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.Author summary: Designing a comfortable and functional prosthetic socket for upper-limb absence is a skilled and time-intensive process, with the overall success of the prosthesis being highly dependent on the fit of the socket. Although digital tools are increasingly used in prosthetic care, many important design steps still depend on clinician experience and are difficult to translate into software. One challenge is that the geometric relationship between a person’s residual limb and the final socket shape is not well understood. In this study, we examined whether simple linear regression models could describe how the shape of the residual limb relates to that of the prosthetic socket. Using 3D scans of limb–socket pairs from 14 people with transradial limb absence, we compared their global and cross-sectional geometric features. We found that overall socket size was strongly related to overall limb size, meaning that broad scaling patterns can be predicted reasonably well. However, local socket geometry was harder to predict near both ends of the model, where design features such as trimlines, suspension, and distal clearance play a larger role. These findings provide an early quantitative foundation for data-driven prosthetic socket design and may help support future digital tools that complement clinical expertise.