Particle-number conservation, causality and linear response in biomedical imaging

Employing the continuity equation for the tracer density and the methods of linear response theory, we develop efficient mathematical tools for the analysis of dynamically taken positron emission tomography (PET) data. Our approach is quite general, allowing a probabilistic description of the fate of a tracer particle in an arbitrary organ and the extraction of detailed information on the chronology of the underlying physiological processes. We illustrate our procedure by applying it to renal data taken by a combined PET/magnetic resonance imaging (MRI) scanner performed with a sugar analogue radio tracer. (c) 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

By employing the continuity equation and linear response theory, efficient mathematical tools were developed for analyzing dynamic PET data. The approach allows for a probabilistic description of tracer particle fate in any organ and extraction of detailed information on underlying physiological processes' chronology. The study illustrated the procedure by applying it to renal data obtained from a PET/MRI scan using a sugar analogue radio tracer.