## 3 Methods: Deriving the Location of the Source  
For this work, the procedure used to convert the raw LORs into a series of locations was the same for both the experimental and simulated data. The source locations were calculated using the PEPT-ML package developed at the University of Birmingham [38]. PEPT-ML is a machine learning tracking algorithm that first calculates the distance between all combinations of pairs of LORs in a given sample size (\(SS\)). If two LORs are spatially closer than a user-defined maximum distance (\(MD\)), they form a \"cutpoint\", which is defined as the midpoint on the shortest line that connects the two LORs. After grouping all the LORs, the resulting cutpoints are then found using the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm [44]. The PEPT-ML algorithm uses a true fraction (\(TF\)) parameter to determine the fraction of cutpoints that are considered to arise from truly coincident LORs and classifies the remaining cutpoints as outliers [38]. The final location of the tracer in 3D is then derived from an average of the positions of the remaining cutpoints. Once these locations are found, HDBSCAN can be applied again with a second pass in order to smooth and reduce noise of the first pass. This algorithm requires seven parameters to run with two passes. The 7 parameters are: sample size 1 (\(SSI\)), overlap 1 (\(OL1\)), maximum distance (\(MD\)), true fraction 1 (\(TF1\)), sample size 2 (\(SS2\)), overlap 2 (\(OL2\)), and true fraction 2 (\(TF2\)). Each use of this algorithm is described with the parameters in shorthand by the term Clustering [\(SSI\), \(OL1\), \(MD\) (mm), \(TF1\), \(SS2\), \(OL2\), \(TF2\)]. PEPT-ML was chosen for this work, instead of the more commonly used Birmingham algorithm, for convenience in applying multiple passes of HDBSCAN, which provide additional smoothing to reduce noise in location data. For example, there was a significant percentage reduction of \(\approx\)94% in positional error when comparing the PEPT-ML algorithm to the Birmingham algorithm when tracking two tracers undergoing circular motion at 42 RPM [38]. It has been demonstrated to have increased precision for certain tracking scenarios [38]. Its source code is also shared open source via the python package installer pip for easy implementation. For the validation tests, the Clustering parameters were kept constant between equivalent tests in the simulation and experiments in order to remove any variations in the results due to the HDBSCAN parameters. These fixed parameters were chosen in such a way as to output location data with a location rate of approximately 1.0 kHz and to allow for a statistically meaningful comparison between the experimental and simulation results (e.g., avoiding the analysis of samples with very small or very large numbers of LORs that may not produce a location after processing with PEPT-ML). In the extended simulations, a gridsearch was used to find the parameter combination that minimised the difference between the output \"tracked\" path and the input \"true\" path. Unless otherwise specified, a combination of sample size (\(SS\)) and overlap (\(OL\)) parameters were used that met this minimum difference condition and output location rate of approximately 1.0 kHz. A short report giving further details on the procedure to optimise PEPT-ML for deriving location data from one of the extended simulations is given in Appendix A. The PEPT-ML parameters used for deriving location data as shown in all the results of this work can be found in Appendix C, Tables A3 and A4. The output location rate \(L\) was calculated using \(L=B/\omega\), where \(B\) was the number of locations and \(\omega\) was the tracking time. The uncertainty in the location rate \(u(L)\) was calculated using a counting uncertainty \(u(L)=\sqrt{L}\). The location rates for all the results of this work can be found in Appendix C, Tables A3 and A4. An overlap in the first pass of PEPT-ML was not implemented in any of the results.