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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 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 2 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 3 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 4 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 5 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 6 Single Shot Methods Multiple Gradient Echo – Echo Planar Imaging (MEPI) University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 7 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 8 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 9 Source: http://commons.ucalgary.ca/at-wld/images/cartoon02.gif University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 10 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 11 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 12 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 13 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 14 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 15 Source: http://www.hagencartoons.com/cartoon159.gif University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 16 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 17 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 18 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 19 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 20 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 21 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 22 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 23 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 24 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 25 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 26 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 27 Depiction of TSD University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 28 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 29 Performance Under Field Inhomogeneity MEPI SS-PARSE University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 30 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 31 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 32 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 33 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 34 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 35 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 36 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 37 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 38 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 39 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 40 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 41 Thank You (Please complete the evaluation form) University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 42 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 43 Extras University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 44 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 45