Introduction
Kinetic analysis of PET data suffers from bias and poor precision due to high noise levels in tissue time activity curves (TACs), especially at the voxel level. The purpose of the present study was to investigate several wavelet based denoising strategies with respect to their capacity to improve accuracy and precision of pharmacokinetic parameters derived from these TACs.
Methods
The wavelet method used in this study was designed for denoising TACs and was implemented as follows. First, each TAC was temporarily extended by adding 4 zero's in front of the TAC and, using multi-exponential extrapolation, 4 points at the end. The resulting TAC was resampled at 64 time points (requirement for the dyadic wavelet, DPWT 1 ). Next, peaks (0–5 min) and tails (5–60 min) of the TACs were calibrated separately to find the best filter combination in terms of type of wavelet function (Daubechies 4–16, Symmlet 4–6, Coiflet 1–3 2 ), the number of times of downscaling and the type of thresholding (VISU or SURE 3 ). After filtering, denoised TACs were obtained by inverse transformation, down scaling and removal of temporary points. Simulations were performed to evaluate the effects of these wavelet-denoising methods on accuracy and precision of pharmacokinetic analyses. Wavelet denoising was applied to simulated noisy TACs based on [11C]-PK11195 data. Time dependent variance was simulated at 4 different noise levels (COV = 2.5, 5, 7.5 and 10%). For each noise level 300 TACS were generated. These noisy TACs were used both with and without wavelet filtering to estimate volume of distribution (Vd) and binding potential (BP) using nonlinear regression analysis.
Results
Daubechies-8 and Symmlet-4 wavelet functions yielded good results for the peak, and Coiflet (2 and 3) for the tail. In all cases SOFT SURE thresholding yielded ‘better’ TACs than VISU soft filtering after downscaling to level 3 (tail) and 5 (peak). Using this optimal set of wavelet parameters, about ∼75 and 100% of filtered TACs showed closer agreement with noiseless TACs then corresponding unfiltered TACs for peak and tail, respectively. Furthermore, use of wavelet filtering resulted in Vd and BP values with less bias and better precision than those without filtering. For example, BP bias reduced from 15 to 7% at a simulated noise level of 7.5%. Although there was only a slight decrease in bias at very high noise levels (>10 %), use of wavelet filtering resulted in a significant reduction of outliers from 15 to 4%.
Conclusion
After careful calibration of wavelet filters, bias and precision of pharmacokinetic parameters, especially BP, can be improved significantly. Furthermore, wavelet denoising seems to be most effective at higher noise levels (5 to 10%), thereby making it a promising tool for improving the quality of parametric images.