A z-score-based reference system for renal volume using three-dimensional ultrasound: from model to clinical tool

BACKGROUND: Accurate assessment of renal volume is crucial for diagnosing nephropathies and evaluating living kidney donors. However, related studies have generally relied on linear models or focused on population-level associations, without providing clinically usable reference standards. This study aimed to develop a physiology-informed and clinically applicable reference system for renal volume through use of advanced nonlinear modeling. METHODS: In this cross-sectional observational study, 634 healthy living kidney donor candidates (aged 20-78 years) were prospectively enrolled at a tertiary medical center. Renal volume was measured with standardized three-dimensional ultrasound (3D-US). Associations with age, sex, body surface area (BSA), and laterality were modeled with a generalized additive mixed model (GAMM), which captured nonlinear relationships. Based on model predictions, standardized z-scores were derived, and clinically interpretable reference intervals were established. Nomograms and an online calculator were developed to facilitate real-world application. RESULTS: A total of 1,268 kidneys were analyzed [median age 51 years, interquartile range (IQR), 46-56 years; 67.0% female]. The GAMM explained 90.1% of the variance in renal volume. Renal volume showed a significant nonlinear association with age, peaking at approximately 53.5 years before declining. BSA was the strongest positive determinant. After adjustment, male sex (-7.93 mL) and right kidney laterality (-5.99 mL) were independently associated with lower renal volume. The derived z-score framework showed good calibration, with approximately 95% of observations within the reference range (-1.96 to +1.96). Nomograms and an online calculator enabled individualized estimation and interpretation of renal volume. CONCLUSIONS: This study established a clinically interpretable reference system for renal volume by integrating 3D-US with nonlinear modeling. The z-score-based framework, supported by nomograms and an online calculator, enables individualized assessment, improving the clinical translation of renal volumetry.