## 7 Discussion
Using the order of magnitude of the deviation of the tracked path from the true path at the turning points, PEPT measurements with the HR++ would be unable to accurately track fluctuations smaller than a millimetre scale. Simulations were also performed of a tracer particle moving on a spiral path and showed that measurements with the HR++ are able to track spiral structures with radii larger than or equal to 2.0 mm, to an uncertainty smaller than the size of the tracer particle. Tracking the path to smaller radii led to an increase in the location uncertainty in terms of an increasing deviation from the true path. The size of the tracer particle is suggested as an acceptable uncertainty based on several assumptions of the radiolabelling of the tracer particle, as the role of positron range has not yet been determined in location calculations with the routine tracer particles. It is expected that the radionuclide is contained in a surface layer of the NRW100 resin material; therefore, positrons from the tracer particle will tend to annihilate within the resin. In practice, this is likely to underestimate the average range of the positron, and it remains an area of future work for GATE simulations to relate the positron range in different media to the accuracy and precision of location measurements. The threshold for fluctuations presented here, which is on the order of magnitude of 1 mm based on results of 2-3 mm from the oscillating and spiral simulations, is considerably larger than the size of the tracer particle and the size of the smallest eddies found in the water phase of flotation pulps, 10 and 100 \(\upmu\)m for laminar and turbulent flow, respectively [39]. However, it is a matter of debate whether particles of the same size as the tracer particle can experience the interior of these microscale eddy structures, and tests with smaller tracer particles were not performed. In combination with the threshold for location uncertainty of the size of the tracer particle, the results presented here suggest that PEPT measurements with the HR++ have greater applicability to systems using larger tracer particles (for a larger acceptable location uncertainty) and with larger fluctuations and characteristic length scales of turbulence. Further work is required to extend the scope of the simulations and explore the role of the varying density of the local media, the tracer activity, and the size of the tracer particle; however, the results of the simulations included here suggest that PEPT measurements performed with PET scanners with lower spatial resolution and/or lower tracer activity would tend to have poorer ability to track turbulent fluctuations than demonstrated in this work. The uncertainty in the measured locations could be reduced by using a different radionuclide for the tracer fabrication, where \({}^{18}\)F generally has a shorter positron range in dense media [51], and by employing a PET scanner with higher instrinsic spatial resolution, such as the microPET system at the University of Tennessee, Knoxville [20] or SuperPEPT at the University of Birmingham [17]. These improvements may make feasible PEPT measurements with smaller tracer particles which, based on current methods for tracer fabrication, are associated with lower radiolabelled activity and would tend to increase the uncertainty values given here. The location rate of the presented PEPT measurements is also significant, where the 1.0 kHz threshold ensures a large sample of LORs are used in the calculation of each location. Where the tracer particle does not move within the sample temporal window,this leads to the calculation of a location with high precision. However, where the particle moves within the window, such as on the spiral path with radii smaller than 2.0 mm, an increase in location rate could be achieved with an overlapping sample size or dynamic sample size. A higher location rate has the potential to improve the tracking result and enable the tracking of the path to smaller radii.