The research team, led by Vishal Pendse, Nader Allam, Calvin C. Ngan, Elaine Lorette, Isabelle Morin-Girard, and Jan Andrysek, enrolled fourteen participants with transradial limb absence, meaning the amputation occurred between the wrist and the elbow. For each participant, the researchers obtained digitized three-dimensional models of both the residual limb and the corresponding prosthetic socket. The challenge then became one of alignment and comparison: how do you meaningfully compare two curved, irregular three-dimensional shapes that are related but not identical? To solve this, the team developed a novel spline-based alignment method, which allowed each limb and its socket to be registered to one another along a common longitudinal axis, establishing a consistent coordinate framework for measurement.

With the limb–socket pairs aligned, the researchers quantified geometry using two complementary families of descriptors. The first family consisted of global measures that characterize each shape as a whole: total volume, total surface area, and proximal–distal length, which captures how long the shape is from its upper end near the elbow to its lower end. The second family consisted of cross-sectional descriptors evaluated at three specific stations along the limb, at 25 percent, 50 percent, and 75 percent of limb length. At each station, the team measured the mediolateral width, the anterior–posterior depth, the circumference, and the cross-sectional area. This combination of global and local metrics was designed to answer two distinct questions: whether overall socket size scales predictably with overall limb size, and whether the finer contours of the socket at particular heights along the forearm can likewise be predicted from the corresponding contours of the limb.

The analytical approach was intentionally simple. For each descriptor, the researchers fitted a simple linear regression, a model of the form in which a single predictor variable, a limb measurement, is used to estimate a single outcome, the corresponding socket measurement. Simple linear regression is among the most transparent tools in statistics: it yields a slope and an intercept that clinicians and engineers can inspect directly, and it makes no hidden assumptions about complex interactions between variables. In a field where many proposed automation approaches behave as opaque black boxes, the choice of an interpretable model was a deliberate design decision, aimed at building a foundation that future digital socket design workflows could understand, audit, and extend.

The results for the global descriptors were strikingly strong. Across volume, surface area, and proximal–distal length, the fitted models achieved R² values ranging from 0.94 to 0.97, meaning that between 94 and 97 percent of the variation in socket geometry could be explained by variation in limb geometry alone. Because a model can sometimes appear excellent on the very data used to fit it while failing on new patients, the team evaluated performance using leave-one-out cross-validation, a rigorous procedure in which the model is repeatedly trained on all but one participant and then tested on the excluded individual. The resulting predicted R² values, ranging from 0.92 to 0.97, confirmed that the strong fits were not statistical artifacts. The practical implication is significant: for transradial amputations, the overall size of a well-designed socket is largely predictable from the overall size of the residual limb.

The cross-sectional descriptors told a more nuanced story. Performance was strongest at the mid-length station, the 50 percent mark along the limb, where the linear models captured the relationship between limb and socket contours with reasonable fidelity. Toward the proximal end, near the elbow, and especially toward the distal end, near where the wrist would have been, the relationships weakened considerably. This gradient of predictive power is not a failure of the method so much as a window into the nature of socket design itself. The mid-forearm region of a socket tends to follow the limb’s anatomy in a relatively straightforward way, while the ends of the socket are where clinical judgment concentrates: trimlines are adjusted to control pressure and motion, suspension strategies are engineered, and clearance is built in at the distal tip to accommodate bony anatomy and prevent painful bottoming-out during use.

Quantitatively, the mean absolute percentage error across all descriptors ranged from 2.5 percent to 13.6 percent, with the lower errors corresponding to the global measures and the higher errors concentrated in the less predictable cross-sectional regions. Retention values, a measure of how much predictive performance survives cross-validation relative to the apparent fit, were generally high across the board, indicating that the models suffered from limited overfitting despite the modest sample of fourteen participants. In other words, the models did not merely memorize the idiosyncrasies of the individuals in the dataset; they captured genuine population-level tendencies in how socket designers translate limb geometry into socket geometry.

These findings matter because they establish a baseline for what simple, data-driven models can and cannot do in upper-limb prosthetics. Prior research had quantified how experienced clinicians rectify, or modify, a digital socket shape relative to a digital limb shape, but the direct geometric mapping from the residual limb to the final socket had remained unclear, even though it is precisely this mapping that any automated design pipeline would need to learn. By demonstrating that broad scaling relationships are captured almost entirely by linear functions of limb size, the study provides both a useful first approximation and a clear demarcation of where more sophisticated modeling will be required. The regions where linear models falter, the proximal and distal ends, are exactly the regions where trimline design, suspension strategy, and distal-end clearance introduce deliberate, clinically motivated deviations from simple scaling.

The study also highlights a methodological contribution that extends beyond its specific results: the spline-based alignment technique used to register limb–socket pairs offers a reusable framework for future geometric analyses of prosthetic interfaces. As three-dimensional scanning, parametric computer-aided design, and additive manufacturing continue to reshape the prosthetics industry, the bottleneck is shifting from fabrication to prediction. Clinicians can already print a socket in hours; the open question is what shape to print. Studies like this one suggest a pragmatic path forward, in which interpretable statistical models handle the predictable bulk of the geometry while structured clinical rules or more flexible machine learning methods govern the regions where design intent dominates.

For patients, the promise of this line of research is a future in which socket design becomes faster, more consistent, and less dependent on the availability of highly experienced practitioners, without sacrificing the individualized judgment that makes a socket truly wearable. For the field, the message is equally clear: even the simplest models, built carefully and validated honestly, can reveal the structure hidden in clinical practice. The straight line, it turns out, describes more of the limb–socket relationship than one might expect, and knowing exactly where it breaks down is the first step toward building something better.

Subject of Research: Linear regression modeling of transradial residual limb and prosthetic socket geometry

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

Article References: Pendse, V., Allam, N., Ngan, C. C., Lorette, E., Morin-Girard, I., & Andrysek, J. (2026). Toward predictive prosthetic socket modeling: Preliminary linear regression models of transradial limb–socket geometry. PLOS Digital Health, 5(10), e0001767. https://doi.org/10.1371/journal.pdig.0001767

Image Credits: AI Generated

DOI: 10.1371/journal.pdig.0001767

Keywords: prosthetics, transradial amputation, socket fit, linear regression, 3D digitization, biomedical engineering, limb–socket geometry, cross-validation, digital health, rehabilitation, predictive modeling, upper-limb prosthesis