126 RSR was calculated from the ratio between the variations in the distance between each pair of TMs in the radial direction (see Figure 2) and their original distance, which is given as: <=<R = >($X! − $XY)Y + ($Z! −$ZY)Y AR&! n=2,……., N (3) where (vx1,vy1) and (vx2,vy2) represent the estimated velocities in the x- and y- directions from the chosen pair of TMs between the (n – 1)th and the nth frames, Dn−1 represents the absolute distance between the chosen pair of TMs at the (n – 1)th frame, and N is the total number of frames in the recording. Because of the framework introduced in (2), Dn−1 remains equal to D1 . As a result, (3) provides an estimate that is related to the Lagrangian strain. From our observations, UP was not the only source of motion influencing the movement of the endometrium in TVUS recordings. Other motions, either coming from different organs, such as bowels and bladder, or caused by heartbeat, respiration, and probe movement during the acquisition, were all recorded during the US scan. Therefore, a bandpass filter was applied to the RSR signals to remove the interference from these undesired motion sources. From the literature, UP during a normal menstrual cycle varies from 0.5 to 4.1 contractions per minute [25], while during IVF treatment, UP appears to show higher frequencies due to the ovarian stimulation, resulting in a range from 0.5 to 5 contractions per minute [12], [26]. The cut-off frequencies of the bandpass filter were therefore set according to the literature based on the application. E. Feature Extraction In this study, we focused on analysing the velocity, direction, and coordination of the UP, which might have a direct impact on the success of pregnancy. Based on the RSR signals, we created a time–space representation of the UP waves propagating along with the endometrium, as shown in Figure 5.4A and B. The RSR signals are aligned in space from the cervix to fundus (y -axis) based on the distance between each pair of TMs. The x -axis represents the time evolution of RSR signals, and the colour code represents the value of the RSR signals. Positive RSR, shown in yellow, indicates uterine relaxation, while
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