# Power functions in plasma metabolite correction

Power functions have been used to fit the fractions of parent radiotracer in plasma.

An extended power function can be used when parent the tracer fraction, fp, is initially 1 or less then 1 (in some cases tracer 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) tracer fraction curves can be fitted with fit_ppf with option -model=PF.

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.

## References:

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.

## Acknowledgements:

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