A survey of formal methods for determining functional joint axes

Axes of rotation e.g. at the knee, are often generated from clinical gait analysis data to be used in the assessment of kinematic abnormalities, the diagnosis of disease, or the ongoing monitoring of a patientʹs condition. They are additionally used in musculoskeletal models to aid in the description of joint and segment kinematics for patient specific analyses. Currently available methods to describe joint axes from segment marker positions share the problem that when one segment is transformed into the coordinate system of another, artefacts associated with motion of the markers relative to the bone can become magnified. In an attempt to address this problem, a symmetrical axis of rotation approach (SARA) is presented here to determine a unique axis of rotation that can consider the movement of two dynamic body segments simultaneously, and then compared its performance in a survey against a number of previously proposed techniques. Using a generated virtual joint, with superimposed marker error conditions to represent skin movement artefacts, fitting methods (geometric axis fit, cylinder axis fit, algebraic axis fit) and transformation techniques (axis transformation technique, mean helical axis, Schwartz approach) were classified and compared with the SARA. Nearly all approaches were able to estimate the axis of rotation to within an RMS error of 0.1 cm at large ranges of motion (90°). Although the geometric axis fit produced the least RMS error of approximately 1.2 cm at lower ranges of motion (5°) with a stationary axis, the SARA and Axis Transformation Technique outperformed all other approaches under the most demanding marker artefact conditions for all ranges of motion. The cylinder and algebraic axis fit approaches were unable to compute competitive AoR estimates. Whilst these initial results using the SARA are promising and are fast enough to be determined “on-line”, the technique must now be proven in a clinical environment.