Skip to main content

NMF in MR Spectroscopy

  • Chapter
  • First Online:
Non-negative Matrix Factorization Techniques

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

Nowadays, magnetic resonance spectroscopy (MRS) represents a powerful nuclear magnetic resonance (NMR) technique in oncology since it provides information on the biochemical profile of tissues, thereby allowing clinicians and radiologists to identify in a non-invasive way the different tissue types characterising the sample under investigation. The main purpose of the present chapter is to provide a review of the most recent and significant applications of non-negative matrix factorisation (NMF) to MRS data in the field of tissue typing methods for tumour diagnosis. Specifically, NMF-based methods for the recovery of constituent spectra in ex vivo and in vivo brain MRS data, for brain tissue pattern differentiation using magnetic resonance spectroscopic imaging (MRSI) data and for automatic detection and visualisation of prostate tumours, will be described. Furthermore, since several NMF implementations are available in the literature, a comparison in terms of pattern detection accuracy of some NMF algorithms will be reported and discussed, and the NMF performance for MRS data analysis will be compared with that of other blind source separation (BSS) techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Nelson, Multivoxel magnetic resonance spectroscopy of brain tumors. Mol. Cancer Ther. 2(5), 497–507 (2003)

    Google Scholar 

  2. X. Leclerc, T. Huisman, A. Sorensen, The potential of proton magnetic resonance spectroscopy (1H-MRS) in the diagnosis and management of patients with brain tumors. Curr. Opin. Oncol. 14, 292–298 (2002)

    Article  Google Scholar 

  3. B. Pickett, J. Kurhanewicz, F. Coakley, K. Shinohara, B. Fein, M. Roach, Use of MRI and spectroscopy in evaluation of external beam radiotherapy for prostate cancer. Int. J. Radiat. Oncol. Biol. Phys. 60(4), 1047–1055 (2004)

    Article  Google Scholar 

  4. L. Kwock, J.K. Smith, M. Castillo, M.G. Ewend, F. Collichio, D.E. Morris, T.W. Bouldin, S. Cush, Clinical role of proton magnetic resonance spectroscopy in oncology: brain, breast, and prostate cancer. Lancet Oncol. 7(10), 859–868 (2006)

    Google Scholar 

  5. S.J. Nelson, Magnetic resonance spectroscopic imaging. IEEE Eng. Med. Biol. 23, 30–39 (2004)

    Article  Google Scholar 

  6. D.D. Lee, H.S. Seung, Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)

    Article  Google Scholar 

  7. A.R. Croitor Sava, C.M. Martinez-Bisbal, D.M. Sima, J. Calvar, V. Esteve, B. Celda, U. Himmelreich, S. Van Huffel, Quantifying brain tumor tissue abundance in HR-MAS spectra using non-negative blind source separation techniques. J. Chemom. 26(7), 406–415 (2012)

    Article  Google Scholar 

  8. S. Ortega-Martorell, P.J.G. Lisboa, Julià-Sapé M. Vellido, C. Arús, Nonnegative matrix factorisation methods for the spectral decomposition of MRS data from human brain tumours. BMC Bioinform. 13, 38 (2012)

    Article  Google Scholar 

  9. S. Ortega-Martorell, P.J. Lisboa, A. Vellido, R.V. Simões, M. Pumarola, M. Julià-Sapé, C. Arús, Convex non-negative matrix factorization for brain tumor delimitation from MRSI data. PLoS ONE 7(10), e4 (2012)

    Google Scholar 

  10. P. Sajda, S. Du, T.R. Brown, R. Stoyanova, D.C. Shungu, X. Mao, L.C. Parra, Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain. IEEE Trans. Med. Imaging 23, 1453–1465 (2004)

    Article  Google Scholar 

  11. Y. Li, D.M. Sima, S. Van Cauter, A.R. Croitor Sava, U. Himmelreich, Y. Pi, S. Van Huffel, Hierarchical non-negative matrix factorization (hNMF): a tissue pattern differentiation method for glioblastoma multiforme diagnosis using MRSI. NMR Biomed. 26(3), 307–319 (2013)

    Article  Google Scholar 

  12. Y. Li, D.M. Sima, S. Van Cauter, A.R. Croitor Sava, U. Himmelreich, Y. Pi, Y. Liu, S. Van Huffel, Unsupervised nosologic imaging for glioma diagnosis. IEEE Trans. Biomed. Eng. 60(6), 1760–1763 (2013)

    Article  Google Scholar 

  13. A.R. Croitor Sava, A. Wright, D.M. Sima, T. Laudadio, S. Van Huffel, A. Heerschap, U. Himmelreich, Automatic magnetic resonance spectroscopic imaging segmentation using blind source separation techniques. Lirias number: 421620, in Proceedings ESMRMB 2013, Toulouse, October 2013, pp. 330–331

    Google Scholar 

  14. T. Laudadio, A.R. Croitor Sava, D.M. Sima, A. Wright, A. Heerschap, S. Van Huffel, Hierarchical non-negative matrix factorization applied to in vivo 3T MRSI prostate data for automatic detection and visualization of tumours. Lirias number: 421618, in Proceedings ESMRMB 2013, Toulouse, October 2013, pp. 474–475

    Google Scholar 

  15. G.H. Golub, C.F. Van Loan, Matrix Computations, 4th edn. (The Johns Hopkins University Press, Baltimore, 2013)

    MATH  Google Scholar 

  16. H. Laurberg, M.G. Christensen, M.D. Plumbley, L.K. Hansen, S.H. Jensen, Theorems on positive data: on the uniqueness of NMF. Comput. Intell. Neurosci. 764206 (2008). doi:10.1155/2008/764206

    Google Scholar 

  17. M.W. Berry, M. Browne, A.N. Langville, V.P. Pauca, R.J. Plemmons, Algorithms and applications for approximate nonnegative matrix factorization. Comput. Stat. Data Anal. 52, 155–173 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. M.C. Martínez-Bisbal, L. Martí-Bonmatí, J. Piquer, A. Revert, P. Ferrer, J.L. Llácer, M. Piotto, O. Assemat, B. Celda, \(^{1}\)H and \(^{13}\)C HR-MAS spectroscopy of intact biopsy samples ex vivo and in vivo \(^{1}\)H MRS study of human high grade gliomas. NMR Biomed. 17(4), 191–205 (2004)

    Article  Google Scholar 

  19. A.R. Croitor Sava, M.C. Martinez-Bisbal, S. Van Huffel, J.M. Cerda, D.M. Sima, B. Celda, Ex vivo high resolution magic angle spinning metabolic profiles describe intratumoral histopathological tissue properties in adult human gliomas. Magn. Reson. Med. 65, 320–328 (2011)

    Article  Google Scholar 

  20. H. Kim, H. Park, Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinformatics 23(12), 1495–1502 (2007)

    Article  Google Scholar 

  21. H. Cha, W.K. Ma, C.Y. Chi, Y. Wang, A convex analysis framework for blind separation of non-negative sources. IEEE Trans. Signal Process. 56(10), 5120–5134 (2008)

    Article  MathSciNet  Google Scholar 

  22. M.D. Plumbley, Algorithms for non-negative independent component analysis. IEEE Trans. Neural Netw. 14(3), 534–543 (2003)

    Article  Google Scholar 

  23. R. Meyer, M. Fisher, S. Nelson, T. Brown, Evaluation of manual methods for integration of in vivo phosphorus NMR spectra. NMR Biomed. 1(3), 131–135 (1988)

    Article  Google Scholar 

  24. L.L. Cheng, I.W. Chang, D.N. Louis, R.G. Gonzalez, Correlation of high-resolution magic angle spinning proton magnetic resonance spectroscopy with histopathology of intact human brain tumor specimens. Cancer Res. 58(9), 1825–1832 (1998)

    Google Scholar 

  25. M. Julià-Sapé, D. Acosta, M. Mier, C. Arús, D. Watson, The interpret consortium: a multi-centre, web-accessible and quality control-checked database of in vivo MR spectra of brain tumour patients. Magn. Reson. Mater. Phys. 19, 22–33 (2006)

    Article  Google Scholar 

  26. A.R. Tate, J. Underwood, D.M. Acosta et al., Development of a decision support system for diagnosis and grading of brain tumours using in vivo magnetic resonance single voxel spectra. NMR Biomed. 19(4), 411–434 (2006)

    Article  Google Scholar 

  27. C. Ding, T. Li, M. Jordan, Convex and semi-nonnegative matrix factorizations. IEEE Trans. Pattern Anal. Mach. Intell. 99(1), 5555 (2008)

    Google Scholar 

  28. I.T. Jolliffe, Principal Component Analysis (Springer, New York, 2002)

    MATH  Google Scholar 

  29. K.S. Opstad, C. Ladroue, B.A. Bell, J.R. Griffiths, F.A. Howe, Linear discriminant analysis of brain tumour (1)H MR spectra: a comparison of classification using whole spectra versus metabolite quantification. NMR Biomed. 20(8), 763–770 (2007)

    Article  Google Scholar 

  30. A. Cichocki, R. Zdunek, S. Amari, Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. Lect. Notes Comput. Sci. 4666, 169–176 (2007)

    Article  Google Scholar 

  31. A. Cichocki, A.H. Phan, Fast local algorithms for large scale nonegative matrix and tensor factorizations. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 3, 708–721 (2009)

    Article  Google Scholar 

  32. N. Gillis, Nonnegative matrix factorization complexity, algorithms and applications. Ph.D. thesis, Louvan-La-Neuve (2011)

    Google Scholar 

  33. Y. Li, D.M. Sima, S. Van Cauter, U. Himmelreich, Y. Pi, S. Van Huffel, Simulation study of tissue type differentiation using non-negative matrix factorization, in Proceedings of BIOSIGNALS 2012, International Conference on Bioinspired Systems and Signal Processing, Vilamoura, Algarve, February 2012, pp. 212–217

    Google Scholar 

  34. F.A. Howe, S.J. Barton, S.A. Cudlip, M. Stubbs, D.E. Saunders, J.R. Murphy, K.S. Opstad, V.L. Doyle, M.A. McLean, B.A. Bell, J.R. Griffiths, Metabolic profiles of human brain tumours using quantitative in vivo 1H magnetic resonance spectroscopy. Magn. Reson. Med. 49, 223–232 (2003)

    Article  Google Scholar 

  35. C.L. Lawson, Solving Least-Squares Problems, vol. 23 (Prentice-Hall, Englewood Cliffs, 1974), p. 161

    Google Scholar 

  36. K.M. Selnaes, I.S. Gribbestad, H. Bertilsson, A. Wright, A. Angelsen, A. Heerschap, M.B. Tessem, Spatially matched in vivo and ex vivo MR metabolic profiles of prostate cancer-investigation of a correlation with Gleason score. NMR Biomed. 26(5), 600–606 (2013)

    Article  Google Scholar 

  37. S.W. Provencher, Estimation of metabolite concentrations from localized in vivo proton NMR spectra. Magn. Reson. Med. 30(6), 672–679 (1993)

    Article  Google Scholar 

  38. J.B. Poullet, D.M. Sima, A.W. Simonetti, B. De Neuter, L. Vanhamme, P. Lemmerling, S. Van Huffel, An automated quantitation of short echo time MRS spectra in an open source software environment: AQSES. NMR Biomed. 20(5), 493–504 (2007)

    Article  Google Scholar 

  39. J.B. Poullet, D.M. Sima, S. Van Huffel, MRS signal quantitation: a review of time- and frequency-domain methods. J. Magn. Reson. 195, 134–144 (2008)

    Article  Google Scholar 

  40. N. Gillis, D. Kuang, H. Park, Hierarchical clustering of hyperspectral images using rank-two nonnegative matrix factorization (2013). arXiv preprint arXiv:1310.7441

  41. T. Laudadio, P. Pels, L. De Lathauwer, P. Van Hecke, S. Van Huffel, Tissue segmentation and classification of MRSI data using canonical correlation analysis. Magn. Reson. Med. 54, 1519–1529 (2005)

    Article  Google Scholar 

  42. A.R. Croitor Sava, D.M. Sima, J.B. Poullet, A.J. Wright, A. Heerschap, S. Van Huffel, Exploiting spatial information to estimate metabolite levels in two-dimensional MRSI of heterogeneous brain lesions. NMR Biomed. 24(7), 824–835 (2011)

    Article  Google Scholar 

  43. M. De Vos, T. Laudadio, A.W. Simonetti, A. Heerschap, S. Van Huffel, Fast nosologic imaging of the brain. J. Magn. Reson. 184, 292–301 (2006)

    Article  Google Scholar 

  44. X. Liu, Y. Li, Y. Pi, S. Van Cauter, Y. Yao, J. Wang, A new algorithm for the fusion of MRSI & MRI on the brain tumour diagnosis, in Proceedings ISMRM 2015, Toronto, Ontario, 30 May–5 June 2015

    Google Scholar 

Download references

Acknowledgments

The work of Teresa Laudadio is partly supported by the following projects: PRIN 2012 entitled SMaSIP (Structured matrices in Signal and Image Processing) and Progetto Premiale MIUR 2012 entitled MATHTECH.

The work of Yuqian Li is supported by Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61401068) and by the China Postdoctoral Science Foundation (Grant No. 2014M552341).

The work of Anca Croitor, Nicolas Sauwen, Diana Sima and Sabine Van Huffel is supported by Research Council KUL: GOA/10/09 MaNet, CoE PFV/10/002 (OPTEC); PhD/Postdoc grants. Flemish Government: FWO: projects: G.0427.10N (Integrated EEG-fMRI), G.0108.11 (Compressed Sensing) G.0869.12N (Tumor imaging) G.0A5513N (Deep brain stimulation); PhD/Postdoc grants; IWT: projects: TBM 080658-MRI (EEG-fMRI), TBM 110697-NeoGuard; PhD/Postdoc grants; iMinds Medical Information Technologies SBO 2014, ICON: NXT_Sleep; Flanders Care: Demonstratieproject Tele-Rehab III (2012–2014). Belgian Federal Science Policy Office: IUAP P7/19/(DYSCO, ‘Dynamical systems, control and optimization’, 2012–2017). Belgian Foreign Affairs-Development Cooperation: VLIR UOS programmes. EU: The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Advanced Grant: BIOTENSORS (no. 339804). This paper reflects only the authors’ views and the Union is not liable for any use that may be made of the contained information. Other EU funding: RECAP 209G within INTERREG IVB NWE programme, EU MC ITN TRANSACT 2012 (no. 316679), ERASMUS EQR: Community service engineer (no. 539642-LLP-1-2013).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. Laudadio .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Laudadio, T., Sava, A.R.C., Li, Y., Sauwen, N., Sima, D.M., Van Huffel, S. (2016). NMF in MR Spectroscopy. In: Naik, G. (eds) Non-negative Matrix Factorization Techniques. Signals and Communication Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48331-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-48331-2_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48330-5

  • Online ISBN: 978-3-662-48331-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics