Bridging the gap in PCNL preoperative planning: software-free stone metrics that outperform conventional measures

Abstract

Objective

Accurate preoperative stone size assessment is crucial for predicting outcomes after percutaneous nephrolithotomy (PCNL), yet a gap persists between the accurate but impractical gold standard (3D software volume) and the practical but suboptimal conventional metrics (maximum diameter and cross-sectional area). This study aimed to validate two novel, software-free stone size metrics—the triaxial diametric product (X) and stacked volume (V)—designed for routine clinical computed tomography (CT) and compare their efficacy in predicting the stone-free rate (SFR) against conventional methods.

Methods

We conducted a retrospective analysis of 283 patients who underwent PCNL. Stone size was measured using four metrics on pre-operative non-contrast CT: maximum diameter (R), maximum cross-sectional area (S), triaxial diametric product (X = x·y·z), and stacked volume (V). The predictive power for SFR was evaluated and compared using receiver operating characteristic (ROC) curve analysis and DeLong’s test.

Results

All four metrics were significant predictors of SFR (p < 0.001). The predictive accuracy, ranked by the area under the curve (AUC), was as follows: maximum diameter (R, AUC = 0.703) < maximum cross-sectional area (S, AUC = 0.734) < triaxial diametric product (X, AUC = 0.789) < stacked volume (V, AUC = 0.801). The novel metrics X and V both significantly outperformed the conventional metrics R and S (p < 0.01), with no significant difference between X and V.

Conclusion

The triaxial diametric product (X) is recommended as a practical and more accurate alternative to conventional metrics for routine clinical practice, especially for stones > 1.5 cm, as it offers an improved balance of predictive accuracy, straightforward calculation, and easy integration into existing workflows without needing specialized software or additional costs. The stacked volume (V) serves as a feasible, software-free tool for practical size estimation in research settings. This study provides urologists with immediately applicable tools to enhance preoperative planning.

Introduction

Urolithiasis is one of the most prevalent urological disorders [1]. Flexible ureteroscopy and percutaneous nephrolithotomy (PCNL) are primary interventions for renal calculi [2, 3]. As PCNL is the recommended first-line treatment for kidney stones larger than 1.5 cm, accurately and efficiently assessing stone size preoperatively to predict procedural efficacy remains a consistent concern for urologists.

Current metrics for stone size lack standardization and are imperfect. Guidelines and routine practice often favor the maximum diameter (R) for its simplicity [4], whereas scoring systems such as the Size, Tract length, Obstruction, Number of involved calyces, and Essence/stone density (S.T.O.N.E.) nephrolithometry score use the maximum cross-sectional area (S) [5]. Most researchers, however, consider three-dimensional (3D) volume—measured using specialized reconstruction software—to be the gold standard for defining stone size [6–9]. Nevertheless, the complexity of 3D volume measurement severely limits its broader clinical use, primarily due to two factors: first, the frequent need for high-resolution CT urography, a costly and non-routine preoperative test; and second, the dependence on specialized 3D reconstruction software, which makes rapid estimation from standard non-contrast computed tomography (NCCT) impractical.

This creates a significant gap between the research gold standard and clinical feasibility. To bridge this gap, we propose and evaluate two novel size metrics designed for direct application on routine NCCT without specialized software: the triaxial diametric product (X) and the stacked volume (V). This retrospective study compares the predictive efficacy of these novel metrics with conventional methods for the stone-free rate following PCNL.

Materials and methods

A total of 354 patients who underwent PCNL at our hospital between January 2021 and December 2022 were screened, and 283 eligible patients were included.

Inclusion Criteria: 1)Adult patients (≥ 18 years old) who underwent percutaneous nephrolithotomy (PCNL) for renal calculi; 2)Availability of both preoperative and postoperative non-contrast computed tomography (NCCT) scans; 3)Complete clinical and radiological data for S.T.O.N.E. score calculation.

Exclusion Criteria: 1)Patients without either preoperative or postoperative NCCT imaging; 2)Pediatric patients (< 18 years old); 3)Patients with concurrent urinary tract anomalies (e.g., horseshoe kidney, ectopic kidney); 4)Patients undergoing simultaneous procedures for other urological conditions; 5)Cases with incomplete medical records or missing essential data for analysis.

The reporting of this study conforms to the STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) guideline [10].

Observation indexes

The observation indexes were divided into three categories:

General condition: age, sex, height, weight, and body mass index (BMI).

Stone size measurements: obstruction, maximum diameter, maximum cross-sectional area, triaxial diametric product, and stacked volume.

Postoperative outcome: stone-free status.

Measurement of indicators

For patients with multiple stones, the largest stone was selected as the index stone for all measurements, consistent with common clinical practice and previous scoring systems.

Four calculations were used to assess stone size:

Maximum diameter (R): The maximum diameter of the stone was measured at each CT level and compared with its longitudinal thickness. The larger of the two values was recorded.

Maximum cross-sectional area (S): Calculated as the area of the largest axial section using orthogonal diameters (maximum diameter × perpendicular diameter).

Triaxial diametric product (X): Defined as x·y·z, where x is the maximum diameter, y is its perpendicular diameter on the same axial slice (effectively defining the maximum cross-sectional area S as x·y), and z is the craniocaudal stone length, calculated as the product of the number of stone-containing slices and the slice thickness. This metric offers a geometrically intuitive approximation of volume.

Stacked volume (V): A simplified volume estimation method calculated as Σ[(x ~ i~ · y ~ i~)], where x ~ i~ and y ~ i~ are orthogonal diameters measured per slice. Considering that NCCT was at a spacing of 5 mm, to balance precision and clinical utility, x and y values were rounded up in 5-mm increments to simplify the calculation:

and so on; y was treated using the same method.This binning strategy, which greatly increased clinical practicality by reducing calculation time by >70% compared to exact mm measurements, results in a unitless value for V.

Postoperative stone clearance was assessed using NCCT imaging after 3 months postoperatively. Patients were classified as stone-free if NCCT showed no high-density shadows in the urinary tract or only spotting shadows of < 4 mm in diameter at the operative site. The presence of high-density shadows of ≥ 4 mm on the operative side was classified as residual stones [3].

Statistical analysis

Statistical analysis was performed using SPSS 26.0 software (IBM Corporation, Armonk, NY, USA). Measurement data were expressed as mean ± standard deviation. A p-value of < 0.05 was considered statistically significant.

Multiple pairwise comparisons of AUCs were performed without adjustment for multiplicity; thus, findings should be interpreted as exploratory.

This was a retrospective study; no formal sample size calculation was performed a priori. Subgroup analyses, particularly those with smaller sample sizes, may be underpowered and should be interpreted cautiously.

Results

Clinical data

A total of 354 patients were screened; 71 were excluded for the following reasons: 33 lacked postoperative CT, 2 were aged < 18 years, 18 had urinary tract anomalies, 13 underwent simultaneous other procedures, and 5 had incomplete records. The final cohort comprised 283 patients. A participant flow diagram is provided in Fig. 1. The baseline demographic and clinical characteristics of the cohort are summarized in Table 1. The study population consisted of 188 men (66.4%) and 95 women (33.6%), with a mean age of 49.25 ± 10.39 years. The mean body mass index (BMI) was 25.20 ± 3.10 kg/m². Stones were located on the left side in 160 patients (56.5%) and on the right side in 123 patients (43.5%).

Fig. 1.

STROBE-compliant participant flow diagram. A total of 354 patients who underwent PCNL between January 2021 and December 2022 were screened. After excluding 71 patients (33 lacked postoperative CT, 2 were aged < 18 years, 18 had urinary tract anomalies, 13 underwent simultaneous other procedures, and 5 had incomplete records), 283 patients were included in the final analysis

Table 1.

Baseline Demographic and Clinical Characteristics of the Patients (n = 283)

Characteristic	Value
Age (years)	49.25 ± 10.39
Sex, n (%)
Male	188 (66.4%)
Female	95 (33.6%)
Height (cm)	166.63 ± 7.90
Weight (kg)	70.16 ± 11.16
BMI (kg/m²)	25.20 ± 3.10
Stone Laterality, n (%)
Left	160 (56.5%)
Right	123 (43.5%)

The stone size measurements obtained by the four different methods are presented in Table 2. The triaxial diametric product (X) and stacked volume (V) showed wider ranges, reflecting their ability to capture three-dimensional stone size.

Table 2.

Stone Size Measurements Using Four Different Metrics

Metric	Range	Mean ± SD
R, mm	13.35–46.12	25.47 ± 6.53
S, mm²	46.89–1026.64	348.69 ± 184.18
X, mm³	792.30–56,465.20	11,471.70 ± 11,907.00
V	15–375	103.55 ± 89.39

R=Maximum Diameter, S = Max Cross-sectional Area, X=Triaxial Diametric Product, V

=Stacked Volume, SD=Standard Deviation

Operative details

All PCNL procedures utilized 18 F puncture channels. A total of 265 patients underwent single-channel puncture, while 18 patients required double-channel puncture. Both double-J stents and nephrostomy tubes were retained postoperatively. A constant-speed, pressure-limiting pump served as the irrigation source during surgery, with a flow rate of 680 mL/min and a pressure limit of 700 mmHg. Lithotripsy was performed using the Auriga XL holmium laser system (StarMedTec GmbH, Starnberg, Germany), manufactured on 19 August 2016. The procedure employed a 600-µm core diameter fiber in lithotripsy mode, with a frequency of 12 Hz and a single-pulse energy of 3,500 mJ. All patients underwent NCCT imaging both preoperatively and after 3 months postoperatively.

Operative outcomes

All PCNL procedures were successfully performed using 18 F puncture channels. Single-channel puncture was performed in 265 patients (93.6%), while 18 patients (6.4%) required a double-channel approach.

Postoperatively, a stone-free status was achieved in 196 patients (69.3%). Complications were observed in 80 patients (28.3%), with the majority being low-grade (Grade 1: 38 patients; Grade 2: 40 patients). Two patients (0.7%) experienced Grade 4 complications (septic shock) requiring intensive care. Complications were graded using the Clavien-Dindo classification. No Grade 3 complications occurred in this cohort.

Statistical analysis

ROC analysis

The surgical outcome was used as the state variable (value: residual), while the maximum diameter (R), maximum cross-sectional area (S), triaxial diametric product (X), and stacked volume (V) were used as test variables in the receiver operating characteristic (ROC) curve analysis. The ROC curves are presented in Fig. 2, and the corresponding areas under the curve (AUCs) are summarized in Table 3.

Fig. 2.

Receiver operating characteristic (ROC) curves for the four stone size metrics in predicting stone-free rate after PCNL. The area under the curve (AUC) values were 0.703 for maximum diameter (R), 0.734 for maximum cross-sectional area (S), 0.789 for triaxial diametric product (X), and 0.801 for stacked volume (V)

Table 3.

Comparison of AUCs of four ROC curves

variable	AUC	S.E.	P	95%CI
R	0.703	0.036	0.000***	0.632-0.773
S	0.734	0.035	0.000***	0.666-0.803
X	0.789	0.030	0.000***	0.730-0.848
V	0.801	0.030	0.000***	0.743-0.859

^*p < 0.05, ^**p < 0.01, ^***p < 0.001

R=Maximum Diameter, S = Max Cross-sectional Area, X=Triaxial Diametric Product, V

=Stacked Volume, S.E.=Standard Error, CI=Confidence Interval

Based on the results, all four methods of stone size assessment were found to be valid predictors of the surgical outcome (p < 0.001). Their accuracy in predicting a stone-free status ranked as follows: maximum diameter (R) < maximum cross-sectional area (S) < triaxial diametric product (X) < stacked volume (V), with corresponding AUC values of 0.703, 0.734, 0.789, and 0.801, respectively. The optimal cut-off values for predicting a stone-free status were determined using Youden’s index and were as follows: maximum diameter (R) = 28.32 mm, maximum cross-sectional area (S) = 343.80 mm², triaxial diametric product (X) = 11,598.25 mm³, and stacked volume (V) = 106.

Pairwise comparison of the ROC curves using DeLong’s test revealed that the triaxial diametric product (X) and stacked volume (V) were statistically superior to the conventional metrics (R and S) (p < 0.01 for all relevant comparisons), while no significant difference was found between X and V themselves (p > 0.05) and the results are presented in Table 4. These results indicate that the triaxial diametric product and stacked volume were significantly more effective than the maximum diameter and maximum cross-sectional area in predicting surgical outcomes.

Table 4.

Pairwise comparison of the AUCs of four ROC curves

pair	z	p	AUC Difference	S.E.	95%CI
R - S	-1.303	0.193	− 0.032	0.263	− 0.079-0.016
R - X	-3.271	0.001**	− 0.086	0.254	− 0.138–0.035
R - V	-3.986	0.000***	− 0.098	0.253	− 0.146–0.050
S - X	-4.138	0.000***	− 0.054	0.251	− 0.080–0.029
S - V	-3.249	0.001**	− 0.066	0.251	− 0.106–0.026
X - V	− 0.715	0.475	− 0.012	0.241	− 0.045-0.021

^*p < 0.05, ^**p < 0.01, ^***p < 0.001

R=Maximum Diameter, S = Max Cross-sectional Area, X=Triaxial Diametric Product, V

=Stacked Volume, Z = Z-score, S.E.=Standard Error, CI=Confidence Interval

Subgroup ROC analysis

Patients were divided into two groups based on the degree of fluid accumulation: Group 1 for mild fluid accumulation and Group 2 for moderate or severe fluid accumulation. Mild hydronephrosis was defined as dilated renal calyces with normal renal papilla morphology and no obstruction or mild hydronephrosis. Moderate hydronephrosis was defined as dilated renal calyces with loss of renal papilla morphology, and severe hydronephrosis was defined as a balloon-like expansion of the renal calyces with thinning of the renal cortex. Use the same method as in 3.4.1 to perform ROC analysis on the two sets of data again.

The results of group 1 are shown in Fig. 3; Table 5. Based on the results, the triaxial diametric product (X) and the stacked volume (V) were found to be valid predictors of the surgical outcome (p < 0.01), while the maximum diameter (R) and cross-sectional area (S) were invalid (p > 0.05). The AUC values of the triaxial diametric product (X) and the stacked volume (V) were 0.707 and 0.746, respectively. There was no significant difference between the triaxial diametric product (X) and the stacked volume (V) (p > 0.05). It is noteworthy that in this subgroup with mild hydronephrosis (Group 1, n = 139), the conventional metrics (R and S) failed to reach statistical significance. This discrepancy with the main analysis may be attributed to the reduced sample size and statistical power in this specific subgroup, which particularly affects the detection of weaker predictive signals from R and S, whereas the more feasible metrics (X and V) remained predictive. These findings should therefore be interpreted with caution.

Fig. 3.

ROC curves for the four metrics in patients with mild hydronephrosis (Group 1, n = 139). AUC values were 0.615 for R (p = 0.204), 0.646 for S (p = 0.099), 0.707 for X (p = 0.007), and 0.746 for V (p = 0.003)

Table 5.

Comparison of AUCs of four ROC curves(Group 1)

variable	AUC	S.E.	P	95%CI
R	0.615	0.091	0.204	0.437-0.793
S	0.646	0.089	0.099	0.472-0.820
X	0.707	0.076	0.007**	0.558-0.856
V	0.746	0.083	0.003**	0.584-0.908

^*p < 0.05, ^**p < 0.01, ^***p < 0.001

R=Maximum Diameter, S = Max Cross-sectional Area, X=Triaxial Diametric Product, V

=Stacked Volume, S.E.=Standard Error, CI=Confidence Interval

The results of group 2 were similar to those in 3.4.1 and are shown in Fig. 4; Table 6. All four methods of stone size assessment were found to be valid predictors of the surgical outcome (p < 0.01). The AUC values for the maximum diameter (R), maximum cross-sectional area (S), triaxial diametric product (X), and stacked volume (V) were 0.652, 0.673, 0.748 and 0.733, respectively. The AUC values of the four ROC curves were compared using DeLong’s test, and the results are presented in Table 7, which are the same as those in 3.4.1.

Fig. 4.

ROC curves for the four metrics in patients with moderate to severe hydronephrosis (Group 2, n = 144). AUC values were 0.652 for R, 0.673 for S, 0.748 for X, and 0.733 for V (all p < 0.01)

Table 6.

Comparison of AUCs of four ROC curves(Group 2)

variable	AUC	S.E.	P	95%CI
R	0.652	0.046	0.001**	0.561-0.742
S	0.673	0.045	0.000***	0.584-0.762
X	0.748	0.042	0.000***	0.666-0.830
V	0.733	0.043	0.000***	0.649-0.818

^*p < 0.05, ^**p < 0.01, ^***p < 0.001

R=Maximum Diameter, S = Max Cross-sectional Area, X=Triaxial Diametric Product, V

=Stacked Volume, S.E.=Standard Error, CI=Confidence Interval

Table 7.

Pairwise comparison of the AUCs of four ROC curves(Group 2)

pair	z	p	AUC Difference	S.E.	95%CI
R - S	− 0.734	0.463	− 0.021	0.297	− 0.078-0.036
R - X	-2.887	0.004**	− 0.096	0.291	− 0.162–0.031
R - V	-2.284	0.022*	− 0.082	0.294	− 0.151–0.012
S - X	-4.129	0.000 ***	− 0.075	0.289	− 0.111–0.039
S - V	-2.749	0.006**	− 0.060	0.292	− 0.103–0.017
X - V	1.008	0.313	0.015	0.285	− 0.014-0.044

^*p < 0.05, ^**p < 0.01, ^***p < 0.001

R=Maximum Diameter, S = Max Cross-sectional Area, X=Triaxial Diametric Product, V

=Stacked Volume, Z = Z-score, S.E.=Standard Error, CI=Confidence Interval

Discussion

Our study demonstrates that both novel stone size metrics - the Triaxial Diametric Product (X) and the Stacked Volume (V) - are significantly effective predictors of stone-free rate after 18 F PCNL. Although the AUC improvements of X and V over R and S were modest (ΔAUC ~ 0.06–0.08), they were statistically significant and may represent a meaningful step toward more accurate size estimation without added cost or complexity. However, the clinical relevance of this incremental gain warrants further prospective evaluation. While the improved predictive value of stone volume is a known principle in research and forms the basis of scoring systems like the S.T.O.N.E. score, the SHAnghai LINgth, Inner structure, Hilar density, (Shanghai Lithometry Index) (SHA.LIN) score, and the Guy’s grading [5, 11, 12], the critical innovation of our work lies in introducing and validating two highly practical methods that bridge the gap between the unfeasible volumetric gold standard and the suboptimal conventional metrics in routine clinical practice.

Stacked Volume (V): A Novel and Feasible Approximation

The Stacked Volume (V) represents, to our knowledge, the first application of a simplified, manual ‘stacked’ volume calculation using a unique binning strategy on standard 5-mm NCCT. Its primary innovation is accessibility: it requires no specialized software, no high-resolution CT, and its calculation method reduced manual measurement time by over 70%. This addresses the core barrier to routine volumetric assessment. While V is less practical than software-derived volumes, its predictive power (AUC 0.801) was reliable and not significantly different from the more complex triaxial product, validating its potential as a viable volumetric estimate for research settings where dedicated software is unavailable.

Triaxial Diametric Product (X): A practical balance for Clinical Practice

The Triaxial Diametric Product (X) is explicitly positioned as a clinically improved alternative to conventional 2D metrics. Its key strengths are profound simplicity, intuitive geometry (familiar to clinicians from tumor measurement), and immediate calculability from standard imaging. It requires no additional training, software, or scans. Its predictive power (AUC 0.789) was statistically equivalent to V and significantly better than R or S. This establishes X as the recommended ‘next step’ for preoperative assessment, offering a significant gain in accuracy without sacrificing the ease of use essential for busy clinical workflows.

Clinical Implications and Recommendations

Our findings translate into clear, actionable recommendations:

For small stones (R < 1.5 cm), maximum diameter (R) remains adequate due to its simplicity and universal understandability.

For larger stones (e.g., > 1.5 cm), where conventional diameter may poorly reflect true burden, we suggest that the Triaxial Diametric Product (X) may offer a more accurate prediction of SFR while maintaining simplicity.

In research contexts requiring finer size estimation (e.g., lithotripsy efficiency studies), the Stacked Volume (V) offers a more practical, software-free volumetric approximation and is recommended for these purposes.

Limitations

This study has several limitations. Its retrospective, single-center design may introduce selection bias. Furthermore, the lack of an external or internal validation cohort limits the generalizability of our findings; future multi-center studies are needed to confirm the predictive performance of these metrics. The mandatory requirement for a 3-month postoperative CT scan, while ensuring objective outcome assessment, may have inadvertently excluded patients with an uneventful recovery who did not return for follow-up or those lost to follow-up. The inherent approximation of V, though essential for clinical feasibility, introduces some error compared to true 3D volume. The subgroup analysis for hydronephrosis was likely underpowered, particularly in the mild hydronephrosis group, which may explain why conventional metrics (R and S) did not reach statistical significance in that subset despite being significant in the overall cohort. These results should therefore be interpreted with caution. Additionally, multiple statistical comparisons of ROC curves were conducted without formal adjustment, which may inflate the risk of Type I error (false-positive findings). Furthermore, Our study did not directly compare X or V with established composite scoring systems such as S.T.O.N.E., CROES, or Guy’s scores, which incorporate additional anatomical and radiological factors. Future studies should evaluate whether integrating X or V into such scores enhances their predictive performance.

Conclusion

In conclusion, the Triaxial Diametric Product (X) and Stacked Volume (V) are associated with improved predictive performance for PCNL outcomes compared to conventional metrics in our cohort. X emerges as a promising and practical tool for the preoperative assessment of large renal stones, offering a favorable balance of improved accuracy and clinical feasibility. V provides a novel, software-free method for obtaining a practical volumetric estimate suitable for research. By providing urologists with these pragmatic tools, this work offers a potential solution to a limitation in current preoperative planning. However, whether the adoption of these metrics translates into improved clinical decision-making or patient outcomes requires prospective evaluation.

Abbreviations

AUC

Area under the curve

CT

Computed tomography

NCCT

Non-contrast computed tomography

PCNL

Percutaneous nephrolithotomy

R

Maximum diameter

ROC

Receiver operating characteristic

S

Maximum cross-sectional area

SFR

Stone-free rate

V

Stacked volume

X

Triaxial diametric product

Authors’ contributions

The author Bingjian Wei and Fan Ning’s contribution to this article:1. Direct participation, including: Brewing and designing experiments; Implementation study; Collect data; Analyze/interpret data.2. Article writing, including: Draft articles; Critically review the intellectual content of the article.3. Work support, including: Statistical analysis; The author Yang Fu, Lu Ji and Shuo Gu’s contribution to this article: Direct participation, including: Implementation study; Collect data; Analyze/interpret data.The author Yunyan Wang’s contribution to this article:1. Direct participation, including: Implementation study; Collect data;2. Work support, including: Administrative, technical or material support; Guidance; Supporting contributions.

Funding

We confirm that this research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

This study was conducted in accordance with the ethical standards of the Helsinki Declaration of 1975, as revised in 2024. This retrospective study was approved by the Institutional Review Board of Huai’an First Affiliated Hospital of Nanjing Medical University. The requirement for informed consent was waived due to the retrospective nature of the study.

Consent for publication

Not applicable. All patient data were fully de-identified to ensure patient confidentiality and anonymity, and no individual person’s data are presented.

Competing interests

The authors declare no competing interests.