∗
2
-based clinical iron estimates. A Monte Carlo simulation was performed with
matching imaging and fit parameters. Results: The sensitivity of CPMG-derived
R
2
triples when a proton density constraint is applied. Over a moderate iron load
range, human data snaps to one of two fit regimes. Simulation data demonstrates
the same increase in sensitivity but does not demonstrate the bimodal behavior
overthemiddleironranges. Conclusion: Aprotondensityconstraintcanincrease
37
the sensitivity of CPMG-based R
2
estimates to iron. Such an increase may allow
for improved adoption of CPMG sequences over multiple single echoes for their
associated scan efficiency improvements and potential for more insight into tissue
iron distribution.
2.1 Introduction
Chronic anemias such as thalassemia and sickle cell disease represent the most
common genetic disorders in the world. Transfusion therapy in these patients
producessevereirondepositionintheliverandotherorgans, leadingtocardiacand
endocrine dysfunction and liver cirrhosis. Iron overload in transfusional siderosis
cannot be treated with phlebotomy. Instead, patients receive iron chelators that
bind and remove iron with dosing specific to their tissue iron content. Determining
safe chelation dosing requires reliable iron quantitation techniques. Before 2005,
needle biopsies were required to quantify liver iron, with their attendant risks
21
and sampling error
22,23,24
. Since then, magnetic resonance imaging systems have
become key tools for diagnosing and monitoring iron overload disorders such as
transfusionalsiderosisinsicklecelldiseaseandthalassemia, hemochromatosis, liver
disease, and a number of neurodegenerative disorders. Both transverse relaxivity
and magnetic susceptibility measurements have been used to estimate tissue iron
concentrations in the liver, heart, endocrine glands, and brain. MRI-based iron
quantitation at 1.5 Tesla(T) is now standard of care.
One common approach for measuring liver iron concentration (LIC) is to esti-
mate the transverse relaxation rate R
2
(1/T
2
) from images formed with a spin echo
(SE) pulse sequence. Most often, protocols obtain a set of single spin echo (SSE)
images at a variety of echo times (TE) and fit an exponential decay curve to the
38
samples in the image domain. This approach yields curvilinear calibration curves
relating SSE-R
2
to LIC that demonstrate high sensitivity at low iron loads and
reduced sensitivity in high iron loads as the curve flattens
4,7
. This high sensitivity,
whichcan appear linearover alimited rangeof iron loads
52,53
, is usefulfor precisely
estimating iron loads below 20
mg
⁄g. Estimating higher LICs in this manner remains
a challenge due the insensitivity of the curve over higher LICs. Nonetheless, SSE
series are attractive due to the straight-forward acquisition and analysis. However,
scan time and the number of required breath holds grows linearly with the number
of echoes desired and later echoes cannot sample useful signal in high-iron patients.
Less commonly, R
2
estimates are made using Carr-Purcell-Meiboom-Gill mul-
tiecho spin echo sequences (CPMG)
46,54,55,49,56
. Such sequences require only one
excitation to form images at a variety of echo times, reducing the scan duration
while still acquiring multiple echoes. Compared to SSE, signal loss is reduced
in later echoes due to the dependence of each echo on preceding echoes, lead-
ing to improved SNR in high-iron subjects. This dependence may also provide
information about cellular iron distribution that cannot be assessed with SSE
images
56
. Gathering the necessary decay information for analysis is challenging
due to CPMG’s echo timing limitations. Constraints on both the minimum echo
time and the interecho spacing, τ, limit CPMG’s sampling more than SSE.
Despite the benefits of CPMG, its timing limitations lead to undersampling
of initial signal decay. Subsequent R
2
estimates demonstrate poor sensitivity to
increasing iron load due to underestimates of tissue’s proton density (S0), which
hinders clinical applicability. Figure 2.1 demonstrates characteristic decay curves
for R
2
values of 166 Hz (left pane, T
2
=6 ms, 1.5T LIC=8.9
mg
⁄g, 3T LIC=15.8
mg
⁄g)
and 333 Hz (right pane, T
2
=3 ms, 1.5T LIC=61.1
mg
⁄g, 3T LIC=28.2
mg
⁄g). The
left pane shows that low and moderate iron loads produce sufficient SNR that
39
constrainedandunconstrainedfittingapproachesagreewithin7%ofeachother, on
par with test-retest variability for MRI-based iron quantitation. Signal from high
iron loads (right pane) demonstrates over 50% disagreement between constrained
and unconstrained R
2
estimates. Most of the error comes from the unconstrained
technique vastly underestimating the early signal decay. By anchoring the fit with
anestimateoftheintersectionpointbetweenthey-axisandthedecaycurve, theR
2
estimate captures the decay effectively. In this work, we investigate the potential
of using a muscle-based S0 constraint to improve the sensitivity of the relationship
between CPMG-derived R
2
and LIC, thereby increasing the clinical applicability
of CPMG series for liver iron estimation without the need to include additional
scans.
2.2 Theory
The choice of signal model can have significant impact on quantitative results
from MRI. In this work, we applied two signal equations to the acquired data: the
Yamada CPMG signal equation and the Jensen model for non-exponential decay
in the liver. The Yamada equation and similar mono-exponentials are the most
common signal models used in MRI while the Jensen model specifically describes
CPMG signal behavior in iron loaded tissue.
The Yamada CPMG model accounts for the R
2
envelope that is traditionally
seen in spin-echo sequences as well as the T
1
weighting that is present. 2.8):
S(t) =S
0
×exp

−R
2
t
!"
1−exp

−TR
T
1
!#
(2.1)
S
0
=k×M
0
(2.2)
40
where S
0
represents proton density as a product of a constant k and the initial
longitudinal magnetization M0, R
2
represents transverse relaxation rate, and t
represents echo formation time.
Although the Yamada equation is commonly used for R
2
relaxometry, it does
not differentiate between the decay processes in SSE and CPMG sequences. Spins
that are stationary with respect to magnetic inhomogeneities with demonstrate
identical SSE and CPMG R
2
estimates. When spins diffuse their echoes are
weighted by the magnetic heterogeneity experienced between any two RF pulses,
leadingtoacohortofspinswhoseapparentdecayissampling-dependent. Although
the echo times produced by SSE and CPMG sequences may match, the distance
between the RF pulses after the first echo will differ. In cases where proton motion
distance and tissue mesostructure scale are similar, as with iron, the diffusion and
sampling scheme will lead to different R
2
estimates from the two sequences. The
Jensen model accounts for this by providing two decay parameters rather than one
- T
1
effects are omitted for brevity:
S(t) =S
0
×e
−RR
2
t
×exp(−a
3
4
(Δt)
3
4
(t−t
s
)
3
8
) (2.3)
where RR
2
represents reduced R
2
,a represents a nonlinear aggregation parameter,
t represents time, and ts is a time shift given by:
t
s
= 2τ
"
1−

τ
Δt
!
2
#
(2.4)
whereτ representsthetimeofthefirstRFpulseand Δtrepresentthetimebetween
successive RF pulses, such that echoes form att = 2τ + 2(n− 1)Δt (or 2nΔt when
τ = Δt). The resulting signal in the presence of iron stores is therefore a function
41
of properties that are intrinsic to the tissue, such as diffusion and iron aggregation,
as well as acquisition parameters such as echo spacing.
2.3 Methods
2.3.1 Imaging
Patients with β-Thalassemia, Sickle Cell Disease, and other rare anemias
received clinically indicated MRI assessments for liver iron content. All scans were
completed on a Philips Achieva 1.5T magnet (Philips HealthTech, Best, Nether-
lands) on software revisions 2.6.1, 2.6.3, or 3.2.2. Imaging series were sampled
from a large clinical dataset to yield a wide range of LIC burdens as part of a
retrospective study jointly approved by institutional review boards at Children’s
Hospital of Los Angeles and Boston Children’s Hospital (IRB#CHLA-15-00010).
All scans were performed with breath holds. Three 8-echo gradient echo sequences
with minimum TEs of 1.16 ms and maximum TEs of 8.6, 11.66, and 16.56 ms
were used to estimate R
∗
2
for use as a standard LIC estimate. An 8-echo CPMG
sequence with TEs from 6.5-52 ms was used to capture R
2
. Expanded imaging
parameters for both protocols are shown in Table 2.1.
2.3.2 Simulation
An internally developed, previously validated Monte Carlo simulation frame-
work was used to generate synthetic signals matching the echo times used in the
clinical scans on a range of 1-50 [mg/g iron/dry tissue weight]
57
. Briefly, liver tis-
sue was modeled as 80μm cubes of liver tissue containing 64 cuboidal hepatocytes
and 18 cylindrical sinusoid regions
58
. Iron overload was modeled by distribut-
ing spheres of iron in the hepatocytes using Gamma distributions to statistically
42
describe their size and spacing. From the iron distributions, magnetic field distur-
bances were calculated based on the field strength and magnetic susceptibility of
iron. 2500 spin cohorts were tracked using a random walk simulation through iron
distributions and obeyed cell and obstacle boundaries. A 3D Bloch equation simu-
lator calculated the magnetization at each timestep. RF excitations and inversions
were modeled as 90
◦
and 180
◦
instantaneous flips; the CPMG phase cycling scheme
was applied. Iron-free relaxation rates T
1
and T
2
were set to 576 ms and 42 ms,
respectively
59
. Iron-mediated T
1
enhancement was not modeled in the simulations
due to the lack of scan repetitions obviating the need for T
1
correction.
2.3.3 Analysis
Image series were segmented for whole liver and bilateral latissimus dorsi skele-
tal muscle regions of interest (ROI) in a single mid-hepatic slice by a cardiologist
with 15 years experience and a graduate student with 5 years experience. R
∗
2
estimates were derived from magnitude gradient echo images using a previously
validated pseudo-pixel wise technique with gradient echo images
60
; R
∗
2
values were
used to generate reference LIC estimates using the Wood R
∗
2
-LIC calibration
4
via
equation 2.5:
FE
R
∗
2
= 0.0254×R
∗
2
+ 0.202 (2.5)
R
2
was estimated by fitting sampled data with a signal model based on
Yamada’s CPMG signal equation
61
. A constant c was added to account for mag-
nitude noise bias and the T
1
weighting was omitted in favor of weighting muscle
signal (see equation 2.8)
S(t) =S
0
×exp

−R
2
t
!
+c (2.6)
43
We also tested Jensen’s iron-specific, non-exponential signal model (see equa-
tion 2.4), including an additional c parameter representing noise bias:
S(t) =S
0
×e
−RR
2
t
×exp(−a
3
4
(Δt)
3
4
(t−t
s
)
3
8
) +c (2.7)
A Levenburg-Marquardt algorithm was used to fit the signal models to magni-
tude images (pseudopixel-wise
60
) and simulation data (all spin cohorts averaged,
magnitude acquired at echo times noted in CPMG protocol). Both fitting models
assumed that RF pulses achieved perfect 90
◦
excitations and 180
◦
inversions. All
research fits were performed using a non-negativity constraint on values of S
0
, R
2
,
a and c.
After fitting both signal models to the data, as second set of fits were generated
after placing a more strict constraint on the value of S
0
. We assumed that the
initial point on the R
2
decay curve should only be weighted by the liver’s proton
density, not the presence of iron. Skeletal muscle was chosen as a surrogate for
proton density because its resistant to iron uptake provided a reliable reference
tissue in all patients. Based on the reported densities of 1.06
kg
⁄L and 1.02
kg
⁄L for
muscle
62
and liver
63
, respectively, we assumed that skeletal muscle and muscle
would have approximately the same S
0
. PDEs were determined in the image
seriesby performingROI-averaged T
2
estimationwith T
1
correctionon theskeletal
muscle signal using the T
1
term from the Yamada equation and assuming muscle
T
1
to be 1008 ms
59
:
S
muscle,corrected
=S
muscle,acquired
×
"
1−exp

−TR
T
1,liver
!#
"
1−exp

−TR
T
1,muscle
!#
(2.8)
44
The PDE in the simulations was known apriori. Liver T
1
was initially estimated
using a T
2
value from a linearized exponential fit and then iteratively refined
three times using an internally derived LIC-T
1
model. In constrained fits, S0
was constrained to±10% of PDE estimate value from T
1
-corrected muscle signal
(equation 2.8). Muscle and liver of all iron loads were assumed to have identical
proton density values.
Constrained and unconstrained T
2
fits were compared using gradient-echo
based reference LIC estimates in human subjects or specified simulation iron loads
as the standard iron load metric.
2.4 Results
Retrospective patient data analysis was completed in 50 patients (24M,26F,
16.4±9.4 years, 24 Thalassemia, 6 Sickle Cell Disease, 5 Diamond-Blackfan Syn-
drome, 15 Other Rare Anemia) with a broad range of LIC. Figure 2.2 demonstrates
the unconstrained R
2
estimates versus R
∗
2
-derived LIC. Linear regression is shown
for comparison with two linear models demonstrated in previous research
64
. The
data compared to the R
2
-MR_HIC (R
2
vs LIC derived from ratio of liver to mus-
cle)
65
and R
2
-LIC (R
2
vs LIC derived from R
∗
2
)
4
models demonstrate adjusted r
2
values of 0.85 and 0.87, respectively, suggesting that the acquired data is represen-
tative of data used in other studies.
Figure 2.3 demonstrates unconstrained and constrained R
2
estimates of human
data and polynomial regression of simulation R
2
vs LIC; the St. Pierre calibration
curve between SSE-R
2
and LIC is included for reference. Unconstrained human
and simulation R
2
estimates demonstrate weak correlation with LIC. Agreement
between unconstrained estimates in patients and simulation data was strong across
45
all iron burdens, with all but 2 patient R
2
estimates falling within the 95% confi-
dence intervals of the simulation estimates. S0-constrained R
2
estimates in both
human and simulation data display a increased sensitivity to LIC. The simulation
fit and St. Pierre reference curve agree within 10% up to an LIC of 30
mg
⁄g. At low
and high iron loads, constrained patient R
2
estimates agreed with constrained sim-
ulation fits, displaying the same increase in R
2
-LIC sensitivity. Over an intermedi-
ate region from 12-22
mg
⁄g LIC, constrained patient R
2
fits demonstrated increased
LIC sensitivity compared to matched unconstrained fits, but most fell significantly
below the confidence interval of the simulated fits.
The both constrained and unconstrained RR
2
estimates demonstrated a weak
dependence on LIC, similar to the behavior of R
2
in the unconstrained Yamada
signal model. The unconstrained RR
2
shows slightly higher sensitivity than the
constrained RR
2
. The a parameter was insensitive to LIC in the unconstrained
fits, demonstrating a curvilinear sensitivity in the constrained fits similar to the
behavior of the constrained R
2
in the Yamada fits.
2.5 Discussion
CPMG sequences have been proposed as rapid alternatives to SSE acquisitions
for LIC determination but remain impractical due to insensitivity between LIC
and R
2
. We demonstrate by analysis of acquired images and synthetic MRI signals
that sensitivity can be improved by including a proton density estimator to capture
rapidinitialsignaldecay. ThesignalfromironloadedtissueacquiredwithaCPMG
sequence is non-exponential
56
— a non-exponential, rapid decay component is
governed by “near-field” iron stores and an exponential slow decay component
called “reduced R
2
” accounts for diffuse iron storage. Adequately sampling the
46
rapid decay component is challenging because the minimum first echo time is
limited around 4 ms for a slice-selective acquisition. Jensen noted that capturing
the initial decay is particularly important in high-iron tissues and his model; the
model permits a first echo time that is shorter than the CPMG interecho spacing
for this reason. However, attempts to vary the interecho spacing or first echo time
over multiple acquisitions to improve fitting constraints reduces the time savings
of using CPMG.
In addition to the acquisition challenges, the problem of separating the fast
and slow decay components with a single CPMG series is ill-posed because there
are three free fit parameters (S0,a,RR
2
) in the Jensen model. In fact, when the
condition a . (Δt)
−3/2
is not met, the rapid-decay signal cannot be detected
at all
56
. Imaging magnets cannot achieve sufficiently short TEs to capture the
rapid decay for even moderate-iron patients. It is therefore attractive to fit with
simplermodelslikeamono-exponentialwhichhasonlytwofreeparameters(S0,R
2
).
Mono-exponential fitting leads to a weighted average of the fast and slow decay
components with the proportion of fast decay signal increasing with LIC
49
. Due
to TE limitations, mono-exponential fitting mostly ignores the fast decay and
almost exclusively fits the slow-decay component of the non-exponential model.
This is apparent in figure 2.4, where unconstrained R
2
tracks the relatively iron-
insensitive RR
2
from both constrained and unconstrained fits of a single CPMG
series while thea parameter increases with liver iron. The agreement between the
constrainedandunconstrainedJensenfitsandtheunconstrainedmono-exponential
R
2
estimates suggests that the lack of a proton density constraint leads to the
fitting of only the slow decay component, which saturates between 2.5 and 8
mg
⁄g.
Previous work by Ghugre
49
demonstrated that increasing echo spacing leads to a
decrease in the fast-decay component of a bi-exponential fit rather than a change
47
in the decay rate of either exponential. This is similar to our finding that the
unconstrained mono-exponential fits primarily capture the slow-decay component.
Due to the complete loss of fast decay species at clinically achievable first
echo times, unconstrained mono-exponential fits will underestimate proton den-
sity. Unconstrained exponential fitting of simulation data underestimated proton
density by up to 70% of its known value. Similar behavior was noted in-vivo when
comparing to a muscle-based proton density estimate. Such a precipitous drop in
S0 cannot be accounted for by the mass of the iron alone. Without a physical
basis for the decrease in S0, applying a constraint can reduce the sampling bias
that favors the slow decay component. This approach is similar to that used to
constrain bi-component exponential fits of SSE data in FerriScan(®, Resonance
Health, Australia)
66
. By using an S0 constraint derived from tissue whose iron
load is independent of disease status, we can effectively increase the weight of the
fast decay component and increase the LIC sensitivity of mono-exponential R
2
estimates. Signal decay in tissue with mild iron overload is primarily governed by
diffuse iron and exhibits slow decay that can be adequately fit with either a con-
strained or unconstrained exponential (figure 2.1, left panel). In high-iron tissues,
the fast decay component is more prevalent and the signal demonstrates primarily
rapid decay that cannot be sampled with long echo times. The decay is recovered
by the application of the proton density constraint (figure 2.1, right panel). How-
ever, signals from moderate iron tissues demonstrate non-negligible fast and slow
decay components. When attempting to apply a constrained mono-exponential,
the fits snap to one of the decay regimes more effectively than the other, leading to
the bimodal fitting distribution demonstrated by our constrained patient fits. We
hypothesize that uncorrected noise rectification may be partially responsible for
this effect
67
. Applying a Rician noise correction or fitting in the complex domain
48
will capture noise behavior better than a bias constant. Fat is also known to be
present in concentrations of about 0-20% in the liver, but the contributions from
fat have been ignored. Over the bimodal regime, the CPMG’s relatively short TR
may lead to amplification of fat brightness in later echoes to artificially decrease
the apparent decay rate. We hope to study the effects of noise and fat in future
work.
The constraints chosen in this work were selected to be wide enough to reason-
ably accommodate all clinical iron burdens without prior knowledge of iron load or
additional scans. For this reason, estimates of non-idealities in the muscle-based
PDE or corrections could not be made. Including additional scans may further
improve constrained estimates by gathering information on other non-idealities.
For example, nonuniform RF excitation due to B
+
1
inhomogeneity or spatial vari-
ation of coil sensitivity could produce images that show signal intensity difference
between muscle and liver, leading to poor S0 constraints. Subsequent fits using the
constraint would demonstrate increased error. Without a B
1
+
correction to ensure
that the muscle-based PDE and the liver signal intensities are appropriately nor-
malized, reducing the variation seen in patient fits will be difficult. Despite perfect
knowledge of the proton density in the simulations and the absence of T
1
effects,
the95%confidenceintervalsonthesimulationfitdataindicatethatS0-constrained
R
2
estimates from CPMG data still have confidence bounds of over 10
mg
⁄g, match-
ing the demonstrated patient variation.
49
2.6 Conclusion
Muscle-based proton density estimators derived from within existing imaging
datasets provide a robust way to increase the sensitivity of CPMG-based R
2
esti-
mates, increasing the potential clinical utility of such a sequence. The effect was
demonstrated in both human and simulated data. Improved selection of scan tim-
ing parameters, signal models, and fitting techniques may improve the accuracy of
estimates that rely on a proton density estimator.
2.7 Acknowledgements
This research is supported by the National Institute of Diabetes, Digestion and
Kidney Diseases of the National Institutes of Health, grant 1R01DK097115-01A1.
Computation for the work described in this paper was supported by the University
of Southern California’s Center for High-Performance Computing (hpc.usc.edu).
50
Spin Echo
Type CPMG Multi echo sequence
TE 6.5, 13, 19.5, 26, 32.5, 39, 45.5, 52 ms
TR 247 ms
NSA 1
Voxel Size 2.5x2.5mm
Slice Thickness 8 mm
Matrix 64x64
Bandwidth 4.1 kHz/pixel
Gradient Echo
Type Multi-echo GRE Sequence
Echo Time 1.16, 2.22, 3.28, 4.35, 5.41, 6.47, 7.54, 8.60 ms (short T
∗
2
)
1.16, 2.66, 4.16, 5.66, 7.16, 8.66, 10.16, 11.66 ms (medium T
∗
2
)
1.16, 3.36, 5.56, 7.76, 9.96, 12.16, 14.36, 16.56 ms (long T
∗
2
)
TR 50 ms
NSA 1
Voxel Size 1.25x1.25mm
Slice thickness 8mm
Matrix 128x128
Bandwidth 1.5 kHz/pixel
Table 2.1: Relevant scan parameters for patient exam.
Measurement Min Max Mean±StDev
Height [cm] 117 179.8 156.2±15.3
Weight [kg] 20.1 89.7 54.3±17.1
Body Surface Area [m
2
] 0.81 2.1 1.5±.3
Body Mass Index [
kg
⁄m
2
] 14.7 34.3 21.9±5.1
Ferritin [
ng
⁄mL] 199 16300 4483±4890
ALT [
U
⁄L] 18 391 74.5±84.5
Table 2.2: Ranges of demographic and laboratory data for the participant popu-
lation
51
0 5 10 15 20 25 30
0
200
400
600
800
1000
1200
Type S0 R2
True 1000.0 6.0
Unc 922.6 6.6
Con 1000.0 6.2
Time (ms)
Signal intensity (a.u.)
T
2
= 6.0 ms

True decay with noise
Sampled echoes
Unconstrained
Unconstrained PDE
Contrained
Constrained PDE
0 5 10 15 20 25 30
0
200
400
600
800
1000
1200
Type S0 R2
True 1000.0 3.0
Unc 492.0 4.7
Con 1000.0 3.1
Time (ms)
Signal intensity (a.u.)
T
2
= 3.0 ms

True decay with noise
Sampled echoes
Unconstrained
Unconstrained PDE
Contrained
Constrained PDE
Figure 2.1: Example of unconstrained and constrained mono-exponential fits for
different R
2
species. When the decay rate is comparable to the first echo time
(left), the proton density is underestimated by 8% and the R
2
is overestimated by
10%. The same trend is seen to a more extreme degree in the right pane where
the R
2
is shorter.
52
0 10 20 30 40
0
100
LIC [mg/g]
R2 [Hz]

patient, unconstrained
Data linear regression
Christafordis R2 Calibration vs MR−HIC
Christafordis R2 Calibration vs R2*−LIC
Figure 2.2: Unconstrained fits of acquired CPMG data plotted against LIC demon-
strated that curves derived by Christoforidis show similar fit to the data. The
disagreement in slope of fit compared to the Christoforidis-R
∗
2
curve likely results
from the apparent saturation of their protocol due to shorted TE of 2.24 ms in the
gradient echo protocol.
53
0 10 20 30 40
0
100
200
300
400
Comparison of Fitting Techniques, Simulation and Human Subject Data
LIC [mg/g]
R2 [Hz]

patient, unconstrained
simulation, unconstrained
simulation, unconstrained 95% CI
0 10 20 30 40
0
100
200
300
400
LIC [mg/g]
R2 [Hz]

patient, S0 constrained
simulation, S0 constrained
simulation, S0 constrained 95% CI
Figure 2.3: Comparison of fitting techniques. Top pane demonstrated the weak
relationship between R
2
and LIC in the unconstrained fits. Lower pane shows
the approximate tripling of the calibration curve with the addition of the PDE
constraint.
54
0 5 10 15 20 25 30 35 40
0
50
100
150
200
LIC (mg/g)
R2
R2

Unconstrained
Constrained
Simulation R2 Unconstrained
0 5 10 15 20 25 30 35 40
0
500
1000
1500
2000
2500
3000
A
Figure 2.4: Constrained vs unconstrained fitting of Jensen curve demonstrates
that sensitivity of the RR
2
parameter (top pane) follows the behavior of the uncon-
strained R
2
estimates. The unconstrained aggregation parameter (lower pane) was
less correlated tissue iron content but demonstrated large variation. In contrast,
the constrained RR
2
saturates quickly; the aggregation parameter (lower pane)
increases with iron for the constrained fits. This suggests that the background
RR
2
may represent saturating ferritin stores while the a parameter represents
large iron particles.
55
Chapter 3
Relaxivity-iron calibration in
hepatic iron overload: Predictions
of a Monte Carlo model
Abstract
3.0.1 Purpose
R
∗
2
(1/T
∗
2
) and single echo R
2
(1/T
2
) have been calibrated to liver iron concen-
tration (LIC) in patients with thalassemia and transfusion-dependent sickle cell
disease at 1.5 Tesla. The R
∗
2
-LIC relationship is linear while that of R
2
is curvi-
linear. However, the increasing popularity of high-field scanners requires general-
izing these relationships to higher field strengths. This study tests the hypothesis
that numerical simulation can accurately determine the field dependence of iron-
mediated transverse relaxation rates.
3.0.2 Methods
We have previously replicated the calibration curves between R
2
and R
∗
2
and
iron at 1.5T from using Monte Carlo models incorporating realistic liver structure,
iron deposit susceptibility, and proton mobility
57
. In this paper, we extend our
model to predict relaxivity-iron calibrations at higher field strengths. Predictions
56
were validated by measuring R
2
and R
∗
2
at 1.5T and 3T in sixβ-thalassemia major
patients.
3.0.3 Results
Predicted R
∗
2
increased two-fold at 3T from 1.5T while R
2
increased by a factor
of 1.47; patient data exhibited a coefficient of variation of 3.6% and 7.2%, respec-
tively, to the best-fit simulated data. Simulations over the 0.25-7T range showed
R
∗
2
increasing linearly with field strength while R
2
exhibited a concave-downward
relationship.
3.0.4 Conclusion
Amodel-basedapproachpredictsalterationsinrelaxivity-ironcalibrationswith
field strength without repeating imaging studies. The model may generalize to
alternative pulse sequences and tissue iron distribution.
3.1 Introduction
MRI has gained clinical acceptance as a non-invasive tool to monitor tissue
iron stores in patients with iron overload syndromes. Relaxation rates R
2
(1/T
2
)
and R
∗
2
(1/T
∗
2
) have been calibrated to liver biopsy on 1.5T scanners to quantify
liver iron concentration (LIC) with clinical accuracy
7,4
. R
∗
2
increases linearly with
LIC while R
2
has a curvilinear relationship. However, these relationships have not
been extensively characterized for higher field strengths.
While one can physically calibrate imaging techniques across field strengths, it
is tedious and expensive. An alternative approach is to use numerical modeling
by generating realistic (iron overloaded) liver geometries and simulating R
2
and
57
R
∗
2
imaging experiments. Such a model has already been successful in predicting
R
∗
2
-iron and R
2
-iron relationships within tolerable limits of clinical accuracy at
1.5T
57
. Here we extend the model to find relaxivity with respect to iron, or iron-
relaxivity calibration, over a range of field strengths. To validate the predictions
of the model, we performed R
2
and R
∗
2
imaging of the liver at 1.5T and 3T in six
patients with transfusional iron burden and 11 non-iron overloaded controls.
3.2 Methods
We modeled the liver architecture as consisting of hepatocytes and sinusoids,
ignoring vascular and biliary structures. As previously described
57
, realistic liver
geometries were simulated as 80 μm blocks consisting of 64 cuboidal hepatocytes.
Sinusoids were represented as 18 cylindrical regions with a diameter of 10 μm
and height of 20 μm. Hepatic iron concentration was in the clinically-relevant
range of 0.5-40 mg/g dry tissue weight and corresponding volume fractions of
iron deposits were determined from prior relationship
68
. Spherical iron deposits
were distributed in this virtual environment based on Gamma distribution func-
tions that represented particle size, inter-particle distance and inter-cellular iron
anisotropy
68
. Sinusoidal iron fraction was determined from a previously derived
relationship
69
. Each iron load geometry was independently generated and repre-
sented a virtual patient. The magnetic susceptibility of the impenetrable spherical
iron deposits was computed assuming a 4:1 mixture of hemosiderin and ferritin and
using literature values of 1.1E-6 and 1.6E-6 m
3
/kg
Fe
respectively
70,71
. 5000 pro-
tons performed a random walk (diffusion coefficient = 0.76 m
2
/ms
61
) through the
magnetic environment and FIDs were computed from phase accruals, providing R
∗
2
estimates. Tissue wet-to-dry weight ratio was assumed to be 4:1
50
. A single echo
58
experiment with echo times (TE) logarithmically spaced between 0.1-30 ms was
also simulated to measure R
2
. Echo times were chosen to maximize the dynamic
range of the simulation for the computation time. Protons could not cross hep-
atocyte boundaries. The model neglected any contact or exchange mechanisms.
Details of MRI simulation have been described earlier
57
.
Monte Carlo simulations were performed at field strengths of 1.5T, 3T, and
ten other field strengths in the range of 0.25-7T. Realistic liver geometry and iron
morphology was employed with hepatic iron concentrations in the range of 0.5-40
mg/g. R
∗
2
and R
2
values were estimated from signal decay curves corresponding to
each iron burden. Simulations were subsequently extended up to 60 mg/g hepatic
iron concentration for comparison. Bland-Altman analysis was performed with
matched pairs of iron-loaded patient and simulation data for R
2
and R
∗
2
at 3T to
determine bias and standard deviation.
In-vivo validation scans were performed as part of a prospective, Institutional
Review Board (IRB)-approved study using a phased array coil on 1.5T and 3T
GE Signa Twinspeed systems. Consent was obtained from six thalassemia major
patients (2 male, 4 female; ages 12-44) or minors’ legal guardians, and 20 non-
iron overload subjects (10 male, 10 female; ages 19-41). Liver R
∗
2
was measured
in a single mid-hepatic slice using a multiple-echo gradient echo sequence with
16 equally spaced echo times(TE) from 1.2 – 17.2 ms, flip angle(FA)=20, repe-
tition time(TR)≈13 ms, bandwidth(BW)=83.3 kHz, number of averaged excita-
tions(NEX)=6, and matrix size=128x128. In patients in whom signal intensity
was completely extinguished by the second echo, the protocol was modified to
have a first TE=0.8 ms, FA=10, TR=10 ms, and NEX=8. The sequence was
repeated at the same gain settings using manually incremented initial echo times
(TE=0.1 or 0.2ms); the first echo time was increased until the liver tissue appeared
59
black. The echoes from each scan were combined and ROIs manually adjusted to
improve sampling of rapid decay. A comprehensive description of the procedure
is described in
72
. Liver R
2
was measured in 4 slices using a 90-90 Hahn spin echo
sequence with TE=[3,3.5,5,8,12,18,30] ms at 1.5T and TE=[4,5,8,12,18,30] ms at
3T, TR=300 ms, BW=62.5 kHz, NEX=1 and matrix size=64x64
72
. R
2
values
were computed in 16 regions of interest (4 per slice) by fitting the mean signal
decay to an (exponential+constant) model
73
. R
2
imaging was not performed in
control subjects.
Relaxation rates at 3T were compared with those at 1.5T for both model and
experimental data. Similarly, the variation in relaxivities (defined below) with field
strength was investigated and characterized using linear and power law relation-
ships over the range 0.25 – 7T. Relaxivity is defined as the increase in the relax-
ation rate with iron concentration, , at a given field strength in units of [mM
-1
*
s
-1
]. Relaxivity enhancement (RE), the increase of relaxivity with field strength,
was calculated between arbitrary field strengths B
0
and 1.5T as follows:
E(B
0
) =
∂R
∂C
|
B
0
∂R
∂C
|
1.5T
(3.1)
where C represents the iron concentration in mg/g dry weight and R represents
either R
2
or R
∗
2
. To generalize the relationship, relaxivity enhancement was plotted
againstfieldstrengthandfittolinearequations. ForR
2
, logtransformationofboth
RE and field strength was needed to linearize the relationship.
For the purpose of this work, relaxation is modeled as follows:
R =R
i
+R
0
(3.2)
60
whereR is the relaxation rate (R
2
or R
∗
2
) of a given tissue sample with iron,R
i
is the intrinsic relaxation rate without iron, and R
0
is the extrinsic relaxation rate
due to iron load.
By applying the RE equation to the relaxation model, we find the following
transformation to translate R
2
and R
∗
2
values from 1.5 Tesla to any arbitrary field
strength:
R(Y )−α
Y
= (R(1.5T )−α
1.5
)×RE
R
(Y ) (3.3)
where R is the relaxation rate (R
2
or R
∗
2
) for a given field strength, α
Y
is the
corresponding intrinsic liver relaxation rate, andRE is the relaxivity enhancement
for a given field strength. The background relaxation was assumed to be 20 s
-1
independent of field strength for the simulations.
3.3 Results
Figure 3.1 shows simulated R
∗
2
and R
2
values as a function of iron concen-
tration for both 1.5T and 3T. Simulated R
∗
2
(Figure 3.1a) rises linearly with iron
concentration for both 1.5T and 3T. The ratio of the slopes (i.e. the predicted RE
at 3T relative to 1.5T) was 2.01± 0.01 (mean± std). Simulated 1.5T values fall
within the 95% confidence intervals derived from liver biopsy studies in humans
4
.
Simulated R
2
estimates (Figure 3.1b) follow a concave downward pattern with
increasing iron concentration at both 1.5 and 3T; this curvilinearity results from
increased static refocusing at high iron concentrations
57,74
. While simulated R
2
is
higher at 3T than at 1.5T, the effect is not as large as for R
∗
2
. The 1.5T R
2
-iron
calibrationfallswithinthe95%confidenceboundsderivedfromhumanliverbiopsy
data
7,4
.
61
Figure 3.5a shows the relationship between R
∗
2
at 3T and 1.5T for both simu-
lation and patient data. The R
∗
2
values are highly correlated with an r
2
of 0.999.
The slopes of the best fit lines were 2.01± 0.01 for the model and 2.00± 0.06
for the patient and control data. Thus, within measurement precision, both model
and patient data demonstrated a two-fold increase in R
∗
2
at 3T relative to 1.5T,
in agreement with reference
72
. Bland-Altman analysis of R
∗
2
(3.5a) demonstrated
no significant bias between observed and predicted R
∗
2
with a standard deviation
of 3.6%; predicted R
∗
2
was calculated from the best-fit line of the simulated 3T-
1.5T relationship. Figure 3.5b shows R
2
at 3T versus 1.5T; the model-predicted
relationship was highly linear with an r
2
of 0.996. The regression slope of the
simulated data was 1.47± 0.01, indicating that R
2
at 3T averaged 47% higher
than measured at 1.5T. For the patient data, the regression slope was 1.34± 0.07.
Bland-Altman analysis again demonstrated that observed and best-fit predicted
R
2
(figure 3.5b) were unbiased and had a standard deviation of only 7.2%.
In order to generalize the effect of magnetic field on relaxivity, simulations were
repeated for multiple field strengths. Figure 3.5 shows model-predicted R
∗
2
and R
2
relaxivities over the range 0.25 – 7T, relative to corresponding relaxivities at 1.5T.
For R
∗
2
, the RE was a linear function of field strength, as expected, but for R
2
it
represented a power law relationship (linear on a log-log scale). The equations of
the best-fit lines are given by
E
R2
(B
0
) = 0.8×B
0.56
0
(3.4)
E
R2∗
(B
0
) =−0.0086 + 0.68×B
0
(3.5)
62
where is the field strength in units of tesla. Note that the second equation is very
close to the expected relationship:
E
R2∗
(Y ) =
Y
1.5
(3.6)
Equations 4 and 5 predict RE factors of 2.03 and 1.48, respectively, for 3T. If R
2
and R
∗
2
calibration curves are known at 1.5T, they can be translated to other field
strengths using equations 3.4 and 3.5.
3.4 Discussion
With the increased migration to 3T scanners, existing calibration curves must
be translated to higher fields. 3T MRI scanners offer higher signal-to-noise ratio,
which can be traded for improved resolution or speed. A 2007 study
72
established
the relationship between R
∗
2
at 3T and 1.5T over a wide range of LIC; R
∗
2
increased
two-fold with field strength in agreement with our model predictions. A recent
publication by Meloni et al. also demonstrated doubling of R
∗
2
at 3T compared to
1.5T
60
. Similar relationships have been shown in cardiac tissue
72,60
. In our study,
1.5T simulations were in excellent agreement with in-vivo calibration curves (Fig.
3.1a) and predicted R
∗
2
enhancement was linear with static magnetic field strength
(Fig. 3.5). This result is expected since higher fields proportionally increase the
magnetization of the iron particles through the equation
M =χH (3.7)
where M is the magnetization, χ is the magnetic susceptibility of the particles,
and H is the applied field. At higher iron concentrations, diffusing water protons
63
encounter spatially larger magnetic inhomogeneities and R
∗
2
is primarily deter-
mined by magnetic susceptibility
57
.
On the other hand, R
2
enhancement demonstrated a non-linear relationship
with field strength (Fig. 3.1b, Fig. 3.5). The higher field strength expands the
range of static refocusing, particularly at higher iron concentrations, partially sat-
urating R
2
at high iron concentrations. This occurs because the iron-dependent
field inhomogeneities grow with field strength. This moves more protons near iron
stores into the static refocusing regime in which the phase accrual can be com-
pletely refocused by a spin echo. The increase in size of this regime increases the
likelihood that a spin will experience a static increase in field strength over its
diffusion window rather than a local field inhomogeneity. Thus, R
2
values at 3T
were only 47% higher than values at 1.5T. The experimental agreement of these
predictions at 3T is excellent (Fig. 3.5). Previously, the field dependence of R
2
had been studied only in the heart over a relatively small range of iron concen-
trations
60
.The R
2
enhancement factor between 1.5T and 3T was reported to be
approximately 1.55
75
, comparing favorably with our estimate of 1.47. The in-vivo
estimateforrelaxivityenhancementfromourliverdatashowedanestimateof1.34;
we believe that limitations in the spin echo pulse sequence caused the estimates for
high-iron decay rates to be less reliable than moderate iron loads and will be cor-
rected with improved pulse sequences. It was not possible for our group to validate
our predictions for higher field strengths, but these data establish testable bench-
marks. We acknowledge that the calculation of RE depends on assuming that the
iron-mediated relaxation dominates that of the base tissue. Our RE values are
targeted at patients with moderate to high iron loads; to determine a RE value for
lower iron loads, the relationship in equation 3 must be applied to account for the
nonlinear enhancement in base tissue relaxation rates.
64
From a practical imaging perspective, these simulations have important conse-
quences. Maximum measurable R
∗
2
and R
2
are hardware limited by the minimum
achievable echo time. Since R
2
values scale more slowly with field strength than
R
∗
2
values, it may be easier to use spin-echo measurements to quantify high LIC
concentrations at higher field. R
∗
2
estimation at high field may require specialized
techniques such as the use of free induction decay measurements, center-out radial
acquisitions, ramp sampling, half pulse excitations, or other variations of ultra-
short echo time imaging
76,77
. In this manuscript, we have demonstrated how a
generalized and validated Monte Carlo model can be used to predict relaxivity-iron
behavior at different field strengths. Future extensions of the model could include
simulating a different MRI pulse sequence including, for example, the multi-echo
CPMG sequence. Iron calibration curves have been obtained experimentally for
CPMG sequences
54,55,49
but differ from the spin echo R
2
relationships. The model
can be used to interrogate complicated CPMG behavior and expose complex inter-
plays among proton diffusion, effective particle size and inter-echo spacing. Fur-
thermore, underlying mechanisms of the nonexponential nature of MRI signal in
the presence of magnetic inhomogeneities can also be studied
49,56
. Lastly, accurate
values for diffusion coefficient (D) of protons in liver tissue are currently lacking;
even the published value of 0.76
51
has a large standard deviation of 0.27. More
recent estimates of the diffusion coefficient show standard deviations of 25-50%
of the estimated ADC
78
. The virtual liver model can be used to calculate an
‘effective D’ and test whether there is any systematic dependence on iron concen-
tration. Accurate values of D are critical for structure, motion and time sensi-
tive sequences like CPMG. It would also be interesting to see if field-dependent
relaxation enhancement (Fig. 3.5) is modified by the diffusion coefficient. R
∗
2
65
enhancement should not change since R
2
’ is unaffected by D while the effect on R
2
enhancement is not clear since R
2
is systematically altered by changes in D
57
.
Figures 3.1 and 3.5 demonstrate some variability that may appear to be iron-
load dependent. Because the iron geometries are generated in an independent
manner, the variability in RE with iron load is a result of the stochastic nature of
the iron generation process rather than the random proton paths. Each simulated
sample represents a single patient and decreasing the variability would require
numerous simulations at each iron load for computational efficiency. These iron
geometries were reused across the field strengths so some apparent variation is
indicative of a single iron distribution’s properties rather than systematic depen-
dence on iron load. This variability could be reduced by performing multiple
simulations at each iron load and averaging the results.
This study was limited by modest validation with experimental data. For the
field-dependent study, R
∗
2
and R
2
was measured in only 6 subjects with significant
iron overload. However, these data spanned a wide range of LIC measurements
(~3-35 mg/g dry wt.)
7
and were in excellent agreement with the model. Since the
choiceofR
∗
2
measurementprotocolrequiredasubjectivedecision, itispossiblethat
a selection bias could be introduced into the high-iron R
∗
2
estimates. Ongoing 3T-
1.5T comparisons in larger patient populations will provide further validation of
the model. We additionally hope to perform scanning at additional field strengths
when such a scanner is available to us. At 3T and above, a customized pulse
sequence will be required to quantify higher R
∗
2
and R
2
values than measured in
the present study. Additionally, no systematic study into the relationship between
the hemosiderin-ferritin ratio and iron load has been conducted; it is conceivable
that molar magnetic susceptibility may depend on liver iron burden.
66
Wehavedemonstratedthatacomputationalmodelutilizingrealisticliverarchi-
tecture and iron morphology can likely extend iron calibrations to higher magnetic
field strengths. Characterization of the R
2
-iron calibration at 3T is novel and
may improve patient access to LIC estimates at centers having only 3T scanners.
However, the real power of the model lies in predicting changes to R
∗
2
and R
2
cali-
bration curves in response to modifications of MRI pulse sequences, field strength,
and systemic disturbances in tissue iron distribution. Non-idealities of the imaging
sequences can also be easily modeled to determine their impact on iron calibra-
tion curves. Understanding key parameters of the relaxivity-iron behavior can
also help in creating tissue-specific models (through autopsy studies) for organs
which iron concentration cannot be probed via biopsy e.g. heart, kidney, and
pancreas. While in silico calibration curves always warrant targeted experimental
verification, Monte Carlo simulation can greatly reduce dependence on expensive
validation studies, shortening the design cycle for novel techniques.
3.5 Acknowledgements
We would like to acknowledge the following sources of funding: General Clin-
ical Research Center (National Institutes of Health, RR00043-43), Department of
Pediatrics at Children’s Hospital Los Angeles (CHLA), National Institute of Dia-
betes, Digestive and Kidney Diseases (1 RO1 DK097115-01A1), National Heart
Lung and Blood Institute of the National Institutes of Health (1 R01 HL75592-
01A1), Novartis Pharma AG., The Wright Foundation, Saban Research Institute
at CHLA. Computation for the work described in this paper was supported by
the University of Southern California Center for High-Performance Computing and
Communications (hpcc.usc.edu).
67
Figure 3.1: Comparison between simulated relaxivities (x) and clinical calibration
curves at 1.5T for both R2* (a) and R2 (b). The clinical calibration curves are
reproduced from the literature
7,4
, and represent the behavior of in vivo patient
data from large clinical trials. Simulated relaxivities at 3T(o) are included for
comparison, although no corresponding clinical calibration curves exist. Note that
the model predictions for R2* are highly linear and in agreement with the clinical
calibration curves at 1.5T.
68
Figure 3.2: Relationship between relaxation rates at 3T and 1.5T. For both R2*
(a) and R2 (b), model predictions (x) were highly linear (R>0.99) across field
strength, and in good agreement with in vivo patient data (o).
69
Figure 3.3: Enhancement of R2* and R2 relaxivities with field strength, relative to
1.5T. For R2*, the predicted enhancement varied linearly with field strength, while
it was curvilinear for R2. At 3T, the predicted relaxivity enhancements agree well
with the values calculated from in vivo data.
70
Figure3.4: Bland-Altmanplotsbetweenmatchedpairsof3Tsimulatedandpatient
data. R2* (a) showed no significant bias and a standard deviation of 3.6%. R2
(b) also showed no bias and a standard deviation of 7.2%.
71
Chapter 4
Spin Echo-Based Liver Iron
Estimates Require B
1
+
Inhomogeneity
Abstract
4.0.1 Purpose
Magneticresonanceimagingisanimportantimagingmodalitytonon-invasively
assess liver iron. RF transmit (B
+
1
) inhomogeneity is known to cause spatial inten-
sity variation that can lead to quantitation errors. In this work, we assess the
severity of B
+
1
inhomogeneity in patients at both 1.5 and 3 Tesla.
4.0.2 Methods
A patient study probed the mean and spatially-dependent excitation error in
spin echo and gradient echo image series. A Monte Carlo simulation framework
was used to quantify the R
2
(1/T
2
) and R
∗
2
(1/T
∗
2
) decay rate errors resulting from
a wide range of B
+
1
errors over the clinically-relevant range of liver iron loads.
72
4.0.3 Results
The patient study revealed that 1.5T and 3T both show significant spatial B
+
1
variationthatvariesbetweenpatients; 3Timagesalsodemonstrateunderexcitation
leading to over 30% error in achieved flip angle. Simulation results estimate that
modest flip angle errors lead to significant R
2
estimate errors that may affect care
and show disagreement with R
∗
2
-based iron estimates.
4.0.4 Conclusion
Voxel-wise error compensation in R
2
estimates is critical at 3T and will improve
accuracy of iron estimates at 1.5T.
4.1 Introduction
Chronic anemias such as thalassemia and sickle cell disease represent the most
common genetic disorders in the world. Transfusion therapy in these patients pro-
duces severe iron deposition in the liver and other organs, leading to cardiac and
endocrine dysfunction and liver cirrhosis. Iron overload in transfusional siderosis
cannot be treated with phlebotomy; instead, patients receive iron chelators that
bind and remove iron with dosing specific to their tissue iron content, necessitating
reliable iron quantitation techniques. Before 2005, needle biopsies were required
to quantify liver iron, with their attendant risks
21
and sampling error
22,23,24
. Since
then, magnetic resonance imaging systems have become key tools for diagnosing
and monitoring iron overload disorders such as transfusional siderosis in sickle cell
disease and thalassemia, hemochromatosis, liver disease, and a number of neu-
rodegenerative disorders. Both transverse relaxivity and magnetic susceptibility
73
measurements have been used to estimate tissue iron concentrations in the liver,
heart, endocrine glands, and brain.
MRI-based iron quantitation at 1.5 Tesla(T) is now standard of care
79
but iron
quantitation in the liver using high-field scanners (3T and above) is limited by
rapid signal decay and susceptibility artifacts. When increasing the field strength
from 1.5T to 3T, field-dependent enhancement causes R
∗
2
(1/T
∗
2
) decay to double,
leading to transverse decay below 0.5 ms in organs such as the liver, well below the
range standard gradient-echo techniques can reliably quantify
58
. Spin echo-based
R
2
(1/T
2
) estimates have shown potential to overcome these limitations at 3T
and already see widespread use at 1.5T
36
. However, spin echo estimates are more
susceptible to spatially-varying excitation error (also called B
+
1
inhomogeneity)
that lead to incorrect flip angles, a well-characterized imaging confounder in high
field
80,81
. Quantifying and correcting for this inhomogeneity could lead to more
accurate liver iron concentration (LIC) estimates.
In this work, we measured B
+
1
scale inhomogeneity at 1.5T and 3T in patients
over a broad range of iron burdens. The scale of the inhomogeneity was used to
simulate the estimate error in R
2
-based LIC estimates at both field strengths using
a Monte Carlo model. We demonstrate significant spatial B
+
1
scale inhomogeneity
at both 1.5T and 3T and show that even modest B
+
1
scale error leads to clinically-
relevant quantitation error across the physiologic LIC range.
4.2 Materials and Methods
4.2.1 Patient Population
Study participants were selected from a population of patients at the Chil-
dren’s Hospital of Los Angeles (CHLA), undergoing clinical treatment for iron
74
overload primarily resulting from transfusional treatment of sickle cell disease,
thalassemia, and other rare anemia syndromes. Participants were recruited and
provided informed consent to participate in an IRB-approved study (CHLA Study
CCI-14-00034). Each participant received a clinically indicated MRI assessment
for iron overload on the 1.5T scanner; a similar research protocol was completed
at 3T.
4.2.2 Patient Assessment
Magnitude-only images were acquired on single-RF-transmit 1.5T and 3T clini-
cal scanners (Philips Achieva, v3.2.2, Best, Netherlands) using 16-element SENSE-
XL torso coils. Liver iron estimates were obtained at 1.5T using a 3-slice gra-
dient echo acquisition with the following parameters: 16 echoes linearly spaced
with TE/TR=0.96-11.47/50ms, FA=30
◦
, matrix/voxel=72x67/1.25x1.25x10mm,
BW=4409Hz/pixel. R
∗
2
estimates were made in hand-segmented regions of inter-
est (ROI) in the liver and an exponential+constant model (see below) was fit to
the data using Levenberg-Marquardt damped least squares minimization with soft-
ware developed at CHLA in MATLAB (Mathworks, Natick, MA); LIC estimates
are made using a R
∗
2
-LIC calibration curve derived from biopsy
4
. The signal model
chosen was:
S(t) =S
0
e
−R
∗
2
t
+c (4.1)
where S(t) represent echo intensity at each echo time t, S
0
represents signal inten-
sity at t=0, R
∗
2
represents relaxation rate, and c represents noise bias.
B
+
1
maps represented in B
+
1
scale (100*[B
+
1 achieved
/ B
+
1 desired
]%) were obtained
at 1.5T and 3T in a single slice using a dual repetition time (TR) B
+
1
mapping
75
sequence
82
with TE/TR
1
/TR
2
=3ms/20ms/120ms, bandwidth of 2894Hz/pixel,
voxel size of 4.2x4.2x8 mm
3
, and one signal average. A second set of B
+
1
maps
were obtained at both fields using an echo time of one millisecond to ensure that
we could sample severely iron loaded patients who demonstrate particularly rapid
T
∗
2
decay.
The maps were manually segmented to quantify the B
+
1
scale inhomogene-
ity found in an iron overloaded patient population. B
+
1
maps were assessed for
dependence on patient weight, BMI, and clinical iron-load. Aggregate patient B
+
1
maps were averaged by non-rigidly warping individual maps to a canonical liver
shape. Because of imperfect registration, some pixels in the canonical liver shape
received contributions from <5 patients and were excluded; each pixel was prop-
erly weighted according to the number of contributing patients. The canonical B
+
1
maps were used to estimate spatial statistics in the right and left lobe.
B
+
1
maps were validated in a phantom (0-16 mM MnCl
2
vials in a 0.5 mM
MnCl
2
bath) with transverse decay rates as low as 1.7 ms prior to use in patients
to ensure that the B
+
1
map had sufficient dynamic range to reliably map the patient
population.
4.2.3 Simulation
An internally developed simulation framework written in MATLAB was used
to create physiologically realistic liver iron geometries in-silico over a range of 1-
50
mg
⁄g (mg-iron/g-dry tissue weight). A detailed description of this model may
be found in previous reports
58,68,57
. Briefly, liver tissue was modeled as 80 μm
cubes of liver tissue containing 64 cuboidal hepatocytes and 18 cylindrical sinusoid
regions
68
. Iron overload was modeled by distributing spheres of iron in the hepa-
tocytes using Gamma statistical distributions describing sphere size and spacing.
76
From the iron distributions, magnetic field disturbances were calculated based on
the field strength and magnetic susceptibility of iron
68
. Simulated protons were
then diffused through the geometries using a random walk simulation obeying cell
boundaries.
The first version of the simulation framework assumed perfect excitation and
refocusing, ignored pulse bandwidth, and did not model longitudinal magnetiza-
tion or T
1
decay. To model B
+
1
scale inhomogeneities, we implemented a full
Bloch simulator to calculate the 3D magnetization of each proton at every time
step. Thesimulationscalculatedrotationsfrominstantaneousexcitationandinver-
sion pulses, realistic iron-free T
2
/T
1
relaxation rates of 42ms/812ms at 3T and
50ms/576ms at 1.5T
59
, and the iron-based phase accrual from the proton’s ran-
dom walk at each 0.05 μs time step. Iron-dependent T
1
changes were ignored due
to minimal longitudinal recovery over the duration of the echo trains simulated
and lack of multiple TRs. Excitations and inversions were modeled as instanta-
neous pulses and achieved angles were scaled by B
+
1
scale for each simulation. For
example, a 90
x
-180
y
single spin echo sequence with 90% excitation efficiency would
be simulated with an excitation pulse of 81
◦
about x and an inversion pulse of 162
◦
about y.
Signals from 2500 separate spin cohorts were superposed to form a transverse
signal for each combination of iron load and B
+
1
scale. Simulations varied B
+
1
scale
from 53% to 127% in single echo and CPMG multiecho spin echo experiments
with 90
◦
excitations and 180
◦
inversions; spin echo and CPMG echo times were
[1.70,2.56,3.86,5.82,8.76,13.2,19.9,30.0] ms and [2.0,4.0,6.0,8.0,10,12,14,16,18,20]
ms, respectively. A complex signal model with a non-negativity constraint on
R
2
was fit to transverse signals to estimate the R
2
relaxation rate of each sample.
R
2
as a function of LIC was determined for each simulated B
+
1
scale by fitting
77
individual results to a 2
nd
order polynomial to capture the nonlinearity of the
behavior.
4.2.4 Software
A historical repository containing snapshots of simulation specification files,
analysis code, and simulation framework, and SHA IDs for sub-repositories may
be found at:
https://github.com/cornercase/snapshot_research_b1_liver_iron
Revision SHA ID: 7858e34557fc5059f50adf311f12af5d464ce337
DOI: 10.5281/zenodo.155955
An actively developed repository containing the simulation framework is available
at:
https://github.com/cornercase/IronBloch
4.3 Results
B
+
1
maps were acquired in 47 subjects (19M, 28F, 29.9±11.6 years of age, 19
β-Thalassemia, 21 Sickle Cell, 7 other rare anemia, LIC=0.2-41.5
mg
⁄g). Mean
B
+
1
scale was found to be uncorrelated with BMI and weight at 1.5T and showed
weak, negative correlation at 3T (see Table 4.1). Figure 4.1 demonstrates B
+
1
inhomogeneity in the liver at 1.5T and 3T from nine representative subjects. At
3T, mean B
+
1
scale was low and the standard deviation was high (69.6%±14.6%).
Statisticsaresummarizedintable4.1. Excitationefficiencywassignificantlyhigher
intherightlobethantheleftlobe(rightmean=73.6%, leftmean=62.1%)butthere
wasconsiderableinter-subjectvariability. MeanachievedB
+
1
scalewasindependent
of liver iron burden (1.5T: r
2
= 0.047, p=0.143; 3T: r
2
= 0.051, p=0.127). Both
78
the spatial homogeneity and the mean achieved B
+
1
scale (99.3%±12.3%) were
better at 1.5T compared to 3T; right and left lobe means were 103.3% and 92.0%
respectively. Thephantomstudy(resultsnotincluded)confirmedthatthespecified
dual TR method had sufficient dynamic range to capture the highest expected
physiologic decay rate; the off-resonance effects of iron could not be replicated.
Simulations were performed examining the impact of B
+
1
inhomogeneity on free
induction decay R
∗
2
estimates, multiple single echo R
2
estimates (Figure 4.2), and
CPMG multiecho R
2
estimates (Figure 4.3). The R
∗
2
iron calibration was robust
to B
+
1
errors (not shown); no change in R
∗
2
-LIC calibration was detectable. Spin
echo simulations demonstrate that calibration error increases significantly with B
+
1
deviation above physiologic iron loads in both single-echo and CPMG sequences.
Multi-echo calibrations were more stable over B
+
1
scale errors of±20% but demon-
strated a larger proportional B
+
1
effect than the single echo calibration for extreme
B
+
1
error in moderate to high iron loads. Uncorrected B
+
1
inhomogeneity in single
echoexperimentscausesystematicoverestimationofR
2
inpatientsat1.5T,though
the effect is less pronounced for small values of inhomogeneity at high iron loads.
Single echo R
2
estimates at 3T produce a less pronounced overestimation up to
25
mg
⁄g of iron; B
+
1
scale error causes R
2
estimates to fall dramatically in higher
iron burdens. CPMG sequences show a slight underestimation of R
2
at below 5
mg
⁄g and a systematic overestimation of R
2
above 5
mg
⁄g. Figure 4.2 and Figure 4.3
demonstrate near-symmetry about 100% flip angle efficiency, indicating equivalent
effects of over and under excitation.
79
4.4 Discussion
This is the first study to examine the magnitude of B
+
1
excitation efficiency
in the liver and its potential impact on clinical liver iron estimates. At 1.5T, full
average excitation was achieved in the liver but variation between right and left
lobeswas12%. SignificantlylargerB
+
1
inhomogeneitieswereobservedintheliverat
3T. We had postulated a potential iron effect because B
0
and B
+
1
inhomogeneities
can interact
82
. Because off-resonance from liver iron can exceed 1000 Hz, we
expected that the excitation bandwidth for standard B
+
1
mapping sequences would
be too narrow, though the phantom study demonstrated a sufficiently short TE.
Further, off-resonance can cause slice misplacement. In spite of this, excitation
efficiency was uncorrelated with liver iron and manual evaluation of the images
did not indicate that slices were meaningfully shifted. At 3T, we observed an
unexpected systematic underexcitation in the liver, averaging just 69.6% of our
specifiedflipangleinwhole-liverROIs. Theeffectwasnotobservedat1.5T.Awide
rangeofironloadswasobserved, makingitunlikelythatwehaveshownincomplete
excitation at 3T resulting from doubling of off-resonance effects relative to 1.5T.
The underexcitation was seen in normal controls, leading us to speculate that
incomplete excitation is due to aggressive specific absorption rate (SAR) models.
Manual increases of the transmit gain improved whole-ROI average B
+
1
scale to
near 100% at 3T, though the observed spatial inhomogeneity remained.
In single echo simulations (Figure 4.2), the estimate error appears to be primar-
ily dependent on decay rate rather than field strength. The overestimation of liver
R
2
occurs up to 200-250 s
-1
in both 1.5T and 3T simulation, representing approxi-
mate LIC burdens of 30 and 15
mg
⁄g respectively. For this range of iron burdens, the
apparent R
2
decay increases with B
+
1
scale error as reduction in amplitude of the
later echoes prematurely pulls the fit decay curve down. At decay rates over 250 s
-1
80
in both 1.5T and 3T simulations, the amplitude of the early echoes is significantly
reduced as well. The correspondingly flat decay curves lead to a reduction in R
2
estimate. Although this effect is less apparent in the 1.5T simulation, reduction in
R
2
is visible for iron loads over 40
mg
⁄g and is more notable for higher B
+
1
error. The
significant decrease in R
2
estimates is clear at 3T for moderate-to-high iron bur-
dens. In cases of moderate-to-fast decay, the underexcitation may cause the first
echo to appear substantially darker; this may lead observers to overestimate iron
burden due to the loss of signal intensity even though the iron is not exclusively
responsible for diminished signal intensity.
For CPMG simulation estimates (Figure 4.3), the phase cycling of the echo
pulses leads to “saw-toothing” that envelopes the true decay curve: the odd echoes
have lower amplitudes than subsequent even echoes. For smaller B
+
1
scale errors,
theerrorismostlyself-correcting. AsB
+
1
becomeslarge, asignificantportionofthe
longitudinal magnetization remains after the excitation pulse and is recovered into
the transverse plane when echo pulses are applied; similarly, transverse magneti-
zation is stored in the longitudinal plane when incomplete echo pulses are applied.
The saw-toothing eventually increases such that the first echo amplitude is smaller
than all of the even echoes, even for very high LIC burdens; the resulting fits show
reduced R
2
estimates. The differing behavior of the 1.5T and 3T calibration curves
in the presence of B
+
1
scale error over 27% is primarily a T
1
effect. The longer T
1
at 3T compared to 1.5T causes less longitudinal magnetization recovery, leading
to a less pronounced addition of transverse signal over the course of the echo train.
Later echoes at 3T therefore demonstrate more realistic decay than 1.5T echoes in
the presence of large B
+
1
inhomogeneity. Nonetheless, the inclusion of longitudinal
magnetization and diminished first echo intensity lead to the apparent reduction
of R
2
for high iron loads in the presence of large B
+
1
error.
81
The patient study demonstrated that B
+
1
spatial inhomogeneity and error in
mean whole-liver flip angle were much smaller at 1.5T than 3T. Nonetheless, a 10%
errorinachievedflipangleinapatientwithanLICof10
mg
⁄gincreasesthepredicted
LIC by 30%. While a difference between 10
mg
⁄g and 13
mg
⁄g does not markedly
changethatpatient’sriskassessment,consistentwiththewidespreaduseof1.5TR
2
techniques in clinical practice
4
, B
+
1
inhomogeneity probably worsens the agreement
betweenLICvaluesestimatedbyR
∗
2
andbyR
2
79,83
byaddingpatient-specificerrors
to the R
2
estimate without affecting R
∗
2
. B
+
1
variation could also contribute to the
observed curvilinearity in the R
2
-iron calibration curve
7
. With perfect excitation,
the R
2
-iron relationship is relatively linear over a wide range of LIC’s but even mild
B
+
1
errors introduce marked concavity to the calibration curve. B
+
1
inhomogeneity
could also potentially confound techniques that rely on proton-density estimators
to stabilize LIC measurements at high iron concentrations. Carefully controlled
studies are warranted to determine whether B
+
1
correction could improve R
2
LIC
measurements at 1.5 Tesla.
In contrast, correcting B
+
1
inhomogeneity is an absolute necessity for R
2
-based
iron estimation at 3T. Eliminating the observed mean underexcitation of the liver
at 3T, even in the presence of the spatial flip angle variation, would immediately
improve iron estimates using existing fitting techniques. RF shimming using multi-
transmit RF systems or updates to transmit gain selection algorithms may help
to improve the observed underexcitation and spatial variation. Adiabatic pulses
cannot be used in this context because their long duration precludes the short
echo times necessary to measure signals in high iron load subjects. Further, many
adiabatic pulses demonstrate significant dependence on off-resonance which will
not be known a priori in iron overloaded patients. When B
+
1
homogeneity cannot
be improved, manual or automatic exclusion of voxels experiencing over±25% B
+
1
82
excitation error would improve LIC estimates. It is especially important when
performing iron estimation using multiple small ROIs because sampling of regions
in the far right and far left lobes in an attempt to sample the whole liver will
lead to significant estimate error. It may also be possible to apply voxel-wise
corrections to echo amplitudes based on acquired B
+
1
maps or fit to a signal model
that considers the effects of B
+
1
, though T
1
or R
∗
2
effects may vary with iron load,
thus necessitating an iterative approach. The success of the simulation framework
in this context would allow for patient-specific corrections to be developed and
potentially allow for bespoke excitation pulses to be developed in near-real-time.
4.5 Conclusions
Patient results demonstrate that significant whole-liver underexcitation is
observed at 3T and spatial flip angle variation is observed at both 1.5T and 3T.
Simulation results demonstrate that B
+
1
effects can cause systematic liver R
2
esti-
mation error up to 30% at 1.5T; error worsens significantly at 3T. To ensure accu-
rate diagnosis and treatment of these patients, B
+
1
mapping is essential for error
compensation at 3T. Passive voxel-wise corrective measures such as voxel exclu-
sion or numerical correction should be applied over 25% B
+
1
excitation error. If
available, measures like RF shimming may actively correct B
+
1
error. Further sim-
ulations and signal modelling will be performed to better understand the effect of
very high levels of B
+
1
inhomogeneity on liver iron estimates and develop correction
schemes to improve R
2
estimates.
83
Field Whole (mean
%±std)
Left
(mean %)
Right
(mean %)
B
+
1
Scale vs
Weight Correla-
tion (r
2
)
B
+
1
Scale vs BMI
Correlation (r
2
)
1.5T 99.3±12.3 92.0 103.3 0.0043 (p=0.66) 0.0092 (p=0.52)
3.0T 69.6±14.6 62.1 73.6 0.20 (p=0.0016) 0.11 (p=0.024)]]
Table 4.1: B
+
1
mean scale values in the whole liver and right and left lobes show
that image series from both 1.5T and 3.0T MRI scanners demonstrate significant
spatial variation in B
+
1
scale. Further, 3.0T images demonstrate significant mean
underexcitation. The mean excitation did not correlate with BMI or weight in
1.5T studies. Underexcitation was weakly associated with weight and BMI at 3T.
4.6 Acknowledgements
This research is supported by the National Institute of Diabetes, Digestion and
Kidney Diseases of the National Institutes of Health, grant 1R01DK097115-01A1.
Computation for the work described in this paper was supported by the University
of Southern California’s Center for High-Performance Computing (hpc.usc.edu).
84
Figure 4.1: Spatial maps of B
+
1
scale in patients demonstrate significantly differ-
ent behavior at 1.5T and 3T. 1.5T maps demonstrate largely uniform excitation
patterns and consistently complete excitation. 3T maps demonstrate significant
spatial variation in B
+
1
as well as a mean achieved B
+
1
of only 69.6%.
85
Figure 4.2: Single echo simulations over a wide range of iron loads and B
+
1
inho-
mogeneities demonstrate that iron is overestimated in the presence of B
+
1
inho-
mogeneity at 1.5T. Further, inaccuracies increase with iron load for a given B
+
1
.
Although 1.5T R
2
estimates tend to increase with B
+
1
variation, 3T maps show
the opposite effect due the combination of fast initial decay and lengthened T
1
resulting in artificially flat decay curves. (B
+
1
Fraction = B
+
1
Scale/100)
Figure 4.3: CPMG simulations over a wide range of iron loads and B
+
1
inhomo-
geneities demonstrates that iron is overestimated in the presence of B
+
1
inhomo-
geneity except with low iron loads at high B
+
1
inhomogeneities. (B
+
1
Fraction =
B
+
1
Scale/100)
86
Chapter 5
Ultra-Short Echo Time Images
Quantify High Liver Iron
ABSTRACT
5.0.1 Purpose:
1.5T gradient echo-based R
∗
2
estimates are standard-of-care for assessing liver
iron concentration(LIC). Despite growing popularity of 3T, echo time (TE) lim-
itations prevent 3T liver iron quantitation in the upper half of the clinical
range(LIC'20
mg
⁄g). Inthiswork, a3Dradialpulsesequencewasassessedtodouble
the dynamic range of 3T LIC estimates.
5.0.2 Theory and Methods:
The minimum TE limits the dynamic range of pulse sequences to estimate
R
∗
2
. 23 chronically-transfused human volunteers were imaged with 1.5T cartesian
gradientecho(1.5T-GRE),3Tcartesiangradientecho(3T-GRE),and3Tultrashort
TE radial(3T-UTE) pulse sequences; minimum TEs were 0.96, 0.76, and 0.19 ms,
respectively. R
∗
2
was estimated with an exponential signal model, normalized to
1.5T equivalents, and converted to LIC. Bland-Altman analysis compared 3T-
based estimates to 1.5T-GRE.
87
5.0.3 Results:
LIC by 3T-GRE was unbiased versus 1.5T-GRE for LIC≤25
mg
⁄g (sd=9.6%);
3T-GRE failed to quantify LIC>25
mg
⁄g. At high iron loads, 3T-UTE was unbiased
(sd=14.5%) compared to 1.5T-GRE. Further, 3T-UTE estimated LIC up to 50
mg
⁄g,
exceeding 1.5T-GRE limits.
5.0.4 Conclusion
3T-UTE imaging can reliably estimate high liver iron burdens. In conjunction
with 3T-GRE, 3T-UTE allows clinical LIC estimation across a wide range of liver
iron loads.
5.1 Introduction
Chronic anemias such as thalassemia and sickle cell disease represent the most
common genetic disorders in the world. Transfusion therapy in these patients
produces severe iron deposition in the liver and other organs, leading to cardiac
and endocrine dysfunction as well as liver cirrhosis. Iron overload in transfusional
siderosis cannot be treated with phlebotomy; instead, patients receive iron chela-
tors that bind and remove iron. Dosing must be adjusted based on tissue iron con-
tent, necessitating reliable iron quantitation techniques. Before 2005, needle biop-
sies were required to measure liver iron, with their attendant risks
21
and sampling
error
22,23,24
. Since then, magnetic resonance imaging systems have become impor-
tant tools for diagnosing and monitoring iron overload disorders including sickle
cell disease, thalassemia, hemochromatosis, and neurodegenerative disorders
4,84
.
Both transverse relaxivity and magnetic susceptibility measurements have been
88
used to estimate tissue iron concentrations in the liver, heart, endocrine glands,
and brain.
MRI-based iron quantitation at 1.5 Tesla(T) is now standard of care
79
. How-
ever, it is estimated that 50% of new magnet installations are 3T and some imaging
centersuseexclusively3Tmagnets; thisnecessitatesdevelopmentofrobustimaging
techniquesforhigh-fieldsystems. Previousstudieshavevalidatedquantitationover
lower iron burdens at 3T
72,60,85
. However, liver iron quantitation with high-field
scanners (3T and above) remains limited by rapid signal decay. When increasing
the field strength from 1.5T to 3T, field-dependent enhancement causes R
∗
2
(1/T
∗
2
)
decay to approximately double, leading to transverse decay times below 0.5 ms
in the liver, well below the range standard gradient-echo techniques can reliably
capture
58
. Inadequate sampling of rapidly decaying signal components leads to an
underestimate of liver iron concentration (LIC). The development of ultra-short
echo time (UTE) sequences has dramatically decreased the minimum achievable
echo time (TE), enabling acquisition of ultra-fast decay species
86
. UTE has shown
promisetoperformstructuralimagingofcartilageandbone. ThereducedTEcould
potentially lead to significantly increased dynamic range in quantitative imaging
approaches used to non-invasively estimate LIC at 3T and above.
In this work, we measured liver R
∗
2
in human volunteers receiving treatment
for transfusional iron overload using cartesian gradient echo (GRE) and UTE
sequences. We obtained 3T LIC estimates in milligrams of iron per gram of dry
liver (
mg
⁄g) for comparison with clinical LIC estimates obtained at 1.5T using a
previously derived relationship between liver R
∗
2
at 1.5T and 3T
58
. We demon-
strate that 3D radial UTE imaging increased the achievable dynamic range of LIC
estimates to match, and possibly exceed, estimates from cartesian gradient echo
89
images obtained at 1.5T, providing a reliable means to quantify high liver iron at
3T.
5.2 Methods
5.2.1 Participant Population
Study participants were selected from a population of patients at the Children’s
Hospital of Los Angeles (CHLA) undergoing chronic transfusion therapy for sickle
cell disease, thalassemia, and other rare anemia syndromes. Participants provided
informed consent to participate in an IRB-approved study (CHLA Study CCI-14-
00034). Each participant received a clinically indicated MRI assessment for iron
overload on a 1.5T scanner followed by a research imaging protocol at 3T. Imaging
data from a repeat clinical visit was available for a single participant and was
weighted proportionally in resulting statistics.
Participant Assessment
Images were acquired on single-RF-transmit Philips Achieva 1.5T and 3T clin-
ical scanners (software revision v3.2.2 or v5.1.7, Philips HealthTech, Best, Nether-
lands) using 16-element SENSE-XL torso coils. Clinical liver iron estimates were
obtained from 1.5T R
∗
2
estimates using a 3-slice gradient echo acquisition, hence-
forth referred to as 1.5T-GRE. Two series - a 16-echo Cartesian gradient echo
series (3T-GRE) and a set of seven single-echo, center-out, stack-of-stars, 3D
radial images with varying echo times (3T-UTE) - were acquired at 3T. Com-
pared to cartesian gradient echo, center-out radial trajectories facilitate signifi-
cantly reduced echo times by beginning readout from the center of k-space; the
removal of the dephasing gradient prior to readout allows the echo to be acquired
90
more quickly after excitation. 3T-UTE echo times were selected with approxi-
mate log spacing to maximize dynamic range. The minimum echo time of 0.19
ms was selected to facilitate quantitation of LIC≥ 60
mg
⁄g; other scan parameters
including gradient strength and slice thickness were selected to permit the short-
est echo time. Relevant sequence parameters for all series are available in Table
5.1. All images were reconstructed on-scanner; the default reconstruction was used
for 1.5T-GRE and 3T-GRE series while 3T-UTE images were reconstructed with
the Philips SENSE implementation without undersampling. Clinical and research
liverR
∗
2
estimatesweremadepixelwiseinhand-segmentedregionsofinterest(ROI)
encompassing the whole liver but avoiding large vasculature and biliary structures.
R
∗
2
estimates were made by fitting an exponential+constant (exp+c) model (see
equation 5.1) to the data using Levenberg-Marquardt least squares minimization
with previously-validated software developed at CHLA in MATLAB (Mathworks,
Natick, MA)
60
. The exp+c signal model, which was used to fit 1.5T-GRE, 3T-
GRE, and 3T-UTE data, is as follows:
S(t) =S
0
e
−R
∗
2
t
+c (5.1)
where S(t) represents echo intensity at each echo time t, S
0
represents signal
intensity at t = 0, R
∗
2
represents relaxation rate, and c represents noise bias and
contributions from slow-decay species. The fitting model was chosen for all scans
to allow for comparison of the 3T-UTE technique with our existing, clinically-
established analysis toolbox
60
. R
∗
2
estimates obtained at 3T were converted to
1.5T R
∗
2
equivalents using a previously-derived relationship
58
:
R(Y )−R
iY
= (R(1.5T )−R
i1.5T
)∗E
R
(Y ) (5.2)
91
E
R
∗
2
(B
0
) =−0.0086 + 0.68∗B
0
(5.3)
where R(Y ) represents the relaxation rate R
∗
2
at a given field strength Y, R
iY
representstherelaxationratefornormalliveratfieldstrengthY,E
R
(Y )represents
therelaxationrateenhancementforR
∗
2
from 1.5T tofieldstrengthY =B
0
givenby
E
R
∗
2
(B
0
). Normal liver R
∗
2
values for 1.5T and 3T were assumed to be 31.1 Hz and
44.4 Hz, respectively, based on internally derived estimates from healthy controls.
These values, derived from a young cohort of patients, are similar to but slightly
lower than previously published values derived in adults
72
; this disagreement is
expected based on the difference in age between the subject populations and the
known increase in liver iron accumulation with age
87,31
.
All LIC estimates were made using the 1.5T R
∗
2
-LIC calibration curve derived
from biopsy
4
. Bland-Altman analysis comparing 1.5T-GRE LIC estimates with
3T-UTE and 3T-GRE LIC estimates was performed; based on the expected failure
of 3T-GRE techniques at high iron burdens, participants were assessed in two
separate cohorts: LIC≤25
mg
⁄g and LIC>25
mg
⁄g .
Phantom
R
∗
2
estimates were validated in a phantom (0-24 mM MnCl
2
vials in a 0.25
mM MnCl
2
bath) constructed of
1
⁄4”-plexiglass sheet measuring 16.5”x12.5”x7.5”.
100-mL Nalgene vials containing (0.0, 0.5, 0.75, 1.0, 1.5, 2.0, 2.5, 3.5, 5.0, 8.0,
12.0, 16.0, 24.0) mM MnCl
2
were suspended on the center line along the longest
dimension or offset 2.25” laterally from the center line. Vials were staggered in
a honeycomb layout to reduce inter-vial susceptibility effects. The phantom was
imaged at 3T with the 3T-GRE and 3T-UTE protocols.
92
Simulation
A simulation evaluating the effects of proton-density fat fraction (PDFF) on
exp+c-derived LIC estimates was conducted. Signals were simulated by super-
posing water and a 6-peak fat model
88
with PDFFs of 0%, 5%, 10%, and 20%.
Decay was simulated as a mono-exponential and decay rates were calculated from a
previously-derived LIC-R
∗
2
relationship
4,58
up to 45
mg
⁄g. Noise was added to match
an approximate first-echo SNR of 40 for images obtained in a normal liver. Signals
for each LIC-PDFF combination were simulated 20 times to provide pixelwise-like
data and sampled at TEs matching the 3T-UTE and 3T-GRE protocols. Sam-
ples were fit using the same exp+c technique as imaging data, pixelwise-like-LIC
estimates were averaged, and the resulting LIC error was determined.
Software
A historical repository containing snapshots of relevant code can be
found at https://github.com/cornercase/snapshot_research_ute_vs_gre_
LIC/releases/tag/v1.1
or via it’s DOI: 10.5281/zenodo.570291.
89
RESULTS
Phantom
Analysis of phantom results (figure 5.1) demonstrated that the 3T-UTE and
3T-GRE protocols successfully quantified R
∗
2
up to 2830 Hz and 1910 Hz, respec-
tively, equivalent to LICs of 35.8
mg
⁄g and 24.4
mg
⁄g. The 3T-GRE results demon-
strated catastrophic failure in the highest concentration vial, showing saturation
93
of R
∗
2
rather than the expected linear increase; the sample was excluded from anal-
ysis. No saturation was observed in the UTE data. Linear regression of 3T-UTE
data gave the following relationship: R
∗
2
3T−UTE
= 117×[mM MnCl
2
] + 1.6 (r
2
=
0.996, r
2
adj
= 0.995). Regression of 3T-GRE results demonstrated a similar linear
relationship: R
∗
2
3T−GRE
= 120×[mM MnCl
2
] + 3.5 (r
2
= 0.999, r
2
adj
= 0.999).
The regressions show less than 3% disagreement in the slope of the R
∗
2
-MnCl
2
relationship.
5.2.2 Participant
A set of 24 imaging series were gathered from 23 participants (11M/12F,
21.5±12.0 years,11 Thalassemia Major, 8 Sickle Cell Disease, 4 other rare ane-
mia, LIC=1.9-40.7
mg
⁄g); additional demographic information is summarized in
table 5.2. Subjects were generally lean, had a broad range of iron overload, and
had mild transaminitis.
Figure 5.3 demonstrates the scatter plot of LIC estimates measured with 3T-
UTE and 3T-GRE compared with LIC estimates from 1.5T-GRE; a line of unity
is displayed for reference. The 3T-GRE data (represented by
) track the unity line until LIC exceeds 22
mg
⁄g (R
∗
2
≈1750 Hz) and then plateau,
similar to the plateau demonstrated by 24 mM MnCl
2
in figure 5.1. In contrast,
LIC by 3T-UTE (represented by ) tracks the unity line up to 40 mg/g. For
some clinical iron estimates near 40
mg
⁄g, the approximate upper limit of the 1.5T
protocol, 3T-UTE produces higher iron estimates than 1.5T-GRE (see shaded
region, figures 5.3&5.5).
The agreement between cartesian GRE measurements at 3T and 1.5T is
summarized by Bland Altman analysis (figure 5.4). For subjects with clinical
LIC≤25
mg
⁄g (represented by ), the 1.5T-GRE and 3T-GRE are unbiased with
94
respect to each other with a standard deviation of 9.6%. Participants with
LIC>25
mg
⁄g (represented by ) demonstrated large bias (37.3%±9.8). The fail-
ure of 3T-GRE fits at high iron loads causes LIC by 3T-GRE to be uncorrelated
with LIC by 1.5T-GRE, causing the bias to grow with the average of the two LIC
estimates.
Figure 5.5 demonstrates the Bland Altman relationship between LIC derived
from 3T-UTE versus 1.5T-GRE. For LIC>25
mg
⁄g , 3T-UTE LIC estimates were
unbiased with a standard deviation of 14.5%. For lower LIC values, UTE overes-
timated LIC compared to 1.5T-GRE by an average of 15.7%±21.9%.
Simulation
Simulation results demonstrated that physiologic amounts of liver fat cause
estimates of LIC by 3T-UTE to overestimate liver iron compared to 3T-GRE. 3T-
UTE error grows with PDFF but is relatively stable across iron loads above 5
mg
⁄g.
after an initial over-estimate of liver iron. Below 5
mg
⁄g, error in LIC by 3T-UTE
grows for all PDFFs, suggesting the maximum echo is too short for the 3T-UTE
protocol to reliably quantify slow decay in the presence of noise, similar to the bias
demonstrated in 5.5. In constrast, the 3T-GRE protocol is relatively robust to
fat effects until the signal decay approaches the upper limit of the dynamic range.
Approaching the upper range limit, LIC by 3T-GRE overestimates LIC by up to
6% before failing. Results are further summarized in a supplemental figure.
DISCUSSION
Rapid decay rates have remained a persistent challenge for estimating high
liver iron loads at 3T and higher field strengths. Although iron quantitation in the
95
heart and liver have been reported at 3T
90,91
, this is the first study to match the
dynamic range of 1.5T-GRE sequences. Our existing 3T-GRE techniques offered
excellent robustness up to 20-25
mg
⁄g, though the exact limit is scanner-dependent
due to differing software options that limit echo spacing and first echo timing and
hardware limitations such as coil blanking intervals and noise characteristics. The
UTE protocol in this study was specifically designed to supplement an existing
clinical quantitation workflow rather than replace it in order to maximize adopt-
ability and permit the use of existing clinical tools without the need for algorithm
or workflow changes. Both the phantom data (figure 5.1) and the human data
(fig 5.3-5.5) suggest that the 3T-UTE can quantify R
∗
2
up to an LIC equivalent of
≥40
mg
⁄g. UTE therefore nearly doubles the range of iron compared to the 1900 Hz
(LIC≈24
mg
⁄g) limit of our 3T-GRE sequence. Further, 3T-UTE may even exceed
the dynamic range of the 1.5T-GRE protocol, quantifying R
∗
2
up to LIC≥49.2
mg
⁄g.
Together, UTE and GRE at 3T in their current forms allow a comprehensive diag-
nostic alternative to 1.5T assessment.
Based on robust performance of 3T-GRE for low LIC quantitation
72
, we opti-
mized the 3T-UTE sequence for performance at iron loads over 20
mg
⁄g. As such,
we chose to acquire UTE data to a maximum TE of 2.0 ms. One downside of
this approach is that only one fat oscillation was sampled. At 3T, out-of-phase fat
oscillations can cause a substantial reduction in magnitude of the echoes between
0.5 and 1 ms. The combination of these fat oscillations and the 3T-UTE protocol’s
chosen echo times lead to non-obvious interactions with the exp+c fitting model
92
,
which assumes that the fat behavior can be sufficiently modeled by the bias term
in equation 5.1. For LICs between 15
mg
⁄g and 20
mg
⁄g, which demonstrate R
∗
2
decay
rates between 1200 Hz and 1800 Hz at 3T, the fat oscillations cause an apparent
acceleration in R
∗
2
decay while the exponential decay suppresses fat oscillation data
96
from the later echoes. This causes overestimation of R
∗
2
and artificially increases
LIC from 3T-UTE between 15 and 20
mg
⁄g. Over this range, the fat oscillations
also interact unfavorably with the bias coefficient from equation 5.1. We found
the S(0)-normalized bias, c, from equation 5.1 tended to be 2-4 times larger for
the 3T-UTE fit than the 3T-GRE fit over the LIC range of 15-20
mg
⁄g; over the
higher and lower LIC ranges, the bias values were similar. This behavior is consis-
tent with previous studies
92
. We speculate that extending 3T-UTE to longer echo
times would improve the quantitation because the bias term will stabilize with
increased oscillations.
The pixelwise exp+c fitting model (equation 5.1) was selected based on its
robustness, biopsy validation, and lack of strict protocol and data export require-
ments
4,93
. Such considerations may be important in driving clinical adoption,
especially when clinical facilities have difficulty acquiring or exporting phase infor-
mation or hope to assess UTE images with established curve fitting workflows
designed for cartesian GRE techniques. Including spectral models of fat in the
fitting algorithm may address the challenges related to bias while also allowing for
the simultaneous estimation of tissue iron and fat content. This would overcome
the 3T-UTE’s previously-noted overestimation of LIC for moderate iron loads.
However, this approach is more challenging due to stricter data and computa-
tional requirements
94
. Further, the addition of fit parameters has been shown to
increase the standard deviation of the R
∗
2
estimates
92
. In certain clinical settings,
it may be preferable to choose between the UTE and GRE estimates depending
on the patient’s expected iron load. In this case, models such as exp+c, which
lack explicit fat models, provide a reliable iron estimate; other fitting models such
as truncated exponential
94
should work as long as appropriate R
∗
2
-LIC calibration
curves are used
95,90
. Though out of scope for this study, we speculate that R
∗
2
97
estimation with complex fitting techniques will meet or exceed the performance of
the magnitude-based technique presented here.
Bland-Altman analysis of the 3T-UTE data shows that it is unbiased with
respect to 1.5T-GRE estimates for LIC>25
mg
⁄g. Disagreement between 3T-UTE
and 1.5T-GRE estimates for LIC40
mg
⁄g (shaded region, Figures 5.3,5.5) suggest an
improvement in the dynamic range from 3T-UTE compared to 1.5T-GRE rather
than a failure of 3T-UTE. Though this could not be experimentally verified, the
relationship between 3T-UTE and 1.5T-GRE was identical to the plateau observed
between 3T-GRE and 1.5T-GRE; i.e., values exceeding the dynamic range “pile
up.” In retrospect, the study would have benefitted from UTE at 1.5T, as well, to
accurately measure LIC>40
mg
⁄g. We have subsequently integrated 1.5T-UTE into
our clinical protocol.
The clinical applicability of the UTE technique is further supported by its
robustness to chest wall motion. In contrast to GRE sequences, which can show
significant respiratory ghosting in free-breathing subjects, no coherent ghosts were
visible in free-breathing UTE scans. The demonstrated robustness of the free-
breathing protocol will immediately improve LIC estimates for participants who
cannot complete a breath-hold of over 10 seconds. Patient comfort is improved
through the negation of breath-holds and the reduction in scan time due to
decreased protocol duration and reduction in repeated series. SNR improvement
relative to breath-holding has been demonstrated with triggered, free-breathing
UTE imaging
96
, but further studies will be needed to compare quantitative differ-
ences between free-breathing and breath-hold protocols in iron imaging.
Although many techniques that shorten TE compared to cartesian sequences
are considered UTE sequences
97
, the term “UTE” is often associated with 2D
imaging that achieves short echo times by combining data from two excitations
98
with half-sinc pulses that use opposite slice-selection gradients
98
. The shortened
TE is achieved because readout takes place in the space traditionally occupied by
the right tail of the sinc pulse. We previously attempted LIC quantitation on both
Philips and GE magnets using half-pulse UTE but were unable to achieve reliable
quantitation. We speculate that the severe off-resonance that occurs in iron-loaded
livers, small timing inaccuracies, and slice-profile effects
86
led to the failure of
this approach. In contrast, 3D UTE techniques such as the one chosen for this
study use a non-selective excitation pulse, which have demonstrated more reliable
R
∗
2
quantitation in phantoms
86
. The non-selective UTE pulse is high-bandwidth
and has a lower duration than the half-sinc pulses used in slice-selective UTE,
preventing off-resonance from causing under-excitation. We believe that this key
difference allows 3D UTE to succeed where 2D UTE failed.
Although this study focused on quantitation at 3T, the UTE protocol shows
promise at other field strengths. Most notably, it may increase the dynamic range
at 1.5T, resolving the demonstrated upper limit of 41
mg
⁄g. Further, the imaging
challenges resulting from the near-linear increase of R
∗
2
with field strength will
compound at higher field strengths. UTE imaging will likely be the best approach
to quantify even low and moderate liver iron at higher field strengths such as 7T.
We therefore expect that the UTE for iron quantitation will grow in popularity at
allfieldstrengths. UTEapproachesmayalsobesynergisticforfat-waterseparation
techniques as well as abdominal QSM
99
.
99
5.3 Conclusion
Non-selective, center-out radial UTE imaging is a robust supplement to GRE
for quantifying liver iron at 3T. Our 3T-UTE protocol accurately tracked 1.5T-
GRE LIC estimates up to 40
mg
⁄g and potentially measures LICs as high as 50
mg
⁄g.
The UTE pulse sequence was available through a clinical science key on both soft-
ware release 3.2.2 and 5.1.7 Philips scanners and did not require breath-holding.
The 3T-UTE protocol functions as a turn-key replacement for GRE imaging in
high-LIC participants at 3T. Further improvement to the protocol and fitting
approach may allow UTE to measure low and moderate iron concentrations with
the same accuracy demonstrated at high iron.
5.4 Acknowledgments
This study was supported by the NIH National Institute of Diabetes and Diges-
tive and Kidney Diseases R01-DK097115. Clinical science support was provided by
Philips Healthcare. Research space and computational resources were generously
provided by Dr. Krishna Nayak of the Magnetic Resonance Engineering Lab.
100
Parameter 1.5T Gradient Echo 3T Gradient Echo 3T UTE
TEs [ms]
0.96-11.5; 16
linearly spaced
0.76-8.8; 16
linearly spaced
0.19, 0.23, 0.35,
0.60, 0.85, 1.0, 2.0
FOV
(AP[cm]xRL[cm])
30x40 30x40 31x31
Slice ( # x thick-
ness[mm])
3x10 3x10 6x15
Matrix 84x84 84x84 88x88
TR [ms]/FA [deg] 50/30 50/30 5/4
Scan time [sec] 14 14 5 per echo time/35 total
Breath-hold [sec] 14 14 none
Gradient strength Max Max Max
Acceleration No No TFE Factor 200
Table 5.1: Relevant scan parameters
101
Measurement Min Max Mean±StDev
Height [cm] 117 179.8 156.2±15.3
Weight [kg] 20.1 89.7 54.3±17.1
Body Surface Area [m
2
] 0.81 2.1 1.5±.3
Body Mass Index [
kg
⁄m
2
] 14.7 34.3 21.9±5.1
Ferritin [
ng
⁄mL] 199 16300 4483±4890
ALT [
U
⁄L] 18 391 74.5±84.5
Table 5.2: Ranges of demographic and laboratory data for the participant popu-
lation
102

5
10
15
20
25
30
35
40
45
Equivalent LIC [
mg
g
]
0 5 10 15 20 25
0
500
1000
1500
2000
2500
3000
3500
MnCl
2
Concentration [
mmol
L
]
Relaxation Rate R
∗
2
[Hz]

UTE R
2
*
Estimate
UTE Linear Regression
GRE R
2
*
Estimates
GRE Linear Regression (excl 24 mM vial)
Figure5.1: PhantomresultsdemonstratelinearcorrelationofMnCl
2
concentration
and R
∗
2
. Regression analysis demonstrated the following relationships: R
∗
2
-UTE
= 117×[mM MnCl
2
] + 1.6 (r
2
= 0.9955, r
2
adj
= 0.9951, p<0.0001); R
∗
2
-GRE =
120×[mM MnCl
2
] + 3.5 (r
2
= 0.9998, r
2
adj
= 0.9998, p<0.0001). The R
∗
2
-GRE
regressionexcludedthehighest-concentrationvialduetoexpectedfailureoffitting.
95% confidence intervals are shown with dashed lines for each regression.
103
Figure 5.2: Example images demonstrating image quality of 3T-UTE (above) and
3T-GRE(below) first echo images and associated R
∗
2
maps. The image selected
is from a subject with high LIC, causing the failure of the 3T-GRE protocol to
capture sufficient signal to perform R
∗
2
estimation.
104
0 10 20 30 40 50
0
5
10
15
20
25
30
35
40
45
50
55
1.5T Clinical LIC Estimate [
mg
g
]
3T LIC Estimate [
mg
g
]

y=x
UTE fits
GRE fits
Figure 5.3: Scatter plot demonstrating LIC estimates made with 3T GRE and 3T
UTE image series compared with clinical estimates. Catastrophic failure in LIC
estimates is apparent in 3T GRE estimates for participants with clinical iron loads
over 25
mg
/g. Points in the shaded region demonstrate 3T-UTE LIC estimates that
exceed the upper limit that 1.5T-GRE can quantify.
105
0 5 10 15 20 25 30 35
−80
−60
−40
−20
0
20
40
60
80
Percent Difference (Diff ÷ mean)*100
Mean LIC [
mg
g
]
Figure 5.4: Bland-Altman analysis of LIC estimates made with 1.5T-GRE and
3T-GRE series. Solid circles ( ) represent participants with clinical LIC≤25
mg
⁄g
(μ=3.0(not significant), σ=9.6). Unfilled circles ( ) represent participants with
clinical LIC>25
mg
⁄g (μ=37.3,σ=9.8). 95% limits of agreement are shown as dashed
lines. Insignificant bias is demonstrated with a dash-and-dotted line. The bias
demonstrated inthe low-LICcohort is thoughtto be a resultof a lackof sufficiently
long TEs in the UTE protocol; simulation results (supplemental results) for the
3T-UTE protocol in low LIC loads supports this conclusion.
106
0 10 20 30 40 50
−80
−60
−40
−20
0
20
40
60
80
Percent Difference (Diff ÷ mean)*100
Mean LIC [
mg
g
]
Figure 5.5: Bland-Altman analysis of LIC estimates made with 1.5T-GRE and 3T-
UTE series. Solid circles ( ) represent participants with clinical LIC≤25
mg
⁄g (μ=-
15.3,σ=21.9). Unfilled circles ( ) represent participants with clinical LIC>25
mg
⁄g
(μ=-2.6(not significant) σ=14.48). 95% limits of agreement are shown as dashed
lines. Insignificant bias is demonstrated with a dash-and-dotted line. Points in
the shaded region demonstrate 3T-UTE LIC estimates that exceed the upper limit
that 1.5T-GRE can quantify.
107
5 10 15 20 25 30 35 40
−15
−10
−5
0
5
10
15
20
25
30
Actual LIC [mg/g]
LIC Estimate Error [%]

No Fat, UTE
5% PDFF, UTE
10% PDFF, UTE
20% PDFF, UTE
No Fat, GRE
5% PDFF, GRE
10% PDFF, GRE
20% PDFF, GRE
Figure 5.6: Simulation of 3T-GRE and 3T-UTE echo times with 0, 5, 10, and 20%
PDFF over an LIC range of 0.5-45
mg
⁄g demonstrate that increasing fat fraction has
a greater effect on R
∗
2
for the UTE sequence than the GRE sequence. In particular,
the 3T-UTE overestimates LIC more as PDFF increases for a given LIC. Further,
at low LIC, the simulations for PDFF=0% indicate that LIC is overestimated
when noise is present and the decay rate is slow. The magnitude of error due to
physiologically realistic PDFF may explain the increased apparent measurement
variation between GRE and UTE.
108
Chapter 6
Chemical Shift Imaging - A
Spectroscopic Approach to
Quantifying Iron
6.1 Abstract
6.1.1 Purpose
There is significant interest in the simultaneous quantitation of tissue iron and
fat content. However, the effects of iron can confound phase-based fat quantita-
tion techniques or cause catastrophic loss of signal at higher iron loads and field
strengths. In this work, we present a modified chemical shift imaging spectroscopy
pulse sequence developed to assess the feasibility of simultaneous quantitation of
R
2
, R
∗
2
, and fat fraction.
6.1.2 Theory and Methods
The minimum TE limits the dynamic range of pulse sequences to estimate
R
∗
2
. 4 chronically-transfused human volunteers were imaged with 1.5T cartesian
gradient echo(1.5T-GRE), 3T cartesian gradient echo(3T-GRE), and modified CSI
pulse sequences; minimum TEs were 0.96, 0.76, and 3.1 ms, respectively. R
∗
2
was
estimated with an exponential signal model with and without a spectral model
109
for fat. Regression analysis compared CSI to clinical R
∗
2
-based LIC estimates. A
phantom was assessed for validation.
6.1.3 Results
Human R
∗
2
estimates with the 3.1 ms echo time correlated well with clinical
estimates (slope=1.09, r
2
adj
=0.9900, p=0.0033). Phantom estimates achieved rea-
sonable estimates of R
∗
2
but demonstrated a steeper relationship between imaging
and CSI R
∗
2
than expected (slope=1.92, r
2
adj
=0.9710, p=0.0097). R
∗
2
fitting was
unsuccessful in all cases. Fat fraction estimation failed but significant spectral
bandwidth is demonstrated in the CSI signals.
6.1.4 Conclusion
Short echo time CSI provides a promising approach to quantify R
∗
2
, R
2
, and
PDFF in high-iron patients at 3T by increasing SNR and acquiring an increased
number of samples for use with spectral techniques.
6.2 Introduction
Magnetic resonance imaging (MRI) is popular for the noninvasive estimation
of tissue iron in patients with transfusional iron overload. Relaxation rates R
2
(
1
⁄T2) and R
∗
2
(
1
⁄T
∗
2
) are often independently obtained at 1.5T to estimate iron
7,4
and are showing increased use with 3T magnets. Although calibrations between
LIC and R
2
and R
∗
2
have been established at 3T, a number of practical challenges
limit the dynamic range of iron measurements for both spin echo and gradient echo
techniques. Further, estimating R
2
via a CPMG multiecho sequence in conjunction
withR
∗
2
atanyfieldstrengthmayprovideadditionalclinicalvalueandhaspotential
110
to expose the mechanisms of chelators used to treat iron overload
6
. Therefore,
methods to obtain both measurements should be established at 3T.
Chemical shift imaging (CSI) is a spectroscopic technique that obtains one
or more echoes of a single phase-encoded voxel after applying an excitation and
an inversion RF pulse. The echo’s free induction decay (FID) is governed by R
∗
2
,
similar to the FID produced after a single RF pulse is applied. Unlike a traditional
FID,theamplitudeoftheechoisenvelopedbytheR
2
decay. Thoughthisapproach
is normally used to examine spectra to identify metabolites or gather chemical shift
data, this technique also has the potential to simultaneously estimate R
∗
2
from the
FID while estimating R
2
from the maximum intensity of the spin echo if processed
in the time domain rather than the Fourier domain. In addition to providing two
quantitative metrics of tissue iron, CSI increases SNR by imaging a large voxel
than a traditional imaging sequence.
In this work, we present a modified CSI sequence that uses a custom RF pulse
to substantially reduce echo time. Human validation of R
∗
2
estimates demonstrates
that the substantial SNR improvements allow quantitation of R
∗
2
in heavily iron-
loaded human subjects. Phantom data demonstrate further proof-of-concept R
∗
2
.
6.3 Theory
Slice-selective RF excitation pulses allow a considerable reduction of scan dura-
tion by exciting only a slice or slab of tissue rather than the whole body, obviating
the need for phase encoding all 3 spatial dimensions. This prevents phase wrap-
ping in the slice selection direction and reduces the number of repetitions required
to produce an image, reducing specific absorption rate (SAR) and total scan dura-
tion. However, these pulses tend to require more time to transmit than “hard”,
111
non-selective RF pulses for an equivalent flip angle. This in turn increases the
minimum echo time that a sequence can achieve.
The performance of a slice-selective pulse is commonly assessed in the Fourier
domain because the slice profile, the shape of the excitation of a cross-sectional
portion of tissue, is given by the Fourier transform of an RF pulse. When a
slice selection gradient is applied during the RF pulse transmission, it creates a
relationship (most commonly linear) between frequency and position. Any spins
within the bandwidth of the pulse are excited. We can determine the shape of the
slice profile with the Fourier transform of the RF pulse waveform.
M
z
(ω)∝F(B
+
1
(t))
T
slice
∝
1
γGzτ
(6.1)
where M
z
is the magnetization profile along the slice direction as a function of
ω (spin frequency), B
+
1
is the excitation waveform at time t, γ is the Larmor
frequency, G
z
is the gradient strength, τ is the duration of the RF pulse, T
slice
represents slice thickness, andF represents the Fourier transform operator.
In general, there is a trade-off between pulse duration and the precision of the
slice profile. For many clinical imaging applications, the increased echo time is
of no importance and improving resolution improves the clinical applicability of
the image, particularly when assessing physiologic structures for physical damage.
For high iron loads, the quantitation is more important than the resolution of the
image. Reduction of echo time is critical to capture rapid decay signals.
AcustomRFpulsewasdesignedtoachieveadequatesliceselectionwhilereduc-
ing the pulse duration to achieve an sufficiently short echo time to capture iron’s
rapid decay exhibited. The pulse is based on a Dolph-Chebyshev window function
and approximately 2-4 times faster than a traditional sinc pulse for a given flip
112
angle and slice thickness. In conjunction with a hard 180
◦
inversion pulse, the CSI
sequence minimum echo time was reduced to 3.1 ms from 7.1 ms. The time savings
is apparent in figure 6.1. The slice profile produced by the Dolph-Chebyshev pulse
(figure 6.3) shows less uniformity than the sinc pulse (figure 6.2). The reduction
in slice profile homogeneity does not preclude the applicability of this pulse to
relaxometry.
6.4 Methods
Study participants were selected from a population of patients at the Chil-
dren’s Hospital of Los Angeles (CHLA) undergoing chronic transfusion therapy
for sickle cell disease, thalassemia, and other rare anemia syndromes. Participants
provided informed consent to participate in an IRB-approved study (CHLA Study
CCI-14-00034). Each participant received a clinically indicated MRI assessment
for iron overload on a 1.5T scanner followed by a research imaging protocol at 3T.
Images were acquired on single-RF-transmit Philips Achieva 1.5T and 3T clini-
cal scanners (software revision v3.2.2, v5.1.7, or v5.1.9, Philips HealthTech, Best,
Netherlands) using 16-element SENSE-XL torso coils. Reference liver iron (imag-
ing) estimates were obtained from R
∗
2
estimates made with 1.5T or 3T imaging
protocols. A 3-slice gradient echo dataset was gathered with the following param-
eters: FOV=30x40cm, slice thickness=10mm, matrix=84x84, TR=50ms, FA=30
◦
,
16 linearly spaced echoes between [0.96-8.8] ms (min TE=0.76 for 3T), transverse
slice plane. 1.5T-R
∗
2
was converted to 3T-R
∗
2
using a previously derived calibra-
tion
58
. Spectroscopy data were obtained with a modified, single-echo CSI sequence
usingaDolph-Chebyshevexcitationpulseand hard inversionpulse with thefollow-
ing scan parameters: TE = [3.1,7.0,11.0,15.0]ms, TR=1000ms, NEX=1, matrix=
113
[36x20], voxel size=10.5x10.5mm, slice thickness=15mm, 1024 samples, spectral
BW=8000 Hz.
A phantom was constructed out of 1-liter Nalgene bottles containing tap water,
1 and 3 mM MnCl
2
solutions, Philips Phantom Standard CuSO
4
Solution 11, and
pure mineral oil. It was assessed with the same protocol as human subjects but
used a coronal slice rather than transverse. The phantom B
1
+
was assess with a
single slice, dual repetition time (TR) B
+
1
mapping sequence
82
with TE/TR
1
/TR
2
=3ms/20ms/120ms, bandwidth of 2894Hz/pixel, voxel size of 4.2x4.2x8 mm
3
, and
one signal average.
Voxels representing liver or phantom solution were identified within the CSI
datasets by a graduate student with 5 years of experience. FIDs were gathered by
removing samples from the echo signal prior to the maximum magnitude sample
present for a given voxel. We hypothesized that iron-mediated center frequency
shift would require additional quadrature demodulation. This was tested by fit-
ting the data with and without a signal-maximizing quadrature demodulation
scheme. The demodulation frequency was determined by finding the maximum
echo amplitude after demodulation over 10 Hz increments for a range of±300
Hz off-resonance. R
∗
2
and R
2
were estimated by applying an ExpC signal model
(equation 6.2) to the magnitude FID of the 3.1ms dataset and the echo peaks of
all datasets, respectively, using software developed in MATLAB. Simultaneous R
∗
2
and proton density fat fraction (PDFF) estimation was also performed by applying
a signal model including a 6-peak spectral model for fat (henceforth “spectral”)
92
to complex 3.1 ms FIDs.
S(t) =S
0
e
−R
∗
2
t
+c (6.2)
114
The spectral model is:
S(t) =S
0
e
−R
∗
2
t
× (W +F∗p) (6.3)
p =a
1
×e
j∗2∗pi∗f
1
∗t
+a
2
×e
j∗2∗pi∗f
2
∗t
+a
3
×e
j∗2∗pi∗f
3
∗t
a
4
×e
j∗2∗pi∗f
4
∗t
+a
5
×e
j∗2∗pi∗f
5
∗t
+a
6
×e
j∗2∗pi∗f
6
∗t
(6.4)
with coefficients:
Coeff 1 2 3 4 5 6
a 0.047 0.039 0.006 0.12 0.70 0.088
f / (B0 * 42.58) -0.6 0.5 1.95 2.6 3.4 3.8
W and F represent water and fat fraction, respectively. All fits constrained S0 to
a range of 90-180% of the maximum signal value present in a voxel’s signal time
course. R
∗
2
was constrained to a range of 10-5500 ms. When present in the fit,
bias values were restricted to a range of 0-1 and PDFF was restricted to 0-20%.
Imaging and CSI R
∗
2
values were compared using linear regression analysis.
SNR was estimated in CSI signals by calculating the quotient of the maxi-
mum echo intensity and the standard deviation of a noise-only voxel. Imaging
SNR was determined by assessing the finding the quotient of signal intensity in
a representative phantom ROI and the standard deviation of a noise-only ROI
67
.
Because the clinical R
∗
2
estimates were made using different protocols, image SNR
was estimated by proxy in a 3D radial image with a TE of 2.27 ms (protocol
otherwise identical to 3T-UTE protocol, chapter 5); the image was chosen as the
nearest echo time available for comparison with the CSI data without on-scanner,
post-acquisition noise correction activated.
115
6.5 Results
Analysisofphantomresultsdemonstratedthatdelineationsbetweenthebottles
(layout demonstrated in figure 6.4) could be identified in the low-resolution CSI
data, indicating that the CSI sequence is capable of discriminating the different
species. The water bottle was not differentiable from the larger MnCl
2
bottles.
Quantified values of R
∗
2
are noted in table 6.1. Regression analysis demonstrated
a fit line of R
∗
2
-CSI = 1.92 R
∗
2
-imaging âĹŠ273.27 (p = 0.00972, r
adj
2
=0.9710).
Imaging and CSI R
2
estimates were uncorrelated. A B
1
+
map is demonstrated in
figure 6.9.
Four human subjects with known moderate to severe liver iron quantities were
assessed with the CSI protocol. Visual inspection of the CSI data demonstrated
significantly reduced spatial resolution (figure 6.6). SNR was estimated in repre-
sentative voxels and found to be approximately 1200 while imaging data demon-
strated an SNR of about 320 in the corresponding regions. Numerical values
for 3T-CSI and clinical 3T-equivalent R
∗
2
values are demonstrated in table 6.2.
R
∗
2
estimates were found to best fit existing patient results without the need for
demodulation. Linear regression of ExpC-CSI R
∗
2
values and imaging R
∗
2
estimates
demonstrated a strong linear correlation (slope=1.09, r
adj
2
=0.9900, p=0.0033);
regression results are summarized in figure 6.7. ExpC R
2
estimates and ExpC R
∗
2
estimates performed on human CSI data with TE≥7.1 ms were uncorrelated with
LIC. Spectral-CSI fitting failed to predict LIC and tended to generate unreason-
ably large proton density fat fraction estimates (see 6.8, right panel). Examples of
signals and fit models are shown in figure 6.8.
116
6.6 Discussion
Quantitation of tissue iron has remained a persistent challenge at higher field
strengths. Though recently developed imaging techniques with reduced echo times
can quantify extreme iron loads (LIC≥40
mg
⁄g) with 1.5T
100
and 3T magnets (chap-
ter 5), the effects of fat, motion, imperfect breath-holding, new sampling trajecto-
ries, and processing techniques remain unexplored. Effects from fat that are negli-
gible at longer echo times cause significant fitting error when UTE approaches are
used, as demonstrated in chapter 5. Chemical shift imaging shows great promise as
a technique to probe these questions and potentially accomplish iron quantitation
in situations where imaging techniques fail.
Initial human subject results show that an unoptimized CSI protocol can match
the dynamic range of clinical 1.5T R
∗
2
quantitation techniques while also providing
spectralinformationthatcannotfeasiblybeacquiredusingimagingsequences. The
strong linear correlation between the R
∗
2
estimates from 3.1 ms CSI FIDs matches
the expected R
∗
2
-LIC calibration within existing clinical measurement variability.
When compared with UTE imaging data, CSI data demonstrates significantly
improved SNR. Though UTE imaging can estimate most clinical iron burdens at
3T, the SNR improvement from CSI may be useful when imaging approaches fail
at extreme LICs or higher field strengths. The substantial SNR improvement over
imaging sequences also allows CSI to capture signals where spin echo imaging
sequences fail. Traditional spin echo sequences are limited to a minimum echo
times of 4-6 ms and fail to quantify moderate to severe liver iron. In contrast, the
high SNR demonstrated in the CSI FIDs outweighed rapid R
2
decay, giving CSI
the potential to achieve a dynamic range in R
2
-based LIC quantitation matching
that of the 1.5T imaging. What’s more, we have achieved first echo times as short
as 0.97 ms in spin echo imaging sequences using modified RF pulses such as those
117
presented in figure 6.1. Further optimization of the protocol using lower excitation
angles and new pulses could potentially drive first echo times below 1 ms, paving
the way for extreme dynamic range gains.
Though existing dynamic range limits of CSI-R
∗
2
-based LIC estimates may be
sufficient for clinical decision making, the failure to estimate R
2
in human CSI data
demonstrates that shorter first echo times may be necessary. Given that human R
∗
2
estimationonly succeededin 3.1ms CSIdata, webelieve thatthe longerecho times
did not capture usable signal. The equivalent 3T-R
2
conversions (noted in table
6.2) would normally require a minimum echo time well below 3.1 ms to quantify
R
2
with images. It is therefore unsurprising that longer echoes could not acquire
usable signal. Further, the success of the 3.1 ms TE at capturing quantifiable data
is somewhat surprising even with improved SNR. Human R
2
estimation ultimately
failed due to an insufficiently sampled decay curve rather than a failure of the
technique itself. It is likely that further reducing minimum TE will allow sufficient
sampling of the R
2
decay curve to achieve reasonable estimates.
Inspection of phantom R
2
estimates found that the fits were reasonable given
thedata. ThissuggeststhatR
2
estimationshouldbepossible. However, thelackof
correlation between imaging and CSI R
2
estimates is not completely understood.
The challenges of using spin echoes for fast decay quantitation have been well-
established at 3T
36,99
and significant B
+
1
inhomogeneity effects are discussed in
chapter 4. The achieved B
+
1
in the phantom range from about 50% to 150%, which
mayberesponsibleforthefailedcorrelation. Therecentdevelopmentoftechniques
such as MR fingerprinting
101
may provide a more robust way to estimate R
2
and
probe tissue morphology than spin echo R
2
estimates alone. MR fingerprinting
normally relies primarily on the relaxation parameters for each tissue. Applying
the Monte Carlo simulation
6
to MR fingerprinting would allow us to directly join
118
our imaging parameters to the underlying iron distribution while also including
confounders such as B
+
1
heterogeneity. It is also likely that improved sampling
schemes would directly improve R
2
estimates and increase robustness of higher
order approaches.
ImprovingdecaysamplingwilllikelyimprovealsoimprovetheusabilityofCSI’s
spectral data. Particularly, a more reliable estimate of proton density may be
possible with shorter TEs. As previously demonstrated, a reliable S
0
estimate can
significantly improve relaxometry estimates as shown in chapter 2. We speculate
that the failure to estimate PDFF is related to a lack of appropriate constraints
for the increased degrees of freedom in the fitting problem. Fat oscillations may
cause underestimates of total proton density, which can have large consequences
on subsequent decay and PDFF estimates. A reliable S
0
estimate would be useful
immediatelyusefulinanchoringallfitsbutthehigherdimensionalityofthespectral
fits particularly stands to benefit from better initial constraints in this case. Using
an S
0
constraint alone or using the theoretically inferior ExpC model to provide
a reasonable constraint for decay parameters will likely increase the robustness
of spectral fits without the need for additional acquisitions. We hope to improve
these approaches when a sufficiently large dataset is gathered.
Although CSI is officially an imaging technique, it straddles the worlds of imag-
ing and spectroscopy. When applying CSI to body imaging, users familiar with
imaging and spectroscopy alike must take care to avoid pitfalls due to assump-
tions they may have developed in their previous research or experience. From
an imaging perspective, the use of multiple phase encoding gradients makes CSI
datasets susceptible to aliasing in two (or three) directions rather than one, as
is common in slice-selective MRI where the readout filter prevents aliasing in the
frequency encoding direction. Combined with the low resolution of the data, it can
119
be challenging to realize that the sequence is not working as intended. Likewise, in
contrast to many spectroscopic approaches water suppression must be disabled or
else the central peak of the signal will be suppressed, confounding R
2
and R
∗
2
esti-
mates. Further, an uncommonly high spectral bandwidth is necessary to capture
large off-resonance and fat oscillations in the signal. Although the term chemical
shift imaging may imply that electron shielding in organic molecules is completely
responsible for the frequency shifts even though the susceptibility of the iron’s
susceptibility causes off-resonance by amplifying the local magnetic field. Finally,
while 35 ms is commonly the shortest echo time used in spectroscopy, the aggres-
sively short echo times presented here are an absolute requirement to capture the
rapid signal decay. For these reasons, the data resulting from this application
of CSI is neither conventional imaging data nor conventional NMR data that a
clinical spectroscopist would be familiar with interpreting; extreme care should be
taken to ensure that the protocol is functioning as expected.
In addition to the theoretical and implementation challenges, a number of prac-
tical challenges must be resolved before CSI is clinically applicable. Due to the
need for phase encoding in two directions to suppress aliasing, the CSI protocols
tend to exhibit long durations. Although the free-breathing acquisitions here were
sufficient to quantify R
∗
2
, the error introduced remains unquantified. Reducing
scan duration sufficiently for use with breath-holding would likely require multi-
coil acceleration techniques. Saturation bands may be helpful but their effect on
the spectral content of the remaining images is unknown. It may also be possible
to reduce the TR, though no signal models have been testing with T
1
effects in this
context. Image segmentation is complicated by the low resolution of the image.
Although choosing landmarks from survey images can allow for correct ROI place-
ment, we have not explored techniques to ensure that partial voluming does not
120
Material CSI R
∗
2
[Hz] Imaging R
∗
2
[Hz]
CuSO
4
150 10
1mM MnCl
2
221 126
3mM MnCl
2
319 342
mineral oil 183 101
Table 6.1: R
2
and R
∗
2
estimates in phantom
Patient 3T-CSI R
∗
2
[Hz] 3T-equivalent R
∗
2
[Hz] 3T-R
2
[Hz] (computed)
1 1380 1484 265
2 927 910 200
3 3516 3322 410
4 1708 1795 295
Table 6.2: 3T-CSI and 3T-equivalent R
∗
2
estimates in four human subjects. Con-
version to R
2
is included for reference.
invalidate fit results. Further, traditional fitting approaches can be confounded
by the spectral content of the signals; significant oscillations can be exposed by
the high bandwidth of the readout which are not usually noticeable in imaging
datasets and lead to the erroneous amplification of decay rates.
6.7 Conclusion
CSI combined with reduced TE through custom RF pulses was successful at
quantifying R
∗
2
in four high iron patients. Phantom data suggest that simulta-
neous R
∗
2
and R
2
estimation can be accomplished with mono-exponential fitting
techniques. With additional validation, optimization of protocol parameters, and
further decreased TEs, we expect that CSI will provide robust liver iron estimates
and potentially fat quantitation with high dynamic range at many field strengths.
121
Figure 6.1: Comparison if sinc (blue), Dolph-Chebyshev (green), and Tukey (red)
excitation pulses for a given flip angle.
Figure 6.2: Achieved slice profile for Sinc Pulse
122
Figure 6.3: Achieved slice profile for Dolph-Chebyshev pulse
Figure6.4: Layoutofthephantomdemonstrating, fromtoptobotton, lefttoright,
bottles of Philips Solution 11, mineral oil, tap water, 1mM MnCl
2
, tap water, and
3mM MnCl
2
.
123
0 50 100 150 200 250 300 350 400 450 500
0
50
100
150
200
250
300
350
400
450
500
Regression of R
2
*
from MRI and CSI
3T MRI R
2
*
(Hz)
3T CSI R
2
*
(Hz)

y = 1.92 x −273.27
p = 0.00972
r
2
=0.9807 r
2
adj
=0.9710
Data
Fit
Confidence bounds
Figure 6.5: Regression of phantom R
∗
2
estimates. The water vial was excluded due
to inability to differentiate it from surrounding MnCl
2
vials in the CSI R
∗
2
and S
0
images. The slope is notably steeper than the expected relationship. However,
the magnet reported an unreliable shim for the CSI sequence, which can lead to
accelerated R
∗
2
decay.
124

[Hz]
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
Figure 6.6: Comparison of standard image and R
∗
2
map with CSI S0 image and R
∗
2
map. Slice location is not preserved between the images shown.
125
500 1000 1500 2000 2500 3000 3500
0
500
1000
1500
2000
2500
3000
3500
4000
Regression of R
2
*
from MRI and CSI
3T MRI R
2
*
(Hz)
3T CSI R
2
*
(Hz)

y = 1.10 x −178.32
p = 0.00334
r
2
=0.9933 r
2
adj
=0.9900
Data
Fit
Confidence bounds
Figure 6.7: Regression of clinically-obtained 3T R
∗
2
estimates and CSI R
∗
2
estimates
in four human subjects.
126
Figure 6.8: A demonstration of signal from a single voxel (blue curve) and resulting
fit (red curve). The ExpC model (left) displays reasonable relaxation estimation
behavior even in the presence of increased spectral content. The spectral fit (right)
fails, likely due to the high order of the model; this often leads to overestimating
PDFF significantly.
127

50
60
70
80
90
100
110
120
130
140
150
Figure 6.9: B
1
+
map demonstrating the wide variety of flip angles achieved in the
phantom.
128
Chapter 7
Conclusion
MRI has become the clinical standard of care to assess iron in a variety of
organs due to its safety, noninvasiveness, reproducibility, and speed. Although the
original techniques that have seen wide-spread clinical adoption were developed
at 1.5T, the proliferation of 3T scanners requires the validation of these quanti-
tative techniques at a new field strength. What’s more, field-dependent enhance-
ment of iron’s signal decay rate leads to the failure of existing scan and analysis
techniques for moderate-to-high iron patients at 3T — both R
∗
2
and R
2
contrast
mechanisms demonstrate catastrophic failure near liver iron loads of about 20
mg
⁄g.
These findings correspond well with the minimum echo time limits of about 0.7
ms and 4 ms in commonly-used cartesian gradient echo and spin echo techniques.
We selected a multi-faceted approach, first involving the development of new MRI
pulse sequences and applying them to phantom and human subject scanning; com-
bined with simulations and updated curve fitting techniques, these new imaging
techniques increase the dynamic range of 3T-LIC measurement. By extending
simulation frameworks to account for 3T non-idealities, developing custom RF
pulses with shorter duration, leveraging center-out k-space acquisitions, better
utilizing acquired images through improved fitting, and characterizing imperfec-
tions encountered at 3T, the limitations of 3T were largely overcome. The results
of this work have ultimately facilitated the expansion 3T’s capabilities to include
iron quantitation across the entire clinically relevant range.
129
7.1 Original contributions
We first addressed the previously-demonstrated insensitivity
49
of R
2
to LIC
at 1.5T by using a proton density constraint derived from muscle tissue. Human
subject data acquired at 1.5T demonstrated the importance of estimating proton
density to ensure R
2
sensitivity for high-iron patients, increasing sensitivity rel-
ative to unconstrained results by 300%. We found that simulated experiments
from our Monte-Carlo framework agreed. Further, the implementation of a con-
strained non-exponential signal model
56
showed the saturation of a background
decay parameter at a similar iron load to the expected saturation of liver ferritin
stores; a second decay parameter in the same model associated with particulate
iron increased continuously, mirroring the behavior of increased hemosiderin con-
centration. Together these results suggest that CPMG spin echo can provide more
information about cellular iron distribution than R
∗
2
or single spin echo-R
2
alone.
It also supports our previous speculation that the function of chelators could be
reasonably probed using spin echo based techniques.
Second, weaddressedthecalibrationofR
2
andR
∗
2
vsLICat3TusingtheMonte
Carlo model. Through this work, we showed that the 3T relaxivity enhancement
forR
2
andR
∗
2
were1.48and2.03, respectively, whencomparedto1.5Tcalibrations.
These results are consistent with experimental results
72
but provide a closed-form
mathematical solution to the relaxivity enhancement as well as an inexpensive way
to validate relativity enhancement for an arbitrary field strength prior to in vivo
validation.
After answering the question of field-dependent enhancement, the impact of a
common imaging confound called B
+
1
inhomogeneity on R
2
and R
∗
2
LIC estimates
was assessed. B
+
1
maps were acquired in human subjects at both 1.5T and 3T
to estimate the magnitude of spatial excitation variation. The inclusion of a 3D
130
Bloch simulator in the Monte-Carlo framework allowed pulse imperfections to be
modeled. The results demonstrated that both spatial flip angle variation and
whole-liver underexcitation can change R
2
-based liver iron estimates. However,
the simulation provides a mechanism to determine the R
2
-LIC calibration curve
if the magnitude of the B
+
1
heterogeneity is known. This may allow for numerical
correction or selective voxel inclusion to ensure accurate R
2
estimates. The spatial
excitation heterogeneity was found to be only relevant to spin-echo imaging. For
gradient-echo imaging, the loss of initial intensity only reduced SNR, which can
cause failure of quantitation at high iron loads; this effect only occurs in images
with readily apparent catastrophic loss of liver signal and does not pose a threat
of going unnoticed in the fitting process.
Although R
∗
2
imaging is robust to excitation heterogeneity, imaging speed still
limits R
∗
2
quantitation to about 2000 Hz when using cartesian readouts on 1.5T
and 3T systems, maximum LICs of about 40
mg
⁄g and 20
mg
⁄g respectively. We over-
came this limitation by developing and validating a human imaging protocol using
3D radial imaging to achieve quantitation to at least 40
mg
⁄g of iron. Further, we
show that it likely quantifies LIC≥50
mg
⁄g. Though previous studies achieved quan-
titation in phantoms with a variety of UTE techniques, only recent attempts to
use half-pulse excitations in human subjects have succeeded
100
. In addition to
extending dynamic range of R
∗
2
-LIC iron quantitation, the radial UTE technique
was found to be robust to chest wall motion, allowing the elimination of breath-
holding for patients who cannot tolerate extended breath-holding. With further
optimization, it may be possible map higher iron loads and show value at lower
field strengths as well.
Finally, we assessed a novel means of characterizing iron at 3T involving CSI
spectroscopy sequences. The CSI approach is particularly interesting because it
131
has the potential to estimate both R
2
and R
∗
2
while also increasing SNR. The inclu-
sion of modified RF pulses reduced the achievable echo time by over 50%, with
further opportunities to reduce the echo time with decreased flip angles. The pulse
sequence demonstrated good correlation between R
∗
2
and LIC in high-iron patients
and achieved successful proof-of-concept R
∗
2
estimation in phantoms. It also pro-
vided improved spectral information which will be useful for fat quantitation.
7.2 Future Work
This work has opened the door to a variety of continuing research areas. The
continued development of the simulation framework allow for more realistic and
varied experiments to be conducted while the new scan and fitting techniques may
be further refined to decrease variability and uncover new data for use in research
and clinical settings. These opportunities are explained below.
Based on the finding that B
+
1
heterogeneity and significant underexcitation reg-
ularly occur in liver imaging, improved corrective measures may reduce variability
by correcting rather than discarding affected pixels. There may be a closed-form
relationship that allows for correction of R
2
maps based on an acquired B
+
1
map
at exam time or as an offline reconstruction. In the absence of a well-posed closed-
form correction, the existence of regions of varying excitation efficiency might be
corrected using the Monte Carlo frame work to build iron-load specific signals for
all iron loads.
The many quantitative techniques to assess total body iron have primarily
depended on biopsy as the gold standard for liver iron quantitation. As such,
iron overload metrics have been compared to one another using Bland-Altman
analysis with LIC(3T versus 1.5T, LIC by R
2
versus LIC by R
∗
2
, LIC by MRI
132
versus LIC by biopsy, SQUID, or CT). However, biopsy has large sampling and
tissue-processing(drying, paraffin extraction) uncertainties; all other indirect met-
rics have subject-specific variations in their calibration curves. Advancements in
gene therapy and bone marrow transplantation have created unique opportuni-
ties to sample total-body iron with improved accuracy: patients can present with
extremely high total body iron resulting from transfusion but can be treated with
phlebotomy once their anemia is cured. Hematocrit and phlebotomized blood vol-
ume permit highly accurate measure of iron removal. With such a metric, many
techniques can be reassessed against an improved gold standard. Though R
2
and
R
∗
2
are currently thought to be equal measures of longitudinal iron quantitation,
phlebotomy would allow a more accurate comparison of the two for a cohort of
patients. Further, iron distribution predictions from the Monte Carlo framework
could be tested; the known iron accessibility differences between hemosiderin and
ferritin
102,103
would allow for in-vivo validation of the Jensen
56
signal model and
improved understanding of chelator pharmacokinetics. Such patients would also
assist with the validation of our finding that the background relaxation rate and
aggregate parameter rate diverge as the iron storage mechanisms shift to accomo-
date high iron quantities. Leveraging the fact that large and small hemosiderin
storesdemonstratedifferentaccessibilities, growingandshrinkingatdifferentrates,
would allow for the validation of divergent behavior demonstrated in the patient
data and Monte Carlo framework in chapter 2. Such studies would assist with the
characterization of chelator behaviors on the different iron populations in the body
and provide new insight into iron storage in the human body.
The success of the UTE imaging approach may be able to offer more than just
increased dynamic range at 3T. The known 40
mg
⁄g limit of 1.5T R
∗
2
methods could
be immediately resolved by back-porting the protocol to 1.5T. Further, the effects
133
of the free-breathing protocol on exhibited measurement variation remain unchar-
acterized. We demonstrated that significant variability results from the exclusion
of a fat model to a greater degree than traditional gradient echo. Developing a
better selection of echo times and imaging parameters may increase the data’s
inherent robustness to fat, improve low-iron variability, and possibly contribute to
the achievement of simultaneous fat and iron quantitation in even moderate-to-
high iron patients.
Finally, the development of custom RF pulses has allowed for slice-selective
spin echo imaging with drastically reduced echo times. The behavior of the result-
ing signals is not fully understood. R
2
quantitation in particular demonstrated
challenges due to the non-exponential nature of the signal, especially when low flip
angles were used to achieve sub-millisecond echo times. Improvements in recon-
struction, such as a repurposing of multislice reconstruction to reduce slice profile
effects, may improve the viability of ultra-short slice-selective RF pulses. The
simulation framework could be used to better understand the signals and validate
mathematical models to describe signal behavior.
7.3 Summary
In closing, we identified a need for improved iron quantitation techniques at
3T. Through the creation and testing of new scanning and fitting approaches in
combination with the characterization of the differences between 1.5T and 3T LIC
quantitation, we have enabled reliable LIC quantitation across the clinically rele-
vant range at 3T. Further, we have exposed numerous opportunities to understand
treatments and better quantify tissue iron at all available field strengths.
134
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Abstract (if available)

Abstract Magnetic resonance imaging (MRI) has facilitated important advancements in the clinical diagnosis and longitudinal monitoring of tissue iron overload disorders. MRI at 1.5 Tesla (T) has supplanted invasive approaches such as liver biopsy with a non-invasive test and allows for iron assessment in organs including the heart, pancreas, and spleen rather than solely relying on the liver as a surrogate for total-body iron. Most MRI approaches depend on iron’s significant paramagnetic effects which noticeably increase R₂(1/T2) or R2* (1/T2*). However, the increasing popularity of 3T MRI scanners, also known as magnets, is threatening the availability of clinical iron overload diagnosis. The proliferation of 3T scanners has not coincided with improvements in signal acquisition and analysis techniques for fast decay species, leading to a reduction in the quantifiable range of tissue iron as field strength grows. Imaging centers without a 1.5T magnet are therefore unable to quantify the upper half of the clinically-relevant iron range. Though previous studies have demonstrated enhancement of R₂ and R2* with field strength, a theoretical basis for the relationship between decay rates and tissue iron at arbitrary field strengths has not been developed. Overcoming these new limitations requires the development of novel scan techniques, improvements to curve fitting approaches, validation of liver iron-relaxation calibration curves, and corrections for non-idealities present at higher field strengths. I pursued these open questions by implementing echo and gradient echo MRI and magnetic resonance spectroscopy (MRI) pulse sequences with reduced echo times, developing and applying a Monte Carlo Bloch simulation framework to conduct experiments in-silico, scanning humans and calibrated phantoms, and comparing results with clinically-obtained standard values. Spin echo-based R₂ estimates were attractive due to the demonstrated sub-linear enhancement with field strength while gradient echo-derived R2* was shown to grow approximately linearly with field strength. However, I found that spin echoes were more susceptible to imaging confounders at 3T than gradient echo approaches. I significantly increased the sensitivity of R₂ to liver iron by deriving signal constraints from within the same image series without additional scan time. Further, I demonstrated that excitation imperfections grew from 1.5T to 3T and quantified the effects on estimated R₂ to demonstrate the need for correction. By developing a ultra-short echo time gradient echo protocol for use in humans, I achieved R2* quantitation robust to 3T imaging confounders

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Asset Metadata

Creator Doyle, Eamon Keenan (author)

Core Title Estimating liver iron non-invasively with high-field MRI

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 11/15/2017

Defense Date 03/16/2017

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

Tag 3.0T,3T,chemical shift imaging,computational modelling,iron overload,iron quantitation,magnetic resonance imaging,MRI,OAI-PMH Harvest,R2*,relaxometry,ultra-short echo time,UTE

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wood, John (committee chair), Coates, Thomas (committee member), Nayak, Krishna (committee member)

Creator Email eamon@cornercase.net,eamonkdoyle@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-456800

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Legacy Identifier etd-DoyleEamon-5919.pdf

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Document Type Dissertation

Rights Doyle, Eamon Keenan

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