Fig 1.
CAD model of the phantom for the 3D-US calibration (left) and its 3D ultrasound image on Slicer (right) with fiducials placed on the tips.
Fig 2.
Setup for the transducer (d) calibration procedure: The phantom (c) was placed in a fixed position inside the water tank with a tracking tool attached on the tank (b) and on the transducer (a).
The mechanical arm held the transducer in a constant position during image acquisition.
Fig 3.
Hand-eye US calibration loop: The transformation between arbitrary US volumes USi and USj can be found indirectly via the tracked sensor positions or directly via 3D intra-modality image registration.
Fig 4.
The 3D volume at 7.4 cm (red) is a sub-set of the volume with 15 cm scan depth (grey).
They are registered to obtain the transform T7.4cm→15cm. Then the calibration matrix at 15 cm depth can be calculated. Thus, this transformation is a simple translation.
Fig 5.
2D spatial US calibration techniques: By applying the pointer method, fiducials were collected on the image by looking at the maximum intensity profile of the pointer tip on the image (Fig 5(a)). N-shaped wires are seen as dots on the images which are detected and segmented by the PLUS software. The result of the segmentation can be identified as the green cursors (see Fig 5(b)).
Fig 6.
US target registration error on 3D Slicer: Points are collected on the image (red dots) and overlaid by applying the transform to the ground truth phantom coordinates (blue dots).
Fig 7.
Example 3D mode US image of the egg-phantom in 3D Slicer: The egg-phantom was segmented and the software returned the segmentation result (green) in the xyz planes and in the 3D volume rendering (right top of the image).
Fig 8.
Checkerboard image of egg phantom images with 3D Slicer.
On the left hand side, the unaligned images can be seen, on the right hand side the images after alignment using the US calibration are overlaid.
Fig 9.
Checkerboard image of prostate images with 3D Slicer: (a) shows the the unaligned images and (b) the images after alignment using the US calibration using the 3D wobbler mode. In (c) the 3D free-hand reconstructed volumes were aligned.
Fig 10.
Full transformation chain from the planning to the treatment room.
Table 1.
Fiducial registration error for the 3D and 2D calibration techniques.
Table 2.
Target registration error for the 3D and 2D calibration techniques.
Fig 11.
Target registration error trend at the scanning depth of 7.4 cm.
The Multi-target (orange line) showed the lowest TRE of all 3D mode calibration methods. By adding more calibration images, the error did not improve markedly. With the Hand-eye method, the error decreased for the first five image samples but it was generally higher compared to the Multi-target method.
Fig 12.
Target registration error trend at the scanning depth of 15 cm.
Like the previous measurements, the Multi-target method (orange line) had target error lower than the Hand-eye.
Table 3.
Mean value and deviations of the egg phantom volumes for the two US modalities from the reference value of 91.6 cm3.
With only one focal zone, the focus was placed manually at the level of the egg phantom center of mass. With three focal zones, the focus was set to cover entirely the width of the egg phantom. The distances listed refer to the ones between the bottom of the egg phantom surface and the transducer aperture.
Table 4.
The registration error for the 3D free-hand mode and the 3D wobbler mode.
Orientations/angles (degree) are relative to the axis of reference position of the transducer, straight in front of the camera.
Table 5.
Registration error arising with patient data for the 3D wobbler mode.
Orientations/angles (degrees) are relative to the axes of the reference position of the transducer given with the first reference scan.
Table 6.
TREtracker and theoretical upper bound.
Rotation of the transducer relative to the reference tool.
Table 7.
Additional error TREcalΔ introduced by the perturbation t and upper bound.
Orientations/angles (degree) of the transducer between the first scan and the other scans.