## 4 Discussion
These findings demonstrate that the radial projection method is less sensitive to background noise than the vertical projection method and that the radial method can provide results similar to the ground truth. This can be attributed to the effective avoidance of signal interference between the arterial vessels using the radial projection method. Specifically, during radial projection, stronger signals from the ICA and CCA are kept separate to prevent signal interference. Furthermore, the signals from the ICA and CCA do not mix with those from other vessels, resulting in only minor interference from the surrounding tissues or background noise. Consequently, the time series derived from the ICA and CCA are minimally affected by other vessels, leading to low and stable MAE and SD values. Additionally, the radial projection method collects data from multiple angles, not only preventing signal overlap between blood vessels but also improving the signal-to-noise ratio (SNR) by more frequently sampling low-frequency components in k-space. By contrast, the vertical projection method is prone to significant signal interference between major vessels. In such cases, temporal noise from the primary vessel is also affected by temporal noise from other large vessels, thereby amplifying the overall signal interference. This persistent interference results in consistently high MAE values, irrespective of the temporal noise levels, indicating that the vertical projection method should have sufficient k-space sampling lines. The radial projection method was shown to be more effective than the vertical projection method, as its performance was stable even at various temporal noise levels, suggesting its potential as an important tool for early diagnosis and treatment evaluation in cerebrovascular diseases. To determine the feasibility of implementing the radial projection method in an actual MRI environment, we compared the PWVs between the simulation, undersampled, and interpolated datasets. The results confirmed the feasibility of the radial projection method, as there was no significant difference in PWVs between the simulation and interpolated datasets (Table 3), indicating that the interpolated dataset could maintain an accuracy comparable to that of the simulation dataset. Furthermore, the findings suggest that a high accuracy can be sufficiently preserved even with data acquired at fewer sampling timepoints in an actual MRI environment. Figure 4 illustrates the peak detection accuracy across various peak points in the simulation, undersampled, and interpolated datasets. The interpolated dataset showed a peak detection performance similar to that of the simulation dataset, indicating that it can detect peak points with high sensitivity, similar to the data acquired at high temporal resolution. This study demonstrated that the radial projection method is feasible in an actual MRI environment and can maintain high accuracy and temporal resolution even with fewer sampling timepoints. However, this study has certain limitations. Currently, this method uses projection angles to avoid major vessels, such as the ICA and CCA. Surrounding vessels, apart from the ICA and CCA, may influence the waveforms of these major arteries. Therefore, it is necessary to select projection angles that can avoid all surrounding vessels, which requires further research. Moreover, the distance between the two vesselsused for PWV calculation in this study may not be accurate because it does not account for the curvature of the actual vascular structures. Thus, it is necessary to utilize vessel segmentation techniques to calculate the actual path length between target vessels for more precise PWV measurements. Additionally, this study did not thoroughly analyze the potential influence of vascular diameters and locations on the mean absolute error (MAE). Future research could benefit from a more detailed investigation of these factors to enhance the robustness and accuracy of the proposed method.