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Investigation of phase-contrast magnetic resonance imaging underestimation of turbulent flow through the aortic valve phantom: experimental and computational study using lattice Boltzmann method

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Abstract

Objective

The accuracy of phase-contrast magnetic resonance imaging (PC-MRI) measurement is investigated using a computational fluid dynamics (CFD) model with the objective to determine the magnitude of the flow underestimation due to turbulence behind a narrowed valve in a phantom experiment.

Materials and methods

An acrylic stationary flow phantom is used with three insertable plates mimicking aortic valvular stenoses of varying degrees. Positive and negative horizontal fluxes are measured at equidistant slices using standard PC-MRI sequences by 1.5T and 3T systems. The CFD model is based on the 3D lattice Boltzmann method (LBM). The experimental and simulated data are compared using the Bland-Altman-derived limits of agreement. Based on the LBM results, the turbulence is quantified and confronted with the level of flow underestimation.

Results

LBM gives comparable results to PC-MRI for valves up to moderate stenosis on both field strengths. The flow magnitude through a severely stenotic valve was underestimated due to signal void in the regions of turbulent flow behind the valve, consistently with the level of quantified turbulence intensity.

Discussion

Flow measured by PC-MRI is affected by noise and turbulence. LBM can simulate turbulent flow efficiently and accurately, it has therefore the potential to improve clinical interpretation of PC-MRI.

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References

  1. Anderson JR, Diaz O, Klucznik R, Zhang YJ, Britz GW, Grossman RG, Lv N, Huang Q, Karmonik C (2014) Validation of computational fluid dynamics methods with anatomically exact, 3D printed MRI phantoms and 4D pcMRI. In: 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, IEEE, pp 6699–6701, https://doi.org/10.1109/EMBC.2014.6945165

  2. Bland JM, Altman D (1986) Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 327(8476):307–310

    Article  Google Scholar 

  3. Caiazzo A, Junk M (2008) Boundary forces in lattice Boltzmann: analysis of momentum exchange algorithm. Comput Math Appl 55(7):1415–1423. https://doi.org/10.1016/j.camwa.2007.08.004

    Article  Google Scholar 

  4. Chai P, Mohiaddin R (2005) Slice location dependence of aortic regurgitation measurements with MR phase velocity mapping. J Cardiovasc Magn Reson 7(4):705–716. https://doi.org/10.1081/JCMR-65639

    Article  PubMed  Google Scholar 

  5. Chapelle D, Fragu M, Mallet V, Moireau P (2013) Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart. Med Biol Eng Comput 51(11):1221–1233. https://doi.org/10.1007/s11517-012-0969-6

    Article  CAS  PubMed  Google Scholar 

  6. Chaturvedi A, Hamilton-Craig C, Cawley PJ, Mitsumori LM, Otto CM, Maki JH (2016) Quantitating aortic regurgitation by cardiovascular magnetic resonance: significant variations due to slice location and breath holding. Eur Radiol 26(9):3180–3189. https://doi.org/10.1007/s00330-015-4120-6

    Article  PubMed  Google Scholar 

  7. Chatzimavroudis GP, Walker PG, Oshinski JN, Franch RH, Pettigrew RI, Yoganathan AP (1997) Slice location dependence of aortic regurgitation measurements with MR phase velocity mapping. Magn Reson Med 37(4):545–551. https://doi.org/10.1002/mrm.1910370412

    Article  CAS  PubMed  Google Scholar 

  8. Chikatamarla S, Ansumali S, Karlin IV (2006) Entropic lattice Boltzmann models for hydrodynamics in three dimensions. Phys Rev Lett 97(1):010201. https://doi.org/10.1103/PhysRevLett.97.010201

    Article  CAS  PubMed  Google Scholar 

  9. d’Humieres D (2002) Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos Trans R Soc Lond Ser A: Math Phys Eng Sci 360(1792):437–451. https://doi.org/10.1098/rsta.2001.0955

    Article  Google Scholar 

  10. Donati F, Myerson S, Bissell MM, Smith NP, Neubauer S, Monaghan MJ, Nordsletten DA, Lamata P (2017) Beyond Bernoulli: improving the accuracy and precision of noninvasive estimation of peak pressure drops. Circ Cardiovasc Imaging 10(1):e005207. https://doi.org/10.1161/CIRCIMAGING.116.005207

    Article  PubMed  PubMed Central  Google Scholar 

  11. Dyverfeldt P, Bissell M, Barker AJ, Bolger AF, Carlhäll CJ, Ebbers T, Francios CJ, Frydrychowicz A, Geiger J, Giese D et al (2015) 4D flow cardiovascular magnetic resonance consensus statement. J Cardiovasc Magn Reson 17(1):72. https://doi.org/10.1186/s12968-015-0174-5

    Article  PubMed  PubMed Central  Google Scholar 

  12. Eckhardt B (2008) Introduction. Turbulence transition in pipe flow: 125th anniversary of the publication of Reynolds’ paper. https://doi.org/10.1098/rsta.2008.0217

  13. Everett RJ, Clavel MA, Pibarot P, Dweck MR (2018) Timing of intervention in aortic stenosis: a review of current and future strategies. Heart 104(24):2067–2076. https://doi.org/10.1136/heartjnl-2017-312304

    Article  PubMed  PubMed Central  Google Scholar 

  14. Fučík R, Eichler P, Straka R, Pauš P, Klinkovský J, Oberhuber T (2019) On optimal node spacing for immersed boundary-lattice Boltzmann method in 2D and 3D. Comput Math Appl 77(4):1144–1162. https://doi.org/10.1016/j.camwa.2018.10.045

    Article  Google Scholar 

  15. Gehrke M, Banari A, Rung T (2020) Performance of under-resolved, model-free LBM simulations in turbulent shear flows. In: Hoarau Y, Peng SH, Schwamborn D, Revell A, Mockett C (eds) Progress in Hybrid RANS-LES Modelling. Springer International Publishing, Cham, pp 3–18. https://doi.org/10.1007/978-3-030-27607-2_1

    Chapter  Google Scholar 

  16. Geier M, Greiner A, Korvink JG (2006) Cascaded digital lattice Boltzmann automata for high Reynolds number flow. Phys Rev E 73(6):066705. https://doi.org/10.1103/PhysRevE.73.066705

    Article  CAS  Google Scholar 

  17. Geier M, Schönherr M, Pasquali A, Krafczyk M (2015) The cumulant lattice Boltzmann equation in three dimensions: theory and validation. Comput Math Appl 70(4):507–547. https://doi.org/10.1016/j.camwa.2015.05.001

    Article  Google Scholar 

  18. Geier M, Pasquali A, Schönherr M (2017) Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion part I: derivation and validation. J Comput Phys 348:862–888. https://doi.org/10.1016/j.jcp.2017.05.040

    Article  Google Scholar 

  19. Geier M, Pasquali A, Schönherr M (2017) Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion Part II: application to flow around a sphere at drag crisis. J Comput Phys 348:889–898. https://doi.org/10.1016/j.jcp.2017.07.004

    Article  CAS  Google Scholar 

  20. Goubergrits L, Riesenkampff E, Yevtushenko P, Schaller J, Kertzscher U, Berger F, Kuehne T (2015) Is MRI-based CFD able to improve clinical treatment of coarctations of aorta? Ann Biomed Eng 43(1):168–176. https://doi.org/10.1007/s10439-014-1116-3

    Article  CAS  PubMed  Google Scholar 

  21. Guo Z, Shu C (2013) Lattice Boltzmann method and its applications in engineering, vol 3. World Scientific, Singapore

    Book  Google Scholar 

  22. Ha H, Lantz J, Ziegler M, Casas B, Karlsson M, Dyverfeldt P, Ebbers T (2017) Evaluation of aortic regurgitation with cardiac magnetic resonance imaging: a systematic review. Sci Rep 7:46618. https://doi.org/10.1038/srep46618

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Iwamoto Y, Inage A, Tomlinson G, Lee KJ, Grosse-Wortmann L, Seed M, Wan A, Yoo SJ (2014) Direct measurement of aortic regurgitation with phase-contrast magnetic resonance is inaccurate: proposal of an alternative method of quantification. Pediatr Radiol 44(11):1358–1369. https://doi.org/10.1007/s00247-014-3017-x

    Article  PubMed  Google Scholar 

  24. Karlin IV, Bösch F, Chikatamarla S (2014) Gibbs’ principle for the lattice-kinetic theory of fluid dynamics. Phys Rev E 90(3):031302. https://doi.org/10.1103/PhysRevE.90.031302

    Article  CAS  Google Scholar 

  25. Kweon J, Yang DH, Kim GB, Kim N, Paek M, Stalder AF, Greiser A, Kim YH (2016) Four-dimensional flow MRI for evaluation of post-stenotic turbulent flow in a phantom: comparison with flowmeter and computational fluid dynamics. Eur Radiol 26(10):3588–3597. https://doi.org/10.1007/s00330-015-4181-6

    Article  PubMed  Google Scholar 

  26. Lee JC, Branch KR, Hamilton-Craig C, Krieger EV (2018) Evaluation of aortic regurgitation with cardiac magnetic resonance imaging: a systematic review. Heart 104(2):103–110. https://doi.org/10.1136/heartjnl-2016-310819

    Article  PubMed  Google Scholar 

  27. 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 Vessels 32(8):1032–1044. https://doi.org/10.1007/s00380-017-0979-2

    Article  PubMed  PubMed Central  Google Scholar 

  28. Morris PD, Narracott A, von Tengg-Kobligk H, Soto DAS, Hsiao S, Lungu A, Evans P, Bressloff NW, Lawford PV, Hose DR et al (2016) Computational fluid dynamics modelling in cardiovascular medicine. Heart 102(1):18–28. https://doi.org/10.1136/heartjnl-2015-308044

    Article  PubMed  Google Scholar 

  29. Nayak KS, Nielsen JF, Bernstein MA, Markl M, Gatehouse PD, Botnar RM, Saloner D, Lorenz C, Wen H, Hu BS et al (2015) Cardiovascular magnetic resonance phase contrast imaging. J Cardiovasc Magn Reson 17(1):71. https://doi.org/10.1186/s12968-015-0172-7

    Article  PubMed  PubMed Central  Google Scholar 

  30. O’Brien KR, Cowan BR, Jain M, Stewart RA, Kerr AJ, Young AA (2008) MRI phase contrast velocity and flow errors in turbulent stenotic jets. J Magn Reson Imaging 28(1):210–218. https://doi.org/10.1002/jmri.21395

    Article  PubMed  Google Scholar 

  31. Ruijsink B, Puyol-Antón E, Usman M, van Amerom J, Duong P, Forte MNV, Pushparajah K, Frigiola A, Nordsletten DA, King AP, et al (2017) Semi-automatic cardiac and respiratory gated MRI for cardiac assessment during exercise. In: molecular imaging, reconstruction and analysis of moving body organs, and stroke imaging and treatment, Springer, pp 86–95

  32. Ruijsink B, Zugaj K, Wong J, Pushparajah K, Hussain T, Moireau P, Razavi R, Chapelle D, Chabiniok R (2020) Dobutamine stress testing in patients with Fontan circulation augmented by biomechanical modeling. PLoS ONE 15(2):e0229015. https://doi.org/10.1371/journal.pone.0229015

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Schlichting H, Gersten K (2016) Boundary-layer theory. Springer, New York

    Google Scholar 

  34. Sharma KV, Straka R, Tavares FW (2017) New cascaded thermal lattice Boltzmann method for simulations of advection-diffusion and convective heat transfer. Int J Therm Sci 118:259–277. https://doi.org/10.1016/j.ijthermalsci.2017.04.020

    Article  Google Scholar 

  35. Sharma KV, Straka R, Tavares FW (2019) Lattice Boltzmann methods for industrial applications. Ind Eng Chem Res 58(36):16205–16234. https://doi.org/10.1021/acs.iecr.9b02008

    Article  CAS  Google Scholar 

  36. Shen X, Schnell S, Barker AJ, Suwa K, Tashakkor L, Jarvis K, Carr JC, Collins JD, Prabhakaran S, Markl M (2018) Voxel-by-voxel 4D flow MRI-based assessment of regional reverse flow in the aorta. J Magn Reson Imaging 47(5):1276–1286. https://doi.org/10.1002/jmri.25862

    Article  PubMed  Google Scholar 

  37. Sotelo J, Dux-Santoy L, Guala A, Rodríguez-Palomares J, Evangelista A, Sing-Long C, Urbina J, Mura J, Hurtado DE, Uribe S (2018) 3D axial and circumferential wall shear stress from 4D flow MRI data using a finite element method and a laplacian approach. Magn Reson Med 79(5):2816–2823. https://doi.org/10.1002/mrm.26927

    Article  PubMed  Google Scholar 

  38. Srichai MB, Lim RP, Wong S, Lee VS (2009) Cardiovascular applications of phase-contrast MRI. Am J Roentgenol 192(3):662–675. https://doi.org/10.2214/AJR.07.3744

    Article  Google Scholar 

  39. Švihlová H, Hron J, Málek J, Rajagopal K, Rajagopal K (2016) Determination of pressure data from velocity data with a view toward its application in cardiovascular mechanics. Part 1. Theoretical considerations. Int J of Eng Sci 105:108–127. https://doi.org/10.1016/j.ijengsci.2015.11.002

    Article  Google Scholar 

  40. Švihlová H, Hron J, Málek J, Rajagopal K, Rajagopal K (2017) Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2: A study of aortic valve stenosis. Int J of Eng Sci 114:1–15. https://doi.org/10.1016/j.ijengsci.2017.01.002

    Article  Google Scholar 

  41. Wendell DC, Samyn MM, Cava JR, Krolikowski MM, LaDisa JF (2016) The impact of cardiac motion on aortic valve flow used in computational simulations of the thoracic aorta. J Biomech Eng 138(9):091001. https://doi.org/10.1115/1.4033964

    Article  Google Scholar 

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Acknowledgements

We would like to acknowledge Dr T. Hussain (UT Southwestern Medical Center Dallas, USA) and A. Wodecki (Czech Technical University in Prague) for valuable discussions.

Funding

The work was supported by the Ministry of Health of the Czech Republic project No. NV19-08-00071, the Czech Science Foundation project No. 18-09539S, the Ministry of Education, Youth, and Sports of the Czech Republic under the OP RDE grant No. CZ.02.1.01/0.0/0.0/16_019/0000765, the Wellcome/EPSRC Centre for Medical Engineering (WT 203148/Z/16/Z), and by the Inria-UT Southwestern Associated Team TOFMOD. In addition, the authors would like to thank IBM Watson iLab for providing access to a system based on IBM Power9 CPUs.

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RF: study conception and design, analysis and interpretation of data, drafting of manuscript, critical revision. RG: study conception and design, acquisition of data, analysis and interpretation of data, drafting of manuscript. PP: analysis and interpretation of data, drafting of manuscript, critical revision. PE: acquisition of data, analysis and interpretation of data, critical revision. JK: acquisition of data, analysis and interpretation of data, critical revision. RSt: study conception and design, analysis and interpretation of data, drafting of manuscript critical revision. JT: study conception and design, critical revision. RC: study conception and design, analysis and interpretation of data, drafting of manuscript, critical revision.

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Correspondence to Radek Fučík.

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Fučík, R., Galabov, R., Pauš, P. et al. Investigation of phase-contrast magnetic resonance imaging underestimation of turbulent flow through the aortic valve phantom: experimental and computational study using lattice Boltzmann method. Magn Reson Mater Phy 33, 649–662 (2020). https://doi.org/10.1007/s10334-020-00837-5

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