Reverse engineering finger extensor apparatus morphology from measured coupled interphalangeal joint angle trajectories - a generic 2D kinematic model

The interphalangeal (IP) finger joints coordinate as a mechanism when the deep flexor is active. This mechanism is created by the complex finger extensor apparatus (EA) - a confluence of end tendons of one or two extensors, radial and ulnar interossei, and lumbrical - which inserts as a single structure into both the middle and distal phalanges. Although the IP-coupling principle was well demonstrated more than half a century ago, the detailed relationship between EA morphology and IP coupling remains not well described. Main reasons are that by dissection the EA's fiber network loses functional consistency, while fibers becoming taut or slack beyond measuring resolutions complicate measuring functional fiber motions. To circumvent these difficulties, we present a two dimensional kinematic multi tendon-string EA model of fiber slackness and tautness through IP motion, including the retinacular and oblique retinacular EA ligaments. The model parameters were the strings' lengths and attachment points. The model's functional redundancies were resolved by individually interactively fitting model IP trajectories to previously measured IP trajectories of 68 fingers. All model trajectories accurately fitted their target IP trajectories for proximal interphalangeal (PIP) joint ranges smaller than 25° to 45°; about half accurately fitted over the entire IP range with the remaining half having maximum approximation errors between 3° to 12°, while all models again converged to target trajectories for full IP flexion. These accuracies suggest the model reflects real functional EA principles, with potential applications in biomechanical modeling, surgical reconstruction, rehabilitation, and prosthetic EA replacements.