1. Compressed Sensing 4D Flow Reconstruction using Divergence-free Wavelet Transform Frank Ong 1, Martin Uecker 1, Umar Tariq 2, Albert Hsiao 2, Marcus Alley 2, Shreyas Vasanawala 2 and Michael Lustig 1 1 University of California, Berkeley 2 Stanford University

2. Speaker Name: Frank Ong I have the following financial interest or relationship to disclose with regard to the subject matter of this presentation: Company Name: GE Healthcare Type of Relationship: Funding Declaration of Financial Interests or Relationships

3. 4D Flow MRI Provides anatomical and functional cardiac information in a single acquisition Ref: Markl et. al JMRI 2003 4D flow showed a regurgitant jet caused by a lesion that could not be well seen on conventional cardiac MRI

4. Clinically Viable 4D flow Want: 1. Reasonable scan time (< 10 minutes) 2. High spatiotemporal resolution for anatomy Approaches used so far: Parallel imaging Compressed sensing Motion correction

5. Goal: Reduce Scan Time Utilize physical property of blood flow in compressed sensing reconstruction Blood flow is divergence-free (What flows in flows out) Divergence-freeNot divergence-free

6. This Work 1. Divergence-free wavelet transform 2. Phase-wrap tolerant reconstruction Joint reconstruction of all velocity encodings Prior Works Loecher et. al ISMRM 2014 Busch et. al MRM 2013 Song et. al MRM 1994

7. Compressed Sensing Reconstruction Data consistency Wavelet denoising Better denoising → Better reconstruction

8. Divergence-free Wavelet Transform Shown to be effective in denoising 4D flow data Divergence-free wavelet denoising Ref: Ong et. al MRM 2014

9. Divergence-free Wavelet Transform Shown to be effective in denoising 4D flow data “Soft” divergence-free constraint Ref: Ong et. al MRM 2014 Non-divergence-free component

10. Compressed Sensing Reconstruction with Divergence-free Wavelet Transform Data consistency Spatial wavelet denoising on magnitude image Divergence-free wavelet denoising on phase images Ref: Fessler et. al ISBI 2004, Zhao et. al TMI 2013

11. Compressed Sensing Reconstruction with Divergence-free Wavelet Transform Phase distortion near phase wraps Magnitude Reference phase Velocity

12. Phase Cycle Spinning Denoising phase wraps creates small distortions Errors accumulate over iterations

13. Phase Cycle Spinning Denoising phase wraps creates small distortions Errors accumulate over iterations + constant phase

14. Phase Cycle Spinning Denoising phase wraps creates small distortions Errors accumulate over iterations + constant phase

15. Phase Cycle Spinning Denoising phase wraps creates small distortions Errors accumulate over iterations + constant phase

16. Phase Cycle Spinning Denoising phase wraps creates small distortions Errors accumulate over iterations

17. Results L1-ESPIRiT + Spatial Wavelet L1-ESPIRiT + Divergence-Free Wavelet Velocity map (SI direction) 20 cardiac phases Size = 256x256x164 Resolution~1.15x1.15x1 mm Undersampled by 4 π- π

18. Results L1-ESPIRiT + Spatial Wavelet L1-ESPIRiT + Divergence-Free Wavelet Speed map 20 cardiac phases Size = 256x256x164 Resolution~1.15x1.15x1 mm Undersampled by 4 150 m/s0 m/s

19. Summary Divergence-free wavelet transform Phase cycle spinning

20. Summary Divergence-free wavelet transform Phase cycle spinning

21. Summary Divergence-free wavelet transform Phase cycle spinning Wavelet code available online: http://www.eecs.berkeley.edu/~mlustig/Software.html

22. Summary Divergence-free wavelet transform Phase cycle spinning Wavelet code available online: http://www.eecs.berkeley.edu/~mlustig/Software.html Thank you Supported by GE Healthcare, NSF Graduate Fellowship, NIH grants P41RR09784, R01EB009690, American Heart Association 12BGIA9660006, and the Sloan Research Fellowship.