## 5 Results: Model Validation
### Validation with Location Data from a Tracer Undergoing Circular Motion  
For the circular motion experiments described in Section 4, the location data derived from simulations and experiments were used to produce 1D profiles of the motion in the \(X\), \(Y\), and \(Z\) dimensions, as shown in Figure 7. The amplitude and frequency fit parameters can be seen in Appendix C, Table A2, which are generally in agreement to one standard uncertainty.  
Location data from PEPT measurements of the NRW-100 PointTracer [591 uCi, 400 um, \({}^{68}\)Ga] moving on a different circular path are shown in Figure 8, with a location rate of approximately 1.0 kHz. This motion has higher speeds than the other circular motion shown in Figure 7. The amplitude and frequency fit parameters can be seen in Appendix C, Table A2. The Gaussian fits to the distributions of the true and tracked locations are generally not in agreement within one standard uncertainty.  
Figure 6: Locations and histograms of the stationary tracer particle at Position 1 in the FOV (see Figure 3) derived from PEPT experiments (“Exp”) and simulations (“Sim”) of LORs with the HR++ scanner. Subplots (**a–c**) show the locations with time in the \(X\), \(Y\), and \(Z\) dimensions, respectively. The histograms (**d–f**) of the location data are shown with Gaussian fits. The goodness of fits were in the range \(0.18\leq\) reduced \(\chi^{2}\leq 0.72\).  
An alternative method to compare the measurements of location data between the experiments and simulations is the path uncertainty (Equation (1)). Tables 3 and 4 show the values of the path uncertainty for the 2 different circular motions used in the validation tests. The path uncertainty is less sensitive to small variations in the centre of the circular motion and starting position on the path, which can lead to differences between the parameters of the sinusoidal fits to the experiment and simulated location data that are greater than one standard uncertainty. The paths for both the ButtonTracer and PointTracer undergoing circular motion at different speeds show similar values in the path uncertainty regardless of whether they were calculated from experimental or simulated location data.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & \(\Delta(X)\) **(mm)** & \(\Delta(Y)\) **(mm)** & \(\Delta(Z)\) **(mm)** \\ \hline Exp & 0.53 & 0.59 & 0.19 \\ Sim & 0.52 & 0.60 & 0.16 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The path uncertainties \(\Delta(X)\), \(\Delta(Y)\), \(\Delta(Z)\) of a tracer particle NRW-100 PointTracer [591 \(\mu\)Ci, 400 \(\mu\)m, \({}^{68}\)Ga] undergoing Circular [27.64 mm, 19.74 Hz, \(C_{x}=1.14\) mm, \(C_{z}=1.73\) mm] calculated from locations from PEPT experiments (“Exp”) and GATE simulations (“Sim”) in each of the \(X\), \(Y\), and \(Z\) dimensions. The values correspond to the data shown in Figure 8.  
Figure 7: Location data for the ButtonTracer [60 \(\mu\)Ci, \({}^{18}\)F] particle undergoing Circular [71.19 mm, 1.06 Hz, \(C_{x}=-1.30\) mm, \(C_{y}=-0.54\) mm] in the \(XY\) plane as determined from PEPT experiments (red dots) and GATE simulations (blue dots). Subplots **(a-c)** show the locations with time in the \(X\), \(Y\), and \(Z\) dimensions.