Functional imaging constrained diffusion for brain PET synthesis from structural MRI

Magnetic resonance imaging (MRI) and positron emission tomography (PET) are increasingly used in multimodal analysis of neurodegenerative disorders. While MRI is broadly utilized in clinical settings, PET is less accessible. Many studies have attempted to use deep generative models to synthesize PET from MRI scans. However, they often suffer from unstable training and inadequately preserve brain functional information conveyed by PET. To this end, we propose a functional imaging constrained diffusion (FICD) framework for 3D brain PET image synthesis with paired structural MRI as input condition, through a new constrained diffusion model (CDM). The FICD introduces noise to PET and then progressively removes it with CDM, ensuring high output fidelity throughout a stable training phase. The CDM learns to predict denoised PET with a functional imaging constraint introduced to ensure voxel-wise alignment between each denoised PET and its ground truth. Quantitative and qualitative analyses conducted on 293 subjects with paired T1-weighted MRI and ¹⁸F-fluorodeoxyglucose (FDG)-PET scans suggest that FICD achieves superior performance in generating FDG-PET data compared to state-of-the-art methods. We further validate the effectiveness of the proposed FICD on data from a total of 1262 subjects through three downstream tasks, with experimental results suggesting its utility and generalizability.