Skip to main content
SpringerLink
Log in

Compartmental Modeling in PET Kinetics

  • Chapter
  • First Online:
Basic Science of PET Imaging

Abstract

In this chapter, we explain how positron emission tomography (PET) data are analyzed to estimate behavior of radiotracer injected. For this purpose, compartmental model and its kinetic parameters are introduced, and concept, mathematical basis, and biological interpretation of the compartmental model and the kinetic parameters are described. General form of the compartmental model is brought for comprehensive understanding of the model. Several approaches for fast estimation of the kinetic parameters are introduced based on general compartmental model. The input function for the compartmental model is important for quantitative analysis of PET data, and the reference region model is one approach to avoid acquisition of the input function.

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 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
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

Notes

  1. 1.

    1 We can also calculate the molar mass if we know the specific activity [GBq/nmol] of the tracer at the injection time.

  2. 2.

    2 It is sometimes called Gjedde-Patlak plot named after two authors describing this approach.

  3. 3.

    3 If the region is in three-dimensional volume, it is called volume of interest (VOI).

References

  1. Wagner CC, Langer O. Approaches using molecular imaging technology use of PET in clinical microdose studies. Adv Drug Deliv Rev. 2011;63:539–46.

    Article  CAS  PubMed  Google Scholar 

  2. Keyes JW. SUV: standard uptake or silly useless value? J Nucl Med. 1995;36:1836–9.

    PubMed  Google Scholar 

  3. Watabe H, Ikoma Y, Kimura Y, Naganawa M, Shidahara M. Pet kinetic analysis–compartmental model. Ann Nucl Med. 2006;20:583–9.

    Article  CAS  PubMed  Google Scholar 

  4. Innis RB, Cunningham VJ, Delforge J, Fujita M, Gjedde A, Gunn RN, Holden J, Houle S, Huang SC, Ichise M, Iida H, Ito H, Kimura Y, Koeppe RA, Knudsen GM, Knuuti J, Lammertsma AA, Laruelle M, Logan J, Maguire RP, Mintun MA, Morris ED, Parsey R, Price JC, Slifstein M, Sossi V, Suhara T, Votaw JR, Wong DF, Carson RE. Consensus nomenclature for in vivo imaging of reversibly binding radioligands. J Cereb Blood Flow Metab. 2007;27:1533–9.

    Article  CAS  PubMed  Google Scholar 

  5. Watabe H, Channing M, Der M, Adams H, Jagoda E, Herscovitch P, Eckelman W, Carson R. Kinetic analysis of the 5-HT2A ligand [11C]MDL 100,907. J Cereb Blood Flow Metab. 2000;20:899–909.

    Article  CAS  PubMed  Google Scholar 

  6. Gunn R, Gunn S, Cunningham V. Positron emission tomography compartmental models. J Cereb Blood Flow Metab. 2001;21:635–52.

    Article  CAS  PubMed  Google Scholar 

  7. Marquardt DW. An algorithm for least-squares estimation of nonlinear parameters. J Soc Indust Appl Math. 1963;11:431–41.

    Article  Google Scholar 

  8. Nelder JA, Mead R. A simplex method for function minimization. Comput J. 1965;7:308–13.

    Article  Google Scholar 

  9. Logan J, Fowler J, Volkow N, Ding Y, Wang G, Alexoff D. A strategy for removing the bias in the graphical analysis method. J Cereb Blood Flow Metab. 2001;21:307–20.

    Article  CAS  PubMed  Google Scholar 

  10. Watabe H, Endres C, Breier A, Schmall B, Eckelman W, Carson R. Measurement of dopamine release with continuous infusion of [11C]raclopride: optimization and signal-to-noise considerations. J Nucl Med. 2000;41:522–30.

    CAS  PubMed  Google Scholar 

  11. Landaw EM, DiStefano JJ. Multiexponential, multicompartmental, and noncompartmental modeling. II data analysis and statistical considerations. Am J Physiol. 1984;246:R665–77.

    CAS  PubMed  Google Scholar 

  12. Carson R, Kiesewetter D, Jagoda E, Der M, Herscovitch P, Eckelman W. Muscarinic cholinergic receptor measurements with [18f]fp-tztp: control and competition studies. J Cereb Blood Flow Metab. 1998;18:1130–42.

    Article  CAS  PubMed  Google Scholar 

  13. Jvd H, Burchert W, Müller-Schauenburg W, Meyer G, Hundeshagen H. Accurate local blood flow measurements with dynamic PET: fast determination of input function delay and dispersion by multilinear minimization. J Nucl Med. 1993;34:1770–7.

    Google Scholar 

  14. Raichle ME, Martin WR, Herscovitch P, Mintun MA, Markham J. Brain blood flow measured with intravenous H2(15)O. II. implementation and validation. J Nucl Med : Off Publ, Soc Nucl Med. 1983;24:790–8.

    CAS  Google Scholar 

  15. Logan J, Fowler J, Volkow N, Wolf A, Dewey S, Schlyer D, MacGregor R, Hitzemann R, Bendriem B, Gatley S. Graphical analysis of reversible radioligand binding from time-activity measurements applied to [N-11C-methyl]-(−)-cocaine PET studies in human subjects. J Cereb Blood Flow Metab. 1990;10:740–7.

    Article  CAS  PubMed  Google Scholar 

  16. Ichise M, Toyama H, Innis R, Carson R. Strategies to improve neuroreceptor parameter estimation by linear regression analysis. J Cereb Blood Flow Metab. 2002;22:1271–81.

    Article  PubMed  Google Scholar 

  17. Kimura Y, Naganawa M, Shidahara M, Ikoma Y, Watabe H. PET kinetic analysis pitfalls and a solution for the logan plot. Ann Nucl Med. 2007;21:1–8.

    Article  PubMed  Google Scholar 

  18. Varga J, Szabo Z. Modified regression model for the Logan plot. J Cereb Blood Flow Metab. 2002;22:240–4.

    Article  PubMed  PubMed Central  Google Scholar 

  19. Gjedde A. Calculation of cerebral glucose phosphorylation from brain uptake of glucose analogs in vivo: a re-examination. Brain Res. 1982;257:237–74.

    Article  CAS  PubMed  Google Scholar 

  20. Patlak C, Blasberg R, Fenstermacher J. Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. J Cereb Blood Flow Metab. 1983;3:1–7.

    Article  CAS  PubMed  Google Scholar 

  21. Cunningham V, Jones T. Spectral analysis of dynamic PET studies. J Cereb Blood Flow Metab. 1993;13:15–23.

    Article  CAS  PubMed  Google Scholar 

  22. Turkheimer F, Sokoloff L, Bertoldo A, Lucignani G, Reivich M, Jaggi JL, Schmidt K. Estimation of component and parameter distributions in spectral analysis. J Cereb Blood Flow Metab. 1998;18:1211–22.

    Article  CAS  PubMed  Google Scholar 

  23. Renkin EM. Transport of potassium-42 from blood to tissue in isolated mammalian skeletal muscles. Am J Physiol. 1959;197:1205–10.

    CAS  PubMed  Google Scholar 

  24. Crone C. The permeability of capillaries in various organs as determined by use of the ‘indicator diffusion’ method. Acta Physiol Scand. 1963;58:292–305.

    Article  CAS  PubMed  Google Scholar 

  25. Matsubara K, Watabe H, Kumakura Y, Hayashi T, Endres CJ, Minato K, Iida H. Sensitivity of kinetic macro-parameters to changes in dopamine synthesis, storage and metabolism: a simulation study for [(18)F]FDOPA PET by a model with detailed dopamine pathway. Synapse. 2011;65:751–62.

    Article  CAS  PubMed  Google Scholar 

  26. Mintun M, Raichle M, Martin W, Herscovitch P. Brain oxygen utilization measured with O-15 radiotracers and positron emission tomography. J Nucl Med. 1984;25:177–87.

    CAS  PubMed  Google Scholar 

  27. Kudomi N, Hayashi T, Watabe H, Teramoto N, Piao R, Ose T, Koshino K, Ohta Y, Iida H. A physiological model for recirculation water correction in CMRO2 assessment with 15O2 inhalation PET. J Cereb Blood Flow Metab. 2009;29:355–64.

    Article  PubMed  Google Scholar 

  28. Frackowiak RS, Lenzi GL, Jones T, Heather JD. Quantitative measurement of regional cerebral blood flow and oxygen metabolism in man using 15O and positron emission tomography: theory, procedure, and normal values. J Comput Assist Tomogr. 1980;4:727–36.

    Article  CAS  PubMed  Google Scholar 

  29. Schain M, Varnäs K, Cselényi Z, Halldin C, Farde L, Varrone A. Evaluation of two automated methods for PET region of interest analysis. Neuroinformatics. 2014;12:551–62.

    Article  PubMed  Google Scholar 

  30. Erlandsson K, Buvat I, Pretorius PH, Thomas BA, Hutton BF. A review of partial volume correction techniques for emission tomography and their applications in neurology, cardiology and oncology. Phys Med Biol. 2012;57:R119–59.

    Article  PubMed  Google Scholar 

  31. Kudomi N, Slimani L, Järvisalo M, Kiss J, Lautamäki R, Naum G, Savunen T, Knuuti J, Iida H, Nuutila P, Iozzo P. Non-invasive estimation of hepatic blood perfusion from H(2)(15)O PET images using tissue-derived arterial and portal input functions. Eur J Nucl Med Mol Imaging. 2008;35:1899–911.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Feng D, Wong KP, Wu CM, Siu WC. A technique for extracting physiological parameters and the required input function simultaneously from pet image measurements: theory and simulation study. IEEE Trans Inf Technol Biomed. 1997;1:243–54.

    Article  CAS  PubMed  Google Scholar 

  33. Kanno I, Iida H, Miura S, Murakami M, Takahashi K, Sasaki H, Inugami A, Shishido F, Uemura K. A system for cerebral blood flow measurement using an H215O autoradiographic method and positron emission tomography. J Cereb Blood Flow Metab. 1987;7:143–53.

    Article  CAS  PubMed  Google Scholar 

  34. Kudomi N, Choi E, Yamamoto S, Watabe H, Kim K, Shidahara M, Ogawa M, Teramoto N, Sakamoto E, Iida H. Development of a GSO detector assembly for a continuous blood sampling system. IEEE Trans Nucl Sci. 2003;50:70–3.

    Article  CAS  Google Scholar 

  35. Iida H, Kanno I, Miura S, Murakami M, Takahashi K, Uemura K. Error analysis of a quantitative cerebral blood flow measurement using H2(15)O autoradiography and positron emission tomography, with respect to the dispersion of the input function. J Cereb Blood Flow Metab. 1986;6:536–45.

    Article  CAS  PubMed  Google Scholar 

  36. Meyer E. Simultaneous correction for tracer arrival delay and dispersion in CBF measurements by the H215O autoradiographic method and dynamic PET. J Nucl Med. 1989;30:1069–78.

    CAS  PubMed  Google Scholar 

  37. Weinberg IN, Huang SC, Hoffman EJ, Araujo L, Nienaber C, Grover-McKay M, Dahlbom M, Schelbert H. Validation of PET-acquired input functions for cardiac studies. J Nucl Med. 1988;29:241–7.

    CAS  PubMed  Google Scholar 

  38. Watabe H, Channing M, Riddell C, Jousse F, Libutti S, Carrasquillo J, Bacharach S, Carson R. Noninvasive estimation of the aorta input function for measurement of tumor blood flow with [15o]water. IEEE Trans Med Imaging. 2001;20:164–74.

    Article  CAS  PubMed  Google Scholar 

  39. Lyoo CH, Zanotti-Fregonara P, Zoghbi SS, Liow JS, Xu R, Pike VW, Zarate CA, Fujita M, Innis RB. Image-derived input function derived from a supervised clustering algorithm: methodology and validation in a clinical protocol using [11C](R)-rolipram. PLoS One. 2014;9:e89101.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Ahn J, Lee D, Lee J, Kim S, Cheon G, Yeo J, Shin S, Chung J, Lee M. Quantification of regional myocardial blood flow using dynamic H2(15)O pet and factor analysis. J Nucl Med. 2001;42:782–7.

    CAS  PubMed  Google Scholar 

  41. Lee J, Lee D, Ahn J, Cheon G, Kim S, Yeo J, Seo K, Park K, Chung J, Lee M. Blind separation of cardiac components and extraction of input function from h(2)(15)o dynamic myocardial pet using independent component analysis. J Nucl Med. 2001;42:938–43.

    CAS  PubMed  Google Scholar 

  42. Naganawa M, Kimura Y, Ishii K, Oda K, Ishiwata K, Matani A. Extraction of a plasma time-activity curve from dynamic brain PET images based on independent component analysis. IEEE Trans Biomed Eng. 2005;52:201–10.

    Article  PubMed  Google Scholar 

  43. Suk H, Lee JS, Li JH, Yang YW, Liu RS, Chen JC. Partial volume correction of the microPET blood input function using ensemble learning independent component analysis. Phys Med Biol. 2009;54:1823–46.

    Article  Google Scholar 

  44. Iida H, Rhodes C, Rd S, Araujo L, Bloomfield P, Lammertsma A, Jones T. Use of the left ventricular time-activity curve as a noninvasive input function in dynamic oxygen-15-water positron emission tomography. J Nucl Med. 1992;33:1669–77.

    CAS  PubMed  Google Scholar 

  45. Watabe H, Jino H, Kawachi N, Teramoto N, Hayashi T, Ohta Y, Iida H. Parametric imaging of myocardial blood flow with 15O-water and PET using the basis function method. J Nucl Med. 2005;46:1219–24.

    PubMed  Google Scholar 

  46. Eberl S, Anayat A, Fulton R, Hooper P, Fulham M. Evaluation of two population-based input functions for quantitative neurological FDG PET studies. Eur J Nucl Med. 1997;24:299–304.

    CAS  PubMed  Google Scholar 

  47. Zanotti-Fregonara P, Hines CS, Zoghbi SS, Liow JS, Zhang Y, Pike VW, Drevets WC, Mallinger AG, Zarate CA, Fujita M, Innis RB. Population-based input function and image-derived input function for [11C](R)-rolipram PET imaging: methodology, validation and application to the study of major depressive disorder. Neuroimage. 2012;63:1532–41.

    Article  PubMed  PubMed Central  Google Scholar 

  48. Watabe T, Shimosegawa E, Watabe H, Kanai Y, Hanaoka K, Ueguchi T, Isohashi K, Kato H, Tatsumi M, Hatazawa J. Quantitative evaluation of cerebral blood flow and oxygen metabolism in normal anesthetized rats: 15O-labeled gas inhalation PET with MRI fusion. J Nucl Med. 2013;54:283–90.

    Article  CAS  PubMed  Google Scholar 

  49. Carson R, Channing M, Blasberg R, Dunn B, Cohen R, Rice K, Herscovitch P. Comparison of bolus and infusion methods for receptor quantitation: application to [18F]cyclofoxy and positron emission tomography. J Cereb Blood Flow Metab. 1993;13:24–42.

    Article  CAS  PubMed  Google Scholar 

  50. Endres C, Kolachana B, Saunders R, Su T, Weinberger D, Breier A, Eckelman W, Carson R. Kinetic modeling of [11C]raclopride: combined PET-microdialysis studies. J Cereb Blood Flow Metab. 1997;17:932–42.

    Article  CAS  PubMed  Google Scholar 

  51. Lammertsma A, Bench C, Hume S, Osman S, Gunn K, Brooks D, Frackowiak R. Comparison of methods for analysis of clinical [11C]raclopride studies. J Cereb Blood Flow Metab. 1996;16:42–52.

    Article  CAS  PubMed  Google Scholar 

  52. Lammertsma A, Hume S. Simplified reference tissue model for pet receptor studies. Neuroimage. 1996;4:153–8.

    Article  CAS  PubMed  Google Scholar 

  53. Wu Y, Carson RE. Noise reduction in the simplified reference tissue model for neuroreceptor functional imaging. J Cereb Blood Flow Metab. 2002;22:1440–52.

    Article  PubMed  Google Scholar 

  54. Gunn R, Lammertsma A, Hume S, Cunningham V. Parametric imaging of ligand-receptor binding in PET using a simplified reference region model. Neuroimage. 1997;6:279–87.

    Article  CAS  PubMed  Google Scholar 

  55. Ichise M, Liow JS, Lu JQ, Takano A, Model K, Toyama H, Suhara T, Suzuki K, Innis RB, Carson RE. Linearized reference tissue parametric imaging methods: application to [11C]DASB positron emission tomography studies of the serotonin transporter in human brain. J Cereb Blood Flow Metab. 2003;23:1096–112.

    Article  PubMed  Google Scholar 

  56. Watabe H, Itoh M, Cunningham V, Lammertsma A, Bloomfield P, Mejia M, Fujiwara T, Jones A, Jones T, Nakamura T. Noninvasive quantification of rcbf using positron emission tomography. J Cereb Blood Flow Metab. 1996;16:311–9.

    Article  CAS  PubMed  Google Scholar 

  57. Logan J, Fowler J, Volkow N, Wang G, Ding Y, Alexoff D. Distribution volume ratios without blood sampling from graphical analysis of PET data. J Cereb Blood Flow Metab. 1996;16:834–40.

    Article  CAS  PubMed  Google Scholar 

  58. Folkersma H, Boellaard R, Vandertop WP, Kloet RW, Lubberink M, Lammertsma AA, Berckel BNM. Reference tissue models and blood–brain barrier disruption: lessons from (R)-[11C]PK11195 in traumatic brain injury. J Nucl Med Off Publ Soc Nucl Med. 2009;50:1975–9.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Radiation Protection and Safety Control, Cyclotron and Radioisotope Center, Tohoku University, 6-3 Aoba, Aramaki, Aoba, Sendai, 980-8578, Japan

    Hiroshi Watabe PhD

Authors
  1. Hiroshi Watabe PhD
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hiroshi Watabe PhD .

Editor information

Editors and Affiliations

  1. Medical Biophysics Department of Physics Faculty of Science, Helwan University, Cairo, Egypt

    Magdy M. Khalil

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Watabe, H. (2017). Compartmental Modeling in PET Kinetics. In: Khalil, M. (eds) Basic Science of PET Imaging. Springer, Cham. https://doi.org/10.1007/978-3-319-40070-9_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40070-9_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40068-6

  • Online ISBN: 978-3-319-40070-9

  • eBook Packages: MedicineMedicine (R0)

Publish with us

Policies and ethics

Search

Navigation