Development and verification of a mathematical model to quantify the joint spaces of the elbow

The purpose of the study was a development and verification of a model to quantify elbow joint spaces focusing on posterolateral rotatory instability. The model was tested for feasibility and applied to open and arthroscopic surgeries. A mathematical kinematic model was created, consisting of two segments representing the humerus and radius and ulna. Model calculations of the joint opening were compared with direct measurements on a mechanical model with attached marker arrays, and compared with values determined by a digital sliding caliper in order to evaluate the mathematical kinematic rigid body model of the elbow joint. Joint angles predicted by the mathematical model were compared with values determined by a two axis goniometer. The evaluation showed significant accordance (intercorrelation coefficient ≥0.8). The highest difference was 1.54° (root mean square: 0.46°) for all movement conditions. Ligament transaction at the open surgery situation affected an increase in joint opening (maximum joint opening: 10.9 mm±0.3). Distances in the ulnohumeral joint space (ligaments intact) under arthroscopic surgery situation varied between 4.0 and 6.8 mm (mean: 5.2 mm±1.0). Thus a possibility is created to achieve an objective assessment of joint space opening to provide a more complete description of the elbow kinematics using this approach.