Comparison of Single Shot Methods for R2* Comparison
Thesis Defense
Rick Deshpande
Committee:
• Dr. Donald Twieg, Chair
• Dr. N. Shastry Akella
• Dr. Georg Deutsch
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Outline

Introduction
 Basics of MRI, fMRI
 Significance of reliable R2* estimation
 Single-shot methods: MEPI and SS-PARSE

Experiment and Analytical Methods
 Trajectory generation
 Data acquisition
 Reconstruction and comparison of accuracy and temporal variability

Discussion

Conclusion

Future scope
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Basics of MRI Image Acquisition
RF pulse
(sinc/Gaussian/square)
1
H nuclei within tissues
1
H nuclei under external magnetic field
Applying a 2D-FFT to
the signal data
generates 2D-images in
the imaging plane.
1
Energy is collected as a
function of 2D-Inverse
Fourier Transform
H get dislodged from
steady state . They
release energy while
returning to steady
state.
Sources:
http://www.cs.sfu.ca/~stella/main/_spins_figure8.gif
http://www.cs.sfu.ca/~stella/main/_spins_figure7.gif
http://videos.howstuffworks.com/discovery-health/14537-human-atlas-mri.jpg
http://www.mr-tip.com/exam_gifs/brain_mri_transversal_t2_002.jpg
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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fMRI
Control/Stimulation acquisition
Estimation of Neuronal activity
↓
BOLD effect
↓
R2*
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Significance of reliable R2* estimation
BOLD Response Model:
*BOLD = Blood Oxygenation Level Dependent
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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R2* Measurement: Multiple Shot Method
Gradient Echo Multiple Shot (GEMS)

Echoes can be closely stacked, thus enabling accurate R2* calculation

Serves as a gold standard in the comparison study
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Single Shot Methods
Multiple Gradient Echo – Echo Planar Imaging (MEPI)
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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SS-PARSE
Single-Shot Parameter Assessment by Retrieval from Signal Encoding
Conventional model
Estimates map: M(x)
Include local phase evolution
& local signal decay
SS-PARSE model
Estimate maps (images) of M(x), R2* (x), ω(x) by solving an inverse
problem.
It uses Progressive Length Conjugate Gradient (PLCG) algorithm which
requires optimal parameters to minimize least squared residuals to
generate parameter maps.
M(x)
w(x)
R2* (x)
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Comparing Conventional MRI & SS-PARSE Methods
Encoding Strategy
(k-trajectory)
k space
Inverse FFT
Modeling
Acquired Data
k, t space
Decoding Strategy
Inverse Estimation
Adapted from Rajiv Menon’s Ph.D. proposal presentation
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Source: http://commons.ucalgary.ca/at-wld/images/cartoon02.gif
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Project Goals - experimental

Create gradient waveforms and generate trajectories for 7 different
gradient strengths (1.9 G/cm to 3.8 G/cm):

Gmax = 1.9 G/cm
Gmax = 3.8 G/cm
Lower k-space coverage
Larger k-space coverage
Fewer data points
More data points
Faster parameter estimation
Slower parameter estimation

Implement the sequence on Varian 4.7 T vertical scanner using phantoms

Compare performance of SS-PARSE with MEPI based on:
1.
2.
3.
4.
Accuracy of R2* estimates (compare with Gradient-Echo results)
Temporal variability of R2* (over time-series of 50 acquisitions)
Find correlation between R2* and TSD values
Find correlation between maximum gradient strength and accuracy
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Project goals – Theoretical Inferences

Factors contributing towards performance of SS-PARSE:
1. Gmax values – Find relationship between
•
Gmax and R2* estimates (compared with gradient-echo values)
2. Shimming – Find effects of field inhomogeneity in SS-PARSE and
MEPI studies.
3. Performance over R2* range - Observe the changes in temporal
behavior over R2* values typically found in human brain tissues
(20 to 40 sec-1 in 4.7 T MRI systems)
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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k-trajectory Generation and Calibration
Calibration data acquired at:
±2, ±4, ±6, ±8, ±10, ±12 mm
displacements in x & y planes
For Gmax:
1.9, 2.29, 2.5, 2.9, 3.2, 3.5 and
3.8 G/cm.
1.9 G/cm
2.29 G/cm
3.2 G/cm
2.5 G/cm
3.5 G/cm
2.9 G/cm
3.8 G/cm
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Phantom For Data Acquisition
R2* Range: 15 sec-1 to 45 sec-1
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Data Acquisition: GEMS, MEPI and SS-PARSE
Hardware:
1.
2.
4.7 T 60 cm-vertical-bore Varian primate MRI system
(Varian Inc., Palo Alto, CA)
SS-PARSE acquisitions
•
Per study
•
Repetition time
•
Slice Thickness
=
=
=
(7x Gmax) x (50x repetitions)
5 second
3 mm
MEPI acquisitions
•
Per study
•
Resolution
•
Repetition time
•
Echo Times
•
Slice Thickness
=
=
=
=
=
50x repetitions at 4 echo times
64 x 64
5 second
22.3, 66.8, 96.4 and 124.2 millisecond
3 mm
•
•
•
GEMS acquisitions
Per study
Resolution
Echo Times
=
=
=
•
Slice Thickness
=
16 x echo times
128 x 128
5, 8, 10, 12, 15, 20, 25, 30, 35, 40, 45, 50,
55, 60, 65 and 70 millisecond
3 mm
3.
Performed total 18 experiments to obtain the R2* values in the desired range (15 to 45 sec-1)
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Source: http://www.hagencartoons.com/cartoon159.gif
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Image Reconstruction and Data Analysis
Software:
Platform:
Matlab (version 7.5, The Mathworks Inc., Natick, MA)
Kubuntu 6.06 64-bit (Linux kernel 2.6.15-52-amd64-k8)
Tweakers for PLCG algorithm:
1. Swoop length (N1):
Number of Samples between two echoes.
Increases with Gmax
2. Data lengths (NLIST):
Incrementally progressive integral multiples of swoops required
for PLCG. They need to be set empirically
3. Tolerances (FLIST):
Minimum desired accuracy of estimation for a data length before
incrementing data length
4. Initial freq. estimate (offr):
Empirically determined value which helps in faster and more
accurate convergence of points in the x,y grid
5. Scaling (ffac):
Sometimes scaling the signal (FID) is essential in order to
correctly estimate the parameters. It is determined empirically.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Development of GUI For Analysis & File Handling
File Handling
PLCG Tweakers
Parameter Maps
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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R2* Evaluation: GEMS and MEPI
MEPI
GEMS
•R2* is computed over a ROI
•
•Monoexponential fitting of
signal to echo times.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Parameters Estimates in SS-PARSE

Reconstruction (SS-PARSE)
Parameter maps were computed using the PLCG algorithm from all the
SS-PARSE acquisitions. Maps were created for all Gmax values (1.9 G/cm to 3.8
G/cm).
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Accuracy of R2* Estimation
• GEMS is used as the gold standard
• Accuracy of estimation at each pixel is computed by using the ratio:
|R2* MEPI - R2* GEMS |
|R2*
SSPARSE
- R2* GEMS|
• If the ratio > 1, SS-PARSE estimation is more accurate at that pixel
• If the ratio < 1, MEPI estimation is more accurate at that pixel.
• The accuracy test was conducted for 20 ROIs, over all Gmax values
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Accuracy of R2* Estimation
SS-PARSE and MEPI estimates and accuracy plot at SS-PARSE Gmax = 2.9 G/cm
1. R2* estimates from SS-PARSE and MEI plotted vs. R2* from GEMS
2. Ratio of R2* accuracy plotted vs. R2* estimates from GEMS
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Accuracy Over Gradient Amplitudes
Accuracy of R2* estimation computed by using the ratio:
|R2* MEPI - R2* GEMS |
|R2* SSPARSE - R2* GEMS|
was > 1 for following percentage points over the Gmax range:
1.
2.
3.
4.
5.
6.
7.
1.9 G/cm:
2.29 G/cm:
2.5 G/cm:
2.9 G/cm:
3.2 G/cm:
3.5 G/cm:
3.8 G/cm:
61.3%
64.2%
66.4%
68.3%
67.6%
65.6%
61.2%
Accuracy of estimation (ratio) was maximum at Gmax = 2.9 G/cm
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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F-test: Difference in Standard Deviation for R2*
Estimation (SS-PARSE and MEPI)

Null hypothesis:
There is no difference in the standard deviation of R2* distributions
obtained using MEPI and SS-PARSE at 95% confidence interval.

The test was performed on 80 pixels (ROI with radius = 5), over 20 R2*
values (tubes), gave a sample size of 1600 pixels for MEPI and SSPARSE.

Rejection of null hypothesis at any pixel would indicate a difference in
standard deviation for that confidence interval.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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F-test: Results Over Gmax Range

Rejection of null hypothesis (with C.I.=95%) at more than 5% of pixel
locations indicates an improvement in performance. [80 pixels]

Over sample size of 1600, the rejection of null hypothesis was:
1.
7.
1.9 G/cm:
2.29 G/cm:
2.5 G/cm:
2.9 G/cm:
3.2 G/cm:
3.5 G/cm:
3.8 G/cm:

Difference in standard deviations is maximum at Gmax = 2.9 G/cm
2.
3.
4.
5.
6.
241 pixels
307 pixels
468 pixels
547 pixels
485 pixels
338 pixels
214 pixels
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Temporal Variation of R2* Over 50 Repetitions
TSD computed for:
• Each pixel over 50 repetitions
• Each ROI over 50 repetitions
• For MEPI and SS-PARSE
• For Gmax with best accuracy
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Comparing Temporal Standard Deviation

Compute the TSD over each pixel in each ROI over 50 repetitions

Find the value: TSDMEPI – TSDSS-PARSE for each pixel

If the difference is +ve, SS-PARSE has lower TSD, thus better
repeatability

TSD comparison is performed for SS-PARSE Gmax with
best accuracy (2.9 G/cm)
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Depiction of TSD
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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TSD Plots
R2* (GEMS) vs. TSD (SS-PARSE)
• Dot indicates TSD at a single
pixel
• Each blob of pixels represents
a tube with a different R2*
R2* (GEMS) vs. TSD (MEPI)
• Scatter plot for the difference
TSD(MEPI) – TSD (SS-PARSE)
shows points around the
difference = 0 line
R2* (GEMS) vs. [TSD (MEPI) and TSD (SS-PARSE)]
• Dots above the difference=0
line show locations where the
performance of SS-PARSE
was better than of MEPI
The difference was > 0 for 79.3% to 97.3% for R2* values between 15 sec-1 and 45 sec-1
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Performance Under Field Inhomogeneity
MEPI
SS-PARSE
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Parameter Estimation Under Field Inhomogeneity

SS-PARSE parameter maps have an one-on-on correspondence with the ROI from
GEMS image (obtained before intention deshimming)

MEPI image appears distorted in one direction and the ROI does not correspond with
ROI from GEMS. Even though we have studied the behavior of MEPI, the same
behavior is also observed in standard EPI scans, which is the common modality used in
clinical fMRI sudies.

R2* computation in MEPI is impossible under field-inhomogeneity because of a
noticeable geometric distortion.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Discussion

PLCG tweakers need to be determined empirically in order to minimize the least
squared residuals.
However once we have arrived at an optimal value for one set, the same value
can be used for all the repetitions.

Accuracy of R2* estimates in SS-PARSE are comparable to estimates in MEPI at
lower values of R2*, but are significantly better at higher values of R2*.
In SS-PARSE, the trajectory samples the center of k-space (k=0) several times at
the beginning and has enough samples required for reconstruction. For MEPI the
signal strength declines around the 3rd and 4th echo; especially in regions with
high R2* values. Using MEPI to generate activation maps in regions with high R2*
can lead to erroneous results.

Temporal variability of R2* estimates in SS-PARSE is comparable to that of MEPI
at lower R2* values, but SS-PARSE has lower variability as R2* increases.
This finding is consistent with theoretical predictions (Cramer-Rao Lower Bound)
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Discussion

In k-trajectory used for SS-PARSE, lower gradient strengths trajectories (Gmax)
give fewer samples, while higher gradient strength trajectories give more samples
More samples result in better conditioning of the inverse problem, and likely, more
accurate parameter maps

The minimum number of samples required for parameter estimation is 4x pixels in
the evaluation grid (3217 x 4).
This is to estimate the 4 unknowns within the estimation grid by solving
simultaneous equations

We saw the performance improve until Gmax reached 2.9 G/cm, after which the
estimation accuracy started to deteriorate.
This performance was pertinent to our experimental setup. In practice we expect
the optimal performance at a Gmax value somewhere between 2.5 G/cm and 3.2
G/cm.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Inverse Problem Conditioning in Heisenberg’s Terms
Source: http://www.markstivers.com/cartoons/Cartoons%202003/Stivers%204-1-03%20Heisenberg%20cafe.gif
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Discussion

By keeping track of local frequencies, SS-PARSE can estimate reliable parameter
maps even under field inhomogeneity. This is not possible in conventional MRI
sequences since they rely solely upon spatial Fourier transform for encoding and
reconstruction.
The data acquired under poor shimming can be reliably reconstructed with
SS-PARSE. However we get noticeable geometric distortion when reconstructing
data obtained using MEPI, making the study more difficult to interpret.

There is a limit to which SS-PARSE can keep a track of frequencies. Theoretically
it is the sampling frequency observed at k=0 which is typically a few kilohertz.
The poor conditioning of the inverse problem limits us from getting reliable maps
at off-resonance frequencies beyond a few hundred Hertz.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Discussion

Continuing the iterative search in PLCG for a longer duration would give
more accurate estimates
However, running the algorithm for longer would give a little improvement
in accuracy. With faster processors and using a parallelized code, these
times can be lowered

Time taken to estimate a parameter map is typically about 10 minutes.
In clinical fMRI analysis, the estimates from first scan can then be used
as starting parameters for remaining scans, thus reducing the estimation
times for subsequent slides to few tens of a second.

Reliability of SS-PARSE is dependent on the stability of scanning
hardware. We need to calibrate the k-trajectory and local phase
information any time there is a change in hardware settings.
However hardware changes are very infrequent – typically every 2 years
in clinical systems.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Source: http://www.yachigusaryu.com/blog/pics/sci_principles_cartoon.jpg
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Conclusions

Gradient waveforms for seven Gmax values were developed for SSPARSE and were used to acquire phantom data

Parameter maps for SS-PARSE were constructed using PLCG algorithm

Performance of SS-PARSE and MEPI was compared using GEMS as
the gold standard

Accuracy of R2* estimation of SS-PARSE was compared with MEPI for a
range of Gmax values.

Performance of SS-PARSE improved with increasing gradient amplitude
until 2.9 G/cm. Thereafter the performance deteriorates.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Conclusions

SS-PARSE has a lower TSD than MEPI. This means it can estimate the
parameters much reliably over several repetitions when used in fMRI
studies.

SS-PARSE is able to reconstruct reliable parameter maps even in the
presence of field inhomogeneities. MEPI on the other hand shows
noticeable geometric distortion under such conditions.

Reliability of SS-PARSE depends on the stability of scanning hardware.
We need to calibrate the k-trajectory and local phase information when
there is a change in hardware settings (Typicall,once in a few years).
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Future Scope

PLCG algorithm requires adjusting the algorithm tweakers heuristically. With
better knowledge about the estimation process we should be able to set the
parameters in a deterministic manner.

With better problem conditioning, and with MRI systems capable of delivering
more than 6.5 G/cm (hardware limit of Varian 4.7 T system), we should be create
trajectories with much higher sampling rates, thus giving accurate parameter
estimation.

Parallel acquisition and multiple shot trajectories, increases the number of sample
points, thus improving conditioning of the inverse problem and leading to more
accurate estimates.
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Acknowledgement

Advisor:
Dr. Donald Twieg

Committee Members
Dr. N. Shastry Akella
Dr. Georg Deutsch

Dr. Stan Reeves (Auburn)

CDFI & VSRC colleagues:
Mark Bolding
Rajiv Menon
Ningzhi Li
Matt Ward
Debbie Whitten
Jerry Millican

Parents and Sister

Friends
Michelle
Jon
Chris

Grant Support:
NIH # R21/R33 EB003292

City of Birmingham
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Thank You
(Please complete the evaluation form)
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Questions
Source: http://www.lifehack.org/wp-content/files/2007/12/question.jpg
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Extras
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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Rosette (k,t)-trajectories acquire more information
on R2* than multiple-echo EPI trajectory
Cramer-Rao Lower Bound for standard deviation of error for
Multiple-Echo EPI (MEPI) and Rosette, SNR=200
MEPI
Rosette
s.d. of R2*
Idealized radial
R2* (sec-1)
University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009
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