Hill function in plasma metabolite correction
An extended Hill function can be used when the parent 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 or a higher fraction:
, where 0 ≤ a ≤ d, b ≥ 1, c > 0, 0 < d ≤ 1, and e ≥ 0.
Parameter d represents the initial level of parent fraction, and parameter a the final level. Parameter e is the time after which the fraction starts to decrease (Tarkia et al., 2012).
Unchanged (parent) tracer fraction curves can be fitted with fit_ppf with option
If parameter d is set to 1 and e to 0, we have the traditional Hill type equation, which always starts from 1, but can still stop decreasing at a certain level (1-a) higher than 0:
Time when half of the isotope label carrying compounds in plasma are metabolites (t½) can then be calculated from equation:
Both parent fractions and two metabolite fractions can be fitted simultaneously with fith2met, assuming that the a single Hill function shape can fit all the fractions.
If measured parent tracer fractions do not seem to reach a steady level during the measurement, or extrapolation is needed and you are not comfortable with the assumption of steady final level, then the power function should be applied instead.
- Power function in metabolite correction
- Metabolite correction
- Fractions of unchanged tracer in plasma
- Fitting PET input curves
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Updated at: 2018-12-08
Created at: 2007-07-18
Written by: Vesa Oikonen