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,

Outline  Introduction Basics of MRI, fMRI Significance of reliable R 2 * 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,

1 H nuclei within tissues 1 H nuclei under external magnetic field RF pulse (sinc/Gaussian/square) 1 H 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: 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,

Control/Stimulation acquisition Estimation of Neuronal activity ↓ BOLD effect ↓ R2* fMRI 4 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

BOLD Response Model: Significance of reliable R 2 * estimation University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, *BOLD = Blood Oxygenation Level Dependent

R 2 * Measurement: Multiple Shot Method Gradient Echo Multiple Shot (GEMS)  Echoes can be closely stacked, thus enabling accurate R 2 * calculation  Serves as a gold standard in the comparison study 6 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Single Shot Methods University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 Multiple Gradient Echo – Echo Planar Imaging (MEPI) 7

SS-PARSE Conventional model Estimates map: M(x) M(x)  (x) R 2 * (x) SS-PARSE model Include local phase evolution & local signal decay Estimate maps (images) of M(x), R 2 * (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. University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 Single-Shot Parameter Assessment by Retrieval from Signal Encoding 8

Comparing Conventional MRI & SS-PARSE Methods Adapted from Rajiv Menon’s Ph.D. proposal presentation University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th,

10 Source: University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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 R 2 * estimates (compare with Gradient-Echo results) 2. Temporal variability of R 2 * (over time-series of 50 acquisitions) 3. Find correlation between R 2 * and TSD values 4. Find correlation between maximum gradient strength and accuracy University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th,

Project goals – Theoretical Inferences  Factors contributing towards performance of SS-PARSE: 1. G max values – Find relationship between G max and R 2 * estimates (compared with gradient-echo values) 2. Shimming – Find effects of field inhomogeneity in SS-PARSE and MEPI studies. 3. Performance over R 2 * range - Observe the changes in temporal behavior over R 2 * 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,

65 ms 1.9 G/cm 2.29 G/cm 2.5 G/cm2.9 G/cm 3.2 G/cm 3.5 G/cm 3.8 G/cm University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009 k-trajectory Generation and Calibration Calibration data acquired at: ±2, ±4, ±6, ±8, ±10, ±12 mm displacements in x & y planes For G max : 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 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th,

Data Acquisition: GEMS, MEPI and SS-PARSE 1. SS-PARSE acquisitions Per study =(7x G max ) x (50x repetitions) Per study =(7x G max ) x (50x repetitions) Repetition time=5 second Repetition time=5 second Slice Thickness=3 mm Slice Thickness=3 mm 2. MEPI acquisitions Per study=50x repetitions at 4 echo times Per study=50x repetitions at 4 echo times Resolution=64 x 64 Resolution=64 x 64 Repetition time=5 second Repetition time=5 second Echo Times=22.3, 66.8, 96.4 and millisecond Echo Times=22.3, 66.8, 96.4 and millisecond Slice Thickness=3 mm Slice Thickness=3 mm 3. GEMS acquisitions Per study=16 x echo times Per study=16 x echo times Resolution= 128 x 128 Resolution= 128 x 128 Echo Times=5, 8, 10, 12, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65 and 70 millisecond Echo Times=5, 8, 10, 12, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65 and 70 millisecond Slice Thickness=3 mm 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) University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th,

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

Image Reconstruction and Data Analysis Software: Matlab (version 7.5, The Mathworks Inc., Natick, MA) Platform: Kubuntu bit (Linux kernel amd64-k8) Tweakers for PLCG algorithm: 1.Swoop length (N1): Number of Samples between two echoes. Increases with G max 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. 17 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Development of GUI For Analysis & File Handling File HandlingPLCG TweakersParameter Maps 18 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

R 2 * Evaluation: GEMS and MEPI R 2 * is computed over a ROI Monoexponential fitting of signal to echo times. MEPI GEMS 19 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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 G max values (1.9 G/cm to 3.8 G/cm). 20 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Accuracy of R 2 * Estimation GEMS is used as the gold standard Accuracy of estimation at each pixel is computed by using the ratio: |R 2 * MEPI - R 2 * GEMS | | R 2 * SSPARSE - R 2 * 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 G max values 21 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Accuracy of R 2 * Estimation 1.R 2 * estimates from SS-PARSE and MEI plotted vs. R 2 * from GEMS 2.Ratio of R 2 * accuracy plotted vs. R 2 * estimates from GEMS SS-PARSE and MEPI estimates and accuracy plot at SS-PARSE G max = 2.9 G/cm 22 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Accuracy Over Gradient Amplitudes Accuracy of R 2 * estimation computed by using the ratio: |R 2 * MEPI - R 2 * GEMS | |R 2 * SSPARSE - R 2 * GEMS | was > 1 for following percentage points over the G max range: G/cm:61.3% G/cm:64.2% G/cm:66.4% G/cm:68.3% G/cm:67.6% G/cm:65.6% G/cm:61.2% Accuracy of estimation (ratio) was maximum at G max = 2.9 G/cm 23 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

 Null hypothesis: There is no difference in the standard deviation of R 2 * distributions obtained using MEPI and SS-PARSE at 95% confidence interval.  The test was performed on 80 pixels (ROI with radius = 5), over 20 R 2 * 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 R 2 * Estimation (SS-PARSE and MEPI) University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th,

 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: G/cm:241 pixels G/cm:307 pixels G/cm:468 pixels G/cm:547 pixels G/cm:485 pixels G/cm:338 pixels G/cm:214 pixels  Difference in standard deviations is maximum at G max = 2.9 G/cm F-test: Results Over G max Range University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th,

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 G max with best accuracy 26 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

 Compute the TSD over each pixel in each ROI over 50 repetitions  Find the value: TSD MEPI – TSD SS-PARSE for each pixel  If the difference is +ve, SS-PARSE has lower TSD, thus better repeatability  TSD comparison is performed for SS-PARSE G max with best accuracy (2.9 G/cm) Comparing Temporal Standard Deviation 27 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Depiction of TSD 28 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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)] 29 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Performance Under Field Inhomogeneity MEPI SS-PARSE 30 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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.  R 2 * computation in MEPI is impossible under field-inhomogeneity because of a noticeable geometric distortion. 31 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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 R 2 * estimates in SS-PARSE are comparable to estimates in MEPI at lower values of R 2 *, but are significantly better at higher values of R 2 *. 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 3 rd and 4 th echo; especially in regions with high R 2 * values. Using MEPI to generate activation maps in regions with high R 2 * 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) 32 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Discussion  In k-trajectory used for SS-PARSE, lower gradient strengths trajectories (G max ) 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 G max 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 G max value somewhere between 2.5 G/cm and 3.2 G/cm. 33 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Source: Inverse Problem Conditioning in Heisenberg’s Terms 34 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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

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

Source: 37 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Conclusions  Gradient waveforms for seven G max 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 R 2 * estimation of SS-PARSE was compared with MEPI for a range of G max values.  Performance of SS-PARSE improved with increasing gradient amplitude until 2.9 G/cm. Thereafter the performance deteriorates. 38 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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). 39 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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

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 EB  City of Birmingham 41 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Thank You (Please complete the evaluation form) University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th,

Questions Source: 43 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

Extras 44 University of Alabama at Birmingham, Department of Biomedical Engineering, Thesis Defense March 16th, 2009

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