1. PLASMA INPUT AND METABOLITE FRACTION MODELS http://pet.utu.fi/staff/vesoik/reports/tpcmod0000.html TPCMOD0009 Models for plasma metabolite correction TPCMOD0010 Modelling input function

2. PLASMA METABOLITES http://pet.utu.fi/staff/vesoik/analysis/doc/metab_corr.html

3. MODELLING PLASMA METABOLITES: WHY? Removes ”noise” in the measured parent tracer fraction curve Interpolation of the fraction curve Extrapolation of the fraction curve Population based average metabolite correction?

4. MODELLING PLASMA METABOLITES: HOW? Linear interpolation (no modelling) Mathematical function fitting Kinetic models http://pet.utu.fi/staff/vesoik/reports/tpcmod0009.pdf

5. MATHEMATICAL FUNCTIONS Exponential functions Hill-type function Watabe’s empirical equation

6. Hill-type functions http://pet.utu.fi/staff/vesoik/programs/doc/fit_hill.html

7. KINETIC MODELS FOR PLASMA METABOLITES Huang et al. 1991, Reith et al. 1990, Gjedde et al. 1991 Carson et al. 1997 Models for [ 15 O]O 2 : Huang et al. 1991, Iida et al. 1993 http://pet.utu.fi/staff/vesoik/reports/tpcmod0009.pdf

8. Huang’s plasma metabolite model http://pet.utu.fi/staff/vesoik/reports/tpcmod0009_app_a.pdf

9. Extended Carson’s plasma metabolite model http://pet.utu.fi/staff/vesoik/reports/tpcmod0009_app_b.pdf

10. New plasma metabolite model http://pet.utu.fi/staff/vesoik/reports/tpcmod0009_app_c.pdf

11. KINETIC PLASMA METABOLITE MODELS MAY FAIL IF: Noise in measured plasma or blood curve Missing plasma samples during tracer infusion

12. MODELLING PLASMA CURVE: WHY? Removes noise Interpolation Extrapolation Reduces bias caused by missing samples Population based curve applying few late-time venous samples

13. MODELLING PLASMA CURVE: HOW? Linear interpolation (no modelling) Spline fitting Mathematical function fitting Kinetic models http://pet.utu.fi/staff/vesoik/reports/tpcmod0010.pdf

14. MATHEMATICAL FUNCTIONS Sum of exponential functions Thompson and Golish bolus input function Gamma variate function Feng et al. (based on compartmental models) http://pet.utu.fi/staff/vesoik/reports/tpcmod0010.pdf http://pet.utu.fi/staff/vesoik/programs/doc/fit_feng.html

15. Examples of Thompson’s function with asymptotic recirculation term by Golish et al.

16. KINETIC MODELS FOR PLASMA CURVE Feng et al. 1993 Graham 1997

17. GRAHAM’S MODEL http://pet.utu.fi/staff/vesoik/reports/tpcmod0010_app_a.pdf

18. GRAHAM’S MODEL FOR PLASMA CURVE AND A METABOLITE http://pet.utu.fi/staff/vesoik/reports/tpcmod0010_app_b.pdf

19. Example fit

20. Example fit (cont.)

21. PROBLEMS Model contains up to 18 parameters Difficult to weight metabolite fractions in relation to plasma Peak is not fitted well: may need a constraint Fast metabolism: are the first measured fractions correct?