Accurate reconstruction of the knee pose from two X-Ray images will allow the study pre-operative kinematics (for custom prosthesis design) and the post-operative evaluation of the intervention.

We used a SSM of the distal femur, based on 24 MRI datasets, from which the mean model and its modes of variation were defined. On the SSM, N landmarks in predefined positions were defined. The user identifies the same landmarks on two X-ray projections. Back-projecting the X-ray from the identified landmarks pixel to the corresponding source, each landmark position in the 3D space is reconstructed and the mean model pose initialised with a corresponding points registration. The silhouette of the SSM is projected on each X-ray image, which is automatically segmented in order to define the bone contours. With a Robust Point Matching algorithm based on Thin Plate Splines the projected silhouette points are deformed to better approximate the contour. For each contour point, the associated silhouette point is computed. We back-projected the ray from each contour point to the source and find on each ray the point with minimum distance to the silhouette. The cost function is the squared sum of the distances for both images. After a first optimisation of the pose, we perform a shape optimisation to find the correct weights for the SSM.

To evaluate our algorithm, we used two Digitally Reconstructed Radiographs (DRR) created as projections at 90° from a CT dataset. The CT based model was reconstructed and the landmarks were defined on it with a rigid registration of the SSM. In order to validate the robustness of our reconstruction method, a random uniform noise distribution (0–50 mm on each direction) was added on each landmark. The reconstruction accuracy was measured as the distance between each reconstructed landmark and the ground truth defined on the CT.

Results show that the population of the errors for the noise levels from 0 to 30 is similar: only the population with 50 mm noise is significantly different from the results obtained with other noise levels.

We can conclude that with a noise level below 50 mm the algorithm is able to return the correct pose of the femur, while with higher noise the initial distribution of the landmarks in the 3D space prevents the correct outcome of the algorithm. The user should select the landmarks within a range of 50 mm on the 3D representation, that is half the dimension of the bounding box containing the model. We can assume that in the real case it will be more difficult to select the proper position of the landmarks, but our method proved to be robust even with misplaced landmarks.

The location of the hip joint center (HJC) allows correct prosthesis aligning and positioning in Computer-Assisted Orthopaedic Surgery (CAOS) applications. For the kinematic HJC localisation, the femur is moved around the pelvis with ad hoc motion trials (“pivoting”). The “Pivoting algorithm” [Siston et al., J Biomech 39 (2006) 125–130] is the functional state-of-the-art method for the hip center localisation. A source of systematic error in HJC localisation algorithms is represented by the pelvis motion during the pivoting. In computer assisted total knee arthroplasty applications, the pelvis pose is not acquired during passive movements. In motion capture applications, Kalman Filter (KF) methodology was used to estimate the pose of hidden segment for rigid body pose estimation.

The purpose of this study was to validate the accuracy and robustness of a Kalman Filter algorithm, applied to a state space formulation based on two links model of the hip joint, to track the HJC position during passive movements of the articulation in CAOS procedure.

The state space model describes femur and pelvis kinematics under the hypothesis of non-laxity of the articulation (ideal spherical joint). The first link models the femoral bone, while the second link models the pelvis. The femur is tracked with a Dynamic Reference Frame (DRF) attached to the distal end, composed by four active markers, while the pelvis is tracked attaching a marker to it. The kinematic relations between the state vector and the observations are non linear function. The state space has been implemented with II order linear dynamics. The position of HJC in the Femur Reference Frame is modeled with non-dynamic state variables.

In order to validate the proposed algorithm, a physical model of the hip joint (femur and pelvis) was realised using SawBones models. An active optical localisation system (Certus, NDI, Ontario, Canada) was used in order to track the coordinates of two DRF rigidly connected on each segment and the coordinates of a marker attached to the pelvis segment (on the Anterior Superior Iliac Spine ASIS). The pelvis phantom is locked on a Mass-Spring-Damper platform with 2 DoFs, which mimics soft tissues behaviour. During the pivoting motion, the poses of the femur DRF and the positions of the ASIS marker of the pelvis DRF were collected. The acquired data were the observable outputs to the KF algorithm, which computes an estimation of the state parameters. The accuracy is evaluated as the Euclidean distance between respectively the estimated and Gold Standard HJC positions in FRF. The KF method performances were compared with the “Pivoting” algorithm. The localisation errors computed for both the methodologies were evaluated with respect to the HJC translation, to the Range Of pivoting Motion (ROM) and to the velocity of femur DRF trajectory (Pearson correlation analysis).

The positive correlation coefficients between HJC translation and the localization errors result statistically significant (p<0.01) for both “Pivoting” (correlation index equal to 0.838) and KF (correlation index equal to 0.415) algorithms; while a negative (correlation index equal to −0.355) and positive (correlation index equal to 0.263) correlation respectively for ROM and Velocity is computed as statistically significant (p<0.05) only for KF algorithm errors. Statistically significant difference (Kruskal-Wallis, p<0.01) between “Pivoting” [median 26.71 mm and inter-quartile range (24.04, 32.18)mm] and KF [median 11.71mm and inter-quartile range (7.74, 18.82)mm] algorithms was assessed for HJC translation greater than 7 mm.

The new method KF proved to be applicable in current CAOS systems. The substantial improvement of KF method is the possibility of reducing the systematical error, caused by pelvis motion during passive movement of the femur, to compute HJC position. On the other hand, tracking the HJC trajectory in real time is a nontrivial task and requires a very accurate filter parameters tuning. Further tests must be made to estimate the in-vivo range of HJC translation during passive pivoting movements and evaluate the performances of KF method with respect to others state-of-the-art methods.