The 3D thumb-tip forces produced by individual do not superimpose linearly

Clinicians and biomechanists commonly assume the thumb-tip force produced by tension in individual tendons superimpose linearly. We tested this assumption experimentally in cadaver thumbs (n=13) by developing a specimen-specific linear model and quantifying the error of this model´s predictive ability. We developed these models by linearly regressing 3D thumb-tip output force/torque against tendon tension. We applied linear optimization to these models to calculate the combination of tendon tensions predicted to maximize 3D thumb-tip force vectors in each of five directions (palmar, dorsal, radial, ulnar, distal) under four neurological conditions (intact, low-median paralysis, transfer A, transfer B), and applied these optimal tensions to the specimen. We quantified the error in the linear model by calculating the magnitude difference and angle between predicted and measured force vectors. This error depended on the direction of maximized thumb-tip force. The measured force vector magnitude was either significantly (p < 0.05) lower (distal and dorsal) or not significantly different (palmar, radial, ulnar) from the predicted magnitude, and the angle between predicted and measured vectors varied greatly (distal: 20°±20°; palmar: 22°±13°; radial: 36°±13°, ulnar: 34°±20°; dorsal: 51°±13°). Our results suggest that the linear assumption is most accurate when the thumb-tip force is in the palmar direction.