## 7 Discussion  
Considering the results of the validation tests performed to compare location data from experimental LORs with the output of the GATE simulation of the HR++, it was shown that the HR++ model is an effective model for PEPT measurements of stationary and moving tracer particles. Specifically, the experiment and simulation location data show agreement within one standard uncertainty for the measurements of the location of a stationary source in different positions around the FOV of the PET scanner, agreement within one standard uncertainty of the parameters of sinusoidal fits to the path of a tracer particle moving on a circular path at low frequency, and agreement in the path uncertainty of a tracer particle moving on a circular path at high frequency. Similarity between PEPT measurements performed in experiments and simulations with different types of tracer particles (button and point) and three different radionuclides (\({}^{18}\)F, \({}^{22}\)Na, \({}^{68}\)Ga) were demonstrated to broaden the application of the model. This validation is not as rigorous as performing the tests advised by the standard protocol NEMA NU 2-2012 [45], which compare measurements between experiments and corresponding GATE simulations in terms of the spatial resolution, scatter fraction, sensitivity, accuracy, and image quality. The standard is used by the medical imaging community and, more recently, by developers of PEPT as a technique at the University of Birmingham [37]. In the absence of the appropriate data from experiments with the HR++ scanner, in particular single-event data, the work presented here used coincidence data to demonstrate the validity of the HR++ GATE model to reproduce PEPT measurements of tracer particles both stationary and moving, where the motion is predictable. Future research will explore the validity of the simulation for scenarios far removed from those presented here, while the current model will be used to develop improvements to data processing techniques and interpretation of PEPT measurements of multiphase flows. The GATE simulations were also used to explore PEPT measurements of tracer particles moving on paths characteristic of flow paths where turbulence is present. When tracking a particle of routine fabrication at PEPT Cape Town (radius 300 \(\upmu\)m and activity 1000 \(\upmu\)Ci) on an oscillating path, it was illustrated that PEPT can track high-speed, linear  
Figure 12: (**a**) Uncertainty in the path \(\Delta R\) as a function of spiral radius. (**b**) \(\Delta(R)\) with acceleration \(a\) of the particle moving along the spiral path. The shaded area shows the size of the tracer on the \(\Delta(R)\) axis of the plot. Fits have been included to guide the eye: in (**a**), an exponential function, \(y=A\ \exp(-bx-d)+c\), with a reduced \(\chi^{2}\) of 0.0017, and (**b**) a hyperbolic sine function, \(y=A\ \text{arcsinh}(bx-d)+c\), with a reduced \(\chi^{2}\) of 0.0018.  
sections of the path; however, sampling artefacts introduce large uncertainty into the PEPT location measurement on the turning points of the path. Specifically, when using a sample of LORs to derive a tracer location, if the tracer does not accelerate within the temporal window, the average location will tend to be on the true path without significant deviation from the true path. This deviation was measured to be 0.30 mm, a size similar to that of the tracer particle. On the other hand, if the tracer experiences acceleration within the sampling temporal window, the average location may not tend to be on the true path, with considerable deviation of over 3 mm. This is likely a regular occurrence when tracking the turning points of high-speed paths. These results illustrate the potential of this sampling artefact to reduce the amplitude of high-speed fluctuations in the path of turbulent, multiphase flows in regions where there is high particle acceleration.