# Computational Modeling of Ultrasound C-Scan Imaging Using Transmitted Signal Peak Density
## 3 Structure Position Detection
### Results and Discussion  
Figure 8a,b shows the peak density for the different positions of the flake at Sectors 2 and 3, respectively. From both plots, it was observed that the peak density did not change with the flake position. Therefore, the frequency spectrums for both sectors at all positions were analyzed to find any additional correlation.  
Figure 8: Peak density at all flake positions in (**a**) Sectors 2 and (**b**) 3.  
Figure 7: Pepper flake positions.  
Figures 9 and 10 show the spectrums at all positions in Sectors 2 and 3, respectively. In both Sectors 2 and 3, the peaks and valleys showed a general pattern with pronounced peaks and valleys. This should be for the case of measuring the wave pressure at the back wall during its gradual compression and rarefaction stages at different frequencies. In both sectors, a similar frequency spectrum pattern was observed. However, a slight change in the pressure magnitude was noticed between peaks and valleys at different positions. Therefore, it was understood that, by studying the magnitude variation for those peaks and valleys, a conclusive correlation could be established between the flake position and magnitude variation. However, peak density was not able to depict the magnitude change in those peaks and valleys, as the increasing pressure value did not affect the peak density. Therefore, another parameter was developed to depict the magnitude variation while capturing the change in peak or valley magnitude. This parameter was named Mean Peak to Valley Distance (MPVD), as it measured the average magnitude difference between all adjacent peaks and valleys. To measure MPVD, the distance (pressure difference) was calculated from one peak to the next valley, and then from that valley to the next peak, and so on. All these distances were then averaged to achieve the final value. Therefore, the MPVD would exhibit a change, while the magnitude of the peaks and valleys changed in various locations.  
Figure 11a,b shows the MPVD results for Sectors 2 and 3 at all the locations of the pepper flake inside the phantom. In both sectors, the MPVD value was found to gradually increase from the central location while following a second-degree polynomial trendline. Furthermore, the increasing rate of the MPVD value was higher while the flake got closer to the back wall (0 to 2 mm) compared to the flake getting closer to the ultrasound source (0 to \(-\)2 mm). The primary reason behind the polynomial trend should be the flake's various positions where it interacted with the compression/rarefaction phases of the sound wave at those positions. However, while the flake moved towards the back wall or bottom of the phantom, the scattered wave from the flake started attenuating less because of the decreasing travel path. Thus, scattered pressure started to increase at the back wall. The increasing pressure contributed to the MPVD value and affected the polynomial trend. Therefore, from \(-\)2 to 0 mm, the difference between MPVD values (negative slope) decreased, while from 0 to 2 mm, the positive slope increased. One important factor is that the difference between MPVD values was very small compared to the original spectrum's pressure magnitude. Therefore, to perform this analysis at the experimental level, the  
Figure 9: Frequency spectrum in Sector 2 for flake positioned at (**a**) \(-\)2 mm, (**b**) \(-\)1.5 mm, (**c**) \(-\)1 mm, (**d**) \(-\)0.5 mm, (**e**) 0 mm, (**f**) 0.5 mm, (**g**) 1 mm, (**h**) 1.5 mm, and (**i**) 2 mm.  
frequency spectrums need to be normalized by reference signal in order to avoid the noise effect during the MPVD calculation [27].