AUTOMATED ESTIMATION OF 3D IN VIVO KNEE KINETATICS WITH DUAL X-RAY IMAGES BY PIXEL-BY-PIXEL COMPARISON FOR TOTAL KNEE ARTHROPLASTY

Abstract

In the knee joint surgery such as total knee arthroplasty (TKA), the implant should be inserted in proper position with correct bone alignment because the abnormal kinematics of implanted knees by implant mal-positioning or mal-alignment could cause failure of surgery. Therefore, quantitative information of a 3D kinematics of the knee joint is very helpful to evaluate the surgical treatment such as planning of size and alignment of the implant. In this study, a 2D/3D image matching method was developed to estimate the kinematics of the knee joint based on an automated pixel by pixel comparison of images.

Two projection images were obtained from the 3D object in two perpendicular directions where the given dual X-ray images were taken. The 3D object was translated and rotated automatically and continuously until its projection images were matched with the X-ray images in a given tolerance range. The optimization algorithm was used to minimise the root mean square error between the gray scale values of each pixel in the projection image and the given X-ray image. For estimating the position and orientation of the knee joint, the 3D knee joint models were reconstructed from CT data. The 3D model was matched with the given dual X-ray images by using the developed 2D/3D image matching method. The tibial and femoral components were then combined into the whole knee joint model. By adding fiducial markers based on clinically conventional method, the posterior and mediolateral translation of femur with respect to tibia as well as the flexion angle were measured.

In the experiment with the cubic phantom, the position errors were below 0.10 mm and the orientation errors were below 0.05 o when using dual X-ray images. For the given dual X-ray images, the relative in vivo kinematics of the femur was measured as the posterior translation was 3.0 mm and the mediolateral translation was 0.9 mm. In addition, the flexion angle of the knee joint from the sagittal view was 51o while the angle measured from the given X-ray image was 50 o.

The previous 2D/3D image matching methods operated manually took long time and was dependent on the operator. Recently, automated image matching method has developed by applying optimization algorithms. In this study, the optimal position and orientation were obtained by the direct pixel by pixel comparison, which are easy to implement and modify the algorithm. The present automated method could accelerate the matching process and stabilise the repeatability. In addition, the image matching method with dual images was used to improve the out-of-plane accuracy since the image matching method with a single X-ray image has a limitation of methodology in detecting out-of-plane translation and rotation though the in-plane accuracy was acceptable. The present 2D/3D image matching method is a powerful tool for the accurate determinations of 3D position and orientation of the knee joint and could provide informative characterization of implant designs and surgical options of the knee surgery.