**4. Discussion**

The clinical detection and segmentation of the atherosclerotic plaque is still a challenging step for an early diagnosis. Machine learning techniques are mainly focused either on the segmentation of the lumen and outer contours [21] or on the detection of calcifications [16,17] or vulnerable FCT [15]. However, it is difficult to find a quantitative study of FCT or the lipid area. Other techniques based on IVUS allow to estimate the 2D strain field in the arterial wall [27,30]. From the strain map, with iterative optimization tools, it is possible to estimate the mechanical properties and the segmentation of the plaque [28,29,31]. However, these cases had high computational cost and depended on the inclusions evaluated. The most difficult issue was to obtain an accurate segmentation of the plaque that could provide good estimations of the FCT. In this paper, we have presented the theoretical basis to segmen<sup>t</sup> the tissues of the atherosclerotic plaque from the representation of different strain variables without any iteration or the need for a large database to train

the methodology. The segmentation procedure was based on the Watershed and Gradient Vector Flow algorithms that extract the tissues. In this article, we focused on the lipid core segmentation due to its role in plaque vulnerability [5]. The accuracy of the results depends on the represented SGVs. This approach allowed us to obtain measurements of the lipid area and FCT and it achieved promising results with many different SGV combinations. The methodology was developed and validated with computational models designed from idealized and real IVUS geometries. The aim was to check if the strain map method was able to segmen<sup>t</sup> the lipid and also to know which are the best SGVs to achieve it. Furthermore, the process was performed with different morphological and IVUS technical variations to prove the versatility of the proposed method.

### *4.1. Segmentation Analysis*

### 4.1.1. Idealized Geometries

Using idealized geometries, the results show that as the FCT was smaller, there were less SGVs available to obtain a proper segmentation. The box-plot of Figure 6 shows that the variability of SI values decreases with larger thicknesses, while the segmentation performance increases. The explanation is that the amount of data available on the fibrous cap is lower and the SGVs in low thicknesses; it marked the lipid contour close to the lumen and it was more difficult for the segmentation process to track the lipid. Therefore, the measure of the FCT presents higher errors. Consequently, the precision of the IVUS technology will delimit the amount of strain information in the fibrous cap and thus the segmentation performance. After analyzing the 105 possible SGV combinations in each geometry with clean FE strains, the median SI value was always above 93% in all cases. That highlights the strong segmentation capacity of the proposed methodology. Previous studies also showed a decrease in the FCT segmentation at lower thicknesses, increasing the relative error of the segmented FCT [28,31]. However, this proposed methodology opened the possibility of using a large number of SGVs for segmentation. Some combinations of SGV, such as *dW*, |*<sup>ε</sup>vMises*| + |*<sup>ε</sup>r<sup>θ</sup>* | or *<sup>ε</sup>yy* + |*<sup>ε</sup>rr*|, had errors close to zero and with negligible variation between thicknesses. After adding a 20 dB SNR to the FE strains, the SGVs were not as smooth as in the previous cases; however, the median SI of each group decreased by most 3%, but all of them were above 90%. Hence, the segmentation method proved that there were large amounts of SGVs that allowed to extract the lipid core regardless of the FCT or the noise addition. Furthermore, the areas of the lumen and the complete plaque were automatically segmented with the proposed method. This provided results similar to those obtained with machine learning [21,22] but without the need to train a neural network.

### 4.1.2. IVUS Geometries

The IVUS geometries allowed testing the segmentation procedure on real human atherosclerotic coronary plaque geometries with distinct lipid core areas and FCT. The results showed that the W-GVF process relied not only on the fibrous cap thickness, but also on the lipid area and stenosis degree, showing a strong dependency on the real IVUS plaques. The segmentation performance varied greatly in each geometry due to their differences. In all cases the median of the SI value was above 88% (with or without noise). The noise addition slightly reduced the segmentation except for the first IVUS plaque, where noisy strains improved the median SI value by 1.87%. The noise addition also increases the variability of the performance. The third IVUS plaque had a calcification that was segmented using the W-GVF technique with a relative error smaller than a 5%. Nevertheless, the study showed that the segmentation procedure was able to track lipids with different areas and morphologies. Since these geometries were analyzed in other studies [28,32], it was possible to compare the segmentation results with those of previous studies. Previous work reached a relative FCT error of between 1.4 and 15.5% depending on the geometry [28]. Other methodologies obtained a mean error above 16% by measuring the FCT on other real geometries [31,47]. In this work, the FCT measure depended on the

chosen SGV. For the SGVs analyzed in Table 2, the mean relative error was 3.11% in the IVUS geometries.

### *4.2. SGV Candidates*

Different studies rate the segmentation performance with a qualitative index, such as thin vs. stable FCT [11,15,18], or by detecting the calcified plaques [16,17]. Those studies that used quantitative values only considered the error of the segmented FCT and lipid area [28,31,47]. Our SI included values to consider the relative error of the FCT, the value of the segmented lipid and its shape, which facilitates the comparison of segmentations between geometries. Studies that used a strain variable for segmenting only used a single strain variable (commonly the modified Sumi's transformation (*dWSimpli fied*) [28,46,47] or von Mises strains [31]). On the contrary, this methodology made it possible to use 105 different strain variables (single SGVs or combinations of SGVs).

The combination of idealized and real IVUS results showed that the segmentation results depended mainly on the FCT and the lipid core area. Nevertheless, there were some variables with a high SI by itself regardless of the geometry case. That was the case of SGVs such as *dW*, |*<sup>ε</sup>min*| or |*<sup>ε</sup>rr*|, which obtained an overall SI value of more than 90% with or without noise. By the combination of different SGV, some variables with low accuracy increased the results. That was the case of |*<sup>ε</sup>r<sup>θ</sup>* |, which had a mean SI value of 67.24% and in combination with |*<sup>ε</sup>vMises*| was the best pair, achieving a mean SI of 97.1% (95.22% with noise). SGV combinations reached higher precision than single SGVs. Some examples were *<sup>ε</sup>yy* <sup>+</sup>|*<sup>ε</sup>rr*| or |*<sup>ε</sup>min*|+|*<sup>ε</sup>Tresca*| with SI mean values of 96.88–95.68% and 96.69–93.67%, respectively (with clean strains–with 20 dB of SNR, repsectively). All of the SGV combinations presented in Table 2 allowed for a very precise segmentation of the lipid in all scenarios with different SGV options.

On the other hand, after analyzing the elastic gradient of the material (*dW*), all *dW* SGVs had a similar representation; however, the *dWsimpli fied* proposed by Le Floc'h et al. [28] had more trouble marking the shoulder of the lipid core and obtained worse segmentation results than *dW* and |*dW*|. The variable *dW* marked the whole lipid contour, and alone proved to be the best SGV for the lipid segmentation. Its absolute value, |*dW*|, was computed in order to obtain better results in combination with the others SGVs; however, it showed similar SI values to *dW* and it was the second-best single SGV option.

### *4.3. Sensitivity analysis*

The best single SGVs and SGV combinations were analyzed in a sensitivity analysis to study the influence of different variables (plaque- and IVUS-related variables). We concluded that the incompressibility of the materials did not affect the segmentation performance in the five selected SGVs. By changing the material behavior of the fibrotic tissue, the SI values remained above 92%, except in one case for *dW*. This parameter was related to the different stiffness between tissues, and it would fail if the lipid and fibrotic tissue had similar stiffness. The addition of inclusions could affect the lipid segmentation if they were placed close to the lipid contour. Nonetheless, the methodology appeared to obtain similar results. Principal strains are widely used because of their non-dependence on the coordinate system [45]; however, the catheter position seemed to have no influence on the process, since the worst SI value obtained was 93.23%. Finally, the pressure and pressure increments did not affect the method due to the fact that the tool is based on gradients of the strains, and they had a similar representation regardless of the modification of pressures. Overall, the results sugges<sup>t</sup> that the proposed methodology had no dependency on the analyzed cases, showing a strong robustness.

### *4.4. Relevance for Clinical Applications*

The new developed technology is an intuitive segmentation tool that could provide morphological information on the atherosclerotic plaque. It could help to reduce segmentation human errors and it could assist clinicians with a new accurate diagnosis support.

From IVUS images and the use of a strain estimator, we can use the representation of different moduli of the gradient of variables to detect the lipid or inclusions contours in a fast way. After that, with the W-GVF segmentation procedure it is possible to extract the lipid core or other tissues and take measurements, which are directly involved with plaque vulnerability. The results show that the performance of certain SGV combinations depended on plaque morphology; however, the SGV combination between |*<sup>ε</sup>min*| and |*<sup>ε</sup>vMises*| presented good segmentation performances for the lipid core, regardless of the plaque geometry. Additionally, other combinations showed in Table 2 appear to be accurate enough for good clinical diagnosis. Single SGVs such as |*<sup>ε</sup>rr*| or *dW* provided accurate segmentations. In addition, *εrr* is the strain variable that can be extracted from IVUS with the highest accuracy, so it will be one of the main candidates for clinical application.

The highlights of this work are presented in the following list in order to summarize the results of the research.

