Fitting functions to PET TTACs
Mathematical functions or compartment models can be fitted to regional tissue time-activity curves (TTACs). Fitting functions to TTACs is usually not necessary, and should be avoided as a pre-processing step before compartmental modelling. Instead, Input functions and plasma parent fractions frequently need to be fitted in order to enable interpolation and extrapolation or to reduce noise. Noise may be a problem with TTACs when assessing TTAC peak value, for example for the purpose of estimating binding potential using transient equilibrium method, and fitting an empirical function to the TTACs may help to determine the peak values without noise-induced bias and variance. Another possible use is to estimate the tracer appearance time for time delay correction, or accounting for the time delay in AUC calculation for ARG methods.
, and can be fitted to PET TTACs with program fit_feng.
Rational functions (ratio of polynomials),
, can well represent the regional tissue data, but are not suitable for extrapolation because of the discontinuities at the zeroes of the divider function. Parameters p1 and q1 are usually fixed to 0 and 1, respectively, and other parameters are ≥0. Rational functions can be fitted to TTACs using fit_ratf.
Specific tumour vascularization function (patent WO/2008/053268, entitled Method and System for Quantification of Tumoral Vascularization),
has been used to fit tissue curves in [18F]FDOPA glioma studies (Zaragori et al., 2021).
, can be fitted to PET TTACs with program fit_wcdf.
have been traditionally used to fit not only input curves but also regional TTACs. If bolus injection is administered into local tissue artery, then tracer washout curve can be well fitted with decreasing exponentials. Program fit_exp can be used for these purposes. Initial parameters for unconstrained multiexponential functions can be calculated using linear methods as suggested by (Jean Jacquelin); this method can be tested with program llsqe3.
TTAC samples can be weighted by 1 / frame length to prevent overfitting the initial part with shorter frames.
Using the fits
- Slope image
- Fitting compartmental models
- Fitting PTACs
- Fitting plasma parent fractions
- Plotting TACs
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Updated at: 2022-01-04
Created at: 2018-05-17
Written by: Vesa Oikonen