Advertisement

Fast and accurate compensation of signal offset for T2 mapping

  • Jan MichálekEmail author
  • Pavla Hanzlíková
  • Tuan Trinh
  • Dalibor Pacík
Research Article
  • 8 Downloads

Abstract

Objective

T2 maps are more vendor independent than other MRI protocols. Multi-echo spin-echo signal decays to a non-zero offset due to imperfect refocusing pulses and Rician noise, causing T2 overestimation by the vendor’s 2-parameter algorithm. The accuracy of the T2 estimate is improved, if the non-zero offset is estimated as a third parameter. Three-parameter Levenberg–Marquardt (LM) T2 estimation takes several minutes to calculate, and it is sensitive to initial values. We aimed for a 3-parameter fitting algorithm that was comparably accurate, yet substantially faster.

Methods

Our approach gains speed by converting the 3-parameter minimisation problem into an empirically unimodal univariate problem, which is quickly minimised using the golden section line search (GS).

Results

To enable comparison, we propose a novel noise-masking algorithm. For clinical data, the agreement between the GS and the LM fit is excellent, yet the GS algorithm is two orders of magnitude faster. For synthetic data, the accuracy of the GS algorithm is on par with that of the LM fit, and the GS algorithm is significantly faster. The GS algorithm requires no parametrisation or initialisation by the user.

Discussion

The new GS T2 mapping algorithm offers a fast and much more accurate off-the-shelf replacement for the inaccurate 2-parameter fit in the vendor’s software.

Keywords

Algorithms Least-squares analysis Software 

Notes

Acknowledgements

We acknowledge the core facility MAFIL of CEITEC, which was supported by the Czech BioImaging large RI project (LM2015062 funded by MEYS CR), for their support with obtaining the scientific data that were presented in this paper. The corresponding author also appreciates the valuable discussions on the theoretical aspects of the algorithm with M. Kozubek from the Centre for Biomedical Image Analysis, Faculty of Informatics, Masaryk University, as well as his comments that helped streamline the manuscript.

Authors' contributions

JM: Study conception and design, analysis and interpretation of data, drafting the manuscript, PH: Analysis and interpretation of data, DP: Acquisition of data, TT: Acquisition of data.

Funding

This work was supported by the Czech BioImaging large infrastructure project (LM2015062 funded by MEYS CR).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest to disclose.

Ethical approval

All procedures that were performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained from all individual participants that were included in the study.

Code availability

The MATLAB code for the algorithm described in this paper is available at https://github.com/tandzin/golden-section.

Supplementary material

10334_2019_737_MOESM1_ESM.docx (1.7 mb)
Supplementary file1 (DOCX 1690 kb)

References

  1. 1.
    Bjarnas TA, Editor (2011) Introduction to Quantitative T2 with emphasis on Medical Imaging. https://sourceforge.net/projects/intro2qt2/. Accessed 7 June 2018
  2. 2.
    Dowell NG, Wood TC (2018) T2: Transverse relaxation time. In: Cercignani M, Dowell NG, Tofts PS (eds) Quantitative MRI of the brain: principles of physical measurement, 2nd edn. CRC Press, Boca Raton, pp 83–95Google Scholar
  3. 3.
    Liney GP, Turnbull LW, Lowry M, Turnbull LS, Knowles AJ, Horsman A (1997) In vivo quantification of citrate concentration and water T2 relaxation time of the pathologic prostate gland using 1H MRS and MRI. Magn Reson Imaging 15:1177–1186CrossRefGoogle Scholar
  4. 4.
    Dinh H, Souchon R, Melodelima C, Bratan F, Mège-Lechevallier F, Colombel M, Rouvière O (2015) Characterization of prostate cancer using T2 mapping at 3T: a multi-scanner study. Diagn Interv Imaging 96:365–372CrossRefGoogle Scholar
  5. 5.
    Storås TH, Gjesdal KI, Gadmar ØB, Geitung JT, Kløw NE (2008) prostate magnetic resonance imaging: multiexponential T2 decay in prostate tissue. J Magn Reson Imaging 28:1166–1172CrossRefGoogle Scholar
  6. 6.
    Pei M, Nguyen TD, Thimmappa ND, Salustri C, Dong F, Cooper MA, Li J, Prince MR, Wang Y (2015) Algorithm for fast monoexponential fitting based on auto-regression on linear operations data. Magn Reson Med 73:843–850CrossRefGoogle Scholar
  7. 7.
    Li X, Hornak JP (1994) T2 Calculations in MRI: linear versus nonlinear methods. J Img Sci Tech 38:154–157Google Scholar
  8. 8.
    Hennig J (1991) Echoes-how to generate, recognize, use or avoid them in mr-imaging sequences. Concepts Magn Reson 3:125–143CrossRefGoogle Scholar
  9. 9.
    Neumann D, Blaimer M, Jakob PM, Breuer FA (2014) Simple recipe for accurate T2 quantification with multi spin-echo acquisitions. Magn Reson Mater Phy 27:567–577CrossRefGoogle Scholar
  10. 10.
    Hennig J (1988) Multiecho imaging sequences with low refocusing flip angles. J Magn Reson Imaging 78:397–407Google Scholar
  11. 11.
    Milford D, Rosbach N, Bendszus M, Heiland S (2015) Mono-exponential fitting in T2-relaxometry: relevance of offset and first echo. PLoS One 10(12):e0145255CrossRefPubMedCentralGoogle Scholar
  12. 12.
    Weigel M (2015) Extended phase graphs: dephasing, RF pulses, and echoes—pure and simple. J Magn Reson Imaging 41:266–295CrossRefGoogle Scholar
  13. 13.
    McPhee KC, Wilman AH (2018) Limitations of skipping echoes for exponential T2 fitting. J Magn Reson Imaging 48:1432–1440CrossRefGoogle Scholar
  14. 14.
    Prasloski T, Mädler B, Xiang Q-S, MacKay A (2012) Applications of stimulated echo correction to multicomponent T2 analysis. Magn Reson Med 67:1803–1814CrossRefGoogle Scholar
  15. 15.
    Umesh Rudrapatna S, Bakker CJG, Viergever MA, van der Toorn A, Dijkhuizen RM (2017) Improved estimation of MR relaxation parameters using complex-valued data. Magn Reson Med 77:385–397CrossRefGoogle Scholar
  16. 16.
    MRI Processor: ImageJ plug-in that calculates parametric maps in MR images. https://imagejdocu.tudor.lu/doku.php?id=plugin:filter:mri_processor:start. Accessed 7 June 2018
  17. 17.
    Bojorquez JZ, Bricq S, Brunotte F, Walker PM, Lalande A (2016) A novel alternative to classify tissues from T1 and T2 relaxation times for prostate MRI. Magn Reson Mater Phy 29:777–788CrossRefGoogle Scholar
  18. 18.
    Akçakaya M, Basha TA, Weingärtner S, Roujol S, Berg S, Nezafat R (2015) Improved quantitative myocardial T2 mapping: impact of the fitting model. Magn Reson Med 74:93–105CrossRefGoogle Scholar
  19. 19.
    Golub GH, Pereyra V (1973) The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate. SIAM J Numer Anal 10:413–432CrossRefGoogle Scholar
  20. 20.
    Luenberger DG, Ye Y (2008) Fibonacci and golden section search. Linear and nonlinear programming. Springer, New York, pp 217–219Google Scholar
  21. 21.
    Sijbers J, den Dekker AJ, Raman E, Van Dyck D (1999) Parameter estimation from magnitude MR images. Int J Imaging Syst Technol 10:109–114CrossRefGoogle Scholar
  22. 22.
    Ridgway G (2008) Rice/Rician distribution. The MathWorks, MATLAB Central, File Exchange. https://www.mathworks.com/matlabcentral/fileexchange/14237-rice-rician-distribution?focused=5109004&tab=example. Accessed 15 Jan 2019
  23. 23.
    Bojorquez JZ, Bricq S, Acquitter C, Brunotte F, Walker PM, Lalande A (2017) What are normal relaxation times of tissues at 3 T? Magn Reson Imaging 35:69–80CrossRefGoogle Scholar
  24. 24.
    Lourakis MIA. Levenberg-Marquardt nonlinear least squares algorithms in C/C++. https://users.ics.forth.gr/~lourakis/levmar/. Accessed 6 April 2018
  25. 25.
    OPTI Toolbox. A free MATLAB toolbox for optimization. https://inverseproblem.co.nz/OPTI/. Accessed 6 April 2018
  26. 26.
    Gudbjartsson H, Patz S (1995) The Rician distribution of noisy MRI data. Magn Reson Med 34:910–914CrossRefPubMedCentralGoogle Scholar
  27. 27.
    Björk M, Zachariah D, Kullberg J, Stoica P (2016) A multicomponent T2 relaxometry algorithm for myelin water imaging of the brain. Magn Reson Med 75:390–402CrossRefGoogle Scholar
  28. 28.
    Cabana JF, Gu Y, Boudreau M, Levesque IR, Atchia Y, Sled JG, Narayanan S, Arnold DL, Pike GB, Cohen-Adad J, Duval T, Vuong MT, Stikov N (2016) Quantitative magnetization transfer imaging made easy with qMTLab: Software for data simulation, analysis, and visualization. Concepts Magn Reson.  https://doi.org/10.1002/cmr.a.21357 Google Scholar
  29. 29.
    MacKay A, Whittall K, Adler J, Li D, Paty D, Graeb D (1994) In vivo visualization of myelin water in brain by magnetic resonance. Magn Reson Med 31:673–677CrossRefGoogle Scholar

Copyright information

© European Society for Magnetic Resonance in Medicine and Biology (ESMRMB) 2019

Authors and Affiliations

  1. 1.Centre for Biomedical Image Analysis, Faculty of InformaticsMasaryk UniversityBrnoCzech Republic
  2. 2.Department of Radiology, Faculty of Medicine and DentistryPalacky UniversityOlomoucCzech Republic
  3. 3.Department of Urology, Medical SchoolMasaryk UniversityBrnoCzech Republic
  4. 4.Department of UrologyUniversity Hospital BrnoBrnoCzech Republic

Personalised recommendations