Kluwer - Handbook of Biomedical Image Analysis Vol

Figure 1.26: Radial scatterer distribution for the arterial structure: blood, intima, media, adventitia, and the transducer sheath.

Figure 1.27: DBC distributions of simulated arterial structures: blood (a) and

intima (b).

Figure 1.28: DBC distributions of simulated arterial structures: media (a) and adventitia (b).

Table 1.4. The typical cell nuclear size was obtained by Perelman et al. [22]. In Fig. 1.29 we can observe the dependency of axial resolution and the ultrasound frequency. To illustrate this, four IVUS simulated images are shown. Low frequency ranging from 10 to 20 MHz corresponds to an axial resolution from 154 to 77 µm, and intermediate frequency from 20 to 30 MHz gives axial resolution from 77 to 51 µm. In these cases, it is possible to visualize accumulations around 100 RBCs. High frequency from 30 to 50 MHz leads to 51–31

µm of axial resolution. Moreover, it is now possible to visualize accumulations of tens of RBCs. The IVUS appearance improves when the frequency increases, allowing different structures and tissue transition interfaces to be better detected.

Table 1.4: Typical IVUS simulation magnitudes

Figure 1.29: Synthetic images generated by low frequency: 10 MHz (a) and 20 MHz (b), intermediate frequency of 30 MHz (c), and high frequency of 50 MHz (d).

1.6.3.2 Optimal Ultrasound Frequency

In order to validate our model, we compare synthetic to real images. We generated synthetic images for a great rank of frequency and used the cross-validation method [23] to find the most similar image to the real one generated using Boston Sci. equipment at 40 MHz frequency. The sum square error (SSE) from the real to the simulated images for each ultrasound simulated frequency is computed. Figure 1.30(a) shows the SSE versus ultrasound frequency. The optimal frequency

Figure 1.30: The optimal ultrasound simulation frequency fo ≈ 46 MHz (a) and the optimal attenuation coefficient (b) α ≈ 0.8 dB/MHz cm are obtained by the cross validation method.

is located in the interval 40–50 MHz. Note that the central frequency of Boston Sci. equipment is 40 MHz; therefore, it can be considered as evidence to show the correctness of the method.

1.6.3.3 Optimal Attenuation Coefficient

We have emulated synthetic IVUS images with different attenuation coefficients; the optimal attenuation coefficient was tested by applying the cross validation method of the synthetic images versus the real images. Figure 1.30(b) shows SSE versus attenuation coefficient α; the optimal attenuation coefficient obtained was 0.8 dB/MHz cm. There is a range of suboptimal attenuation coefficient values for a fixed ultrasound frequency due to the great axial variability of scatterers. However, the attenuation coefficient can be taken as constant for each simulated region [28]; however, in the transition zones (lumen/intima, intima/media, and media/adventitia) the attenuation gives great variability. For this reason, we must average the attenuation coefficient value. It is very important to confirm that the optimal frequency is approximating the standard central ultrasound frequency of 40 MHz and that the attenuation coefficient is near the standard values of biological tissues, which ranges from 0.5 to 1 dB/MHz cm. This result can be used in different ways: first, to check the used simulation parameters in

Figure 1.33: Horizontal ((a) and (b)) and vertical directions ((c) and (d)) gray-level profile average projections, from real (Fig. 1.32(a)) and simulated (Fig. 1.32(b)) IVUS images.

is the average gray-level projection that allows a simple form to find the main image correlated characteristics in an 1D shape gray-level profile. Gray-level baseline, video noise, instrumental noise, reticle influence, and the main graylevel distribution coming from the main arterial structures are roughly visible from the gray-level average projection. The average gray-level projection gives a global measure of the similarity between real and simulated images. The similarity measured can be computed, for example, by the local attenuation coefficient of the projection profile of each ROI [28]. Figure 1.33 gives the projections in the horizontal and vertical directions for the real (Fig. 1.32(a)) and simulated (Fig. 1.32(b)) IVUS images. The correlation coefficients mand b (Fig. 1.34) for the gray-level average projection in the horizontal (m = 0.63, b = 13.53) and vertical (m = 0.75, b = 9.07) directions show a positive correlation between the real and simulated data. Figure 1.35 shows two selected regions of interest of the real (Fig. 1.32(a)) and simulated (Fig. 1.32(b)) images. We can see a good gray-level distribution and a soft gray-level decay from the center to the peripheries of the IVUS image, produced by the inverse relation between the ultrasound intensity and the penetration depth. The other reason is that the normal attenuation is caused by the scattering intensity given by the tissue impedance. Figure 1.36

Figure 1.38: Real (a) and simulated (c) Cartesian images and their corresponding real (b) and simulated (d) polar transformation.

from the real and simulated polar images and the correlation coefficients were obtained. Figure 1.39(a) shows the gray-level average vertical projection for the real and simulated ROIs data (delineated in red in Fig. 1.38). We can see that the gray-level profiles of the transition of arterial structure in the lumen/intima, intima/media, and media/adventitia are very well simulated, the linear correlation coefficients being m = 0.93 and b = 1.61 (Fig. 1.39(b)). The global horizontal profile of the polar images along the projection θ (Figs. 1.40(a) and (b)) gives very important and comparative information about the real and simulated graylevel average of arterial structures. The information that can be extracted is relative to the global gray-level distribution. The histogram (Fig. 1.40(b)) of gray-level differences between the horizontal profiles of real and simulated data indicates a very good correspondence (mean µ = 8.5 and deviation σ = 10.2). Figure 1.41(a) shows the global projection in the radial direction (the vertical profile). We can see a very good correspondence between the gray-level shape profiles (mean µ = 5.7 and deviation σ = 8.5). The histogram (Fig. 1.41(b)) of gray-level difference confirms the good correlation between the real and simulated IVUS data.