Statistical Analysis of GSR Particles Morphometry Using the CART Method

A total of 86,518 particles were detected in the collected samples. Of these, 2522 particles (approximately 3% of the total) were classified as characteristic GSR particles, in accordance with ASTM E1588-20 [3]. Characteristic GSR particles were present in all analyzed samples, with the highest count originating from 9 mm caliber ammunition. The number of particles detected—categorized by ammunition type, shooter, and region of the shooter’s body—is detailed in Table 3: Regarding the recovery of these particles after sample collection, the number of characteristic GSR particles after discharging 5.56 and 7.62 mm cartridges was markedly lower than that detected for 9 mm and 0.40 caliber ammunition, even when supplementary swabs from the shooters’ chest and facial regions were analyzed. Although it has been reported that residues from long weapons tend to accumulate preferentially on the face and torso [26], GSR dispersion is a multifactorial phenomenon. Key determinants include the firing hand (adjacent to the ejection port), the support hand (near gas exhaust apertures), ammunition design, barrel length, shooter’s grip and stance, pre-shot cleaning, and other weapon-specific parameters [27,28]. Ditrich et al. [29] and Chohra et al. [30] demonstrated significant inter-weapon variation in particle dispersal patterns. For instance, revolvers (short firearm) release residues in close proximity to the shooter, whereas shotguns and repeating rifles generate comparatively sparse particle clouds. In line with these findings, the present study recorded the highest particle concentrations on shooters’ hands for both long and short firearms. Similarly, Brozek-Mucha [31] reported greater particle counts on hand swabs compared to facial swabs after discharging short weapons [17,26,31]. These observations highlight the importance of considering weapon architecture and handling dynamics when interpreting GSR distribution in forensic reconstructions. Although the number of characteristic GSR particles recovered is generally lower than that of other particle types classified under ASTM E1588-20 [3] (i.e., consistent and commonly associated particles), the observed variation in dispersion patterns also contributes to the relatively low number of characteristic GSR particles recovered (2522). Regarding secondary transfer of particles and/or previous contamination, it is important to emphasize that such occurrences can significantly impact the interpretation of GSR findings. Particles may be transferred through indirect contact with contaminated surfaces, objects, or individuals, particularly in confined or shared environments. Moreover, the presence of characteristic GSR particles on control samples before shooting highlights the need for stringent contamination control measures and thorough background screening in forensic protocols. The data presented in Table 3 exclude characteristic GSR particles detected in the control samples. The analyzed control samples identified 168 particles with both regular (spheroidal) and irregular morphologies. Among these, the highest contamination levels were observed in the samples from 0.40 ammunition, with shooters 2 and 5 identified as the primary sources of contamination. A salient finding was that background contamination was present in every pre-fire control swab, irrespective of the ammunition caliber. Shooter 4 yielded the fewest control particles, presumably owing to a more stringent decontamination protocol. Residues nevertheless persisted after each shot—despite interim cleaning of both firearm and hands—implicating secondary transfer, most plausibly from the holster or ancillary gear. Systematic scrutiny of control data is essential for quantifying false positive risk in forensic casework. In operational settings such as law-enforcement duty, secondary GSR transfer can undermine evidential reliability [31,32]. We implemented a hand-cleaning regimen to mitigate this hazard and collected 30 paired samples to evaluate its efficacy. Before cleaning, 176 characteristic particles were recovered from weapons and hands; post cleaning, the count dropped to just 14. These results underscore the necessity of decontaminating both hands and firearms before firing, and interpreting residual particles in light of potential cross-transfer mechanisms. Despite the post-cleaning decline in particle abundance, SEM retained sufficient analytical sensitivity to detect and classify every residual GSR particle, underscoring the method’s robustness under low contamination conditions. Once characteristic GSR particles were verified, high-resolution micrographs were archived in a database that served as the training set (504 samples were used) for an automated morphometric workflow. This algorithm extracted FD and the shape descriptors C, R, and AR. Automated analysis yielded a comprehensive morphometric profile for 2522 particles. For regular spheroidal particles, a single FD measurement adequately represents size. In contrast, irregular or non-spheroidal morphotypes may require multiple dimensional metrics to be fully characterized [33]. Because FD is defined as the maximum chord length of an object irrespective of orientation [34], it was adopted as the principal metric for length assessment across all particle classes. Of the 2552 characteristic GSR particles analyzed, 76% had diameters ranging from 1 to 10 µm. Within this range, 56.2% of the particles originated from 9 mm caliber ammunition, 22.3% from 0.40 ammunition, 11.2% from 5.56 mm caliber ammunition, and 10.3% from 7.62 mm caliber ammunition. When each ammunition type is considered individually, 92% of the particles generated by 9 mm ammunition, 82% of those from 0.40 ammunition, and 65% of those from 7.62 mm ammunition had diameters between 1 and 10 µm. In contrast, the majority of particles produced by 5.56 mm ammunition fell within the 11–40 µm range. The study conducted by Kara [16] analyzed the FD of 1200 characteristic GSR particles collected from five European 9 mm caliber ammunition types produced by the manufacturers MKE, GECO, S&B, WIN, and LIBRA. The results indicated that 91% of the analyzed particles had an FD between 1 µm and 10 µm [16]. Comparing Kara’s [16] findings with those of this study, for samples collected from the same caliber and within the same measurement range, there was a difference of only 1%, with this study identifying 92% of particles within this range. These results highlight a strong trend indicating that characteristic GSR particles from 9 mm caliber ammunition predominantly exhibit an FD between 1 and 10 µm. In the case of 5.56 and 7.62 mm caliber ammunition, the average FD values obtained in this study—29.21 and 21.23 µm, respectively—were slightly higher than those reported by Kara and Tahillioglu [17], who observed mean values of 26.77 µm for 5.56 mm and 18.16 µm for 7.62 mm particles [17]. These variations may reflect differences in experimental conditions, ammunition batches, or firearm models used during testing. For 0.40 caliber ammunition, an average FD of 16.08 µm was recorded; however, no comparable data were found in the literature, limiting direct analysis. The absence of reference values for certain calibers emphasizes the need for further studies to expand GSR morphometric databases to improve comparative assessments in forensic investigations. After presenting the FD results, a new classification for morphological classes of characteristic GSR particles from the four national ammunitions analyzed in this study was created (see Table 2). According to Blott and Pye [13], the term “regular” is used to describe shapes with straight edges or those that have a continuously curved outline, in two or three dimensions. When a particle exhibits significant indentations (concavities) and projections (convexities) on its surface, it can be described as irregular. Of the regular particles, 57% are regular spheroidal, a value slightly lower than that found in the literature, which considers 70% of characteristic GSR particles to be spheroidal [35], 36% are regular non-spheroidal, 6.7% are irregular rounded, and 0.3% are irregular angular. The new classification supports the qualitative evaluation of particle occurrence frequency for each type of ammunition. This revised classification system facilitates the qualitative assessment of particle occurrence frequency for each ammunition type. To highlight the morphological variations observed in the analyzed samples, all characteristic GSR particle classes are illustrated in Figure 2. By evaluating the combination of two variables—FD and particle morphology—it is possible to observe clear differences in the morphometric profiles of characteristics GSR particles from long firearms (5.56 and 7.62 mm) compared to those from short firearms (9 mm and 0.40). These differences are illustrated in the box plots (Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7). Specifically, when analyzing the characteristics of GSR particles according to ammunition type, it becomes evident that the median FD values for particles originating from long firearms are higher than those observed for particles from short firearms (Figure 3). Regular spheroidal particles exhibit the lowest median FD values among all morphological classes, with a median of 3.35 µm. Although FD measurements in this class range from 0.09 to 9.77 µm, the highest concentration of particles falls within the 2.58 to 4.75 µm range. Among the short firearms, particles from 0.40 ammunition have a median FD of 3.37 µm, with most particles also concentrated between 2.56 µm and 4.77 µm. When comparing the median FD of 0.40 ammunition with that of 9 and 7.62 mm ammunition, the values are quite similar—3.18 and 3.36 µm, respectively. However, differences emerge in the distribution ranges: while 9 mm particles are most frequently found between 1.73 and 3.18 µm, 7.62 mm particles, like those from 0.40 ammunition, are concentrated in the 2.49 to 4.75 µm range. Among regular spheroidal particles, 5.56 mm ammunition (a long firearm) exhibits the highest median FD value, at 4.34 µm. The majority of these particles fall within the 3.02 to 6.84 µm range, indicating that regular spheroidal particles from 5.56 mm ammunition tend to be larger than those from other calibers (Figure 4). Non-spheroidal regular particles have a median FD value of 4.02 µm, with the highest concentration of particles ranging from 3.18 to 5.51 µm, although the full range extends from 1.60 to 9.93 µm. Within this morphological class, the results suggest that ammunition from long firearms tends to produce particles with larger FD values compared to short firearms. Specifically, 5.56 mm ammunition exhibits the highest median FD in this class, at 4.89 µm (Figure 5), reinforcing the trend of larger particle sizes associated with long firearms. The irregular rounded particle class has a median FD of 4.02 µm, similar to that observed in class 2. However, most particles in this category are distributed within the FD range of 2.84 to 5.48 µm. Within this class, particles originating from short firearm ammunition exhibit lower median FD values compared to those from long firearms. Notably, particles from 7.62 mm ammunition present the highest median FD value in this class, measuring 5.79 µm (Figure 6). The irregular angular class presented only seven particles, with a median FD value higher than the other classes, being 6.60 µm (Figure 7). This class occurred mainly in short firearms, with four particles in 9 mm ammunition, two particles in 0.40 ammunition, and one particle in 5.56 mm ammunition. The analysis of characteristic GSR particles was approached from the perspective of particle morphometry. The results indicate that regular particles can exhibit diameters larger than those previously reported in the literature and display highly specific morphologies depending on the type of ammunition. This finding offers a new perspective on the relevance of morphometric analysis, a method already employed in other scientific fields to better understand diverse processes. Among the parameters commonly used to characterize particle morphometry—such as Length, FD, AR, C and R—none have yet been systematically applied to characteristic GSR particles [5,6,7,8,9,10,11,12,13,14,15,16,18]. In this study, the focus was placed on analyzing FD, AR, R, and C. The data were initially examined using frequency histograms. The histograms (Figure 8) reveal that the samples do not follow symmetrical distributions for the evaluated parameters. Since the distribution is not normal, using the mean as an estimator is not advisable, as it lacks robustness of validity. Confidence intervals based on the mean are generally imprecise when the underlying distribution deviates from normality. Robustness of validity refers to the ability of confidence intervals for population location to have a 95% probability of covering the true population location, regardless of the underlying distribution. The median, on the other hand, is an example of an estimator that tends to exhibit robustness of validity [36]. Non-parametric Mood tests for the median were conducted, with the null hypothesis (H₀) stating that the population medians are all equal, and the alternative hypothesis (H₁) stating that the population medians are not all equal. All tests were performed at a 95% confidence level. The four parameters selected for the study were analyzed in two phases: Comparing the medians based on the type of weapon (long or short) and comparing the medians across different ammunition calibers. The results revealed that the parameters FD and C exhibited significant differences in their median values for both the weapon type comparison and the ammunition type evaluation. Conversely, the parameters R and AR showed no differences in median values. The results from the CART method analysis corroborated the findings of the Mood tests, confirming the same level of importance for the parameters FD and C (Figure 9). The graph generated by the CART methodology ranks the variables based on their importance in node divisions, with values ranging from 0 to 100%. The most important variable is assigned a value of 100%, while the relevance of the other variables is expressed as a proportion relative to this maximum importance. This analysis indicates that the most significant predictor variable in the model is FD, followed by the shape descriptor C. In contrast, the shape descriptors AR and R exhibit limited relevance. The variables FD and C contribute the most to the improvement of the model when performing predictor splits, suggesting that the algorithm identifies them as the most discriminative among the evaluated features [36]. To determine the most appropriate decision tree for the study, the graph of misclassification cost versus the number of terminal nodes was analyzed (Figure 10). Terminal nodes represent a trade-off between model complexity and classification accuracy, with the optimal number being selected based on the minimization of misclassification cost. This analysis prioritizes trees with fewer nodes and the lowest achievable misclassification cost. The graph reveals a milestone identified by Minitab at the tree with four terminal nodes, which is considered the optimal model for this dataset. This tree is labeled “Optimal” because it represents the smallest tree whose misclassification cost falls within one standard error of the minimum observed misclassification cost. The four-terminal-node tree exhibits a misclassification cost of approximately 0.5817. Although the tree with five terminal nodes has a slightly lower misclassification cost (approximately 0.57), and the six-node tree achieves the minimum cost (approximately 0.584), the difference is marginal (Figure 10). Therefore, the tree with four terminal nodes was selected for further analysis. This choice is justified by the fact that increasing the number of nodes leads to minimal gains in predictive performance, with misclassification costs remaining close to the optimal value. As such, the increased model complexity is not warranted. In this study, the first node of the tree (short firearm class) (node 1) was established by a cut in the proportion of short and long firearm ammunition. Of the total count of 2522 characteristic GSR particles, node 1 indicated that 67.3% were identified as originating from 9 mm and 0.40 ammunition. The second node, called node 2, made the cut considering the FD value ≤ 9.173 μm. Among the 1884 particles selected with this criterion, 79.3% were considered from short firearms. This initial binary division already presented the first terminal node 4 to the right of the tree, considering FD values greater than 9.173 μm. Node 3 was generated from the cut considering the variable C with the value ≤ 0.529. With this parameterized value, the algorithm classified 73.9% of the characteristic GSR particles as originating from 9 mm and 0.40 ammunition. Considering the condition C > 0.529, terminal node 3 was generated. Terminal node 1 resulted from a subsequent split based on the FD value ≤ 6.166 µm, in which 76.8% of the characteristic GSR particles were classified as originating from 9 mm and 0.40 caliber ammunition. FD values greater than 6.166 µm led to the formation of terminal node 2, where 59.1% of the particles were associated with short-barreled firearms (Figure 11). In addition to the decision tree, further results were obtained and are described in the Table 4. The performance of the decision tree model was evaluated using a confusion matrix, which provides a detailed assessment of the model’s classification accuracy through four key statistical metrics. The true positive rate (sensitivity or power) reflects the model’s ability to correctly identify the occurrence of an event, indicating how effectively it classifies particles when the predicted class matches the actual one. Conversely, the false positive rate (Type I error) represents the probability of incorrectly classifying a non-event as an event, thus capturing the model’s tendency to generate false alarms. The false negative rate (Type II error) measures the likelihood of failing to detect an actual event, revealing potential weaknesses in the model’ sensitivity. Lastly, the true negative rate (TNR) quantifies the model’s capacity to correctly identify non-events, contributing to a balanced evaluation of sensitivity and specificity [36]. Together, these metrics provide a comprehensive understanding of the classification model’s strengths and limitations in differentiating between particle classes based on their morphometric characteristics, ensuring its reliability in forensic analysis. The results in Table 4 show that the true positive rate is above 80% in both training and testing, which is considered satisfactory for the analysis. According to Lima [37], training refers to the iterative execution phase of the algorithm that occurs before the final implementation, while testing represents the algorithm’s execution after the optimal decision tree has been established. A ROC curve was generated to validate these results, plotting the rate of correctly classified events on the Y-axis and the rate of incorrectly classified events on the X-axis. The area under the curve was 0.75 during the training period and 0.73 during the testing period. According to the literature, this result is acceptable because a perfect ROC curve has an area under the curve equal to 1, indicating the tree’s ability to separate the model categories perfectly. Trees with an area under the curve equal to 0.5 demonstrate an inability to separate the model categories [36] (Figure 12). The results obtained using the CART classification method indicate a 76% accuracy in identifying the type of firearm based on GSR particle morphometry, considering the analyzed measurement parameters.