Exploring key factors affecting stone retention rates in percutaneous nephrolithotomy from a three-dimensional structural perspective: a retrospective study

Abstract

Background

Percutaneous nephrolithotomy (PCNL) is a mainstream minimally invasive strategy for renal calculi. Despite widespread use, residual calculi after PCNL remain a key clinical challenge. Precise preoperative evaluation of renal collecting system anatomy and rational planning of the percutaneous access route are critical for improving stone-free rates. This study aimed to explore whether morphological features of the target calyx can predict stone clearance from a non-target puncture calyx and establish a model for assessing residual stone risk.

Methods

A retrospective study was conducted including 105 PCNL cases (67 stone-free, 38 with residual stones) with distinct puncture and target calyces between January 2023 and June 2025. Three-dimensional (3D) models were reconstructed from preoperative computed tomography (CT) urography to measure spatial anatomical parameters. Patient characteristics, stone features, and 3D metrics were entered into binary logistic regression to screen independent predictors and construct a nomogram. Model performance was evaluated using receiver operating characteristic (ROC), calibration curves, decision curve analysis (DCA), and internal validation (n=29).

Results

Three independent predictors were identified: punctured calyx length-to-width ratio [odds ratio (OR) =6.89, P=0.020], inter-calyceal axis angle (OR =0.929, P<0.001), and target calyx length-to-width ratio (OR =8.925, P=0.003). The model showed excellent discrimination with an area under the curve (AUC) of 0.905, sensitivity of 86.8%, and specificity of 80.6% at the optimal cutoff of 0.291. The Hosmer-Lemeshow test indicated good calibration (χ²=12.467, P=0.132). Calibration and DCA confirmed favorable accuracy and clinical utility. Internal validation yielded an AUC of 0.829, verifying model stability and reliability.

Conclusions

A predictive model combining calyceal length-to-width ratios and inter-calyceal axis angle can effectively predict stone clearance in the target calyx. This model provides a valuable reference for optimizing calyx selection and improving stone-free outcomes in PCNL.

Introduction

Percutaneous nephrolithotomy (PCNL) is widely used in clinical practice for the management of complex renal calculi. Compared with other minimally invasive procedures for upper urinary tract stones, PCNL offers a relatively high stone-free rate (SFR) and is less influenced by stone location, density, or composition (1). Accordingly, PCNL is recommended as the first-line treatment for renal stones larger than 20 mm (2). Nevertheless, the reported single-session SFR for PCNL ranges from 4% to 26% (3), suggesting considerable room for improvement. In the treatment of complex renal stones, surgeons frequently encounter multiple calculi distributed across different calyces. Because the risk of complications increases with the number of percutaneous access tracts (4), selecting a single puncture site that can efficiently reach multiple target calyces is of significant importance. A recent meta-analysis demonstrated that the use of three-dimensional (3D)-printed models before PCNL can significantly improve operative time, stone clearance, puncture accuracy, length of hospital stays, blood loss, and complication rates (5). However, this approach increases both procedural time and cost, and still does not quantify the rationale for selecting an optimal access site. In order to address this gap, the present study employs 3D reconstruction of the collecting system to quantitatively evaluate the spatial relationship between the puncture calyx and target calyces during PCNL. Through integrating these quantitative metrics, we aim to provide a method that can predict the feasibility of stone clearance within the target calyx, thereby providing guidance for rational access-site selection. We present this article in accordance with the TRIPOD reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2026-0628/rc).

Methods

Study design and population

A retrospective study was conducted on patients diagnosed with renal calculi who underwent PCNL at the Department of Urology, Jinhua Municipal Central Hospital (Affiliated Jinhua Hospital, Zhejiang University School of Medicine) between January 2023 and June 2025. Only cases in which the puncture calyx and the target calyx were located in different renal calyces were included. The analysis was performed at the level of individual renal calyces, yielding a total of 105 eligible cases. Inclusion criteria include (I) preoperative diagnosis of renal calculi confirmed by computed tomography urography (CTU); (II) completion of standard-channel (F24) PCNL (all cases were isolated PCNL without combined laparoscopic nephroureterolithotomy) with the puncture and target calyces situated in different renal calyces, holmium laser was used uniformly (10–20 W, 10–20 Hz). All cases used an Amplatz sheath with suction (−10 to −20 kPa). All procedures were performed by three attending surgeons (≥15 years of experience; >2,000 PCNL cases) with standardized protocols and preoperative case conferences.; (III) abdominal computed tomography (CT) re-examination was performed within one week postoperatively. Patients with residual stones ≥5 mm were allocated to the residual-stone group, while those with residual stones ≤4 mm were classified into the stone-free group (6); and (IV) patients with single calyceal stones with or without renal pelvic stones. Exclusion criteria include (I) anatomical abnormalities of the affected kidney, such as severe renal rotation or horseshoe kidney; and (II) history of secondary procedures, including repeat PCNL or renal puncture with fistula formation. After applying these criteria, a total of 105 renal calyces were included for analysis. To further verify the effectiveness of the prediction model, we enrolled 29 patients who met the inclusion criteria from June 2025 to January 2026 as the internal validation set (n=29) (Figure 1). This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of Jinhua Municipal Central Hospital (Affiliated Jinhua Hospital, Zhejiang University School of Medicine) (No. 2022-282). Informed consent was taken from all the patients.

Figure 1.

Flowchart of patient recruitment. 3D, three-dimensional; CT, computed tomography; CTU, computed tomography urography; DCA, decision curve analysis; ROC, receiver operating characteristic.

Data collection

We collected general demographic information (age and sex) and preoperative CTU data in Digital Imaging and Communications in Medicine (DICOM) format for all participants. 3D reconstructions of the renal collecting system (rendered as translucent light blue) and renal calculi were generated using 3D Slicer by a urologist trained in 3D reconstruction. On the reconstructed stereoscopic images, the line connecting the center of the calyceal dome and the center of the calyceal neck was defined as the central axis of each calyx. The calyx containing the stone was designated as the target calyx. For both the puncture calyx and the target calyx, the length of the central axis (L for the puncture calyx; L1 and L2 for the target calyx) and the width of the calyceal neck were measured (Figure 2). Using the spatial vector coordinates calculated from the central axes of the puncture calyx and the target calyx, the spatial angle between the two vectors was computed. The detailed calculation method and formula are provided in Appendix 1. The length-to-width ratio of each calyx was subsequently calculated. Stone volume (7) and maximum Hounsfield unit (HU) values were obtained using the Segment Statistics module in 3D Slicer. Residual stones (8) were defined as calculi with a maximal diameter greater than 4 mm on CT performed one week postoperatively.

Figure 2.

3D visualization of the collecting system (semi-transparent light blue), stones (yellow and brown), the central axis of the puncture calyx (L), and the central axes of the two target calyces (L1, L2). 3D, three-dimensional.

Statistical analysis

All the statistical analyses were conducted using IBM SPSS version 26.0 and R version 4.2.0. Continuous variables with a normal distribution were presented as mean ± standard deviation, and compared between groups using the independent-samples t-test. Continuous variables with a non-normal distribution were expressed as median and interquartile range (IQR) and compared using the Mann-Whitney U test. Categorical variables were summarized as counts and percentages and analyzed using the Chi-squared test or Fisher’s exact test, as appropriate. Variables showing statistically significant differences in univariate analysis were entered into a multivariate binary logistic regression model to identify independent predictors. Model discrimination and calibration were assessed using the area under the receiver operating characteristic (ROC) curve (AUC) and calibration plots, respectively. Youden index was applied to determine the optimal cutoff value of the nomogram to maximize sensitivity and specificity. DCA was performed to evaluate the clinical utility of the predictive model. A two-sided P value <0.05 was considered statistically significant.

Results

Univariate analysis

In this study, 105 cases were included and grouped according to the presence or absence of postoperative residual stones in the target calyx: the stone-free group (n=67) and the residual-stone group (n=38). A total of 12 cases (11.4%) required flexible cystoscope assistance via the Amplatz sheath; these were classified as residual. No statistically significant differences were observed between the two groups with respect to sex, age, puncture calyx location, stone HU value, stone volume, puncture calyx length, puncture calyx width, target calyx length, or target calyx width. Significant between-group differences were identified for the target calyx length-to-width ratio and the inter-calyceal angle. Although the puncture calyx length-to-width ratio yielded a P value of 0.059, approaching the significance threshold, it was retained for subsequent multivariate analysis (Table 1).

Table 1. Patients, stones, and anatomic collecting system characteristics.

Parameters	Stone free (n=67)	Stone residue (n=38)	t/χ2	P
Age	55.84 ± 12.87	57.11 ± 11.74	−0.501	0.617
Gender
Male	40 (59.7)	25 (65.8)	0.381	0.537
Female	27 (40.3)	13 (34.2)
Puncture calyx location
Middle calyx	44 (65.7)	26 (68.4)	0.082	0.774
Upper or lower calyx	23 (34.39)	12 (31.6)
Stone HU value
≥1,000	54	30	0.041	0.839
<1,000	13	8
Stone volume (mm3)	1,480.92±2,033.65	2,002.97±5,009.10	−0.753	0.453
Punctured calyx length (mm)	12.27±3.99	13.51±4.43	−1.474	0.143
Punctured calyx width (mm)	13.89±4.61	13.16±3.80	0.833	0.407
Punctured calyx length-to-width ratio	0.94±0.34	1.08±0.39	−1.907	0.059
Target calyx length (mm)	12.09±6.26	13.52±4.77	−1.221	0.225
Target calyx width (mm)	13.76±4.61	12.37±4.84	1.464	0.146
Target calyx length-to-width ratio	0.89±0.37	1.20±0.50	−3.381	0.001
Angle (°)	88.67±23.92	54.72±24.99	6.877	<0.001

Data are presented as mean ± standard deviation, n, or n (%). HU, Hounsfield unit.

Multivariate analysis

Binary logistic regression was performed using the target calyx length-to-width ratio, the inter-calyceal angle, and the puncture calyx length-to-width ratio as independent variables. The resulting model is shown in Table 2. The Hosmer-Lemeshow goodness-of-fit test indicated satisfactory model calibration (χ²=12.467, P=0.132). In order to minimize the risk of overfitting, collinearity diagnostics were conducted for all independent variables. Variance inflation factors (VIFs) were 1.018, 1.015, and 1.027, respectively, confirming that collinearity was not a concern. The regression analysis identified the target calyx length-to-width ratio (OR =8.925, P=0.003), inter-calyceal angle (OR =0.929, P<0.001), and puncture calyx length-to-width ratio (OR =6.89, P=0.020) as independent predictors of residual stones in the target calyx. Based on these variables, the corresponding nomogram was generated to visually illustrate the distribution patterns (Figure 3).

Table 2. Logistic regression analysis.

Variable	B	Standard error	Wald	Sig.	Exp(B)
Punctured calyx length-to-width ratio	1.93	0.829	5.426	0.020	6.890
Angle	−0.074	0.016	22.541	<0.001	0.929
Target calyx length-to-width ratio	2.189	0.729	9.016	0.003	8.925
Constant	0.521	1.18	0.195	0.659	1.684

Sig., significance.

Figure 3.

Nomogram predicting the likelihood of target calyx stone residue after PCNL. PCNL, percutaneous nephrolithotomy.

Predictive performance and clinical utility of the nomogram

The predictive performance for estimating target calyx stone clearance was evaluated using ROC analysis. The model achieved an AUC of 0.905 [95% confidence interval (CI): 0.848–0.963], demonstrating excellent discriminatory ability (Figure 4). The optimal cutoff value identified for the nomogram was 0.291, corresponding to a sensitivity of 86.8% and a specificity of 80.6% (Youden index: 0.674) (Table 3). Calibration analysis showed close agreement between the predicted and observed probabilities of stone clearance, indicating strong model calibration and predictive accuracy (Figure 5). In addition, DCA was used to assess the clinical utility of the model. As shown in Figure 6, applying this nomogram yielded a positive net benefit across a wide range of threshold probabilities (0–0.92), supporting its value in guiding clinical decision-making.

Figure 4.

ROC curve for predicting residual stone formation after PCNL in training set. AUC, area under the curve; FPR, false positive rate; ROC, receiver operating characteristic; TPR, true positive rate.

Table 3. ROC information.

Test outcome variable	AUC	95% CI	Standard error	Sig.	Optimal cut-point	Sensitivity	Specificity	Accuracy	Youden index
Angle	0.168	0.082–0.253	0.044	<0.001	60.408	0.63158	0.95522	0.8381	0.5868
Target calyx length-to-width ratio	0.712	0.607–0.817	0.053	<0.001	0.8551	0.81579	0.55224	0.64762	0.36803
Punctured calyx length-to-width ratio	0.617	0.503–0.731	0.058	0.047	0.96823	0.65789	0.62687	0.6381	0.28476
Regression model	0.905	0.848–0.963	0.029	<0.001	0.29124	0.86842	0.80597	0.82857	0.67439

ROC, receiver operating characteristic; Sig., significance.

Figure 5.

Calibration curve of the predictive model for residual stone in the training set.

Figure 6.

DCA curve of the Predictive Model for Residual Stone in training set (the x-axis indicates the threshold probability, and the y-axis represents net benefit). DCA, decision curve analysis.

Predictive performance in internal validation set

We evaluated the model fit, discrimination, and calibration using the internal validation set data. The ROC curve of the validation set showed that the AUC of the prediction model was 0.829 (95% CI: 0.680–0.978) (Figure 7). The DCA curve demonstrated that the model was applicable across a wide range of risk thresholds (0.1–0.9), with a particularly pronounced net benefit advantage in the intermediate risk range (0.2–0.7) critical for clinical decision-making (Figure 8). The calibration curve showed that the bias-corrected curve was highly consistent with the ideal line (Figure 9). The likelihood ratio test (P=0.0011 <0.05), C-index of 0.829 (95% CI: 0.680–0.978, P<0.001), and goodness-of-fit test (P=0.3173).

Figure 7.

ROC curve for predicting residual stone formation after PCNL in the validation set. FPR, false positive rate; PCNL, percutaneous nephrolithotomy; ROC, receiver operating characteristic; TPR, true positive rate.

Figure 8.

DCA curve of the predictive model for residual stone in the validation set (the x-axis indicates the threshold probability, and the y-axis represents net benefit). DCA, decision curve analysis.

Figure 9.

Calibration curve of the predictive model for residual stone in the validation set.

Discussion

This study is the first to examine renal calyces as the primary unit of analysis and to construct a nomogram that predicts the risk of residual stones in the target calyx during PCNL based on quantitative 3D structural parameters. Our findings indicate that a larger length-to-width ratio of both the target calyx and the puncture calyx, as well as a smaller angle between their respective central axes, is associated with an increased likelihood of residual stones in the target calyx. These structural characteristics may impede endoscopic maneuverability or limit the effective transmission of lithotripsy energy, thereby reducing stone clearance efficiency. The nomogram developed from these independent predictors exhibited strong discriminatory performance, with an AUC of 0.905, indicating excellent predictive capability. Furthermore, decision curve analysis demonstrated substantial net clinical benefit. Overall, the predictive model proposed in this study can assist clinicians in estimating the risk of postoperative residual stones in the target calyx after the puncture calyx has been selected.

To date, numerous preoperative scoring systems have been developed to predict stone clearance rates following PCNL. The STONE score estimates operative outcomes based on stone size, skin-to-stone distance, degree of hydronephrosis, number of involved calyces, and stone density (9). The CROES score incorporates variables such as sex, body mass index (BMI), stone burden and location, anatomic abnormalities, and prior treatment history (10). The Guy’s stone score evaluates stone location, complexity, and renal anatomy (11). Biswas et al. prospectively assessed the predictive performance of these three systems in 252 patients (12), reporting comparable accuracy of these three scores for predicting postoperative SFRs, with AUC values of 0.852, 0.842, and 0.832, respectively. These findings are consistent with those of Tailly et al. (13) in a large multicenter comparative study. Vernez et al. (14) concluded in a review that none of the existing systems demonstrated clear superiority, highlighting the continued need for more accurate predictive tools. With advancements in artificial intelligence, machine learning (ML) methods have been increasingly applied to refine PCNL outcome prediction (15,16). Liu et al. (17) developed predictive models using three ML algorithms, yielding promising AUC values: 0.836 for the gradient boosting decision tree (GBDT) model, 0.830 for extreme gradient boosting (XGBoost), and 0.803 for the Random Forest model. Meanwhile, growing attention has been directed toward understanding the renal collecting system from a 3D perspective to inform optimal puncture planning (18). A meta-analysis by Ai et al. (5), which included seven studies evaluating PCNL assisted by 3D-printed models, demonstrated significantly higher stone clearance rates in the 3D-assisted group compared with conventional PCNL (OR =2.64, 95% CI: 1.59–4.38, P<0.001). However, the time and financial costs associated with 3D printing remain substantial (19), and only one in seven patients expressed willingness to pay additional fees for such models (20). Furthermore, Nayyar et al. (21) introduced the concept of a “puncture zone” from a 3D standpoint. This was defined as the largest hypothetical cone that can encompass the puncture calyx, providing an intuitive spatial framework to facilitate understanding and planning of PCNL access pathways. Compared with previous studies, the present research incorporates a comprehensive set of spatial parameters, including puncture calyx length and width, target calyx length and width, the length-to-width ratios of both calyces, and the angle between their central axes (22). By quantifying the 3D spatial relationship between the puncture calyx and the target calyx, this study identifies structural indicators that are predictive of stone clearance efficiency within the target calyx. All 3D measurements can be readily and conveniently performed using widely available 3D reconstruction software based on routine preoperative CTU, with no requirement for additional imaging or extra cost. The three quantitative 3D parameters obtained in this model enable accurate prediction of the postoperative SFR, can be systematically incorporated into routine preoperative planning, and help surgeons optimize puncture calyx selection and overall surgical strategy. Our findings indicate that a larger inter-calyceal angle, along with smaller length-to-width ratios for both the target and puncture calyces, is associated with a higher probability of achieving stone clearance in the target calyx. In other words, when the angle between the two calyces is wide, and both calyces exhibit a shallow and broad morphology, the likelihood of successful clearance increases. As a core indicator reflecting the anatomical morphology of the calyx, the impact of the calyx length-to-width ratio on stone retention is mainly achieved through the following two aspects: on the one hand, it affects the flexibility of endoscopic operation; when the calyx length-to-width ratio is large, the calyx is elongated, and the range of motion of the endoscope is limited after entering, making it difficult to fully cover all areas in the calyx, which easily leads to incomplete lithotripsy and increases the risk of retention; on the other hand, it affects the effect of fragment clearance; the channel of the elongated calyx is narrow, the resistance to stone fragment discharge is large, and it is easy to accumulate at the tip of the calyx, which is difficult to completely remove through negative pressure suction or irrigation; while the calyx with a small length-to-width ratio is short and thick, with sufficient endoscopic operation space, high lithotripsy efficiency, smoother fragment discharge, and lower risk of stone retention. The optimal cutoff values for these variables were 60.408 for the angle, 0.855 for the target calyx length-to-width ratio, and 0.968 for the puncture calyx length-to-width ratio. When the predicted probability of stone retention is ≥0.291, it indicates a high risk of stone retention in this calyx. The following strategies should be prioritized in clinical surgical planning: Preferentially avoid such calyces for puncture; select calyces with predicted probability <0.291; If puncture of a high‑risk calyx is unavoidable, it is necessary to anticipate the possibility of using a flexible cystoscope for lithotripsy through the Amplatz sheath and increasing the number of puncture tracts during the operation before surgery, and fully inform the patient; postoperative follow-up and monitoring should be strengthened, and secondary surgery (such as repeat PCNL or flexible nephroscopy lithotripsy) should be performed in a timely manner if necessary to reduce the risk of complications related to stone retention. In this study, the surgical procedure was prone standard-channel PCNL. Further investigation is needed to determine the applicability of this model in other specific PCNL scenarios: (I) for mini-PCNL, the efficiency of stone fragment clearance may be affected due to the smaller tract diameter. The anatomical structure-related predictive factors obtained in this study still hold a certain reference value, but the cut-off value may require further adjustment, which needs verification in subsequent studies; (II) for supine PCNL, the puncture path and calyceal exposure method differ from those in the traditional prone position, which may influence the degree of impact of calyceal anatomy on stone retention. This also requires verification in follow-up studies; (III) for different lithotripsy devices (such as pneumatic ballistic lithotripsy) and flexible nephroscope-assisted surgery, the applicability of the conclusions of this study needs further analysis in conjunction with device characteristics, as flexible nephroscopy can improve calyceal accessibility and may reduce the impact of calyceal anatomy on stone retention. Predictive performance in internal validation set

indicated that the model can effectively assist in individualized clinical intervention decisions, avoiding overtreatment or undertreatment. The calibration curve’s high consistency with the ideal line aligned with the goodness-of-fit test results, confirming the reliable calibration of the model. In addition to predicting the risk of residual stones, our model can also provide valuable guidance for urologists in surgical decision-making regarding procedure selection. Multiple surgical modalities are available for the management of complex renal calculi, including PCNL, laparoscopic pyelolithotomy, and roboticassisted pyelolithotomy. A recent systematic review comparing these approaches demonstrated that no single technique is universally superior, and clinical outcomes are largely determined by patient selection and anatomical characteristics (23). Therefore, preoperative anatomical evaluation of complex renal calculi using our predictive model may offer a practical and reliable reference to support clinical decision-making.

This study has several limitations. First, univariate analysis did not identify significant differences in stone burden scores as defined by previous criteria (24), and thus these variables were not included in the multivariate model. We speculate that this may be partly attributable to the high lithotripsy efficiency of the integrated suction-assisted lithotripter used during surgery (25), which may have mitigated the influence of stone burden on clearance outcomes. Moreover, our analysis focused specifically on individual renal calyces, which are relatively confined anatomical units, rather than on the entire collecting system, as in previous studies. This narrower anatomical focus may reduce the impact of stone burden, although this hypothesis requires confirmation in larger cohorts. The predictive performance of this model may be limited when applied to patients requiring multiple access tracts or intraoperative flexible nephroscopy. Second, owing to the retrospective nature of this study, external validation using larger and more diverse populations is needed for verification before the model can be widely applied. Although internal validation of the model has been completed in the present study, external validation has not yet been performed, which limits the robustness and generalizability of our predictive model. Further external validation in independent and multi‑center cohorts is required prior to widespread clinical implementation to improve its applicability and clinical value. We plan to conduct a prospective study in collaboration with multiple centers, collect case data from different regions and different surgical procedures, and externally validate the prediction model constructed in this study to further improve the generalizability of the study conclusions.

Conclusions

In conclusion, the nomogram developed in this study provides an effective tool for predicting the likelihood of target calyx stone clearance based on the selection of a specific puncture calyx. By incorporating quantitative spatial parameters into preoperative planning, this model may assist surgeons in selecting the most appropriate access calyx and optimizing individualized treatment strategies for PCNL.

Supplementary

The article’s supplementary files as

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of Jinhua Municipal Central Hospital (Affiliated Jinhua Hospital, Zhejiang University School of Medicine) (No. 2022-282). Informed consent was taken from all the patients.

Data Sharing Statement

Available at https://qims.amegroups.com/article/view/10.21037/qims-2026-0628/dss

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DOI: 10.21037/qims-2026-0628