Abstract
Velocity measurements with magnetic resonance velocimetry offer outstanding possibilities for experimental fluid mechanics. The purpose of this study was to provide practical guidelines for the estimation of the measurement uncertainty in such experiments. Based on various test cases, it is shown that the uncertainty estimate can vary substantially depending on how the uncertainty is obtained. The conventional approach to estimate the uncertainty from the noise in the artifact-free background can lead to wrong results. A deviation of up to \(-75\,\%\) is observed with the presented experiments. In addition, a similarly high deviation is demonstrated with the data from other studies. As a more accurate approach, the uncertainty is estimated directly from the image region with the flow sample. Two possible estimation methods are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aja-Fernández S, Alberola-López C, Westin CF (2008) Noise and signal estimation in magnitude MRI and Rician distributed images: a LMMSE approach. Image Process IEEE Trans 17(8):1383–1398. doi:10.1109/TIP.2008.925382
Aja-Fernández S, Tristán-Vega A, Alberola-López C (2009) Noise estimation in single-and multiple-coil magnetic resonance data based on statistical models. Magn Reson Imaging 27(10):1397–1409. doi:10.1016/j.mri.2009.05.025
Benson MJ, Elkins CJ, Yapa SD, Ling JB, Eaton JK (2012) Effects of varying reynolds number, blowing ratio, and internal geometry on trailing edge cutback film cooling. Exp Fluids 52(6):1415–1430. doi:10.1007/s00348-012-1260-1
Bernstein MA, Grgic M, Brosnan TJ, Pelc NJ (1994) Reconstructions of phase contrast, phased array multicoil data. Magn Reson Med 32(3):330–334. doi:10.1002/mrm.1910320308
Bruschewski M, Scherhag C, Schiffer HP, Grundmann S (2016) Influence of channel geometry and flow variables on cyclone cooling of turbine blades. J Turbomach 138(6). doi:10.1115/1.4032363
Buchenberg WB, Wassermann F, Grundmann S, Jung B, Simpson R (2015) Acquisition of 3D temperature distributions in fluid flow using proton resonance frequency thermometry. Magn Reson Med. doi:10.1002/mrm.25874
Coletti F, Elkins CJ, Eaton JK (2013) An inclined jet in crossflow under the effect of streamwise pressure gradients. Exp Fluids 54(9):1589. doi:10.1007/s00348-013-1589-0
Constantinides CD, Atalar E, McVeigh ER (1997) Signal-to-noise measurements in magnitude images from NMR phased arrays. Magn Reson Med 38(5):852–857. doi:10.1002/mrm.1910380524
den Dekker AJ, Sijbers J (2014) Data distributions in magnetic resonance images: a review. Phys Med 30(7):725–741. doi:10.1016/j.ejmp.2014.05.002
Dietrich O, Raya JG, Reeder SB, Reiser MF, Schoenberg SO (2007) Measurement of signal-to-noise ratios in MR images: influence of multichannel coils, parallel imaging, and reconstruction filters. J Magn Reson Imaging 26(2):375–385. doi:10.1002/jmri.20969
Elkins CJ, Alley MT (2007) Magnetic resonance velocimetry: applications of magnetic resonance imaging in the measurement of fluid motion. Exp Fluids 43(6):823–858. doi:10.1007/s00348-007-0383-2
Freudenhammer D, Baum E, Peterson B, Böhm B, Jung B, Grundmann S (2014) Volumetric intake flow measurements of an IC engine using magnetic resonance velocimetry. Exp Fluids 55(5):1724. doi:10.1007/s00348-014-1724-6
Fukushima E (1999) Nuclear magnetic resonance as a tool to study flow. Annu Rev Fluid Mech 31(1):95–123. doi:10.1146/annurev.fluid.31.1.95
Gladden LF, Sederman AJ (2013) Recent advances in flow MRI. J Magn Reson 229:9–11. doi:10.1016/j.jmr.2012.11.022 (frontiers of in vivo and materials MRI research)
Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A (2002) Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 47(6):1202–1210. doi:10.1002/mrm.10171
Grundmann S, Sayles E, Elkins CJ, Eaton J (2012a) Sensitivity of an asymmetric 3d diffuser to vortex-generator induced inlet condition perturbations. Exp Fluids 52(1):11–21. doi:10.1007/s00348-011-1205-0
Grundmann S, Wassermann F, Lorenz R, Jung B, Tropea C (2012) Experimental investigation of helical structures in swirling flows. Int J Heat Fluid Flow 37:51–63. doi:10.1016/j.ijheatfluidflow.2012.05.003
Gudbjartsson H, Patz S (1995) The Rician distribution of noisy MRI data. Magn Reson Med 34(6):910–914. doi:10.1002/mrm.1910340618
Hansen MS, Kellman P (2015) Image reconstruction: an overview for clinicians. J Magn Reson Imaging 41(3):573–585. doi:10.1002/jmri.24687
Henkelman RM (1985) Measurement of signal intensities in the presence of noise in mr images. Med Phys 12(2):232–233. doi:10.1118/1.595711
Issakhanian E, Elkins C, Eaton J (2012) In-hole and mainflow velocity measurements of low-momentum jets in crossflow emanating from short holes. Exp Fluids 53(6):1765–1778. doi:10.1007/s00348-012-1397-y
Kaufman L, Kramer DM, Crooks LE, Ortendahl DA (1989) Measuring signal-to-noise ratios in MR imaging. Radiology 173(1):265–267. doi:10.1148/radiology.173.1.2781018
Koay CG, Basser PJ (2006) Analytically exact correction scheme for signal extraction from noisy magnitude MR signals. J Magn Reson 179(2):317–322. doi:10.1016/j.jmr.2006.01.016
Lathi BP (1998) Modern digital and analog communication systems, 3rd edn. Oxford University Press, New York
Lo KP, Elkins CJ, Eaton JK (2012) Separation control in a conical diffuser with an annular inlet: center body wake separation. Exp Fluids 53(5):1317–1326. doi:10.1007/s00348-012-1360-y
Markl M, Frydrychowicz A, Kozerke S, Hope M, Wieben O (2012) 4D flow MRI. J Magn Reson Imaging 36(5):1015–1036. doi:10.1002/jmri.23632
Moran PR (1982) A flow velocity zeugmatographic interlace for NMR imaging in humans. Magn Reson Imaging 1(4):197–203. doi:10.1016/0730-725X(82)90170-9
NEMA (2014) Determination of signal-to-noise ratio (SNR) in diagnostic magnetic resonance imaging. NEMA Standards Publication MS 1-2008 (R2014). http://www.nema.org/Standards/Pages/Determination-of-Signal-to-Noise-Ratio-in-Diagnostic-Magnetic-Resonance-Imaging.aspx
Onstad A, Elkins C, Medina F, Wicker R, Eaton J (2011) Full-field measurements of flow through a scaled metal foam replica. Exp Fluids 50(6):1571–1585. doi:10.1007/s00348-010-1008-8
Pelc NJ, Bernstein MA, Shimakawa A, Glover GH (1991) Encoding strategies for three-direction phase-contrast MR imaging of flow. J Magn Reson Imaging 1(4):405–413. doi:10.1002/jmri.1880010404
Pelc N, Sommer F, Li K, Brosnan T, Herfkens R, Enzmann D (1994) Quantitative magnetic resonance flow imaging. Magn Reson Q 10(3):125–147. http://www.ncbi.nlm.nih.gov/pubmed/7811608
Piro M, Wassermann F, Grundmann S, Leitch B, Tropea C (2016) Progress in on-going experimental and computational fluid dynamic investigations within a CANDU fuel channel. Nucl Eng Design 299:184–200. doi:10.1016/j.nucengdes.2015.07.009
Poustchi-Amin M, Mirowitz SA, Brown JJ, McKinstry RC, Li T (2001) Principles and applications of echo-planar imaging: a review for the general radiologist 1. Radiographics 21(3):767–779. doi:10.1148/radiographics.21.3.g01ma23767
Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P et al (1999) SENSE: sensitivity encoding for fast MRI. Magn Reson Med 42(5):952–962. doi:10.1002/(SICI)1522-2594(199911)42:5<952:AID-MRM16>3.0.CO;2-S
Reeder SB, Wintersperger BJ, Dietrich O, Lanz T, Greiser A, Reiser MF, Glazer GM, Schoenberg SO (2005) Practical approaches to the evaluation of signal-to-noise ratio performance with parallel imaging: application with cardiac imaging and a 32-channel cardiac coil. Magn Reson Med 54(3):748–754. doi:10.1002/mrm.20636
Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller O (1990) The NMR phased array. Magn Reson Med 16(2):192–225. doi:10.1002/mrm.1910160203
Scott DW (2012) Multivariate density estimation and visualization. In: Handbook of computational statistics, Springer, pp 549–569. doi:10.1002/9781118575574.ch6
Sijbers J, Poot D, den Dekker AJ, Pintjens W (2007) Automatic estimation of the noise variance from the histogram of a magnetic resonance image. Phys Med Biol 52(5):1335. doi:10.1088/0031-9155/52/5/009
Sijbers J, den Dekker AJ (2004) Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magn Reson Med 51(3):586–594. doi:10.1002/mrm.10728
Wassermann F, Hecker D, Jung B, Markl M, Seifert A, Grundmann S (2013) Phase-locked 3D3C-MRV measurements in a bi-stable fluidic oscillator. Exp Fluids 54(3):1487. doi:10.1007/s00348-013-1487-5
Zhang S, Block KT, Frahm J (2010) Magnetic resonance imaging in real time: advances using radial flash. J Magn Reson Imaging 31(1):101–109. doi:10.1002/jmri.21987
Acknowledgments
This work was supported by the Bundesministerium für Wirtschaft und Technologie (BMWi) under Grant Number 20T1108C.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bruschewski, M., Freudenhammer, D., Buchenberg, W.B. et al. Estimation of the measurement uncertainty in magnetic resonance velocimetry based on statistical models. Exp Fluids 57, 83 (2016). https://doi.org/10.1007/s00348-016-2163-3
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-016-2163-3