Fig 1.
(a) Rendered CT volume after thresholding to visualize the aortic valve. (b) An enlarged view of the aortic valve. The blue, green and red dots refer to the coronary ostia, the aortic hinges, and the aortic commissures, respectively. The commissure between the right-coronary and non-coronary hinges and the commissure between the left-coronary and non-coronary hinges are occluded in this view.
Fig 2.
View customization for manually marking the landmarks and diagnosing.
(a) Original view. (b) Customized view. Red, green and blue lines indicate the X, Y and Z axes, respectively. Transverse plane is carefully rotated about X an Y axes to have a view parallel to the aortic annulus because the aorta pose is not clear in the original view.
Table 1.
Summary of the previous methods.
Fig 3.
The voxel difference feature at x.
The yellow dot refers to x i.e., the sample that needs to calculate the feature. The feature exploits the difference between the intensity at the green and red dotted positions. The distance vectors of these points from x are the feature offset parameters v1 and v2, respectively. In this figure, The component along Z-axis is considered zero for the parameters for visualization purposes. (a) The case of a random pair of the parameters. (b) and (c) The case of either one of the parameters being 0.
Fig 4.
A single walk towards a target point in a 3D volume.
The red dot is the target ground truth point. (a) The blue arrows refer to the learned unit directions to the ground truth at each voxel. (b) A walker starts from the blue point (i.e., the initial voxel) and updates to its next position taking a step towards the learned direction at the current position. After a certain steps, it starts moving around the ground truth point. The expectation of the step positions gives the target position.
Fig 5.
A colonial walk from multiple random points.
The red dot is the target ground truth position. The orange dot refers to the first unknown point that misguides the walker. Initial point of the 1st walk is unknown to the regression tree. The 2nd walker converges and make dense step cloud around the target. The first misguider point of the N-th walk is not the initial point but a point through its way. The walker with the minimum walk variance is considered to be the best-guided walker.
Fig 6.
The proposed two-phase model for learning the aortic valve landmarks.
(a) A representative point inside the valve area is detected in the global phase. In local phase, all the eight landmarks are localized from the estimated point in the global phase. (b) The point inside valve area is detected by colonial walk in the whole volume. (c) All the landmarks are localized locally by colonial walk from the globally estimated point.
Fig 7.
The dependency of the average localization error (in mm) on the step length (in voxels) and the number of steps.
The blue and red dots in (a), (b) and (c) are the initial and the target ground truth positions, respectively. The walker fails to reach the target because of too small step length. Scattered movement is noticed for a very big step length. Relatively smooth movement is noticed for an optimal step length. (d) Dependency of the average localization error on the total number of steps for different step lengths.
Fig 8.
Colonial walk-localized landmarks in a test volume of a normal patient during the cross-validation on 40 non-TAVI volumes.
(a) Successful walk with the minimum walk variance towards the non-coronary hinge point in global phase. The blue point refers to the initial position of the walker. (b) Local estimation of the non-coronary and right-coronary hinge points, the commissure point between them, and the right coronary ostium. (c) Corresponding ground truth.
Fig 9.
Localized landmarks in a TAVI volume using the models trained on 40 non-TAVI volumes.
(a) Localized landmarks in volumetric view. (b) Short axis view. (c) LVOT view.
Table 2.
Fourfold cross validation test results on 40 non-TAVI volumes.
Table 3.
Localization results in 31 TAVI volumes using the models trained on 40 non-TAVI volumes.
Table 4.
Final cross-validation test results on 71 volumes.
Fig 10.
Localization error for different initial points in an unknown TAVI volume exploiting the knowledge of non-TAVI volumes only.
(a) Logarithm of the localization error for different initial points on an axial slice near the target. (b) flattened and sampled representation of the corresponding localization error. The average error and minimum error is indicated in contrast with the error triggered by the minimum walk variance.
Fig 11.
Complementary cumulative distribution function (CCDF) of the high localization error cases.
refers to the probability of error being greater than e. The colonial walk has reduced the probability of high error cases improving the localization for problematic volumes in RTW.
Table 5.
Estimation error (in mm) of sizing parameters obtained from the localized landmarks.
Fig 12.
Walk variance relation to the localization error.
(a) High error for high variance walk and low error for low variance walk is observed. (b) Localization error is presented against logarithm of walk variance.
Fig 13.
The case of high localization error.
(a) A volume with typical error. (b) A volume with high error. Red, green and blue lines indicate the X, Y and Z axes, respectively. Rotation about X and Y axes is applied to have the axial view-plane parallel to the hinge plane for both volume to compare. The amount of rotation about Y-axis in case of the volume with high error was significantly higher comparing to the case of the volume with typical error.