Fitting the fractions of parent tracer in plasma
Why to fit the fraction curves?
The chromatographic methods used in the metabolite analysis are slow, and hampered by the fast decay of radioactivity, especially with C-11 labeled tracers. The fractions can often be determined only from sparse samples withincreased uncertainty with time. Fitting of a mathematical function to the fraction curves may be required to achieve an acceptable metabolite correction. Fitted fractions can be applied in the metabolite correction using metabcor as usual.
How to fit the fraction curves?
Functions
Different functions can be applied to different tracers. For most tracers fitting the "Hill type" (sigmoidial) function can be recommended: in practise, the curves of unchanged tracer fractions often do show a sigmoid shape, and could not be described by declining exponential functions. This may be caused by slow injection of tracer, or a redistribution phase of tracer from an initial deposition to a highly perfused tissue, e.g. lungs (Suhara et al., 1998). Hill function may even work better than compartment model (Wu et al., 2007).
![Fraction of authentic [11C]flumazenil in plasma](pic/flumazenil_hill.png)
![Total and authentic [11C]flumazenil concentration in plasma](pic/flumazenil_plasma.png)
Figures 1 and 2. "Hill type" function fitted to the measured fractions of authentic [11C]flumazenil in plasma; total plasma radioactivity concentration (black), and concentration of authentic [11C]flumazenil (red), calculated by multiplying each total plasma concentration by value of function at each sample time.
Hill function
Hill-type function for parent tracer fractions is:
Time when half of isotope label carrying compounds in plasma
are metabolites (t½) can then be calculated from equation:
Unchanged (parent) tracer fraction curves can be fitted with fit_hill. 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.
Sum of exponentials
However, if declining exponential functions are preferred, they can be fitted to the fraction curves using fit_fexp; this function has for example been used for [11C]PK11195 (Kropholler et al., 2005).
Other functions
For certain tracers, the fraction of unmetabolized parent tracer in plasma is not approaching 1.0 at the injection time, but may even be increasing during the first few minutes of the study. This has been shown for a tracer ([11C]DASB) binding to 5-HT transporters, possibly caused by transient trapping of parent tracer in the lungs, while the radioactive metabolite has no affinity for the 5-HT transporter (Parsey et al., 2006). A power-function-damped 2-exponential function was shown to fit the metabolite data better improve test-retest reproducibility (Parsey et al., 2006).
Another possible function for parent tracer fraction have been proposed by Watabe et al. (2000) and extensions to it by Meyer et al. (2004) and Hinz et al. (2007). The two first functions can be fitted to parent fractions using fit_ppf.
Function parameters
Function parameters are saved into specific fit file format, which are ASCII text files.
Program fit2dat can be used to calculate the fitted fraction curve for other purposes, e.g. for drawing graphs.
Population average of fractions
If the fractions of unchanged tracer in plasma or blood are very variable or measurements are missing for a few subjects, then a population based method should be considered.
