A Novel Parameter for Predicting Postoperative Stone Free Status in Percutaneous Nephrolithotomy: The Stone Volume–Density Index

Technical Summary: The Stone Volume–Density Index (SVDI) for Predicting PNL Outcomes

Problem Statement
Percutaneous nephrolithotomy (PNL) is the standard treatment for renal stones larger than 2 cm and complex stone burdens. However, success rates vary widely (40–90%), and complication rates range from 10% to 25%. Existing multi-parameter scoring systems, such as the Guy's Stone Score and S.T.O.N.E. nephrolithometry, rely on subjective scoring or linear dimensions, with Area Under the Curve (AUC) values for predicting stone-free status typically ranging between 0.62 and 0.76. While recent evidence suggests stone volume is superior to linear size, and stone density (Hounsfield units, HU) influences fragmentation, no study has investigated a simple composite index combining both volume and density to predict PNL outcomes.

Methodology
This retrospective study analyzed data from 336 adult patients who underwent conventional PNL at a tertiary center between January 2021 and June 2026.

• Data Collection: Preoperative non-contrast computed tomography (NCCT) images were reviewed by three urologists to reach a consensus on stone measurements.
• Parameters Measured:
  • Stone Size: Longest axis on axial slice.
  • Stone Area: Calculated via ellipse formula ($A = \pi \times (a/2) \times (b/2)$).
  • Stone Volume: Calculated via modified ellipsoid formula ($V = (4/3)\pi \times (a/2) \times (b/2) \times (c/2)$).
  • Mean HU: Weighted average of Hounsfield units across three central slices.
  • Stone Volume–Density Index (SVDI): Calculated as the product of Stone Volume (cm³) and Mean HU.
• Outcomes:
  • Success: Stone-free status or clinically insignificant residual fragments (<4 mm) at one month.
  • Failure: Residual fragments >4 mm.
  • Complications: Any grade I–V event within 30 days, classified by the modified Clavien–Dindo system.
• Statistical Analysis: Receiver Operating Characteristic (ROC) curves and DeLong pairwise comparisons were used to evaluate discriminative ability. Multivariate logistic regression (using both raw and log-transformed SVDI) identified independent predictors. Model fit was assessed using Akaike Information Criterion (AIC) and Nagelkerke $R^2$.

Key Contributions
The primary contribution of this work is the introduction and validation of the Stone Volume–Density Index (SVDI) as a single, arithmetic composite parameter. Unlike complex scoring systems requiring subjective grading, SVDI is derived directly from standard NCCT measurements (Volume × Mean HU). The study provides a specific cut-off value for clinical application and compares SVDI's predictive performance against traditional parameters (size, area, volume, and HU) and existing scoring methodologies.

Results

• Overall Outcomes: The stone-free rate was 74.4% (250/336), and the complication rate was 17.9% (60/336).
• Predicting Failure (Stone-Free Status):
  • SVDI Performance: SVDI yielded the highest AUC (0.771) for predicting failure.
  • Comparisons: SVDI demonstrated statistically significant superiority over Stone Size (AUC 0.728; $p=0.044$) and Mean HU (AUC 0.592; $p<0.001$). While SVDI numerically outperformed Stone Volume (AUC 0.753) and Stone Area (AUC 0.750), these differences did not reach statistical significance in pairwise comparisons ($p>0.05$).
  • Cut-off Value: An SVDI threshold of ≥3817 provided the optimal balance, with 83.7% sensitivity and 60.4% specificity.
  • Multivariate Analysis: Independent predictors of failure included multiple calyceal involvement (OR=3.02), secondary case status (OR=3.06), and log-transformed SVDI (OR=1.82).
  • Model Fit: The model using log(SVDI) achieved the best fit (AIC=300.3) compared to models using stone size, volume alone, or separate volume and HU parameters. A likelihood ratio test confirmed that adding density (HU) to volume significantly improved the model ($p=0.018$).
• Predicting Complications:
  • No stone parameter (including SVDI, volume, or HU) demonstrated adequate discriminative power for complications (all AUCs < 0.60).
  • The only independent protective factor identified was the tubeless procedure with intraoperative double-J stent placement (OR=0.17; $p=0.004$).

Significance and Claims
The paper claims that SVDI is a simple, objective composite parameter that offers the highest discriminative performance among stone-specific metrics for predicting PNL failure.

• Clinical Utility: The authors suggest the SVDI cut-off (≥3817) can be used for preoperative counseling to estimate the likelihood of residual stones, plan for multi-session procedures, or consider alternative/combined approaches (e.g., ECIRS).
• Incremental Value: While SVDI's superiority over stone volume alone was not statistically significant in ROC comparison, model-based analyses (AIC and likelihood ratio tests) confirm that incorporating density information provides incremental predictive value beyond volume alone.
• Limitations on Complications: The study modestly concludes that stone burden parameters are insufficient for predicting complications, which are likely driven by patient factors, surgical technique, and surgeon experience rather than stone characteristics alone.
• Comparison to ML: The authors note that while machine learning models may achieve higher AUCs, SVDI offers a distinct advantage by requiring no specialized software or complex infrastructure, relying instead on standard arithmetic.

The study acknowledges limitations including its retrospective design, manual volume calculation (ellipsoid formula) rather than 3D reconstruction, lack of stone composition data, and the use of only pneumatic lithotripsy, suggesting that external validation across different modalities is necessary.