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Optimization of 4D flow MRI velocity field in the aorta with divergence-free smoothing

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Abstract

Divergence-free smoothing with wall treatment (DFSwt) method is proposed for processing with four-dimensional (4D) flow magnetic resonance imaging (MRI) data of blood flows to enhance the quality of flow field with physical constraints. The new method satisfies the no-slip wall boundary condition and applies wall function of velocity profile for better estimating the velocity gradient in the near-wall region, and consequently improved wall shear stress (WSS) calculation against the issue of coarse resolution of 4D flow MRI. In the first testing case, blood flow field obtained from 4D flow MRI is well smoothed by DFSwt method. A great consistency is observed between the post-processed 4D flow MRI data and the computational fluid dynamics (CFD) data in the interested velocity field. WSS has an apparent improvement due to the proposed near-wall treatment with special wall function comparing to the result from original 4D flow MRI data or the DFS-processed data with no wall function. The other five cases also show the same performance that smoothed velocity field and improved WSS estimation are achieved on 4D flow MRI data optimized by DFSwt. The improvements will benefit the study of hemodynamics regarding the determination of location or the potential possibility of lesions.

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References

  1. Markl M, Frydrychowicz A, Kozerke S, Hope M, Wieben O (2012) 4D flow MRI. J Magn Reson Imaging 36:1015–1036. https://doi.org/10.1002/jmri.23632

    Article  PubMed  Google Scholar 

  2. Fredriksson AG, Svalbring E, Eriksson J, Dyverfeldt P, Alehagen U, Engvall J, Ebbers T, Carlhäll CJ (2016) 4D flow MRI can detect subtle right ventricular dysfunction in primary left ventricular disease. J Magn Reson Imaging 43:558–565

    Article  Google Scholar 

  3. Szajer J, Ho-Shon K (2018) A comparison of 4D flow MRI-derived wall shear stress with computational fluid dynamics methods for intracranial aneurysms and carotid bifurcations—a review. Magn Reson Imaging 48:62–69

    Article  Google Scholar 

  4. Frydrychowicz A, Berger A, Del Rio AM et al (2012) Interdependencies of aortic arch secondary flow patterns, geometry, and age analysed by 4-dimensional phase contrast magnetic resonance imaging at 3 Tesla. Eur Radiol 22:1122–1130

    Article  Google Scholar 

  5. Lawley CM, Broadhouse KM, Callaghan FM, Winlaw DS, Figtree GA, Grieve SM (2018) 4D flow magnetic resonance imaging: role in pediatric congenital heart disease. Asian Cardiovasc Thorac Ann 26:28–37

    Article  Google Scholar 

  6. Shalhub S, Schäfer M, Hatsukami TS, Sweet MP, Reynolds JJ, Bolster FA, Shin SH, Reece TB, Singh N, Starnes BW, Jazaeri O (2018) Association of variant arch anatomy with type B aortic dissection and hemodynamic mechanisms. J Vasc Surg 68:1640–1648

    Article  Google Scholar 

  7. Tan G, Soon J, Khoo P, et al. (2019) Original Article A review of aortic disease research in Malaysia. 74:67–78

  8. Hope TA, Markl M, Wigström L et al (2007) Comparison of flow patterns in ascending aortic aneurysms and volunteers using four-dimensional magnetic resonance velocity mapping. J Magn Reson Imaging An Off J Int Soc Magn Reson Med 26:1471–1479

    Google Scholar 

  9. Bogren HG, Buonocore MH, Valente RJ (2004) Four-dimensional magnetic resonance velocity mapping of blood flow patterns in the aorta in patients with atherosclerotic coronary artery disease compared to age-matched normal subjects. J Magn Reson Imaging An Off J Int Soc Magn Reson Med 19:417–427

    Google Scholar 

  10. Bieging ET, Frydrychowicz A, Wentland A, Landgraf BR, Johnson KM, Wieben O, François CJ (2011) In vivo three-dimensional MR wall shear stress estimation in ascending aortic dilatation. J Magn Reson Imaging 33:589–597

    Article  Google Scholar 

  11. Sughimoto K, Takahara Y, Mogi K, Yamazaki K, Tsubota K’, Liang F, Liu H (2014) Blood flow dynamic improvement with aneurysm repair detected by a patient-specific model of multiple aortic aneurysms. Heart Vessel 29:404–412

    Article  Google Scholar 

  12. Gallo D, De Santis G, Negri F et al (2012) On the use of in vivo measured flow rates as boundary conditions for image-based hemodynamic models of the human aorta: implications for indicators of abnormal flow. Ann Biomed Eng 40:729–741

    Article  CAS  Google Scholar 

  13. Natsume K, Shiiya N, Takehara Y, Sugiyama M, Satoh H, Yamashita K, Washiyama N (2017) Characterizing saccular aortic arch aneurysms from the geometry-flow dynamics relationship. J Thorac Cardiovasc Surg 153:1413–1420

    Article  Google Scholar 

  14. Westerweel J, Scarano F (2005) Universal outlier detection for PIV data. Exp Fluids 39:1096–1100

    Article  Google Scholar 

  15. Gunes H, Rist U (2007) Spatial resolution enhancement/smoothing of stereo–particle-image-velocimetry data using proper-orthogonal-decomposition–based and Kriging interpolation methods. Phys Fluids 19:64101

    Article  Google Scholar 

  16. Song SM, Napel S, Glover GH, Pelc NJ (1993) Noise reduction in three-dimensional phase-contrast MR velocity measurementsl. J Magn Reson Imaging 3:587–596

    Article  CAS  Google Scholar 

  17. Busch J, Giese D, Wissmann L, Kozerke S (2013) Reconstruction of divergence-free velocity fields from cine 3D phase-contrast flow measurements. Magn Reson Med 69:200–210

    Article  Google Scholar 

  18. Ong F, Uecker M, Tariq U, et al. (2013) Improved visualization and quantification of 4D flow MRI data using divergence-freewavelet denoising. In: Biomedical Imaging (ISBI), 2013 IEEE 10th International Symposium on. IEEE, 1186–1189

  19. Wang C, Gao Q, Wang H, Wei RJ, Li T, Wang JJ (2016) Divergence-free smoothing for volumetric PIV data. Exp Fluids 57:15

    Article  Google Scholar 

  20. Boussel L, Rayz V, Martin A, Acevedo-Bolton G, Lawton MT, Higashida R, Smith WS, Young WL, Saloner D (2009) Phase-contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: comparison with computational fluid dynamics. Magn Reson Med An Off J Int Soc Magn Reson Med 61:409–417

    Article  Google Scholar 

  21. Potters WV, van Ooij P, Marquering H, vanBavel E, Nederveen AJ (2015) Volumetric arterial wall shear stress calculation based on cine phase contrast MRI. J Magn Reson Imaging 41:505–516

    Article  Google Scholar 

  22. Riminarsih D, Karyati CM, Mutiara AB, Wahyudi B (2016) Wall shear stress calculation based on MRI image in patients with abdominal aortic aneurysm (AAA). In: Informatics and Computing (ICIC), International Conference on. IEEE, 442–446

  23. Kendall A, Koochesfahani M (2008) A method for estimating wall friction in turbulent wall-bounded flows. Exp Fluids 44:773–780

    Article  Google Scholar 

  24. Li F, Gao Q, Qiao E, Yin G, Zhang RJ, Zhao SH, Wang W (2020) Contributing factor of proximal arch dilation in patients with bicuspid aortic valve—wall shear stress or upward extension of ascending aorta dilation? Heart Surg Forum 23:E435–E440. https://doi.org/10.1532/hsf.2925

    Article  PubMed  Google Scholar 

  25. Li H, Manjunath BS (1995) Multisensor-Image-Fusion-Using-the-Wavelet-Transform_1995_Graphical-Models-and-Image-Processing.pdf. Graph Model image Process 57:235–245

    Article  Google Scholar 

  26. Huang T, Yang G, Tang G (1979) A fast two-dimensional median filtering algorithm. IEEE Trans Acoust 27:13–18

    Article  Google Scholar 

  27. Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9:62–66

    Article  Google Scholar 

  28. Kazhdan M, Bolitho M, Hoppe H (2006) Poisson surface reconstruction. Eurographics Symposium on Geometry Processing

    Google Scholar 

  29. Garcia D (2010) Robust smoothing of gridded data in one and higher dimensions with missing values. Comput Stat Data Anal 54:1167–1178

    Article  Google Scholar 

  30. Lantz J, Renner J, Karlsson M (2011) Wall shear stress in a subject specific human aorta - influence of fluid-structure interaction. Int J Appl Mech 3:759–778

    Article  Google Scholar 

  31. Uus A (2016) Patient-specific blood flow modelling in diagnosis of coronary artery disease

  32. Miyazaki S, Itatani K, Furusawa T, Nishino T, Sugiyama M, Takehara Y, Yasukochi S (2017) Validation of numerical simulation methods in aortic arch using 4D Flow MRI. Heart Vessel 32:1032–1044

    Article  Google Scholar 

  33. Doğan NÖ (2018) Bland-Altman analysis: a paradigm to understand correlation and agreement. Turkish J Emerg Med 18:139–141. https://doi.org/10.1016/j.tjem.2018.09.001

    Article  Google Scholar 

  34. Kilner PJ, Yang GZ, Mohiaddin RH, Firmin DN, Longmore DB (1993) Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping. Circulation 88:2235–2247

    Article  CAS  Google Scholar 

  35. Frydrychowicz A, Winterer JT, Zaitsev M et al (2007) Visualization of iliac and proximal femoral artery hemodynamics using time-resolved 3D phase contrast MRI at 3T. J Magn Reson Imaging An Off J Int Soc Magn Reson Med 25:1085–1092

    Google Scholar 

  36. Stalder AF, Russe MF, Frydrychowicz A, Bock J, Hennig J, Markl M (2008) Quantitative 2D and 3D phase contrast MRI: optimized analysis of blood flow and vessel wall parameters. Magn Reson Med 60:1218–1231

    Article  CAS  Google Scholar 

  37. Oyre S, Ringgaard S, Kozerke S, Paaske WP, Erlandsen M, Boesiger P, Pedersen EM (1998) Accurate noninvasive quantitation of blood flow, cross-sectional lumen vessel area and wall shear stress by three-dimensional paraboloid modeling of magnetic resonance imaging velocity data. J Am Coll Cardiol 32:128–134

    Article  CAS  Google Scholar 

  38. Cibis M, Potters WV, Gijsen FJ, Marquering H, van Ooij P, vanBavel E, Wentzel JJ, Nederveen AJ (2016) The effect of spatial and temporal resolution of cine phase contrast MRI on wall shear stress and oscillatory shear index assessment. PLoS One 11:1–15. https://doi.org/10.1371/journal.pone.0163316

    Article  CAS  Google Scholar 

  39. Garcia J, Barker AJ, Markl M (2019) The role of imaging of flow patterns by 4D flow MRI in aortic stenosis. JACC Cardiovasc Imaging 12:252–266. https://doi.org/10.1016/j.jcmg.2018.10.034

    Article  PubMed  Google Scholar 

  40. Rodríguez-Palomares JF, Dux-Santoy L, Guala A, Kale R, Maldonado G, Teixidó-Turà G, Galian L, Huguet M, Valente F, Gutiérrez L, González-Alujas T, Johnson KM, Wieben O, García-Dorado D, Evangelista A (2018) Aortic flow patterns and wall shear stress maps by 4D-flow cardiovascular magnetic resonance in the assessment of aortic dilatation in bicuspid aortic valve disease. J Cardiovasc Magn Reson 20:28. https://doi.org/10.1186/s12968-018-0451-1

    Article  PubMed  PubMed Central  Google Scholar 

  41. Geiger J, Rahsepar AA, Suwa K, Powell A, Ghasemiesfe A, Barker AJ, Collins JD, Carr JC, Markl M (2018) 4D flow MRI, cardiac function, and T 1 -mapping: association of valve-mediated changes in aortic hemodynamics with left ventricular remodeling. J Magn Reson Imaging 48:121–131. https://doi.org/10.1002/jmri.25916

    Article  PubMed  Google Scholar 

  42. van Ooij P, Markl M, Collins JD, Carr JC, Rigsby C, Bonow RO, Malaisrie SC, McCarthy PM, Fedak PWM, Barker AJ (2017) Aortic valve stenosis alters expression of regional aortic wall shear stress: new insights from a 4-dimensional flow magnetic resonance imaging study of 571 subjects. J Am Heart Assoc 6:1–14. https://doi.org/10.1161/JAHA.117.005959

    Article  Google Scholar 

  43. Lenz A, Petersen J, Riedel C, Weinrich JM, Kooijman H, Schoennagel BP, Adam G, von Kodolitsch Y, Reichenspurner H, Girdauskas E, Bannas P (2020) 4D flow cardiovascular magnetic resonance for monitoring of aortic valve repair in bicuspid aortic valve disease. J Cardiovasc Magn Reson 22:1–10. https://doi.org/10.1186/s12968-020-00608-0

    Article  Google Scholar 

  44. Rahiminejad M, Haghighi A, Dastan A et al (2012) Fluid-structure interaction study in rigid and compliant airways. Acta Mech Sinica 38:1836–1853

    Google Scholar 

  45. Soudah E, Casacuberta J, Gamez-Montero PJ et al (2017) Estimation of wall shear stress using 4D flow cardiovascular MRI and computational fluid dynamics. J Mech Med Biol 17:1–14

    Article  Google Scholar 

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Funding

This work was supported by the National Natural Science Foundation of China (grant 12072320).

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Zhejiang University, Yuquan Campus, 38 Zheda Road, Xihu District, Hangzhou, 310027, China

    Qi Gao

  2. Hangzhou Shengshi Technology Co., Ltd., Hangzhou, China

    Xingli Liu, Mansu Jin & RunJie Wei

  3. The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China

    Hongping Wang

  4. Artificial Organ Technology Lab, Bio-manufacturing Research Centre, School of Mechanical and Electric Engineering, Soochow University, Suzhou, China

    Peng Wu

  5. Department of Structural Heart Disease, Chinese Academy of Medical Sciences & Fuwai Hospital; State Key Laboratory of Cardiovascular Disease, Peking Union Medical College, 167 Beilishi Road, Xicheng District, 100037, Beijing, China

    Wei Wang & Fei Li

  6. Cardiac Surgery, Qingdao Municipal Hospital, Qingdao, China

    Zhaozhuo Niu

  7. Department of Magnetic Resonance Imaging, Chinese Academy of Medical Sciences & Fuwai Hospital, Peking Union Medical College, 167 Beilishi Road, Xicheng District, 100037, Beijing, China

    Shihua Zhao

  8. Department of Cardiac Surgery, Peking University First Hospital, Beijing, China

    Fei Li

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  1. Qi Gao
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  8. Zhaozhuo Niu
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  10. Fei Li
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Contributions

Qi Gao, Fei Li, and Xingli Liu made contributions to design this study and draft the manuscript; Shihua Zhao collected MRI data and critically revised the manuscript; Peng Wu, Runjie Wei, Hongping Wang, and Mansu Jin were in charge of post-processing of 4D flow MRI analysis. Wei Wang and Zhaozhuo Niu analyzed clinical data and did substantial contribution to design and critical revision of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Qi Gao, Shihua Zhao or Fei Li.

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Gao, Q., Liu, X., Wang, H. et al. Optimization of 4D flow MRI velocity field in the aorta with divergence-free smoothing. Med Biol Eng Comput 59, 2237–2252 (2021). https://doi.org/10.1007/s11517-021-02417-8

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