Power functions in plasma metabolite correction
An extended power function can be used when the parent radiopharmaceutical fraction, fp, is initially 1 or less then 1 (in some cases radiopharmaceutical is metabolized already in vasculature before reaching sampling site), and then approaches 0:
, where 0 < a ≤ 1, b > 1, c > 0, 0 < d ≤ 1, and e ≥ 0.
Parameter d represents the initial level of parent fraction, and parameter e is the time after which the fraction starts to decrease.
Unchanged (parent) radiopharmaceutical fraction curves can be fitted with
fit_ppf with option
If parameter d is set to 1, we have essentially the same function as was proposed by Meyer et al. (2004), and if additionally parameter b is set to 2 and delay parameter e = 0, the function is the same as used by Watabe et al. (2000).
If you prefer a function that approaches a steady level above 0, then use the Hill functions.
The x axis value t for a known fp can be solved from the extended power function, giving equation:
The derivative of the extended power function is
- Hill function in plasma metabolite correction
- Metabolite correction
- Fractions of unchanged radiotracer in plasma
- Fitting PET input curves
Hinz R, Bhagwagar Z, Cowen PJ, Cunningham VJ, Grasby PM. Validation of a tracer kinetic model for the quantification of 5-HT2A receptors in human brain with [11C]MDL 100,907. J Cereb Blood Flow Metab. 2007; 27: 161-172. doi: 10.1038/sj.jcbfm.9600323.
Meyer PT, Bier D, Holschbach MH, Boy C, Olsson RA, Coenen HH, Zilles K, Bauer A. Quantification of cerebral A1 adenosine receptors in humans using [18F]CPFPX and PET. J Cereb Blood Flow Metab. 2004; 24(3): 323-333. doi: 10.1097/01.WCB.0000110531.48786.9D.
Watabe H, Channing MA, Der MG, Adams HR, Jagoda E, Herscovitch P, Eckelman WC, Carson RE. Kinetic analysis of the 5-HT2A ligand ([11C]MDL 100,907. J Cereb Blood Flow Metab. 2000; 20: 899-909. doi: 10.1097/00004647-200006000-00002.
Thanks to Matteo Tonietto for notifying of a typo in the equation.
Updated at: 2018-12-18
Created at: 2007-07-18
Written by: Vesa Oikonen