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. 2026 May 14;30(1):114. doi: 10.1007/s10151-025-03244-x

Three-cavity clearance significantly reduces the postoperative fistula rate and abscess recurrence following glandular perianal abscess: a single-center real-world study

Y Xuan 1,#, X-Y Zhang 1,#, J Wang 1,#, C-X Zhang 1, J-L Liu 1, X-R Ye 1, Y Yang 1, H-Y Jin 1,✉
PMCID: PMC13364938  PMID: 42132969

Abstract

Objective

The aim of this study was to further analyze the efficacy and safety of three-cavity clearance (TCC) in the treatment of glandular perianal abscesses, explore the risk factors for postoperative anal fistula and perianal abscess recurrence, and build a prediction model to increase the success rate of TCC in treating perianal abscesses.

Methods

Clinical data were collected from patients who underwent TCC at the Second Affiliated Hospital of Nanjing University of Chinese Medicine from January 2018 to January 2024. Risk factors for perianal abscess recurrence and anal fistula after TCC were analyzed using univariate and multivariate logistic regression. A predictive nomogram model was established on the basis of independent risk factors, and its predictive performance was evaluated. Additionally, risk function curves were used for postoperative anal fistula and abscess recurrence across different abscess locations with statistical significance assessed via log-rank tests.

Results

A total of 308 patients were included from January 2018 to January 2024, with an average follow-up time of 37.9 ± 16.8 months. The postoperative fistula rate was 4.9%, and the abscess recurrence rate was 8.1%. One patient reported occasional fluid leakage after the operation, with a Wexner score of 1 point. The total success rate was 87.0%. Logistic regression analysis revealed that the abscess site, combined diabetes, nutritional status and history of abscess surgery were risk factors for recurrence and anal fistula formation after TCC (p < 0.05). The area under the receiver-operating characteristic curve (ROC) curve was 0.889 (95% CI 0.82–0.95), and the specificity and sensitivity were 95.5% and 75%, respectively.

Conclusions

TCC for perianal abscess can significantly increase the success rate of treatment and reduce the postoperative fistula rate and abscess recurrence. The abscess site, combined diabetes, nutritional status, and history of abscess surgery are independent risk factors for fistula and abscess recurrence after TCC. Current research implies that TCC is a safe and effective surgery for perianal abscess and is worthy of further study and application.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10151-025-03244-x.

Keywords: Glandular perianal abscess, Three-cavity clearance, Real-world study, Risk factors, Success rate

Introduction

Background

Perianal abscess is a potentially debilitating condition most often originating from a glandular infection in the anal canal, and remains one of the more common anorectal conditions encountered in practice [1]. Perianal abscess occurs more often in male than female individuals, with a ratio of approximately 2:1, and may occur at any age, with peak incidence among 20–40 year olds [2, 3]. In about 30–50% of patients, fistula follows a previous anorectal abscess, which can lead to the formation of a primary track and a secondary track in about 25% of patients presenting with anal fistula [4].

The problem with conventional drainage

Conventional treatment, which is the most common treatment method, has centered on prompt incision and drainage to alleviate acute symptoms. However, 30–70% of patients develop anal fistula or have abscess recurrence after incision and drainage, which requires secondary surgery [5, 6]. To reduce the postoperative anal fistula and abscess recurrence rates, some surgeons directly open the suspected fistula and use the cutting seton procedure during the same operation. However, there is a high risk of postoperative fecal incontinence caused by injury to the anal sphincter [7, 8].

The rationale and objective for our study

Therefore, according to the physiological and pathological mechanisms of perianal abscess, we divided the anorectal space into the following three cavities: the submucosal cavity between the mucosa and the internal sphincter, the intersphincteric cavity between the internal and external sphincters, and the cavity outside the external sphincter (including the ischiorectal, retrorectal, and pelvirectal cavities). By opening these three cavities without injuring the sphincter, it is possible to completely drain the infected cavities and reduce the postoperative fistula and perianal abscess rates (Fig. 1) [9, 10]. Our previous multicenter randomized controlled trial confirmed that the postoperative fistula rates and abscess recurrence rates after TCC decrease apparently without anal incontinence [11]. Our team analyzed the efficacy and safety of treatment with TCC on the basis of these real-world data, aiming to improve the success rate of TCC in the treatment of perianal abscess.

Fig. 1.

Fig. 1

Diagram of the three cavities. (a), (b), and (e) show the cavities outside the external sphincter: (a) shows the subcutaneous cavity, (b) shows the ischiorectal cavity, and (e) shows the posterior rectal cavity; (c) shows the submucosal cavity (cavity between mucosa and internal sphincter); (d) shows the intersphicteric cavity (cavity between internal and external sphincters)

Methods

Design

The clinical data of patients who underwent TCC surgery were analyzed using univariate and multivariate logistic regression to identify the independent risk factors for perianal abscess recurrence and anal fistula. On this basis, a predictive nomogram model was constructed and its predictive efficacy was evaluated. At the same time, the impact of different abscess locations on postoperative anal fistula and abscess recurrence was analyzed using the risk function curve. This research was approved by the hospital’s ethics committee, and registered in the Chinese Clinical Trial Registry (ChiCTR1800016958, retrospectively registered).

Data collection

Inclusion criteria

All patients admitted to the Department of Anorectal Surgery at the Second Affiliated Hospital of Nanjing University of Chinese Medicine from January 2018 to January 2024 who underwent TCC for glandular perianal abscess were included and followed up. Patients were divided into a success group and a failure group according to whether they presented with postoperative anal fistula or recurrence. Sex, age, disease duration, history of perianal abscess surgery, combined diseases, nutritional status, abscess location through endorectal ultrasound and magnetic resonance imaging, and operation time were recorded. Postoperative follow-up included the formation of anal fistulas, the recurrence of abscesses, and cases of anal incontinence. Postoperative anal function was evaluated using the Wexner score.

Exclusion criteria

Patients with Crohn’s disease, ulcerative colitis, those who were receiving chemotherapy for malignant tumors or who were undergoing simple drainage surgery, and individuals who were receiving immunosuppressants were excluded.

Statistical methods

SPSS 26.0 software was used for data analysis. Data are expressed as numbers and percentages (n, %), and the χ2 test was used for comparisons between groups. The Kolmogorov–Smirnov test is used to check for normality. Univariate and multifactorial logistic regression analysis was used to select factors affecting recurrence and anal fistula after TCC. Multifactorial logistic regression analysis was performed, with the recurrence of perianal abscess and the formation of anal fistula after TCC as the dependent variable (1 = occurrence and 0 = nonoccurrence), and a history of abscess surgery (1 = yes and 0 = no), comorbid diabetes (1 = yes and 0 = no), preoperative nutritional status (1 = low risk, 2 = medium risk, and 3 = high risk), and abscess site (1 = intersphincteric abscess, 2 = ischiorectal abscess, 3 = pelvic abscess, and 4 = retrorectal abscess) was used in the univariate analysis of the success group and failure group. The rms program package in R version 3.5.3 software was used to construct a nomogram risk prediction model. Calibration curves were drawn to verify the consistency of the nomogram model. ROC curves were plotted, and the area under the curve (AUC) was calculated to evaluate the model’s discrimination ability. The cumulative risk function was used to plot curves of postoperative anal fistula and recurrence for abscesses at different sites after TCC, and the log-rank test was performed to compare the risk rates of postoperative recurrence or anal fistula formation of abscesses at different sites. Differences in the data with p < 0.05 were considered statistically significant.

Nutritional status and malnutrition screening

Malnutrition universal screening tool (MUST) is recommended as the most valid nutritional screening tool for routine use in gastrointestinal surgery[12]. Therefore, in this study, the nutritional status of the patients before the operation was evaluated using the MUST score (Table 1).

Table 1.

MUST score calculation

Indicator Scoring criteria Score
BMI (kg/m2)  > 20.0 0
18.5–20.0 1
 < 18.5 2
Weight loss  < 5% (over 3–6 months) 0
5–10% (over 3–6 months) 1
 > 10% (over 3–6 months) 2
Acute disease effect If patient is acutely ill and there has been or is likely to be no nutritional intake for > 5 days 2

Three-cavity clearance surgical method

The procedure is performed under spinal or general anesthesia and requires a surgeon experienced in anorectal surgery. The patient is placed in the lateral position. The procedure requires a surgeon experienced in anorectal surgery due to the need to accurately identify and navigate the anatomical planes involved. This method starts by making incisions in the area where the abscess is most swollen (Fig. 2A), and after cutting through the skin, the space outside the external sphincter is fully drained (Fig. 2B). The area is then separated along the intersphincteric groove until normal tissue is reached. Once adequate drainage of pus occurs, the intersphincteric pus cavity is separated (Fig. 2C). Finally, an incision is made in the submucosal space (Fig. 2D), the mucosa and submucosal tissues around the submucosal space along the surface of the internal sphincter are removed, and the incision is appropriately enlarged. If necessary, the infected hemorrhoid is ligated, the wound margins are trimmed, and the bleeding is stopped thoroughly before the incision is filled with sterilized petrolatum gauze. An exhaust tube can be appropriately placed in the anal canal, and sterile gauze can be applied as both a pressure dressing and an external sterile dressing.

Fig. 2.

Fig. 2

TCC procedure. (A) Make an incision at the center where the abscess fluctuates most evidently. (B) Drainage of external sphincter cavities. (C) Divide intersphincteric cavity. (D) Make an incision in submucosal cavity, cut the mucosa and submucosal tissue around the cavity along the sphincter surface, and ligate the hemorrhoids around the infected area. (E) Place an exhaust tube and sterile gauze in the anal canal

Result

From January 2018 to January 2024, a total of 308 patients were included in the study, with an average follow-up time of 37.9 ± 16.8 months. The wound healing time of the patients was 36.5 ± 14.0 days, the postoperative anal fistula rate was 4.9% (15/308), and the abscess recurrence rate was 8.1% (25/308), among which 23 patients presented with recurrence at the original site and 2 patients presented with recurrence at other sites. One patient developed occasional fluid leakage after surgery, with a Wexner score of 1 point. The total success rate was 87.0% (268/308) (Table 2).

Table 2.

Postoperative recurrence and anal fistula formation after TCC (cases, %)

Total cases Failure cases
Total Anal fistula formation Abscess recurrence
Gender Male 258 35 (11.4%) 13 (4.2%) 22 (7.2%)
Female 50 5 (1.5%) 2 (0.6%) 3 (0.9%)
Surgical history Yes 23 13 (4.2%) 3 (0.9%) 10 (3.2%)
No 285 27 (8.8%) 12 (3.9%) 15 (4.9%)
Comorbid diabetes Yes 35 15 (4.9%) 5 (1.6%) 10 (3.9%)
No 273 25 (8.1%) 10 (3.2%) 15 (4.9%)
Comorbid hypertension Yes 45 3 (0.9%) 0 (0%) 3 (0.9%)
No 263 37 (12.0%) 15 (4.8%) 22 (7.2%)
Preoperative nutritional status (MUST) Low risk 285 28 (9.0%) 11 (3.5%) 17 (5.5%)
Medium risk 20 10 (3.2%) 3 (0.9%) 7 (2.3%)
High risk 3 2 (0.6%) 1 (0.3%) 1 (0.3%)
Abscess site Intersphincteric abscess 240 11 (3.6%) 4 (1.3%) 7 (2.3%)
Ischiorectal abscess 30 3 (0.9%) 1 (0.3%) 2 (0.6%)
Retrorectal abscess 33 23 (7.5%) 9 (2.9%) 14 (4.6%)
Pelvirectal abscess 5 3 (0.9%) 1 (0.3%) 2 (0.6%)

Univariate analysis of factors influencing the recurrence and formation of anal fistula after TCC for perianal abscess

There was no significant difference in sex, age, disease duration, combined hypertension, or operation time between the two groups (p > 0.05). The proportion of patients with a history of abscess surgery, comorbid diabetes, preoperative nutritional status (nutritional status was assessed with malnutrition universal screening tool), and retrorectal abscess was significantly greater in the failure group than in the success group (p < 0.05) (Table 3).

Table 3.

Univariate analysis of factors influencing recurrence and fistula formation after TCC

Factor Success group (268 cases) Failure group (40 cases) χ2 p-Value
Gender 0.471 0.492
 Male 223 35
 Female 45 5
Age 2.593 0.107
 > 50 years 64 5
 ≤ 50 years 204 35
Disease duration 0.238 0.626
 > 7 days 39 7
 ≤ 7 days 229 33
History of abscess surgery 41.688  < 0.001
 Yes 10 13
 No 258 27
Comorbid hypertension 1.863 0.172
 Yes 42 3
 No 226 37
Comorbid diabetes 31.177  < 0.001
 Yes 20 15
 No 248 25
Operation time 1.379 0.240
 > 30 min 64 13
 ≤ 30 min 204 27
Preoperative nutritional status (MUST) 34.418  < 0.001
 Low risk 257 28
 Medium risk 10 10
 High risk 1 2
Abscess sites 118.931  < 0.001
 Intersphincteric abscess 229 11
 Ischiorectal abscess 27 3
 Pelvirectal abscess 2 3
 Retrorectal abscess 10 23

Multifactorial logistic regression analysis of factors influencing the recurrence and formation of anal fistula after TCC for perianal abscess

Results revealed that the abscess site, combined diabetes, nutritional status, and history of abscess surgery were independent risk factors for postoperative recurrence of abscess and anal fistula (p < 0.05) (Table 4).

Table 4.

Multivariate logistic regression analysis of factors influencing fistula formation after perianal abscess incision and drainage

Factor Assignment B SE Wald χ2 p OR 95% CI
History of abscess surgery Yes = 1, No = 0 1.748 0.696 6.298 0.012 5.743 1.466–22.488
Combined diabetes Yes = 1, No = 0 1.488 0.641 5.393 0.020 4.429 1.261–15.554
Abscess site

Intersphincteric abscess = 1,

Ischiorectal abscess = 2,

Pelvirectal abscess = 3,

Retrorectal abscess = 4

1.331 0.188 50.365  < 0.001 3.786 2.621–5.468
Preoperative nutritional status (MUST)

Low risk = 1

Medium risk = 2

High risk = 3

1.528 0.568 7.249 0.007 4.611 1.516–14.028
Constant −6.675 0.883 57.125  < 0.001

Construction of the nomogram prediction model

A nomogram prediction model was built on the basis of the four independent risk factors listed in Table 4. The results revealed that the weight of the abscess site increased by 100 points, a history of abscess surgery added a weight of 44 points, preoperative nutritional status added a weight of 79 points, and combined diabetes added a weight of 39 points (Fig. 3).

Fig. 3.

Fig. 3

Nomogram risk model for predicting the recurrence and formation

Validation of the nomogram prediction model

The nomogram prediction model was verified using the bootstrap method. The ideal curve fit well with the calibration curve, which indicated that the measured values were consistent with the predicted values (Fig. 4a). The ROC curve was plotted for model discrimination, and results revealed that the area under the curve was 0.889 (95% CI 0.82~0.95) and the specificity and sensitivity were 95.5% and 75%, respectively, which indicates the high prediction accuracy of the nomogram model (Fig. 4b). Evaluating the clinical effectiveness of the model using the decision curve analysis, the decision curve of the model presents a full fan-shaped pattern (Fig. 4c). Within the probability threshold range of 0.2 to 0.8, the model’s decision curve is always above the “all” line and the “none” line, indicating that when the model’s threshold probability is between 0.2 and 0.8, using this model for clinical decision-making can achieve a greater net benefit than the “no intervention” or “all intervention” schemes, demonstrating the good clinical effectiveness of this model.

Fig. 4.

Fig. 4

Validation of the nomogram risk model (a): the calibration curve of the nomogram model for predicting recurrence and anal fistula after TCC; (b): the ROC curve of the nomogram risk model for predicting recurrence and anal fistula after TCC; (c): decision curve analysis (DCA)

Plotting the risk function

A cumulative risk function was performed by the Kaplan‒Meier method. Patients were divided into groups according to the site of abscess: the intersphincteric abscess group, the ischiorectal abscess group, the pelvic abscess group, and the petrorectal abscess group. The risk function of recurrence was plotted with perianal abscess recurrence as a positive event (Fig. 5a), anal fistula formation as a positive event (Fig. 5b), and perianal abscess recurrence and anal fistula formation as positive events (Fig. 5c); the differences were statistically significant (p < 0.05).

Fig. 5.

Fig. 5

Risk function plots for recurrence and anal fistula formation after TCC (a): the risk function plot for recurrence after TCC; (b): the risk function plot for anal fistula formation after TCC; (c): risk function plot for recurrence and anal fistula formation after TCC

Discussion

Perianal abscess is a common perianal infectious disease, with 20,000–100,000 new cases per year, mostly in young men, with 90% of perianal abscesses caused by anal gland infections. Incision and drainage are the most commonly used surgical methods for perianal abscess, but the postoperative anal fistula rate is approximately 7–66%, and the recurrence rate is approximately 4–31%. When two or more surgeries are required, the pain and negative effects on a patient’s work and quality of life are increased [13]. To reduce the postoperative anal fistula rate, some surgeons directly open the suspected fistula or use the cutting seton procedure during the same operation, which is called a “radical abscess incision.” A meta-analysis (involving 6 studies and 479 subjects) revealed that, compared with those with incision and drainage, the rates of abscess recurrence and anal fistula were significantly lower after radical abscess incision (RR 0.13, 95% CI 0.07–0.24, p = 0.38) and the risk of postoperative anal incontinence was significantly greater (RR 3.06, 95% CI 0.7–13.34, p = 0.14), which severely affected the quality of life of patients [14].

On the basis of the pathophysiology of perianal abscess formation, our research team proposed the concept of “three-cavity infection.” On this basis, we further propose “three-cavity clearance.” Preliminary clinical observations, prospective cohort studies, and multicenter randomized controlled trials have confirmed that “three-cavity clearance” can significantly reduce the postoperative anal fistula rate and abscess recurrence and preserve the sphincter without damaging anal function. The clinical outcomes far exceed those reported by international peers [9–11, 15]. Excluding our study, 17 studies on TCC for perianal abscesses indicate that TCC can significantly improve the postoperative success rate for perianal abscess and reduce the anal fistula rate after surgery to less than 10%. TCC has become the preferred surgery for glandular perianal abscess.

Although TCC has improved the success rate of glandular perianal abscess treatment to approximately 90%, the question remains of whether we can further enhance its efficacy. What are the characteristics of patients who develop postoperative fistulas or who experience abscess recurrence? Can we make further clinical improvements? Our analysis of 308 patients who underwent TCC for glandular perianal abscess revealed that the rate of anal fistula formation was 4.9%, the rate of abscess recurrence was 8.1%, and the total success rate was 87.0%. The univariate analysis suggests that the proportion of patients with a history of abscess surgery, comorbid diabetes, and retrorectal abscess had significantly greater rates of recurrence and anal fistula formation following TCC (p < 0.05). Furthermore, multifactorial analysis revealed four independent risk factors: a history of abscess surgery (OR 5.743, 95% CI 1.466–22.488, p = 0.012), abscess site (OR 3.786, 95% CI 2.621–5.468, p < 0.001), preoperative nutritional status (OR 4.611, 95% CI 1.516–14.028, p = 0.007), and combined diabetes (OR 4.429, 95% CI 1.261–15.554, p = 0.02).

Among them, a history of abscess surgery added a weight of 44 points to the nomogram risk model. The possible reasons are as follows: patients with a history of perianal surgery often have obvious scars in the anal elastic pad tissue or are replaced by local scars, which results in greater sphincter tension and a greater likelihood of inducing duct stenosis and anal gland infection [16]. It has also been reported that local lesions have formed in patients with a history of abscess. Even if clinical symptoms are alleviated or disappear, the source of infection still exists. When body resistance weakens or the infection is aggravated for other reasons, the probability of anal fistula may increase [17]. On the basis of the anal gland infection theory, the key to successful surgical outcomes is the thorough removal of the primary infection source—the submucosal infected cavity formed by the infection that penetrates the internal sphincter—known as the internal opening. Therefore, preoperative magnetic resonance imaging (MRI) or ultrasound inference and intraoperative probe exploration of the location of the internal opening are particularly important.

Second, the site of abscess, which is another independent risk factor, was weighted by 100 points in the nomogram risk model, and by plotting the risk function, we found a greater risk of postoperative anal fistula and recurrence in petrorectal abscess patients (p < 0.05). According to the three-cavity clearance theory, potentially infected cavities, such as the submucosal cavity and intersphincteric cavity, are fully incised and drained during the operation while opening the retrorectal cavity. Owing to the large amount of loose connective tissue in the retrorectal space and the presence of lateral rectal ligaments on both sides, the pus spread to this space despite ligaments on both sides. In this case, the tissue was pulled by the levator ani muscle so that the pus converged upward. The pus space was deep and large, and the volume of drained pus was more than 100 mL, which can easily lead to retained pus [18]. To avoid rapid wound closure, in principle, the drainage incision should not be smaller than the diameter of the abscess so that no dead space is left in the retrorectal space [19–21]. Skin slices or drainage tubes should be added as appropriate to achieve full drainage, and the abscess cavity should be thoroughly cleaned during postoperative dressing changes. The drainage strips should be placed on the top of the abscess cavity and close to the wound so that the abscess cavity is completely filled from the base, which reduces the risk of abscess recurrence and anal fistula formation. In addition, according to the plotted risk function, a proportion of patients are at risk of abscess recurrence or anal fistula formation after 2–3 years.

Third, the patient’s preoperative nutritional status also has a significant impact on postoperative recovery. When patients suffer from malnutrition, it affects immune system. Even if the surgical drainage is unobstructed, the small amount of bacteria remaining in the body or the newly invading bacteria after the surgery, due to the weakened immune function, cannot be completely eliminated. Bacteria are prone to regrow in the original site. In addition, after surgical drainage, the abscess cavity requires a complete healing process to fill in and undergo tissue reconstruction. This process requires a large amount of protein. If the abscess cavity fails to close or the healing quality is extremely poor due to malnutrition, it is likely to form a deep sinus tract, which is prone to reinfection and leads to recurrent abscesses. Last but not the least, surgery itself leads to inflammation corresponding with the extent of the surgical trauma, and leads to a metabolic stress response [22]. During the postoperative period the patient is in a catabolic state where energy and protein are utilized from the body’s stores. Fat and protein stores become the primary reservoir, with an obligatory generation of the required glucose. To achieve proper healing and functional recovery (restitutio adintegrum), a good nutritional status is particularly necessary [23].

Furthermore, diabetes mellitus was also a significant factor in the univariate analysis and should also be a focus of further study. Studies have shown that patients with perianal abscesses are more likely to relapse when their blood glucose control is poor at the first admission (HbA1c > 7.5%) [24]. Moreover, persistent hyperglycemia can damage endothelial cell function, hinder protein synthesis in surgical wounds, and slow the growth of granulation tissue and capillaries, which leads to delayed or even nonhealing of the postoperative incision [25]. Therefore, patients with diabetes mellitus should have their blood glucose level monitored closely before and after surgery, and attention should be given to the control of blood glucose, which can help improve the prognosis.

Limitations

This study has several limitations that should be acknowledged. First, as a single-center study, our findings may lack generalizability due to institutional selection bias and homogeneous clinical practices. Nevertheless, the sample size, particularly within the recurrence subgroup (n = 40), is relatively limited. This may affect the statistical power and the robustness of the multivariate regression analysis. Finally, the technique’s novelty, as a newly proposed procedure, long-term efficacy, and safety lack validation through large-scale studies with extended follow-up. The absence of standardized protocols and a defined learning curve may affect reproducibility across surgeons and institutions.

Conclusions

The abscess site, combined diabetes, nutritional status, and history of abscess surgery are influencing factors for postoperative anal fistula and perianal abscess recurrence, and retrorectal abscess poses a greater risk. The nomogram model and risk function curves are important in clinical practice for individually predicting the risk of postoperative complications of perianal abscess. This study further confirms that the model has good predictive consistency and reliability. This indicates that the model can be used to screen high-risk populations and control variable risk factors to further improve the success rate of three-cavity clearance for perianal abscess prevention and improve prognosis. In the future, we will continue to expand on the included sample size, further explore the risk factors for the development of postoperative complications of perianal abscess, and build a more efficient and reliable nomogram model.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contribution

Yan Xuan and Xin-Yi Zhang: writing—original draft. Jun-Wang and Jian-Lei Liu: data curation, formal analysis, and visualization. Ye and Yang: conceptualization and methodology. Hei-Ying Jin and Chun-Xia Zhang: supervision, review, and editing.

Funding

This study was supported by the Jiangsu Province Key Research and Development Project (BE2023786), the Jiangsu Provincial Traditional Chinese Medicine Science and Technology Development Program (ZD202421).

Data availability

Data are provided within the manuscript or supplementary information files.

Declarations

Conflict of interest

The authors declare no competing interests.

Footnotes

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Y. Xuan, X.-Y. Zhang, and J. Wang contributed equally to this work.

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