Graphene Nanoribbon Sensors for Prosthetic Socket Wear-Time Monitoring: A Lambert W Function Framework

Abstract Objective measurement of prosthetic socket use, encompassing wear time together with the pressures, strains, and microclimate at the limb--socket interface, would strengthen prosthetic rehabilitation research by complementing self-report measures, which are prone to recall error and social desirability bias. Existing thermal wear-time sensors face a fundamental limitation inside prosthetic sockets: the silicone liner worn over the residual limb attenuates body heat, and in the Limbkit study of 3D-printed sockets a validated commercial temperature microsensor consequently recorded zero wear time despite reported daily use of \SIrange{11}{15}{\hour}. Here we present a theoretical framework based on graphene nanoribbon (GNR) quantum sensors that addresses this limitation through the Lambert~W function branch-point enhancement mechanism, with sensitivity scaling as liner-attenuated differentials with millikelvin-scale noise-equivalent temperature differences, and that instrumenting the liner itself removes the thermal barrier entirely. A multi-modal architecture sensing temperature, pressure, strain, and humidity provides redundant wear classification and a route toward monitoring skin health at the interface.