Wavelet Analysis of Dynamic PET Data: Application to the Parametric Imaging of Benzodiazepine Receptor Concentration

Abstract

Receptor density and ligand affinity can be assessed using positron emission tomography (PET). Biological parameters (Bmax′, k1, k2, kon/VR, koff) are estimated using a compartmental model and a multi-injection protocol. Parametric imaging of the ligand–receptor model has been shown to be of special interest to study certain brain disorders. However, the low signal-to-noise ratio in kinetic curves at the pixel level hampers an adequate estimation of model parameters during the optimization procedure. For this reason, mapping requires a spatial filter, resulting in a loss of resolution. Filtering the kinetic curves in the frequency domain using the Fourier transform is not appropriate, because of difficulties in choosing a correct and efficient cutoff frequency. A wavelet-based filter is more appropriate to such tracer kinetics. The purpose of this study is to build up parametric images at the pixel level while conserving the original spatial resolution, using wavelet-based filtering. Data from [11C]flumazenil studies, mapping the benzodiazepine receptor density, were used. An invertible discrete wavelet transform was used to calculate the time–frequency signals of the time–concentration PET curves on a pixel-by-pixel basis. Kinetic curves observed from large regions of interest in high and low receptor-density regions were used to calibrate the threshold of wavelet coefficients. The shrunken wavelet coefficients were then transformed back to the original domain in order to obtain the filtered PET signal. Maps of all binding parameters were obtained at the pixel level with acceptable coefficients of variation of less than 30% for the Bmax′ parameter in most of the gray matter. A strong correlation between model parameter estimates using the usual regions of interest and parametric imaging was observed for all model parameters (r = 0.949 for the parameter Bmax′). We conclude that wavelet-based filters are useful for building binding parameter maps without loss of the original spatial resolution of the PET scanner. The use of the wavelet-based filtering method can be extended far beyond the multi-injection protocol. It is likely to be also effective for other dynamic PET studies.