A three-dimensional definition for the flexion/extension and abduction/adduction angles

Flexion/extension and abduction/adduction, two major parameters for the description of joint rotations, are used to define planer anatomical orientations of body segments. These two-dimensional definitions have been used extensively in the biomechanical literature for reporting and representing both two-dimensional and three-dimensional joint rotations. Whether these traditional two-dimensional measurements represent true joint rotations in three dimensions has not been investigated. A quantitative error analysis is presented to show how large an error can be produced in the flexion/extension and abduction/adduction angles when using two-dimensional measurements to represent three-dimensional joint rotations. The results indicate that for an out-of-plane flexion the error in abduction angle measured by previous methods increases with both flexion and initial abduction angle and become very sensitive when the flexion angle exceeds 40 degrees. Although the error can be less than 2 degrees for flexion below 20 degrees when the initial abduction angle is at 30 degrees, it can be as large as 9 degrees for 60 degrees of flexion with an initial 10 degrees of abduction; nearly double the real abduction angle. Therefore, two-dimensional measurements of flexion/extension and abduction/adduction can be erroneous and overestimated for a three-dimensional joint rotation. To overcome the problem new definitions are proposed for the true flexion/extension and abduction/adduction angles as two independent parameters for three-dimensional joint rotation.