Skip to main content

Advertisement

SpringerLink
Log in

An expectation-maximisation approach for simultaneous pixel classification and tracer kinetic modelling in dynamic contrast enhanced-magnetic resonance imaging

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

Traditionally, tracer kinetic modelling and pixel classification of DCE-MRI studies are accomplished separately, although they could greatly benefit from each other. In this article, we propose an expectation-maximisation scheme for simultaneous pixel classification and compartmental modelling of DCE-MRI studies. The key point in the proposed scheme is the estimation of the kinetic parameters (K trans and K ep) of the two-compartmental model. Typically, they are estimated via nonlinear least-squares fitting. In our scheme, by exploiting the iterative nature of the EM algorithm, we use instead a Taylor expansion of the modelling equation. We developed the theoretical framework for the particular case of two classes and evaluated the performances of the algorithm by means of simulations. Results indicate that the accuracy of the proposed method supersedes the traditional pixel-by-pixel scheme and approaches the theoretical lower bound imposed by the Cramer–Rao theorem. Preliminary results on real data were also reported.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Ahearn TS, Staff RT, Redpath TW, Semple SIK (2005) The use of the Levenberg–Marquardt curve-fitting algorithm in pharmacokinetic modelling of DCE-MRI data. Phys Med Biol 50:N85–N92

    Article  PubMed  CAS  Google Scholar 

  2. Beets R, Beets G (2004) Rectal cancer: review with emphasis on MR imaging. Radiology 232:335–346

    Article  PubMed  Google Scholar 

  3. Brix G, Semmler W, Port R (1991) Phrmacokinetic parameters in CNS Gd-DTPA enhanced MR imaging. J Comput Assist Tomogr 15:621–628

    Article  PubMed  CAS  Google Scholar 

  4. Cheng M (2008) Investigation and optimization of parameters accuracy in dynamic contrast-enhanced MRI. J Reson Imaging 28:736–743

    Article  Google Scholar 

  5. Choyke PL, Dwyer AJ, Knopp MV (2003) Functional tumor imaging with dynamic contrast-enhanced magnetic resonance imaging. J Magn Reson Imaging 17:509–52

    Article  PubMed  Google Scholar 

  6. Collins J, Padhani R (2004) Dynamic magnetic resonance imaging of tumor perfusion. IEEE Eng Med Biol Mag September/October:65–83

  7. De Lussanet QG, Backes WH, Griffioen AW, Padhani AR, Baeten CI, Van Baardwijk A, Lambin P, Beets GL, Van Engelshoven JMA, Beets-Tan RGH (2005) Dynamic contrast-enhanced magnetic resonance imaging of radiation therapy-induced microcirculation changes in rectal cancer. Int J Radiat Oncol Biol Phys 63(5):1309–1315

    Article  PubMed  Google Scholar 

  8. Dempster A, Laird N, Rubin D (1997) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc 39:1–38

    Google Scholar 

  9. Gong Y, Brady M (2008) Texture-based simultaneous registration and segmentation of breast DCE-MRI. LNCS 5116:174–180

    Google Scholar 

  10. Guo Y, Sivaramakrishna R, Lu CC, Suri JS, Laxminarayan S (2006) Breast image registration techniques: a survey. Med Biol Eng Comput 44(1):15–25

    Article  PubMed  Google Scholar 

  11. Jackson A, O’Connor JPB, Parker GJM, Jayson GC (2007) Imaging tumor vascular heterogeneity and angiogenesis using dynamic contrast-enhanced magnetic resonance imaging. Clin Cancer Res 13(12):3449–3459

    Article  PubMed  Google Scholar 

  12. Kelm BM, Menze BH, Nix O, Zechmann CM, Hamprecht FA (2009) Estimating kinetic parameter maps from dynamic contrast-enhanced MRI using spatial prior knowledge. IEEE Trans Med Imaging 10(28):1534–1546

    Article  Google Scholar 

  13. Koh T, Hou Z (2002) A numerical method for estimating blood flow by dynamic functional imaging. Med Eng Phys 24:151–158

    Article  PubMed  CAS  Google Scholar 

  14. Kuhl CK, Schild HH (2000) Dynamic image interpretation of MRI of the breast. J Magn Reson Imaging 12:965–974

    Article  PubMed  CAS  Google Scholar 

  15. Lavini C, de Jonge MC, van de Sande MGH, Tak P, Nederveen J, Maas M (2007) Pixel-by-pixel analysis of DCE MRI curve patterns and an illustration of its application to the imaging of the musculoskeletal system. Mag Reson Imaging 25:604–612

    Article  Google Scholar 

  16. Lawrence S, Lee K (1998) An adiabatic approximation to the tissue homogeneity model for water exchange in the brain. Theoretical derivation. J Cereb Blood Flow Metab 18:1365–1377

    Article  Google Scholar 

  17. Leach MO, Brindle KM, Evelhoch JL, Griffiths JR, Horsman MR, Jackson A, Jayson G, Judson IR, Knopp MV, Maxwell RJ, Mcintyre D, Padhani AR, Price P, Rathbone R, Rustin G, Tofts PS, Tozer GM, Vennart W, Waterton JC, Williams SR, Workman P (2003) Assessment of antiangiogenic and antivascular therapeutics using MRI: recommendations for appropriate methodology for clinical trials. Br J Radiol 76:S87–S91

    Article  PubMed  Google Scholar 

  18. Rijpkema M, Kaanders JHAM, Joosten FBM, van der Kogel AJ, Heerschap A (2001) Method for quantitative mapping of dynamic MRI contrast agent uptake in human tumors. J Magn Reson Imaging 14:457–463

    Article  PubMed  CAS  Google Scholar 

  19. Schmid VJ, Whitcher B, Padhani AR, Taylor NJ, Yang GZ (2006) Bayesian methods for pharmacokinetic models in dynamic contrast-enhanced magnetic resonance imaging. IEEE Trans Med Imaging 25(12):1627–1636

    Article  PubMed  Google Scholar 

  20. Seber GAF, Wild CJ (2003) Nonlinear regression. Wiley Interscience/Wiley, Hoboken/New Jersey

    Google Scholar 

  21. Simpson NE, He Z, Evelhoch JL (1999) Deuterium NMR tissue perfusion measurements using the tracer uptake approach: I. Optimization of methods. Magn Reson Med 42:42–52

    Article  PubMed  CAS  Google Scholar 

  22. Su MY, Cheung YC, Fruehauf JP, Yu H, Nalcioglu O, Mechetner E, Kyshtoobayeva A, Chen SC, Hsueh S, McLaren CE, Wan YL (2003) Correlation of dynamic contrast enhancement MRI parameters with microvessel density and VEGF for assessment of angiogenesis in breast cancer. J Magn Reson Imaging 18:467–477

    Article  PubMed  Google Scholar 

  23. Tofts PS (1997) Modeling tracer kinetics in dynamic Gd-DTPA MR imaging. J Magn Reson Imaging 7:91–101

    Article  PubMed  CAS  Google Scholar 

  24. Varini C, Degenhard A, Nattkemper TW (2006) Visual exploratory analysis of DCE-MRI data in breast cancer by dimensional data reduction: a comparative study. Biomed Signal Process Control 1:56–63

    Article  Google Scholar 

  25. Walker-Samuel S, Leach MO, Collins DJ (2006) Evaluation of response to treatment using DCE-MRI: the relationship between initial area under the gadolinium curve (IAUGC) and quantitative pharmacokinetic analysis. Phys Med Biol 51:3593–3602

    Article  PubMed  CAS  Google Scholar 

  26. Xiaohua C, Brady M, Lok-Chuen J, Moore N (2008) Simultaneous segmentation and registration of contrast-enhanced breast MRI. LNCS 3565:126–137

    Google Scholar 

  27. Yang C, Karczmar GS, Medved M, Stadler WM (2004) Estimating the arterial input function using two reference tissues in dynamic contrast-enhanced MRI studies: fundamental concepts and simulations. Magn Reson Med 52:1110–1117

    Article  PubMed  Google Scholar 

  28. Yankeelova TE, Lucia J, Lepagea M, Lib R, Debuskd L, Lind PC, Pricea R, Gorea JC (2005) Quantitative pharmacokinetic analysis of DCE-MRI data without an arterial input function: a reference region model. Magn Reson Imaging 23:519–529

    Article  Google Scholar 

  29. Zhang Y, Brady M, Smith S (2001) Segmentation of brain MR images through a hidden markov random field model and the expectation maximisation algorithm. IEEE Trans Med Imaging 20:45–57

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the editor and the anonymous reviewers whose constructive comments immensely improved the article.

Author information

Authors and Affiliations

  1. Department of Biomedical, Electronic and Telecommunication Engineering, University ‘Federico II’ of Naples, via Claudio, 21, 80131, Naples, Italy

    Mario Sansone, Roberta Fusco & Marcello Bracale

  2. First Department of Radiology, National Cancer Institute “Fondazione G. Pascale”, Naples, Italy

    Roberta Fusco & Antonella Petrillo

  3. SUN, Diagnostic Imaging, Naples, Italy

    Mario Petrillo

Authors
  1. Mario Sansone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberta Fusco
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antonella Petrillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mario Petrillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Marcello Bracale
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Sansone.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sansone, M., Fusco, R., Petrillo, A. et al. An expectation-maximisation approach for simultaneous pixel classification and tracer kinetic modelling in dynamic contrast enhanced-magnetic resonance imaging. Med Biol Eng Comput 49, 485–495 (2011). https://doi.org/10.1007/s11517-010-0695-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-010-0695-x

Keywords

Search

Navigation