Accuracy of Position and Pose Estimates of Ultrasound Probe Relative to Bony Anatomy

Many procedures in orthopedic surgery rely on navigation to accurately place instrumentation. These methods include fluoroscopic, stereotactic and robotic approaches. While contemporary systems have been successful at dramatically lowering reoperation rates, they may not always be available due to their significant costs ($850,000-$1,200,000) or appropriate due to their ionizing radiation. There is an interest in developing lower-cost, radiation-free, and accurate navigation. We propose to address this issue using ultrasound measured distances to nearby bone surfaces. Distances can be processed by a state-estimation algorithm to determine the position and pose of the probe relative to a preoperative CT scan. Recent studies have shown that ultrasound can accurately identify bone surfaces, and algorithms based on range measurements are used for accurate localization in mobile robotics. This study evaluates the feasibility of combining these techniques to make sufficient position and pose measurements in an anatomically realistic model. We assessed position and pose estimation accuracy in a simplified 2D space using a linear 2D ultrasound (L-14W/60, Ultrasonix Corp., Canada) to image (1) an adult L4 vertebra model (∼80 mm across), and (2) a set of ‘V’ shapes characterized by their internal angle. The probe was immersed in a water bath at ten different positions and orientations and images were acquired. The US probe position was measured using an NDI Vega optical tracker (Northern Digital Inc., Canada). The images were manually segmented and distance measurements to the model surface computed. We used a multistart interior point optimization algorithm to compute a position and pose that minimized an objective function based on the average squared distances between the predicted and measured distances to the model surface. We then computed the errors relative to the position reported by the optical tracker. The mean localization error of the probe around the anatomically-realistic model was 0.7mm in translation and 2° in rotation. The algorithm obtained similar errors within a range of initial position estimates of up to 12 mm and 20° from the true position. Errors in the parametric study decreased from 1.65 mm and 3.8° for a ‘V’ angle of 90° to 0.3 mm and 0.5° for a ‘V’ angle of 150°. These accuracies suggest that the proposed technique is sufficiently accurate to justify further development. Limitations include the use of a conventional 2D US probe, the 2D plane scenario rather than the real 3D use case, and the use of manual bone segmentation as opposed to an automated algorithm. Future work is planned to address these limitations.

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