Direct pharmacokinetic parameter estimation using weighted least squares

Conventional dynamic PET studies estimate pharmacokinetic parameters using a two-step procedure of first reconstructing the spatial activity volume for each temporal frame independently before applying a pharmacokinetic model to the resulting spatio-temporal activity distribution. This indirect procedure leads to low SNR due to using only a subset of the temporal data when reconstructing each image. Our work concentrates on the estimation of parameters directly from the (raw or pre-corrected) dPET temporal projections. We present here a one-step direct pharmacokinetic algorithm based on the Ordered Subset (OS) Weighted Least Squares (WLS) iterative estimation algorithm. We explicitly incorporate a priori temporal information by modelling the Time Activity Curves (TACs) as a sum of exponentials convolved with an Input Function. Our OS-WLS-PK algorithm is appropriate for both 3D projection data which has been Fourier Rebinned into 2D slices, as well as when the data has been pre-corrected for attenuation, randoms and scatter. The main benefit of spectral analysis applied to dynamic PET reconstruction is that no particular pharmacokinetic model needs to be specified a priori, with only the input function needing to be sampled at scan time. We test our algorithm on highly realistic SORTEO generated data and show it leads to more accurate parameter estimates than when conventional graphical methods are used.

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