1. Case Study: Effect of resolution enhancement on the accuracy of 4D flow MRI data
Ali Bakhshinejad
April 21, 2018

2. Introduction

3. The First Image
”The heart of itself is not the beginning of life but is a vessel made of dense muscle vivified and nourished by an artery and a vein as are the other muscles. The heart is of such density that fire can scarcely damage it.” -Leonardo da Vinci
Ali Bakhshinejad

4. Fluid Dynamics Visualization
Ali Bakhshinejad

5. 4D Flow MRI
Phase contrast cardiovascular magnetic resonance with flow-encoded in three spatial dimension as well as time (3D + 1D = 4D), termed as 4D flow MRI or 4D Phase Contrast MRI (4D PCMR).1
1 Michael Markl et al. “4D flow MRI”. . In: Journal of Magnetic Resonance Imaging 36.5 (Nov. 2012), pp. 1015–1036. issn: doi:
/jmri url:
Ali Bakhshinejad

6. 4D Flow MRI
4D Flow MRI refers to time resolved three-dimensional (3D) spatial encoding combined with three-directional velocity-encoded phase contrast MRI.
The typical spatial resolution for 4D flow MRI is 1.5 × 1.5 × to 3 × 3 × 3 mm3 and temporal resolution of 30 − 40 ms and acquisition times in the order of 5 to 25 min.
Ali Bakhshinejad

7. 4D Flow MRI
Ali Bakhshinejad
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8. 4D Flow MRI
Ali Bakhshinejad
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9. Limits Noisy nature of MRI such as: Low resolution Sparse in time
� Random Noise
� Eddy currents
� Phase wrapping
� Non-divergence-free flow field
Low resolution Sparse in time
Ali Bakhshinejad
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10. Why data correction is important?
Figure: Effect of flow patterns on the cell orientation in a controlled environment.2
2 Peter F Davies et al. “Turbulent fluid shear stress induces vascular endothelial cell turnover in vitro (hemodynamic forces/endothelial growth control/atherosclerosis)”. In: Cell Biology 83 (1986), pp. 2114–2117. url:
Ali Bakhshinejad
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11. Post-processing 4D Flow MRI data

12. Post-processing 4D Flow MRI data
CFD-independent methods,
CFD methods based on 4D flow MRI, 4D flow MRI-CFD coupled methods.

13. Method 1 - Ensemle Kalman Filter
Ensemble bound- ary conditions
In-vivo 4D- PCMR data
Ensemble CFD simulations
k = k + 1
Vascular geometry from MRA
Simulated noisy 4D-PCMR scan a.k.a observations:
State-output error cross covariance:
Ensemble predicted state:
[P ] = Xˆ
1 1 l 1 lT
e N − 1 Xˆ yk
x = f x , u
( )
k k−1 k−1
fi ai i
Output error covariance:
Ensemble state estimate:
Ensemble predicted output: 1
Analysis
x = x + [K] y + v − y
k k k k k
ai fi i fi
( )
( )
e q − 1
Kalman gain:
T ( T )−1
[K]k = [P ]e [H] [H] [P ]e [H] + [R]e
[R] = [Υ] [Υ]T
[A ] = x x · · · x
a a1 a2 1 k
yfi = [H] xfi
k k k k aN l
k k

14. Results

15. Results
UCSF-134
Figure: (a) Shows the location of the aneurysm inside the data block, (b) shows the path of particle movement in noisy data, and (c) shows the particle path in the reconstructed data.2
2 Ali Bakhshinejad et al. “Merging Computational Fluid Dynamics and 4D Flow MRI Using Proper Orthogonal Decomposition and Ridge Regression”.
In: Journal of Biomechanics (May 2017). issn: doi: /j.jbiomech url:

16. Results
UCSF-134
Fill in/Wash out simulation

17. Conclusion

18. Conclusion
Three different 4D flow MRI post-processing algorithms were developed.
One is based on proper orthogonal decomposition (POD) and ridge regression. Another is based on POD and Dynamic Mode Decomposition (DMD).
The last one is based on ensemble Kalman filter (EnKF).
Benchmark tests were run on the POD algorithm and state-of-the-art de-noising methods. In all cases, we have shown that POD algorithm recovers data with better overall error metrics.
Reconstruction of low resolution, noisy 4D flow MRI data into arbitrary high spatial and temporal resolution is possible using either of our algorithms.

19. Publications

20. Publications Journal Article
Bakhshinejad A., Fathi M., Baghaie A., Nael K., Rayz V.L., D’Souza R.M. (2017) 4D Flow MRI Denoising and Spatial Resolution Enhancement: Application of Proper Orthogonal Decomposition Coupled with Dynamic Mode Decomposition. Under review.
Fathi M., Bakhshinejad A., Baghaie A., Saloner D., Sacho R., Rayz V.L., D’Souza R.M. (2017) Denoising and Spatial Resolution Enhancement of 4D Flow MRI Using Proper Orthogonal Decomposition and Lasso Regularization. Under review.
Bakhshinejad, A., Baghaie, A., Vali, A., Saloner, D., Rayz, V. L., & D’Souza, R. M. (2017). Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression. Journal of Biomechanics, 58,
Conference Presentations
Roshan M. D’Souza, Ali Bakhshinejad, Ahmadreza Baghaie and Vitaliy L. Rayz Reconstructing High Fidelity Hemodynamic Flow Fields by Merging Patient-Specific Computational Fluid Dynamics (CFD) and 4D Phase Contrast Magnetic Resonance Data, ISMRM Workshop.
Ali Bakhshinejad, Ahmadreza Baghaie, Vitaliy L. Rayz and Roshan M. D’Souza, A proper orthogonal decomposition approach towards merging CFD and 4D-PCMR flow data, The 28th Society for Magnetic Resonance Angiography
Bakhshinejad, A., & D’Souza, R. M. (2015). A brief comparison between available bio-printing methods. In 2015 IEEE Great Lakes Biomedical Conference (GLBC) (pp. 1-3). IEEE.