Sairam Geethanath, Ph.D. Medical Imaging Research Centre Dayananda Sagar Institutions, Bangalore

Sairam Geethanath, Ph.D. Medical Imaging Research Centre Dayananda Sagar Institutions, Bangalore

Contrast SNR MRI Speed Data provided by Baek

Number of non-zero coefficients in a data vector Importance due to conservation of energy Sinusoidal signal for 3 hours in time domain or frequency domain? Move towards time-frequency transforms

CS: what is it all about? Matlab demo Steps ahead on CS Resources on CS

Childlike question on compression Acceleration technique involving both acquisition and reconstruction paradigms Technically challenging, pragmatically feasible and clinically valuable

2D FFT Good data quality but takes a long time! Hence, may not be suitable for certain imaging protocols. Limits spatial and temporal resolutions Higher spatial resolution aids in morphological analysis of tumors breast DCE-MRI Temporal resolution is important for accurate pharmacokinetic analysis. Several approaches like keyhole, parallel imaging and other fast sequences have been used. 200 X 2D IFFT 150 100 50 1 0 Data provided by Baek

X 2D IFFT 70 60 50 40 30 20 10 70 60 50 40 30 20 10 Uniform Sampling 120 X 2D IFFT 100 80 80 60 60 40 40 20 20 Incoherent Sampling

Wavelet Transform Complete data reconstruction Most objects in nature are approximately sparse in a transformed domain. Utilize above concept to obtain very few measurements and yet reconstruct with high fidelity [1,2] X Only 33% of complete data Data provided by Baek [1] David L. Donoho, IEEE Transactions on Information theory, Vol.52, no. 4, April 2006 [2] Candes, E.J. et al., IEEE Transactions on Information theory, Vol.52, no.2, Feb. 2006

Generate a 2D phantom Cartesian undersampling of data Obtain undersampled data and zfwdc recon Choice of ROI if required for diagnostic evaluation purposes Recon params, post L-curve optimization Nonlinear conjugate gradient iterative reconstruction Comparative quality

Point spread function analyses 1. Incoherence 2. Design of this sampling mask

K-space trajectories with 2 constraints: 1. Slew rate 2. Smoothness of k-space coverage

Every MRI method: Angiography DWI/DTI/SWI/DCE-MRI/ASL fmri/mrsi/cmr. Because MRI is inherently a slow acquisition process, mostly dictated by the physics of acquisition Magnetic Resonance Fingerprinting

1. Rapid 1 H MR metabolic imaging 2. Accelerated DCE-MRI 3. Swifter Sweep Imaging with Fourier Transform (SWIFT) MRI

It has been well established that magnetic resonance imaging (MRI) provides critical information about cancer [3]. Magnetic resonance spectroscopic imaging (MRSI) furthers this capability by providing information about the presence of certain metabolites which are known to be important prognostic markers of cancer [4] (stroke, AD, energy metabolism, TCA cycle). MRSI provides information about the spatial distribution of these metabolites, hence enabling metabolic imaging. [3] Huk WJ et al., Neurosurgical Review 7(4) 1984; [4] Preul MC et al., Nat. Med. 2(3) 1996;

Increased choline level Reduced N-Acetylaspartate (NAA) level Reduced creatine level CANCER NORMAL [5] [5] H Kugel et al., Radiology 183 June 1992

Long acquisition times for MRSI A typical MRSI protocol (32 X 32 X 512) takes ~ 20 minutes Difficult to maintain anatomical posture for long time Increases patient discomfort, likelihood of early termination of study Discourages routine clinical use of this powerful MRI technique To increase throughput (decreased scanner time, technician time) Reduction of acquisition time is usually accomplished by under sampling measured data (k-space). Limitations of Shannon-Nyquist criterion. Compressed sensing provides a framework to achieve sub-nyquist sampling rates with good data fidelity.

MRSI data Scanner TR(ms) TE(ms) # Averages Grid Size FOV (mm 3 ) Brain - normal (N=6) Siemens 3.0T Trio Tim 1700 270 4 16 x 16 x 1024 100 x 100 x 15 Brain cancer (N=2) Philips 3.0T Achieva 1000 112 112 2 2 18 x 21 x 1024 19 x 22 x 1024 180 x 210 x15 190 x 220 x 15 Prostate cancer (N=2) Philips 3.0T Achieva 1200 1000 140 140 1 1 14 x 10 x 1024 16 x 12 x 1024 25 x 50 x 33 20 x 51 x 26 Brain - normal (N=6) Brain - cancer (N=2) Prostate -cancer (N=2)

Minimal data processing done using jmrui [7] FID Apodization Gaussian (~3Hz) Removal of water peak using HLSVD Phase correction To allow correct integration of the real part of the spectra QUEST based quantitation. [8] To generate specific metabolite maps. [7] A. Naressi, et al., Computers in Biology and Medicine, vol. 31, 2001. [8] H. Ratiney, et al., Magnetic Resonance Materials in Physics Biology and Medicine, vol. 16, 2004.

1X 5X Cho Cr NAA

1X Normal Brain cancer Cancer Cho NAA Cho Cr Cho Cr 2 Cr 2 Cr NAA Cr Prostate cancer Normal Cancer Cit Cho + Cr Cit 2X 5X 10X

Brain - Normal Metabolite maps Brain - cancer Prostate - cancer

Mean SD of pooled data for each data type 2 tailed paired t-test Ratio: CNI for brain data and (Cho + cr)/cit for prostate data Excluded voxels with denominator value of 0 in 1X case For CS cases, if the denominator had a value of 0, the ratio was set to 0 P value less than 0.05 was chosen as a significant difference (* p <0.05) Brain (Normal) Brain (Cancer) Prostate (Cancer) NAA (a.u.) Cr (a.u.) Cho (a.u.) Cit (a.u.) Ratio 1X 200 96.8 51.83 27.6 13.8 8.87 0.075 0.047 2X 200 98.9 51.99 34.5 13.8 10.2 0.073 0.064 5X 202 110 51.71 30.7 13. 9 10.6 0.082 0.152 10X 241 138* 65.22 39.3* 17.9 13.2* 0.086 0.083* 1X 10.7 6.35 4.23 2.43 3.21 1.38 0.468 0.519 2X 10.8 6.45 4.27 2.60 3.21 1.37 0.625 1.50 5X 10.6 7.42 4.19 2.35 3.21 1.36 0.712 1.82 10X 11.1 8.78 3.72 1.72* 3.27 1.47 0.837 1.89* 1X 499 821 2010 1730 188 166 19.25 25.23 2X 427 830 1850 1460 194 131 14.10 10.21 5X 382 541 1830 1450 193 131 16.12 16.44 10X 378 540 1470 958* 135 111* 16.38 23.59

RMSE 1 N N i 1 ( i i '') 2 N = total number of elements of the MRSI data; Θ, Θ = the data reconstructed from full k-space and undersampled k-space respectively.

Application of compressed sensing on 1 H MRSI has been performed for the first time It has been demonstrated that compressed sensing based reconstruction can be successfully applied on 1 H MRSI in vivo human brain (normal and cancer), prostate cancer data and in vitro, computer generated phantom data sets Our results indicate a potential to reduce MRSI acquisition times by 75% thus significantly reducing the time spent by the patient in the MR scanner for spectroscopic studies Current and future work involves the implementation of compressed sensing based pulse sequences on preclinical and clinical scanners Other groups in the world are working on this demonstration now!

Rapid 1 H MR metabolic imaging Accelerated DCE-MRI Swifter Sweep Imaging with Fourier Transform (SWIFT) MRI

C(t) = f(δr 1 (t)) T1 weighted images for baseline T1 shortening contrast agent Tissue perfusion, microvascular density and extravascular -extracellular volume -- tumor staging, monitor treatment response [10] Yankeelov TE, et. al MRI;23(4). 2005 *Model implemented by Dr. Vikram Kodibagkar in MATLAB [10]

[11] Vanvaals JJ et. al. JMRI; 3(4) 1993 [12] Jim J et. al. IEEE TMI 2008 [13] Lustig M et. al. MRM;58(6) 2007 I post-contrast I pre-contrast I diff S post (ω) S pre (ω) y diff Data was normalized to a range of 0 to 1 before retrospective reconstruction Keyhole for DCE CS for DCE S pre (ω) = L pre (ω) + H pre (ω) (1a) S post (ω) = L post (ω) + H pre (ω) (1b) Є( I diff ) = FI diff y diff 2 + λ LI WI diff 1 +λ TV (I diff ) (2) [11] [12,13]

5 DCE-MRI breast cancer data sets consisting of 64 frames (4 precontrast images and 60 post-contrast images) were used for retrospective reconstructions. The contrast agent used was Omniscan (intravenously administered through the tail vein at a dose of 0.1 mmol/kg). Reconstructions based on 2 approaches: keyhole and compressed sensing, were performed as function of masks and acceleration factors were performed. These reconstructions were quantified by the root mean square error metric defined below N RMSE 1 N i 1 ( i i '') 2

Masks Recon Original Keyhole Keylines Keythresh CS_Gauss CS_Glines CS_Thresh 2X 3X 4X 5X 2X 3X 4X 5X

Keyhole CS Keylines CS_Gauss Keyhole CS_Glines Keythresh CS_Thresh Starts at frame 1 Starts at frame 6 (post-contrast)

K trans Ve Original Keyhole Keylines Keythresh CS_Gauss CS_Glines CS_Thresh 2X 3X 4X 5X 2X 3X 4X 5X

ROI Intensity ROI Intensity ROI Intensity T1w precontrast T1w postcontrast 0.250 0.225 Muscle 0.200 T2w Overlay 0.175 0.40 0.35 Well perfused region Original Keyhole Keylines Keythresh Gauss Glines Gthresh 0.150 0 10 20 30 40 50 60 0.250 Frame # Poorly perfused region 0.30 0.225 0.25 0.200 0.20 Original Keyhole Keylines Keythresh Gauss Glines Gthresh 0.15 0 10 20 30 40 50 60 Frame # 0.175 Original Keyhole Keylines Keythresh Gauss Glines Gthresh 0 10 20 30 40 50 60 Frame #

Muscle Well perfused Poorly perfused

It has been shown here and previously that DCE MRI can be reliably accelerated through methods like compressed sensing and keyhole reconstructions to obtain increased spatial and/or temporal resolution. CS based masks Gauss and Gthresh provide better performance when compared to Glines mask, which out do the keyhole masks as observed by the RMSE graphs. Keyhole based masks keyhole mask performs relatively poorer when compared to keythresh and keylines masks Acceleration factors the values of RMSE increases with acceleration as expected (not shown); the CS masks show a RMSE of less than 0.075 even at an acceleration factor of 5 while keyhole masks result in a RMSE of less than 0.1

Rapid 1 H MR metabolic imaging Accelerated DCE-MRI Swifter Sweep Imaging with Fourier Transform (SWIFT) MRI

Sweep imaging with Fourier transformation [14] Time domain signals are acquired during a swept radiofrequency excitation in a time shared way This results in a significantly negligible echo time. Insensitive to motion, restricted dynamic range, low gradient noise Bovine tibia [14] D.Idiyatullin et al., JMR, 181, 2006. [14] GRE SWIFT Photograph

Full k-space recon was performed using gridding. The volume was restricted to a range of [0,1] by normalizing it to the highest absolute value. Prospective implementation is straight forward due to the nature of k-space trajectory. Acceleration of 5.33 X was achieved directly proportional to time saved MR data is sparse in the total variation domain. Since the data in this case is 3D, a 3D total variation norm is most apt. Reconstruction involves minimization of the convex functional given below. This is accomplished by a custom implementation of non-linear conjugate gradient algorithm. Є(m) = F u m y 2 +λ TV TV(m) where m is the desired MRI volume, F u is the Fourier transform operator, TV is the 3D total variation operator,. 2 is the L2 norm operator, λ TV is the regularization parameter for the TV term respectively, and Є is the value of the cost function.

The initial estimate of the volume is given by the zero-filled case with density compensation (zfwdc). This produces artifacts which are incoherent as can be seen in the zfwdc images. A total of 8 iterations were used and the recon was performed in 4 mins. NRMSE given by RMSE/ range of input; i.e. 1; hence NRMSE = RMSE calculated as given below N 1 2 RMSE ( i i '') N i 1 N = total number of elements of the MRI volume; Θ, Θ = the data reconstructed from full k- space and undersampled k-space respectively.

Original Zero filled with density compensation 5.33 X

Intensity (au) Intensity (au) Intensity (au) 0.6 0.4 Original 0.2 0.0 50 100 150 Pixel number Zero filled with density compensation 0.6 0.4 0.2 (Zfwdc) 0.0 50 100 150 Pixel Number 0.6 5X 0.4 0.2 0.0 50 100 150 Pixel Number

Original 5X Scan time ~ 8 min Estimated scan time ~1.6 min

Original Zfwdc 5 X

Review on CS MRI Critical reviews in biomedical engineering 2013 http://nuit-blanche.blogspot.in/ Miki Lustig, UC Berkley John M Pauly, Stanford www.ismrm.org

25+ member team (14 + 11 ) Impact factor > 15 for 2012 13 Considered world experts in CS Work on CS has been showcased in the American Society of Neuroradiologists 2013 annual conference Several groups worldwide are working on our idea including Oxford and Yale http://www.dayanandasagar.edu/mirc-home.html

Human Scan Scanning Started from: 5-07-2013 Number of volunteers scanned till 18-08-2013: 20

Mr. Rajesh Harsh, Mr. Ravindran Nair, Mr. T.S. Datta, Mr. R.S.Verma MIRC students Knowledge partners for MRI India Consortium: AIIMS, Harvard, NYU, Minnesota, Auburn ASU, KCL/ICL, Wipro-GE Healthcare Scientists/Participants Management of DSCE