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Efficient and accurate 3D FISP-MRF at 0.55 Tesla

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Efficient and accurate 3D FISP-MRF at 0.55 Tesla

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Content Efficient and Accurate 3D FISP-MRF at 0.55 Tesla
by
Zhibo Zhu
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL AND COMPUTER ENGINEERING)
May 2025
Copyright 2024 Zhibo Zhu

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Acknowledgements
I joined MREL in August 2018 and have received countless support and
assistance since. I want to give my thanks to my advisor, Dr. Krishna Nayak, for his
guidance and patience during my path to PhD. I always remember our first conversion,
in which he offered a passionate welcome. I always remember his first teaching, which
was not about research but presentation. And I always remember our discussion about
my progress during quarantine, which motivated me to push forward. Without him, I
would not be able to complete this dissertation. I also would like to thank for Dr. Justin
Haldar. He shared MRI knowledge and provided me with opportunity in MRI research
and these encouraged me to become a researcher. I am also grateful for Dr. Zhaoyang
Fan and Dr. Mark Griswold, who provided helpful suggestions and resources on my
research and this dissertation.
I would like to thank all members in MREL. We always support each other and
thrive together. I enjoyed every minute with you.
Finally, my greatest gratitude to my family. My parents put their expectations and
love in my name, Zhibo, which means to achieve the richest knowledge. With my wife,
Jin, we build our own family of love and happiness. You have my greatest love, as
always.

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Table of Contents
Acknowledgements ....................................................................................................... ii
List of Tables ................................................................................................................ vi
List of Figures...............................................................................................................vii
Abstract....................................................................................................................... xiv
Chapter 1 Introduction ................................................................................................... 1
Chapter 2 Background.................................................................................................... 6
2.1 Qualitative MRI................................................................................................................ 7
2.1.1 NMR Phenomenon and Bloch Equations .................................................................................7
2.1.2 From MR Signals to MR Images ............................................................................................11
2.1.3 Contrast manipulation ............................................................................................................13
2.2 Conventional Quantitative MRI ...................................................................................... 17
2.2.1 T1 Mapping using Inversion Recovery Sequences..................................................................17
2.2.2 T2 Mapping using Spin Echo Sequences................................................................................18
2.2.3 Tracer Kinetic Estimation using Dynamic Contrast Enhancement MRI ...................................19
2.2.4 Quantitative Magnetization Transfer Imaging .........................................................................20
2.3 Modern Multiparametric qMRI Methods ......................................................................... 22
2.3.1 DESOPT1 and DESPOT2......................................................................................................22
2.3.2 Magnetic Resonance Fingerprinting.......................................................................................24
2.4 Applications of qMRI...................................................................................................... 25
2.4.1 Detecting diffused liver and heart diseases ............................................................................25
2.4.2 Monitoring longitudinal changes in brain ................................................................................28
2.4.3 More examples ......................................................................................................................29
2.5 0.55 Tesla MRI .............................................................................................................. 30
2.5.1 Potential Impact of 0.55T MRI................................................................................................30
2.5.2 Opportunities for Brain MRF at 0.55T.....................................................................................30
2.5.3 Challenges for Brain MRF at 0.55T........................................................................................31
2.5.4 Precision analysis for Brain MRF at 0.55T..............................................................................35
Chapter 3 Sparse Pre-Contrast T1 Mapping for High-Resolution Whole-Brain DCE-MRI .... 39
3.1 Introduction.................................................................................................................... 39
3.2 Methods ........................................................................................................................ 41
3.2.1 Variable Flip Angle T1 Mapping ..............................................................................................41
3.2.2 Sparse T1 Estimation .............................................................................................................42
3.2.3 Direct T1 Estimation ...............................................................................................................43
3.2.4 Evaluation in a Digital Reference Object ................................................................................44
3.2.5 In-Vivo Experimental Methods ...............................................................................................45
3.2.6 Evaluation in a Healthy Adult..................................................................................................46

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3.2.7 Prospective Application to Brain Tumor Patients ....................................................................46
3.3 Results .......................................................................................................................... 47
3.3.1 Validation using a Digital Reference Object............................................................................47
3.3.2 Validation in a Healthy Adult Volunteer...................................................................................49
3.3.3 Demonstration in Brain Tumor Patients ..................................................................................51
3.4 Discussion ..................................................................................................................... 55
3.5 Conclusion..................................................................................................................... 59
Appendix 3.A: Impact of Pre-contrast T1 (errors) on Quantitative DCE-MRI (errors)............. 59
Patlak Model...................................................................................................................................61
Extended Tofts-Kety Model .............................................................................................................62
Error Propagation Analysis .............................................................................................................64
Chapter 4 EJicient 3D FISP-MRF at 0.55 T using Long Spiral Readouts and
Concomitant Field EJect Mitigation .............................................................................. 70
4.1 Introduction.................................................................................................................... 70
4.2. Theory .......................................................................................................................... 71
4.2.1 Concomitant Field Effects in the 3D Axial SOS FISP-MRF .....................................................71
4.2.2 MaxGIRF-Subspace Reconstruction ......................................................................................73
4.3. Method ......................................................................................................................... 74
4.3.1 Pulse Sequence Design.........................................................................................................74
4.3.2 Numerical Simulation .............................................................................................................76
4.3.3 Imaging System .....................................................................................................................76
4.3.4 Reconstruction.......................................................................................................................77
4.3.5 Phantom Experiments............................................................................................................78
4.3.6 In-vivo Experiments ...............................................................................................................79
4.4. Results ......................................................................................................................... 79
4.4.1 Numerical Simulations ...........................................................................................................79
4.4.2 Spatial Blurring and MRF Results in Phantoms......................................................................81
4.4.3 Spatial Blurring and MRF Precision in Healthy Subjects.........................................................86
4.5. Discussion .................................................................................................................... 94
4.6. Conclusion.................................................................................................................... 98
4.7 Supporting Information................................................................................................... 99
4.7.1 Accuracy of 3D FISP-MRF at 0.55 T ......................................................................................99
4.7.2 Concomitant Field Effects on FISP-MRF Gradient Dephasing..............................................101
Chapter 5 Toward accurate MRF T2 in structured material at 0.55 T using MT-suppressed
excitations ................................................................................................................. 104
5.1 Introduction...................................................................................................................104
5.2 Method .........................................................................................................................106

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5.2.1 Pulse sequence design........................................................................................................106
5.2.2 Dictionary simulation............................................................................................................107
5.2.3 Experiment ..........................................................................................................................108
5.2.4 Image Reconstruction ..........................................................................................................108
5.2.5 Data Analysis.......................................................................................................................108
5.3 Results .........................................................................................................................109
5.4 Discussion ....................................................................................................................116
5.5 Conclusion....................................................................................................................118
Chapter 6 Summary ................................................................................................... 120
References................................................................................................................ 124

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List of Tables
Table 2.1. A summary of precision analysis methods, the associated reconstruction
and comments............................................................................................................. 38
Table 3.1. Patient demographics, qualitative scores, and T1 values for White Matter
(WM) and Brain Tumor (BT) regions of interest. Volume T1 datasets were qualitatively
scored by a Neuroradiologist using the following Likert-scale: 0, non-diagnostic; 1,
diagnostic with mediocre quality; 2, diagnostic with high quality. Small ROI’s were
manually drawn to also yield T1 measurements, reported as mean ± standard
deviation...................................................................................................................... 52

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List of Figures
Figure 2.1. Example contrast weighted MR images: (A) T1-weighted IRSE, TR = 4000
ms, TE = 12 ms, TI = 400 ms, FA = 90°, (B) T2-weighted SESE, TR = 4000 ms,
TE = 75 ms, FA = 90°, (C) T1-weighted MPRAGE, TR = 500 ms, TI = 250 ms,
TE = 3.05 ms, FA = 20° and (D) T2-weighed SESE images at 3 echo times, TR = 3500
ms, TE = [20, 40, 80] ms, FA = 90°. ............................................................................. 16
Figure 2.2. Demonstration of IRSE-based T1 mapping approach. T1-weighted IRSE
images are acquired at 8 different inversion times along the inversion recovery curve.
Here, acquired images are used to fit a mono-exponential recovery model to estimate
a T1 value per voxel..................................................................................................... 18
Figure 2.3. Demonstration of SESE-based T2 mapping approach. T2-weighted SESE
images are acquired at 7 different echo times along the transversal decay curve.
Here, acquired images are used to fit a mono-exponential decay model to estimate a
T2 value per voxel........................................................................................................ 19
Figure 2.4. Two examples of patients with autoimmune liver disease. (A)(B) Male, age
22 and (C)(D) male, age 20. Both (A) and (C) show axial T2-weighted fat-suppressed
image. In (A), there is observable hyperintensity associated with fibrosis tissues, which
is accordingly shown in the iron corrected T1map in (B). The liver has normal
appearance in (C), however, the iron corrected T1 map demonstrates homogeneous
appearance of the liver but with an mildly elevated overall mean value when being
compared against the population-based value (This figure is adapted from the original
figure presented by Dillman et al.98.)............................................................................ 27
Figure 2.5. LGE images, native T1 maps and extracellular volume maps in HCM,
amyloidosis and Anderson-Fabry’s disease. These diseases are not apparent on LGE
images, however, native T1 values are deviated from normal ranges, e.g., increased in
both HCM and amyloidosis, these are reduced in Fabry disease. (This figure is
adapted from the original figure presented by Dall’Armellina and Das99)...................... 28
Figure 3.1. Illustration of Cartesian spiral sampling. Each panel illustrates the (ky,kz)
matrix with white dots denoting the phase encodes that are acquired. Flip angles are
logarithmically spaced from 1.5º to 15º. An undersampling factor R=10 is illustrated,
which corresponds to 60.48 seconds VFA scan time. Note that 15º is 4 times more
densely sampled than other FA’s, for all undersampling factors. .................................. 43
Figure 3.2. Brain Tumor Digital Reference Object (DRO) results. (A) T1 histograms for
the noiseless DRO, (B) T1 histograms for the 3T-mimicking noisy DRO, (C) T1 mean
values and (D) T1 standard deviation values. All are plotted as a function of (A, B)
undersampling factor or (C, D) VFA scan time. VFA scan time axis is in logarithmic
scale. The top row represents BT ROI, and bottom row represents WM ROI. The red
dot represents the reference T1 value in (A)(B) and the undersampling level matching

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the prospective undersampling are marked bold in (C)(D). As expected, precision gets
monotonically worse with higher undersampling factor. In the noiseless case, when R
≤ 16 (VFA scan time ≥137.63 s), the T1 bias is <1 ms and standard deviation is <40
ms for both tissues. In the 3D-mimicking case, when R≤10, the T1 bias is <10 ms and
standard deviation is <110 ms (WM) and <250 ms (BT)............................................... 48
Figure 3.3. Healthy volunteer results. Fully sampled datasets were retrospectively
under-sampled with 10 realizations of the pseudo-random data sampling pattern. (A)
WM T1 histogram as a function of undersampling factor, (B) mean T1 and (C) T1
standard deviation as a function of VFA scan time. VFA scan time axis is in logarithmic
scale. The mean T1 from fully sampled data is shown as the blue dashed line in (B).
Bias is insignificant (<30 ms) until R ≥ 16. Precision gets worse with higher
undersampling factor, but imprecision due to this method is not detectable until R≥10.
When R ≤ 10 (VFA scan time ≥100.8 s), T1 mapping bias <11 ms, and standard
deviation is <214 ms.................................................................................................... 49
Figure 3.4. Illustration of T1 spatial and absolute fractional difference maps from the
healthy volunteer. Direct reconstruction of the fully sampled data is taken as the
reference. Qualitatively, for R≤10, we see minor error in WM or GM. Errors appear
isolated to CSF (bias>1278.5 ms, SD>557.6 ms) and muscle (bias>156.9 ms,
SD>209.8 ms), whose T1 values are generally less of interest in brain DCE-MRI.
Importantly, no spatial patterns indicating systemic errors were observed in the error
maps. For R>10, we observe severe error corruption of T1 maps in GM and WM
regions. ....................................................................................................................... 50
Figure 3.5. Representative M0 and T1 maps from 3 patients with high grade glioma.
Maps are volumetric, and axial, coronal, and sagittal slices through the tumor section
are shown for each patient. (left) M0 maps with tumor ROI drawn in red. (right) T1
maps showing good delineation of WM, GM, CSF, and Tumor. WM and GM regions
have the expected homogeneity. In addition to tissue differential, these maps also
reveal the locations of craniotomy (green arrow) and post-surgical cavities (blue
arrow) that are filled with proteinaceous fluid such as blood in high spatial resolution.. 53
Figure 3.6. Closeup of T1 maps from the 3 patients in Figure 5. Maps are zoomed into
the tumor region (delineated by white dashed box in Figure 5), with narrow display
range. The proposed method captures T1 heterogeneity. T1 coefficient of variation are
10.84%, 9.96%, and 7.31% for the top, middle, and bottom rows, respectively. All
cases show spatial variations in T1. For example, T1 is longer in tumor center (e.g.
light green arrow) than in tumor rim (e.g. green arrow) and peritumoral regions (e.g.
dark green arrow)........................................................................................................ 54
Figure 3.7. Error analysis in TK estimation in the Patlak model. The 1st row shows
partial derivatives of �� and �� of pre-contrast T1 values (1700±255 ms) and the 2nd
row shows the first order error of �� and �� as a function of ±255 ms (±15%) �T1.

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Parker’s (blue), Georgiou’s (red) and in-vivo measured (yellow) VIF’s were analyzed.
As the first row shows, partial derivatives were positive and decreased as T1
increased. Consequently, errors in TK parameters were positively related to T1 errors
and T1 error propagation was slower T1 increased. As the 2nd row shows, a ±255 ms
(±15%) �T1 results in ±0.0064, ±0.0043 and ±0.0085 error in ��, and ±0.0074 min-1,
±0.0053 min-1 and ±0.0028 min-1 error in �� in Parker’s, Georgiou’s and in-vivo
measured VIF, respectively.......................................................................................... 66
Figure 3.8. Partial derivatives of �� and �� of pre-contrast T1 values (1700±255 ms)
in the ETK model. The 1st row shows the 2D plot of partial derivatives of ��, and the
2nd row shows the 2D plot of partial derivatives of �� as a function of both rate
constant �� and T1. Like the Patlak model, both derivatives monotonically decreased
as T1 increases, however, they are not monotonic functions of ��. Especially for the
partial derivative of ��, it had different polarities depending on �� value. ................... 67
Figure 3.9. The first order error in TK parameters as a function of �T1 in the ETK
model. Errors are plotted for ±255 ms (±15%) �T1. The 1st and 2nd row show the first
order error of �� and ��, respectively, and errors were analyzed using Parker’s (left),
Georgiou’s (middle) and in-vivo measured (right) VIF. Errors were also evaluated at
three different �� values to demonstrate dependencies on ��. For ��, result is
similar to that in Patlak model, while it is noticeable that �� will be amplified at higher
�� region, e.g., tumor. For ��, result is more complicated due to the derivative
polarity change for different ��................................................................................... 69
Figure 4.1. Continuous-time FA schedule. Pre-inversion and inter-partition delay are
not shown.................................................................................................................... 75
Figure 4.2. Representative spiral k-space trajectories and phase accrual due to
concomitant fields. Spiral trajectories of 3 different readout lengths (top row) and their
corresponding phase accruals due to concomitant fields at 4 different distances from
isocenter (bottom row). Note that the phase accrual is nonlinear during the
slew-limited regime of a spiral readout and becomes linear during the
amplitude-limited regime of a spiral readout. The axes in the bottom row were chosen
to highlight the relationship between phase accrual and readout duration/axial slice
offset distance. ............................................................................................................ 80
Figure 4.3. Numerical simulation of MR fingerprinting signals and expected SNR.
Signal evolutions are shown for (A) the ACR phantom (T1 = 100 ms, T2 = 100 ms) and
(B) healthy white matter at 0.55 T (T1 = 500 ms, T2 = 80 ms). SNR simulations are
shown in (C). The SNR efficiency curve (red) was calculated as the square root of the
ratio between readout duration and TR, i.e., ��/��, signal curves (solid blue and
yellow) were calculated as the average magnitude from (A) and (B), respectively, and
the SNR curves (dashed blue and yellow) were calculated as the element-wise
multiplication between SNR efficiency and simulated signal curves. All curves in (C)
were then normalized with respect to the shortest readout used in this study............... 81

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Figure 4.4. Reconstructed MRF time-series images of the grid structure of the ACR
phantom using different readout lengths. The MRF time-series images were
reconstructed from MRF data at � ≈ 0.7 seconds per partition. The grid structure was
placed at a 75-mm distance from isocenter to purposely induce a large phase accrual
due to concomitant fields. Spatial blurring worsened as a readout time lengthened in
gridding+subspace reconstructions (top row, left to right), and was successfully
mitigated in MaxGIRF+subspace reconstructions (bottom row). .................................. 82
Figure 4.5. A zoomed-in view of reconstructed images for �� = 2.9 ms ((A)-(C))
and 9.5 ms ((D)-(F)), at �� = 0 mm ((A)(D)) and 75 mm (others). Images before
blurring correction are shown in (A)(B)(D)(E), and after correction are shown in (C)(F).
No detectable structural difference can be observed between (A) and (D), and (C) and
(F), however, noticeable geometric distortions can be observed by comparing (A) and
(C), and (D) and (F)..................................................................................................... 83
Figure 4.6. Comparison between MRF T1 and T2 means and reference values from
the ISMRM/NIST phantom. Results with (red) and without (blue) blurring mitigation are
both reported. T1 and T2 comparison are shown in the top and bottom row,
respectively. There were no significant differences between values with and without
mitigation. Although there were noticeable biases between MRF results and reference
values for �� = 2.9 ms at T1 or T2 < 100 ms, such biases were progressively
reduced as the readout duration increased. This is shown in zoomed-in subplots in
each panel. ................................................................................................................. 84
Figure 4.7. Subspace constrained reconstrued MRF time-series images of the
ISMRM/NIST phantom NiCl2 array. �� = 2.9 ms (left), 9.5 ms (mid) and 16.5 ms
(right) are shown. The images were reconstructed from MRF data at � ≈ 0.7 seconds
per partition. Zoomed-in views (solid red boxes) of vial #5 (dashed red boxes) are
provided in each subfigure’s right bottom corner. Results without concomitant field
effect correction are shown in the 1st row, and with correction are shown in the 2nd
row. Spatial blurring became stronger as long readout (left to right) and is mitigated
after MaxGIRF correction. Blurring residuals emerged when �� ≥16.5 ms (not
shown). ....................................................................................................................... 85
Figure 4.8. MRF T1 maps from the ISMRM/NIST phantom. Zoomed-in views (solid
red boxes) of vial #5 (dashed red boxes) are provided in each subfigure’s right bottom
corner. Obvious spatial blurring appeared to be thickened boundaries, enlarged vials
and overlapping of structures before correction. This was reduced after MaxGIRF
correction. Blurring residuals are visible for �� ≥16.5 ms (not shown).................. 86
Figure 4.9. MRF time-series images, T1 and T2 maps before and after MaxGIRF
correction at 3 readout durations. The slice offset �� = 57.5 mm. As expected, the
spatial blurring caused by concomitant field induced phase worsened as longer
readout duration but was largely mitigated by MaxGIRF correction. Visually, sharper

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boundaries between different tissues such as white matter and gray matter were
preserved. Zoomed-in view (green boxes) are provided in each panel. Note that some
detailed structures could not be fully recovered for �� = 16.5 ms, such as
ambiguous tissue delineation or structural disappearance (red arrows). ...................... 89
Figure 4.10. MRF time-series images, T1 and T2 maps before and after MaxGIRF
correction at 3 readout durations. These results contain the same information as
Figure 4.9, except that the slice offset �� = 57.5 mm. ................................................. 91
Figure 4.11. MRF time-series images, T1 and T2 maps before and after MaxGIRF
correction at 3 readout durations. These results are from the other subject and the
slice offset �� = 57.5 mm (same as Figure 4.9)........................................................... 93
Figure 4.12. Representative MRF T1 and T2 standard deviation maps (left) and
averaged MRF T1 and T2 standard deviation values in WM ROI as a function readout
duration (right). The points corresponding to the maps are marked on the right plot.
Standard deviation values are calculated from 100 pseudo replicas per voxel. Use of
MaxGIRF concomitant field correction (solid) provides improved precision over nocorrection (dashed) for all readout durations and for both T1 and T2. The proposed
MaxGIRF+subspace reconstruction shows improved precision for all examined, which
we attribute to the increased readout duty cycle. For T2, precision approached stability
for �� ≥ 10 ms, which we attribute to that improving scan efficiency was no longer
sensible, e.g., either physiological variation floor or dictionary quantization error floor
was reached................................................................................................................ 94
Figure 4.13. Comparison of estimated T1 and T2 values for the ISMRM/NIST system
phantom between the proposed MRF method (y axis) and reference values (x axis).
Results before (blue) and after (red) the proposed blurring mitigation were reported.
The black dashed line is the identity line. There were no significant differences
between results before and after mitigation. Although there were noticeable biases
between MRF and reference values for T1 < 200 ms and T2 < 100 ms for �� =
2.9 ms, such biases were reduced for all other ��. Other than that, MRF method
shows good accuracy in the ISMRM/NIST phantom. ................................................. 100
Figure 4.14. Comparison of estimated T1 and T2 values in white matter for a healthy
adult. T1 (blue) and T2 (red) biases against literature references (T1 = 493 ms and T2
= 89 ms) as a function of ��. Results before (dashed) and after (solid) proposed
blurring mitigation are reported. For all 6 readout durations examined, the proposed
method produced T1 estimation with good accuracy within ±5.5 ms range, but
underestimated T2 by 24.7 ms to 30.6 ms.................................................................. 101
Figure 5.1. FA pattern per partition plot versus time point and example spiral readout
trajectory. There are 555 time points per partition, corresponding to 7.78 seconds
and 8.89 seconds when �� is 2ms or 4ms, respectively. The total scan times are 11
minutes and 51 seconds, and 13 minutes and 11 seconds, respectively. The spiral

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duration is 9.5 ms, and 14 interleaves are required to fully sample 2D k-space. The
axes in the trajectory plot are in normalized units [-0.5 0.5]........................................ 107
Figure 5.2. Simulated excitation profiles for the 3 RF pulses (blue) and the assumed
bound pool absorption lineshape at 0.55T (black). Bound pool T2 is assumed to be
18 µs. The effective bound pool saturation should be determined based on the
overlap between each profile and absorption lineshape. Under these settings, both
hard pulses have much narrower on-resonance bandwidth and lower side-lobe
magnitude, and thus create much less bound pool saturation. The full widths at half
maximum of each profile are 4000 Hz (Sinc), 634 Hz (Hard, �� = 2 ms) and 317 Hz
(Hard, �� = 4 ms). .................................................................................................. 110
Figure 5.3. FISP MRF T2 maps from 3 volunteers using different RF pulse designs.
Tissues differentials are preserved, specifically the visible boundaries between white
matter and gray matter. (left to right) T2 estimates progressively and substantially
increase as MT effects are suppressed with the modified RF pulses, as illustrated by
red arrows................................................................................................................. 111
Figure 5.4. FISP MRF T1 maps from 3 volunteers using different RF pulse designs.
Tissues differentials are preserved, specifically the visible boundaries between white
matter and gray matter. (left to right) T1 estimates progressively decreased as MT
effects are suppressed with the modified RF pulses, as illustrated by blue arrows..... 112
Figure 5.5. WM FISP MRF T2 violin plots. Violin plots from the three RF pulse
designs are shown in different colors (Blue: Sinc, �� = 2 ms, red: Hard, �� = 2
ms, and yellow: Hard, �� = 4 ms) as well as indicated on the x-axis. Each
volunteer’s reference T2 is displayed as a dashed black line in each T2 plot. FISP
MRF T2 mean values approached reference values after using hard RF pulses
design, while standard deviation values were not significantly affected. This suggests
a substantial improvement in T2 accuracy, without compromising precision. .............. 113
Figure 5.6. WM FISP MRF T1 violin plots. Violin plots from the three RF pulse
designs are shown in different colors (Blue: Sinc, �� = 2 ms, red: Hard, �� = 2
ms, and yellow: Hard, �� = 4 ms) as well as indicated on the x-axis. FISP MRF T1
mean values decreased after using hard RF pulses design, while standard deviation
values were not significantly affected......................................................................... 114
Figure 5.7. Violin plots of MRF T2 standard deviation values across the pseudo
replicas dimension. Violin plots from the three RF pulse designs are shown in
different colors (Blue: Sinc, �� = 2 ms, red: Hard, �� = 2 ms, and yellow: Hard,
�� = 4 ms) as well as indicated on the x-axis. These violin plots do not change
drastically in standard deviation values, and the values scale with each plot’s mean. 115
Figure 5.8. Violin plots of MRF T1 standard deviation values across the pseudo
replicas dimension. Violin plots from the three RF pulse designs are shown in
different colors (Blue: Sinc, �� = 2 ms, red: Hard, �� = 2 ms, and yellow: Hard,

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�� = 4 ms) as well as indicated on the x-axis. Same observations to Figure 5.7 can
be made.................................................................................................................... 116

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Abstract
Quantitative Magnetic Resonance Imaging (qMRI) is a categary of useful MR
imaging techniques that evaluate parametric properties of biological tissues, e.g.,
relaxation times in brain white matter. These techniques aim to provide diagnosable
quantities that are sensitive to global and/or longitudinal changes and physiological
variations. qMRI can complement traditional qualitative diagnostic methods. qMRI is not
widely used due to practical issues such as potential long exam time. Magnetic
Resonance Fingerprinting (MRF) techniques have been developed such that a high
quality and volumetric relaxation maps can be produced within a few minute. MRF has
popularized qMRI applications to multiple body parts and at multiple magnetic field
strengths.
With the resurgence of interest in mid- and low-field MRI, such as the 0.55 T MR
system in Dynamic Imaging Science Center in USC, MRF techniques have gained
growing research and clinical tractions. At 0.55 T, a basic Fast Imaging with SteadyState Precession (FISP)-MRF approach has been shown feasible and promising,
however, substantial quantification biases. Although several hypotheses about these
biases have been proposed, solutions seemed to be suboptimal, and the biases
remained unresolved. Therefore, how to perform this approach in a more Signal-toNoise Ratio (SNR) efficient optimized way and how to improve its quantification
accuracy have become interesting research problems.
In this dissertation, I propose a more efficient and accurate FISP-MRF approach
at 0.55 T. I start with improving 0.55 T FISP-MRF SNR efficiency and the approach
produces more precise results but does not unaddress biases. It includes higher

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readout duty cycle, constrained reconstruction and artifacts mitigation. Then, I focus on
refining RF excitation designs, which helps to suppress the sources of bias, resulting in
more accurate quantification.

1
Chapter 1 Introduction
Magnetic Resonance Imaging (MRI) is a powerful and non-invasive medical
imaging technique developed based on Nuclear Magnetic Resonance (NMR)
phenomenon1–3. Compared to other widely used medical imaging tests such as
Computed Tomography (CT), MRI is excellent at imaging soft tissues, nervous system
and blood vessels, etc., and has no radiation. This is done by sensing protons energy
release, which is caused by combined effects imposed by a main magnetic field B0,
radiofrequency (RF) pulse B1 and signal localization process. MRI has been
increasingly used to examine body internal structure4 with fine details through almost
every part of a body, e.g., brain, vocal, chest, abdominal and musculoskeletal.
In its simplest form, an MRI signal can be determined based on proton density
(PD), and relaxations, e.g., longitudinal relaxation time T1 and transversal relaxation
times T2 and T2
*
. PD determines the largest possible signal amount and relaxation times
affect signal evolution as a function of time. Since different tissues are found to have
potentially different PDs and relaxation times4, we can control their signals by using
pulse sequences. Pulse sequences, as the most fundamental tool in MRI, are designed
to control pulsed RF energy transferred to the subjects and timings of acquiring signals.
Therefore, different tissues are differentiated based on their signals. These differentials
are known to formulate “contrast”.
Nowadays, MRI has been well-developed based on these “contrast weighted”
imaging, including established diagnostic protocols and completed systems training
radiologists to qualitatively read and interpret MR images and make diagnoses. The
term “weighted” comes from that desired contrast can be selected by weighting

2
contributions from tissues properties. For example, MR images can be called “T1-
weighted images” if their contrast is mainly determined by tissues T1 properties. Besides
PDs and relaxation times, other useful contrast includes diffusion5,6, Magnetization
Transfer (MT)
7–10 and contrast enhancement11–13, etc. Note that contrast itself is not a
physical quantity nor has physical meaning, contrast weighted MRI is sometimes called
qualitative MRI.
Qualitative MRI has several shortcomings. It is very sensitive to subjects’ global
changes and cross center and/or vendors’ variabilities. Also, diagnosing based on
qualitative MRI highly relies on readers’ intuitive. To overcome this, people have been
and are working on building a standard for repeatable and reproducible MR studies and
exams. Such studies and exams require identical pulse sequence protocols deployed
among different centers, but vendors’ variabilities such as implementation differences
and subjects’ global physiological changes are harder to be controlled. Therefore,
interpretable MRI results that are less vulnerable to hardware and software differences
and readers’ variabilities would be beneficial.
One solution in seeking such MRI results is quantitative MRI (qMRI)
14. In qMRI,
contributors to signal and contrast formation can be calculated from qualitative images.
As its name indicates, these contributors are measurable quantities. For example,
tissues T1 and T2 properties can be calculated from a set of different T1 andT2 weighted
MR images. This requires understanding of signal and contrast formation, which is
commonly achieved by modeling corresponding physical processes. Since 1950s, qMRI
have been reported to have increasing research and diagnostic values as abnormalities
and lesion have noticeable properties strayed away from normal ranges15.

3
Unfortunately, this technique was not commonly used due to several limitations –
Quantitative models required long MR scans collecting sufficient contrast weighted
information and fitting data into these models itself was a computationally expensive
process14. Therefore, vast clinical applications of qMRI were not practical. Some
examples are: Conventional T1 and T2 mapping method using Inversion Recovery (IR)
and Spin Echo (SE) based sequences which cost hour-long scans with limited spatial
coverage and tracer kinetic parameters mapping using DCE MRI which demands on
sufficient temporal resolution.
With development of both hardware and software, fast qMRI method have been
proposed such as Look-Locker technique and Modified Look-Locker Imaging (MOLLI),
Car-Purcell-Meiboom-Gill (CPMG) sequence, DESPOT1/2 and other multiparametric
methods. These methos have been increasingly used with development of high and
ultra-high field MRI since 1990s. Nowadays, qMRI surprisingly not only produces
quantitative MR results but also these results can be used to produce synthetic MRI
with high diagnostic efficiency. Unlike qualitative MRI, qMRI is more interpretable and it
reflects physiological changes better, it is more useful in both longitudinal monitoring
and inter-subject comparison. Similar to qualitative MRI, qMRI has a high demand on
high repeatability and reproducibility.
In this dissertation, I will focus on a popular multiparametric qMRI method called
Magnetic Resonance Fingerprinting (MRF)
16,17 at 0.55T. MRF is a time-efficient method
for MRI multi-parameter relaxometry, and has gained clinical and research traction, at
magnetic field strengths of 1.5 T and 3 T. It can extend beyond relaxometry with
modifications to encode magnetization transfer18,19, diffusion, and flow20. Potential

4
clinical applications of MRF include brain16,17,21,22, prostate 23–26 and abdomen27,28. In
brain, MRF produces repeatable results in patients with Gliomas of different grades29–33,
and these results show a trend that the Glioma lesion and its peri-regions have longer
T1 as higher grade (more malignant).
It has also been demonstrated feasible on high-performance mid-field systems
such as 0.55T34 and 0.75T35 . With the advances in hardware, mid and low field MRI
now provides diagnostic-level imaging quality with improved scan efficiency and is
becoming more accessible for multiple reasons. For example, with a lower main field
strength, the magnet footprint is less restricted36 and due to reduced necessary coil
windings, the size of the bore can be wider (80 cm) which allows oversized subjects
such as the obese. Also, a lower field strength scanner is potentially more affordable
due to the reduced cost of purchasing, installing, maintaining and repairing. Mid field
MRI benefits from improved field homogeneity (B0 and B1
+) and faces reduced signal-tonoise-ratio (SNR) due to polarization, increased concomitant field effects and stronger
MT effects. SNR loss risk is typically compensated by using more SNR efficient pulse
sequences, and applying denoising reconstruction algorithms, yet MT effects belong to
an open research problem.
This dissertation in structured in the following way: Chapter 1 (this chapter)
introduces current status of qualitative and quantitative MRI and 0.55 T MRI. Chapter 2
will provide background of these terms each with examples, including qualitative
contrast weighted MRI (MPRAGE, SE), review on conventional quantitative MRI
methods (T1, T2, DCE, qMTI), multiparametric methods (DESPOT1/2, MRF). Chapter 3
will describe my work on performing a model-based pre-contrast T1 mapping method for

5
brain tumor DCE MRI with sparse 3D sampling at 3 T. Chapter 4 will describe my work
on efficient 0.55T 3D brain FISP-MRF using long spiral readouts and concomitant field
effects mitigation. Chapter 5 will describe my work on more accurate 0.55 T 3D brain
FISP-MRF using MT-suppressed RF excitations. And Chapter 6 will conclude this
dissertation and provides a discussion on potential future work.

6
Chapter 2 Background
MRI has century-long history37. It is based on NMR phenomenon, which was first
observed and measured in molecule beam by Isidor Rabi in 19383. Soon after, in 1946,
this technique was successfully applied in liquid by Felix Bloch38 and in solid by Edward
Mills Purcell39. These experiments, both having earned Nobel Prize in Physics, built the
physics fundamental for future development of MRI. Briefly, NMR describes a
phenomenon such that NMR signal can be detected in 3 sequential steps: (1) Alignment
of nuclear spins with external magnetic field B0, (2) perturbation of the alignment using a
weaker and oscillating magnetic field B1 at specific radiofrequency (the Larmor
frequency) and (3) detection of NMR signal during the precession of tipped-aways spins
around B0. Seemingly straightforward, however, it took another 27 years before the first
MR image met the world in 1973 by Paul Lauterbur40. After that, quick development
occurred as the MR images of a living mouse in 197441 and the MR images of human
subject in 197742. Nowadays, MRI techniques has gain sensational development such
as submillimeter resolution43, whole body coverage, broad coverage of field strengths
(from 64 mT44 to 11.7 T45), parallel imaging46–48, compressed sensing49,50, AI-assisted
reconstruction51, etc., providing high research and clinical values.
In this chapter, background of this dissertation will be provided. It will start with an
explanation of several key concepts in MRI, including Bloch equations with relaxations,
signal localization and contrast. Several work-horse examples in clinical MRI using T1-
and T2-weighted contrast will be given. In the next section, how qMRI is performed will
be explained and conventional qMRI method examples will be covered. Then, it will
introduce modern multiparametric qMRI methods with a focus on MRF. The last but not

7
the least, this chapter will conclude with a section about 0.55 T MRI with discussion on
its opportunities and challenges, which are tightly related to motivation of this
dissertation.
2.1 Qualitative MRI
2.1.1 NMR Phenomenon and Bloch Equations
Nucleons, i.e., protons and neutrons as the component of nuclei, have the
quantum property of spin which is similar to the angular momentum of a spinning
sphere. This spin property or simply spin is measured as the spin quantum number �.
Protons and neutrons both have a spin of !
" and even number of protons or neutrons
pair up in nondegenerate atomic orbitals resulting in 0 overall spin. Therefore, a nonzero spin number � is observed when presence of odd number of protons or neutrons,
which further results in non-zero angular moment �
⃗ and magnetic dipole moment �⃗,
such as
�⃗ = ��
⃗ (2.1)
Here, � is the gyromagnetic ratio which defined as the ratio between a particle’s
magnetic moment and angular moment. The most frequently used � in MRI is from
protons in water, � = 267.52 Mrad⋅s-1⋅T-1 or �̅= 42.58 Mhz⋅T-1. In the rest parts, � will be
directly using this value for protons if no further clarifications.
Instead of examining each spin, a bulk magnetization is defined as the vector
sum of individual magnetic moments when studying NMR in macroscopic systems.
When an external magnetic field is absent, all magnetic moments are randomly
distributed and therefore there is 0 net magnetization. When there is presence of such a

8
field B0, magnetic moments tend to align or anti-align with the direction of B0 and a nonzero net magnetization is formed such as
�@@⃗ = A�⃗ (2.2)
This alignment is also known as magnetization polarization. Its magnitude, B�@@⃗B, is tightly
related to the amount of largest possible signal observed in an MR experiment. It has
multiple dependencies on the main field strength, temperature and the total number of
spins/proton density. Here, the magnitude and direction of � is given for reference,
�@@⃗ = �"ℏ"�#�$
4�%�$
�@⃗ (2.3)
In Equation 2.3, ℏ is the reduced Plank constant, �# is main magnetic field strength, �&
is the total number of spins, �% is the Boltzmann constant and �$ is the absolute
temperature. In addition, �@⃗ is the unit vector of the positive direction of �-axis which is
usually referred as the direction of B0. A fact is that all particles with non-zero spin also
experience precession when being exposed to an external magnetic field, so do bulk
magnetization as the vector sum of all spins. In specific, individual �⃗ and �@@⃗ precess
around present magnetic field at Larmor frequency,
�# = ��# (2.4)
This process can be well described in classical mechanics: By examining the torque
that �⃗ experiences from a magnetic field, we have
J
�⃗ = �⃗ × �@⃗
�⃗ = �
��
⃗ = 1
�
�
�� ⃗ ⇒
�
�� ⃗ = ��⃗ × �@⃗ (2.5)
Equation 2.5 is known as Larmor equation, and it holds for �@@⃗ in macroscopic view,

9
�
�� @@⃗ = ��@@⃗ × �@⃗ (2.6)
Equation 2.6 is known as Bloch equation without relaxation and it is expressed in the
laboratory frame. When �@⃗ = �#�@⃗, �@@⃗ and �@⃗ are aligned and '
'(
�@@⃗ = 0@⃗.
To tip �@@⃗ away from �@⃗
# to enable signal generation, another magnetic field �@⃗
!
which is weaker, oscillating near Larmor frequency and has time-varying envelope is
required. �@⃗
! is orthogonal to �@⃗
# and is usually referred as RF pulse. Applying �@⃗
! is called
RF excitation. After excitation, �@@⃗ moves on cone around the main field and recovers to
equilibrium. This process is known as relaxation and it is well characterized by
longitudinal and transversal relaxation times, T1 and T2. Here, Equation 2.6 can be
rewritten with additional relaxation terms,
�
�� @@⃗ = ��@@⃗ × �@⃗ − �)(�) − �#
�!
�@⃗ − �*(�)
�"
�⃗ − �+(�)
�"
�⃗ (2.7)
Since �@@⃗ is precessing at �#, it is more convenient to use a rotating frame of reference
at the same angular velocity such that �@@⃗ is static. Given 3 axes of the rotating frame,
i.e., �′, �′ and �′, their corresponding unit vectors are: �⃗′ ≡ �⃗�,-.!(, �⃗′ ≡ �⃗�,-.!( and �@⃗′ ≡
�@⃗. Let �@@⃗
/01 and �@⃗
/01 be magnetization and magnetic field in the rotating frame,
respectively, then
X
�@@⃗
/01 = �*" �⃗
2 + �+" �⃗
2 + �)"�@⃗2 = �@@⃗
�@⃗
/01 = �!,*" �⃗
2 + �!,+" �⃗
2 + �#,)"�@⃗2 (2.8)
Equation 2.7 can be further rewritten by substituting with Equation 2.8, such as
�
�� @@⃗
/01 = ��@@⃗
/01 × �@⃗
/01 − �)" (�) − �#
�!
�@⃗2 − �*" (�)
�"
�⃗
2 − �+" (�)
�"
�⃗
2 (2.9)
Combining Equation 2.8 and 2.9,

10
�
�� @@⃗
/01 = ��@@⃗
/01 × ]�@⃗
/01 − �#
�
�@⃗2
^ − �)" (�) − �#
�!
�@⃗2 − �*" (�)
�"
�⃗
2 − �+" (�)
�"
�⃗
2
= ��@@⃗
/01 × _�!,*" �⃗
2 + �!,+" �⃗
2
` − �)" (�) − �#
�!
�@⃗2 − �*" (�)
�"
�⃗
2 − �+" (�)
�"
�⃗
2 (2.10)
Equation 2.10 describes that magnetization is forced to precess around �@⃗
!,/01 in the
rotating frame and relaxation occurs. When short RF pulses are used (< 10 ms), these
processes are separately analyzed for simplicity in practice, such that there is no
relaxation during RF excitation, and �@⃗ ≈ �#�@⃗ after excitation. Let � = 0 be zero time point
after excitation, Equation 2.10 can be solved for �*" , �+" and �)" ,
⎩
⎪
⎨
⎪
⎧�*" (�) = �*" (0)�
, (
4#
�+" (�) = �+" (0)�
, (
4#
�)" (�) = �)′(0)�
, (
4$ + �# ]1 − �
, (
4$^
(2.11)
It is convenient to express transversal component �*2+2(�) in the complex plane, such
that �*2+2(�) = �*2(�) + ��+2(�) and �*2+2(�) = �*2+2(0)�
, %
&#. Formally, relaxation times
T1 and T2 are defined as the time measured as longitudinal magnetization recovers from
0 to 63% of the thermal equilibrium M0 and transversal magnetization decays to 37% of
its initial state right after excitation. Equation 2.11 indicates that both processes obey a
mono exponential model, however, this is not true for transversal decay in practice,
mainly due to presence of multiple isochromats. Multiple isochromats experience
individual transversal relaxation and they precess at different frequencies so that their
individual magnetization loses phase coherence and their combined magnetization
decays much more quickly compared to a single isochromat model. A new relaxation
time T2
* is defined to characterize this new decay process.

11
2.1.2 From MR Signals to MR Images
Signal localization: The actual MR signals �(�) detected is proportional to
�*+(�) and its value depends on a few other nuance parameters �(�⃗) such as RF
transmitter gain and coil sensitivities. Assume single isochromat for simplicity, �(�) is
expressed as
�(�) = h �(�⃗)�*+(�⃗, 0)�,-.!(�
, (
4#(6⃗)
09:;<1
��⃗ (2.12)
As Equation 2.12 indicates, �(�) is combined signals from all excited particles in an
object. In fact, there are a few more steps before an MR image being created since �(�)
in Equation 2.12 is combined signals from all excited particles in a volume. The first step
is signal localization which is achieved by localized coil sensitivities and spatial
encodings using gradient fields. Specifically for spatial encoding using gradient fields,
particles will have their Larmor frequencies slightly alters during the presence of
gradient fields. This allows signals to be differentiated from different spatial locations.
Let �(�⃗) = �(�⃗)�*+(�⃗, 0)�
, %
&# be the MR image. During the presence of gradient fields
�⃗ = l�* �+ �)m
4
, �(�) is expressed as
�(�) = h �(�⃗)�,-.!(,-= ∫ ?⃗&(@) %
! '@⋅6⃗
09:;<1
��⃗ (2.13)
By demodulating �(�) at frequency �#,
�(�) = h �(�⃗)�,-= ∫ ?⃗&(@) %
! '@⋅6⃗
09:;<1
��⃗
= h h h �(�⃗)�,-= ∫ ?'(@) %
! '@*,-= ∫ ?((@) %
! '@+,-= ∫ ?)(@) %
! '@)��
BC
,C
BC
,C
BC
,C
(2.14)

12
Define �*(�) ≡
!
"D � ∫ �*(�) (
# ��, �+(�) ≡
!
"D � ∫ �+(�) (
# �� and �)(�) ≡
!
"D � ∫ �)(�) (
# ��,
Equation 2.14 becomes
�_�*, �+, �)`
= h h h �(�⃗)�,-"DE'(()*,-"DE((()+,-"DE)(())��
BC
,C
BC
,C
BC
,C
= ℱ{�(�⃗)} (2.15)
Equation 2.15 indicates that MR signals are the Fourier transform of the MR image after
spatial encoding using gradient fields. Such MR signals are called “k-space”52,53.
Therefore, an MR image can be reconstructed by applying inverse Fourier transform on
its k-space data. A simple example reconstruction with k-space data sampled at
Cartesian grids is given in the following.
Assume sampled k-space data �_�Δ�*, �Δ�+, �Δ�)`, � = − F
" , ⋯ ,
F
" − 1, � =
− G
" , ⋯ ,
G
" − 1, � = − H
" , ⋯ ,
H
" − 1 and all Δ�’s meet Nyquist rate54.
�x(�, �, �) = Δ�*Δ�+Δ�) A A A �_nΔ�*, �Δ�+, �Δ�)`�-IJKE'*BLKE(+BMKE))N
H
",!
MO,H
"
G
" ,!
LO,G
"
F
",!
JO,F
"
(2.16)
In practice, �x(�, �, �) is evaluated in discrete manner, such that
�x_�*, �+, �)` = Δ�*Δ�+Δ�) A A A �_�Δ�*, �Δ�+, �Δ�)`�-IJKE'J'K*BLKE(J(K+BLKE)J)K)N
H
",!
MO,H
"
G
" ,!
LO,G
"
F
",!
JO,F
"
(2.17)
If we select Δ� = !
FK*
, Δ� = !
GK+
and Δ� = !
HK)
, Equation 2.17 becomes
�x_�*, �+, �)` = ��Δ�*Δ�+Δ�)iFFT~�_�Δ�*, �Δ�+, �Δ�)`l�*, �+, �)m (2.18)

13
Equation 2.18 indicates that discrete MR images can be efficiently reconstructed from
Cartesian k-space data by applying inverse Fast Fourier Transform (iFFT)
55,56. In fact,
applying iFFT is one of the most popular MR image reconstruction methods even for
non-Cartesian k-space data by pre-interpolating non-Cartesian data onto Cartesian
grids57.
2.1.3 Contrast manipulation
After signal localization, signals are further differentiated from different tissue
properties. Different tissues produce different signal intensities depending on their
properties including proton density, relaxation times, diffusion, magnetization transfer,
etc. And contrast can be manipulated by controlling pulse sequence such as
magnetization preparation, timings and excitation. They affect the signal differences to
be primarily related to desired tissue properties. For example, a basic spin echo (SE)
sequence produces T2-weighted images using long repetition time (TR), appropriate
echo time (TE) and refocusing RF pulses. In specific, a 90*° excitation pulse is played
every TR and a 180+° is played at TE/2 after excitation. By properly rewriting Equation
2.11, we have
Ä
�*"+" (��) = �)" (��)�
,4P
4#
�)" (��) = �# ]1 − �
,4Q
4$ ^
(2.19)
With long TR and proper TE, �)" (��) ≈ �)" (0) and �*2+2(��) differences between
tissues are primarily determined by T2 values and their magnetization equilibrium
(proportional to proton density).

14
Another example is Inversion Recovery (IR) sequence which can produce strong
T1-weighted contrast using long TR, short TE and inversion pre-pulses. For every TR, a
90*° excitation pulse is played after inversion time (TI) after an inversion pulse.
Assuming a 180° inversion, we have
Ä
�*"+" (��) = �)" (��)�
,4P
4#
�)" (��) = −�#�
,4R
4$ + �# ]1 − �
,4R
4$ ^
(2.20)
In IR sequence, we can control TI to nullify signals from material near specific T1 value.
For example, when �� = −�! ln !
"
, �)" (��) is 0.
Another famous T1 contrast example is Gradient Echo (GRE) sequence which
can also produce strong T1-weighted contrast but using short TR and TE and only
excitation pulses with low flip angle value58. Since there is no refocusing, signals
experience T2
* decay instead and due to short TR with spoiling, i.e., transversal
magnetization loses phase coherence or completely decays by the end of each TR, its
signal requires a few RF excitations to approach a steady state. Let �)2[�] be the
longitudinal magnetization before the (n+1)th excitation, e.g., �)2[0] = �#, �*2+2[�] be
the transversal magnetization at TE after the (n+1)th excitation and �$$ be the
longitudinal magnetization at steady state, then we have
Ä
�*"+" [�] = �)" [� − 1]�
,4P
4#
∗
sin �
�)" [�] = �)
2[� − 1]�
,4Q
4$ cos � + �# ]1 − �
,4Q
4$ ^
(2.21)
Equation 2.21 indicates that longitudinal magnetization can be iteratively expressed,
and in steady state, �)" [�] = �)" [� − 1], and therefore,

15
⎩
⎪
⎨
⎪
⎧
�$$ = 1 − �
,4Q
4$
1 − �
,4Q
4$ cos �
�#
�*"+" = �$$�
,4P
4#
∗ sin �
(2.22)
�*"+" are primarily determined by excitation flip angle, tissues T1 values and their proton
density. With proper �, short TR and TE, tissues signals are differentiated by their T1
values and hence corresponding MR images are T1-weighted images. This contrast can
be further improved by adding inversion preparation steps, such as in Magnetization
Prepared RApid Gradient Echo (MPRAGE) sequence59 with delay time (TD). After
preparation, tissues’ inverted magnetization regrows for a duration of TI, similar to IR
sequence. However, this inversion is followed by a GRE scheme with N �* excitations,
short excitation gaps �, short TE and a duration of TD that is reserved for magnetization
to recover before next inversion preparation. In steady state, MPRAGE signals are
given in the following,
⎩
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎧
G++
G!
=
!,S
,&-
&$B
.
,&-/01
&$ 234 56$,.
, 1
&$78$,6.
, 1
&$ 234 57
0,$
9
$,.
, 1
&$ 234 5
B
S
,&-/01
&$ <0&0 T,S
,&:
&$ <0&0 T
!BS
,&:
&$ <0&0 T
�)" [�] = �#
⎣
⎢
⎢
⎢
⎢
⎡U!,S
,
&$VW!,XS
, (1
&$ <0& TY
<,$
Z
!,S
, 1
&$ <0& T
+ ]�
, 1
&$ cos �^
J,!
]1 − �
,&=
&$^ +
�
,&=
&$ ]�
, 1
&$ cos �^
J,!
G++
G! ⎦
⎥
⎥
⎥
⎥
⎤
�*"+" [�] = �)" [�]�
,&>
&#
∗ sin �
(2.23)
Equation 2.23 is derived from the same iterative process as Equation 2.20 but a
different initial conditions. Figure 2.1 shows several examples contrast weighted
image

16
These sequences all produce naïve contrast such that their contrast is mainly
related to a single property. Therefore, it is feasible to evaluate this property if we
manipulate the contrast. Taking SE sequence as an example, if a series of MR images
are produced at different TE while other settings are identical, the imaged tissues will
show T2-weighted contrast at varied levels and this variety is determined by their T2
values. Then we can evaluate T2 values by fitting MR image series into a model
described by Equation 2.18. In the following sections, examples of such quantitative
methods will be explained.
Figure 2.1. Example contrast weighted MR images: (A) T1-weighted IRSE, TR = 4000
ms, TE = 12 ms, TI = 400 ms, FA = 90°, (B) T2-weighted SESE, TR = 4000 ms, TE = 75
ms, FA = 90°, (C) T1-weighted MPRAGE, TR = 500 ms, TI = 250 ms, TE = 3.05 ms, FA =
20° and (D) T2-weighed SESE images at 3 echo times, TR = 3500 ms, TE = [20, 40, 80]
ms, FA = 90°.

17
2.2 Conventional Quantitative MRI
2.2.1 T1 Mapping using Inversion Recovery Sequences
In many diseases such as Glioma and cardiomyopathies, tissues T1 values are
affected. As aforementioned, IR sequences can produce strong T1-weighed contrast as
inverted magnetization regrowth obeys to tissues’ T1 values60. This recovery process
can be well characterized as a function of time, as depicted as differentiated curves
shown in Figure 2.2 with examples images. When sampling along these curves at
multiple different time points or TI’s, i.e., acquiring MR images using multiple singlepoint IR sequences of different TI’s, evaluating T1 values per imaging voxel by fitting the
acquired signals into the T1 relaxation model is feasible. This is the fundamental of IR
based T1 mapping and it is referred as the conventional gold standard T1 mapping
method.
Similar concepts are applied in Saturation Recovery (SR) based methods, in
which an inversion pre-pulse is replaced by a 90° saturation pulse61. Although accurate,
the method suffers from long scan time since similar sequences must be repeated
multiple times and their TR must be long enough (> 5x T1) for sufficient T1 relaxation.
For example, 2 2D IR sequences both with 5-second TR and separately acquiring data
at 2 TI’s may cost more than 40 minutes in total which is already too long to be
efficiently used in routine clinical scans. To overcome this, improved IR based method
such as Look Locker sequence62 and Modified Look Locker Imaging (MOLLI)
63 which
make more measurements following each inversion instead of single-point
measurement are developed. Nowadays, MOLLI has become the most popular
myocardial T1 mapping method.

18
Figure 2.2. Demonstration of IRSE-based T1 mapping approach. T1-weighted IRSE
images are acquired at 8 different inversion times along the inversion recovery curve.
Here, acquired images are used to fit a mono-exponential recovery model to estimate a
T1 value per voxel.
2.2.2 T2 Mapping using Spin Echo Sequences
The most typical T2-weighted MRI is acquired using SE sequences. Similar to IR
sequences, signal transversal decay curves can also be depicted as a function of time
and curves with corresponding to T2 values can be differentiated, as shown in Figure
2.3 with examples images. For example, a series of single-point SE images is acquired
at different time points or TE’s, and T2 values can be evaluated per voxel by
mathematically fitting acquired data into the T2 decay model. This is the fundamental of
SE based T2 mapping and it is also referred as the conventional gold standard T2
mapping method. Just like basic IR based T1 mapping, this T2 mapping method also
suffers from long scan time due to repeating sequences with long TR.
To overcome this, Fast Spin Echo (FSE) method was developed in which multiple
refocusing pulses and corresponding SE data acquisitions are performed at an Echo
Spacing (ESP) between successive RF excitations. Although much faster, FSE method
observes stimulated echo issue in practice and stimulated echoes may not obey a

19
mono-exponential decay model. This issue is caused by successive non-180°
refocusing pulses and partial magnetization is tipped back and forth between
transversal plan and longitudinal direction – spins have phase memories so they
naturally refocus to form stimulated echoes when tipped back to the transversal plane.
As a result, extra care is required for accurate T2 mapping using FSE.
Another issue with applying FSE in in-vivo experiments is Magnetization Transfer
(MT) effects. Briefly, MT effects produce additional signal reduction because of RF
energy deposit and chemical exchange. Such reduction is more noticeable when using
large-angle RF pulses or large number of RF pulses, and transversal decay appears to
accelerate as a result. Therefore, FSE T2 mapping may underestimate T2 if presence of
MT effects. Nowadays, T2 mapping techniques are widely used in detecting alveoli
anomalies and/or airs sacs in lung, such as emphysema.
Figure 2.3. Demonstration of SESE-based T2 mapping approach. T2-weighted SESE
images are acquired at 7 different echo times along the transversal decay curve. Here,
acquired images are used to fit a mono-exponential decay model to estimate a T2 value
per voxel.
2.2.3 Tracer Kinetic Estimation using Dynamic Contrast Enhancement MRI

20
Dynamic contrast enhanced (DCE) MRI is another useful clinical application to
analyze microvascular properties of tissues and tracer kinetic (TK) information. Subjects
are injected with T1-shrotening contrast agent (CA), such as gadolinium, and series of
T1-weighed GRE images are acquired before the injection as baseline images and after
certain injection delay to ensure the wash-in and -out of CA is captured. Therefore, a
temporal enhancement pattern can be depicted as a function of time. By analyzing this
pattern, TK parameters, such arterial input function (AIF), and microvascular properties,
such as permeability (Ktrans), fractional plasma volume (vp) and extravascular
extracellular space fraction (ve), can be evaluated per voxel. This analysis requires to
model the presence of CA based on Equation 2.21, such as (assuming the Patlak
model)
⎩
⎪⎪
⎨
⎪⎪
⎧
�(�⃗,�) = �#(�⃗) 1 − �
,4Q⋅U !
4$(6⃗)
B6⋅[\(6⃗,()V
1 − �
,4Q⋅U !
4$(6⃗)
B6⋅[\(6⃗,()V
cos �
�
, 4P
4#
∗(6⃗) sin �
��(�⃗,�) = �(6]J$(�⃗) h ��(�⃗, �)
(
#
�� + ��(�⃗, �)�^(�⃗, �)
(2.24)
When assuming the Extended Tofts Kety Model,
��(�⃗,�) = �(6]J$(�⃗, ) h ��(�⃗, �)
(
#
�
,_%?@<+(6⃗)
`.(6⃗) ((,@)
�� + ��(�⃗, �)�^(�⃗, �) (2.25)
Note that this model also requires knowledge of T1 values per voxel before the arrival of
CA and hence DCE MRI analysis is always accompanied with pre-contrast T1 mapping
process.
2.2.4 Quantitative Magnetization Transfer Imaging

21
RF energy deposit and chemical occur between restricted water molecules and
free bulk water. This is usually described in a binary spin bath model or just two-pool
model64–69. Restricted water molecules, as the name indicates, consist of water
molecules close to macromolecules and hydration layer and thus have restricted
motion. They are referred as bound pool (pool �) and have unobservable T1b and
extremely short T2b relaxation, e.g., T2b ~ 10 µs, and therefore produce negligible
signals in most clinical MRI8,70. On the other hand, free bulk water is the major MR
signal source and is referred as free pool (pool �). Protons in bound pool cross-relax
with protons in free pool, and additional signal change can be purposefully produced.
This is feasible since bound pool has a much boarder absorption lineshape compared to
free pool and thus can be pre-saturated using specially designed off-resonance pulses,
i.e., MT pulses8.
When signal change is induced in this controlled way, such change is quantified
as MT ratio (MTR) and can be used as a contrast mechanism, known as MT contrast
(MTC)
7,71. This technique is useful in various applications such as MR angiography and
DCE-MRI to improve target contrast72,73. MTC can be manipulated via sequence
parameters and is also dependent on tissues’ properties, and thus MTR is a fractional
than can be easily varied. To produce more interpretable information about MT,
quantitative MTI (qMTI) was developed74,75 aiming at evaluating MT parameters, such
as exchange rates (forward rate ka and reverse rate kb) and fractional bound pool size
(F, assuming free pool size is 1), and each pool’s relaxations (T1a,2a and T1b,2b). Just like
T1 and T2 mapping methods, qMTI is done by fitting acquired multiple MTC data into the

22
two-pool model. Note that two-pool model is sensitive to field inhomogeneities so that
qMTI is usually accompanied with these field measurements67,70.
2.3 Modern Multiparametric qMRI Methods
2.3.1 DESOPT1 and DESPOT2
Conventional quantitative T1 and T2 mapping methods, although accurate,
requires longer scan time compared to routine clinical qualitative MRI. To make T1 and
T2 mapping practical for clinical usage, faster and more efficient methods were
developed, such as MOLLI for T1 mapping63 and Multi Contrast Spin Echo (MCSE) T2
mapping76. However, they may be considered as not efficient enough either because a
single contrast mechanism is used or they require complicated corrections. To
overcome this, multiparametric qMRI methods are demanded and such methods can
encode multiple contrast and evaluate corresponding parameters within limited time. In
this section, we will focus on a set of multiparametric qMRI method: Driven Equilibrium
Single Pulse Observation of T1 and T2 (DESPOT1/T2)
77.
DESPOT177,78 uses a series Spoiled Gradient Echo (SPGR) sequences of
different FAs to manipulate T1-weighted contrast and thus it is referred as Variable Flip
Angle (VFA) T1 mapping. Since these SPGR sequences use short TR (~10 ms) and
only 2 different FAs are required at minimum, it is a fast T1 mapping method alternative
to IR based T1 mapping and it approximates proton density (PD) per voxel
simultaneously. Additionally, its results will be used in the following DESPOT277.
Mathematically, measured VFA signals is expressed as,

23
�(�⃗, �-) = �#(�⃗) 1 − �
, 4Q
4$(6⃗)
1 − �
, 4Q
4$(6⃗) cos �-
�
, 4P
4#
∗(6⃗) sin �- (2.26)
In Equation 2.26, both TR and TE are pre-determined constants, and �- is the �-th FA
out of in total N different FA’s. Additionally, transversal relaxation term �
, &>
&#
∗ (?A⃗) is
negligible if TE is set much shorter than T2
*
. For simplicity, let �!(�⃗) = �
, &:
&$(A?⃗)
. Equation
2.26 can be written in a linear form, such as,
�#(�⃗) sin �- _1 − �!(�⃗)` + �(�⃗, �-)�!(�⃗) cos �- = �(�⃗, �-) (2.27)
And Equation 2.27 can be further used to establish a matrix-vector multiplication form of
VFA signals, such as
í
sin �! �(�⃗, �!) cos �!
⋮ ⋮
sin �F �(�⃗, �F) cos �F
îï
�#(�⃗)_1 − �!(�⃗)`
�!(�⃗) ñ = í
�(�⃗, �!)
⋮
�(�⃗, �F)
î (2.28)
Solve Equation 2.28 for �#(�⃗) and �!(�⃗), and T1 values per voxel is calculated as
�!(�⃗) = − 4Q
ab P$(6⃗)
.
DESPOT277 technique uses a series of balanced Steady State Free Precession
(bSSFP)
79 sequences of different FAs and their signals can be expressed as,
�(�⃗, �-) = �#(�⃗)
1 − �
, 4Q
4$(6⃗)
1 − ó�
, 4Q
4$(6⃗) − �
, 4Q
4#(6⃗)ò cos �- − �
, 4Q
4$(6⃗)�
, 4Q
4#(6⃗)
�
, 4P
4#(6⃗) sin �- (2.29)
Again, �
, &>
&#(A?⃗) is negligible if TE is set much shorter than T2 and let �"(�⃗) = �
, &:
&#(A?⃗) for
simplicity, a matrix-vector multiplication form of Equation 2.29 is,

24
í
sin �! �(�⃗, �!)cos �!
⋮ ⋮
sin �F �(�⃗, �F)cos �F
î
⎣
⎢
⎢
⎢
⎡
�#(�⃗)_1 − �!(�⃗)`
1 − �!(�⃗)�"(�⃗)
�!(�⃗) − �"(�⃗)
1 − �!(�⃗)�"(�⃗) ⎦
⎥
⎥
⎥
⎤
= í
�(�⃗, �!)
⋮
�(�⃗, �F)
î (2.30)
Solve Equation 2.30 for P$(6⃗),P#(6⃗)
!,P$(6⃗)P#(6⃗) and using �!(�⃗) measured from DESPOT1, and then
T2 values per voxel is calculated as �!(�⃗) = − 4Q
abc D,>$(A?⃗)
D>$(?A⃗),$
d
in which � = P$(6⃗),P#(6⃗)
!,P$(6⃗)P#(6⃗)
.
2.3.2 Magnetic Resonance Fingerprinting
MRF has been most successful in the brain16,29, where it provides fast, and highly
repeatable and reproducible quantification of tissue parameters80, such as longitudinal
and transverse relaxation times and proton density (T1, T2 and PD). Its key features are:
(1) Pseudo randomized acquisition (known as the MRF schedule), e.g., repetition and
echo time and flip angle (TR, TE and FA), and SNR efficient readout trajectories, e.g.,
variable density spiral (VDS)
81, and (2) pattern matching the reconstructed MRF timeresolved images with a calculated signal evolution dictionary. The dictionary uses the
matched MRF schedule and a pre-determined set of tissue parameters.
Significance of MRF for Quantitative Relaxometry: These afore-mentioned
features allow the measured signal time-courses to be differentiated and quantitative
results can be produced per voxel. Its advantage in the reduction in scan time
compared to the conventional approaches, which perhaps is the best appreciated in
MRI, leads to its successful applications in different body parts such as brain22,29,30,
liver28 and prostate23,25,26. 3D MRF with whole-brain coverage can be performed
<10min82–86. MRF also provides the opportunity of performing both the inter- and intrasubject comparison at a large scale and has become an option for monitoring brain

25
tumors such as Glioma and can be used for further downstream applications such as
tumor grading30,87.
Significance of MRF for Synthetic MRI: MRF is also one candidate providers
of parametric maps to synthetic MRI88. Synthetic MRI focuses on measuring tissues
properties using a fast MR scan. Current Synthetic MR is capable of synthesizing 12
contrast-weighted MR images and producing tissue segmentations and parametric
maps using a 5-minute MR scan. Its volumetric results, including synthesized desired
contrast weighted MR images and parametric maps, are useful for radiologists to read
and help in decision making.
2.4 Applications of qMRI
Tissues’ NMR properties are affected when there is presence of disease, and this
can be reflected in qualitative MR images under appropriate contrast mechanism. For
example, qualitative diagnosis is based on differentiating two tissues with their contrast
maximized, which has been shown to be enough useful in simple cases. More complex
cases include, but not limited to, diffused diseases, longitudinal changes of pathologies,
presence of more than 2 tissues requiring differentials and usage of multiple contrast
mechanisms89. In these cases, commonly used contrast weighted images may have
ambiguous or missing presentations of abnormalities.
2.4.1 Detecting diffused liver and heart diseases
Diffused diseases are a type of diseases whose lesions are not concentrated.
Therefore, it is challenging to find a confident healthy control region and make diagnosis

26
by region-of-interest based comparison on contrast weighted images. Some examples
include liver and heart diseases, and more. In liver sickle cell diseases, for example,
assessment of liver iron load is useful and iron load is associated with transversal
relaxation90,91, however, liver may be hardly visible on a gradient echo image due to low
signals, making both qualitative diagnostic and quantification challenge, as
demonstrated. Alternatively, this can be done using ultrashort TE imaging92–94. Figure
2.4 demonstrates an example of autoimmune liver disease, in which liver may have
normal appearance on T2-weighted images, however, a T1 measurement will clearly
show a heterogenous appearance of liver and a mild elevation in T1
95. Similar situations
can be seen in heart diseases such as hypertrophic cardiomyopathy (HCM),
amyloidosis and Anderson-Fabry’s disease. In these diseases, healthy tissues are
replaced by fibrosis tissues, but these are not detectable by conventional late
gadolinium enhancement (LGE) imaging96 and they appear similar. Fortunately, they
can be easily detected by an observation of changed pre-contrast T1 and can be further
identified based on T1 changing trend, e.g., prolonged or shortened97. An example is
demonstrated in Figure 2.5.

27
Figure 2.4. Two examples of patients with autoimmune liver disease. (A)(B) Male, age
22 and (C)(D) male, age 20. Both (A) and (C) show axial T2-weighted fat-suppressed
image. In (A), there is observable hyperintensity associated with fibrosis tissues, which
is accordingly shown in the iron corrected T1map in (B). The liver has normal
appearance in (C), however, the iron corrected T1 map demonstrates homogeneous
appearance of the liver but with an mildly elevated overall mean value when being
compared against the population-based value (This figure is adapted from the original
figure presented by Dillman et al.98.)

28
Figure 2.5. LGE images, native T1 maps and extracellular volume maps in HCM,
amyloidosis and Anderson-Fabry’s disease. These diseases are not apparent on LGE
images, however, native T1 values are deviated from normal ranges, e.g., increased in
both HCM and amyloidosis, these are reduced in Fabry disease. (This figure is adapted
from the original figure presented by Dall’Armellina and Das99)
2.4.2 Monitoring longitudinal changes in brain
In contrary to diffused diseases, focal diseases in brain are already detectable on
contrast weighted MR images (under proper contrast mechanisms). Although
detectable, qualitative diagnosis faces challenges such as lack of identifications of the
same diseases but of different types or at different grades, which are useful diagnostic
information in diseases such as multiple sclerosis (MS), glioma and glioblastoma,
Parkinson’s diseases, and more to name. For example, there is investigation interest in

29
normal appearing white matter (NAWM) of different MS types: Primary progressive MS
(PPMS), relapsing remitting MS (RRMS) and secondary progressive MS (SPMS).
Researchers have shown that there is an increasing trend in T1 in normal white matter,
PPMS NAWM, RRMS and SPMS100–102. qMRI also plays a role in monitoring tumor
progression for Glioblastoma patients. Researchers have shown that it is feasible to
identifying peritumoral regions of low-grad Glioma and Glioblastoma using MRF29, and
measuring brain T1 values can be valuable in providing feedback in tumor changes,
such as predicting103 and detecting104,105 contrast enhancement in tumors. Besides
applications in white matter, other researchers also found shorter T1 in deep gray matter
in patients with Parkinson’s disease106, and cortex T1 decreasing in Parkinson’s disease
patients is three times larger than the controls over a 6.5-year span107. These are more
examples of longitudinal monitoring value of qMRI.
2.4.3 More examples
In addition to values in detecting diffused diseases and longitudinal monitoring
lesion regions, qMRI can extend these values in accurate identification and prediction.
For example, post-contrast T1 mapping can be used to differentiate tumor recurrence
and radiation necrosis, which offers possibilities in differentiating tumors from postsurgery brain changes108,109. Based on longitudinal monitoring results, disease
predictions can also be made on fresh patients at early stages in different body parts
(brain105, knee110,111, etc.). In summary, qMRI is gradually playing a heavier role in many
clinical applications and becoming an important complement to conventional qualitative
MRI.

30
2.5 0.55 Tesla MRI
2.5.1 Potential Impact of 0.55T MRI
Contemporary mid and low field MRI provides diagnostic-level imaging quality
with improved scan efficiency and is becoming more accessible for multiple reasons112–
115. For example, with a lower main field strength, the magnet footprint is less
restricted36 and due to reduced necessary coil windings, the size of the bore can be
wider (80 cm) which allows oversized subjects such as the obese and also helps
subjects with claustrophobia. Also, a lower field strength scanner is potentially more
affordable due to the reduced cost of purchasing, installing, maintaining and repairing.
2.5.2 Opportunities for Brain MRF at 0.55T
Improved field homogeneity: The static off-resonance is proportional to the
main field strength, which means at 0.55T, the field homogeneity is improved by 60-
80% compared to 1.5T and 3T. It allows longer readout gradients duration without
causing more off-resonance artifacts112.
Scaled relaxometry: Both the longitudinal and transversal relaxometry of brain
tissues are affected by switching from higher field strength to 0.55T. Compared to 1.5T
MRI, brain semisolid tissues T1 values are found to be shortened by 32% and T2 and T2
*
values are prolonged by 26% and 40%112, respectively. MRI contrast is also affected
and a potentially better differentiation between different brain tissues becomes possible.
The prolonged T2 and T2
* also favor longer readout durations since a more uniform kspace profile is achievable.

31
Reduced specific absorption rate (SAR): SAR is greatly reduced, e.g., �� ∝
(��#)". This allows us to utilize higher B1 (larger FA) and/or heavier MR experiments
(larger RF duty cycle) without drastically increasing tissue heating.
Summary: There are several opportunities to explore when optimizing 0.55T
MRF.
1. Higher SNR efficient readouts such as longer spiral to: (a) improve SNR without
compromising on spatial resolution and extra scan time and (b) higher spatial
resolution without compromising on SNR.
2. More intense excitations.
These rely on a dedicated MRF pulse design at 0.55T. These opportunities are not
completely beneficial. For example, as the readout gradients are active for a longer
duration, it causes stronger concomitant field effects which will be explained in the next
subsection.
2.5.3 Challenges for Brain MRF at 0.55T
SNR loss. The signal and the noise in 1H MRI are dependent on multiple factors.
MR signal is related to the equilibrium polarization and tissue NMR relaxation
parameters, that are related to other factors such as field strength, temperature,
sequence timings, etc. This proposal will focus on the reduced SNR due to polarization
at lower field strengths, and how to compensate. Noise is assumed to be i.i.d. complex
additive white Gaussian noise (AWGN) thermal noise. The readout bandwidth is
assumed to be constant across field strengths.

32
There are several possible reasons that the main field strength is affecting the
SNR, and most of them are directly related to the amount of signal measured.
1. The equilibrium bulk magnetization is linearly proportional to the main field
strength, e.g., �# ∝ �#. Compared to 3 T, 0.55 T MRF naturally has a ~5.5x
lower ceiling of the highest possible signal.
2. Longitudinal and transversal relaxations (T1 and T2) of MR signals have
dependencies the main field strength36. For semi-solid tissues like white matter,
T1 is shortened and T2 is prolonged as lower field strength36,112. Unlike �# being
reduced, this effect brings in SNR gain from relaxometry perspectives, since
magnetizations are allowed to recover faster (longitudinal, R1 = 1/T1) and decay
more slowly (transversal, R2 = 1/T2) between RF pulses.
3. MT effect is stronger at lower field strength. MT effect largely affects the SNR of
pulse sequences using a long pulse train like fast spin echo sequence116,117 and
can have further impact on sequences involving varying RF magnitude such as
variable flip angle67,118 (and MRF falls onto both types). It results from the
different absorption lineshapes between different magnetization pools. A simple
two-pool model partially describes the effect by modeling energy transfer
between the bound and free pool. The bound pool has a wider absorption
lineshape and faster transversal relaxation. Thus, this pool doesn’t produce
measurable signals but keeps transferring the RF energy absorbed to its
neighbor free pool, which leads to a “partial saturation” and a signal reduction. At
lower field strength, the bound pool absorption lineshape becomes narrower

33
which means more bound pool protons are involved in the transfer so the partial
saturation becomes stronger.
In general, 0.55T MRF is facing an SNR loss challenge mainly caused by change
of field strength. There are multiple ways to address the SNR loss problem. For
example, reducing spatial resolution is a quick way to recover SNR, however, it is
compromising and should only be considered when SNR is far below sufficiency. In
order to maintain both the spatial resolution and scan time cost at a diagnostic and
practical level, improving SNR efficiency of the sequence and post processing to
denoise is of higher interest. This proposal will fucus on two ways to address the
problem: (1) High SNR efficiency 3D MRF pulse sequence design and (2) denoising via
advanced reconstruction.
Concomitant field effects. Concomitant fields are the higher order spatially
varying magnetic fields accompanying the imaging gradient fields, as indicated by the
Maxwell’s equations119,120. Its effect can be viewed as “dynamic off-resonance”
analogous to the static off-resonance. The effects on spiral MRF are spatial blurring just
as what is typically seen from static off-resonance. Unlike static off-resonance, which is
proportional to the main field strength, concomitant field effect is inversely proportional
to the main field strength and additionally increases with the off isocenter distance and
the usage of higher gradient amplitude. The effects depend on imaging prescription. It
has been shown that ignoring the blurring causes accuracy issues in MRF results121.
Examining and correcting concomitant field effects becomes necessary, especially
when performing 3D imaging (off isocenter distance is substantial) and using readout
gradients for longer duration (for high SNR efficiency).

34
Concomitant field effects can be mitigated or corrected in multiple ways. King et
al.120 proposed a frequency segmented deblurring method which required to
approximate concomitant gradient terms. This method later was improved with better
computation efficient and was capable of simultaneously address static off-resonance
and concomitant fields artifacts122,123. Also, concomitant field effects can be corrected
with the aid of NMR field probes123,124. As described by Wilm et al.125, NMR field probes’
measurements can be used to form an accurate higher order encoding model and
applying this model successfully produced high quality MR images125–127. However, this
approach was not widely used due to the high cost of owning an MRI system and field
monitoring devices. Alternatively, magnetic field evolutions can be characterized by
characterizing gradient distortions such as gradient impulse response functions
(GIRFs)
128,129. GIRF based methods have proven to be effective compromise to field
monitoring devices130–133.
MT effects. MT effects accounts for cross relaxation or spin exchanges of water
molecules between free pool and bound pool of tissues and they are inherent for
biological materials. They are known to cause estimation biases in different qMRI
applications such as VFA T1 mapping and MCSE T2 mapping. The common points
among those qMRI applications are that multiple RF pulses are used in short
succession. These RF pulse behave to saturate the longitudinal component of bound
pool by �,e(.)) ffffffffff@:E with saturation rate �(�)) õõõõõõõõõ defined as
�(�)) õõõõõõõõõ = ��"
�Qg
h |�!(�)|
"�(�))��
@:E
#
(2.31)
Equation 2.31 indicates �(�)) õõõõõõõõõ depends on 2 major factors: RF pulse characteristics
including its duration and amplitude squared, and the absorption lineshape �(�)) in

35
which �) is the off-resonance frequency. Two widely used absorption lineshapes are
Gaussian and super-Lorentzian lineshapes8,64,68, and they are mathematically defined
as, respectively,
�(�) = �"
�
1
1 + (��")" (2.32)
�(�) = h û2
�
�"
|3�" − 1|
�,"c
"D.4#
hi#,!
d
#
��
!
#
(2.33)
Both lineshapes will be narrower as longer T2 values. Since slightly increasing T2 values
are observed at 0.55 T compared to higher field strength MRI and chemical shifts are
reduced, bound pool absorption lineshape is hypothesized to be narrower at 0.55 T,
indicating potentially more on-resonance bound pool magnetization, faster longitudinal
saturation, more cross relaxation and more signal loss. MT effects’ impact on 0.55 T
MRI is not yet conclusive, since they may serve as improved contrast mechanism for
multiple applications where stronger background suppression or saturation is desired.
However, when being ignored, they may cause huger biases in qMRI which is not
acceptable if quantification accuracy is the first-place task.
2.5.4 Precision analysis for Brain MRF at 0.55T
Precision analysis is useful in analyzing noise in developed methods, especially
when noise is spatially varying (such as a result of parallel imaging). There are multiple
ways to perform such analysis, for example, direct image noise matrix approaches46,
multiple replica methods134, error propagation analysis135, etc. These approaches have
different advantages and disadvantages, and may also be associated with different
reconstruction approaches.

36
Direct image noise matrix approaches: A class of accurate and quantitative
methods that focus on analytically calculating SNR. Hence, the prior knowledge about
the exact image linear reconstruction is required. These approaches can produce
accurate SNR per spatial location, which is especially useful in calculating noise
amplifications as a result of parallel imaging, however, they are in general memory
consuming, e.g., ~�(�j) to �(�k) where � is number of rows or columns of image
matrix (such as the widely used 256).
Statistical methods: Another class of precision analysis methods involving
Monte-Carlo simulation. For example, “actual multiple replica methods”134 acquire the
identical k-space data multiple times and separately feed these data to the same
reconstruction. As a result, they produce reconstructed images per replica and can
calculate the noise variations per voxel along the replica dimension. It assumes that
noise is the only variations between replicas and treat reconstruction as a “black box”
(no need to know how reconstruction works). Apparently, actual multiple replicas
methods require prolonged exam time for repeating scans, and this makes the methods
sensitive to motions, physiological noise and/or instrumental drifts. To account for these,
“pseudo replica methods”134 are alternatively proposed which differ from the actual
replica methods by adding synthesized noise to k-space data to create multiple replicas.
They additionally require the prior knowledge of noise distribution in k-space.
Error propagation analysis methods136: Analytical methods that are capable of
analyzing biases from different sources. These methods are commonly used by
quantitative MRI model fitting, and hence require the knowledge of signal models.
Besides, the knowledge of signal models makes the analysis go beyond limitation of

37
linear reconstruction and noise-induced variations. They evaluate the reconstruction
sensitivity to other sources, including but not limited to system imperfections (e.g., field
inhomogeneity) and/or upstream perturbations, e.g., biased inputs.
Other approaches: There are other approaches working in more or less similar
ways as mentioned above. For example, Cramer-Rao analysis produces theoretical
uncertainty low bound estimation and is useful in designing the optimal method with the
best precision137. For implicit reconstruction approaches such as deep-learning based
reconstruction, it is possible to measure standard deviation values of relative absolute
errors on purely training and test sets at different SNR levels138.
Table 2.1 contains a summary of precision analysis approaches. In this work, the
precision of MRF T2 and T1 maps will be analyzed. Although a signal evolution model
exists and a direct estimation of T1 and T2 from acquired k-space data is doable139,
analytically calculating the noise per voxel is challenging due to high non-linearity of the
problem, and noise propagation analysis is complicated due to evolutionary signals.
Therefore, this analysis will use the pseudo replica method134. This method can
efficiently work on a single dataset along with noise covariance information, and is
applicable to MRF reconstruction using dictionary matching34. However, several
limitations exist. The pseudo replica method is limited to produce an analysis subject to
thermal noise only, and does not account for biases or perturbations from other
sources, e.g., system imperfections and physiological causes. Also, it does not gurantee
the optimality of the method as the method is not optimized.

38
Table 2.1. A summary of precision analysis methods, the associated reconstruction and
comments.

39
Chapter 3 Sparse Pre-Contrast T1 Mapping for HighResolution Whole-Brain DCE-MRI
3.1 Introduction
Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) is a
powerful imaging tool that can reveal the spatial distribution of vascular parameters,
including permeability and plasma volume, through tracer-kinetic (TK) modeling140,141. It
involves collecting a series of T1-weighted images during the arrival and passage of T1-
shortening contrast agent142,143. Quantitative DCE-MRI has demonstrated value in
diagnosing and monitoring of various brain diseases, including tumors144,145, multiple
sclerosis146,147, and Alzheimer’s disease148.
Widespread clinical application is limited by low spatial resolution, insufficient
spatial coverage and long data acquisition. Recent studies have overcome these
limitations by using parallel imaging techniques149,150, and compressed sensing151 or
model-based reconstruction techniques, to simultaneously achieve high spatial
resolution and whole-brain coverage. For example, Lebel et al. demonstrated a method
combining compressed sensing and parallel imaging152, that was later validated in brain
tumor patients by Guo et al.
153 Several more recent works have demonstrated the
benefits of model-based reconstruction that incorporate the model used for DCE
parameter quantification. For example, Dickie et al. proposed joint estimation of T1 and
tracer-kinetic maps154 to improve accuracy and precision, Guo et al. demonstrated a
direct estimation of tracer-kinetic parameters155 and a joint estimation with patient-

40
specific arterial input function156, and Lingala et al. demonstrated the use of dictionarybased constraints157. Most of these previous works either employed fully sampled T1
mapping, which is not feasible in the clinic, or assumed a fixed T1 value for brain tissue,
which is not realistic.
Pre-contrast M0 and T1 maps with matching spatial resolution and coverage are
required for these methods to be practically applied in patients. This can be achieved
via variable flip angle (VFA)
158 or inversion recovery (IR)
159 imaging. IR is considered as
the gold standard for T1 mapping, and substantial bias exists between VFA and IR.
Despite this bias, VFA is the most widely used approach for pre-contrast T1 mapping in
DCE-MRI because it is faster and acquisition parameters can be precisely matched to
the 3D spoiled gradient recalled echo (SPGR) sequence that is used for the main DCEMRI scan. However, high-resolution whole-brain full-sampling VFA imaging may be
impractical due to the long scan time required. This leads to an unmet need for
resolution and coverage matched rapid pre-contrast T1 mapping. Lebel et al.
demonstrated that T1 mapping is feasible using sparsely sampled VFA acquisition
integrated with DCE-MRI160. Maier et al. demonstrated sparse T1 mapping estimation
using total variation (TV) and total generalized variation (TGV) constraints161 in healthy
volunteers. Note that the appropriateness of spatial smoothness constraints in brain
tumor patients is unclear due to potential T1 heterogeneity. These works collectively
show the potential value of model-based and/or constrained reconstruction techniques
to accelerate VFA T1 mapping.
In this work, we evaluate a time-efficient direct T1 mapping approach specifically
for high-resolution whole-brain quantitative DCE-MRI in brain tumor patients. We utilize

41
a brain tumor Digital Reference Object (DRO) to determine accuracy under both
noiseless and 3T-mimicking scenarios. We evaluate the approach in vivo by
retrospectively undersampling fully sampled VFA data from a healthy volunteer to
identify possible artifacts and image quality issues. Finally, we apply the approach to
prospectively undersampled VFA scans to assess heterogeneity of T1 measurements in
high grade glioma patients.
3.2 Methods
3.2.1 Variable Flip Angle T1 Mapping
VFA mapping involves the collection of a series of T1-weighted SPGR images
with different prescribed flip angles �-. VFA imaging is sensitive to B1
+ inhomogeneity162,
which requires the acquisition of a B1
+ scale map (�!) to estimate actual flip angles �- =
�!�-. We utilize the SPGR steady state signal model that describes signal �- as a
function of M0, T1, actual flip angle �-, and TR:
�-(�#, �!, �-) = �# sin �- (1 − �!#)
1 − �!# cos �-
(3.1)
where �!# = �
,&:
&$ . Note that the effect of T2
* decay is neglected due to short and
unchanging TE. Voxel-based pre-contrast M0 and T1 values can be efficiently estimated
through a SPGR model fitting process:
£
�#(1 − �!#)
�!#
§ = �l •
�!
�"
⋮
�FEF
¶ (3.2)
where � = [sin �- �- cos �-], as described by Deoni et al.162,163. Note that M0 and T1
are jointly estimated and are therefore correlated. In this work, we focus on T1 accuracy

42
and precision since it is crucial for quantitative DCE-MRI164,165 and is measured in
meaningful physical units. Appendix 3.A contains an analysis of the impact of precontrast T1 mapping error on quantitative DCE-MRI.
3.2.2 Sparse T1 Estimation
When VFA data/images are under-sampled, it is possible to perform sparse
image reconstruction for each flip angle prior to T1 estimation on a voxel-by-voxel
basis166–168. However, this does not leverage shared information across the images.
Alternatively, T1 mapping can be performed for the entire volume in a single step
directly from the under-sampled k-space data. This skips the intermediate step of
forming images for each flip angle, and instead relies on accurate forward models. The
key benefit is that T1 information is extracted from the data in an optimal way, from an
information-theoretic perspective. In this work, we allocated four times as many PE lines
to measurements with the last flip angle FA7 compared to all other flip angles FA1-6.
This is because denser sampling of k-space at the last flip angle comes at no additional
scan time cost as it is already needed for the pre-contrast phase of the DCE-MRI scan.
We define the VFA scan time � to be the time required for FA1-6. The undersampling
factor R is defined as the total number of PE’s required for 7 Nyquist sampled FA’s
divided by the number of acquired PE’s. When R=1, t=6T/7, where T is the time
required for Nyquist sampling of all seven flip angles. When R>1, t=3T/5R, because
FA7 is given 4-fold more scan time than the other flip angles. Figure 3.1 shows the
Cartesian Spiral sampling pattern for each FA. The phase encoding (PE) order follows a

43
phyllotaxis spiral trajectory. Each arm of the spiral contained roughly 45 phase encodes
that fall on a Cartesian grid and whose locations were pseudo-randomly generated.
Figure 3.1. Illustration of Cartesian spiral sampling. Each panel illustrates the (ky,kz)
matrix with white dots denoting the phase encodes that are acquired. Flip angles are
logarithmically spaced from 1.5º to 15º. An undersampling factor R=10 is illustrated, which
corresponds to 60.48 seconds VFA scan time. Note that 15º is 4 times more densely
sampled than other FA’s, for all undersampling factors.
3.2.3 Direct T1 Estimation
Direct T1 estimation can be performed by solving the following inverse problem,
(�#, �!) = min
G!,4$
1
2 ‖�i��(�#, �!, �) − �‖M#
" (3.3)
Data consistency measures the distance between forward signal model applied to the
estimate and the sampled data at measured locations in (k, FA) space, where �i is the
under-sampled Fourier transform operator, � is the coil sensitivity, � is the steady state
SPGR forward model including the measured �!, and � is the measured k-space data.
A necessary condition for the problem to be well-posed is that the number of
measurements are larger than the number of unknowns, e.g., FEFmno ([)
Q
>2�, where � is
the subspace spanned by coils, � is the number of voxels and � is the undersampling
factor. This indicates that the problem will be ill-posed if �>FEFmno ([)
" . Ideally, dim (�) is
equal to number of coils, �q, if coils are linearly independent to each other. In this work,

44
the aforementioned problem is solved using the Nonlinear Conjugate Gradient (NCG)
method initialized with M0=0 and T1=1000 ms within the field of view.
3.2.4 Evaluation in a Digital Reference Object
An anatomically realistic DRO169,170 was used to evaluate accuracy and precision
of M0 and T1 maps as a function of noise level and undersampling rate. Each healthy
tissue type in the DRO was assigned T1 values based on literature171, e.g., 1084 ms for
WM, and M0 values were normalized with respect to cerebrospinal fluid (CSF). To the
best of our knowledge, brain tumor such as glioma, has T1 values longer than healthy
tissues, with literature reporting 1392-3601 ms172–174. Therefore, we set T1 to be 2000
ms for BT in the DRO. The DRO has a matrix size of 256x256x12, matching a spatial
resolution of 0.94x0.94x5 mm3. Simulated scan settings, e.g., FA, TR and TE, are
identical to our in-vivo experiment settings, including phase encoding in the axial plane.
An 8-channel coil sensitivity map was simulated based on in-vivo measurement at 3 T
MRI scanner (HD23, GE Healthcare). Noise was simulated at a level matching typical 3
T MRI at our center, and one order of magnitude lower and higher. Undersampling
factors in range from 1x to 40x were considered for the noiseless case. In the noiseless
case, for each undersampling factor we considered up to 10 different realizations in
order to account for potential variability in the sampling. For experiments under noise
corruption, we considered undersampling factors ranging from 1x to 40x, each factor
with one sampling pattern realization and up to 50 noise realizations, which was found
enough to stabilize estimation of bias and standard deviation (SD) of T1 estimates.

45
Our analysis focused on white matter (WM) and brain tumor (BT) regions of
interest (ROI’s). T1 values within these ROI’s are reported in histograms for each
undersampling factor and/or noise level. We also compare reconstructed T1 values with
the assigned ground truth. Mean and SD of T1 values are plotted as a function of
undersampling factor, and coefficient of variation is computed to numerically reflect the
accuracy and precision of the results and their evolution as the undersampling factor
increases.
3.2.5 In-Vivo Experimental Methods
In-vivo experiments were performed on a clinical 3T MRI scanner (MR750, GE
Healthcare) with a 12-channel Head-Neck-Spine receiver coil. Imaging protocols were
approved by the relevant Institutional Review Board and all subjects provided written
informed consent. B1
+ mapping was performed using the Bloch-Siegert approach175.
Data were acquired with a coronal slab orientation, with superior-inferior as the readout
direction. The VFA flip angles were logarithmically spaced from 1.5° to 15°. Acquisition
settings: 4.9 ms TR, 1.9 ms TE, 240×240×240 mm3 FOV, 2 mm slice thickness, and
256×240×120 matrix size. The pulse sequence was derived from the vendor product
sequence and modified to acquire specific phase encodes and tip angles; the sequence
used slab-selective excitations and the RF and gradient spoiling were unchanged.
For the retrospective study (one healthy volunteer, full sampling), the acquisition
time was 16 minutes and 48 seconds. For the prospective study (13 patients), the
acquisition time was 576 seconds consisting of both T1 mapping (245 sec) and Sparse
DCE (5 sec per frame, contrast injection at ~4 min), and a fully sampled 40x40 phase

46
encoding grid of the k-space center was acquired for FA=1.5° (8 seconds of scan time)
for coil sensitivity estimation. The coil sensitivity maps were estimated from this image,
by dividing the individual-coil low-resolution anatomic images by the coil-combined
image. There is also a brief transient approach to steady state every time there is a
change in the applied FA. We discarded the first 4.5 seconds for the first FA, and the
first 2 seconds for each subsequent FA. This was adequate to ensure spins were within
±7% of their steady-state value for T1’s in the range 1300 to 2500 ms.
All reconstructions were performed off-line. Tissue masks (e.g. WM) for fully
sampled healthy volunteer data were extracted using the FMRIB's Automated
Segmentation Tool (FAST) toolbox176 (https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FAST) using
fully sampled images at 10.22° which had the best GM-WM CNR.
3.2.6 Evaluation in a Healthy Adult
Fully sampled VFA measurement was obtained from one healthy adult volunteer
(M/26). Raw data were retrospectively subsampled in (k, FA) space with undersampling
factors ranging from 1x to 40x, each with up to 10 realizations of the randomized
sampling pattern. Our analysis focused on WM ROIs. Results are reported and
analyzed in a similar fashion as for noisy DRO study, except that T1 maps estimated
from fully sampled scans served as reference. In addition, a T1 spatial map and an
absolute fractional difference spatial map are employed to show spatial patterns in T1
values.
3.2.7 Prospective Application to Brain Tumor Patients

47
Methods were evaluated prospectively in 13 patients with high-grade glioma
brain tumor (4M/9F, Age range 42-80 years). These data were acquired between
December 2016 and April 2019. The vendor-provided 3D spoiled gradient echo
sequence was modified to include sparse VFA sampling with R=4 prior to sparse DCEMRI, as described by Lebel et al.160. The resulting T1 maps were qualitatively evaluated
by a Neuroradiologist for visual quality (noise, tissue inhomogeneity, tissue differential),
evidence of tumor, post-surgical cavity and artifacts. These maps were also given a
qualitative score on a three-point Likert scale. The score was defined as follows: 0=nondiagnostic due to artifacts and/or difficulty visualizing tissue boundaries; 1=diagnostic,
may have mild artifacts, adequate visualization of tissue boundaries; 2=diagnostic with
high quality, no visible artifacts, and well-defined tissue boundaries).
Small ROIs were manually drawn for WM, BT, temporalis and surgical cavities,
and mean and SD of T1 values are reported for these ROI’s. The ROI’s of the tumor
were hand-drawn by a board certified Neuroradiologist with 9 years of experience. They
were selected based on the imaging morphology and signal intensity of the tumoral and
peri-tumoral tissue. The selections were based on the assessment of the imaging
features, including regional mass effect, volume loss, and findings suggestive of cellular
tumor (based on a visual qualitative assessment of the T1 mapping signal compared to
other intracranial structures), which are all findings that are commonly used to assess
for neoplasm on conventional MR imaging sequences.
3.3 Results
3.3.1 Validation using a Digital Reference Object

48
Figure 3.2 shows results of noiseless and 3T-mimicking noisy DRO cases.
Results gathering 10 undersampling realizations and results gathering 50 noise
realizations are reported for noiseless and noisy cases, respectively. The SNR level of
50 is chosen for display since it is the closest to our clinical protocol. In Figure
3.2(A)(B), histograms of both tissues behave as approximately impulse for R≤10, and
approximately Gaussian for R≥16 for noiseless cases. In the noisy cases, histograms
are approximately Gaussian for R≤10 and are almost flat for R≥16. This can be also
seen numerically from Figure 3.2(C)(D). As expected, T1 SD gets monotonically larger
with higher undersampling factor. In the noiseless case, when R≤10 (VFA scan time
≥137.63 s), the T1 bias is <1 ms and SD is <40 ms for both tissues. In the 3D-mimicking
case, when R≤10, the T1 bias is <10 ms and SD is <110 ms (WM) and <250 ms (BT),
and when R>16, the T1 mean starts changing randomly and its SD overshoots in BT.
Figure 3.2. Brain Tumor Digital Reference Object (DRO) results. (A) T1 histograms for the
noiseless DRO, (B) T1 histograms for the 3T-mimicking noisy DRO, (C) T1 mean values and (D)
T1 standard deviation values. All are plotted as a function of (A, B) undersampling factor or (C,
D) VFA scan time. VFA scan time axis is in logarithmic scale. The top row represents BT ROI, and
bottom row represents WM ROI. The red dot represents the reference T1 value in (A)(B) and the

49
undersampling level matching the prospective undersampling are marked bold in (C)(D). As
expected, precision gets monotonically worse with higher undersampling factor. In the noiseless
case, when R ≤ 16 (VFA scan time ≥137.63 s), the T1 bias is <1 ms and standard deviation is <40
ms for both tissues. In the 3D-mimicking case, when R≤10, the T1 bias is <10 ms and standard
deviation is <110 ms (WM) and <250 ms (BT).
3.3.2 Validation in a Healthy Adult Volunteer
Figure 3.3 shows the results of T1 mapping using healthy volunteer data. As
undersampling increases, the histograms become broader and have thicker tails. This
matches what we observe in Figure 3.2. Bias is small until R≥16, and SD increases
with higher undersampling factor, but imprecision due to this method is not detectable
until R≥10. When R≤10 (VFA scan time ≥100.8 s), T1 mapping bias <11 ms, and SD is
<214 ms (coefficient of variation <15%).
Figure 3.3. Healthy volunteer results. Fully sampled datasets were retrospectively undersampled with 10 realizations of the pseudo-random data sampling pattern. (A) WM T1 histogram
as a function of undersampling factor, (B) mean T1 and (C) T1 standard deviation as a function of
VFA scan time. VFA scan time axis is in logarithmic scale. The mean T1 from fully sampled data
is shown as the blue dashed line in (B). Bias is insignificant (<30 ms) until R ≥ 16. Precision gets
worse with higher undersampling factor, but imprecision due to this method is not detectable until
R≥10. When R ≤ 10 (VFA scan time ≥100.8 s), T1 mapping bias <11 ms, and standard deviation
is <214 ms.
Figure 3.4 shows a series of T1 spatial maps of a representative healthy
volunteer for each undersampling factor, and the associated absolute fractional

50
difference maps. When R≤10, there is less error within WM and GM in which mean
fractional difference was <8.46% and <14.76%, respectively, and error concentrated
around tissues of less interest. For example, bias in CSF and temporalis is
respectively >1278.5 ms and >156.9 ms. No spatial patterns related to the data
sampling method were observed. As R increases, we can observe error started to
increase in WM and GM regions.
Figure 3.4. Illustration of T1 spatial and absolute fractional difference maps from the healthy
volunteer. Direct reconstruction of the fully sampled data is taken as the reference. Qualitatively,
for R≤10, we see minor error in WM or GM. Errors appear isolated to CSF (bias>1278.5 ms,
SD>557.6 ms) and muscle (bias>156.9 ms, SD>209.8 ms), whose T1 values are generally less
of interest in brain DCE-MRI. Importantly, no spatial patterns indicating systemic errors were

51
observed in the error maps. For R>10, we observe severe error corruption of T1 maps in GM and
WM regions.
3.3.3 Demonstration in Brain Tumor Patients
The prospective dataset contained a variety of tumor locations and time points
during treatment. Demographics, qualitative diagnostic scores and T1 values of WM, BT,
temporalis and cavity-fillings are reported in Table 3.1. BT T1 values are reported from
the time point with the most clear and substantial evidence of tumor, determined based
on the longitudinal progression verified by contrast enhancement. No distinct artifacts
were observed. One case received a qualitative score of 1, and this case has strong T1
inhomogeneity in CSF. All other cases received a qualitative score of 2. Out of thirteen
cases, three showed no obvious tumor based on T1 and post-contrast readings, while all
other cases showed brain tumor and/or post-surgical abnormalities. There is noticeably
higher SD in temporalis T1, and cavity-fillings have substantially longer T1 (>4000 ms)
than WM and BT. Figure 3.5 shows three representative examples with orthogonal
cross sections of each tumor. These maps show clear T1 differentiation of WM, GM, and
BT/abnormality regions, as well as post-surgical cavities, with high spatial resolution.
Figure 3.6 shows zoomed versions of the same T1 maps that showcase the ability to
capture T1 heterogeneity.

52
Table 3.1. Patient demographics, qualitative scores, and T1 values for White Matter (WM) and
Brain Tumor (BT) regions of interest. Volume T1 datasets were qualitatively scored by a
Neuroradiologist using the following Likert-scale: 0, non-diagnostic; 1, diagnostic with mediocre
quality; 2, diagnostic with high quality. Small ROI’s were manually drawn to also yield T1
measurements, reported as mean ± standard deviation.

53
Figure 3.5. Representative M0 and T1 maps from 3 patients with high grade glioma. Maps
are volumetric, and axial, coronal, and sagittal slices through the tumor section are shown
for each patient. (left) M0 maps with tumor ROI drawn in red. (right) T1 maps showing
good delineation of WM, GM, CSF, and Tumor. WM and GM regions have the expected

54
homogeneity. In addition to tissue differential, these maps also reveal the locations of
craniotomy (green arrow) and post-surgical cavities (blue arrow) that are filled with
proteinaceous fluid such as blood in high spatial resolution.
Figure 3.6. Closeup of T1 maps from the 3 patients in Figure 5. Maps are zoomed into
the tumor region (delineated by white dashed box in Figure 5), with narrow display range.
The proposed method captures T1 heterogeneity. T1 coefficient of variation are 10.84%,
9.96%, and 7.31% for the top, middle, and bottom rows, respectively. All cases show
spatial variations in T1. For example, T1 is longer in tumor center (e.g. light green arrow)
than in tumor rim (e.g. green arrow) and peritumoral regions (e.g. dark green arrow).

55
3.4 Discussion
This study evaluated direct estimation of native M0 and T1 maps at 3T through
simulation as well as in in-vivo studies of a healthy subject and brain tumor patients.
Simulations in DROs revealed T1 measurement variability of this approach to be
dominated by noise at undersampling factors less than or equal to 10, while errors due
to undersampling dominated above. We anticipate this cutoff point to differ for other field
strengths (e.g., 1.5T), coil configurations, protocols (e.g., resolution, FOV), anatomies
(e.g., breast, prostate) and imaging tasks (e.g., other quantitative MRI applications).
Simulation on noise corrupted T1 measurements also demonstrated the T1 errors in BT
to be more susceptible to undersampling than in WM regions. Therefore, it is important
to focus performance analysis on clinically relevant regions of interest, rather than
global metrics.
We utilized a 3DFT acquisition with Cartesian spiral subsampling because that it
is important to maintain the same spatial distortions between the T1 mapping and the
DCE sequence. These are largely impacted by the pulse sequence, prescription, and
readout trajectory and bandwidth. A limitation of this study is that we did not compare
different subsampling approaches. Such an analysis has been performed for sparse
DCE-MRI acquisitions170. We utilized the same sub-sampling strategy for T1 mapping as
is being used for sparse DCE-MRI at our institution.
Results of retrospective in-vivo scans were consistent with results from the 3Tmimicking noisy DRO, which confirms the ability of the simulation to predict in-vivo
performance. Specifically, both T1 mean and SD values increased with higher
undersampling, as shown in Figure 3.2CD and Figure 3.3BC. Up to the critical

56
undersampling factor of 10, the trend can be explained by noise amplification related to
parallel imaging, since the increase was only observed in the noisy cases. However, for
undersampling factors above 10, the formulated problem becomes ill-posed, causing
variations in the mean and increased standard deviation in both noisy and noiseless
cases. We expect that this “critical R” is dependent on several factors, including the
receiver coil configuration and the number of VFA flip angles. For example, the “critical
R” is likely to be larger if one uses higher-density coil arrays that provide greater
degrees of freedom in the subspace spanned by the coil sensitivity maps.
We noticed no spatial patterns related to data sampling in the T1 error maps at
R≤10 in the healthy volunteer study. There were, however, mild spatial variations in T1
error with tissue type. For instance, we saw negligible error in WM, and higher error in
CSF. This is consistent with the expected reduction in T1 precision as true T1 increases.
The proposed method was successfully applied to a small cohort of patients with highgrade glioma. The T1 values in BT regions are heterogeneous and are longer than
those of WM in the same subjects, with values consistent with literature172–174 (1392-
3601 ms).
We observed spatial heterogeneity and the presence of sharp features in BT
ROI’s. This indicates the need for pre-contrast T1 mapping to provide equally fine
spatial-resolution compared with DCE-MRI and indicates that the use of spatial
constraints/regularization could mask these features. Parametric constraints along the
flip angle dimension or appropriately defined low rank constraints may be viable. The
proposed method allowed clear visualization of post-surgical cavities which have
substantially longer T1 values. The proposed method depicted the expected tissue

57
boundaries with high spatial resolution and whole-brain coverage, providing adequate
quality for voxel-wise quantitative DCE-MRI. However, we were not able to observe
clear boundaries between cellular tumor and cavities, likely because there could be
mixture with more complicated T1 characteristics, such as edema.
Error propagation analysis revealed that ±15% error in mean brain tumor T1
results in at most 0.008 and 0.007 min-1 (Patlak), and 0.016 and 0.033 min-1 absolute
error (ETK) in the DCE estimated pharmacokinetic parameters, �^ and �(, respectively.
However, there are many dependencies, and error propagation depends on the TK
model, true T1 and the polarity of the error. TK error is always positively related to precontrast T1 error in the Patlak model, however, the relationships for the ETK model are
more complicated, as discussed in the Appendix.
This study has several limitations. First, there is a general lack of commonly
accepted glioma T1 values likely because of inter-tumor heterogeneity due factors such
as tumor grade, age, and treatment. For this reason, realistic simulation of brain tumors
in DROs remains challenging and possible sub-optimal in terms of its ability to
accurately capture real brain DCE-MRI exams. This study addresses this with a range
of parameter values based on published literature, and refinement of this approach is
subject to future research.
The second limitation consists of only using one healthy subject for in-vivo
validation of the proposed method. Acquiring fully sampled VFA scans is time
consuming which impedes the generation of larger datasets for this study. For identical
reasons, acquiring such scans for brain tumor patients as the target cohort was not
practical because of the severity of the disease and patient unwillingness to consent to

58
such extensive research exams. Tumor ROI’s were directly drawn on the T1 maps to be
evaluated which caused circularity in the patient study that we were unable to avoid.
Failure to account for MT and motion effects is the third limitation of the study.
Better accuracy and precision may be achieved by incorporating MT and head motion
modeling, or by implementing controlled saturation magnetization transfer introduced by
Teixeira et al.177. An example of demonstrating improved MT-balanced VFA T1 mapping
has been shown by Lee et al178.
The fourth limitation is that the FA settings were not optimized for this application.
We used 7 flip angles logarithmically spaced from 1° to 15° based on the expectation
that T1 values in BT ROI’s can fall in a broad range. We used a large number of flip
angles to improve sensitivity over this broad range of T1, but this was not optimized via
simulation or phantom experiment.
Lastly, the proposed reconstruction involves a non-linear and non-convex
optimization problem. This is computationally complex and can be numerically unstable.
In the prospective study, reconstruction required roughly 3 hours per 3D dataset, on a
computation node of USC Center for Advanced Research Computing. The long
reconstruction time is caused by the recurring gradient computation. This can be
potentially shortened with better initial guesses such as low-resolution estimates of M0
and T1 maps.
In this study, 10-fold undersampling was found to be the upper bound for
adequately accurate pre-contrast T1 mapping. This result is specific to the body part and
disease of interest, and our DCE-MRI setup, including field strength, receiver coil, and
imaging parameters. To apply this approach to a different scanner or body part and

59
disease, we suggest starting with a disease-appropriate DRO, locally measured coil
sensitivity profiles and noise covariance measurements. Then repeat the steps in this
paper to determine the undersampling limit.
3.5 Conclusion
We have demonstrated the feasibility of direct pre-contrast T1 mapping suitable
for high-resolution whole-brain quantitative DCE-MRI, with 150 seconds of VFA scan
time. The proposed method is validated in DROs and in one healthy volunteer and
achieved T1 bias ≤11 ms, and coefficient of variation ≤15% at an undersampling factor
of 4. Prospective application to BT patients demonstrated no distinct artifacts, diagnostic
image quality, and T1 maps with high definition and with values consistent with
published literature.
Appendix 3.A: Impact of Pre-contrast T1 (errors) on Quantitative DCE-MRI (errors)
Here, we summarize the impact of pre-contrast �! mapping errors on quantitative
DCE-MRI tracer-kinetic (TK) parameter mapping errors. This is a form of error
propagation analysis. DCE-MRI TK parameters �, can include �(, �^, �S, etc.,
depending on the model used. Here, we examine the Patlak and Extended Tofts-Kety
(ETK) models which are commonly used in brain tumor DCE-MRI.
DCE-MRI utilizes spoiled gradient echo (SPGR) imaging. Consider the steadystate SPGR signal equation:
�((�#, �!, �(�), �) = �#
(1 − �!(�)) sin �
1 − �!(�) cos �
(3. A. 1)

60
where �# is the equilibrium magnetization, �! is the pre-contrast longitudinal
relaxation time, �(�) is the contrast agent concentration, � is the flip angle, and �!(�) =
�!#�,4Q∙6$[(() with �!# = �,4Q∙Q$ and �! = 1/�!, according to the Fast Exchange Limit
(FXL). We can estimate the first order error by:
Δ� = ��
��!
Δ�! (3. A. 2)
Therefore, we must evaluate one partial derivative, which is possible using the
chain rule:
��
��!
= A ��
��(�-)
��(�-)
��!
F
-O!
��!
��!
(3. A. 3)
where � is the TK parameter of interest, e.g., �^ or �(. We are evaluating the
dependence on the estimated T1 (and not the DCE scan or vascular input function
estimation). Therefore, we compute the partial derivative of estimated concentration
(�(�-)) as a function of pre-contrast �!, given measured DCE signals as constants. We
differentiate both sides of Eqn (A. 1) w.r.t �! to get:
0 = �#
sin � ∙ �� ∙ �!(�)
(1 − �! (t)cos �)" (1 − cos �) ∙
�[�! + �!�(�-)]
��!
= �#
sin � ∙ �� ∙ �!(�)
(1 − �!(�) cos �)" (1 − cos �) ï1 + �!
��(�-)
��!
ñ (3. A. 4)
Therefore, we have:
��(�-)
��!
= − 1
�!
(3. A. 5)
This is the same for all time points. As a result, we have:
��
��!
= 1
�!�!
"A ��
��(�-)
F
-O!
(3. A. 6)

61
Patlak Model
Consider first the Patlak model, which is a widely used linear compartment
model. According to the Patlak model CA concentration is a linear function of the tracer
kinetic parameters:
�(�) = �^(�)�^ + �( h �^(�)
(
#
�� (3. A. 7)
where �^(�) is the time-varying contrast agent plasma volume concentration (mM).
�^(�) is often called the vascular input function (VIF). The function should be
determined by sampling the delivery of contrast agent from a vessel directly interacting
with the tissue of interest. In this Appendix, three �^(�)’s were either generated from
different population-based models (Parker et al.179 and Georgiou et al.180) or estimated
by averaging multiple in-vivo data from our patient DCE-MRI study. This model can be
expressed as a matrix-vector multiplication, as follows:
�( = •
�(�!)
�(�")
⋮
�(�F)
¶ = �°
�^
�(± (3. A. 8)
� =
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎡�^(�!) h �^(�)
($
#
��
�^(�") h �^(�)
(#
#
��
⋮ ⋮
�^(�F) h �^(�)
(0
#
��⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎤
(3. A. 9)
The solution for °
�^
�(± that minimizes the sum of squared residuals (also called the
least square solution) is:
°
�^
�(± = �l�( (3. A. 10)

62
�^ and �( are linear functions of �(, therefore all partial derivatives for the leastsquares estimator reside as entries in the �l matrix as follows:
⎣
⎢
⎢
⎢
⎡
��^
��(
��(
��( ⎦
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡ ��^
��(�!)
��^
��(�") …
��(
��(�!)
��(
��(�") …
��^
��(�F)
��(
��(�F)⎦
⎥
⎥
⎥
⎤
= �l (3. A. 11)
Extended Tofts-Kety Model
As another model widely used in the evaluation of brain tumors, consider the
Extended Tofts-Kety model which has a non-linear dependence on vascular
parameters. The ETK model is as follows:
�(�) = �^(�)�^ + �( h �^(�)
(
#
�,E.G((,@)
�� (3. A. 12)
where �S^ = _%
`.
is a rate constant.
While the model nonlinearity does not allow for an explicit solution to the vascular
parameter estimator, local first derivatives can be obtained through implicit
differentiation or an additional linearization step. In the following, we assume constant �S
constant for simplicity.
We take the derivative w.r.t �(�-) on both sides of (3. A. 12) to get:
1 = �^(�-)
��^
��(�-) +
��(
��(�-)
h �^(�)
(H
#
�,E.G((H,@)
��
+
��(
��(�-)
�( h − �- − �
�S
(H
#
�^(�)�,E.G((H,@)
�� (3. A. 13)
This will convert the nonlinear model of parameters to a linear model of partial
derivatives. Thus, we can construct another matrix-vector multiplication as follows:

63
�- = �
⎣
⎢
⎢
⎢
⎡ ��^
��(�-)
��(
��(�-)⎦
⎥
⎥
⎥
⎤
(3. A. 14)
In which �- is a column vector whose �-th entry is 1, and
� =
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎡ �^(�!) h ]1 − �( �! − �
�S
^ �^(�)�,E.G(($,@)
($
#
��
�^(�") h ]1 − �( �" − �
�S
^ �^(�)�,E.G((#,@)
(#
#
��
⋮ ⋮
�^(�F) h ]1 − �( �F − �
�S
^ �^(�)�,E.G((0,@)
(0
#
��⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎤
(3. A. 15)
When � is evaluated at some �( = �, the derivatives are the least square
solution to (�. 14), that is,
⎣
⎢
⎢
⎢
⎡ ��^
��(�-)
��(
��(�-)⎦
⎥
⎥
⎥
⎤
¥
_%OE
= �l�- (3. A. 16)
Alternatively, we can use linear approximation. A continuous and differentiable
function �(�) can be well approximated around � = �· by
�(�) ≈ ��(�)
�� ¸
�O�t
� + ï�(�·) − ��(�)
�� ¸
�Ot�
·�ñ (3. A. 17)
Equation (�. 12) can be linearly approximated at some �( = � as follows:
�(�-) = �^(�-)�^ +
��(�-)
��( ¸
_%OE
�( + �(�,�-) (3. A. 18)
In which
��(�-)
��( ¸
_%OE
= h ]1 − �
�- − �
�S
^ �^(�)�
, E
`.
((H,@) (H
#
�� (3. A. 19)

64
�(�,�-) = � h �^(�)�
, E
`.
((H,@) (H
#
�� − ��(�-)
��( ¸
_%OE
� (3. A. 20)
We then can construct another matrix-vector multiplication such as
�( − �(�, �) = �°
�^
�(± (3. A. 21)
In which
� =
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡�^(�!) ��(�!)
��( ¸
_%OE
�^(�") ��(�")
��( ¸
_%OE
⋮ ⋮
�^(�F)
��(�F)
��( ¸
_%OE⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤
(3. A. 22)
Like (�. 10), the least square solution to (3. A. 21) is
°
�^
�(± ≈ �l[�( − �(�, �)] (3. A. 23)
Similar as (�. 11), the derivatives reside as follows:
⎣
⎢
⎢
⎢
⎡ ��^
��(�-)
��(
��(�-)⎦
⎥
⎥
⎥
⎤
¥
_%OE
=
⎣
⎢
⎢
⎢
⎡ ��^
��(�!)
��^
��(�") …
��(
��(�!)
��(
��(�") …
��^
��(�F)
��(
��(�F)⎦
⎥
⎥
⎥
⎤
= �l (3. A. 24)
Error Propagation Analysis
Error propagation analysis was performed for the two TK models as outlined in
the previous section. The analysis was evaluated with three different VIF’s and three
different �S^ values (if necessary) to demonstrate the dependencies on them. In
addition, all analysis assumed a T1 range of 1700±255 ms, roughly matching the mean
T1 of BT in our patient study with ±15% variations.

65
Figure 3.7 shows error propagation analysis results in the Patlak model. The 1st
row shows partial derivatives of �^ and �( of pre-contrast T1 values (1700±255 ms) and
the 2nd row shows the first order error of �^ and �( as a function of ±255 ms (±15%) ΔT1
for the VIFs by Parker et al.179 (blue), Georgiou et al.180 (red) and the cohort-based invivo brain VIF measured at our institution. As the first row shows, partial derivatives
were positive and decreased as T1 increased. Consequently, errors in TK parameters
were positively related to T1 errors and T1 error propagation was slower as T1 increased.
Quantitatively, a ±255 ms ΔT1 results in ±0.0064, ±0.0043 and ±0.0085 error in �^, and
±0.0074 min-1, ±0.0053 min-1 and ±0.0028 min-1 error in �( in Parker’s, Georgiou’s and
in-vivo measured VIF, respectively.

66
Figure 3.7. Error analysis in TK estimation in the Patlak model. The 1st row shows partial
derivatives of �^ and �( of pre-contrast T1 values (1700±255 ms) and the 2nd row shows
the first order error of �^ and �( as a function of ±255 ms (±15%) �T1. Parker’s (blue),
Georgiou’s (red) and in-vivo measured (yellow) VIF’s were analyzed. As the first row
shows, partial derivatives were positive and decreased as T1 increased. Consequently,
errors in TK parameters were positively related to T1 errors and T1 error propagation was
slower T1 increased. As the 2nd row shows, a ±255 ms (±15%) �T1 results in ±0.0064,
±0.0043 and ±0.0085 error in �^, and ±0.0074 min-1, ±0.0053 min-1 and ±0.0028 min-1
error in �( in Parker’s, Georgiou’s and in-vivo measured VIF, respectively.

67
Figure 3.8 shows the Partial derivatives of �^ and �( of pre-contrast T1 values
(1700±255 ms) in the ETK model. The 1st row shows the 2D plot of partial derivatives of
�^, and The 2nd row shows the 2D plot of partial derivatives of �( as a function of both
rate constant �S^ and T1. Like the Patlak model, both derivatives monotonically
decreased as T1 increases, however, they are not monotonic functions of �S^. Especially
for the partial derivative of �(, it reached its positive extreme at �S^ around 0.64, 0.62
and 0.54 min-1 and had polarity change at �S^ around 1.35, 1.32 and 0.92 min-1.
Figure 3.8. Partial derivatives of �^ and �( of pre-contrast T1 values (1700±255 ms) in
the ETK model. The 1st row shows the 2D plot of partial derivatives of �^, and the 2nd row
shows the 2D plot of partial derivatives of �( as a function of both rate constant �S^ and
T1. Like the Patlak model, both derivatives monotonically decreased as T1 increases,
however, they are not monotonic functions of �S^. Especially for the partial derivative of
�(, it had different polarities depending on �S^ value.

68
Figure 3.9 shows the first order error in �^ and �( as a function of ΔT1 in the ETK
model in the 1st and 2nd row, respectively. Errors are plotted for ±255 ms (±15%) ΔT1 for
Parker’s179 (left), Georgiou’s180 (middle) and in-vivo measured (right) VIF’s. Errors were
also evaluated at three different �S^ values to demonstrate dependencies on �S^. Δ�^
was positively related to ΔT1, however, it shrank and then was amplified at �S^
increases. With ±255 ms ΔT1, Δ�^ extended to ±0.015, ±0.010 and ±0.016 in maximum
at �S^=1.5 min-1 for Parker’s, Georgiou’s and in-vivo measured VIF, respectively.
For Δ�(, result is more complicated due to the derivative polarity change. With ±255 ms
ΔT1, Δ�( extended to ±0.008, ±0.007 and ±0.020 in maximum at �S^=1.5 min-1 for
Parker’s, Georgiou’s and in-vivo measured VIF, respectively. Note that �S^=1.5 min-1 did
not necessarily give the maximum Δ�(, however, it was of more interest since high �S^
values were expected in tumor regions.

69
Figure 3.9. The first order error in TK parameters as a function of �T1 in the ETK model.
Errors are plotted for ±255 ms (±15%) �T1. The 1st and 2nd row show the first order error
of �^ and �( , respectively, and errors were analyzed using Parker’s (left), Georgiou’s
(middle) and in-vivo measured (right) VIF. Errors were also evaluated at three different
�S^ values to demonstrate dependencies on �S^. For �^, result is similar to that in Patlak
model, while it is noticeable that ��^ will be amplified at higher �S^ region, e.g., tumor. For
�(, result is more complicated due to the derivative polarity change for different �S^.
Briefly, an error of ±15% in mean brain tumor T1 results in at most 0.008 and
0.007 min-1 absolute error (Patlak), and 0.016 and 0.033 min-1 absolute error (ETK) in
the DCE estimated pharmacokinetic parameters, �^ and �(, respectively.

70
Chapter 4 Efficient 3D FISP-MRF at 0.55 T using Long Spiral
Readouts and Concomitant Field Effect Mitigation
4.1 Introduction
Magnetic Resonance Fingerprinting (MRF)
16,17 is a time-efficient imaging
approach that can provide quantitative tissue parameter maps (e.g., relaxation times)
with 3D coverage and millimeter or sub-millimeter resolution. Instead of acquiring
multiple contrast-weighted images and fitting data to assumed signal models, MRF
utilizes pseudo-randomized acquisitions in a single sequence such that a combination
of tissue parameters generates a unique time-resolved signal evolution. Then a
measured signal evolution per voxel is matched with a physics-based dictionary to
estimate underlying tissue parameters. Since its first appearance in 2013, MRF has
gained research and clinical traction in several different body regions and at different
field strengths22,27,30,137,181,182. MRF has been shown to be repeatable and reproducible
at 1.5T and 3T183, which are essential for monitoring disease diagnosis based on tissue
parameter mapping. Researchers have also developed several variants of MRF for
diffusion imaging20,23,24, fat fraction estimation121, and quantitative magnetization
transfer imaging18,19,68. MRF has better acquisition efficiency16,184, e.g., more samples
are acquired per unit time, compared to conventional single parametric quantitative
MRI. It is then especially advantageous in SNR-starved situations such as high spatial
resolution imaging and/or low-field imaging1,17. Researchers have shown that brain MRF
is feasible and practical at 0.55T34 and can produce parametric maps with isotropic
resolution at millimeter level185.

71
Mid-field (i.e., 0.35 – 1 T) brain MRI is also of high interest. Researchers have
been putting efforts in assessing the utility of brain imaging at 0.55 T using protocols
similar to those widely used at 1.5 T and 3 T. It was reported that brain MRI at 0.55 T
produced images with acceptable quality112. To overcome the reduced SNR due to
reduced equilibrium polarization, an SNR-efficient acquisition is highly desired36,112. For
example, long spiral readouts may partially compensate for the reduced SNR, which is
possible due to improved field homogeneity at 0.55T. However, a mitigation strategy for
concomitant field effects is crucial because concomitant fields become severe at lower
field strengths and at high gradient amplitude. In most gradient systems, which are
symmetric in left-to-right and anterior-to-posterior directions, concomitant fields can be
well represented with a vector Taylor expansion186. Concomitant fields are found to
cause undesired phase accrual that causes spatial blurring120 in spiral imaging. Such
artifacts can be mitigated by different strategies such as demodulation, adapted offresonance correction187,188 and/or a high-order encoding approach133.
In this study, we evaluated the performance of 3D axial stack-of-spirals (SOS)
FISP-MRF using 14 spiral readouts with mitigation of concomitant field effects based on
the MaxGIRF framework133. We demonstrate a noticeable performance improvement in
FISP-MRF with long spiral readouts after mitigation of concomitant field effects by
analyzing the degree of spatial blurring and MRF T1 and T2 standard deviations as a
function of a readout duration.
4.2. Theory
4.2.1 Concomitant Field Effects in the 3D Axial SOS FISP-MRF

72
Mathematically, the amount of concomitant field-induced phase during a readout
gradient waveform is given by (up to the 2nd order)120,189:
�-(�,�) ≈ h �-,)
" (�)
8�#
(�" + �") +
�-,*
" (�) + �-,+
" (�)
2�#
�" − �-,*(�)�-,)(�)
2�#
�� − �-,+(�)�-,)(�)
2�#
��
(
#
�� (4.1)
where the index � represents the waveform index, � = [� � �]4 (at isocenter, � = � =
� = 0), and the beginning of readout gradients is considered as time point 0, i.e., � = 0.
In axial MRI, since �-,)(�) = 0, Equation (4.1) can be simplified as follows:
�-(�,�) ≈ h �-,*
" (�) + �-,+
" (�)
2�#
�"
(
#
�� (4.2)
Note that readout gradients now cause concomitant fields to induce extra phase which
is quadratic to slice offset �, and the extra phase leads to spatial blurring in spiral
imaging120,133. If transverse magnetization is sufficiently spoiled or decayed by the end
of each TR, concomitant phase accrual across consecutive TR’s is assumed to be
eliminated for a simpler analysis. This is clearly valid if TR is >>T2, and is sometimes
assumed when adequate gradient spoiling is used. This assumption is useful since it
allows simplifying the concomitant field effects in an axial SOS FISP-MRF for two
reasons: (1) In axial SOS imaging, different spiral arms produce phase accrual with
negligible difference (relative difference < 0.1%) and (2) transversal magnetization
residuals are spoiled by the dephasing gradients. This indicates that the concomitant
field-induced phase is approximately the same per TR, is spatially dependent on the
slice distance from isocenter, and does not accumulate through time. In other words, it
behaves similar to phase accrual induced by static off-resonance except that it has
predictable spatial dependencies and hence, it does not affect the magnitude of a FISPMRF signal evolution with sufficient gradient spoiling.

73
4.2.2 MaxGIRF-Subspace Reconstruction
The MaxGIRF encoding framework133 was adapted into the state-of-art subspace
and low-rank modeling MRF reconstruction181,190 for simultaneous denoising and static
off-resonance and concomitant field effects mitigation. Specifically, the conventional
Fourier encoding operator was upgraded into a MaxGIRF encoding operator, i.e., being
element-wise multiplied by spatially dependent phase terms described in Equation (4.1)
or (4.2). The cost function is shown in Equation (4.3):
�æ = min
� A‖Ω(��q��H) − �q‖ℓ#
"
FI
qO!
(4.3)
Where Ω: ℂFDFH×G ⇒ ℂFD×G is the undersampling operator, �: ℂF×G ⇒ ℂFDFH×G is the
MaxGIRF encoding operator, �q: ℂF×G ⇒ ℂF×G is the sensitivity encoding operator for
the �-th coil, �H ∈ ℂH×G is the rank-� approximated temporal subspace basis estimated
from a separately generated MRF signal evolution dictionary, and �q ∈ ℂFD×G is the
measured k-space data from the �-th coil. �æ ∈ ℂF×H is known as the reconstructed
singular value images85,181,190 and the reconstructed MRF time-series images can be
represented as �G = �æ�H. Additionally, � is the number of discrete voxels in the image
domain per time frame, � is the number of time frames, �E is the number of k-space
samples per spiral interleave, �- is the total number of spiral interleaves, and �q is the
total number of receiver channels.
Since the MaxGIRF encoding is not affecting temporal subspace basis formation,
this problem can still be efficiently solved by easily combining the low rank
approximated MaxGIRF encoding algorithm133 and low rank and subspace modeling

74
algorithm181. When ignoring concomitant field related terms, � is simply a Fourier
encoding operator and Equation (4.3) will be downgraded into a subspace modeling
and low rank constrained reconstruction problem. Also note that solving Equation (4.3)
has implicitly increased computation complexity by a value of the rank number used for
encoding operator approximation133.
4.3. Method
4.3.1 Pulse Sequence Design
FISP-MRF sequences were implemented using the open-source Pulseq191
framework on a whole body 0.55T system (prototype MAGNETOM Aera, Siemens
Healthineers, Erlangen, Germany) equipped with high-performance shielded gradients
(45 mT/m amplitude, 200 T/m/s slew rate). Fourteen MRF sequences with different
redout durations ranging from 2.9 ms to 22.0 ms with ~1ms increment were
implemented. The readout trajectories were designed using the variable density spiral
trajectory toolbox described by Lee et al.192 and time-optimal multidimensional gradient
waveform design193 with 0th-moment nulling. These sequences shared the same spatial
coverage (300 x 300 x 240 mm3), spatial resolution and slice thickness (1.2 x 1.2 x 5
mm3), echo time (TE = 1.4 ms), and inversion time (TI = 20.66 ms). We followed the
same 3D acquisition strategy described by Campbell-Washburn et al.34, but with 48
partition-encoding steps to reduce spatial aliasing along the slab-select direction.
Detailed pulse sequence design parameters are provided in the available code
repository.

75
Each sequence has a different constant repetition time (TR) due to that because
a gradient downtime was minimized as to maximize SNR efficiency. Therefore, we
defined a continuous flip angle (FA) schedule and resampled it for each sequence to
maintain approximately the same scan time: ~7.3 sec acquisition time, 2 sec delay per
pass/partition, and 7min 30±3sec total scan time. The continuous FA schedule is shown
in Figure 4.1.
Figure 4.1. Continuous-time FA schedule. Pre-inversion and inter-partition delay are not
shown.

76
4.3.2 Numerical Simulation
To demonstrate the dependencies of the concomitant field-induced phase
accrual, the phase accrual was simulated for 3 representative spiral readout trajectories
(2.9/9.5/16.5 ms) at 4 different slice positions equally spaced between isocenter and � =
+150 mm. To demonstrate the impacts of a long readout duration and the resultant
adapted TR schedule on the SNR of FISP-MRF, signal evolutions at TE = 1.4 ms were
simulated for each sequence using two different entries: (1) T1/T2 = 100/100 ms
matching the values of the ACR phantom and (2) T1/T2 = 500/80 ms matching the
values of healthy white matter (WM) at 0.55 T112. For each entry, a temporally averaged
signal intensity was calculated per readout duration, and the resulted values were
normalized with respect to the value from the shortest readout duration to reflect the
relative changes caused by TR schedule changes. Further, an SNR gain curve was
simulated by multiplying these values with corresponding relative SNR efficiency values
in an element-wise fashion.
4.3.3 Imaging System
All experiments were performed on a whole body 0.55T system equipped with
high-performance shielded gradients as mentioned above. A 16-channel head/neck coil
was used for both phantom and in-vivo experiments, except that the neck components
(occupying 4 channels) were turned off for phantom experiments. The gradient impulse
response function (GIRF)
128,129 measurement method as described by CampbellWashburn et al.130 was used for readout trajectories correction. A static off-resonance

77
map and a �!
B maps were separately acquired using vendor provided sequences for
correction and reconstruction.
4.3.4 Reconstruction
For each MRF schedule, 21 dictionaries were generated accounting for �!
B
correction, corresponding to �!
B values ranging from 0.5 to 1.5 with an increment of
0.05. For each dictionary, 225 T1 values and 128 T2 values were sampled using variable
increments from 10 ms to 3500 ms and 2 ms to 2000 ms, respectively, resulting in
24878 combinations of T1 and T2 values per �!
B values. No other parameters were
included. The dictionary generation time ranged from 2 to 9 hours per schedule, as it
increased as the time frame dimension grew.
All acquired data were reconstructed using (1) Fourier encoding and subspace
constrained reconstruction, denoted as gridding+subspace and (2) MaxGIRF
encoding and subspace constrained reconstruction, denoted as MaxGIRF+subspace.
The MATLAB LSQR solver was used to iteratively solve the problem with 100 maximum
iterations that is sufficient for the convergence of gridding+subspace reconstruction.
However, 50 maximum iterations were used for MaxGIRF+subspace reconstruction due
to increased computational cost. Image reconstruction was performed in a slice-by-slice
manner by taking advantage of a fully sampled Cartesian �) dimension. All
reconstruction programs were performed on a Hyperplane 2U system with 4 TB memory
and 4 NVIDIA A100 GPUs. The total reconstruction times of gridding+subspace and
MaxGIRF+subspace approaches varied based on number of time frames in a dataset.
For 3D dataset, the gridding+subspace reconstruction cost ~1 hour and ~20 minutes for

78
the shortest and the longest readout, respectively. The MaxGIRF+subspace cost ~12
hour and ~45 minutes for the shortest and the longest readout, respectively.
4.3.5 Phantom Experiments
An ACR MRI phantom (pre-2019 model)194 and an ISMRM/NIST system
phantom195 were scanned using 14 FISP-MRF sequences. The total scan time for all 14
sequences was ~2-2.5 hours. For the ACR MRI phantom experiments, the center of an
imaging slab was always prescribed at the grid structure. Data acquisitions were initially
performed with the grid structure placed at the isocenter and then repeated with the grid
structure placed at a 75-mm distance from isocenter after moving the scanner table.
MRF time-series images were used to demonstrate the dependencies of spatial blurring
on off-center distance � and readout time � separately. Edge maps were extracted from
a single time frame for qualitative blurring assessment. Specifically, the subtraction
between an original magnitude image and a magnitude image after filtering with a zeromean Gaussian kernel with a standard deviation of 0.5 was used.
For the ISMRM/NIST system phantom experiments, the center of the phantom
was placed at the isocenter, and the phantom was rotated around the right-left axis so
that its NiCl2 array, i.e., the T1 array, was in the axial plane. All sequences were
performed only once at the isocenter. For accuracy analysis, MRF T1 for each NiCl2
vials and T2 for MnCl2 vials were measured as means from a manually drawn circle ROI
for each vial. These values were compared against reference measurements from
inversion recovery based T1 mapping and single echo spin echo based T2 mapping to
examine the impact of applying different readout durations on MRF estimation accuracy.

79
Reconstructed MRF time-series images and a T1 map from the NiCl2 (T1) array were
used to examine the performance of concomitant field-induced spatial blurring
mitigation.
4.3.6 In-vivo Experiments
Two healthy volunteers (1F/1M, both 29) were scanned. To maintain a practical
scan time, 6 sequences were selected and used (�/;xm = 2.9/6.1/9.5/13.2/16.5/22.0 ms).
Both subjects were recruited under the University of Southern California IRB approval
and an informed consent was acquired for each subject.
To assess the influence of different readout durations, image reconstruction for
one dataset was repeated with 100 pseudo-replicas34 for slices at � = 2.5 mm and � =
57.5 mm. In specific, 100 independent realizations of multi-channel additive white
Gaussian noise was colored using the noise covariance matrix measured from separate
noise only scans and then added to raw k-space data per 3D dataset. Reconstruction
was performed on each replica, resulting in 100 results for each 3D dataset. Thereafter,
a T1/T2 standard deviation value (SD) per voxel was calculated across the replica
dimension which demonstrated the variability mostly caused by the thermal noise. A
region-of-interest (ROI) based analysis was performed with focus on WM. ROIs were
generated by the segmentation tool MedSAM-Lite 3D Slicer196.
4.4. Results
4.4.1 Numerical Simulations

80
The phase accrual curves appear to be approximately linear as a function of the
spiral readout length and grow faster as a function of the distance from isocenter.
Figure 4.2 shows representative spiral trajectories of 3 different spiral lengths (�/;xm =
2.9/9.5/16.5 ms) and their corresponding accumulated phases due to concomitant fields
obtained with Equation (4.1). Both axes in the 2nd row are optimized to highlight the
dependencies of the accumulated phase on the spiral length and slice offset.
Figure 4.2. Representative spiral k-space trajectories and phase accrual due to
concomitant fields. Spiral trajectories of 3 different readout lengths (top row) and their
corresponding phase accruals due to concomitant fields at 4 different distances from
isocenter (bottom row). Note that the phase accrual is nonlinear during the slew-limited
regime of a spiral readout and becomes linear during the amplitude-limited regime of a
spiral readout. The axes in the bottom row were chosen to highlight the relationship
between phase accrual and readout duration/axial slice offset distance.

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For both phantom and WM simulation, signal intensities increased as the number
of FAs decreased from the schedule. Using a small number of FAs corresponds to a
decrease in the number of time frames, which is the consequence of adapting TR and
maintaining the total scan time constant for various spiral readout lengths. Figure 4.3A
and 4.3B shows simulated FISP-MRF signal curves of various spiral readout lengths,
where a more blueish curve represents a curve with longer readout length. As a result,
increased SNR is expected when extending readout duration since more signals would
be acquired per time frame and the acquired signal intensities would be stronger. The
simulated SNR is shown in Figure 4.3C.
Figure 4.3. Numerical simulation of MR fingerprinting signals and expected SNR. Signal
evolutions are shown for (A) the ACR phantom (T1 = 100 ms, T2 = 100 ms) and (B) healthy
white matter at 0.55 T (T1 = 500 ms, T2 = 80 ms). SNR simulations are shown in (C). The
SNR efficiency curve (red) was calculated as the square root of the ratio between readout
duration and TR, i.e., …�6S]'/��, signal curves (solid blue and yellow) were calculated as
the average magnitude from (A) and (B), respectively, and the SNR curves (dashed blue
and yellow) were calculated as the element-wise multiplication between SNR efficiency
and simulated signal curves. All curves in (C) were then normalized with respect to the
shortest readout used in this study.
4.4.2 Spatial Blurring and MRF Results in Phantoms
Spatial blurring worsened as the readout time � increased and even became
severe when the grid structure of the ACR phantom was placed at a 75-mm distance

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from isocenter. The thickness of the grid border was 2 pixels at �/;xm = 2.9 ms, 4 pixels
for � from 4 ms to 9.5 ms, and >5 pixels and unrecognizable for larger �. Artifactual grid
lines reappeared with abnormal intensities for �/;xm > 16.5 ms. These measurements
were obtained without mitigation. With mitigation, the thickness of the grid border was 1
pixel for �/;xm from 2.9 ms to 9.5 ms, 2 pixels for �/;xm from 11.1 ms to 13.2 ms, and >3
pixels but still recognizable for larger �/;xm. Artifactual grid structures were not observed.
Representative images at � ≈ 0.7 are shown in Figure 4.4.
Figure 4.4. Reconstructed MRF time-series images of the grid structure of the ACR
phantom using different readout lengths. The MRF time-series images were
reconstructed from MRF data at � ≈ 0.7 seconds per partition. The grid structure was
placed at a 75-mm distance from isocenter to purposely induce a large phase accrual due
to concomitant fields. Spatial blurring worsened as a readout time lengthened in
gridding+subspace reconstructions (top row, left to right), and was successfully mitigated
in MaxGIRF+subspace reconstructions (bottom row).

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Figure 4.5 shows zoomed-in views of MRF time-series images without and with
deblurring for two readout lengths (2.9/9.5 ms) scanned at two distances from isocenter.
Images acquired with two readout lengths at the isocenter do not show any noticeable
spatial blurring (Figure 4.5A vs 4.5D). However, both images were blurred at a 75-mm
distance from isocenter and blurring was more severe for the longer readout length
(Figure 4.5B vs 4.5E). Spatial blurring due to concomitant fields was reduced after
mitigation (Figure 4.5B and 4.5E). In addition, geometric distortions due to gradient
nonlinearity were observed when comparing images acquired at isocenter and at offisocenter (Figure 4.5A vs 4.5C and Figure 4.5D vs 4.5F).
Figure 4.5. A zoomed-in view of reconstructed images for �6S]' = 2.9 ms ((A)-(C)) and
9.5 ms ((D)-(F)), at �� = 0 mm ((A)(D)) and 75 mm (others). Images before blurring
correction are shown in (A)(B)(D)(E), and after correction are shown in (C)(F). No
detectable structural difference can be observed between (A) and (D), and (C) and (F),

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however, noticeable geometric distortions can be observed by comparing (A) and (C),
and (D) and (F).
Figure 4.6 shows MRF T1 (top row) and T2 (bottom row) means plotted against
reference values for 3 representative readout durations. As the plots showed, there
were no significant differences between results with (red) and without (blue) blurring
mitigation. However, there were noticeable mismatches between MRF results and
reference values for �/;xm = 2.9 ms for T1 < 100 ms and T2 < 100 ms. Such mismatches
were progressively mitigated as readout duration increased.
Figure 4.6. Comparison between MRF T1 and T2 means and reference values from the
ISMRM/NIST phantom. Results with (red) and without (blue) blurring mitigation are both
reported. T1 and T2 comparison are shown in the top and bottom row, respectively. There
were no significant differences between values with and without mitigation. Although there
were noticeable biases between MRF results and reference values for �6S]' = 2.9 ms at
T1 or T2 < 100 ms, such biases were progressively reduced as the readout duration
increased. This is shown in zoomed-in subplots in each panel.

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Figure 4.7 shows representative MRF time-series images at ~0.7 sec of the
ISMRM/NIST NiCl2 array with zoomed-in views to vial 5. Spatial blurring due to
concomitant fields was observed since the imaging slice was located at a 57.5-mm
distance from isocenter. It is interesting to note that spatial blurring appeared to have
dependencies on the T1 and T2 values of vials. For example, blurring worsens faster for
vials with either short T1 and T2 values (<60 ms, vials 11-14) or long T1 and T2 values
(>1000 ms, vials 1-3), and was also harder to be fully corrected.
Figure 4.7. Subspace constrained reconstrued MRF time-series images of the
ISMRM/NIST phantom NiCl2 array. �6S]' = 2.9 ms (left), 9.5 ms (mid) and 16.5 ms (right)
are shown. The images were reconstructed from MRF data at � ≈ 0.7 seconds per
partition. Zoomed-in views (solid red boxes) of vial #5 (dashed red boxes) are provided
in each subfigure’s right bottom corner. Results without concomitant field effect correction
are shown in the 1st row, and with correction are shown in the 2nd row. Spatial blurring
became stronger as long readout (left to right) and is mitigated after MaxGIRF correction.
Blurring residuals emerged when �6S]' ≥16.5 ms (not shown).

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Figure 4.8 shows estimated T1 maps from the ISMRM/NIST phantom. Without
mitigation, spatial blurring caused an artifactual enlargement in the size of vials and T1
biases, and vials started to overlap with each other as the readout time lengthened.
With mitigation, blurring artifacts were reduced but noticeable artifacts due to residual
blurring were observed for vials with long T1 values, e.g., vials 1-3.
Figure 4.8. MRF T1 maps from the ISMRM/NIST phantom. Zoomed-in views (solid red
boxes) of vial #5 (dashed red boxes) are provided in each subfigure’s right bottom corner.
Obvious spatial blurring appeared to be thickened boundaries, enlarged vials and
overlapping of structures before correction. This was reduced after MaxGIRF correction.
Blurring residuals are visible for �6S]' ≥16.5 ms (not shown).
4.4.3 Spatial Blurring and MRF Precision in Healthy Subjects
Figure 4.9 shows (A) representative MRF time-series images at ~0.7 sec, (B)
MRF T1 maps, and (C) MRF T2 maps at a 57.5-mm distance from isocenter. In each
panel, results without and with MaxGIRF encoding were shown in the 1st and 2nd rows,

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respectively, and zoomed-in views are provided (green boxes). Substantial spatial
blurring was observed with longer readout time and largely mitigated with MaxGIRF
encoding. Sharper boundaries between white matter and gray matter were preserved
but detailed structures were not fully resolved for readout times >16.5 ms. Results at a
2.5-mm distance from isocenter are shown in Figure 4.10. Results from the other
volunteer are shown in Figure 4.11.

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Figure 4.9. MRF time-series images, T1 and T2 maps before and after MaxGIRF
correction at 3 readout durations. The slice offset �� = 57.5 mm. As expected, the spatial
blurring caused by concomitant field induced phase worsened as longer readout duration
but was largely mitigated by MaxGIRF correction. Visually, sharper boundaries between
different tissues such as white matter and gray matter were preserved. Zoomed-in view
(green boxes) are provided in each panel. Note that some detailed structures could not
be fully recovered for �6S]' = 16.5 ms, such as ambiguous tissue delineation or structural
disappearance (red arrows).

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Figure 4.10. MRF time-series images, T1 and T2 maps before and after MaxGIRF
correction at 3 readout durations. These results contain the same information as Figure
4.9, except that the slice offset �� = 57.5 mm.

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Figure 4.11. MRF time-series images, T1 and T2 maps before and after MaxGIRF
correction at 3 readout durations. These results are from the other subject and the slice
offset �� = 57.5 mm (same as Figure 4.9).
Figure 4.12 shows the proposed MRF T1 and T2 standard deviation maps
calculated from 100 pseudo replicas (left) and full curves of averaged standard
deviations calculated from 100 pseudo-replicas as a function of the readout time (right).
Standard deviation maps from �6S]' = 16.5 ms with MaxGIRF encoding are shown for
the demonstration purpose. The standard deviations of WM T1 and T2 were 16.5 ms and
3.0 ms, respectively. More importantly, there was an observable trend that the standard
deviations decreased with longer spiral readout time. Figure 4.13 shows 3
representative T1 and T2 standard deviation maps from �6S]' = 2.9, 9.5 and 16.5 ms.
For all 6 readout durations examined, our results show good accuracy in T1 values
within ±5.5 ms range, but substantially underestimated T2 by 24.7 ms to 30.6 ms. This
matches previously reported 0.55 T 3D brain MRF using similar FA schedule and spiral
readouts34.

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Figure 4.12. Representative MRF T1 and T2 standard deviation maps (left) and averaged
MRF T1 and T2 standard deviation values in WM ROI as a function readout duration (right).
The points corresponding to the maps are marked on the right plot. Standard deviation
values are calculated from 100 pseudo replicas per voxel. Use of MaxGIRF concomitant
field correction (solid) provides improved precision over no-correction (dashed) for all
readout durations and for both T1 and T2. The proposed MaxGIRF+subspace
reconstruction shows improved precision for all examined, which we attribute to the
increased readout duty cycle. For T2, precision approached stability for �6S]' ≥ 10 ms,
which we attribute to that improving scan efficiency was no longer sensible, e.g., either
physiological variation floor or dictionary quantization error floor was reached.
4.5. Discussion
We have demonstrated 3D brain axial SOS FISP-MRF with improved scan
efficiency at 0.55 T. Improved efficiency was achieved using a 3D acquisition with a long
spiral readout while the long spiral readout worsened concomitant field effects. We
successfully integrated the MaxGIRF framework into a low-rank and subspace modelbased reconstruction to mitigate spatial blurring due to static off-resonance and
concomitant fields. The proposed MaxGIRF+subspace reconstruction was examined in

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the ACR MRI phantom, the ISMRM/NIST phantom, and 2 healthy volunteers. All results
were reasonable, suggesting the potential of performing efficient 3D brain FISP-MRF
using a 0.55 T MRI system.
3D axial SOS FISP-MRF sequences used in this work were implemented using
the open-source Pulseq framework based on the previous 3D FISP-MRF work at 0.55
T34,197. We focused on reproducing the same protocol but with modifications such as
using full gradient strength and resampling of the same continuous FA schedule were
necessary to maximize SNR efficiency. This continuous FA schedule was specially
defined to repeat per pass/partition. As a result, these sequences had flexible TR values
and different number of time frames with constant total scan time, and would produce
comparable contrast. Our FISP-MRF pulse sequence can be easily adapted to other
vendors supporting the Pulseq framework. Modifications to the sequence source code
(written in MATLAB) to match the specifications of different scanners and creating a
tailored Pulseq file are the only necessary steps.
Concomitant field effects become stronger and requires attention when using
higher gradient strength, longer gradient active time, and lower main field strength,
which were all hit in this study. Here, axial spiral acquisitions were used, where spatial
blurring due to concomitant fields is proportional to a distance from isocenter and
becomes worse for longer spiral readouts. To mitigate spatial blurring for FISP-MRF, the
MaxGIRF framework was integrated into a low-rank and subspace model-based
reconstruction. The MaxGIRF framework essentially replaces Fourier encoding with
higher-order encoding that additionally models the extra phase due to static offresonance and concomitant fields. The phase is assumed to be the major source of

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spatial blurring in this study. The proposed MaxGIRF+subspace reconstruction provides
high image quality via simultaneous image reconstruction and deblurring, and was
validated using both phantom and in-vivo experiments.
Using long spiral readouts in 0.55 T 3D MRF were beneficial. In-vivo results
partially reproduced previous 0.55 T 3D brain MRF, and it has improvements by
showing a trend of improved precision with longer readout time from the 100 pseudoreplicas. As the simulation shows, such improvement resulted not only from increased
SNR efficiency but also from overall higher signal intensities of the adapted MRF
schedules, and it was perceptible before dropping below the dictionaries’ quantization
error due to the pattern matching process instead of direct fitting process137. This
indicated that there was still redundancy in the MRF schedules, and further optimization
such as shortening scan time by truncating time frames per pass in this work is
possible. However, one should be careful when designing new schedules: Sufficient
parameter sensitivity is necessary towards tissues of interest. This is tightly related to
MRF schedule optimization task. Also, it should be noted that precision improvement
was only meaningful after blurring mitigation. In this work, for example, concomitant field
effects mitigation was necessary when processing an imaging slice that was
substantially far from the isocenter. Otherwise, it would not benefit from high SNR
efficiency but instead suffer from overwhelming blurring of a long spiral readout.
There are several limitations in this work. First, substantial in-vivo T2
underestimation exists. Such underestimation matches with other researchers’
reports17,18,34 and the hypothesis is it was largely caused by ignorance on Magnetization
Transfer effects. On the other, there were also 0.55 T MRF reporting in-vivo T2 with

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more accurate values185. Improving 0.55 T MRF accuracy is our work in progress. This
can be done by incorporating MT effects mitigation18,198, such as including MT effects
encoding in the pulse sequence and including MT parameters, i.e., exchange rates and
macromolecule pool size, in dictionary generation. Alternatively, suppressing MT effects
using pulse sequences with less on-resonance saturation is also possible. Second,
corrections for other sources of blurring and signal perturbation were ignored. These
sources, for example, transversal T2 decay and center frequency drift, were
hypothesized to cause blurring residuals in long readout experiments. Taking
transversal T2 decay as an example, apparent in-vivo T2 values at 0.55T are not smaller
than 30 ms34,112 in the literature, which can cause as high as ~48.0% signal decay
during a 22.0-ms spiral readout. However, we have not observed severe issues related
to T2 decay even in the ISMRM/NIST phantom, as indicated by Figure 4.6 and Figure
4.7. Another possible source of blurring is center frequency drift, which can be
monitored and compensated per spiral readout. In this work, a simple center frequency
calibration was applied before each scan and assumed no intra-scan center frequency
drift during data acquisitions. In addition, gradient nonlinearity was also ignored as this
topic was beyond the scope of this work. However, gradient nonlinearity correction
could be potentially incorporated in the framework of a high order encoding model.
Second, concomitant field-induced phase was assumed not to accumulate through a
scan due to the dephasing design in a FISP-MRF sequence for simplicity. Accordingly,
this was ignored in dictionary generation. In our opinion, this phase accumulation, if not
negligible, has limited impacts on FISP-MRF signal evolution. In analogy to static offresonance, concomitant field phase is caused by another highly spatial oriented off-

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resonance source, yet it only occurs during gradient active duration. Therefore, FISPMRF signal evolution magnitude should remain unaffected but with extra signal phases
to be determined. In axial SOS case, extra phases amount varies little within a slice so
that it is equivalent to different constant phase per slice. In non-axial cases, these
phases vary by readout gradients even in the same spatial location as the different
readouts no longer induce similar phase accrual patterns. Extra exploration of these
effects on signal evolution along the temporal dimension might be of interest using the
EPG formalism199 or signal navigator200. However, more complicated corrections should
be anticipated due to that these effects are also highly spatially dependent. The last but
not the least, the MaxGIRF framework was excessively costly in computation. Its
increased computation time came not only from the increased complexity due to the
low-rank modeling of a high-order encoding operator but also from repeated executions
of the core NUFFT operator. However, axial acquisitions reduce the complexity of
concomitant field effects that possibly enables a further simplification in reconstruction,
e.g., approximating the low-rank modeling using only one spiral readout trajectory or
simple extra demodulation instead of substituting the encoding operator when static offresonance is approximately constant. Such simplifications possibly avoid running an
iterative reconstruction with an increased computation complexity.
4.6. Conclusion
We demonstrate improved 3D FISP-MRF of the brain at 0.55 T using long spiral
readouts and concomitant field effects mitigation. With a proper mitigation method of
spatial blurring, MRF T1 and T2 standard deviations were reduced by 45.3% and 50.7%,

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respectively, when a spiral readout increased from 2.9 ms to 22.0 ms. There was
unresolved, residual blurring when a spiral readout was longer than 16.5 ms, suggesting
a possible operational regime.
4.7 Supporting Information
4.7.1 Accuracy of 3D FISP-MRF at 0.55 T
Accuracy was evaluated in an ISMRM/NIST system phantom 201, and one
healthy volunteer (male, age 28). Reference T1 values were measured using singlepoint Inversion Recovery Spin Echo (IRSE) sequences with 8 inversion times (TR =
4000 ms, the shorted TE, TI = [50, 100, 200, 400, 600, 800, 1000, 1600] ms), and
reference T2 values were measured using Single Echo Spin Echo (SESE) sequences
with 7 echo times (TR = 4000 ms, TE = [25, 50, 75, 100, 125, 150, 200] ms). All
experiments were performed on a whole body 0.55 T system (prototype MAGNETOM
Aera, Siemens Healthineers, Erlangen, Germany) equipped with high-performance
shielded gradients (45 mT/m amplitude, 200 T/m/s slew rate). A 16-channel head/neck
coil was used for signal reception. Static off-resonance maps and �!
B maps were
separately acquired using vendor provided sequences.
T1 and T2 results of the proposed MRF of different readout durations were
compared against reference T1 and T2 values. For the ISMRM/NIST phantom, in
specific, the proposed MRF T1 or T2 values were reported against reference T1 values of
each NiCl2 vial or T2 values of each MnCl2 vial, respectively, for each readout duration.
Figure 4.13 shows the ISMRM/NIST phantom results for all vials. There were no
significant differences between results before and after the proposed blurring mitigation,

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and the proposed MRF values showed good agreement with reference values, except
for �/;xm = 2.9 ms when T1 < 200 ms and T2 < 100 ms. Figure 4.14 shows the in-vivo
results for white matter regions of interest. The proposed MRF T1 and T2 biases,
calculated as �!,"
yz{ − �!,"
z;| are reported as a function of readout duration. Proposed MRF
T1 was accurate within ±5.5 ms. Proposed MRF underestimated T2 by 24.7-30.6ms,
and this underestimation was independent of readout duration. Such underestimation
matched with previous work34,202, and we hypothesize that it was partially caused by onresonance MT effects which is stronger at lower field strength 18,34 and improving T2
accuracy is the work in progress 198. Similar to the phantom results, there were no
significant differences between results before and after the proposed blurring correction.
Figure 4.13. Comparison of estimated T1 and T2 values for the ISMRM/NIST system
phantom between the proposed MRF method (y axis) and reference values (x axis).
Results before (blue) and after (red) the proposed blurring mitigation were reported. The
black dashed line is the identity line. There were no significant differences between results
before and after mitigation. Although there were noticeable biases between MRF and
reference values for T1 < 200 ms and T2 < 100 ms for �6S]' = 2.9 ms, such biases were

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reduced for all other �6S]'. Other than that, MRF method shows good accuracy in the
ISMRM/NIST phantom.
Figure 4.14. Comparison of estimated T1 and T2 values in white matter for a healthy adult.
T1 (blue) and T2 (red) biases against literature references (T1 = 493 ms and T2 = 89 ms)
as a function of �6S]' . Results before (dashed) and after (solid) proposed blurring
mitigation are reported. For all 6 readout durations examined, the proposed method
produced T1 estimation with good accuracy within ±5.5 ms range, but underestimated T2
by 24.7 ms to 30.6 ms.
4.7.2 Concomitant Field Effects on FISP-MRF Gradient Dephasing
FISP-MRF relies on this gradient dephasing to maintain T2 sensitivity, as
researchers have reported that increasing gradient moment would lead to reduction in
estimated T2 and loss of T2 differentials between tissues 203. In this work, we assumed
concomitant field phases didn’t accumulate through TR’s for two practical reasons
1. To allow the MaxGIRF higher order encoding to model concomitant field effects for
each time frame independently.
2. To relax the demand on comprehensive dictionaries accounting for concomitant
field effects on FISP-MRF signal evolution.

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When assuming sufficient spoiling (ignoring transverse magnetization residuals),
higher order encoding can model concomitant field induced phases as an additional offresonance source that is independent for each time frame. It was also hinting
conventional FISP-MRF dictionaries can be used since FISP-MRF has been shown to
less vulnerable to B0 inhomogeneity 17, especially when being designed in a constant
TR fashion 204. The rationale is as follows.
The assumption included that a proper 4� dephasing was maintained for FISPMRF and concomitant field effects did not create significant additional intra-voxel
dephasing for axial stack-of-spiral acquisition. For a voxel from a slice whose center is
at � = |�#| mm and its thickness being Δ�, the amount of additional intra-voxel
dephasing Φ is determined by the concomitant phase difference between slice top and
bottom. It has the following relationship (roughly):
Φ ∝ (2|�#|Δ�)
Hence, undesired intra-voxel dephasing would become a problem when the slice
thickness is large and/or a slice is too far away. For a slice that located at � = 0 mm,
there is no additional intra-voxel dephasing at all, as phase accrual is symmetric and
cancels out; For a slice that located at �# = 120 or -120 mm (border slices), there was
<� additional dephasing for a slice thickness of 5 mm for all settings used in this study.
We believe this is within acceptable tolerances, as other researchers have shown 203.
If imaging with a larger S-I extent or thicker slices, there are still ways to mitigate
this. One can compensate these phases using dedicated gradient design 205, which is
possible in 2D multi-slice but difficult in 3D imaging. One can also use more

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comprehensive dictionaries accounting for each unique spatial location. This makes
dictionary generation and matching less practical, but is do-able.

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Chapter 5 Toward accurate MRF T2 in structured material at
0.55 T using MT-suppressed excitations
5.1 Introduction
FISP Magnetic Resonance Fingerprinting (FISP-MRF)
17,86 produces accurate
and precise relaxometry in many tissues, and in system phantoms made of doped
water, e.g., the ISMRM/NIST phantom206. In structured materials, including brain white
matter (WM), there can be significant biases partially due to the presence of
Magnetization Transfer (MT) effects18,68. MT effects 8,70 include bidirectional
magnetization exchange and cross relaxation between free water and bound pool
magnetization (denoted pool � and �, respectively). This process results in deviation
from a single pool model9,68–70,207, and biased results.
For example, FISP-MRF at 0.55 T34,198,202 with a conventional acquisition and
single-pool model results in WM T2 underestimation of roughly 40%. This bias is larger
than observations at 1.5 T and 3 T207–210 likely due to stronger on-resonance MT
saturation. On-resonance MT saturation is hypothesized to be stronger at lower field
strengths because the bound pool would have a more condensed absorption lineshape
around central frequency compared to higher field. This is based on chemical shifts
being proportionally smaller, and experimental observations that many biological tissues
have longer apparent T2. Solutions to this MT confounding factor exist in the literature.
Cohen et al.211 described a CEST-MRF approach for brain tumor using CEST saturation
encoding that varies per temporal point and deep learning reconstruction. West et al.19
described an MT-MRF approach simultaneously using constant on-resonance and

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varying off-resonance RF power per excitation. Hilbert et al.18 demonstrated optionally
adding constant MT encodings during spin relaxation gaps. These approaches involve
modeling and estimating MT parameters, which requires comprehensive signal
simulation and sacrifices precision. Also, these approaches favor wide chemical
shifts10,212 and scenarios with high SNR, and can successfully create adequate
differentials between MT-related and relaxation-related signal evolutions at 1.5 T and 3
T.
At 0.55 T, these methods are sub-optimal because chemical shifts are narrower,
and SNR is generally lower due to reduced equilibrium polarization. It has been shown
that the standard deviation of 0.55 T FISP-MRF T1 and T2 maps are 1.8x larger after
pattern matching with dictionaries modeling MT effects, indicating a significant loss of
precision198. This is partially due to a lack of sufficient differentials and the increased
complexity of comprehensive dictionaries. It is necessary to cover a broader range of
MT parameter values to produce quantitatively interpretable results. Doing so, however,
would even further compromise precision.
Instead of accounting for MT effects, this work hypothesizes that MT effects can
be suppressed using pulse sequence design. Non-selective low-bandwidth RF
excitations are specifically employed, inspired by previous investigations of onresonance MT effects by steady-state sequences74,75. Taking hard pulses as an
example, they can have much narrower excitation bandwidths compared to Sinc-Gauss
pulses with the same duration. Hard pulses also have smaller mean saturation rates8.
These allow hard pulses to produce less incidental on-resonance bound pool saturation.
They also suppress inhomogeneous saturation as the bound pool is no longer

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modulated by slice-selection gradients71,213,214. Further suppression of on-resonance MT
effects is possible by elongating RF durations and TR, however, at a sacrifice of scan
efficiency, e.g., readout duty cycle. To compensate this, we combined this approach with
an efficient 0.55 T FISP-MRF197 using long spiral readout.
5.2 Method
5.2.1 Pulse sequence design
A baseline 3D FISP-MRF sequence with pre-inversion preparation and 4�
dephasing was implemented in the Pulseq open-source framework191. It was based on
the specification of a whole-body 0.55T MRI scanner (prototype MAGNETOM Aera,
Siemens Healthineers, Erlangen, Germany) equipped with high-performance shielded
gradients (45 mT/m amplitude, 200 T/m/s slew rate). This sequence used a slabselective Sinc-Gauss RF pulse (�Qg = 2 ms, tbw = 8) with a stack-of-spirals (SOS)
trajectory. Readout gradient waveforms were designed in a variable density fashion with
0th moment nulling193. To achieve a 300x300x180 mm3 field-of-view and 1.2x1.2x2.5
mm3 in-plane resolution, the acquisition consisted of 72 partition encodings and 14
spiral interleaves were required to fully sample a 2D plane in k-space. The duration of a
spiral interleaf was 9.5 ms. For each partition, a 180° inversion pulse (TI = 20.6 ms) was
appended to the beginning and 555 TRs/timeframes were followed. The fixed durations
of TR and TE were 14.02 ms and 1.59 ms, respectively. The FA pattern as a function of
time points is shown in Figure 5.1.
Two additional sequences were developed by replacing a slab-selective SincGauss pulse with a non-selective low bandwidth hard pulse. The hard pulse durations �Qg

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were 2 and 4 ms, respectively. For the pulse sequence with a �Qg of 4ms, the TR was
increased by 2 ms accordingly. The total scan times of FISP-MRF sequences were 11:51
and 13:11 min.
Figure 5.1. FA pattern per partition plot versus time point and example spiral readout
trajectory. There are 555 time points per partition, corresponding to 7.78 seconds and
8.89 seconds when �Qg is 2ms or 4ms, respectively. The total scan times are 11 minutes
and 51 seconds, and 13 minutes and 11 seconds, respectively. The spiral duration is 9.5
ms, and 14 interleaves are required to fully sample 2D k-space. The axes in the trajectory
plot are in normalized units [-0.5 0.5].
5.2.2 Dictionary simulation
Dictionaries were simulated by sampling 225 T1 (10-3500 ms) and 128 T2 (2-
2000 ms) with varying increments using the conventional single pool model. This
resulted in a total of 24878 entries in total after discarding non-biologically relevant
entries, e.g., T2 > T1. B1
+ correction was performed by simulating separate dictionaries
with 21 B1
+ values ranging from 0.5 to 1.5 with an increment of 0.05. This process was
repeated for the 2 unique TR values.

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5.2.3 Experiment
Three healthy volunteers (3M, age 29-35) were imaged under a protocol
approved by our Institutional Review Board, after providing written informed consent. All
volunteers were scanned with three FISP-MRF sequences, and with four 2D single
echo spin echo (SESE) sequences (TR = 3500 ms, TE = [20, 40, 80, 160] ms) for
reference T2. Static off-resonance maps and B1
+ maps were acquired using vendor
provided protocols. All imaging was performed with sagittal prescription.
5.2.4 Image Reconstruction
MRF time series images were reconstructed using a variant of MaxGIRF
encoding133 and subspace modeling constraints181, as described in Zhu et al.197
MaxGIRF encoding is computationally expensive, therefore we applied concomitant
field phase approximations using the mean value of the extra phase induced by each
spiral readout gradient. For axial prescription, this approximation causes negligible
errors as the concomitant field phase differences between different spiral readout
gradients are less than 0.1% within the FOV. For sagittal (used in this study) and
coronal prescription, these differences are less than 2%. With this approximation,
reconstruction time was reduced by >7-fold.
5.2.5 Data Analysis
MRF T1 and T2 precision was estimated using the pseudo-replica method34,134. We
generated 100 pseudo replicas for each raw dataset, with complex multi-coil additive
white Gaussian noise simulated using the noise covariance matrix measured from noise

109
only scans. The identical reconstruction procedure was repeated for each pseudo-replica,
and the standard deviation across the replica dimension was calculated per voxel for both
MRF T1 and T2 maps.
Analysis was performed using a manually drawn WM region-of-interest (ROI).
We report MRF T2 and T1 from the ROI’s and compared MRF T2 against reference T2
measurements within the same ROI’s.
5.3 Results
Figure 5.2 shows the simulated excitation profile for each excitation RF envelope
(75°), and the assumed bound pool absorption lineshape at 0.55 T. The RF energy of
examined pulses is 51.41, 13.97 and 6.99 µT2ms/rad. The bound pool transversal
relaxation time �",} was assumed to be 18 µs which is longer than the literature value at
1.5 T64. By this analysis, the effective mean saturation rates for the hard pulses is
expected to be roughly 63% and 87% less than that of the conventional pulse.

110
Figure 5.2. Simulated excitation profiles for the 3 RF pulses (blue) and the assumed
bound pool absorption lineshape at 0.55T (black). Bound pool T2 is assumed to be 18 µs.
The effective bound pool saturation should be determined based on the overlap between
each profile and absorption lineshape. Under these settings, both hard pulses have much
narrower on-resonance bandwidth and lower side-lobe magnitude, and thus create much
less bound pool saturation. The full widths at half maximum of each profile are 4000 Hz
(Sinc), 634 Hz (Hard, �Qg = 2 ms) and 317 Hz (Hard, �Qg = 4 ms).
Figure 5.3 shows 2D T2 maps from each FISP-MRF sequence and each
volunteer. These parametric maps show clear tissues differentials, e.g., boundaries
between brain WM and gray matter (GM). Notice that in white matter, MRF estimated T2
increased when using the proposed non-selective low-bandwidth hard pulses. 2D T1
maps are provided in Figure 5.4.

111
Figure 5.3. FISP MRF T2 maps from 3 volunteers using different RF pulse designs.
Tissues differentials are preserved, specifically the visible boundaries between white
matter and gray matter. (left to right) T2 estimates progressively and substantially increase
as MT effects are suppressed with the modified RF pulses, as illustrated by red arrows.

112
Figure 5.4. FISP MRF T1 maps from 3 volunteers using different RF pulse designs.
Tissues differentials are preserved, specifically the visible boundaries between white
matter and gray matter. (left to right) T1 estimates progressively decreased as MT
effects are suppressed with the modified RF pulses, as illustrated by blue arrows.
Figure 5.5 contains FISP MRF T2 violin plots from WM ROIs for each volunteer
using the three RF pulses. The reference mean T2 values from the same ROIs is
displayed in each T2 plot. Using the proposed non-selective low-bandwidth hard pulses,
WM T2 underestimation was substantially reduced from 36.3%-38.0% to <10%. There

113
was no significant change in standard deviation values. WM T1 violin plots are provided
in Figure 5.6. WM T1 estimates decreased by 4.4%-8.9%.
Figure 5.5. WM FISP MRF T2 violin plots. Violin plots from the three RF pulse designs
are shown in different colors (Blue: Sinc, �Qg = 2 ms, red: Hard, �Qg = 2 ms, and yellow:
Hard, �Qg = 4 ms) as well as indicated on the x-axis. Each volunteer’s reference T2 is
displayed as a dashed black line in each T2 plot. FISP MRF T2 mean values approached
reference values after using hard RF pulses design, while standard deviation values were
not significantly affected. This suggests a substantial improvement in T2 accuracy, without
compromising precision.

114
Figure 5.6. WM FISP MRF T1 violin plots. Violin plots from the three RF pulse designs
are shown in different colors (Blue: Sinc, �Qg = 2 ms, red: Hard, �Qg = 2 ms, and yellow:
Hard, �Qg = 4 ms) as well as indicated on the x-axis. FISP MRF T1 mean values
decreased after using hard RF pulses design, while standard deviation values were not
significantly affected.
Figure 5.7 and 5.8 show violin plots of standard deviation values of FISP MRF T2
and T1 across the pseudo replicas dimension for all subjects. For each subject,

115
distributions of standard deviation values of different sequences does not drastically
change, and each violin plot’s standard deviation value scales with it mean.
Figure 5.7. Violin plots of MRF T2 standard deviation values across the pseudo replicas
dimension. Violin plots from the three RF pulse designs are shown in different colors (Blue:
Sinc, �Qg = 2 ms, red: Hard, �Qg = 2 ms, and yellow: Hard, �Qg = 4 ms) as well as indicated
on the x-axis. These violin plots do not change drastically in standard deviation values,
and the values scale with each plot’s mean.

116
Figure 5.8. Violin plots of MRF T1 standard deviation values across the pseudo replicas
dimension. Violin plots from the three RF pulse designs are shown in different colors (Blue:
Sinc, �Qg = 2 ms, red: Hard, �Qg = 2 ms, and yellow: Hard, �Qg = 4 ms) as well as indicated
on the x-axis. Same observations to Figure 5.7 can be made.
5.4 Discussion
We demonstrate a practical approach for significantly mitigating MRF T2 bias in
structured materials at 0.55T. Specifically, in healthy volunteers, we evaluated
quantification performance of 3D FISP-MRF sequences with three RF excitation pulses:

117
1) a conventional slab-selective Sinc-Gauss pulse, 2) a non-selective low-bandwidth
hard pulse and 3) a non-selective low-bandwidth hard pulses with a longer duration
(lower bandwidth). We observed that using non-selective low-bandwidth pulses
substantially reduced FISP-MRF T2 underestimation compared with reference
measurements in the same locations and with published literature. FISP-MRF T1 was
slightly reduced but still within a reasonable range, and was not compared against a
reference method in this study. No significant changes to standard deviation were
observed. We attribute the accuracy improvement to the suppressed MT effects which
is mechanistically expected based on the change in RF excitation pulses. This strategy
avoided the need for more comprehensive dictionaries modeling MT parameters or
using a two-pool model, which would have compromised precision.
On-resonance RF pulses are expected to produce more incidental MT saturation
at 0.55T compared to higher field strengths. For slab selective RF pulses, this effect is
exacerbated, as they have a broader spectrum when �Qg is short. They may also cause
more inhomogeneous MT saturation due to modulation by the necessary slab-selection
gradients. In contrast to selective RF pulses, non-selective pulses have a weaker onresonance MT saturation impact. We consider such excitations to be MT-suppressed,
and they produce MR signals closer to single-pool model predictions. We speculate that
MT suppression can be further enhanced (if needed) by elongating �Qg and/or TR, but
this will cause reduction of readout duty cycle and therefore SNR efficiency.
In this work, we applied an efficient FISP-MRF approach using 9.5 ms
readouts197, which is longer than typical, in order to partially compensate for the lower
SNR efficiency at 0.55 T. However, doing so caused undesired concomitant field effects.

118
To maintain straight-forward mitigation as described in previous work, we chose SoS
acquisition in this work. We assumed negligible concomitant gradient phases from nonreadout gradient waveforms due to their short duration, i.e., <1 ms. Thus, SoS had the
minimal inter-partition differences in concomitant field effects, and we mitigated the
effects solely caused by readout gradients. For more advanced acquisition trajectories
such as Spiral Projection Imaging (SPI)
85,215,216, the concomitant field effects (if
significant) can vary between timeframes and spatial locations requiring more
sophisticated correction.
This study has limitations. First, we used sagittal prescription and a 180 mm FOV
in the R-L direction. This was done to reduce the number of required kz steps when
using non-selective excitation. With axial prescription, the proposed approach is likely to
require more kz steps, i.e., oversampling. Second, we used asymmetric spatial
resolution, i.e., 1.2x1.2 mm2 in plane and 2.5 mm slice thickness. Isotropic resolution is
ultimately desired, and this can be achieved by increasing number of phase encoding
partitions, i.e., wider k-space coverage, with optional interleaved undersampling along
the Cartesian encoding direction86 or switching to other sampling schemes such as
SPI85,215. Third, we did not compare MRF T1 against reference T1 measurements. To our
knowledge, T1 accuracy is not a documented problem for FISP-MRF, nor is it known to
be connected to MT effects. However, we noticed a small reduction (~5-9%) in WM
mean T1 when using the proposed approach, which may warrant further investigation.
5.5 Conclusion
We demonstrate a more accurate FISP-MRF approach at 0.55T using nonselective RF excitations. Importantly, T2 underestimation in structured material,

119
specifically brain WM, was reduced to less than 10%, without having to compromise
precision.

120
Chapter 6 Summary
FISP-MRF17,86 provides efficient multiparametric quantifications. Compared to its
twin approach, TruFISP-MRF16,217, FISP-MRF is known to be less vulnerable to system
imperfections such static field inhomogeneity, yet it might produce less signal (when an
identical schedule is used) due to its dephasing design. Therefore, it is commonly
favored at high field MRI. When migrating to mid- and low-field MRI, e.g., <1 Tesla, the
risk of SNR reduction should be the first to be examined since it has been shown that
SNR affects FISP-MRF accuracy137. Previously, researchers have shown that 3D brain
FISP-MRF is feasible at 0.55 T34, and this was achieved using a high performance
gradient setting (amplitude 45 mT/m and slew rate 200 mT/m/s) to but with short
acquisition and slow data sampling. In that way, it maintained limited blurring from static
off-resonance, concomitant field phases and T2
* decay, and reasonable SNR by narrow
readout bandwidth and 5 mm slice thickness (for comparison, <3 mm is used at higher
field). Although this approach has been shown to be accurate in water phantoms and
highly repeatable in healthy volunteer34,202, it was still substantially underestimating
brain T2 even with a B1
+ correction. Such biases have been shown to be partially related
to MT effects in structural materials18,68. They are addressable at high field through
efficient off-resonance saturation techniques and comprehensive modeling18,19,211.
These solutions, however, seemed suboptimal for 0.55 T due to reduced chemical shifts
and increased SNR burden. Hence, these are opportunities for two substantial
improvements, and are the focus of this dissertation.
First, a more efficient FISP-MRF approach for 0.55 T from data acquisition
perspective, e.g., using longer spiral readout, was developed and demonstrated. By

121
elongating spiral readouts and TR, readout cycle and was increased and more
longitudinal recovery was allowed. These together led to an SNR boost up to 2x
because of higher readout duty cycle and higher signal intensity per timeframe. This
was inspired by the fact that long readout is more feasible at low field MRI due to
improve field homogeneity and slower transversal decay. This approach also combined
temporal subspace model constraints and higher order encoding for further SNR
recovery and necessary blurring mitigation caused by static off-resonance and
concomitant field phases during readout. It was assumed that these phase did not
impact a MRF signal evolution, but this be of interest to be investigated and examined.
and Results showed standard deviation values due to thermal noise progressively
reduced as readout elongated, yet the biases remained largely unaffected. This meant
that the biases were more likely to be biological-related. The proposed approach
showed improved efficiency, which is helpful in producing more precise results and
pushing for higher resolution in the next improvement.
Second, a more accurate FISP-MRF was demonstrated by suppressing onresonance MT effects. On-resonance MT effects in structural materials have been
shown to partially contribute to the biases. Unlike 1.5 T or higher field, encoding MT
effects into FISP-MRF is more challenging at 0.55 T due to narrow chemical shifts (less
efficient off-resonance saturation) and loss of SNR (harder to differentiate MT effects
from others). Alternatively, non-selectively hard pulse excitations were used with >60%
less on-resonance MT and this avoided comprehensive signal modeling, which worsens
quantification precision. Results showed reduced FISP-MRF T2 underestimation from
~40% to <10% without compromising on standard deviation values. The proposed

122
approach is, therefore, a better solution to address MT-related biases at 0.55 T. It also
combined previous efficiency improvement to produce higher resolution FISP-MRF at
0.55 T (1.2x1.2x2.5 mm3). The ultimate goal is to achieve a millimeter-level isotropic
resolution, which is doable in multiple ways (e.g., interleaved undersampling with more
phase encoding steps or SPI acquisition). Investing the feasibility of combining isotropic
resolution imaging with work in this dissertation is of interest.
In addition to further investigation of technical development of the current
approach, there are several extra points of interest for future investigations. First,
evaluating repeatability and reproducibility of the proposed FISP-MRF approach at
different cites with a 0.55 T scanner is interesting and useful. Although such evaluations
have been performed on scanners by different vendors, MRF repeatability and
reproducibility have been widely studied at 1.5 T and 3 T183,209,218 with different gradient
specifications in both MR phantoms and healthy brains. For the proposed approach, In
specific, its repeatability can be studied on the current scanner with more volunteers,
while for its reproducibility evaluation, this has to be done by a cross cite study. When
performing this cross cite study, differences in 0.55 T scanners specifications, e.g., Aera
XQ vs. Free.MAX, have to be accounted. Unlike this dissertation, performing the
proposed approach on a scanner with a weaker gradient strength will lead to less
efficient scans but also different concomitant field effects. Understanding this
reproducibility will help establishing a common protocol producing acceptable reference
ranges of different materials and healthy, and also benefit popularizing MRF approach
at 0.55 T. This study can be further strengthened by including patient validations. The
0.55 T MRF approach can have more clinical impacts if MRF reference ranges of

123
several diseases can be provided with stark contrast to normal ranges of healthy
tissues.
In summary, 2 improved 0.55 T FISP-MRF approaches were developed,
demonstrated and evaluated for 0.55 T 3D brain FISP-MRF. The proposed approaches
together produces more accurate and precise parametric results at higher spatial
resolution. Various pulse sequence design techniques, constrained reconstruction and
higher order encoding model are used. Future research may include investigating
concomitant field effects in FISP-MRF signal evolution and developing isotropic
resolution.

124
References
1. Rabi II. On the Process of Space Quantization. Physical Review. 1936;49(4):324-328.
doi:10.1103/PhysRev.49.324
2. Rabi II. Space Quantization in a Gyrating Magnetic Field. Physical Review.
1937;51(8):652-654. doi:10.1103/PhysRev.51.652
3. Rabi II, Zacharias JR, Millman S, Kusch P. A New Method of Measuring Nuclear
Magnetic Moment. Physical Review. 1938;53(4):318-318.
doi:10.1103/PhysRev.53.318
4. Odeblad E, Bryhn U. Proton magnetic resonance of human cervical mucus during the
menstrual cycle. Acta radiol. 1957;47(4):315-320. doi:10.3109/00016925709170899
5. Carr HY, Purcell EM. EJects of DiJusion on Free Precession in Nuclear Magnetic
Resonance Experiments. Physical Review. 1954;94(3):630-638.
doi:10.1103/PhysRev.94.630
6. Stejskal EO, Tanner JE. Spin DiJusion Measurements: Spin Echoes in the Presence of
a Time-Dependent Field Gradient. J Chem Phys. 1965;42(1):288-292.
doi:10.1063/1.1695690
7. WolJ SD, Balaban RS. Magnetization transfer contrast (MTC) and tissue water proton
relaxation in vivo. Magn Reson Med. 1989;10(1):135-144.
doi:10.1002/MRM.1910100113
8. Graham SJ, Henkelman RM. Understanding pulsed magnetization transfer. Journal of
Magnetic Resonance Imaging. 1997;7(5):903-912. doi:10.1002/jmri.1880070520
9. van Gelderen P, Jiang X, Duyn JH. EJects of magnetization transfer on T 1 contrast in
human brain white matter. Neuroimage. 2016;128:85-95.
doi:10.1016/j.neuroimage.2015.12.032
10. Priovoulos N, Jacobs HIL, Ivanov D, Uludağ K, Verhey FRJ, Poser BA. High-resolution
in vivo imaging of human locus coeruleus by magnetization transfer MRI at 3T and 7T.
Neuroimage. 2018;168:427-436. doi:10.1016/j.neuroimage.2017.07.045
11. Yang S, Law M, Zagzag D, et al. Dynamic contrast-enhanced perfusion MR imaging
measurements of endothelial permeability: diJerentiation between atypical and
typical meningiomas. AJNR Am J Neuroradiol. 2003;24(8):1554-1559. Accessed May
11, 2020. http://www.ncbi.nlm.nih.gov/pubmed/13679270

125
12. O’Connor JPB, Jackson A, Parker GJM, Roberts C, Jayson GC. Dynamic contrastenhanced MRI in clinical trials of antivascular therapies. Nat Rev Clin Oncol.
2012;9(3):167-177. doi:10.1038/nrclinonc.2012.2
13. Lebel RM, Jones J, Ferre JC, Law M, Nayak KS. Highly accelerated dynamic contrast
enhanced imaging. Magn Reson Med. 2014;71(2):635-644. doi:10.1002/mrm.24710
14. Gulani V, Seiberlich N. Quantitative MRI: Rationale and Challenges. In: ; 2020:xxxviili. doi:10.1016/B978-0-12-817057-1.00001-9
15. Damadian R. Tumor Detection by Nuclear Magnetic Resonance. Science (1979).
1971;171(3976):1151-1153. doi:10.1126/science.171.3976.1151
16. Ma D, Gulani V, Seiberlich N, et al. Magnetic resonance fingerprinting. Nature.
2013;495(7440):187-192. doi:10.1038/nature11971
17. Jiang Y, Ma D, Seiberlich N, Gulani V, Griswold MA. MR fingerprinting using fast
imaging with steady state precession (FISP) with spiral readout. Magn Reson Med.
2015;74(6):1621-1631. doi:10.1002/mrm.25559
18. Hilbert T, Xia D, Block KT, et al. Magnetization transfer in magnetic resonance
fingerprinting. Magn Reson Med. 2020;84(1):128-141. doi:10.1002/MRM.28096
19. West DJ, Cruz G, Teixeira RPAG, et al. An MR fingerprinting approach for quantitative
inhomogeneous magnetization transfer imaging. Magn Reson Med. 2022;87(1):220-
235. doi:10.1002/mrm.28984
20. Afzali M, Mueller L, Sakaie K, et al. MR Fingerprinting with b-Tensor Encoding for
Simultaneous Quantification of Relaxation and DiJusion in a Single Scan. Magn
Reson Med. 2022;88(5):2043-2057. doi:10.1002/mrm.29352
21. Ma D, Jiang Y, Chen Y, et al. Fast 3D Magnetic Resonance Fingerprinting for a WholeBrain Coverage. 2017;00:1-8. doi:10.1002/mrm.26886
22. Badve C, Yu A, Rogers M, et al. Simultaneous T1 and T2 Brain Relaxometry in
Asymptomatic Volunteers Using Magnetic Resonance Fingerprinting. Tomography.
2015;1(2):136-144. doi:10.18383/j.tom.2015.00166
23. Yu AC, Badve C, Ponsky LE, et al. Development of a Combined MR Fingerprinting and
DiJusion Examination for Prostate Cancer. Radiology. 2017;283(3):729-738.
doi:10.1148/radiol.2017161599
24. Panda A, OʼConnor G, Lo WC, et al. Targeted Biopsy Validation of Peripheral Zone
Prostate Cancer Characterization With Magnetic Resonance Fingerprinting and

126
DiJusion Mapping. Invest Radiol. 2019;54(8):485-493.
doi:10.1097/RLI.0000000000000569
25. Panda A, Obmann VC, Lo WC, et al. MR Fingerprinting and ADC Mapping for
Characterization of Lesions in the Transition Zone of the Prostate Gland. Radiology.
2019;292(3):685-694. doi:10.1148/radiol.2019181705
26. Sushentsev N, Kaggie JD, Buonincontri G, et al. The eJect of gadolinium-based
contrast agent administration on magnetic resonance fingerprinting-based T1
relaxometry in patients with prostate cancer. Sci Rep. 2020;10(1):20475.
doi:10.1038/s41598-020-77331-4
27. Chen Y, Jiang Y, Pahwa S, et al. MR Fingerprinting for Rapid Quantitative Abdominal
Imaging. Radiology. 2016;279(1):278-286. doi:10.1148/RADIOL.2016152037
28. Fujita S, Sano K, Cruz G, et al. MR Fingerprinting for Liver Tissue Characterization: A
Histopathologic Correlation Study. Radiology. 2023;306(1):150-159.
doi:10.1148/radiol.220736
29. Badve C, Yu A, Dastmalchian S, et al. MR Fingerprinting of Adult Brain Tumors: Initial
Experience. AJNR Am J Neuroradiol. 2017;38(3):492. doi:10.3174/AJNR.A5035
30. de Blank P, Badve C, Gold DR, et al. Magnetic Resonance Fingerprinting to
Characterize Childhood and Young Adult Brain Tumors. Pediatr Neurosurg.
2019;54(5):310-318. doi:10.1159/000501696
31. Dastmalchian S, Kilinc O, Onyewadume L, et al. Radiomic analysis of magnetic
resonance fingerprinting in adult brain tumors. Eur J Nucl Med Mol Imaging.
2021;48(3):683-693. doi:10.1007/s00259-020-05037-w
32. Konar AS, Shah AD, Paudyal R, et al. Quantitative Relaxometry Metrics for Brain
Metastases Compared to Normal Tissues: A Pilot MR Fingerprinting Study. Cancers
(Basel). 2022;14(22):5606. doi:10.3390/cancers14225606
33. Tippareddy C, Onyewadume L, Sloan AE, et al. Novel 3D magnetic resonance
fingerprinting radiomics in adult brain tumors: a feasibility study. Eur Radiol.
2023;33(2):836-844. doi:10.1007/S00330-022-09067-W
34. Campbell-Washburn AE, Jiang Y, Körzdörfer G, Nittka M, Griswold MA. Feasibility of
MR fingerprinting using a high-performance 0.55 T MRI system. Magn Reson Imaging.
Published online June 8, 2021. doi:10.1016/j.mri.2021.06.002

127
35. Guenthner C, Peereboom SM, Dillinger H, et al. Ramping down a clinical 3 T scanner:
a journey into MRI and MRS at 0.75 T. Magnetic Resonance Materials in Physics,
Biology and Medicine. 2023;36(3):355-373. doi:10.1007/s10334-023-01089-9
36. Marques JP, Simonis FFJ, Webb AG. Low-field MRI: An MR physics perspective.
Journal of Magnetic Resonance Imaging. 2019;49(6):1528-1542.
doi:10.1002/jmri.26637
37. Goudsmit SA. The discovery of the electron spin. Published online 1925.
38. Bloch F. Nuclear Induction. Physical Review. 1946;70(7-8):460-474.
doi:10.1103/PhysRev.70.460
39. Purcell EM, Torrey HC, Pound R V. Resonance Absorption by Nuclear Magnetic
Moments in a Solid. Physical Review. 1946;69(1-2):37-38.
doi:10.1103/PhysRev.69.37
40. LAUTERBUR PC. Image Formation by Induced Local Interactions: Examples
Employing Nuclear Magnetic Resonance. Nature. 1973;242(5394):190-191.
doi:10.1038/242190a0
41. Lauterbur PC. Magnetic resonance zeugmatography. Pure and Applied Chemistry.
1974;40(1-2):149-157. doi:10.1351/pac197440010149
42. Damadian R, Goldsmith M, MinkoJ L. NMR in cancer: XVI. FONAR image of the live
human body. Physiol Chem Phys. 1977;9(1):97-100.
43. Bauman G, Lee NG, Tian Y, Bieri O, Nayak KS. Submillimeter lung MRI at 0.55 T using
balanced steady-state free precession with half-radial dual-echo readout (bSTAR).
Magn Reson Med. 2023;90(5):1949-1957. doi:10.1002/mrm.29757
44. Lim TR, Suthiphosuwan S, Micieli J, et al. Low-Field (64 mT) Portable MRI for Rapid
Point-of-Care Diagnosis of Dissemination in Space in Patients Presenting with Optic
Neuritis. American Journal of Neuroradiology. 2024;45(11):1819-1825.
doi:10.3174/ajnr.A8395
45. Boulant N, Mauconduit F, Gras V, et al. In vivo imaging of the human brain with the
Iseult 11.7-T MRI scanner. Nat Methods. 2024;21(11):2013-2016.
doi:10.1038/s41592-024-02472-7
46. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: Sensitivity encoding
for fast MRI. Magn Reson Med. 1999;42(5):952-962. doi:10.1002/(SICI)1522-
2594(199911)42:5<952::AID-MRM16>3.0.CO;2-S

128
47. Griswold MA, Jakob PM, Heidemann RM, et al. Generalized autocalibrating partially
parallel acquisitions (GRAPPA). Magn Reson Med. 2002;47(6):1202-1210.
doi:10.1002/mrm.10171
48. Uecker M, Lai P, Murphy MJ, et al. ESPIRiT - An eigenvalue approach to
autocalibrating parallel MRI: Where SENSE meets GRAPPA. Magn Reson Med.
2014;71(3):990-1001. doi:10.1002/mrm.24751
49. Donoho DL. Compressed sensing. IEEE Trans Inf Theory. 2006;52(4):1289-1306.
doi:10.1109/TIT.2006.871582
50. Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing
for rapid MR imaging. Magn Reson Med. 2007;58(6):1182-1195.
doi:10.1002/mrm.21391
51. Lin DJ, Johnson PM, Knoll F, Lui YW. Artificial Intelligence for MR Image
Reconstruction: An Overview for Clinicians. Journal of Magnetic Resonance Imaging.
2021;53(4):1015-1028. doi:10.1002/jmri.27078
52. Likes RS. Moving gradient zeugmatography. Published online December 22, 1981.
53. Ljunggren S. A simple graphical representation of fourier-based imaging methods.
Journal of Magnetic Resonance (1969). 1983;54(2):338-343. doi:10.1016/0022-
2364(83)90060-4
54. Nyquist H. Certain Topics in Telegraph Transmission Theory. Transactions of the
American Institute of Electrical Engineers. 1928;47(2):617-644. doi:10.1109/TAIEE.1928.5055024
55. Cooley JW, Tukey JW. An Algorithm for the Machine Calculation of Complex Fourier
Series. Math Comput. 1965;19(90):297. doi:10.2307/2003354
56. Cooley J, Lewis P, Welch P. Historical notes on the fast Fourier transform. IEEE
Transactions on Audio and Electroacoustics. 1967;15(2):76-79.
doi:10.1109/TAU.1967.1161903
57. Fessler JA. On NUFFT-based gridding for non-Cartesian MRI. Journal of Magnetic
Resonance. 2007;188(2):191-195. doi:10.1016/j.jmr.2007.06.012
58. Frahm J, Haase A, Matthaei D. Rapid NMR imaging of dynamic processes using the
FLASII technique. Magn Reson Med. 1986;3(2):321-327.
doi:10.1002/mrm.1910030217

129
59. Mugler JP, Brookeman JR. Three-dimensional magnetization-prepared rapid gradientecho imaging (3D MP RAGE). Magn Reson Med. 1990;15(1):152-157.
doi:10.1002/mrm.1910150117
60. Bydder GM, Hajnal JV, Young IR. MRI: Use of the inversion recovery pulse sequence.
Clin Radiol. 1998;53(3):159-176. doi:10.1016/S0009-9260(98)80096-2
61. Hyde JS. [19] Saturation-transfer spectroscopy. In: ; 1978:480-511.
doi:10.1016/S0076-6879(78)49021-4
62. Look DC, Locker DR. Time saving in measurement of NMR and EPR relaxation times.
Review of Scientific Instruments. 1970;41(2):250-251. doi:10.1063/1.1684482
63. Messroghli DR, Radjenovic A, Kozerke S, Higgins DM, Sivananthan MU, Ridgway JP.
Modified Look-Locker inversion recovery (MOLLI) for high-resolution T 1 mapping of
the heart. Magn Reson Med. 2004;52(1):141-146. doi:10.1002/mrm.20110
64. Sled JG, Pike GB. Quantitative imaging of magnetization transfer exchange and
relaxation properties in vivo using MRI. Magn Reson Med. 2001;46(5):923-931.
doi:10.1002/mrm.1278
65. Yarnykh VL. Pulsed Z-spectroscopic imaging of cross-relaxation parameters in
tissues for human MRI: Theory and clinical applications. Magn Reson Med.
2002;47(5):929-939. doi:10.1002/mrm.10120
66. Tofts PS, Cercignani M, Tozer DJ, et al. Tozer et al. Quantitative Magnetization Transfer
Mapping of Bound Protons in Multiple Sclerosis, Magn Reson Med 2003;50:83-91.
Magn Reson Med. 2005;53(2):492-493. doi:10.1002/mrm.20370
67. Rui RP, Malik SJ, Hajnal J V. Fast quantitative MRI using controlled saturation
magnetization transfer. Magn Reson Med. 2019;81(2):907-920.
doi:10.1002/mrm.27442
68. Malik SJ, Teixeira RPAG, Hajnal J V. Extended phase graph formalism for systems with
magnetization transfer and exchange. Magn Reson Med. 2018;80(2):767-779.
doi:10.1002/mrm.27040
69. A.G. Teixeira RP, Malik SJ, Hajnal J V. Fast quantitative MRI using controlled saturation
magnetization transfer. Magn Reson Med. 2019;81(2):907-920.
doi:10.1002/mrm.27442
70. Henkelman RM, Stanisz GJ, Graham SJ. Magnetization transfer in MRI: a review.
Published online 2001. doi:10.1002/nbm.683

130
71. Dixon WT, Engels H, Castillo M, Sardashti M. Incidental magnetization transfer
contrast in standard multislice imaging. Magn Reson Imaging. 1990;8(4):417-422.
doi:10.1016/0730-725X(90)90050-C
72. Elster AD, King JC, Mathews VP, Hamilton CA. Cranial tissues: appearance at
gadolinium-enhanced and nonenhanced MR imaging with magnetization transfer
contrast. Radiology. 1994;190(2):541-546. doi:10.1148/radiology.190.2.8284413
73. Mathews VP, Elster AD, King JC, Ulmer JL, Hamilton CA, Strottmann JM. Combined
eJects of magnetization transfer and gadolinium in cranial MR imaging and MR
angiography. American Journal of Roentgenology. 1995;164(1):169-172.
doi:10.2214/ajr.164.1.7998532
74. Gloor M, ScheJler K, Bieri O. Quantitative magnetization transfer imaging using
balanced SSFP. Magn Reson Med. 2008;60(3):691-700. doi:10.1002/MRM.21705
75. Gloor M, ScheJler K, Bieri O. Nonbalanced SSFP-based quantitative magnetization
transfer imaging. Magn Reson Med. 2010;64(1):149-156. doi:10.1002/mrm.22331
76. Nöth U, Shrestha M, Schüre JR, Deichmann R. Quantitative in vivo T2 mapping using
fast spin echo techniques – A linear correction procedure. Neuroimage.
2017;157:476-485. doi:10.1016/j.neuroimage.2017.06.017
77. Deoni SCL, Rutt BK, Peters TM. Rapid combined T1 and T2 mapping using gradient
recalled acquisition in the steady state. Magn Reson Med. 2003;49(3):515-526.
doi:10.1002/mrm.10407
78. Deoni SCL. High-resolution T1 mapping of the brain at 3T with driven equilibrium
single pulse observation of T1 with high-speed incorporation of RF field
inhomogeneities (DESPOT1-HIFI). Journal of Magnetic Resonance Imaging.
2007;26(4):1106-1111. doi:10.1002/jmri.21130
79. Carr HY. Steady-State Free Precession in Nuclear Magnetic Resonance. Physical
Review. 1958;112(5):1693-1701. doi:10.1103/PhysRev.112.1693
80. Dupuis A, Chen Y, Hansen M, et al. Quantifying 3D MR fingerprinting
( 3D-MRF ) reproducibility across subjects, sessions, and scanners
automatically using MNI atlases. Magn Reson Med. 2024;91(5):2074-
2088. doi:10.1002/mrm.29983
81. Lee JH, Hargreaves BA, Hu BS, Nishimura DG. Fast 3D imaging using variable-density
spiral trajectories with applications to limb perfusion. Magn Reson Med.
2003;50(6):1276-1285. doi:10.1002/mrm.10644

131
82. Liao C, Bilgic B, Manhard MK, et al. 3D MR fingerprinting with accelerated stack-ofspirals and hybrid sliding-window and GRAPPA reconstruction. Neuroimage.
2017;162:13-22. doi:10.1016/j.neuroimage.2017.08.030
83. Cao X, Ye | Huihui, Liao | Congyu, Li Q, He H, Zhong | Jianhui. Fast 3D brain MR
fingerprinting based on multi-axis spiral projection trajectory. Magn Reson Med.
2019;82:289. doi:10.1002/mrm.27726
84. Chen Y, Fang Z, Hung SC, Chang WT, Shen D, Lin W. High-resolution 3D MR
Fingerprinting using parallel imaging and deep learning. Neuroimage.
2020;206:116329. doi:10.1016/j.neuroimage.2019.116329
85. Cao X, Liao C, Iyer SS, et al. Optimized multi-axis spiral projection MR
fingerprinting with subspace reconstruction for rapid whole-brain high-isotropicresolution quantitative imaging. Magn Reson Med. 2022;88(1):133-150.
doi:10.1002/mrm.29194
86. Ma D, Jiang Y, Chen Y, et al. Fast 3D Magnetic Resonance Fingerprinting for a WholeBrain Coverage. Magn Reson Med. 2018;79:2190-2197. doi:10.1002/mrm.26886
87. Badve C, Yu A, Dastmalchian S, et al. MR fingerprinting of adult brain tumors: Initial
experience. In: American Journal of Neuroradiology. Vol 38. American Society of
Neuroradiology; 2017:492-499. doi:10.3174/ajnr.A5035
88. Riederer SJ, Suddarth SA, Bobman SA, Lee JN, Wang HZ, MacFall JR. Automated MR
image synthesis: feasibility studies. Radiology. 1984;153(1):203-206.
doi:10.1148/radiology.153.1.6089265
89. Gulani V, Seiberlich N. Quantitative MRI: Rationale and Challenges. In: ; 2020:xxxviili. doi:10.1016/B978-0-12-817057-1.00001-9
90. Wood JC, Zhang P, RienhoJ H, Abi-Saab W, Neufeld E. R2 and R2* are equally
eJective in evaluating chronic response to iron chelation. Am J Hematol.
2014;89(5):505-508. doi:10.1002/ajh.23673
91. Wood JC. Use of Magnetic Resonance Imaging to Monitor Iron Overload. Hematol
Oncol Clin North Am. 2014;28(4):747-764. doi:10.1016/j.hoc.2014.04.002
92. KraJt AJ, LoeJler RB, Song R, et al. Quantitative ultrashort echo time imaging for
assessment of massive iron overload at 1.5 and 3 Tesla. Magn Reson Med.
2017;78(5):1839-1851. doi:10.1002/mrm.26592
93. Tipirneni-Sajja A, KraJt AJ, McCarville MB, et al. Radial Ultrashort TE Imaging
Removes the Need for Breath-Holding in Hepatic Iron Overload Quantification by R2*

132
MRI. American Journal of Roentgenology. 2017;209(1):187-194.
doi:10.2214/AJR.16.17183
94. Doyle EK, Toy K, Valdez B, Chia JM, Coates T, Wood JC. Ultra-short echo time images
quantify high liver iron. Magn Reson Med. 2018;79(3):1579-1585.
doi:10.1002/mrm.26791
95. Yoon JH, Lee JM, Paek M, Han JK, Choi BI. Quantitative assessment of hepatic
function: modified look-locker inversion recovery (MOLLI) sequence for T1 mapping
on Gd-EOB-DTPA-enhanced liver MR imaging. Eur Radiol. 2016;26(6):1775-1782.
doi:10.1007/s00330-015-3994-7
96. Haaf P, Garg P, Messroghli DR, Broadbent DA, Greenwood JP, Plein S. Cardiac T1
Mapping and Extracellular Volume (ECV) in clinical practice: a comprehensive
review. Journal of Cardiovascular Magnetic Resonance. 2016;18(1):89.
doi:10.1186/s12968-016-0308-4
97. McCommis KS, Goldstein TA, Abendschein DR, et al. Roles of myocardial blood
volume and flow in coronary artery disease: an experimental MRI study at rest and
during hyperemia. Eur Radiol. 2010;20(8):2005-2012. doi:10.1007/s00330-010-1740-
8
98. Dillman JR, Trout AT, Tkach JA. Relaxometry: Applications in the Body. In: ; 2020:215-
237. doi:10.1016/B978-0-12-817057-1.00012-3
99. Dall’Armellina E, Das A. Relaxometry: Applications in the Heart. In: ; 2020:239-265.
doi:10.1016/B978-0-12-817057-1.00011-1
100. Vrenken H, Geurts JJG, Knol DL, et al. Normal-appearing white matter changes vary
with distance to lesions in multiple sclerosis. AJNR Am J Neuroradiol.
2006;27(9):2005-2011.
101. Vrenken H, Rombouts SARB, Pouwels PJW, Barkhof F. Voxel-based analysis of
quantitative T1 maps demonstrates that multiple sclerosis acts throughout the
normal-appearing white matter. AJNR Am J Neuroradiol. 2006;27(4):868-874.
102. Vrenken H, Geurts JJG, Knol DL, et al. Whole-brain T1 mapping in multiple sclerosis:
global changes of normal-appearing gray and white matter. Radiology.
2006;240(3):811-820. doi:10.1148/radiol.2403050569
103. Hattingen E, Müller A, Jurcoane A, et al. Value of quantitative magnetic resonance
imaging T1-relaxometry in predicting contrast-enhancement in glioblastoma
patients. Oncotarget. 2017;8(32):53542-53551. doi:10.18632/oncotarget.18612

133
104. Müller A, Jurcoane A, Kebir S, et al. Quantitative T1-mapping detects cloudyenhancing tumor compartments predicting outcome of patients with glioblastoma.
Cancer Med. 2017;6(1):89-99. doi:10.1002/cam4.966
105. Lescher S, Jurcoane A, Veit A, Bähr O, Deichmann R, Hattingen E. Quantitative T1
and T2 mapping in recurrent glioblastomas under bevacizumab: earlier detection of
tumor progression compared to conventional MRI. Neuroradiology. 2015;57(1):11-
20. doi:10.1007/s00234-014-1445-9
106. Baudrexel S, Nürnberger L, Rüb U, et al. Quantitative mapping of T1 and T2*
discloses nigral and brainstem pathology in early Parkinson’s disease. Neuroimage.
2010;51(2):512-520. doi:10.1016/j.neuroimage.2010.03.005
107. Nürnberger L, Gracien RM, Hok P, et al. Longitudinal changes of cortical
microstructure in Parkinson’s disease assessed with T1 relaxometry. Neuroimage
Clin. 2017;13:405-414. doi:10.1016/j.nicl.2016.12.025
108. Wang B, Zhang Y, Zhao B, et al. Postcontrast T1 Mapping for DiJerential Diagnosis of
Recurrence and Radionecrosis after Gamma Knife Radiosurgery for Brain
Metastasis. American Journal of Neuroradiology. 2018;39(6):1025-1031.
doi:10.3174/ajnr.A5643
109. Wiggermann V, Lapointe E, Litvin L, et al. Longitudinal advanced MRI
case report of white matter radiation necrosis. Ann Clin Transl Neurol. 2019;6(2):379-
385. doi:10.1002/acn3.704
110. Owman H, Tiderius CJ, Neuman P, Nyquist F, Dahlberg LE. Association between
findings on delayed gadolinium-enhanced magnetic resonance imaging of cartilage
and future knee osteoarthritis. Arthritis Rheum. 2008;58(6):1727-1730.
doi:10.1002/art.23459
111. Palmer A, Fernquest S, Rombach I, et al. Diagnostic and prognostic value of delayed
Gadolinium Enhanced Magnetic Resonance Imaging of Cartilage (dGEMRIC) in early
osteoarthritis of the hip. Osteoarthritis Cartilage. 2017;25(9):1468-1477.
doi:10.1016/j.joca.2017.05.004
112. Campbell-Washburn AE, Ramasawmy R, Restivo MC, et al. Opportunities in
interventional and diagnostic imaging by using high-performance low-field-strength
MRI. Radiology. 2019;293(2):384-393. doi:10.1148/radiol.2019190452
113. Shetty AS, Ludwig DR, Ippolito JE, Andrews TJ, Narra VR, Fraum TJ. Low-FieldStrength Body MRI: Challenges and Opportunities at 0.55 T. RadioGraphics.
2023;43(12). doi:10.1148/rg.230073

134
114. Grigo J, Masitho S, Fautz HP, et al. Usability of magnetic resonance images acquired
at a novel low-field 0.55 T scanner for brain radiotherapy treatment planning. Phys
Imaging Radiat Oncol. 2023;25:100412. doi:10.1016/j.phro.2023.100412
115. Chaudhari AJ, Lim Y, Cui SX, et al. Real-time MRI of the moving wrist at 0.55 tesla. Br J
Radiol. 2023;96(1151). doi:10.1259/bjr.20230298
116. Constable RT, Anderson AW, Zhong J, Gore JC. Factors influencing contrast in fast
spin-echo MR imaging. Magn Reson Imaging. 1992;10(4):497-511. doi:10.1016/0730-
725X(92)90001-G
117. Thomas DL, De Vita E, Roberts S, Turner R, Yousry TA, Ordidge RJ. High-resolution
fast spin echo imaging of the human brain at 4.7 T: Implementation and sequence
characteristics. Magn Reson Med. 2004;51(6):1254-1264. doi:10.1002/mrm.20106
118. Mossahebi P, Yarnykh VL, Samsonov A. Analysis and correction of biases in crossrelaxation MRI due to biexponential longitudinal relaxation. Magn Reson Med.
2014;71(2):830-838. doi:10.1002/mrm.24677
119. Norris DG, Hutchison JMS. Concomitant magnetic field gradients and their eJects on
imaging at low magnetic field strengths. Magn Reson Imaging. 1990;8(1):33-37.
doi:10.1016/0730-725X(90)90209-K
120. King KF, Ganin A, Zhou J, Bernstein MA. Concomitant Gradient Field EJects in Spiral
Scans. Magn Reson Med. 1999;41:103-112. doi:10.1002/(SICI)1522-
2594(199901)41:1
121. Ostenson J, Damon BM, Welch EB. MR fingerprinting with simultaneous T1, T2, and
fat signal fraction estimation with integrated B0 correction reduces bias in water T1
and T2 estimates. Magn Reson Imaging. 2019;60:7-19.
doi:10.1016/j.mri.2019.03.017
122. Chen W, Sica CT, Meyer CH. Fast conjugate phase image reconstruction based on a
Chebyshev approximation to correct for B0 field inhomogeneity and concomitant
gradients. Magn Reson Med. 2008;60(5):1104-1111. doi:10.1002/mrm.21703
123. Cheng JY, Santos JM, Pauly JM. Fast concomitant gradient field and field
inhomogeneity correction for spiral cardiac imaging. Magn Reson Med.
2011;66(2):390-401. doi:10.1002/mrm.22802
124. De Zanche N, Barmet C, Nordmeyer-Massner JA, Pruessmann KP. NMR probes for
measuring magnetic fields and field dynamics in MR systems. Magn Reson Med.
2008;60(1):176-186. doi:10.1002/mrm.21624

135
125. Wilm BJ, Barmet C, Pavan M, Pruessmann KP. Higher order reconstruction for MRI in
the presence of spatiotemporal field perturbations. Magn Reson Med.
2011;65(6):1690-1701. doi:10.1002/mrm.22767
126. Wilm BJ, Barmet C, Gross S, et al. Single-shot spiral imaging enabled by an expanded
encoding model: D emonstration in diJusion MRI. Magn
Reson Med. 2017;77(1):83-91. doi:10.1002/mrm.26493
127. Engel M, Kasper L, Barmet C, et al. Single-shot spiral imaging at 7 T.
Magn Reson Med. 2018;80(5):1836-1846. doi:10.1002/mrm.27176
128. Addy NO, Wu HH, Nishimura DG. Simple method for MR gradient system
characterization and k -space trajectory estimation. Magn Reson Med.
2012;68(1):120-129. doi:10.1002/mrm.23217
129. Vannesjo SJ, Haeberlin M, Kasper L, et al. Gradient system characterization by
impulse response measurements with a dynamic field camera. Magn Reson Med.
2013;69(2):583-593. doi:10.1002/MRM.24263/FORMAT/PDF
130. Campbell-Washburn AE, Xue H, Lederman RJ, Faranesh AZ, Hansen MS. Real-time
distortion correction of spiral and echo planar images using the gradient system
impulse response function. Magn Reson Med. 2016;75(6):2278-2285.
doi:10.1002/MRM.25788/FORMAT/PDF
131. Stich M, Wech T, Slawig A, et al. Gradient waveform pre-emphasis based on the
gradient system transfer function. Magn Reson Med. 2018;80(4):1521-1532.
doi:10.1002/mrm.27147
132. Robison RK, Li Z, Wang D, Ooi MB, Pipe JG. Correction of B 0 eddy current eJects in
spiral MRI. Magn Reson Med. 2019;81(4):2501-2513. doi:10.1002/mrm.27583
133. Lee NG, Ramasawmy R, Lim Y, Campbell-Washburn AE, Nayak KS. MaxGIRF: Image
reconstruction incorporating concomitant field and gradient impulse response
function eJects. Magn Reson Med. 2022;88(2):691-710. doi:10.1002/MRM.29232
134. Robson PM, Grant AK, Madhuranthakam AJ, Lattanzi R, Sodickson DK, McKenzie CA.
Comprehensive quantification of signal-to-noise ratio and g -factor for image-based
and k -space-based parallel imaging reconstructions. Magn Reson Med.
2008;60(4):895-907. doi:10.1002/mrm.21728
135. Cheng HM, Wright GA. Rapid high-resolution T 1 mapping by variable flip angles:
Accurate and precise measurements in the presence of radiofrequency field
inhomogeneity. Magn Reson Med. 2006;55(3):566-574. doi:10.1002/mrm.20791

136
136. Cheng HLM, Wright GA. Rapid high-resolutionT1 mapping by variable flip angles:
Accurate and precise measurements in the presence of radiofrequency field
inhomogeneity. Magn Reson Med. 2006;55(3):566-574. doi:10.1002/mrm.20791
137. Zhao B, Haldar JP, Liao C, et al. Optimal experiment design for magnetic resonance
fingerprinting: Cramér-rao bound meets spin dynamics. IEEE Trans Med Imaging.
2019;38(3):844-861. doi:10.1109/TMI.2018.2873704
138. Barbieri M, Brizi L, Giampieri E, et al. A deep learning approach for magnetic
resonance fingerprinting: Scaling capabilities and good training practices
investigated by simulations. Physica Medica. 2021;89:80-92.
doi:10.1016/j.ejmp.2021.07.013
139. Zhao B, Setsompop K, Ye H, Cauley SF, Wald LL. Maximum Likelihood
Reconstruction for Magnetic Resonance Fingerprinting. IEEE Trans Med Imaging.
2016;35(8):1812-1823. doi:10.1109/TMI.2016.2531640
140. Tofts PS, Brix G, Buckley DL, et al. Estimating kinetic parameters from dynamic
contrast-enhanced t1-weighted MRI of a diJusable tracer: Standardized quantities
and symbols. Journal of Magnetic Resonance Imaging. 1999;10(3):223-232.
doi:10.1002/(SICI)1522-2586(199909)10:3<223::AID-JMRI2>3.0.CO;2-S
141. Sourbron SP, Buckley DL. On the scope and interpretation of the Tofts models for
DCE-MRI. Magn Reson Med. 2011;66(3):735-745. doi:10.1002/mrm.22861
142. O’Connor JPB, Jackson A, Parker GJM, Roberts C, Jayson GC. Dynamic contrastenhanced MRI in clinical trials of antivascular therapies. Nat Rev Clin Oncol.
2012;9(3):167-177. doi:10.1038/nrclinonc.2012.2
143. Heye AK, Culling RD, Valdés Hernández MDC, Thrippleton MJ, Wardlaw JM.
Assessment of blood-brain barrier disruption using dynamic contrast-enhanced MRI.
A systematic review. Neuroimage Clin. 2014;6:262-274.
doi:10.1016/j.nicl.2014.09.002
144. Law M, Yang S, Babb JS, et al. Comparison of cerebral blood volume and vascular
permeability from dynamic susceptibility contrast-enhanced perfusion MR imaging
with glioma grade. American Journal of Neuroradiology. 2004;25(5):746-755.
145. Larsson HBW, Stubgaard M, Frederiksen JL, Jensen M, Henriksen O, Paulson OB.
Quantitation of blood-brain barrier defect by magnetic resonance imaging and
gadolinium-DTPA in patients with multiple sclerosis and brain tumors. Magn Reson
Med. 1990;16(1):117-131. doi:10.1002/mrm.1910160111

137
146. Cramer SP, Simonsen H, Frederiksen JL, Rostrup E, Larsson HBW. Abnormal bloodbrain barrier permeability in normal appearing white matter in multiple sclerosis
investigated by MRI. Neuroimage Clin. 2014;4:182-189.
doi:10.1016/j.nicl.2013.12.001
147. Yang S, Law M, Zagzag D, et al. Dynamic contrast-enhanced perfusion MR imaging
measurements of endothelial permeability: diJerentiation between atypical and
typical meningiomas. AJNR Am J Neuroradiol. 2003;24(8):1554-1559.
148. Montagne A, Barnes SR, Sweeney MD, et al. Blood-Brain barrier breakdown in the
aging human hippocampus. Neuron. 2015;85(2):296-302.
doi:10.1016/j.neuron.2014.12.032
149. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: Sensitivity encoding
for fast MRI. Magn Reson Med. 1999;42(5):952-962. doi:10.1002/(SICI)1522-
2594(199911)42:5<952::AID-MRM16>3.0.CO;2-S
150. Uecker M, Lai P, Murphy MJ, et al. ESPIRiT - An eigenvalue approach to
autocalibrating parallel MRI: Where SENSE meets GRAPPA. Magn Reson Med.
2014;71(3):990-1001. doi:10.1002/mrm.24751
151. Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing
for rapid MR imaging. Magn Reson Med. 2007;58(6):1182-1195.
doi:10.1002/mrm.21391
152. Lebel RM, Jones J, Ferre JC, Law M, Nayak KS. Highly accelerated dynamic contrast
enhanced imaging. Magn Reson Med. 2014;71(2):635-644. doi:10.1002/mrm.24710
153. Guo Y, Lebel RM, Zhu Y, et al. High-resolution whole-brain DCE-MRI using
constrained reconstruction: Prospective clinical evaluation in brain tumor patients.
Med Phys. 2016;43(5):2013. doi:10.1118/1.4944736
154. Dickie BR, Banerji A, Kershaw LE, et al. Improved accuracy and precision of tracer
kinetic parameters by joint fitting to variable flip angle and dynamic contrast
enhanced MRI data. Magn Reson Med. 2016;76(4):1270-1281.
doi:10.1002/mrm.26013
155. Guo Y, Lingala SG, Zhu Y, Lebel RM, Nayak KS. Direct estimation of tracer-kinetic
parameter maps from highly undersampled brain dynamic contrast enhanced MRI.
Magn Reson Med. 2017;78(4):1566-1578. doi:10.1002/mrm.26540
156. Guo Y, Lingala SG, Bliesener Y, Lebel RM, Zhu Y, Nayak KS. Joint arterial input function
and tracer kinetic parameter estimation from undersampled dynamic contrast-

138
enhanced MRI using a model consistency constraint. Magn Reson Med.
2018;79(5):2804-2815. doi:10.1002/mrm.26904
157. Lingala SG, Guo Y, Bliesener Y, et al. Tracer kinetic models as temporal constraints
during brain tumor DCE-MRI reconstruction. Med Phys. 2020;47(1):37-51.
doi:10.1002/mp.13885
158. Fram EK, Herfkens RJ, Johnson GA, et al. Rapid calculation of T1 using variable flip
angle gradient refocused imaging. Magn Reson Imaging. 1987;5(3):201-208.
doi:10.1016/0730-725X(87)90021-X
159. Look DC, Locker DR. Time saving in measurement of NMR and EPR relaxation times.
Review of Scientific Instruments. 1970;41(2):250-251. doi:10.1063/1.1684482
160. Lebel RM, Guo Y, Lingala SG, Frayne R, Nayak KS. Highly accelerated DCE imaging
with integrated T1 mapping. In: ISMRM 25th Scientific Sessions. ; 2017:138.
161. Maier O, Schoormans J, Schloegl M, et al. Rapid T 1 quantification from high
resolution 3D data with model-based reconstruction. Magn Reson Med.
2019;81(3):2072-2089. doi:10.1002/mrm.27502
162. Deoni SCL. High-resolution T1 mapping of the brain at 3T with driven equilibrium
single pulse observation of T1 with high-speed incorporation of RF field
inhomogeneities (DESPOT1-HIFI). Journal of Magnetic Resonance Imaging.
2007;26(4):1106-1111. doi:10.1002/jmri.21130
163. Deoni SCL, Rutt BK, Peters TM. Rapid combined T1 and T2 mapping using gradient
recalled acquisition in the steady state. Magn Reson Med. 2003;49(3):515-526.
doi:10.1002/mrm.10407
164. Larsson C, Kleppestø M, Grothe I, Vardal J, Bjørnerud A. T 1 in high-grade glioma and
the influence of diJerent measurement strategies on parameter estimations in DCEMRI. Journal of Magnetic Resonance Imaging. 2015;42(1):97-104.
doi:10.1002/jmri.24772
165. Fennessy FM, Fedorov A, Gupta SN, Schmidt EJ, Tempany CM, Mulkern R V. Practical
considerations in T1 mapping of prostate for dynamic contrast enhancement
pharmacokinetic analyses. Magn Reson Imaging. 2012;30(9):1224-1233.
doi:10.1016/j.mri.2012.06.011
166. Sutton BP, Noll DC, Fessler JA. Fast, iterative image reconstruction for MRI in the
presence of field inhomogeneities. IEEE Trans Med Imaging. 2003;22(2):178-188.
doi:10.1109/TMI.2002.808360

139
167. Cheng HLM, Wright GA. Rapid high-resolutionT1 mapping by variable flip angles:
Accurate and precise measurements in the presence of radiofrequency field
inhomogeneity. Magn Reson Med. 2006;55(3):566-574. doi:10.1002/mrm.20791
168. Lee Y, Callaghan MF, Nagy Z. Analysis of the precision of variable flip angle T1
mapping with emphasis on the noise propagated from RF transmit field maps. Front
Neurosci. 2017;11(MAR):106. doi:10.3389/fnins.2017.00106
169. Bosca RJ, Jackson EF. Creating an anthropomorphic digital MR phantom - An
extensible tool for comparing and evaluating quantitative imaging algorithms. Phys
Med Biol. 2016;61(2):974-982. doi:10.1088/0031-9155/61/2/974
170. Bliesener Y, Lingala SG, Haldar JP, Nayak KS. Impact of (k,t) sampling on DCE MRI
tracer kinetic parameter estimation in digital reference objects. Magn Reson Med.
2020;83(5):1625-1639. doi:10.1002/mrm.28024
171. Stanisz GJ, Odrobina EE, Pun J, et al. T1, T2 relaxation and magnetization transfer in
tissue at 3T. Magn Reson Med. 2005;54(3):507-512. doi:10.1002/mrm.20605
172. Müller A, Jurcoane A, Kebir S, et al. Quantitative T1-mapping detects cloudyenhancing tumor compartments predicting outcome of patients with glioblastoma.
Cancer Med. 2017;6(1):89-99. doi:10.1002/cam4.966
173. Hattingen E, Müller A, Jurcoane A, et al. Value of quantitative magnetic resonance
imaging T1-relaxometry in predicting contrast-enhancement in glioblastoma
patients. Oncotarget. 2017;8(32):53542-53551. doi:10.18632/oncotarget.18612
174. Badve C, Yu A, Dastmalchian S, et al. MR fingerprinting of adult brain tumors: Initial
experience. In: American Journal of Neuroradiology. Vol 38. American Society of
Neuroradiology; 2017:492-499. doi:10.3174/ajnr.A5035
175. Sacolick LI, Wiesinger F, Hancu I, Vogel MW. B 1 mapping by Bloch-Siegert shift.
Magn Reson Med. 2010;63(5):1315-1322. doi:10.1002/mrm.22357
176. Zhang Y, Brady M, Smith S. Segmentation of brain MR images through a hidden
Markov random field model and the expectation-maximization algorithm. IEEE Trans
Med Imaging. 2001;20(1):45-57. doi:10.1109/42.906424
177. A.G. Teixeira RP, Malik SJ, Hajnal J V. Fast quantitative MRI using controlled saturation
magnetization transfer. Magn Reson Med. 2019;81(2):907-920.
doi:10.1002/mrm.27442
178. Lee N, Zhu Z, Nayak KS. Variable flip angle T1 mapping with MT-balanced RF pulses.
In: ISMRM 28th Scientific Session. ; 2020:3793.

140
179. Parker GJM, Roberts C, Macdonald A, et al. Experimentally-derived functional form
for a population-averaged high-temporal-resolution arterial input function for
dynamic contrast-enhanced MRI. Magn Reson Med. 2006;56(5):993-1000.
doi:10.1002/mrm.21066
180. Georgiou L, Wilson DJ, Sharma N, Perren TJ, Buckley DL. A functional form for a
representative individual arterial input function measured from a population using
high temporal resolution DCE MRI. Magn Reson Med. 2019;81(3):1955-1963.
doi:10.1002/mrm.27524
181. Zhao B, Setsompop K, Adalsteinsson E, et al. Improved magnetic resonance
fingerprinting reconstruction with low-rank and subspace modeling. Magn Reson
Med. 2018;79(2):933-942. doi:10.1002/mrm.26701
182. Sarracanie M. Fast Quantitative Low-Field Magnetic Resonance Imaging With
OPTIMUM-Optimized Magnetic Resonance Fingerprinting Using a Stationary SteadyState Cartesian Approach and Accelerated Acquisition Schedules. Invest Radiol.
2022;57(4):263-271. doi:10.1097/RLI.0000000000000836
183. Körzdörfer G, Kirsch R, Liu K, et al. Reproducibility and Repeatability of MR
Fingerprinting Relaxometry in the Human Brain. Radiology. 2019;292(2):429-437.
doi:10.1148/radiol.2019182360
184. Gaur S, Panda A, Fajardo JE, Hamilton J, Jiang Y, Gulani V. Magnetic Resonance
Fingerprinting. Invest Radiol. 2023;58(8):561-577.
doi:10.1097/RLI.0000000000000975
185. Cao X, Liao C, Zhu Z, et al. Making MR more accessible through precision
quantitative MRI at 0.55T with optimized 3D MRF. In: ISMRM 33rd Scientific Session. ;
2024:3825-3825.
186. Bernstein MA, Zhou XJ, Polzin JA, et al. Concomitant gradient terms in phase contrast
MR: Analysis and correction. Magn Reson Med. 1998;39(2):300-308.
doi:10.1002/mrm.1910390218
187. Noll DC, Meyer CH, Pauly JM, Nishimura DG, Macovski A. A homogeneity correction
method for magnetic resonance imaging with time-varying gradients. IEEE Trans Med
Imaging. 1991;10(4):629-637. doi:10.1109/42.108599
188. Noll DC, Pauly JM, Meyer CH, Nishimura DG, Macovskj A. Deblurring for non-2D
fourier transform magnetic resonance imaging. Magn Reson Med. 1992;25(2):319-
333. doi:10.1002/mrm.1910250210

141
189. Norris DG, Hutchison JMS. Concomitant magnetic field gradients and their eJects on
imaging at low magnetic field strengths. Magn Reson Imaging. 1990;8(1):33-37.
doi:10.1016/0730-725X(90)90209-K
190. McGivney DF, Pierre E, Ma D, et al. SVD Compression for Magnetic Resonance
Fingerprinting in the Time Domain. IEEE Trans Med Imaging. 2014;33(12):2311-2322.
doi:10.1109/TMI.2014.2337321
191. Layton KJ, Kroboth S, Jia F, et al. Pulseq: A rapid and hardware-independent pulse
sequence prototyping framework. Magn Reson Med. 2017;77(4):1544-1552.
doi:10.1002/mrm.26235
192. Lee JH, Hargreaves BA, Hu BS, Nishimura DG. Fast 3D imaging using variable-density
spiral trajectories with applications to limb perfusion. Magn Reson Med.
2003;50(6):1276-1285. doi:10.1002/mrm.10644
193. Hargreaves BA, Nishimura DG, Conolly SM. Time-optimal multidimensional gradient
waveform design for rapid imaging. Magn Reson Med. 2004;51(1):81-92.
doi:10.1002/mrm.10666
194. Phantom Test Guidance for Use of the Large MRI Phantom for the MRI Accreditation
Program 2 Large Phantom Guidance 4/17/18 Contents.
195. Russek SE, Boss M, Jackson EF, et al. Characterization of NIST/ISMRM MRI System
Phantom. In: ISMRM 20th Scientific Session. ; 2012:2456.
https://archive.ismrm.org/2012/2456.html
196. Ma J, He Y, Li F, Han L, You C, Wang B. Segment anything in medical images. Nat
Commun. 2024;15(1):654. doi:10.1038/s41467-024-44824-z
197. Zhu Z, Lee NG, Tian Y, Nayak KS. EJicient MRF at 0.55T with long readouts and
concomitant field eJect correction. In: ISMRM 32nd Scientific Session. ; 2023:2364.
Accessed September 21, 2023.
https://cds.ismrm.org/protected/23MPresentations/abstracts/2364.html
198. Zhu Z, Nayak KS. Evaluating 0.55T FISP MRF using EPG-X Formalism. In: ISMRM 33rd
Scientific Session. ; 2024:3554-3554. Accessed July 16, 2024.
https://submissions.mirasmart.com/ISMRM2024/Itinerary/PresentationDetail.aspx?
evdid=5312
199. Weigel M. Extended phase graphs: Dephasing, RF pulses, and echoes - pure and
simple. Journal of Magnetic Resonance Imaging. 2015;41(2):266-295.
doi:10.1002/jmri.24619

142
200. Hu S, Chen Y, Zong X, Lin W, Griswold M, Ma D. Improving motion robustness of
3D MR fingerprinting with a fat navigator. Magn Reson Med.
2023;90(5):1802-1817. doi:10.1002/mrm.29761
201. Stupic KF, Ainslie M, Boss MA, et al. A standard system phantom for magnetic
resonance imaging. Magn Reson Med. 2021;86(3):1194-1211.
doi:10.1002/mrm.28779
202. Zhu Z, Lee NG, Tian Y, et al. Evaluation of MR Fingerprinting at 0.55T. In: ISMRM 31st
Scientific Session. ; 2022:3492. Accessed November 6, 2022.
https://cds.ismrm.org/protected/22MPresentations/abstracts/3492.html
203. Anderson C, Wang C, Gu Y, et al. Gradient Moment Dependent T2 Accuracy in FISP
Magnetic Resonance Fingerprinting (MRF) at 7T. In: ISMRM 25th Scientific Session. ;
2017:5211-5211.
204. Flassbeck S, Schmidt S, Breithaupt M, Bachert P, Ladd ME, Schmitter S. On the
Influence of Intra-Voxel Dephasing in FISP-MRF with Variable Repetition Time. In:
ISMRM 25th Scientific Session. ; 2017:1492-1492.
205. Wang Z, Ramasawmy R, Feng X, Campbell-Washburn AE, Mugler JP, Meyer CH.
Concomitant magnetic-field compensation for 2D spiral-ring turbo
spin-echo imaging at 0.55T and 1.5T. Magn Reson Med. 2023;90(2):552-568.
doi:10.1002/mrm.29663
206. Stupic KF, Ainslie M, Boss MA, et al. A standard system phantom for magnetic
resonance imaging. Magn Reson Med. 2021;86(3):1194-1211.
doi:10.1002/mrm.28779
207. Zhang J, Kolind SH, Laule C, MacKay AL. How does magnetization transfer influence
mc DESPOT results? Magn Reson Med. 2015;74(5):1327-1335.
doi:10.1002/mrm.25520
208. Stanisz GJ, Odrobina EE, Pun J, et al. T1, T2 relaxation and magnetization transfer in
tissue at 3T. Magn Reson Med. 2005;54(3):507-512. doi:10.1002/mrm.20605
209. Buonincontri G, Kurzawski JW, Kaggie JD, et al. Three dimensional MRF obtains highly
repeatable and reproducible multi-parametric estimations in the healthy human
brain at 1.5T and 3T. Neuroimage. 2021;226:117573.
doi:10.1016/j.neuroimage.2020.117573

143
210. Bieri O, Weidensteiner C, Ganter C. Robust T 2 estimation with
balanced steady state free precession. Magn Reson Med.
2024;91(6):2257-2265. doi:10.1002/mrm.30037
211. Cohen O, Yu VY, Tringale KR, et al. CEST MR fingerprinting (CEST-MRF) for brain tumor
quantification using EPI readout and deep learning reconstruction. Magn Reson Med.
2023;89(1):233-249. doi:10.1002/mrm.29448
212. Mougin O, Clemence M, Peters A, Pitiot A, Gowland P. High-resolution imaging of
magnetisation transfer and nuclear Overhauser eJect in the human visual cortex at 7
T. NMR Biomed. 2013;26(11):1508-1517. doi:10.1002/nbm.2984
213. Santyr GE. Magnetization transfer eJects in multislice MR imaging. Magn Reson
Imaging. 1993;11(4):521-532. doi:10.1016/0730-725X(93)90471-O
214. Ou X, Gochberg DF. MT eJects and T 1 quantification in single-slice spoiled gradient
echo imaging. Magn Reson Med. 2008;59(4):835-845. doi:10.1002/mrm.21550
215. Johnson KO, Robison RK, Pipe JG. Rigid Body Motion Compensation for Spiral
Projection Imaging. IEEE Trans Med Imaging. 2011;30(3):655-665.
doi:10.1109/TMI.2010.2091146
216. Cao X, Ye H, Liao C, Li Q, He H, Zhong J. Fast 3D brain MR fingerprinting based on
multi-axis spiral projection trajectory. Magn Reson Med. 2019;82(1):289-301.
doi:10.1002/MRM.27726
217. Boyacioglu R, Wang C, Ma D, McGivney DF, Yu X, Griswold MA. 3D magnetic
resonance fingerprinting with quadratic RF phase. Magn Reson Med.
2021;85(4):2084-2094. doi:10.1002/mrm.28581
218. Statton BK, Koerzdoerfer G, Smith J, Finnegan ME, Quest RA, Grech-Sollars M.
Temperature dependence, accuracy, and repeatability of T1 and T2 relaxation times
for the ISMRM / NIST system phantom measured using MR fingerprinting.
2021;(May):1-15. doi:10.1002/MRM.29065

Abstract (if available)

Abstract Quantitative Magnetic Resonance Imaging (qMRI) is a categary of useful MR imaging techniques that evaluate parametric properties of biological tissues, e.g., relaxation times in brain white matter. These techniques aim to provide diagnosable quantities that are sensitive to global and/or longitudinal changes and physiological variations. qMRI can complement traditional qualitative diagnostic methods. qMRI is not widely used due to practical issues such as potential long exam time. MagneticResonanceFingerprinting (MRF) techniques have been developed such that a high quality and volumetric relaxation maps can be produced within a few minutes. MRF has popularized qMRI applications to multiple body parts and at multiple magnetic field strengths. With the resurgence of interest in mid- and low-field MRI, such as the 0.55 T MR system in Dynamic Imaging Science Center in USC, MRF techniques have gained growing research and clinical tractions. At 0.55 T, a basic Fast Imagingwith Steady-State Precession (FISP)-MRF approach has been shown feasible and promising, however, with substantial quantification biases. Although several hypotheses about these biases have been proposed, solutions seemed to be suboptimal, and the biases remained unresolved. Therefore, how to perform this approach in a more Signal-to-Noise Ratio (SNR) efficient optimized way and how to improve its quantification accuracy have become interesting research problems. In thisdissertation, I propose a more efficient and accurate FISP-MRF approach at 0.55 T. I start with improving 0.55 T FISP-MRF SNR efficiency and the approach produces more precise results but does not unaddress biases. It includes higher readout duty cycle, constrained reconstruction and artifacts mitigation. Then, I focus on refining RF excitation designs, which helps to suppress the sources of bias, resulting in more accurate quantification.

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Asset Metadata

Creator Zhu, Zhibo (author)

Core Title Efficient and accurate 3D FISP-MRF at 0.55 Tesla

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical and Computer Engineering

Degree Conferral Date 2025-05

Publication Date 01/28/2025

Defense Date 12/06/2024

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

Tag 0.55 T MRI,brain MRI,magnetic resonance fingerprinting,magnetic resonance imaging,OAI-PMH Harvest

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nayak, Krishna Shrinivas (committee chair), Fan, Zhaoyang (committee member), Haldar, Justin (committee member)

Creator Email zhibozhu.one@gmail.com,zhibozhu@usc.edu

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