Biomed. Eng.-Biomed. Tech. 2016; 61(5): 543–549 *Corresponding author: Korbinian Glatzeder, Institute of Biomechanics and Orthopaedics, German Sport University Cologne, Am Sportpark Müngersdorf 6, 50933 Cologne, Germany, E-mail: k.glatzeder@dshs-koeln.de Ralf Müller: Institute of Biomechanics and Orthopaedics, German Sport University Cologne, Am Sportpark Müngersdorf 6, 50933 Cologne, Germany Boris Hollinger: ARCUS Sportklinik, Rastatter Str. 17–19, 75179 Pforzheim, Germany Wolfgang Potthast: Institute of Biomechanics and Orthopaedics, German Sport University Cologne, Am Sportpark Müngersdorf 6, 50933 Cologne, Germany; and ARCUS Sportklinik, Rastatter Str. 17–19, 75179 Pforzheim, Germany Korbinian Glatzeder*, Ralf Müller, Boris Hollinger and Wolfgang Potthast Development and verification of a mathematical model to quantify the joint spaces of the elbow DOI 10.1515/bmt-2015-0224 Received June 24, 2015; accepted January 6, 2016; online first February 4, 2016 Abstract: 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 arthro- scopic 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 cali- per 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 deter- mined 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 open- ing (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 kin- ematics using this approach. Keywords: biomechanics; elbow instability; elbow liga- ment deficit; elbow surgery; kinematic elbow model; motion capture; posterolateral rotatory instability. Introduction Posterolateral rotatory instability (PLRI) of the elbow describes a condition in which the radius and ulna rotate externally in relation to the distal humerus [42]. This leads to posterior subluxation of the radial head relative to the capitellum [9] without associated instability of the proxi- mal radioulnar joint [25]. A common way to diagnose PLRI is during clinical examination using the posterolateral pivot shift test (PST) developed by O’Driscoll. In this test the examiner supinates the forearm and applies a valgus moment and an axial compression force to the elbow joint while it is flexed from full extension [23]. The main mechanisms of injuries are trauma, dislocation or sublux- ation: the elbow is the second most common joint to get dislocated in adults. Dislocation represents 11–28% of all elbow injuries, with an incidence of six to eight cases per 100,000 person years [16]. Elbow injuries that lead to PLRI occurs predominantly in athletes in throwing sports such as baseball, or in tennis [4]. The recent increase in throw- ing injuries has triggered research to focus on the medial ulnar collateral ligament of the elbow joint and its impor- tance to these athletes, even though most elbow instability is actually related to dysfunction of the lateral ligaments [32]. Osborne and Cotterill [28] describe a posterior insta- bility of the radial head and connects it to a laxity of the posterolateral capsule. Symeonides et al. [37] and Burgess and Tullos [6] report a similar instability and a difficulty in treatment of these patients. The primary stabilizing structure that prevents PLRI is the lateral ulnar collateral ligament according to biomechanical studies [10, 23, 25]. A section of only the anterior band of the lateral collateral ligament is insufficient to induce instability according to Seki et al. [34]. Recent studies suggest that instability may involve a combination of structures including the radial collateral ligament (RCL) and the annular ligament [11, 17, 27]. The different views of the authors imply that further research is needed on the involved tissues, especially in relation to the objective valuation of the joint space. In the light of this, a part of this paper focuses on the quantifica- tion of the resulting joint space of the humeroulnar joint with intact ligamentum annulare radii and radial collat- eral ligament, as well as with the ligaments cut through (Figure 1).