A sound and efficient measure of joint congruence

In the medical world, the term "congruence" is used to describe by visual inspection how the articular surfaces mate each other, evaluating the joint capability to distribute an applied load from a purely geometrical perspective. Congruence is commonly employed for assessing articular physiology and for the comparison between normal and pathological states. A measure of it would thus represent a valuable clinical tool. Several approaches for the quantification of joint congruence have been proposed in the biomechanical literature, differing on how the articular contact is modeled. This makes it difficult to compare different measures. In particular, in previous articles a congruence measure has been presented which proved to be efficient and suitable for the clinical practice, but it was still empirically defined. This article aims at providing a sound theoretical support to this congruence measure by means of the Winkler elastic foundation contact model which, with respect to others, has the advantage to hold also for highly conforming surfaces as most of the human articulations are. First, the geometrical relation between the applied load and the resulting peak of pressure is analytically derived from the elastic foundation contact model, providing a theoretically sound approach to the definition of a congruence measure. Then, the capability of congruence measure to capture the same geometrical relation is shown. Finally, the reliability of congruence measure is discussed.