A 3D Slicer module for calibration of spatially tracked 3D ultrasound probes

Abstract

Purpose: Many applications in the field of image-guided therapy could benefit from using 3D ultrasound (US) imaging. To locate the US volume within the treatment room, it is necessary to find the transformation from US space into the tracking space by means of a spatial calibration, which is often cumbersome and time-consuming. Our goal is to offer an open-source module for 3D Slicer to overcome those limitations. The approach is based on surface matching of geometrical shapes within an US phantom. For evaluation, the calibration accuracy was measured using two metrics.

Methods: - Calibration: A voxel usVox_v of a 3D US image is transformed into the tracking space as follows: tr_v = tr_T_pr x pr_T_us x us_A_usVox x usVox_v where a_v is a point in space a, and a_T_b € R_4x4 and a_A_b 2 € R_4x4 are a homogenous rigid and scaling transformation, respectively, that map from space a onto space b. The terms tr, pr, us, usVox refer to tracking, US probe, US volume (mm) and US volume (voxels), respectively. As illustrated in Fig. 1, the unknown transformation is calculated in the calibration step with pr_T_us = (tr_T_pr)-1 x tr_T_ph x ph_T_ct x ct_T_us where ph and ct refer to phantom and computed tomography (CT), respectively. A landmark-based registration provides tr_T_ph x ph_T_ct, as the optical markers of the phantom are obtained in both tracking and CT spaces. A surface matching algorithm of the segmented geometrical shapes of the phantom in the CT and US spaces provides ct_T_us. - Module description: The inputs of the developed 3D Slicer module are a sequence of N US volumes, the corresponding N tracked poses of the US probe, the surface model created from CT data, fiducials (coordinates of the optical marker centroids) in tracking (F_tr) and in CT (F_ct) spaces, and a linear transformation to store pr_T_us. In addition, adjustable parameters are start and end indices of the US volumes used, and the variance, lower and upper thresholds used for the Canny edge detection to segment the geometrical shapes in the US volumes. The module first calculates tr_T_ct based on F_tr and F_ct. Then, the module obtains a surface model from each US volume after the Canny edge detection. Having surface models in both spaces, the iterative closest point algorithm is applied to find ct_T_us with 200 randomly sampled points of each model. pr_T_us is obtained for each US volume since all transformations are determined. An average of N pr_T_us is calculated for final prTus.

Evaluation: A 3D US probe (X6-1, Philips Healthcare) was used and volumes (matrix size 416 x 312 x 256, voxel size 0.59 x 0.53 x 0.93 mm^3) were recorded from the US station (EPIQ 7, Philips Healthcare) via the PLUS Toolkit in 3D licer. An optical tracking system (Atracsys fusionTrack 500) with passive markers was used to track the US probe and phantom. The multimodality calibration phantom (CIRS Inc.) for the Clarity radiotherapy positioning system (Elekta) containing ten cylinders and two spheres was used for imaging. The US probe was placed on the phantom in four different poses and ten volumes (N) were acquired at each pose. Cropping the US volumes and pre-aligning them to the CT surface model within 3D Slicer was necessary to provide only the geometrical shapes of the phantom in a proper initial alignment. Then, four (pr_T_us)_i were calculated based on the ten volumes of each pose i. For a first evaluation metric, a tracked stylus with a 2-mm lead bead at its tip was immersed in a water tank at room temperature after calibrating the stylus to obtain the tip position in the tracking space (reference). Six different positions of the tip were acquired with the tracking system. For each position, an US volume containing the lead bead was recorded and the tip was manually selected. For each (pr_T_us)_i and tip position, the distance between the tip position (US volume) transformed into the tracking space and its corresponding reference was calculated. For a cross-validation (second metric), each (pr_T_us)_i was used to place three US surface models (each corresponded to the first volume of the other three poses used for calibration) in the tracking space. The Hausdorff distance between each US surface model (approximately 25,000 vertices) and CT surface model, both transformed into the tracking space, provided three distance measurements for each pose.

Results: Figure 2 shows the module and the registered surface models for checking the calibration. The root mean square (RMS) and maximum values of the stylus tip distances and Hausdorff distances (surfaces) for each (pr_T_us)_i are shown in Table 1. The RMS distance of the stylus tip is around three times higher than that of the surfaces. There are multiple possible error sources. First, pivoting of the stylus to find its tip and the manual selection of the tip in the US volume will cause significant error. Additionally, the experiment was performed in a water tank and thus the different speed of sound can cause a nonlinear error of around 4% [1]. These error sources are not applicable for the first metric. Nevertheless, the RMS error of the stylus tip in this 3D US probe calibration study was similar to the mean error of a previous study [2].

Conclusion: The open source 3D Slicer module provides a user-friendly method for 3D US probe calibration and its approach is feasible even when using only one pose of the probe. Future work will focus on extending the module by including other surface matching algorithms, an automated preprocessing step and directly calculating the calibration accuracy.

References: [1] Mercier L, Langø T, Lindseth F, Collins L (2005) A review of calibration techniques for freehand 3D ultrasound systems. Ultrasound Med Biol 31(4):449–471. [2] Bergmeir C, Seitel M, Frank C, De Simone R, Meinzer H-P, Wolf I (2009) Comparing calibration approaches for 3D ultrasound probes. Int J CARS 4:203–213.