INTEGRATING THE ECHOGRAPHY IN COMPUTER ASSISTED ORTHOPAEDIC SURGERY: THE CALIBRATION STEP

Abstract

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.