A novel four-dimensional image registration method for radionuclide therapy dosimetry

A novel method for registering sequential SPECT scans (4DRRT) is described, whereby all sequential scans acquired in the course of a therapy or a pre-therapy tracer study may be registered in one pass. The method assumes that a mono-exponential decay function can be fitted to the series of sequential SPECT scans. Multiple volumes, presenting with different decay rates, are fitted with different mono-exponential functions. The MSSE (mean sum of squared errors in the least-squares fit algorithm), over the volume used for registration, is the cost function minimized at registration. Simulated data were used to assess the effect of thresholding, smoothing, noise and the multi-exponential nature of the four-dimensional (4D) SPECT studies on the performance of 4DRRT, resulting in three-dimensional (3D) residual registration errors <3.5 mm. The 4DRRT method was then compared to the following 3D registration methods: the correlation coefficient, the sum of absolute differences, the variance of image ratios and the mutual information. The comparisons, using both simulated and clinical data, were based on the standard deviation of the effective decay time distribution, generated from the registered 4D dataset, and showed that image registration using 4DRRT is simpler and more robust compared to the 3D techniques, especially when multiple tumour sites with different decay rates are present.