Fiducial marker-based correction for involuntary motion in weight-bearing C-arm CT scanning of knees. Part I. Numerical model-based optimization

Abstract

Purpose: Human subjects in standing positions are apt to show much more involuntary motion than in supine positions. The authors aimed to simulate a complicated realistic lower body movement using the four-dimensional (4D) digital extended cardiac-torso (XCAT) phantom. The authors also investigated fiducial marker-based motion compensation methods in two-dimensional (2D) and three-dimensional (3D) space. The level of involuntary movement-induced artifacts and image quality improvement were investigated after applying each method.

Methods: An optical tracking system with eight cameras and seven retroreflective markers enabled us to track involuntary motion of the lower body of nine healthy subjects holding a squat position at 60° of flexion. The XCAT-based knee model was developed using the 4D XCAT phantom and the optical tracking data acquired at 120 Hz. The authors divided the lower body in the XCAT into six parts and applied unique affine transforms to each so that the motion (6 degrees of freedom) could be synchronized with the optical markers' location at each time frame. The control points of the XCAT were tessellated into triangles and 248 projection images were created based on intersections of each ray and monochromatic absorption. The tracking data sets with the largest motion (Subject 2) and the smallest motion (Subject 5) among the nine data sets were used to animate the XCAT knee model. The authors defined eight skin control points well distributed around the knees as pseudo-fiducial markers which functioned as a reference in motion correction. Motion compensation was done in the following ways: (1) simple projection shifting in 2D, (2) deformable projection warping in 2D, and (3) rigid body warping in 3D. Graphics hardware accelerated filtered backprojection was implemented and combined with the three correction methods in order to speed up the simulation process. Correction fidelity was evaluated as a function of number of markers used (4-12) and marker distribution in three scenarios.

Results: Average optical-based translational motion for the nine subjects was 2.14 mm (± 0.69 mm) and 2.29 mm (± 0.63 mm) for the right and left knee, respectively. In the representative central slices of Subject 2, the authors observed 20.30%, 18.30%, and 22.02% improvements in the structural similarity (SSIM) index with 2D shifting, 2D warping, and 3D warping, respectively. The performance of 2D warping improved as the number of markers increased up to 12 while 2D shifting and 3D warping were insensitive to the number of markers used. The minimum required number of markers for 2D shifting, 2D warping, and 3D warping was 4-6, 12, and 8, respectively. An even distribution of markers over the entire field of view provided robust performance for all three correction methods.

Conclusions: The authors were able to simulate subject-specific realistic knee movement in weight-bearing positions. This study indicates that involuntary motion can seriously degrade the image quality. The proposed three methods were evaluated with the numerical knee model; 3D warping was shown to outperform the 2D methods. The methods are shown to significantly reduce motion artifacts if an appropriate marker setup is chosen.

Figure 1

Seven markers (small circles on the body) were suitably placed to track a lower body. Six joint centers (big circles in the body) were estimated from the markers. Figure generated using OpenSim available on Simtk.org.

Figure 2

Transformation procedures to map ${\vec{v}}_{\mathrm{upper}}^{\mathrm{XCAT}}$ onto ${\vec{v}}_{\mathrm{upper}}^{\mathrm{marker}}$ in the upper leg. The same steps were used to transform ${\vec{v}}_{\mathrm{lower}}^{\mathrm{XCAT}}$ onto ${\vec{v}}_{\mathrm{lower}}^{\mathrm{marker}}$ in the lower leg except for step (7). The vectors are labeled with (1)–(7) representing each step. The vectors were transformed to the next step using a translation matrix T, a rotation matrix R, and a scaling matrix S.

Figure 3

The XCAT knee model was tessellated and rendered as shown in (b). To avoid unrealistic wrinkles in the acute angle of the joint as shown in the windowed region in (a), weighting based on the proximity to the joint was applied.

Figure 4

Based on ray casting, 248 Projections with a pixel resolution of 620 × 480 were generated. Two projection views through the volume (AP and oblique) are shown.

Figure 5

A projection was shifted by the deviation (Δu, Δv) of the markers’ mean from the 2D references’ mean in a detector coordinates (u, v). The left shows the projection before shifting and the right shows the projection after shifting.

Figure 6

A projection was warped using approximate TPS mappings. The markers (×) were mapped smoothly onto the 2D references (+). The left and right show the projection before and after warping, respectively. The grid lines were inserted to better see overall warping of the projection.

Figure 7

Reconstructed slices of the projections generated using the tracking data of Subject 2 with the largest motion. The first row (a) shows central axial slice and the second row (b) shows lower off-center axial slice containing tibia and fibula. The third row (c) shows upper off-center axial slice containing femur. The fourth row (d) shows sagittal slice and the fifth row (e) shows coronal slice. The slices were reconstructed with and without the motion correction methods according to the label at the bottom of each column.

Figure 8

(a) and (b) An image quality comparison of motion compensated axial slice images of Subject 2 using different number of markers. The data points were interpolated using smooth cubic B-splines (the dotted lines). (c) Individual marker locations in an AP view and sequential ID number. Markers with an ID number from 1 to 11 were used for reconstruction with 11 markers.