Characterization of 3D joint space morphology using an electrostatic model (with application to osteoarthritis)

Joint space morphology can be indicative of the risk, presence, progression, and/or treatment response of disease or trauma. We describe a novel methodology of characterizing joint space morphology in high-resolution 3D images (e.g. cone-beam CT (CBCT)) using a model based on elementary electrostatics that overcomes a variety of basic limitations of existing 2D and 3D methods. The method models each surface of a joint as a conductor at fixed electrostatic potential and characterizes the intra-articular space in terms of the electric field lines resulting from the solution of Gauss' Law and the Laplace equation. As a test case, the method was applied to discrimination of healthy and osteoarthritic subjects (N = 39) in 3D images of the knee acquired on an extremity CBCT system. The method demonstrated improved diagnostic performance (area under the receiver operating characteristic curve, AUC > 0.98) compared to simpler methods of quantitative measurement and qualitative image-based assessment by three expert musculoskeletal radiologists (AUC = 0.87, p-value = 0.007). The method is applicable to simple (e.g. the knee or elbow) or multi-axial joints (e.g. the wrist or ankle) and may provide a useful means of quantitatively assessing a variety of joint pathologies.