128 1) UP Velocity: A moving window, including 600 frames (20s), was applied to segment the time–space representation over time. This duration allows including at least one full UP wave cycle in the time window. Within each segment, 2-D fast Fourier transform was applied to the time–space representation, providing a frequency representation in the k -space domain. UP velocities in both C2F and F2C directions can be explicitly estimated from the peaks in the first quadrant (representing C2F propagation) and the second quadrant (representing F2C propagation) of the k -space. Figure 4A and B shows the frequency representations of Figure 4A and B within one of the moving windows (t = 40 –60s). The evolution of UP velocities in both directions is shown in Figure 4E and F. The temporal and spatial frequencies of the dominant peristaltic motion were identified at the peaks of the spectrum. The corresponding UP velocity, vUP , was then calculated as the ratio between the temporal frequency, B_, , and spatial frequency, B_& as: $ [\ = BUBX (4) 2) UP Direction: Theoretically, the direction of the propagation can be determined by the sign of vUP . Propagation from C2F is here indicated by a positive sign, while propagation from F2C is indicated by a negative sign. However, as discussed in [9] and [11], more complex UP patterns can also be observed. Opposing propagation, which shows both C2F and F2C propagation, is often observed after ovulation to support embryo implantation; recoiling propagation, which consists of reflection and superposition of multiple peristaltic waves, can also be observed, as well as more complex propagation. Figure 5A shows an example of a complex propagation pattern during the EL phase.
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