# Power functions in plasma metabolite correction

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

An extended power function can be used when parent the tracer fraction,
*f _{p}*, 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-HT_{2A} receptors in
human brain with [^{11}C]MDL 100,907.
*J Cereb Blood Flow Metab.* 2007; 27: 161-172.

Meyer PT, Bier D, Holschbach MH, Boy C, Olsson RA, Coenen HH, Zilles K,
Bauer A. Quantification of cerebral A_{1} adenosine receptors in humans
using [^{18}F]CPFPX and PET.
*J Cereb Blood Flow Metab.* 2004; 24(3): 323-333.

Watabe H, Channing MA, Der MG, Adams HR, Jagoda E, Herscovitch P,
Eckelman WC, Carson RE. Kinetic analysis of the 5-HT_{2A} ligand
([^{11}C]MDL 100,907.
*J Cereb Blood Flow Metab.* 2000; 20: 899-909.

## Acknowledgements:

Thanks to Matteo Tonietto for notifying of a typo in the equation.

Tags: Metabolite correction, Parent fraction, Fitting

Updated at: 2013-12-12

Written by: Vesa Oikonen