Skip to main content
SpringerLink
Log in

Continuous Time Dynamic PET Imaging Using List Mode Data

  • Conference paper
  • First Online:
Information Processing in Medical Imaging (IPMI 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1613))

Abstract

We describe a method for computing a continuous time estimate of dynamic changes in tracer density using list mode PET data. The tracer density in each voxel is modeled as an inhomogeneous Poisson process whose rate function can be represented using a cubic B-spline basis. An estimate of these rate functions is obtained by maximizing the likelihood of the arrival times of each detected photon pair over the control vertices of the spline. By resorting the list mode data into a standard sinogram plus a “timogram” that retains the arrival times of each of the events, we are able to perform efficient computation that exploits the symmetry inherent in the ordered sinogram. The maximum likelihood estimator uses quadratic temporal and spatial smoothness penalties and an additional penalty term to enforce non-negativity. Corrections for scatter and randoms are described and the results of studies using simulated and human data are included.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barrett, H.H., White, T., Parra, L.C.: List-mode likelihood. Journal of the Optical Society of America, 14 (1997) 2914–2923

    Article  Google Scholar 

  2. Bartels, R.H., Beatty, J.C., Barsky, B.A.: An introduction to splines for use in computer graphics and geometric modeling. M. Kaufmann Publishers, Los Altos, CA (1986)

    Google Scholar 

  3. de Boor, C.: A Practical Guide to Splines. Vol. 27 of Applied Mathematical Sciences. Springer-Verlag, New York (1978)

    MATH  Google Scholar 

  4. Fessler, J.A.: Penalized weighted least-squares image reconstruction for PET. IEEE Transactions on Medical Imaging 13 (1994) 290–300

    Article  Google Scholar 

  5. Geman, S., McClure, D.E.: Statistical methods for tomographic image reconstruction. In Proceedings of The 46th Session of The ISI, Bulletin of The ISI 52 (1987)

    Google Scholar 

  6. Gu, C., Qiu, C.: Smoothing spline density estimation: Theory. The Annals of Statistics 21 (1993) 217–234

    Article  MATH  MathSciNet  Google Scholar 

  7. Herscovitch, P., Markham, J., Raichle, M.E.: Brain blood flow measured with intravenious H2 15O. I. Theory and error analysis. Journal of Nuclear Medicine 24 (1983) 782–789

    Google Scholar 

  8. Huang, S.C., Phelps, M.E.: Principles of Tracer Kinetic Modeling in Posistron Emission Tomography and Autoradiography. In: Positron Emission Tomography and Autoradiography. Principles and Applications for the Brain and Heart. Raven Press, New York (1986)

    Google Scholar 

  9. Huffman, D.A.: A method for the construction of minimum-redundancy codes. Proceedings of the Institute of Radio Engineers 40 (1952) 1098–1101

    Google Scholar 

  10. Johnson, C., Yan, Y., Carson, R., Martino, R., Daube-Witherspoon, M.: A system for the 3D reconstruction of retracted-septa PET data using the EM algorithm. IEEE Transactions on Nuclear Science 42 (1995) 1223–1227

    Google Scholar 

  11. Kaufman, L.: Maximum likelihood, least squares, and penalized least squares for PET. IEEE Transactions on Medical Imaging 12 (1993) 200–214

    Article  Google Scholar 

  12. Lee, S.-J., Rangarajan, A., Gindi, G.: Bayesian image reconstruction in SPECT using higher order mechanical models as priors. IEEE Transactions on Medical Imaging 14 (1995) 669–680

    Article  Google Scholar 

  13. Luenberger, D.: Linear and nonlinear programming. Addison-Wesley, Reading, Mass (1989)

    Google Scholar 

  14. Matthews, J., Bailey, D., Price, P., Cunningham, V.: The direct calculation of parametric images from dynamic PET data using maximum-likelihood iterative reconstruction. Physics in Medicine and Biology 42 (1997) 1155–1173

    Article  Google Scholar 

  15. Mumcuoglu, E.U., Leahy, R., Cherry, S.R., Zhou, Z.: Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images. IEEE Transactions on Medical Imaging 13 (1994) 687–701

    Article  Google Scholar 

  16. Ollinger, J.M.: Algorithms for parameter estimation in dynamic tracer studies using postiron emission tomography. PhD thesis, Washington University School of Medicine, St. Louis, MO (1986)

    Google Scholar 

  17. O’Sullivan, F. Image radiotracer model parameters in PET: A mixture analysis approach. IEEE Transactions on Medical Imaging 12 (1993) 399–412

    Article  Google Scholar 

  18. Parra, L., Barrett, H.H.: List-mode likelihood: EM algorithm and image quality estimation demonstrated on 2D PET. IEEE Transactions on Medical Imaging 17 (1998) 228–235

    Article  Google Scholar 

  19. Qi, J., Leahy, R.M., Cherry, S.R., Chatziioannou, A., Farquhar, T.H.: High resolution 3D bayesian image reconstruction using the microPET small animal scanner. Physics in Medicine and Biology 43 (1998) 1001–1013

    Article  Google Scholar 

  20. Qi, J., Leahy, R.M., Hsu, C., Farquhar, T.H., Cherry, S.R.: Fully 3D Bayesian image reconstruction for ECAT EXACT HR+. IEEE Transactions on Nuclear Science 45 (1998) 1096–1103

    Article  Google Scholar 

  21. Snyder, D.: Parameter estimation for dynamic studies in emission-tomography systems having list-mode data. IEEE Transactions on Nuclear Science 31 (1984) 925–931

    Article  Google Scholar 

  22. Snyder, D., Miller, M.: Random Point processes in time and space, 2nd edition. Springer-Verlag, New York (1991)

    MATH  Google Scholar 

  23. Snyder, D.L.: Utilizing side information in emission tomography. IEEE Transactions on Nuclear Science 31 (1984) 533–537

    Article  Google Scholar 

  24. Wahba, G.: Interpolating spline methods for density estimation. I: Equi-spaced knots. The Annals of Statistics 3 (1975) 30–48

    Article  MATH  MathSciNet  Google Scholar 

  25. Watson, C.C., Newport, D., Casey, M.E., deKemp, R.A., Beanlands, R.S., Schmand, M.: Evaluation of simulation based scatter correction for 3D PET cardiac imaging. IEEE Transactions on Nuclear Science 44 (1997) 90–97

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213-3890, USA

    Thomas E. Nichols

  2. Signal & Image Processing Institute, University of Southern California, Los Angeles, CA, 90089-2564, USA

    Jinyi Qi & Richard M. Leahy

Authors
  1. Thomas E. Nichols
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinyi Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Richard M. Leahy
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Applied Informatics, József Attila University, Árpád tér 2., H-6720, Szeged, Hungary

    Attila Kuba

  2. Institute of Nuclear Medicine, Charles University of Prague, Salmovska 3, CZ-120 00, Prague, Czech Republic

    Martin Šáamal

  3. Department of Medical Physics, University College London, Gower Street, London, WC1E 6BT, UK

    Andrew Todd-Pokropek

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nichols, T.E., Qi, J., Leahy, R.M. (1999). Continuous Time Dynamic PET Imaging Using List Mode Data. In: Kuba, A., Šáamal, M., Todd-Pokropek, A. (eds) Information Processing in Medical Imaging. IPMI 1999. Lecture Notes in Computer Science, vol 1613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48714-X_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-48714-X_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66167-2

  • Online ISBN: 978-3-540-48714-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation