Calibration transfer in wearable Achilles shear-wave tensiometry

Abstract

To determine when a between-session change in Achilles tendon peak force or force impulse retains its direction under uncertain shear-wave calibration. Affine squared-speed calibration was combined with sagittal ankle moment balance. Both session-specific intercepts were retained. Exact inverse bounds were derived for multiplicative and additive transfer errors, and deterministic calculations used a first-session peak of 3000 N, transfer gain 0.90–1.10, force offset −200–200 N, and a 0.6 s loading pulse. The study analysed mathematical force functions, without participant or instrument records. The transferred estimate obeys F̂₂ = αF₂ + β. At M = 150 N m, moment arms of 45–55 mm and non-Achilles moments of 0–15 N m admit tendon forces of 2454.55–3333.33 N. With the specified transfer limits, an estimated peak must fall below 2500 N to establish a decrease from 3000 N, or exceed 3500 N to establish an increase. Setting α = 1.08 and β = 150 N converts a true peak of 2700 N to 3066 N, reversing the apparent direction. The same transfer changes the loading-pulse impulse from 990 to 1159.2 N s while preserving its normalised shape. A 2% multiplicative limit and 45 N additive limit bound relative force error by 5% at forces of at least 1500 N. A directional force conclusion requires a force-change interval that excludes zero. Peak force, accumulated impulse and normalised waveform shape require separate interpretation because an additive calibration error affects each quantity differently.