Federated optimisation of kinetic analysis problems

Abstract

Positron Emission Tomography (PET) data is intrinsically dynamic, and kinetic analysis of dynamic PET data can substantially augment the information provided by static PET reconstructions. Yet despite the insights into disease that kinetic analysis offers, it is not used clinically and seldom used in research beyond the preclinical stage. The utility of PET kinetic analysis is hampered by several factors including spatial inconsistency within regions of homogeneous tissue and relative computational expense when fitting complex models to individual voxels. Even with sophisticated algorithms inconsistencies can arise because local optima frequently have narrow basins of convergence, are surrounded by relatively flat (uninformative) regions, have relatively low-gradient valley floors, or combinations thereof. Based on the observation that cost functions for individual voxels frequently bear some resemblance to each-other, this paper proposes the federated optimisation of the individual kinetic analysis problems within a given image. This approach shares parameters proposed during optimisation with other, similar voxels. Federated optimisation exploits the redundancy typical of large medical images to improve the optimisation residuals, computational efficiency and, to a limited extent, image consistency. This is achieved without restricting the formulation of the kinetic model, resorting to an explicit regularisation parameter, or limiting the resolution at which parameters are computed.

Keywords: Dynamic images; Kinetic analysis; Magnetic resonance imaging; Optimisation; Positron emission tomography.