II.2.1 The Deformable Model
The method works by fitting a deformable model to an ultrasound image. The model used was a Doo-Sabin model, a generalization of quadratic B-splines originally described by Doo and Sabin [6]. The model was based on the model used by Orderud et al.[16], but some changes were made. The model consists of two distinct sub-models: one modeling the left ventricle(LV), the other modeling the left ventricular outflow tract(OT). Figure II.1 shows the models.
The aortic and LV models are simultaneously deformed to perform the segmentation of respective structures. The LV model was meant to find the general shape of the left ventricle, including the position of the mitral valve. The OT cylinder determined the position of the aortic valve.
II.2.2 The Kalman Filter
The model was fitted to the image using a Kalman filter process[10]. The Kalman filter fits a model by optimizing the state vectorx, which determines the properties of the model. The filter also provides a covariance matrixP as output, giving a measure of the uncertainty of each entry ofx. P’s diagonal entries give the standard deviation of the state vector.
The measurements of the ultrasound image used as input into the Kalman process consisted of edge detection of the current frame. The edge detection was done relative to the surface points in the direction of the surface normal vectors on the model from the prediction step. The edge detector used a step edge algorithm, searching for the biggest change in intensity along the normal vector for 3 cm. The Kalman filter updated the state vector based on the measurements.
Figure II.2: An example of the models fitted to a TEE ultrasound image using the algorithm described in Section II.2.2.
This was described in greater detail in an article by Orderud and Torp[16]. An example of the models described in Section II.2.1 fitted to a TEE ultrasound image is shown in Figure II.2.
The process was manually tuned on 18 ultrasound images to determine the initialization values for the Kalman filter, with the exception of the global value of rotation around the y-axis, which was handled in its own step, as detailed in Section II.2.3. The tuning images were kept separate from the images used for validation. The input of the algorithm was only the ultrasound image. No user input was used.
Once models were fitted to the image, the placement of the models was used to determine the alignment of the standard view. An example of the finished standard views based on the landmarks from the algorithm is shown in Figure II.3.
II.2.3 Initialization of Kalman Filter
The Kalman filter’s initial value of rotation in the x-z plane was determined in its own stage due to the large variation in the true value between files. A preliminary model, identical to the model used in the rest of the algorithm, was rotated to eight different angles. These angles spanned the angles 0 to 360 degrees, meaning there was 45 degrees between them. The rotated models were fitted to the image using a Kalman filter and the output covariance matrices from the filter were analyzed to find the best fit.
The best fitted model was determined using the values of the covariance matrix.The k-th element of the diagonal ofP is the variance of the k-th element of x. Adding together the elements on the diagonal corresponds to adding together the uncertainty of each element in the state vector.
The diagonal entries corresponding to the nodes close to the apex of the LV model were excluded and the weights of the remaining nodes were set to 0.5.
Because of the importance of the OT cylinder, the variance of the three states directly related to it were given increased importance, and were multiplied by 3.
Materials and Methods
Figure II.3: An example of the result of the fitting algorithm and the resulting standard views. At top left is the apical long axis with aorta in view, at top right is the 2 chamber view, at the bottom left is the 4 chamber view, and at the bottom right is the short axis view.
For the global variables, most significance was placed on its rotations, as those are most related to proper OT cylinder placement. Thus only those values were used. The formula was:
s=
3
X
i=1
V ar(xRi) + 0.5
18
X
i=1,i̸∈xA
V ar(xLVi) + 3·
3
X
i=1
V ar(xOTi)
HerexR are the indexes of entries relating to global rotation,xA are indexes of entries relating to the apex of the LV,xLV are the entries relating to the LV andxOT are the entries related to the OT. The formula was determined through testing on ultrasound images kept separate from the validation files.
The starting depth was set as 75 % of the depth of the centre of the image in the case of a full volume acquisition and in the centre of the image in the case of zoomed images.
Once initialization was done, the Kalman filter can be run, setting the starting rotation according to the above algorithm. Once the model was fitted to the image, landmarks on the model was used to determine the standard view.
Figure II.4: A long axis view of one ultrasound image, with landmarks placed to mark the centre of the mitral valve and the aorta. The red dot is the manually placed mitral centre, the blue is the mitral valve calculated by the algorithm.
The green is the manually placed aorta and the yellow is the automatically placed aortic valve center.
II.2.4 Determining Standard Views
Once the model was fitted to the image, landmarks on the model were used to determine the standard view. The long axis view was determined by landmarks on the LV model. 60 points were placed around the base and used to estimate the centre of the mitral valve. 6 points were placed evenly on the midwall of the LV, and were used to estimate the centre of the model. The long axis of the model was set to be the line going through the centre of the mitral valve and the centre of the model.
Two landmarks were placed on each side of the OT cylinder, so that the average of them would be the centre of the cylinder. The apical long axis view was defined as the plane that contain both the long axis and the centre of the OT cylinder.
The 2-chamber and 4-chamber planes were set to be 60 and 120 degrees off from the apical long axis view, respectively. Finally, the short axis view should have its centre at the estimated centre of the mitral valve and should go through the OT cylinder.
An example of the estimated standard views can be seen in Figure II.3.
II.2.5 Evaluation of Images
106 TEE 4D anonymized ultrasound images were used to evaluate the algorithm.
All of the images were of the mitral valve, some showing the entire left ventricle.
The images were collected from several institutions under data agreements ensuring compliance with applicable privacy legislations. All ultrasound images used as figures in this article came from the same data, and can be used as such under the same data agreements. All data was provided by GE, and was previously acquired for research purposes using GE Vivid echocardiographic
Results
Figure II.5: A short axis view of one ultrasound image, with landmarks placed to mark the centre of the mitral valve and the aorta. The red dot is the manually placed mitral centre used as ground truth, the green is the manually placed aortic valve centre and the yellow is the automatic aortic valve centre. The two lines marks the angle used for evaluation of aorta error.
systems E95 and S70 (GE Vingmed Ultrasound, Horten Norway) with a 6VT-D TEE probe.
For each of these images landmarks had been placed to mark the mitral valve and aortic valve and these were used as a ground truth. The landmarks were originally placed as part of a different project done by Andreassen et al.[1] using GE’s 4D AutoMVQ software(EchoPAC SoftwareOnly v204, GE Vingmed Ultrasound, Horten Norway). Figure II.4 shows an example of landmark placement on an image.
Each image was evaluated on two criteria. The first measure was the distance between the estimated centre of the mitral valve from the algorithm and the centre from the ground truth in 3D space. The second measure used was the angle between three points: the algorithm’s estimate of the aortic valve, the centre of the mitral valve from the ground truth, and the aorta placement from the ground truth. In an ideal case, where the two aorta placements are the same, the result should be 0 degrees. For angle calculation, the points were projected unto a plane, depth of the points were not considered. An image showing how the mitral valve/aorta angle error was determined is shown in Figure II.5.