Toward predictive prosthetic socket modeling: Preliminary linear regression models of transradial limb–socket geometry

Socket fit is essential for successful upper-limb prosthetic devices, yet current design workflows remain labor-intensive and dependent on clinician experience. Several digital and algorithmic approaches have been proposed to partially automate socket design, many of which rely on characterizing conventional design practice. In upper-limb prosthetics, prior research has quantified transradial socket rectification practices, but the direct geometric relationship between the residual limb and final socket remains unclear despite its importance to digital socket design workflows. This study examined whether simple linear regression models could provide a preliminary, interpretable description of limb–socket geometric relationships in transradial socket design. Fourteen participants with transradial limb absence were included, whose digitized limb–socket pairs were aligned using a novel spline-based method. Relationships were quantified using global descriptors (volume, surface area, and proximal–distal length) and cross-sectional descriptors at 25%, 50%, and 75% of limb length (mediolateral length, anterior–posterior length, circumference, and cross-sectional area). For each descriptor, simple linear regressions were fit to predict socket geometry from limb geometry, and model performance was evaluated using leave-one-out cross-validation. Global descriptors demonstrated strong linear relationships, with R² values ranging from 0.94 to 0.97 and predicted R² values from 0.92 to 0.97, indicating that overall socket size is largely predictable from limb size. Cross-sectional descriptors showed more variable performance, with the strongest results at mid-length and weaker relationships toward the proximal and distal ends. Mean absolute percentage error ranged from 2.5% to 13.6% across descriptors, while retention values were generally high, indicating limited overfitting. These findings suggest that simple linear models can capture broad scaling relationships between transradial limbs and sockets, but are less able to explain localized geometry in regions where trimline design, suspension strategy, and distal-end clearance play a greater role.