Active Shape Models (ASM) have been widely used in the literature for the extraction of the tibial and the femoral bones from MRI. These methods use Statistical Shape Models (SSM) to drive the deformation and make the segmentation more robust. One crucial step for building such SSM is the shape correspondence (SC). Several methods have been described in the literature. The goal of this paper is to compare two SC methods, the Iterative Median Closest Point-Gaussian Mixture Model (IMCP-GMM) and the Minimum Description Length (MDL) approaches for the creation of a SSM, and to assess the impact on the accuracy of the femur segmentation in MRI.

28 MRI of the knee have been used. The validation has been performed by using the leave-one-out cross-validation technique. An ASMMDL and an ASMIMCP-GMMM has been built with the SSMs computed respectively with the MDL and IMCP-GMM methods. The computation time for building both SSMs has been also measured.

For 90% of data, the error is inferior to 1.78 mm and 1.85 mm for respectively the ASMIMCP-GMM and the ASMMDL methods. The computation time for building the SSMs is five hours and two days for respectively the IMCP-GMM and the MDL methods.

Both methods seem to give, at least, similar results for the femur segmentation in MRI. But (1) IMCP-GMM can be used for all types of shape, this is not the case for the MDL method which only works for closed shape, and (2) IMCP-GMM is much faster than MDL.

Functional approaches for the localisation of the hip centre (HC) are widely used in Computer Assisted Orthopedic Surgery (CAOS). These methods aim to compute the HC defined as the centre of rotation (CoR) of the femur with respect to the pelvis. The Least-Moving-Point (LMP) method is one approach which consists in detecting the point that moves the least during the circumduction motion. The goal of this paper is to highlight the limits of the native LMP (nLMP) and to propose a modified version (mLMP).

A software application has been developed allowing the simulation of a circumduction motion of a hip in order to generate the required data for the computation of the HC. Two tests have been defined in order to assess and compare both LMP methods with respect to (1) the camera noise (CN) and (2) the acetabular noise (AN).

The mLMP and nLMP error is respectively: (1) 0.5±0.2mm and 9.3±1.4mm for a low CN, 21.7±3.6mm and 184.7±13.1mm for a high CN, and (2) 2.2±1.2mm and 0.5±0.3mm for a low AN, 35.2±18.5mm and 13.0±8.2mm for a high AN.

In conclusion, mLMP is more robust and accurate than the nLMP algorithm.

The hip centre (HC) in Computer Assisted Orthopedic Surgery (CAOS) can be determined either with anatomical (AA) or functional approaches (FA). AA is considered as the reference while FA compute the hip centre of rotation (CoR). Four main FA can be used in CAOS: the Gammage, Halvorsen, pivot, and least-moving point (LMP) methods. The goal of this paper is to evaluate and compare with an in-vitro experiment (a) the four main FA for the HC determination, and (b) the impact on the HKA.

The experiment has been performed on six cadavers. A CAOS software application has been developed for the acquisitions of (a) the hip rotation motion, (b) the anatomical HC, and (c) the HKA angle. Two studies have been defined allowing (a) the evaluation of the precision and the accuracy of the four FA with respect to the AA, and (b) the impact on the HKA angle.

For the pivot, LMP, Gammage and Halvorsen methods respectively: (1) the maximum precision reach 14.2, 22.8, 111.4 and 132.5 mm; (2) the maximum accuracy reach 23.6, 40.7, 176.6 and 130.3 mm; (3) the maximum error of the frontal HKA is 2.5°, 3.7°, 12.7° and 13.3°; and (4) the maximum error of the sagittal HKA is 2.3°, 4.3°, 5.9°, 6.1°.

The pivot method is the most precise and accurate approach for the HC localisation and the HKA computation.

INTRODUCTION

In orthopedic surgery, the lower limb alignment defined by the HKA parameter i.e. the angle between the hip, knee and ankle centers, is a crucial clinical criterion used for the achievement of several surgeries. It can be intraoperatively determined with Computer Assisted Orthopedic Surgery (CAOS) systems by computing the 3D location of these joint centres. The hip centre used for the computation of the HKA is defined by the experts as the anatomical centre of the femoral head. However, except for Total Hip Replacement procedure, the hip joint is not accessible and the hip center is computed using functional methods. The two most common are the Least Moving Point (LMP) and the Pivoting (PIV).

One of the advantages of Computer Assisted Orthopaedic Surgery is to obtain functional and morphological information in real time during the procedure. 3D models can be built, without preoperative images, based on elastic 3D to 3D registration methods. The bone morphing algorithm is one of them. It allows to specifically build the 3D shape of bones using a deformable model and a set of spare points obtained on the patient. These points are obtained with a pointer tracker visible by the station which digitises the surface of the bone. However, it’s not always possible to digitise directly the bone in the context of minimal invasive surgery. In this case, the lack of information leads to an inaccurate reconstruction of bone’s surfaces. To collect such missing information we propose to rely on ultrasound (US) images despite the fact that ultrasound is not the best modality to image bones.

To use this method, a segmentation step is first needed to detect automatically the bone in US images. Then, a calibration step of the US probe is carried out to obtain the 3D position of any point of the 2D ultrasonic images using 3D infra-red localizer. Several methods can be carried out to calibrate US probes, however to take into account surgical constraints such as accuracy, robustness, speed and ease of use, we decided to implement the single wall procedure.

The calibration step consists in the estimation of a transformation matrix which carries out the connection between the 2D reference system of the US image and a 3D reference system in the space. To estimate correctly this matrix, a wall is scanned with different motions of the US probe. The images are then processed to automatically detect the lines representing the wall in the US images. A preliminary step allows to clean the images using a threshold and a gradient operation. Then, a method based on the Hough transform detects the lines on the images. Once all the images are processed, the calibration parameters can be estimated by using a new method which minimises the distance between the real plane and the points obtained with the US images. This optimisation step is composed of the genetic algorithms and of the Levenberg-Marquardt (LM) method. The first algorithm allows to obtain a good initialisation in a defined space for the LM algorithm. This good initialisation found thanks to the stochastic behaviour of the genetic algorithms is very important otherwise the LM algorithm could detect local minimum and the calibration parameters could be wrong.

The accuracy of the calibration method is assessed by measuring the distance between the position of a known point in the space and the same point obtained with the US image and the calibration. 40 calibrations matrices are used to estimate correctly the accuracy. An average accuracy of 1.22 mm and a standard deviation (Std. Dev.) of 0.42 mm are measured. The accuracy of the system is quite high but the reproducibility is too low to use this approach in a clinical environment. The main reason of this lack of reproducibility is the thickness of the US beam.

A slight modification in the design of the calibration tool will allow to increase the reproducibility. We will then have an efficient and automatic calibration procedure with the required accuracy and robustness, usable for clinical purposes.