Harmonization of brain PET images in multi-center PET studies using Hoffman phantom scan

Background: Image harmonization has been proposed to minimize heterogeneity in brain PET scans acquired in multi-center studies. However, standard validated methods and software tools are lacking. Here, we assessed the performance of a framework for the harmonization of brain PET scans in a multi-center European clinical trial. / Method: Hoffman 3D brain phantoms were acquired in 28 PET systems and reconstructed using site-specific settings. Full Width at Half Maximum (FWHM) of the Effective Image Resolution (EIR) and harmonization kernels were estimated for each scan. The target EIR was selected as the coarsest EIR in the imaging network. Using “Hoffman 3D brain Analysis tool,” indicators of image quality were calculated before and after the harmonization: The Coefficient of Variance (COV%), Gray Matter Recovery Coefficient (GMRC), Contrast, Cold-Spot RC, and left-to-right GMRC ratio. A COV% ≤ 15% and Contrast ≥ 2.2 were set as acceptance criteria. The procedure was repeated to achieve a 6-mm target EIR in a subset of scans. The method’s robustness against typical dose-calibrator-based errors was assessed. / Results: The EIR across systems ranged from 3.3 to 8.1 mm, and an EIR of 8 mm was selected as the target resolution. After harmonization, all scans met acceptable image quality criteria, while only 13 (39.4%) did before. The harmonization procedure resulted in lower inter-system variability indicators: Mean ± SD COV% (from 16.97 ± 6.03 to 7.86 ± 1.47%), GMRC Inter-Quartile Range (0.040–0.012), and Contrast SD (0.14–0.05). Similar results were obtained with a 6-mm FWHM target EIR. Errors of ± 10% in the DRO activity resulted in differences below 1 mm in the estimated EIR. / Conclusion: Harmonizing the EIR of brain PET scans significantly reduced image quality variability while minimally affecting quantitative accuracy. This method can be used prospectively for harmonizing scans to target sharper resolutions and is robust against dose-calibrator errors. Comparable image quality is attainable in brain PET multi-center studies while maintaining quantitative accuracy

Application of modified Patankar schemes to stiff biogeochemical models for the water column

In this paper, we apply recently developed positivity preserving and conservative Modified Patankar-type solvers for ordinary differential equations to a simple stiff biogeochemical model for the water column. The performance of this scheme is compared to schemes which are not unconditionally positivity preserving (the first-order Euler and the second- and fourth-order Runge–Kutta schemes) and to schemes which are not conservative (the first- and second-order Patankar schemes). The biogeochemical model chosen as a test ground is a standard nutrient–phytoplankton–zooplankton–detritus (NPZD) model, which has been made stiff by substantially decreasing the half saturation concentration for nutrients. For evaluating the stiffness of the biogeochemical model, so-called numerical time scales are defined which are obtained empirically by applying high-resolution numerical schemes. For all ODE solvers under investigation, the temporal error is analysed for a simple exponential decay law. The performance of all schemes is compared to a high-resolution high-order reference solution. As a result, the second-order modified Patankar–Runge–Kutta scheme gives a good agreement with the reference solution even for time steps 10 times longer than the shortest numerical time scale of the problem. Other schemes do either compute negative values for non-negative state variables (fully explicit schemes), violate conservation (the Patankar schemes) or show low accuracy (all first-order schemes)