Data search from the abovementioned hospitals identified 124 organ donors whose cause of death was major trauma. Of these, seven (5%) were excluded for incomplete data. Following data collection and cleaning, multivariate analysis by clustering heatmap was performed using the selected variables. To determine the optimal number of clusters, three methods were compared, as demonstrated in Fig. 1.

A According to the elbow method, the optimal number of clusters is two. B According to the silhouette method, the optimal number of clusters is two. C According to the gap statistics method, the optimal number of clusters is four

According to the elbow method and the silhouette index, two clusters could be considered. According to the gap statistics, four clusters can be identified. By observation of the heatmap, it is possible to note two main clusters, one of which can be further divided into three subgroups [15] (Fig. 2).

Clustering heatmap of 117 trauma donors has identified two main clusters. Pre_HR, pre-hospital heart rate; Pre_SI, pre-hospital shock index; ED_pH, pH level measured in the emergency department; ED_BE, base excess levels measured in the emergency department; Pre_SBP, pre-hospital systolic blood pressure; ED_SBP, emergency department systolic blood pressure; Pre_GCS, pre-hospital Glasgow Coma Scale; ED_GCS, emergency department Glasgow Coma Scale; BMI, body mass index; ISS, injury severity score; ED_CA, cardiac arrest at admission to emergency department; ED_Lac, lactate levels measured in emergency department; ED_HR, emergency department heart rate; ED_SI, emergency department shock index; Pre_CA, pre-hospital cardiac arrest; delta_SI, difference between pre-hospital and emergency department shock index. Organ: total number of donated organs, from 1 to 8 (including heart, lungs, liver, kidneys, and pancreas). Hospital: 1, Niguarda; 2, Papa Giovanni; 3, Policlinico

The two main clusters are composed of almost an equal number of patients (Cluster 1 is made of 58 subjects vs. 59 subjects in Cluster 2). They do not differ in patient distribution by hospitals (33 vs. 32 from Niguarda, 23 vs. 20 from Papa Giovanni, and 2 vs. 7 from Policlinico, p = 0.224). Regarding patient-related variables included in the analysis, the clusters do not differ in gender distribution; there are 41 males in Cluster 1 and 44 males in Cluster 2 (70% vs. 74%, p = 0.792). However, the clusters significantly differ in patient age (29.39 ± 18.87 vs. 61.26 ± 14.36, p < 0.001) and BMI (22.8 ± 3.66 vs. 26.43 ± 3.62, p < 0.001). As for pre-hospital and emergency department trauma-related variables, the clusters significantly differ in Pre_SBP (70.04 ± 58.06 vs. 138.9 ± 35.78, p < 0.001), Pre_GCS (3.41 ± 0.879 vs. 5.88 ± 3.62, p < 0.001), Pre_CA (46.55% vs. 0%, p < 0.001), ED_SBP (91.76 ± 35.72 vs. 136.52 ± 37.59, p < 0.001), ED_HR (104.47 ± 36.81 vs. 87.09 ± 23.87, P < 0.001), ED_GCS (3.0 ± 0 vs. 3.88 ± 2.45, p = 0.001), ED_CA (15% vs. 0%, p = 0.001), and ED_SI (1.27 ± 0.746 vs. 0.683 ± 0.303, p < 0.001). However, there are no significant differences in Pre_HR (73.06 ± 57.55 vs. 86.94 ± 26.9, p = 0.527) and Pre_SI (0.784 ± 0.733 vs. 0.716 ± 0.479, p = 0.678). The clusters significantly differ in the laboratory arterial-blood gas analysis variables that were examined: pH (7.12 ± 0.232 vs. 7.28 ± 0.11, p < 0.001), base excess (− 11.6 ± 7.36 vs. − 4.86 ± 4.33, p < 0.001), and lactate (7.09 ± 4.49 vs. 3.18 ± 1.6, p < 0.001).

The last variable used to characterize the clusters was ISS, which significantly differs between the clusters (42.93 ± 17.38 vs. 34.19 ± 13.27, p = 0.002). We can identify the source of this difference by looking into the abbreviated injury score (AIS) of each solid organ of interest. In Cluster 1, seven (12%) livers were classified as AIS ≥ 2, while all Cluster 2 livers were uninjured, meaning AIS of zero (p = 0.006). The same is true for pancreas injury; in Cluster 1, five (8%) were injured with AIS ≥ 1, while in Cluster 2, none were injured (p = 0.027). Lung, traumatic injuries of AIS ≥ 2 were quite common in both groups yet more prevalent in Cluster 1 (72% vs. 45%, p = 0.004). No significant difference regarding heart injuries (0% vs. 1.69%, p > 0.999) nor kidney injuries (8% vs. 5%, p = 0.458) were found. The brain injury severity was similar between the clusters (4.54 ± 1.16 vs. 4.81 ± 0.473, p = 0.293).

A significant difference between the clusters was found with regard to the total number of DCS procedures applied (4.31 ± 2.54 vs. 1.98 ± 1.54, p < 0.001). In particular, more subjects in Cluster 1 had DCS applied already in the injury scene (62% vs. 11%, p < 0.001). Looking into the damage control resuscitation maneuvers considered in this study, more Cluster 1 patients received vasoactive agents both in the pre-hospital settings (40% vs. 5%, p < 0.001) and in the ED (58% vs. 23%, p < 0.001). The same is true for tranexamic acid in the pre-hospital settings (38% vs. 8%, p < 0.001) and in the ED (43% vs. 18%, p = 0.008). More Cluster 1 patients were administered with crystalloids in the ED (76% vs. 59%, p = 0.024) and required activation of massive transfusion protocol (37% vs. 16%, p = 0.019). Regarding damage control surgeries (EPP, thoracostomy, laparotomy, thoracotomy, craniotomy, ODC, and angiography), the average number of applied procedures was significantly higher in Cluster 1 (1.67 ± 1.8 vs. 0.83 ± 0.91, p = 0.004).

With regard to the donation of solid organs, Cluster 1 has produced significantly more hearts (65% vs. 34%, p = 0.001). Almost all subjects were liver donors with no significant difference between clusters (96% vs. 94%, p > 0.999). However, Cluster 1 produced more split livers (22% vs. 3%, p = 0.002). No significant difference regarding lung donation (29% vs. 15%, p = 0.108), kidney donation (96% vs. 90%, p = 0.272), or pancreas donation (29% vs. 27%, p = 0.954) was found. On average, Cluster 1 donated more organs per donor than Cluster 2 (4.5 ± 1.62 vs. 3.59 ± 1.43, p = 0.001). Interestingly, the functional response rate, defined as the proportion of organs that did not have primary dysfunction in the first 30 days from all transplanted organs, was equal (93% vs. 93%, p = 0.929).

A logistic regression model of heart donation as a function of cluster and age was performed further to investigate the effect of age on organ donation. The estimation results showed a significant interaction between age and cluster (p = 0.04). Figure 3 shows the probability of heart donation as a function of age for the two clusters. It is noticeable that this probability decreases more rapidly in Cluster 2 (characterized by a higher mean age) than in Cluster 1 (characterized by a lower mean age). For example, comparing a 40-year-old patient to a 50-year-old patient, the odds ratio of heart donation is 3.16 (95% CI 1.65–6.07) in Cluster 2 and 1.48 (95% CI 1.08–2.01) in Cluster 1.

Logistic regression of heart donation (dependent variable) as a function of age and cluster (independent variables) demonstrating that the effect of age is different in each cluster