Automated method for clinic and morphologic analysis of bones using implicit modeling technique

Bone morphology and moprhometric estimation provide important and useful information for computed assisted-surgery, follow-up evaluation and personalized prosthesis design. Obtaining this data without any operator supervision or setting remains a practical goal. We present here an automated method that estimates clinic, anatomic and morphometric parameters based on bone-mesh representation. The method uses 2 steps. In the first one, the bone of interest is introduced as an implicit function modeling its morphology as a quadric surface. This function blends together basic geometries such as spheres, cylinders, quadratics and superquadratics and approximates its external shape. Given a mesh representation of a patient-bone, Levenber-Marquardt optimization technique computes Cartesian coordinates of the basic geometries. In second step, heuristic plans use these spatial data to locate, through the mesh representation, punctual landmarks. In order to compute subsequently complex clinic and anatomic landmarks relatives to axes, curves, surfaces, and regions, compound-heuristic plans are dressed using implicit parameters and previous punctual landmarks. Each plan is expressed as a energy-cost function that involves geometric, radial and normal terms. The method has been successfully used to locate clinic, anatomic and morphometric parameters of femur bone. Validation of the technique is performed with qualitative and quantitative procedures. A total of 9 femurs are reconstructed using a retroprojection technique. In all models, the method converges to the same parameters with acceptable clinical accuracy. As automated method, this schema presents practical advantage and remains sufficiently general to be applied to other bones and tracks most of anatomic parameters.