Annals of Nuclear Medicine

, Volume 22, Issue 1, pp 1–11 | Cite as

PET kinetic analysis: error consideration of quantitative analysis in dynamic studies

  • Yoko IkomaEmail author
  • Hiroshi Watabe
  • Miho Shidahara
  • Mika Naganawa
  • Yuichi Kimura
Review Article


Positron emission tomography dynamic studies have been performed to quantify several biomedical functions. In a quantitative analysis of these studies, kinetic parameters were estimated by mathematical methods, such as a nonlinear least-squares algorithm with compartmental model and graphical analysis. In this estimation, the uncertainty in the estimated kinetic parameters depends on the signal-to-noise ratio and quantitative analysis method. This review describes the reliability of parameter estimates for various analysis methods in reversible and irreversible models.


PET Compartmental model Error analysis 


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  1. 1.
    Kety SS. The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol Rev 1951;3:1–41.PubMedGoogle Scholar
  2. 2.
    Reivich M, Kuhl D, Wolf A, Greenberg J, Phelps M, Ido T, et al. The [18F]fluorodeoxyglucose method for the measurement of local cerebral glucose utilization in man. Circ Res 1979;44:127–137.PubMedGoogle Scholar
  3. 3.
    Mintun MA, Raichle ME, Kilbourn MR, Wooten GF, Welch MJ. A quantitative model for the in vivo assessment of drug binding sites with positron emission tomography. Ann Neurol 1984;15:217–227.PubMedCrossRefGoogle Scholar
  4. 4.
    Watabe H, Ikoma Y, Kimura Y, Naganawa M, Shidahara M. PET kinetic analysis: compartmental model. Ann Nucl Med 2006;20:583–588.PubMedCrossRefGoogle Scholar
  5. 5.
    Koeppe RA, Holthoff VA, Frey KA, Kilbourn MR, Kuhl DE. Compartmental analysis of [11C]flumazenil kinetics for the estimation of ligand transport rate and receptor distribution using positron emission tomography. J Cereb Blood Flow Metab 1991;11:735–744.PubMedGoogle Scholar
  6. 6.
    Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes in C. Cambridge: Cambridge University Press; 1988.Google Scholar
  7. 7.
    Luenberger DG. Optimization by vector space methods. New York: Wiley; 1969. p. 271–311.Google Scholar
  8. 8.
    Marquardt DW. An algorithm for least squares estimation of nonlinear parameters. SIAM J Soc Ind Appl Math 1963;2:431–441.CrossRefGoogle Scholar
  9. 9.
    Ikoma Y, Yasuno F, Ito H, Suhara T, Ota M, Toyama H, et al. Quantitative analysis for estimating binding potential of the peripheral benzodiazepine receptor with [11C]DAA1106. J Cereb Blood Flow Metab 2007;27:173–184.PubMedCrossRefGoogle Scholar
  10. 10.
    Ikoma Y, Takano A, Ito H, Kusuhara H, Sugiyama Y, Arakawa R, et al. Quantitative analysis of 11C-Verapamil transfer at the human blood-brain barrier for evaluation of P-glucoprotein function. J Nucl Med 2006;47:1531–1537.PubMedGoogle Scholar
  11. 11.
    Ikoma Y, Toyama H, Yamada T, Uemura K, Kimura Y, Senda M, et al. Creation of a dynamic digital phantom and its application to a kinetic analysis. Kaku Igaku 1998;35:293–303.PubMedGoogle Scholar
  12. 12.
    Feng D, Ho D, Chen K, Wu LC, Wang JK, Liu RS, et al. An evaluation of the algorithms for determining local cerebral metabolic rates of glucose using positron emission tomography dynamic data. IEEE Trans Med Imaging 1995;14:697–710.PubMedCrossRefGoogle Scholar
  13. 13.
    Ichise M, Toyama H, Innis RB, Carson RE. Strategies to improve neuroreceptor parameter estimation by linear regression analysis. J Cereb Blood Flow Metab 2002;22:1271–1281.PubMedCrossRefGoogle Scholar
  14. 14.
    Logan J, Fowler JS, Volkow ND, Wolf AP, Dewey SL, Schlyer DJ, et al. 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;10:740–747.PubMedGoogle Scholar
  15. 15.
    Kimura Y, Naganawa M, Shidahara M, Ikoma Y, Watabe H. PET kinetic analysis: pitfall and solution for Logan plot. Ann Nucl Med 2007;21:1–8.PubMedCrossRefGoogle Scholar
  16. 16.
    Slifstein M, Laruelle M. Effects of statistical noise on graphic analysis of PET neuroreceptor studies. J Nucl Med 2000;41:2083–2088.PubMedGoogle Scholar
  17. 17.
    Logan J, Fowler JS, Volkow ND, Ding YS, Wang GJ, Alexoff DL. A strategy for removing the bias in the graphical analysis method. J Cereb Blood Flow Metab 2001;21:307–320.PubMedCrossRefGoogle Scholar
  18. 18.
    Varga J, Szabo Z. Modified regression model for the Logan plot. J Cereb Blood Flow Metab 2002;22:240–244.PubMedCrossRefGoogle Scholar
  19. 19.
    Carson RE. PET parameter estimation using linear integration methods: bias and variability consideration. In: Uemura K, Lassen NA, Jones T, Kanno I, editors. Quantification of brain function: tracer kinetics and image analysis in brain PET. Amsterdam: Elsevier Science; 1993. p. 499–507.Google Scholar
  20. 20.
    Ogden RT. Estimation of kinetic parameter in graphical analysis of PET imaging data. Stat Med 2003;22:2557–2568.CrossRefGoogle Scholar
  21. 21.
    Burger C, Buck A. Requirements and implementation of a flexible kinetic modeling tool. J Nucl Med 1997;38:1818–1823.PubMedGoogle Scholar
  22. 22.
    Olsson H, Halldin C, Swahn CG, Farde L. Quantification of [11C]FLB457 binding to extrastriatal dopamine receptors in the human brain. J Cereb Blood Flow Metab 1999;19:1164–1173.PubMedCrossRefGoogle Scholar
  23. 23.
    Carson RE, Yan Y, Daube-Witherspoon ME, Freedman N, Bacharach SL, Herscovitch. An approximation formula for the variance of PET region-of-interest values. IEEE Trans Med Imaging 1993;12:240–250.PubMedCrossRefGoogle Scholar
  24. 24.
    Lammertsma AA, Hume SP. Simplified reference tissue model for PET receptor studies. Neuroimage 1996;4:153–158.PubMedCrossRefGoogle Scholar
  25. 25.
    Logan J, Fowler JS, Volkow ND, Wang GJ, Ding YS, Alexoff DL. Distribution volume ratios without blood sampling from graphical analysis of PET data. J Cereb Blood Flow Metab 1996;16:834–840.PubMedCrossRefGoogle Scholar
  26. 26.
    Hume SP, Myers R, Bloomfield PM, Opacka-Juffry J, Cremer JE, Ahier RG, et al. Quantitation of carbon-11-labeled raclopride in rat striatum using positron emission tomography. Synapse 1992;12:47–54.PubMedCrossRefGoogle Scholar
  27. 27.
    Lammertsma AA, Bench CJ, Hume SP, Osman S, Gunn K, Brooks DJ, et al. Comparison of methods for analysis of clinical [11C]raclopride studies. J Cereb Blood Flow Metab 1996; 16:42–52.PubMedCrossRefGoogle Scholar
  28. 28.
    Gunn RN, Lammertsma AA, Hume SP, Cunningham VJ. Parametric imaging of ligand-receptor binding in PET using a simplified reference region model. Neuroimage 1997;6:279–287.PubMedCrossRefGoogle Scholar
  29. 29.
    Wu Y, Carson RE. Noise reduction in the simplified reference tissue model for neuroreceptor functional imaging. J Cereb Blood Flow Metab 2002;22:1440–1452.PubMedCrossRefGoogle Scholar
  30. 30.
    Ichise M, Ballinger JR, Golan H, Vines D, Luong A, Tsai S, et al. Noninvasive quantification of dopamine D2 receptors with Iodine-123-IBF SPECT. J Nucl Med 1996;37(3):513–520.PubMedGoogle Scholar
  31. 31.
    Ichise M, Liow JS, Lu JQ, Takano A, Model K, Toyama H, et al. 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;23:1096–1112.PubMedCrossRefGoogle Scholar
  32. 32.
    Ikoma Y, Suhara T, Toyama H, Ichimiya T, Takano A, Sudo Y, et al. Quantitative analysis for estimating binding potential of the brain serotonin transporter with [11C]McN5652. J Cereb Blood Flow Metab 2002;22:490–501.PubMedCrossRefGoogle Scholar
  33. 33.
    Sokoloff L, Reivich M, Kennedy C, Des Rosiers MH, Patlak CS, Pettigrew KD, et al. The [14C]deoxyglucose method for the measurement of local cerebral glucose utilization: theory, procedure, and normal values in the conscious and anesthetized albino rat. J Neurochem 1977;28:897–916.PubMedCrossRefGoogle Scholar
  34. 34.
    Phelps ME, Huang SC, Hoffman EJ, Selin C, Sokoloff L, Kuhl DE. Tomographic measurement of local cerebral glucose metabolic rate in humans with (F-18)2-fluoro-2-deoxy-D-glucose: validation of method. Ann Neurol 1979;6:371–388.PubMedCrossRefGoogle Scholar
  35. 35.
    Dhawan V, Moeller JR, Strother SC, Evans AC, Rottenberg DA. Effect of selecting a fixed dephosphorylation rate on the estimation of rate constants and rCMRGlu from dynamic [18F]Fluorodeoxyglucose/PET data. J Nucl Med 1989;30:1483–1488.PubMedGoogle Scholar
  36. 36.
    Taguchi A, Toyama H, Kimura Y, Senda M, Uchiyama A. Comparison of the number of parameters using nonlinear iteration methods for compartment model analysis with 18F-FDG brain PET. Kaku Igaku 1997;34:25–34.PubMedGoogle Scholar
  37. 37.
    Huang SC, Yu DC, Barrio JR, Grafton S, Melega WP, Hoffman JM. Kinetics and modeling of L-6-[18F]fluoro-DOPA in human positron emission tomographic studies. J Cereb Blood Flow Metab 1991;11:898–913.PubMedGoogle Scholar
  38. 38.
    Hoshi H, Kuwabara H, Leger G, Cumming P, Guttman M, Gjedde A. 6-[18F]fluoro-L-DOPA metabolism in living human brain: a comparison of six analytical methods. J Cereb Blood Flow Metab 1993;13:57–69.PubMedGoogle Scholar
  39. 39.
    Cumming P, Gjedde A. Compartmental analysis of Dopa decarboxylation in living brain from dynamic positron emission tomograms. Synapse 1998;29:37–61.PubMedCrossRefGoogle Scholar
  40. 40.
    Huang SC, Phelps ME, Hoffman EJ, Sideris K, Selin CJ, Kuhl DE. Noninvasive determination of local cerebral metabolic rate of glucose in man. Am J Physiol 1980;238:E69–E82.PubMedGoogle Scholar
  41. 41.
    Carson RE, Huang SC, Green MV. Weighted integration method for local cerebral blood flow measurements with positron emission tomography. J Cereb Blood Flow Metab 1986;6:245–258.PubMedGoogle Scholar
  42. 42.
    Blomqvist G. On the construction of functional maps in positron emission tomography. J Cereb Blood Flow Metab 1984;4:629–632.PubMedGoogle Scholar
  43. 43.
    Kimura Y, Naganawa M, Yamaguchi J, Takabayashi Y, Uchiyama A, Oda K, et al. MAP-based kinetic analysis for voxel-by-voxel compartment model estimation: detailed imaging of the cerebral glucose metabolism using FDG. Neuroimage 2006;29:1203–1211.PubMedCrossRefGoogle Scholar
  44. 44.
    Turkheimer FE, Aston JA, Banati RB, Riddell C, Cunningham VJ. A linear wavelet filter for parametric imaging with dynamic PET. IEEE Trans Medical Imaging 2003;22:289–301.CrossRefGoogle Scholar
  45. 45.
    Patlak CS, Blasberg RG. Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data: generalizations. J Cereb Blood Flow Metab 1985;5:584–590.PubMedGoogle Scholar
  46. 46.
    Lucignani G, Schmidt KC, Moresco RM, Striano G, Colombo F, Sokoloff L. Measurement of regional cerebral glucose utilization with fluorine-18-FDG and PET in heterogeneous tissue: theoretical considerations and practical procedure. J Nucl Med 1993;34:360–369.PubMedGoogle Scholar
  47. 47.
    Yu DC, Huang SC, Barrio JR, Phelps ME. The assessment of the non-equilibrium effect in the “Patlak analysis” of Fdopa PET studies. Phys Med Biol 1995;40:1243–1254.PubMedCrossRefGoogle Scholar
  48. 48.
    Millet P, Delforge J, Pappata S, Syrota A, Cinotti L. Error analysis on parameter estimates in the ligand-receptor model: application to parameter imaging using PET data. Phys Med Biol 1996;41:2739–2756.PubMedCrossRefGoogle Scholar
  49. 49.
    Watabe H, Endres CJ, Breier A, Schmall B, Eckelman WC, Carson RE. Measurement of dopamine release with continuous infusion of [11C]raclopride: optimization and signal-tonoise considerations. J Nucl Med 2000;41:522–530.PubMedGoogle Scholar
  50. 50.
    Turkheimer F, Sokoloff L, Bertoldo A, Lucignani G, Reivich M, Jaggi JL, et al. Estimation of compartment and parameter distribution in spectral analysis. J Cereb Blood Flow Metab 1998;18:1211–1222.PubMedCrossRefGoogle Scholar
  51. 51.
    Kukreja SL, Gunn RN. Bootstrapped DEPICT for error estimation in PET functional imaging. Neuroimage 2004;21:1096–1104.PubMedCrossRefGoogle Scholar
  52. 52.
    Ogden RT, Tarpey T. Estimation in regression models with externally estimated parameters. Biostatistics 2006;7:115–129.PubMedCrossRefGoogle Scholar
  53. 53.
    Ogden RT, Ojha A, Erlandsson K, Oquendo MA, Mann JJ, Parsey RV. In vivo quantification of serotonin transporters using [(11)C]DASB and positron emission tomography in humans: modeling considerations. J Cereb Blood Flow Metab 2007;27:205–217.PubMedCrossRefGoogle Scholar
  54. 54.
    Efron B, Tibshirani RJ. An introduction to the bootstrap. New York: Chapman and Hall; 1993.Google Scholar
  55. 55.
    Buvat I. A non-parametric bootstrap approach for analyzing the statistical properties of SPECT and PET images. Phys Med Biol 2002;47:1761–1775.PubMedCrossRefGoogle Scholar

Copyright information

© The Japanese Society of Nuclear Medicine 2008

Authors and Affiliations

  • Yoko Ikoma
    • 1
    Email author
  • Hiroshi Watabe
    • 1
  • Miho Shidahara
    • 2
  • Mika Naganawa
    • 2
    • 3
  • Yuichi Kimura
    • 2
  1. 1.Department of Investigative RadiologyNational Cardiovascular Center Research InstituteSuitaJapan
  2. 2.Molecular Imaging CenterNational Institute of Radiological SciencesChibaJapan
  3. 3.Japan Society for the Promotion of ScienceTokyoJapan

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