*2.3. Statistical Methods*

Numbers (percentages) were used to represent the distribution of gender, AO 2018 classification, and Denis zone [16]. The mean (standard deviation [SD]) and median (interquartile range [IQR]) were used to show the distribution of age, the radiographic displacement measurement (including the inlet ratio, outlet ratio, deformity index, asymmetry, deformity ratio, vertical displacement [VD], and horizontal displacement [HD]) in preand postoperative periods, VD change (preoperative minus postoperative values), and HD change (preoperative minus postoperative values). Generalized estimating equations (GEE) were used to estimate differences in outcomes (including the EQ−5D−5L [18], EQ−VAS, and Majeed pelvic scores [19]) among different time windows. The model was adjusted for age and gender. We also used the GEE model to assess the association between outcomes and different radiographic displacement measurements. The model was adjusted for age, gender, and time windows.

#### **3. Results**

As shown in Table 2, a total of 23 patients were enrolled in this study. There were 15 men and 8 women (65.2% vs. 34.8%), and the mean age was 47.8 (19.3) years. More than half of the patients were in the 61C1 (60.9%) category according to the AO 2018 classification, followed by those in the 61C3 (26.1%), 61C2 (8.70%), and 62C2 (4.35%) categories.


**Table 2.** Patients' characteristics (*n* = 12).

Abbreviations: SD = standard deviation, IQR = interquartile range, VD = vertical displacement, and HD = horizontal displacement.

As time progressed, the functional outcomes improved, and the patients returned to a near-normal life within one year. The EQ−5D−5L score increased with time, from 0.14 at 6–8 weeks to 0.94 at one year. The differences for the time trend were 0.32 in the crude GEE model (95% confidence interval [CI]: 0.25, 0.39) and 0.31 in the adjusted GEE model (95% CI: 0.25, 0.37) (Table 3, Figure 6). The EQ−VAS and Majeed pelvic scores also increased with time. The differences for the time trend were 0.17 for the EQ−VAS (95% CI: 0.14, 0.30) and 0.20 for the Majeed pelvic score in the adjusted GEE model (95% CI: 0.18, 0.22).

**Table 3.** Distribution of outcomes among time windows.


\* Adjusted for age and gender in the GEE model. Abbreviations: SD = standard deviation, CI = confidence interval, and GEE = Generalized estimating equations.

**Figure 6.** EQ−5D−5L, EQ−VAS, and Majeed pelvic scores over time.

In this study, three image-evaluation methods, including the measurement of the inlet–outlet ratio, the cross−measurement method, and ADM, were used pre-and postoperatively. The association between the EQ−5D−5L score and the radiographic displacement measurement is presented in Table 4. For the preoperative radiographic displacement measurements, the EQ−5D−5L score increased by 2.141 per outlet ratio unit (95% CI: 0.041, 4.241). In the postoperative period, the EQ−5D−5L score increased by 1.359 per inlet ratio unit and 1.804 per outlet ratio (95% CI: 1.301, 2.307) but decreased by 0.01 per HD (95% CI: −0.018, −0.002) after adjusting for age, gender, and the follow-up time. This shows that changes in the horizontal direction are more correlated with EQ−5D−5L recovery.


**Table 4.** Association between EQ−5D−5L scores and measurements in the GEE model.

\* Adjusted for age, sex, and time window. \*\* *p*-values < 0.05 represent statistical significance. Abbreviations: GEE = Generalized estimating equations, CI = confidence interval, VD = vertical displacement, and HD = horizontal displacement.

The association between the EQ−VAS score and the radiographic displacement measurements is shown in Table 5. The association was significant only with the inlet ratio in the postoperative period. The EQ−VAS score increased by 1.270 per inlet ratio (95% CI: 0.093, 2.447) in the adjusted GEE model. However, there were no significant associations between the Majeed pelvic score and any of the radiographic displacement measurements (Table 6).



\* Adjusted for age, sex, and time window; \*\* *p*-values < 0.05, representing statistical significance. Abbreviations: GEE = Generalized estimating equations, CI = confidence interval, VD = vertical displacement, and HD = horizontal displacement.


**Table 6.** Association between the Majeed Pelvic Score and measurements in the GEE model.

\* Adjusted for age, sex, and time window; \*\* *p*-values < 0.05, representing statistical significance. Abbreviations: GEE = Generalized estimating equations, CI = confidence interval, VD = vertical displacement, and HD = horizontal displacement.

#### **4. Discussion**

The present study revealed that the displacement of SPD in spinopelvic fixation provides good vertical reduction results. During surgery, a reduction in the vertical direction is easier to achieve by fluoroscopy. A vertical anatomical reduction is often mentioned and highlighted for the treatment of unequal feet. A vertical displacement causes differences in the lower extremities, abnormal motor gaits, and lower Majeed scores.

It is sometimes difficult to achieve a perfect horizontal reduction due to comminuted sacroiliac fractures or an indirect reduction in the sacroiliac joints with complex anatomical structures radiologically.

Regarding horizontal reduction, the analysis showed that patients with a short-term follow-up showed a lower tolerance for postoperative horizontal displacement. Only a few studies have focused on the relationship between the inferior quality of horizontal displacement reduction and unsatisfying functional outcomes. We believe that the inferior quality of the horizontal reduction results in a change in the lever arm of the peak moment of the hip, which causes greater work in terms of hip abduction, adduction, flexion, and extension in the affected side in patients with SPD (Figure 7). As a result, the centroid experiences a mid-lateral shift, which may increase the metabolic cost and mechanical work of the lower extremities [20,21]. With rehabilitation, patients improved their function over time, but the change of the lever arm may contribute to unsatisfaction, increasing metabolic costs, and increased mechanical work in the short term postoperatively. No significant correlation was found in the asymmetric index. This could be because the integrity of the pelvic ring was restored postoperatively, while the SI joint was left without a complete reduction.

**Figure 7.** Coronal view of the hip illustrating the change of the lever arm around the hip's center. When we set the hip's center as a fulcrum, there are two opposing forces across the hip's center: the body weight (white arrow) and abductor muscles (gray arrow). The lever arm for body weight is longer. In patients with SPD, horizontal displacement of the hip's center often extends the lever arm for body weight, causing increased work to balance the moment.

Our results revealed that the patient's function will return to normal in one year. The postoperative gait analyses of patients with various pelvic ring fractures by Kubota et al. [22,23] showed that there was a complete recovery of peak hip abduction, and a partial recovery of peak hip extension and hip strength were noted at the 12-month follow-up. The horizontal displacement of the pelvis may affect the offset change of the hip joint, which is associated with abductor function. Dean et al. [24] concluded that patients with type C pelvic fractures had weaker hip abductor strengths, lower peak hip abduction moments, slower walking speeds, lower peak hip abductions, and lower peak hip extensions in the short-term after the surgery; however, at the 12-month follow-up, the bilateral hip strength (abduction, adduction, flexion, and extension), bilateral peak hip moment (abduction, adduction, flexion, and extension), peak hip power, or walking speed did not differ between groups. We reasoned that an insufficient hip abduction strength may in turn lead to differences in short-term functional outcomes [22–24].

There is no perfect assessment tool, and the measurements of pelvic radiographs have not yet been well validated [25]. This is the first study to connect functional outcomes to radiological assessments. We found that the questionnaires and assessment tools for functional outcomes were often subjective and generalized; therefore, currently, we can hardly ascribe the unsatisfying hip function to the postoperative horizontal residual displacement. Although reduction is important, the evaluation of the association between the radiological displacement and functional outcomes requires better tools. In patients with SPD, there will be multi-axial displacements, including horizontal, vertical, and rotational displacements. The plain radiographs could only reveal the measurement of horizontal or vertical displacements, whereas the rotational displacement could be assessed by CT. It is reported that CT or three-dimensional reconstruction-based displacement measurements of pelvic ring injury displacement may provide a more accurate assessment [26].

This study had some limitations. First, a tomographic analysis is warranted to assess the rotation, but a customized view along the long axis of the pelvic bone is required for a correct assessment. Second, this was a single-center, observational, retrospective study with a small number of participants. However, as patients suffering from pelvic fractures with SPD are relatively rare, greater-scale research is difficult to carry out. To improve patients' functional outcomes and satisfaction, this study sets a template for future research focusing on this topic. Further studies with more patient data would help to improve the understanding of the correlation between the functional outcomes and reductions in different dimensions.
