Fig 1.
Two examples of kinematic constraints during interventions.
Collision due to the patient size (a), and other medical devices (b).
Fig 2.
Philips Allura FD20 Xper C-arm possible rotations.
(a) RAO/LAO rotation with cranial CRA/ CAU tilt, (b) CRA/CAU rotation with RAO/LAO tilt. Rotation axes for RAO/LAO and CRA/CAU rotations are Z and X, respectively, which are shown in the blue color.
Fig 3.
Possible rotations are divided into arcs with less than 80°.
(a) RAO/LAO arcs with CRA/CAU obliques shown in the purple, green, and red colors, (b) CRA/CAU arcs with RAO/LAO obliques shown in the blue color, (c) and (d) spherical plot of arcs with a forbidden area, (e) and (f) spherical plot of the arcs after removing those that intersected the forbidden area, (g) and (h) spherical plot of these remaining arcs after sparsification. Only these arcs were in the search space for trajectory optimization. (Kinematic constraints are simulated as forbidden areas on the geometry of the system and are shown as yellow rectangles.).
Fig 4.
Possible rotations are divided into arcs with an 80° maximum and are shown in different colors.
(a) RAO/LAO arcs with CRA/CAU obliques shown in the purple, green, and red colors, (b) CRA/CAU arcs with RAO/LAO obliques shown in the blue color, (c) and (d) spherical plot of arcs with an illustration of two forbidden areas as the area inside the yellow rectangles, (e) and (f) spherical plot of the residual arcs after removing those which were inside the forbidden area, (g) and (h) spherical plot of the residual arcs after sparsification. Only those remaining arcs were included in the search space for our trajectory optimization. (Kinematic constraints are simulated as forbidden areas on the geometry of the system and are shown as yellow rectangles.).
Fig 5.
Illustration of the search strategy proposed for the on-the-fly trajectory optimization, with the optimized trajectory that included three arcs selected for the neck target with one forbidden area simulation.
(a-d) Optimizing the first best arc, (e-h) optimizing the second best arcs, and (i-k) optimizing the third best arc. The number close to each arc shows the value of FSIM achieved related to that arc. The sign (*) shows that the arc included more than 10% of its angular range in the forbidden area, and therefore, was rejected from the search space and FSIM was not calculated.
Fig 6.
Three VOI selected for our experiments, (a) T3/T4 regions of the thoracic spine (Target 1), (b) T10/T11 regions of the thoracic spine (Target 2), and (c) C1/C2 region of the cervical spine (Target 3).
Fig 7.
3D visualization of the optimized trajectories with respect to the C-arm circular trajectory for the Target 1 with one simulated forbidden area (a) and two simulated forbidden areas (b).
(Trajectories were the same when simulating one or two forbidden areas).
Fig 8.
Reconstructions with one forbidden area (the reconstructions are also the same for two forbidden areas, as the trajectories happened to be the same) related to Target 1 using (a) optimized trajectory that included two arcs based on simulation data, (b) optimized trajectory that included two arcs based on real data, (c) C-arm circular trajectory based on real data, and (d) partial circular trajectory based on real data.
The display window uses the range 200–3000 HU for (a), and a range of 0–21 in gray values for (b-d), respectively.
Fig 9.
Reconstructions with one forbidden area (the reconstructions are also the same for two forbidden areas, as trajectories happened to be the same) related to Target 1 using (a) optimized trajectory that included three arcs based on simulation data, (b) optimized trajectory that included three arcs based on real data, (c) C-arm circular trajectory based on real data, and (d) partial circular trajectory based on real data.
The display window uses a range of 200–3000 HU for (a) and a range of 0–21 in gray values for (b-d), respectively.
Table 1.
The angular range and projection number of the three selected arcs for the optimized trajectories related to both thorax targets using one simulated forbidden area, and total of projections number for the final optimized trajectories related to both Target 1 and Target 2.
(For both Target 1 and Target 2, the three selected arcs were the same when considering one or two simulated forbidden areas; therefore, the numbers reported here are the same when using two forbidden areas.).
Table 2.
The angular range and projection number of the three selected arcs for the optimized trajectories related to Target 3 using one or two simulated forbidden areas.
(For Target 3, the three selected arcs were different when considering one or two simulated forbidden areas.).
Table 3.
Relative deviations (%) of image quality measures FSIM and UQI related to Target 1 and Target 2 for both optimized and partial circular trajectories using one forbidden area (for both Target 1 and Target 2, the three selected arcs were the same when considering one or two simulated forbidden areas; therefore, the reconstructed images and the computed image quality metrics reported here are the same when using two forbidden areas).
Table 4.
Relative deviation (%) of image quality measures FSIM and UQI related to Target 3 for both optimized and partial circular trajectories using one and two simulated forbidden areas.