A collimator optimization method for quantitative imaging: Application to Y‐90 bremsstrahlung SPECT

Purpose: Post‐therapy quantitative 90 Y bremsstrahlung single photon emission computed tomography (SPECT) has shown great potential to provide reliable activity estimates, which are essential for dose verification. Typically 90 Y imaging is performed with high‐ or medium‐energy collimators. However, the energy spectrum of 90 Y bremsstrahlung photons is substantially different than typical for these collimators. In addition, dosimetry requires quantitative images, and collimators are not typically optimized for such tasks. Optimizing a collimator for 90 Y imaging is both novel and potentially important. Conventional optimization methods are not appropriate for 90 Y bremsstrahlung photons, which have a continuous and broad energy distribution. In this work, the authors developed a parallel‐hole collimator optimization method for quantitative tasks that is particularly applicable to radionuclides with complex emission energy spectra. The authors applied the proposed method to develop an optimal collimator for quantitative 90 Y bremsstrahlung SPECT in the context of microsphere radioembolization.Methods: To account for the effects of the collimator on both the bias and the variance of the activity estimates, the authors used the root mean squared error (RMSE) of the volume of interest activity estimates as the figure of merit (FOM). In the FOM, the bias due to the null space of the image formation process was taken in account. The RMSE was weighted by the inverse mass to reflect the application to dosimetry; for a different application, more relevant weighting could easily be adopted. The authors proposed a parameterization for the collimator that facilitates the incorporation of the important factors (geometric sensitivity, geometric resolution, and septal penetration fraction) determining collimator performance, while keeping the number of free parameters describing the collimator small (i.e., two parameters). To make the optimization results for quantitative 90 Y bremsstrahlung SPECT more general, the authors simulated multiple tumors of various sizes in the liver. The authors realistically simulated human anatomy using a digital phantom and the image formation process using a previously validated and computationally efficient method for modeling the image‐degrading effects including object scatter, attenuation, and the full collimator‐detector response (CDR). The scatter kernels and CDR function tables used in the modeling method were generated using a previously validated Monte Carlo simulation code.Results: The hole length, hole diameter, and septal thickness of the obtained optimal collimator were 84, 3.5, and 1.4 mm, respectively. Compared to a commercial high‐energy general‐purpose collimator, the optimal collimator improved the resolution and FOM by 27% and 18%, respectively.Conclusions: The proposed collimator optimization method may be useful for improving quantitative SPECT imaging for radionuclides with complex energy spectra. The obtained optimal collimator provided a substantial improvement in quantitative performance for the microsphere radioembolization task considered.