Comparison of Single Shot Methods for R2* Comparison Thesis Defense Rick Deshpande Committee: Dr....

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 1

http://en.wikipedia.org/wiki/Copyleft

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


1H nuclei within tissues 1H nuclei under external magnetic field

RF pulse (sinc/Gaussian/square)

1H get dislodged from steady state . They release energy while returning to steady

state.

Energy is collected as a function of 2D-Inverse

Fourier Transform

Sources:http://www.cs.sfu.ca/~stella/main/_spins_figure8.gifhttp://www.cs.sfu.ca/~stella/main/_spins_figure7.gifhttp://videos.howstuffworks.com/discovery-health/14537-human-atlas-mri.jpghttp://www.mr-tip.com/exam_gifs/brain_mri_transversal_t2_002.jpg

Applying a 2D-FFT to the signal data

generates 2D-images in the imaging plane.

Basics of MRI Image Acquisition

University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 20093

Control/Stimulation acquisition

Estimation of Neuronal activity↓

BOLD effect ↓

R2*

fMRI

4University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

BOLD Response Model:

Significance of reliable R2* estimation


*BOLD = Blood Oxygenation Level Dependent

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


Single Shot Methods


Multiple Gradient Echo – Echo Planar Imaging (MEPI)

7

SS-PARSE

Conventional model Estimates map: M(x)

M(x) w(x) R2* (x)

SS-PARSE model

Include local phase evolution & local signal decay

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.


Single-Shot Parameter Assessment by Retrieval from Signal Encoding

8

Encoding Strategy (k-trajectory)

k space k, t spaceModeling

Acquired Data

Comparing Conventional MRI & SS-PARSE Methods

Decoding StrategyInverse FFTInverse Estimation

Adapted from Rajiv Menon’s Ph.D. proposal presentation


http://en.wikipedia.org/wiki/Copyleft

10

Source: http://commons.ucalgary.ca/at-wld/images/cartoon02.gif


Project Goals - experimental Create gradient waveforms and generate trajectories for 7 different gradient

strengths (1.9 G/cm to 3.8 G/cm):

Implement the sequence on Varian 4.7 T vertical scanner using phantoms

Compare performance of SS-PARSE with MEPI based on:1. Accuracy of R2

* estimates (compare with Gradient-Echo results)

2. Temporal variability of R2* (over time-series of 50 acquisitions)

3. Find correlation between R2* and TSD values

4. Find correlation between maximum gradient strength and accuracy

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


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)


65 ms

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


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.

13

Phantom For Data Acquisition

R2* Range: 15 sec-1 to 45 sec-1


Data Acquisition: GEMS, MEPI and SS-PARSE

1. SS-PARSE acquisitions• Per study = (7x Gmax) x (50x repetitions)

• Repetition time = 5 second• Slice Thickness = 3 mm

2. MEPI acquisitions• Per study = 50x repetitions at 4 echo times• Resolution = 64 x 64• Repetition time = 5 second• Echo Times = 22.3, 66.8, 96.4 and 124.2 millisecond• Slice Thickness = 3 mm

3. GEMS acquisitions• Per study = 16 x echo times• Resolution = 128 x 128• Echo Times = 5, 8, 10, 12, 15, 20, 25, 30, 35, 40, 45, 50,

55, 60, 65 and 70 millisecond• Slice Thickness = 3 mm

Performed total 18 experiments to obtain the R2* values in the desired range (15 to 45 sec-1)

Hardware: 4.7 T 60 cm-vertical-bore Varian primate MRI system (Varian Inc., Palo Alto, CA)



Source: http://www.hagencartoons.com/cartoon159.gif

16

Image Reconstruction and Data Analysis

Software: Matlab (version 7.5, The Mathworks Inc., Natick, MA)Platform: 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.17University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Development of GUI For Analysis & File Handling

File Handling PLCG Tweakers Parameter Maps


R2* Evaluation: GEMS and MEPI

•R2* is computed over a ROI

• •Monoexponential fitting of signal to echo times.

MEPI

GEMS


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).


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


Accuracy of R2* Estimation

1. R2* estimates from SS-PARSE and MEI plotted vs. R2

* from GEMS2. Ratio of R2

* accuracy plotted vs. R2* estimates from GEMS

SS-PARSE and MEPI estimates and accuracy plot at SS-PARSE Gmax = 2.9 G/cm


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. 1.9 G/cm: 61.3%2. 2.29 G/cm: 64.2%3. 2.5 G/cm: 66.4%4. 2.9 G/cm: 68.3%5. 3.2 G/cm: 67.6%6. 3.5 G/cm: 65.6%7. 3.8 G/cm: 61.2%

Accuracy of estimation (ratio) was maximum at Gmax = 2.9 G/cm


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 SS-PARSE.

Rejection of null hypothesis at any pixel would indicate a difference in standard deviation for that confidence interval.

F-test: Difference in Standard Deviation for R2*

Estimation (SS-PARSE and MEPI)


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. 1.9 G/cm: 241 pixels

2. 2.29 G/cm: 307 pixels

3. 2.5 G/cm: 468 pixels

4. 2.9 G/cm: 547 pixels

5. 3.2 G/cm: 485 pixels

6. 3.5 G/cm: 338 pixels

7. 3.8 G/cm: 214 pixels

Difference in standard deviations is maximum at Gmax = 2.9 G/cm

F-test: Results Over Gmax Range


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


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)

Comparing Temporal Standard Deviation


Depiction of TSD


TSD Plots

The difference was > 0 for 79.3% to 97.3% for R2* values between 15 sec-1 and 45 sec-1

• Dot indicates TSD at a single pixel

• Each blob of pixels represents a tube with a different R2*

• Scatter plot for the difference TSD(MEPI) – TSD (SS-PARSE) shows points around the difference = 0 line

• Dots above the difference=0 line show locations where the performance of SS-PARSE was better than of MEPI

R2* (GEMS) vs. TSD (SS-PARSE)

R2* (GEMS) vs. TSD (MEPI)

R2* (GEMS) vs. [TSD (MEPI) and TSD (SS-PARSE)]


Performance Under Field Inhomogeneity

MEPI

SS-PARSE


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.


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)


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.


Source: http://www.markstivers.com/cartoons/Cartoons%202003/Stivers%204-1-03%20Heisenberg%20cafe.gif

Inverse Problem Conditioning in Heisenberg’s Terms


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.


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.


Source: http://www.yachigusaryu.com/blog/pics/sci_principles_cartoon.jpg


Conclusions

Gradient waveforms for seven Gmax values were developed for SS-PARSE 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.


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).


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.


Acknowledgement

Advisor:Dr. Donald Twieg

Committee MembersDr. N. Shastry AkellaDr. Georg Deutsch

Dr. Stan Reeves (Auburn)

CDFI & VSRC colleagues:

Mark BoldingRajiv MenonNingzhi LiMatt WardDebbie WhittenJerry Millican

Parents and Sister

FriendsMichelleJonChris

Grant Support:

NIH # R21/R33 EB003292

City of Birmingham


Thank You

(Please complete the evaluation form)


Questions

Source: http://www.lifehack.org/wp-content/files/2007/12/question.jpg


Extras


Cramer-Rao Lower Bound for standard deviation of error for Multiple-Echo EPI (MEPI) and Rosette, SNR=200

Rosette (k,t)-trajectories acquire more information on R2* than multiple-echo EPI trajectory

MEPI Rosette

Idealized radial

s.d

. of

R2*

R2* (sec-1)


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Comparison of Single Shot Methods for R2* Comparison Thesis Defense Rick Deshpande Committee: Dr....

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