The helical axis of anatomical joints: calculation methods, literature review, and software implementation

The calculation of the helical axis, a.k.a. screw axis, is a functional technique that was introduced for the characterization of the motion and the stability of a human joint. Examples are its applications in the design of prostheses and its use for evaluating the joint performance in post-operatory follow-up. The typical way of studying the variations in the helical axis is to instantaneously compare it to some reference. The reference is typically assumed as (i) an anatomical or geometrical reference (e.g., the condyle to condyle axis or an anatomical plane); (ii) a functional reference, i.e., some axis calculated in a functional way. Calculating the helical axis means determining its orientation and its position, based on the recorded motion of the joint. This paper reviewed the calculation methods of the helical axis, its clinical applications, and the most relevant findings. The operative equations of the most common procedures were clearly and synthetically illustrated. More in detail, the focus of this review was set on the calculation of (i) the instantaneous helical axis; (ii) the finite helical axis; (iii) the average helical axis; (iv) a functional coordinate system attached to the helical axis; and (v) the analysis of the time variations of helical axis. The calculation of those quantities was implemented in MATLAB and the code was proposed as supplementary material. The calculation of the discussed quantities was demonstrated on a sample dataset.