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

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.

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.

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.

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.