Quantifying Joint Congruence With an Elastic Foundation

Abstract

The level of congruence between the articulating surfaces of a diarthrodial joint can vary substantially between individuals. Quantifying joint congruence using the most widespread metric, the “congruence index,” is not straightforward: the areas of the segmented bone that constitute the articular surfaces require accurate identification, their shape must be carefully described with appropriate functions, and the relative orientation of the surfaces measured precisely. In this work, we propose a new method of measuring joint congruence, which does not require these steps. First, a finite element (FE) simulation of an elastic layer compressed between each set of segmented bones is performed. These are then interpreted using the elastic foundation model, enabling an equivalent, but simpler, contact geometry to be identified. From this, the equivalent radius (quantification of joint congruence) is found. This defines the radius of a sphere contacting plane (or “ball on flat”) that produces an equivalent contact to that in each joint. The minimal joint space width (in this joint position) can also be estimated from the FE simulations. The new method has been applied to ten healthy instances of the thumb metacarpophalangeal (MCP) joint. The ten thumb MCPs had similar levels and variability of congruence as the other diarthrodial joints that have been characterized previously. This new methodology enables efficient quantification of joint congruence and minimal joint space width directly from CT- or MRI-derived bone geometry in any relative orientation. It lends itself to large data sets and coupling with kinematic models.