# Dynamic Cell Imaging in PET with Optimal Transport Regularization

## TL;DR

This paper introduces a new PET image reconstruction method using optimal transport regularization that effectively tracks small numbers of cells with high accuracy, even under low radioactivity conditions, by enforcing temporal consistency.

## Contribution

The method uniquely combines all detected events for dynamic reconstruction and automatically determines the number of cells without additional complexity.

## Key findings

- Robust performance on simulated data with low radioactivity
- Automatic detection of number of tracked cells
- Achieves 5.3 mm tracking accuracy for moving cells

## Abstract

We propose a novel dynamic image reconstruction method from PET listmode data that could be particularly suited to tracking single or small numbers of cells. In contrast to conventional PET reconstruction our method combines the information from all detected events not only to reconstruct the dynamic evolution of the radionuclide distribution, but also to improve the reconstruction at each single time point by enforcing temporal consistency. This is achieved via optimal transport regularization where in principle, among all possible temporally evolving radionuclide distributions consistent with the PET measurement, the one is chosen with least kinetic motion energy. The reconstruction is found by convex optimization so that there is no dependence on the initialization of the method. We study its behaviour on simulated data of a human PET system and demonstrate its robustness even in settings with very low radioactivity. In contrast to previously reported cell tracking algorithms, our technique is oblivious to the number of tracked cells. Without any additional complexity one or multiple cells can be reconstructed, and the model automatically determines the number of particles. For instance, four radiolabelled cells moving at a velocity of 3.1 mm/s and a PET recorded count rate of 1.1 cps (for each cell) could be simultaneously tracked with a tracking accuracy of 5.3 mm inside a simulated human body.