The convex-concave rule and the lever law.

The convex–concave rule is considered an important theory during treatment decision-making (Kirby et al., 2007). According to this rule (Fig. 1) the therapist moves a bone with a convex joint surface opposite to the direction of restricted movement of the distal aspect of the bone (e.g. the head of humerus inferiorly for restricted shoulder abduction). However, a concave joint surface is mobilized in the same direction as the direction of the restricted bone movement (e.g. the tibia condyles anteriorly for restricted knee extension) (Kaltenborn, 2002: p 34). Recent studies are questioning this principle. On 3D reconstructions of helical CT data of 3 asymptomatic shoulders Baeyens et al. (2000) for example observed a posterior translation of humeral head during external rotation in 90 abduction. However, the convex–concave rule predicts an anterior glide for external rotation. This observation could also be made in 3 symptomatic shoulders with minor instability (Baeyens et al., 2001). The same method of 3D reconstructions of helical CT data was used in the analyses of pro-and supination of the forearm (Baeyens et al., 2006). It was found for example a posterior translation of the radial head during supination in the proximal radio-ulnar joint, while the convex–concave rule predicts anterior gliding of the radial head's joint surface on the radial notch of ulna. Cattrysse et al. (2005) used an electromagnetic tracking device to study coupled motions of the acromioclavicular, glenohumeral and humero-ulnar joints on cadavers. With mathematical calculations they deduced intra-articular kinematics which were not according to the convex–concave principle. Brandt et al. (2007) found in their literature review inconsistent evidence, poor meth-odological quality, and heterogeneity of the studies, so that no clear conclusion could be drawn on the direction of translation of the humeral head. Johnson et al. (2007) evaluated the effect of the gliding mobilization in 20 patients with adhesive capsulitis (frozen shoulder). Half of the patients were mobilized anteriorly and the other half posteriorly. They found pain alleviation in both groups, but the posterior mobilization group had better results in range of motion – although the convex–concave rule predicts anterior gliding of the humeral head during external rotation. The aim of this paper is to explain the mechanics of the convex– concave rule and then to discuss possible misinterpretations in the above mentioned studies. 2. Mechanics of the convex–concave rule During the movement of a bone around an axis (¼osteokinematics), its joint surface is doing complex …