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This paper addresses the problem of extrapolating very sparse three-dimensional (3-D) data to obtain a complete surface representation. A new method that uses statistical shape models is proposed and its application to computer-assisted anterior cruciate ligament (ACL) reconstruction is detailed. The rupture of the ACL has become one of the most common knee injuries. One problem during reconstruction is to find the optimal attachment points for the graft. Therefore a system for computer-assisted reconstruction of the ACL has been proposed by TIMC laboratory. During surgery the surgeon collects several data points on the tibial and femoral joint surface with a 3-D localizer system. These 3-D data are used to find those attachment points resulting in a low anisometry of the graft, while preventing impingement between the graft and the femoral notch. As the collected data points only cover a small surface patch of the femur, it is desirable to extrapolate these data to also have a visualization in those areas where no data points are available. A sufficiently good approximation of the actual femur by the model would further allow us to better deal with the notch impingement problem of the graft. The chosen approach is to fit a deformable model to the data points, it can be subdivided into two steps, constructing the model and fitting this model to the data. To incorporate a priori knowledge into the model, the allowed deformations are determined by the statistics of the shape variation of a set of training objects. Matching the training objects together is obtained by elastic registration of surface points using octree splines. The fitting process of the sparse intra-operative data with the statistical model results in a non-linear multi-dimensional function minimization. A hybrid search strategy combining local and global methods is used to avoid local minima. First experimental results with a model generated from 10 femurs are presented, including fitting of the model with both simulated and real intra-operative data.

Anterior cruciate ligament reconstruction is a delicate task. The procedure of choice is the patellar tendon bone autograft, but an anisometric position of this tendon often leads to failure. We allows positioning of the central part of the ligament graft at the least anisometric sites. The system uses a workstation and a three-dimensional optical localizer to create images that represent knee kinematics. The surgeon uses these images to guide the surgery. This technique has been validated on eight cadavers and 12 patients.

The tibial slope is an important datum in knee surgery; the levelling by a uni- or bicompartmental prosthesis preserving both cruciate ligaments requires to maintain this slope. The postoperative rehabilitation of the A.C.L. plasties, especially those performed with a patellar tendon and the surgical cure of a genu recurvatum, must integrate this notion. Even if the anatomical slopes are usable in prosthetic surgery, they do not seem precise enough in the field of A.C.L. and tibia recurvatum surgery. In these indications, the authors propose to determine the functional tibial slope defined as being the complement of the angle formed by the tangent to the tibial medial plateau and the lateral mechanical axis of the leg. Measured to an average of 7 degrees on 238 knees, the average median functional slope cannot be deduced from anatomical slopes; it must be measured on a lateral teleradiographic view of the lower limb, the knee being in full extension and X-rayed in true posterior and inferior lateral view.