Validation of the Image Simulation Model
Once the generic basic model of IVUS image formation is defined, we need to compare it to real images contrasting expert opinion to test its use. For this purpose, we defined procedures to extract quantitative parameters that permit the measurement of the global and local similarities of the images obtained. The main goal of this simulation is to give a general representation of the principal characteristics of the image. The comparison of real and simulated images should be done on the global image descriptors. We concentrated on the distribution of the gray levels. Data such as transducer dimensions (Fig. 1.14), the catheter as well as the reticle locations, operation frequency, band width, and original and secondary beam number used for the simulation are standard values obtained from Boston Sci. [24]. However, the optimal values of frequency and attenuation coefficient are obtained by the cross validation procedure [23]. The dimensions, scatterer number, and the backscattering crosssection of the simulated arterial structures were obtained from different literature [7,10,11,19,22,24]. Typical values of the RBCs "voxel" numbers took into account the typical hematocrit percentage [11] (Section 1.4.4). Instrumental and video noise has been incorporated into the simulated image, due to electronics acquisition data, and the acquisition and processing to the video format.
The zones of greater medical interest (lumen, lumen/intima, intima/media, and media/adventitia) were simulated for several real IVUS images. The smoothing image protocol is not known so that the corresponding tests were done until the maximal similarity to the real images was found, based on the use of three progressive methods. (1) The empty pixels are filled using the average of eight neighbors, (2) a median filter is used, and (3) a Gaussian filter is applied in order to find the noise reduction. The quantitative parameters used for the image comparison were directed for global and local image regions, and are described below.
1. Graylevel average projections px and py, that is horizontal and vertical image projections, are defined for an m x n image I as [25]:
2. We define a global linear correlation between real (x) and simulated (y) data as follows:
where m and b are the linear correlation coefficients.
3. Contrast to noise ratio signal (CNRS) as figure of merit, defined as [26]:
where m, fi2, o\, and a2 are the mean and the standard deviations inside the ROIs.
1.6.1 Scatterer Radial Distribution
The radial scatterer distribution is an important factor for a good image simulation. The scatterers under consideration in this simulation are: the transducer sheath, blood, intima, media, and adventitia. We can obtain the arterial structure configuration from an emulated form and from a real validated IVUS image. For the study of the synthetic images, we have used two procedures:
1. Standard data. Typical geometric arterial parameters and their interfaces such as lumen/intima, intima/media, and media/adventitia are obtained from standard literature.
2. Validated data. Geometrical parameters are obtained from manually segmented IVUS images.
In order to investigate the image dependencies of IVUS parameters (frequency, attenuation coefficient, original beam number, secondary beam, and smoothing procedures), we have used a standard data procedure, using a concentric scatterer distribution for this modality. To compare simulated images to real data, we use manually segmented real images, which correspond to the validated data procedure. In manually delineated structures of IVUS images, we extract the position radius Rk of lumen, intima, media adventitia, and transducer sheath. Figure 1.25 shows typical 2D spatial scatterer distributions obtained from standard procedure for the most important arterial structures and the scatterer artifact caused by the transducer sheath.
The radial scatterer distributions play a crucial role in the definition of the IVUS images because they define the ultrasound attenuation in the axial direction. Medical doctors have special interest in graylevel transition in the interface of two media. For instance, the lumen/intima transition defines the frontiers of the lumen. These transitions can only be found through a good radial scatterer distribution.
The radial scatterers distribution of the typical arterial structures and the transducer sheath are shown in Fig. 1.26.
1.6.2 DBC Distribution
The klayers DBCk values for a typical simulated arterial structure are shown in Figs. 1.27 and 1.28 where the count of scatterers of each tissue is shown as
Scatterers distribution
Scatterers distribution
0.05 0.04 0,03 0.02 0.01 0 0.01 0,02 0.03 0.04 0.05
Figure 1.25: Typical concentric 2D scatterer distribution for the most important simulated arterial structures (blood, intima, media, and adventitia) and the scatterer artefact generated by the transducer sheath.
0.05 0.04 0,03 0.02 0.01 0 0.01 0,02 0.03 0.04 0.05
Figure 1.25: Typical concentric 2D scatterer distribution for the most important simulated arterial structures (blood, intima, media, and adventitia) and the scatterer artefact generated by the transducer sheath.
a function of the crosssection of scatterers. The numerical values are given in Table 1.3 [27].
1.6.3 IVUS Image Features 1.6.3.1 Spatial Resolution
A good spatial resolution gives the possibility of improving the visualization of the lumen/intima transition and studying the structures, which gives important information for medical doctors. Typical numerical parameters such as scatterers number Nk, klayer average radial position Rk, its standard deviation , the DBC klayer mean /xk, and its standard deviation ak are given in Table 1.3. The typical IVUS parameters used in this simulation are given in
Figure 1.26: Radial scatterer distribution for the arterial structure: blood, intima, media, adventitia, and the transducer sheath.
Figure 1.26: Radial scatterer distribution for the arterial structure: blood, intima, media, adventitia, and the transducer sheath.
Blood lntima
Blood lntima
Figure 1.27: DBC distributions of simulated arterial structures: blood (a) and intima (b).
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).
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 ¡m, and intermediate frequency from 20 to 30 MHz gives axial resolution from 77 to 51 ¡m. In these cases, it is possible to visualize accumulations around 100 RBCs. High frequency from 30 to 50 MHz leads to 5131 ¡m 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.
Parameter 
Magnitude 
Ultrasound speed 
1540 m/sec 
Maximal penetration depth 
2E  2 m 
Transducer angular velocity 
1800 rpm 
Transducer emission radius 
3E  4 m 
Attenuation coefficient a 
0.8 dB/MHz cm 
Ultrasound frequency 
1050 MHz 
Beam scan number 
160400 
Video noise 
8 gray level 
Instrumental noise 
12.8 gray level 
Beta parameter 
P = 38.5 ad 
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).
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 crossvalidation 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
SSE Frequency
5S£ Attenuation coefficient
SSE Frequency
optimal freqt 
jency  
1 1.5 2 Frequency In Hz
1 1.5 2 Frequency In Hz
5S£ Attenuation coefficient
1 
1  
optim 
al atteru 
ata on coefficient  
Attenuation coefficient in [dBJMHr cm] Attenuation coefficient in [dBJMHr cm] Figure 1.30: The optimal ultrasound simulation frequency fo « 46 MHz (a) and the optimal attenuation coefficient (b) a « 0.8 dB/MHz cm are obtained by the cross validation method. is located in the interval 4050 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 CoefficientWe 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 a; 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 the case of ultrasound frequency and second to find structures of interest when the attenuation coefficient is known. 1.6.3.4 The Beam Number InfluenceFigure 1.31 shows the appearance of several simulated IVUS images when the original and intermediate beam numbers are changed. We obtained the best appearance when the original beam number was 80 and the secondary beam number was 240. In total, 320 beams were used by the simulation. We can see that the IVUS appearance in the tangential direction is significantly affected by the beam number change. The total number of beams for the standard IVUS equipment is normally between 240 and 360 beams [24]. 1.6.4 Real versus Simulated IVUSIn order to compare the real and simulated IVUS images, we have generated 20 synthetic images with morphological structures corresponding to the structures of a set of real images. We have used a real IVUS image with manually delimited lumen, intima, and adventitia to obtain the average radius location Rk for each arterial structure. We applied the optimal frequency of 46 MHz and attenuation coefficient of 0.8 dB/MHZ cm. Figure 1.32(a) shows an IVUS real image of right coronary artery, obtained with a 40 MHz Boston Sci. equipment. Figure 1.32(b) shows a simulated image obtained at the optimal ultrasound simulation frequency of 46 MHz. In the real image, we can observe a guide zone artifact (12 to 1 o'clock) due to the presence of guide; this artifact will not be simulated in this study. The horizontal ECG baseline appears as an image artifact on the bottom of the real image. The global appearance of each image region (lumen, intima, media, and adventitia) and its corresponding interface transitions (lumen/intima, intima/media, and media/adventitia) are visually well contrasted, compared to the real image. A good quantitative global measure for comparison Real image Simulated image Real image Simulated image 10G 150 Figure 1.32: Real (a) and simulated (b) IVUS images segmentation. ROIs are given as squares. Manual segmentation of the vessel is given in (a). 10G 150 Figure 1.32: Real (a) and simulated (b) IVUS images segmentation. ROIs are given as squares. Manual segmentation of the vessel is given in (a). A Basic Model for IVUS Image Simulation Real gray level average a 40
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