Fitting the fractions of unchanged tracer in plasma
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 with increased uncertainty with time. Fitting of an empirical mathematical function to the fraction curves reduces variation and enables extrapolation, and may thus be required to achieve an acceptable metabolite correction.
Parent fraction fitting could also enable simple correction of ex vivo tracer metabolism during blood sample preparation before the chromatographic methods (Oikonen, 2014), but this approach must be validated for each tracer and metabolite analysis protocol.
Different functions can be applied to different tracers (Tonietto et al., 2016). For most tracers fitting the sigmoidal “Hill type” or power functions 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). Metabolites should not appear in blood samples before the circulation time (normally 1 min) is passed, unless tracer is metabolized in the lungs or by enzymes in blood. Parent tracer fraction at t=0 may be <1.0 if the administered radioligand is not 100% pure, which is common in preclinical animal studies.
Hill function may even work better than a compartment model (Wu et al., 2007).
Declining exponential functions may be preferred in some cases, especially in small animal studies where circulation is fast and the initial ‘shoulder’ cannot be observed. For example, this function
Simple two-exponential function with background was used in [18F]fallypride radiometabolite analysis study (Peyronneau et al., 2013):
Two-exponential function can even be used to fit sigmoidal data, as proposed by Blomqvist et al. (1990):
, where b1 ≠ b2.
One-phase exponential (monoexponential) function
, where A0 and Ai represent the level at time 0 and at infinity, respectively, and k represents the decay constant, may also be useful in fitting parent tracer fractions, and plasma-to-blood ratio data with certain tracers.
Cumulative gamma distribution function
Naganawa et al (2014a, 2014b) fitted a function based on cumulative (regularized) gamma distribution to plasma parent fraction data from [11C]GR103545 and [11C]LY2795050 (tracers for κ opioid receptors) PET studies, but the function would be applicable to most PET tracers. The function has four parameters (a-d), where a and b define the overall and end level of the parent fraction, and c and d affect the shape of the gamma distribution function.
Standard gamma distribution function has two parameters x and α, gammadist(x, α). The proposed function for the plasma parent tracer fractions as a function of time, t, is:
Tonietto et al (2015) validated a method where the bolus injection is modelled as a boxcar function, convoluted with power, Hill, or exponential function.
For certain tracers, the fraction of non-metabolized 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 extension to power function was used by Hinz et al. (2007).
Fraction data are usually either not weighted, or weighted by 1 / sampling frequency to prevent overfitting the initial part with more frequent sampling. However, fractions could also be weighted based on count statistics (Tsujikawa et al., 2014).
Function parameters are saved into specific fit file format, which are ASCII text files.
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.
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Created at: 2007-07-18
Updated at: 2018-10-10
Written by: Vesa Oikonen