Comparative clinical efficacy and cost-effectiveness of modified tension band wiring techniques in patellar fracture repairs

Abstract

Patellar fractures challenge knee function recovery. Traditional tension band wiring (TBW) suffers from K-wire complications and inadequate fracture site compression, prompting modified techniques. We hypothesized that a cerclage-free modified TBW (Group A) would outperform titanium cable TBW (Group B) and titanium cable TBW with cerclage (Group C) in cost, complications, and functional outcomes. In this retrospective study (Level IV evidence), 83 patients (aged 18–80) with unilateral closed transverse patellar fractures (December 2018–2023) were grouped by fixation method. Group A incurred the lowest hospital costs, and Group C had the highest. Operation time was significantly shorter in Group B. However, Groups A and B outperformed Group C in postoperative recovery time, early functional exercise initiation, Lysholm score at 1 year postoperatively, and complication rates. Modified TBW without cerclage demonstrated cost efficiency, reduced complications associated with earlier rehabilitation initiation compared to cerclage-augmented techniques.

1. Background

Over the years, the surgical treatment of patellar fractures has experienced a transformative evolution. The 1950s marked a pivotal moment with the introduction of the tension band wiring technique, swiftly gaining the esteemed endorsement of the AO Association.^[1] This technique, lauded for its superiority over nonsurgical interventions and patellectomy, was widely adopted as the preferred approach for addressing patellar fractures.

However, despite its widespread acceptance, the technique was not without its challenges. The primary concern centered around using longitudinally smooth Kirschner wires (K-wires), which, while integral to the fixation of fracture ends, were vulnerable to complications such as loosening and migration.^[2] Furthermore, the limitation of K-wires in providing direct compression at the fracture site was a notable drawback.

While cannulated screw fixation has emerged as an innovative alternative, providing enhanced biomechanical stability for patellar fracture stabilization, the rigorous surgical demands of this method have limited its widespread adoption in clinical practice.^[3] Conversely, titanium cables have gained popularity among medical professionals.^[4] Their durability, flexibility, and diminished risk of complications associated with K-wires have established them as a favorable option for patellar fracture treatment.

This study introduces a novel modified tension band wire fixation technique designed to overcome the limitations of traditional K-wire tension bands in managing patellar fractures. A retrospective analysis was conducted to evaluate the clinical efficacy of various internal fixation methods for patellar fractures, aiming to delineate the benefits and drawbacks of this newly modified technique and assess its clinical viability.

2. Materials and methods

2.1. Patient selection

This part of the study is retrospective, collecting patellar fracture cases treated surgically in the Department of Orthopedic Trauma at the First Hospital of Jilin University from December 2018 to December 2023. Cases were grouped according to the internal fixation technique: Group A for the modified tension band wire internal fixation group; Group B for the modified tension band titanium cable internal fixation group; Group C for the modified tension band titanium cable with cerclage internal fixation group. Details of the surgical technique are shown in Figure 1.

Figure 1.

Details of the surgical technique are presented. Group A for the modified tension band wire internal fixation group; Group B for the modified tension band titanium cable internal fixation group; Group C for the modified tension band titanium cable with cerclage internal fixation group.

These groupings were based on the type of internal fixation. The selection of internal fixation technique was based on a combination of factors, including fracture stability (assessed intraoperatively), surgeon experience with specific techniques, and patient-specific considerations (e.g., bone quality). Cerclage augmentation (Group C) was more frequently chosen for fractures with subtle instability or comminution not captured by the AO 34-A/C classification, as noted in surgical records. The differences between the groups are as follows: Group A used K-wires, which are woven in a “figure-eight” pattern, but Group B used cable and woven in the same way, while Group C added one more cable as cerclage internal fixation based on Group B.

The study enrolled patients meeting the following inclusion criteria: individuals aged 18 to 80, presenting with unilateral closed transverse patellar fractures classified as either AO type 34-A or AO type 34-C and having complete clinical data available. Crucially, patient consent for participation in the research was obtained. Excluded from the study were those with open, pathological, or old fractures, multiple fractures or concurrent injuries, a history of knee surgery or any relevant medical history that could compromise knee joint function, vascular, nerve, or other limb diseases impeding fracture healing, incomplete clinical records, or those who declined to take part in the investigation.

The study reviewed cases from the Department of Orthopedic Trauma at the First Hospital of Jilin University over the past 5 years, encompassing 524 cases of surgically treated patellar fractures. Of these fractures, 326 were excluded for failing inclusion criteria: 189 had open/pathological/old fractures, 78 had multiple concurrent injuries, 41 had incomplete clinical records, and 18 declined participation. A further 115 cases were excluded due to small group sizes (n < 10) for specific fixation techniques, leaving 83 cases for analysis (Fig. 2).

Figure 2.

Flow diagram. The reasons for excluding 441 of the initial 524 cases.

2.2. Surgical intervention

The surgical procedure for our innovative technique closely adheres to the principles of the classical tension band method and does not require specialized tools – standard orthopedic trauma instruments such as K-wire forceps, cutters, suction tips, needle wires, and K-wires are adequate. The procedure unfolds through several meticulously executed stages. Initially, the patellar fracture is anatomically realigned using reduction forceps, with the correct positioning verified under fluoroscopic imaging. Two 2.0 mm K-wires are then inserted perpendicularly to the fracture line, positioned 5 mm from the joint surface, to stabilize the break. The next critical step involves double-strand wire suturing. Two-needle wires are woven in a “figure-eight” pattern, each carefully threaded near the intersection of the patella and K-wire, weaving under ligaments and the K-wire to ensure minimal intrusion into soft tissues. Excess lengths are trimmed after tightening and knotting each wire, leaving at least three knots for security. The K-wires are subsequently manipulated for added stability. Using forceps, the wires are bent 2 to 3 cm above the patella’s upper border, initially to 130° with a suction tip, then 170° or higher, before trimming and shaping the ends into hooks. These hooks are rotated and gently hammered into the bone to anchor the wires securely. Excess wire at the patella’s distal end is clipped, leaving a 5 mm remnant to deter wire migration. To further consolidate the repair, a non-absorbable suture is applied in a purse-string fashion around the patella’s edge. Finally, the fixation’s integrity is validated by actively flexing and extending the knee, followed by radiographic examination in anteroposterior and lateral projections to ascertain the quality of reduction and fixation. This surgical regimen is meticulously planned to achieve precise fracture reduction, reinforce stability via an adapted tension band approach, and mitigate risks associated with soft tissue inflammation or implant complications.

2.3. Observational indicators

Clinical data during hospitalization were collected, and follow-up was conducted for patients meeting the criteria. The following data were collected: gender, age, side of fracture, AO classification, preoperative time (emergency or elective), hospitalization costs, operation time, internal fixation method, bleeding situation, incision length and method, postoperative hospital stay, time to first exercise (patient-initiated knee flexion and extension activities), knee joint function (Lysholm score),^[5] VAS score,^[6,7] postoperative complication status, and retention of internal fixation.

Postoperative rehabilitation protocols were standardized: all patients initiated passive range-of-motion exercises on postoperative day 2, with active exercises permitted once pain (VAS < 4) and stability were confirmed (typically days 3 to 5). Progression to weight-bearing was allowed at 6 to 8 weeks based on radiological healing.

2.4. Statistical methods

Data were analyzed and plotted using SPSS 27 and GraphPad Prism 8 software. Normality was tested using the Shapiro–Wilk test, and homogeneity of variance was assessed using the Levene test.^[8,9] Metric data conforming to a normal distribution were expressed as mean ± standard deviation (Mean ± SD), and non-normally distributed data were expressed as median and interquartile range (M, IQR). If statistical data conformed to a normal distribution, one-way ANOVA or Welch ANOVA was used for multiple group comparisons, followed by LSD or Tamhane T2 methods for pairwise comparisons between groups.^[10] All P-values were adjusted for multiple comparisons using Bonferroni correction where appropriate. For non-normally distributed data (e.g., operation time, hospital stay, identified via the Shapiro–Wilk test), multiple group comparisons were performed using the Kruskal–Wallis test, followed by Dunn post hoc test for pairwise comparisons.^[11] Categorical data were expressed as counts and percentages (n, %), and group comparisons were made using the chi-square test. A P-value of <0.05 was considered statistically significant.

3. Results

3.1. Baseline characteristics

Group A consisted of 28 cases, Group B of 34 cases, and Group C of 21 cases. In Group A, there were 12 males and 16 females, with 19 patellar fractures on the left side and 9 on the right. The AO classification included 10 Type A and 18 Type C fractures. The average age was 52.39 ± 13.55 years, and the hospital stay was (6, 3.8) days. In Group B, there were 18 males and 16 females, with 20 patellar fractures on the left side and 14 on the right. The AO classification included 13 Type A and 21 Type C fractures. The average age was 50.85 ± 14.55 years, and the hospital stay was (5, 4) days. In Group C, there were 8 males and 13 females, with 10 patellar fractures on the left side and 11 on the right. The AO classification included 12 Type A and 9 Type C fractures. The average age was 50.81 ± 12.76 years, and the hospital stay was (6, 9) days. The basic characteristics, including the number of cases, gender, side of fracture, fracture classification, age, and hospital stay, showed no statistically significant differences (P > .05), indicating comparability among the 3 groups for further study, as shown in Table 1.

Table 1.

Patient basic information comparison.

Group	Number of cases	Gender		Fracture side		AO type		Age (yr)	Hospital stay (d)	Hospital costs (Yuan)
		Male	Female	Left	Right (yr)	A	C
A	28	12	16	19	9	10	18	52.39 ± 13.55	(6, 3.8)	19,368.89 ± 3134.86
B	34	18	16	20	14	13	21	50.85 ± 14.55	(5, 4)	28,988.47 ± 5448.21
C	21	8	13	10	11	12	9	50.81 ± 12.76	(6, 9)	47,112.26 ± 5333.81
P-value		.522		.362		.269		.889	.112	<.001*

Group A represents the modified tension band wire internal fixation, Group B represents the modified tension band titanium cable internal fixation, and Group C represents the modified tension band titanium cable with cerclage internal fixation. Normally distributed values are presented as X̅ ± SD, and non-normally distributed values are presented as (M, IQR).

M, IQR = median and interquartile range, SD = standard deviation.

^*A statistically significant difference between groups (P < .05).

However, a statistically significant difference was observed in hospital costs (P = .000) in multigroup analysis, as shown in Figure 3. The hospital costs for the 3 groups were as follows: Group A (19,368.89 ± 3134.86) Yuan < Group B (28,988.47 ± 5448.21) Yuan < Group C (47,112.26 ± 5333.81) Yuan. Each group comparison showed differences. The costs associated with different surgical methods are significantly different, with the modified tension band wire internal fixation incurring the least cost and the modified tension band titanium cable with cerclage internal fixation incurring the most.

Figure 3.

Hospital costs multiple comparisons among groups. Group A represents the modified tension band wire internal fixation, Group B represents the modified tension band titanium cable internal fixation, and Group C represents the modified tension band titanium cable with cerclage internal fixation. * indicates a statistically significant difference.

3.2. Surgical outcomes

To understand the intraoperative situation, this study compared the operation time, intraoperative blood loss, incision length, and VAS score on the third postoperative day for the 3 groups of patients, as shown in Table 2.

Table 2.

Patient surgical outcomes.

Group	Operation time (min)	Blood loss (mL)	Incision length (cm)	VAS score
A	(80, 24)	(75, 100)	(10. 0.75)	(3, 1.1)
B	(63, 13.5)	(60, 55)	(10, 0)	(3, 0)
C	(68, 16)	(60, 50)	(10, 0)	(3, 1)
P-value	.005*	.369	.946	.267

Normally distributed values are presented as X̅ ± SD, and non-normally distributed values are presented as (M, IQR).

M, IQR = median and interquartile range, SD = standard deviation.

^*A statistically significant difference.

Intraoperative blood loss (P = .369), incision length (P = .946), and VAS score (P = .267) on the third postoperative day (P > .05) showed no statistically significant differences. The operation time for the 3 groups, P = .05, showed a statistically significant difference. The differences in operation time among the groups are shown in Figure 4. The multiple comparisons of operation time indicate a statistically significant difference between Group A and Group B (P < .05).

Figure 4.

Operation time multiple comparisons among groups. Group A represents the modified tension band wire internal fixation, Group B represents the modified tension band titanium cable internal fixation, and Group C represents the modified tension band titanium cable with cerclage internal fixation. * indicates a statistically significant difference.

3.3. Clinical outcomes

To compare the clinical efficacy of the 3 groups, this study focused on the following aspects: postoperative hospital stay, time to initial functional exercise (patient-initiated knee flexion and extension exercise), fracture healing time (as reported by the patient), Lysholm score at 1 year postoperatively, complication rate, and rate of internal fixation removal. The results are shown in Table 3.

Table 3.

Patient clinical outcomes.

Group	Postoperative hospital stay (d)	Initial functional exercise (d)	Fracture healing time (wk)	Lysholm score	Complication rate (%)	Internal fixation removal rate (%)
A	(4, 5)	2.68 ± 1.335	(12, 1)	(86, 13)	(4, 14.3)	(10, 35.7)
B	(3, 4.5)	2.26 ± 0.994	(12, 1)	(81, 13.25)	(4, 12.9)	(16, 47.1)
C	(6, 10.1)	4.86 ± 2.242	(12, 1)	(78, 13)	(9, 42.9)	(12, 57.1)
P-value	.011*	<.001*	.746	.009*	.019*	.323

Normally distributed values are presented as X̅ ± SD, and non-normally distributed values are presented as (M, IQR), with metric data using (n, %).

M, IQR = median and interquartile range, SD = standard deviation.

^*A statistically significant difference between groups (P < .05).

Multiple group comparisons found no statistically significant difference in fracture healing time (P = .746) and internal fixation removal rate (P = .323) (P > .05). However, postoperative hospital stay (P = .011), initial functional exercise time (P = .000), Lysholm score at 1 year postoperatively (P = .009), and complication rate (P = .019) showed P-values <0.05, indicating statistically significant differences. The comparison of postoperative situations suggests that different surgical methods are not significantly associated with differences in fracture healing indices. However, there are apparent differences in patient postoperative recovery and functional mobility, as shown in Table 4.

Table 4.

Multiple comparisons of postoperative hospital stay, initial functional exercise time, lysholm score, and complication rate.

	A vs B	A vs C	B vs C
Postoperative hospital stay (d)	adj.P = 1	adj.P = .234	adj.P = .014*
Initial exercise time (d)	P = .697	P = .003*	P = .001*
Lysholm score	adj.P = .27	adj.P = .018*	adj.P = .049*
Complication rate (%)	P > .0125	P > .0125	P < .0125*

adj.P represents the adjusted significance value using the Bonferroni correction method.

^*A statistically significant difference between groups (P < .05). The rate comparison among multiple groups was considered statistically significant with P < .0125.

According to the table, in terms of postoperative hospital stay, the comparison between Group B and Group C (adj.P = .014), adj.P < .05, indicates a statistically significant difference, suggesting that patients in Group B had a shorter hospital stay and could be discharged earlier. In terms of the initial exercise time, the comparison between Group A and Group C (P = .003) and Group B and Group C (P = .001), P < .05, shows a statistically significant difference. This indicates that Groups A and B could initiate functional exercise earlier than Group C after surgery.

In terms of the Lysholm score at 1 year postoperatively, the comparison between Groups A and C (adj.P = .018) and Groups B and C (adj.P = .049), adj.P < .05 indicates a statistically significant difference, suggesting that Groups A and B had better knee joint function recovery compared to Group C. The 3-point difference in Lysholm scores between Group B (81) and Group C (78) was statistically significant but below the established MCID (>5), suggesting limited clinical relevance. In contrast, the earlier initiation of functional exercise in Groups A and B (mean difference 4.2 days vs Group C) may have meaningful implications for preventing joint stiffness.

3.4. Complications

Regarding complication rates, the comparison between Groups B and C, P < .0125, shows a statistically significant difference, indicating that Group B had a lower complication rate than Group C.

One case in Group A experienced internal fixation failure with the K-wire protruding from the fixed fracture end. However, this occurred 4 months postoperatively, when the fracture had already healed. The failed internal fixation was removed 1 year after surgery without significantly impacting the patient’s functional recovery. There were 2 cases of internal fixation irritation in Group A, caused by wire knots stimulating subcutaneous tissue, which resolved after the removal of the internal fixation. One case of limited activity was observed, and upon careful questioning of the patient’s history, it was found that the internal fixation was removed 9 months postoperatively.

In Group B, there were 3 cases of internal fixation irritation. During the removal of the internal fixation 1 year postoperatively, it was discovered that the titanium cable ends were not neat, with fine titanium wires present. These fine wires can stimulate the subcutaneous tissue of the knee joint during patient movement. There were also two cases of internal fixation failure similar to Group A, where the K-wire protruded after the fracture had healed.

In Group C, there were 5 cases of internal fixation irritation. Upon removal of the internal fixation 1 year postoperatively, the placement of the titanium cable locking buckles caused the symptoms. One case of poor wound healing was adequately managed by extending the suture removal time and increasing the frequency of dressing changes. There were 3 cases of limited knee joint activity, and follow-up revealed that the patients felt the cerclage titanium cable limited knee flexion, as shown in Table 5.

Table 5.

Complications in the 3 groups.

	Group A	Group B	Group C
Poor wound healing	–	–	1
Deep infection	–	–	–
Implant failure	1	2	–
Implant irritation	2	2	5
Limited mobility	1	–	3

4. Discussion

Earlier medical research has indicated that nonsurgical treatment or patellectomy for displaced patellar fractures may lead to various long-term adverse outcomes.^[12] This is due to the indispensable role of the patella at the front of the knee joint, especially in protecting the joint and buffering pressure.^[13] These anatomical and biomechanical perspectives have prompted orthopedic surgeons to adopt surgical treatment for patellar fractures.^[14] In 1950, the AO Association proposed an improved tension band scheme for fixing patellar fractures,^[15] which has since become the primary technique for treating displaced patellar fractures.^[1,16,17] The tension band technique ingeniously transforms the tensile force on the anterior surface of the patella into pressure on the joint surface, achieving stability dynamically.^[18] Its reliable fixation and promotion of early joint activity have significantly improved treatment outcomes.^[19] However, this method is not perfect. Firstly, the tension band is fixed by longitudinal K-wires, which have a smooth surface and are prone to loosening and displacement and do not exert direct vertical pressure on the fracture ends. Additionally, the superficial position of the patella means that the physical properties of K-wires and tension bands may lead to local soft tissue irritation or necrosis.^[20]

Therefore, orthopedic experts continue to research and develop innovative techniques based on the principle of tension bands to improve and refine this fixation method.^[21] For example, using titanium cables instead of wires, as the physical properties of titanium cables are considered to better conform to the bone surface and provide better mechanical effects.^[22] Furthermore, the new modified tension band wire fixation technique proposed by this research team has achieved good clinical efficacy by changing the fixation method of the wire and surgical details. Titanium cable tension bands and titanium cable tension bands with cerclage internal fixation for patellar fractures have gained popularity among clinical doctors in recent years, with an increasing use rate. However, these fixation techniques have advantages and disadvantages, and there is no clear consensus on the best fixation method for treating patellar fractures.

Our study aimed to compare 3 surgical methods for treating patellar fractures, specifically focusing on the outcomes of the enhanced tension band wire technique. The findings indicate that all 3 methods are viable for treating patellar fractures, with no significant differences in surgical outcomes, including blood loss, incision length, and VAS score on the third postoperative day. This suggests that the 3 treatment methods have similar requirements for the surgical field, consistent efficacy in improving patient pain, and no significant difference in blood loss during surgery. There was no difference in the surgical incision, which may be because all 3 surgical methods belong to open reduction and internal fixation, requiring total exposure of the patella to complete the anatomical reduction of the patella. The primary source of patient pain is the displacement and separation of the fracture ends, which stimulates the surrounding soft tissue. The VAS score on the third postoperative day reflects the degree of pain experienced by the patient after surgery. There were no significant differences in the VAS data among the 3 groups of cases, which may be because all 3 surgical methods can provide strong internal fixation, improving patient pain by controlling the relative position change of the fracture ends.

Also, multiple group comparisons found no statistically significant difference in fracture healing time and internal fixation removal rate, indicating that the 3 surgical techniques can all meet the requirements for fracture healing. Regarding the internal fixation removal rate during follow-up, we found that many patients lacked a clear understanding of whether internal fixation needed to be removed, often due to external factors such as suggestions from fellow patients, traditional concepts, difficulties with MRI examinations, and economic concerns. Therefore, we believe that patients in such cases need clearer education and popularization of scientific knowledge.^[23]

However, multiple comparisons of operation time indicated that there was a statistically significant difference. This suggests that the titanium cable tension band internal fixation technique required the least time, whereas the double-wire internal fixation technique took longer. This result is somewhat different from our usual understanding. After analyzing the characteristics of the 3 surgical techniques, we found that the titanium cable tension band took less time because the titanium cable fixation requires specialized auxiliary instruments that can quickly complete the fixation, whereas the double-wire tension band took longer due to the need for more manipulation in the “figure-eight” winding of the wires.^[24]

Additionally, the double-strand wire tension band group demonstrated advantages in terms of lower hospitalization costs, shorter postoperative recovery time, earlier functional exercise, and a lower complication rate when compared to the titanium cable tension band with the cerclage group. Our results found a clear difference in hospitalization costs among the patients. Upon analyzing the surgical instruments used, it was found that the high commodity price of titanium cables led to a significant cost difference between the double-wire tension band internal fixation technique and the titanium cable internal fixation with cerclage technique, indicating an excellent economic advantage for the double-wire tension band internal fixation technique. The cost-effectiveness of the techniques mentioned in this study is indeed remarkable when compared to traditional methods like screws and plates. The key factors contributing to these cost differences include lower material costs and simplified surgical procedures.

We also observed several vital points that warrant attention. Firstly, regarding postoperative hospital stays, patients experienced shorter stays and earlier discharge with the titanium cable internal fixation technique compared to the titanium cable tension band with cerclage. This statistically significant difference highlights the potential for titanium cable internal fixation to expedite patient recovery and hospital discharge processes. Turning to the initial functional exercise time, both double-strand wire tension bands showed statistically significant advantages over titanium cable tension bands with cerclage. This suggests that patients treated with a double-strand wire tension band may be able to initiate functional exercises sooner after surgery compared to those receiving a titanium cable tension band with cerclage. This finding is consistent with the underlying principle of tension band techniques, which aims to facilitate early mobilization and prevent joint stiffness.^[25] When examining the Lysholm score at the 1-year mark postsurgery, we found that the titanium cable tension band with the cerclage group had a statistically lower score, suggesting slightly inferior functional recovery outcomes. This discrepancy aligns with the concept that early and effective functional exercise is crucial for optimal recovery, and the potential complications arising from the cerclage component might have limited postoperative mobility, contributing to a less favorable functional outcome.

These observations reinforce the consensus among orthopedic surgeons on the importance of strong internal fixation and prompt initiation of functional exercises. The reduced functionality associated with the titanium cable tension band with the cerclage technique may indeed be linked to the restrictions in mobility and possible complications it introduces for some patients, emphasizing the need for careful consideration when selecting the most appropriate fixation method.^[26] This underscores the value of continued exploration and refinement of surgical techniques to optimize patient outcomes, especially regarding early rehabilitation and long-term functional recovery.

The study has several limitations, including the potential for selection bias, as patient preferences or surgeon expertise could influence the choice of surgical technique. A key limitation is that Group C may have included more complex fractures, as cerclage was sometimes used for subtle instability. This could independently contribute to longer recovery times and higher complications, rather than the cerclage itself. The study also does not account for potential differences in postoperative care or patient compliance, which could affect recovery times and functional outcomes. Additionally, the reliance on patient-reported outcomes, such as the Lysholm score, could introduce subjective bias. Importantly, our findings indicate associations between cerclage-free techniques (Groups A and B) and favorable outcomes (lower costs, earlier exercise) in this cohort. However, these associations may be influenced by unmeasured factors (e.g., fracture complexity, rehabilitation adherence), limiting causal inference. Therefore, these limitations suggest that the results should be interpreted cautiously and that further research with a more controlled design may be necessary to confirm the findings.

5. Conclusions

The double-strand wire tension band group and the titanium cable tension band group have significant advantages over the titanium cable tension band with the cerclage group regarding postoperative recovery time and early functional exercise. The modified TBW without cerclage is associated with cost efficiency and favorable early outcomes in selected patellar fractures. However, due to the retrospective design, these findings should be interpreted as hypothesis-generating, with confirmation needed in prospective, randomized studies.

Author contributions

Conceptualization: Ning Gai, Jihang Yao, Fukun Lin, Yiming Liu, Baochang Qi.

Data curation: Fukun Lin, Baochang Qi.

Formal analysis: Ning Gai, Jihang Yao, Yiming Liu.

Investigation: Fukun Lin.

Project administration: Baochang Qi.

Resources: Yiming Liu.

Software: Ning Gai, Jihang Yao.

Supervision: Fukun Lin.

Writing – original draft: Yiming Liu.

Writing – review & editing: Ning Gai, Jihang Yao, Fukun Lin, Baochang Qi.