  Dynamic Positron Emission Tomography (dPET) imaging and Time-Activity Curve
(TAC) analyses are essential for understanding and quantifying the
biodistribution of radiopharmaceuticals over time and space. Traditional
compartmental modeling, while foundational, commonly struggles to fully capture
the complexities of biological systems, including non-linear dynamics and
variability. This study introduces an innovative data-driven neural
network-based framework, inspired by Reaction Diffusion systems, designed to
address these limitations. Our approach, which adaptively fits TACs from dPET,
enables the direct calibration of diffusion coefficients and reaction terms
from observed data, offering significant improvements in predictive accuracy
and robustness over traditional methods, especially in complex biological
scenarios. By more accurately modeling the spatio-temporal dynamics of
radiopharmaceuticals, our method advances modeling of pharmacokinetic and
pharmacodynamic processes, enabling new possibilities in quantitative nuclear
medicine.
