2.1.

Depth-Resolved Attenuation

With an assumption that the backscattered light is a fixed fraction to the attenuated light ${\mu }_b(d)=\alpha {\mu }_t(d)$ the integration from $d$ to infinite of Eq. (1) will be

The attenuation can be estimated with the OCT image intensities as

2.2.

Backscatter Term Estimation

Suppose an A-line from a homogeneous region starts at depth $d_1$ and ends at depth $d_2$. Within this region, both the attenuation and the backscatter coefficients at each depth $d\in (d_1,d_2)$ are the same ${\mu }_t(d)={\tilde{\mu }}_t$ and ${\mu }_b(d)={\tilde{\mu }}_b$, thus Eq. (1) can be simplified as

Within the homogeneous region, ${\tilde{\mu }}_t$ and ${\tilde{\mu }}_b$ can be estimated as the slope and the offset of the linear function fitted with $\ln [I_b(d)/\beta L^{\prime }]$, as it has been proposed that in the work of Schmitt et al.¹⁶ Noting that the $L^{\prime }$ is a constant relative to $d$, linear fitting $\ln [I_b(d)]$ gives the same estimation of the attenuation coefficient. However, the estimation of $L^{\prime }$ is necessary for the estimation of backscatter coefficient.

With the DR model, we consider $d_1$ and $d_2$ are the start and the end of a pixel, then $e^{-2·r·{\tilde{\mu }}_t}$ approximates to 1 since $r$ is then very small. Dividing Eq. (5) by a factor of $e^{-2{\int }_0^{d_1}{\mu }_t(u)\mathrm{d}u}$ and taking the logarithm, we get a similar intersection to be our backscatter term as

2.3.

DR-CF Cut-Off Algorithm

One of the main concerns regarding the pixel-wise DR algorithm is the assumption that the integral of intensity should be taken to infinity. However, infinity in practice is usually substituted with a large value, the maximum depth $D$ of the signal in the case of OCT images. This causes little effect on the estimated attenuation of the superficial tissue region, where the signal is much stronger than the noise. However, as it approaches the end of an A-line, the estimated attenuation coefficient with the noise-dominant signal will be exaggerated and thus is unreliable.

In order to avoid this, we applied the DR-CF algorithm to determine a cut-off depth. Noting that

The second term is a constant, the logarithm of the integral intensities follows a linear function with respect to the depth within this region, and the attenuation can be calculated from the slope. With the DR-CF algorithm, the left term is always decreasing, thus it guarantees that the estimated values are positive and the high noise tolerance of the CF-approach is maintained. Since the deeper signals are influenced strongly by noise, it is difficult to perceive the local variations, but the general decreasing trend can still be estimated with the DR-CF algorithm.

The cut-off algorithm is described in Algorithm 1. The linear fitting is implemented in MATLAB (R2016a, The MathWorks, Inc., Natick, Massachusetts) with the least square approximation. In Algorithm 1 step 2, the size of the sliding window size is chosen to be 21 pixels for each A-line. After fitting, an error image $I_{\mathrm{err}}$ is calculated, and then a threshold of the squared error $5\times {10}^5$ was experimentally chosen to create a binary image $I_{\mathrm{bw}}$ in step 3. In order to determine a continuous border with the regional maximum got in step 3, a morphological closing of $I_{\mathrm{bw}}$ is used in step 4, where the octagon operator is used with a radius of 6 pixels.

Algorithm 1

Determine the DR-CF cut off border.

3.1.

Data Description

Coronary segments were dissected from the cadaver hearts and imaged ex vivo by optical frequency domain imaging (OFDI). The samples were pinned on a rubber sheet and immersed in a water bath with 0.9% saline solution. A 0.014-in. guidewire was introduced into the vessel followed by an OFDI catheter (LUNAWAVE, Terumo). Sequential images were acquired at a pullback rate of $20\mathrm{mm}/\mathrm{s}$ ($158\text{frames}/\mathrm{s}$, 512 A-lines per frame). The source light has a center wavelength of 1300 nm and a bandwidth of 124 nm. The depth resolution for each A-line used in this work is $5.4\mu \mathrm{m}\mathrm{per}\text{pixel}$, which has been calculated with the refractive index stored in the raw data as 1.447.

3.1.2.

Matching of IVOCT and histology, and differentiation and delineation of specific tissue type on histology and IVOCT

In each pathological cross section, two pathologists (CN and ST) identified the following tissue categories in histology: lipid, calcification, mixed calcified plaque, necrotic core, and macrophage. The remaining tissue was identified as fibrous plaque. The identified tissues in histology were independently delineated by the pathologists such that each region of interest (ROIs) included only one type of tissue [Figs. 1(a)–1(d)].

Fig. 1

(a)–(d) The histological cross sections and (a’)–(d’) the corresponding IVOCT cross sections. Star (*) marks the guide wire. The attenuation coefficients and the backscatter term are labeled as (a)–(d).att and (a)–(d).bcs, respectively. Noisy region behind the determined cut-off border is marked with dark blue overlay in attenuation and backscatter cross section. Plaques of interest are labeled in pathological cross sections, which have been aligned with other-related IVOCT images.

The histological cross section and the corresponding IVOCT cross section were matched using the lumen shape and tissue appearance in both images by two cardiologists (Y.S. and Y.O.). IVOCT cross sections with insufficient image quality and significant artifacts such as tangential artifacts were not used for the analysis. Based on the contours delineated by the pathologists in histology, the two cardiologists delineated the same tissue in matched IVOCT images in QCU-CMS (Quantitative Coronary Ultrasound-Clinical Measurement Systems, LKEB, Leiden University Medical Center, Leiden, The Netherlands) [Fig. 1(a’)–1(d’)]. When the border of the tissue could clearly be detected on IVOCT, the delineation followed the borderlines. When the border could not be clearly perceived, the contours in histological images were superimposed on the IVOCT images in order to yield a high reproducibility. If there were more than two layers of different ROIs in one cross section, only the most adluminal ROI was employed for the analysis considering the light property.

The two pathologists (G.N. and S.T.) were blinded to the IVOCT delineation and IVOCT light property analysis. At the stage of IVOCT delineation, to enable accurate colocalization of the histology with IVOCT images, two cardiologists (Y.S. and Y.O.) were unblinded to the histological identification. However, these cardiologists were blind to the following IVOCT light property analysis. The IVOCT light property analysis was performed independently from the either histological identification or the IVOCT delineation process.

3.2.

Implementation

The experimental flow of analyzing the IVOCT values was designed as it is shown in Fig. 2.

Fig. 2

The work flow for the experiment.

3.3.

Statistical Analysis

The data were processed and analyzed with MATLAB. For each delineated region, the distribution of intensities, attenuation, and the backscatter term are analyzed. The mean, standard deviation (std), median, maximum (max), 95th percentile (95th per.), minimum (min), skewness, and kurtosis values were calculated within each delineated region. Values between different tissue types were compared with the two-sample $t$-test. Both three-dimensional (3-D) scatter plots of the intensity, attenuation coefficient, and backscatter term and their principal component analysis (PCA) projected two-dimensional (2-D) scatter plot are generated.

5.1.

Attenuation Coefficient

The light transmission model of OCT signals was used as it has been introduced in the work of Vermeer et al. The attenuating term is modeled as $e^{-2{\mu }_{t}r}$, while it has been modeled as $e^{-m_{t}r}$ in some CF approaches in the work of van Soest et al. The direct result of using this factor 2 in the exponential term is that the estimated attenuation coefficients are expected to be smaller than those previously reported in some of the studies. This difference affects only the absolute values rather than the comparative trend; therefore, we focus more on the comparative trend of the estimated values when comparing to the literature.

The attenuation coefficients of neointima have been reported as $0.35\pm 1.38{\mathrm{mm}}^{-1}$ without lipid-laden and $2.00\pm 1.16{\mathrm{mm}}^{-1}$ with lipid-laden in the work of Yonetsu et al.²⁹ For the in-stent restenosis lesions of drug-eluting stents (DES) and bare-metal stents (BMS), the attenuation coefficients have been estimated as $1.69\pm 0.84$ and $1.74\pm 0.81{\mathrm{mm}}^{-1}$, respectively, in the study of Nagoshi et al.³⁰ These values have been estimated with the LightLab software. Despite the estimation algorithm being unknown, these reported values are within the similar range of estimated attenuation coefficients of the fibrous tissue (mean: $1.75\pm 0.48{\mathrm{mm}}^{-1}$, median: $1.67\pm 0.47{\mathrm{mm}}^{-1}$). Taking the factor 2 into consideration, the estimated attenuation coefficient of the fibrous tissue (mean: $3.52\pm 1.92{\mathrm{mm}}^{-1}$, median: $3.36\pm 1.88{\mathrm{mm}}^{-1}$) is comparable to that reported as 2 to $5{\mathrm{mm}}^{-1}$ in the work of van Soest et al.⁹ and relatively lower than that reported as $6.4\pm 1.2{\mathrm{mm}}^{-1}$ in the work of Xu et al.⁸

For regions with macrophages infiltration, the range reported by van Soest et al. is $12{\mathrm{mm}}^{-1}$, and even can be as high as $15{\mathrm{mm}}^{-1}$ in a given example, which tends to be much higher than the other tissue types. Although we found attenuation coefficients of regions with calcification and macrophages much lower than what has been reported in these two studies, the comparative relationship of the values is the same, where the value of macrophages (mean: $3.41\pm 0.38{\mathrm{mm}}^{-1}$, median: $3.22\pm 0.45{\mathrm{mm}}^{-1}$) is the highest, and the value of the calcification (mean: $0.87\pm 0.24{\mathrm{mm}}^{-1}$, median: $0.68\pm 0.16{\mathrm{mm}}^{-1}$) is lower than that of fibrous tissue (mean: $1.75\pm 0.48$, median: $1.67\pm 0.47$).

For the lipid-rich regions, we found a mean attenuation value of $2.60\pm 0.13{\mathrm{mm}}^{-1}$ and median $2.45\pm 0.12{\mathrm{mm}}^{-1}$. This is lower than what has been reported in the literature; $13.7\pm 4.5$⁸ and $>8.5$³¹, but higher than fibrotic tissue which fits in the reported trends. A reason for this is that the cardiologists did draw the similar shape in IVOCT as was seen in the pathological slides (Fig. 1). Due to the high attenuation, the back border of the lipidic region is not seen in IVOCT and the deeper regions are dominated by noise. To avoid the inclusion of noise in the statistical parameters, we introduced the cut-off algorithm to remove the noisy regions. In order to compare relatively high values within the superficial limited regions of the lipid plaque, a higher percentile (95th) was considered for comparison as well. It should be noted that the 95th percentile of the estimated values within the lipid-rich region can be as high as $4.73\pm 0.28{\mathrm{mm}}^{-1}$ and that of macrophages can be $6.05\pm 0.85{\mathrm{mm}}^{-1}$, which is much higher than that for other tissue types. The comparative relationship in the mean, median, and 95th percentile values of the estimated attenuation coefficient is Cal < Fib < Lip < Mac.

With respect to the necrotic tissue cores, since the plaques with macrophages and lipid were labeled separately, the necrotic cores chosen in this work are expected to have fewer macrophages infiltrations. This is shown in the estimated attenuation that the necrotic core (mean $1.89\pm 0.54$, median $1.72\pm 0.44$) is lower than lipid (mean $2.60\pm 0.13$, median $2.45\pm 0.12$) and macrophages (mean $3.41\pm 0.38$, median $3.22\pm 0.45$), and is just above the fibrotic tissue (mean $1.75\pm 0.48$, median $1.67\pm 0.47$). In the work of van Soest,⁹ the necrotic core ($\ge 10{\mathrm{mm}}^{-1}$) has been “read” as lipid plaque when compared to the study of Xu et al. We carefully inspected the regions in the IVOCT images, which were annotated as necrotic core by pathologists, but could not identify bright regions or spots as were shown in the work of van Soest thus resulting in a lower mean and median attenuation and backscatter. Therefore, the discrepancy compared to the work of van Soest is caused by a difference in the data.

It should be noted that two clusters of values are observed in the median and mean values of the calcified plaque in the PCA projected 2-D plot (Fig. 3 and 4). This can be caused by the large variation in the median/mean values of the intensities (mean: $142.49\pm 15.05$, median: $143.06\pm 15.11$) and the backscatter term (mean: $5.24\pm 0.42$, median: $5.21\pm 0.41$). However, it is worth noting that the distribution of the median/mean values in the attenuation is relatively condensed (mean: $0.87\pm 0.24$, median: $0.68\pm 0.16$), and the range of values is significantly different from any other tissue type.

5.2.

Backscatter Term

As it has been stated, the DR attenuation was estimated with the precondition that the attenuation and the backscatter coefficients are linearly related to each other. Rather than estimating the backscatter coefficient, the proposed calculation of the backscatter term in our work is based on the principle that the “offset” of the linear fitting is the backscatter-related term, the exponential of which has been shown to be linearly related to the actual backscatter coefficient in the work of Schmitt et al.¹⁶ Applying this principle, the DR model was extended to estimate this term pixel wise. Our analysis of the optical model shows that this term is related to both the backscatter coefficient and the initial power of the incident light. Results show that this term provides different comparative graphs and additional information for tissue differentiation. For example, fibrotic tissue was not significantly different from macrophages for the mean intensities, but they are statistically different in mean values of the estimated backscatter term (Fig. 4).

To the best of our knowledge, only three studies have reported the backscatter coefficient in the literature of tissue analysis within vessel walls.^8,29,30 The estimated values with the LightLab software have been reported for neointima as $6.19\pm 0.81$ without lipid-laden and $6.56\pm 0.60$ with lipid-laden,²⁹ and have been reported as $6.92\pm 0.42$ and $7.14\pm 0.41$ for the in-stent restenosis lesions of DES and BMS, respectively.³⁰ This range is comparable to that of our estimated values of the fibrous region (mean: $6.22\pm 0.32{\mathrm{mm}}^{-1}$, median: $6.24\pm 0.34{\mathrm{mm}}^{-1}$).

The backscatter coefficient has been measured by Xu et al.⁸ as $18.6\pm 6.4{\mathrm{mm}}^{-1}$ for fibrous tissue, $28.1\pm 8.9{\mathrm{mm}}^{-1}$ for lipid-rich tissue, and $4.9\pm 1.5{\mathrm{mm}}^{-1}$ for the calcified plaque. Although the absolute values are not comparable to our values due to different experimental settings and a fundamentally different approach for the estimation as mentioned before, we still observe similar patterns. The fibrous plaque has been reported to have “high backscatter and low attenuation,” while our results do show that backscatter for fibrotic tissue is relatively high with relatively low attenuation. When comparing fibrous regions to macrophage regions, it is worth noting that the mean, median, and the 95th percentile values for the former are lower, suggesting a more compact distribution. This may relate to the speckle pattern caused by the inhomogeneous distribution of the foam cells. The estimated value in calcified regions (mean: $5.24\pm 0.42$, median: $5.21\pm 0.41$) is significantly lower than that in fibrous regions (mean: $6.22\pm 0.32$, median: $6.24\pm 0.34$). The lipid is not significantly different from fibrous regions in the mean and median of the estimated backscatter term, but the prior is higher than the latter in the 95th percentile values (95th percentile: $7.06\pm 0.08$ versus $6.78\pm 0.30$).

5.3.

IVOCT Intensity

Most studies in the literature focused on the comparisons of only the attenuation coefficient,^{9,20–24,28,32} or the IVOCT intensities,^6,7 while a few studies combined the attenuation and the backscatter coefficients.^8,29,30 The two-sample $t$-test results suggest that the IVOCT image intensity does additionally contribute to the differentiation of the tissue types. For example, for the fibrotic versus necrotic tissue, the mean values of neither the attenuation nor the backscatter term are significantly different (Fig. 7), while the mean values of the intensities are significantly different.

On the other hand, it has been found in our previous work that the IVOCT intensities can be affected by the eccentric position of the catheter when light travels a long distance through the flush medium or enters the arterial wall with a large incident angle.⁴³ In this analysis, this bias on intensities has been minimized by using only the lesions with front edges that are almost perpendicular to the incident light from the catheter. However, it is usually difficult to avoid this bias in clinical data. It has been shown that the intensities can be normalized with the summation of the total amount of incident light, yet additional statistical analysis on healthy tissues is required. From the principle equations for estimating attenuation coefficient and backscatter term, one may note that these two optical parameters are normalized with the summation of the total amount of intensities, and thus are expected to be less affected by this particular bias. Therefore, practical analysis with in vivo data is suggested to be focused more on these two estimated optical properties.

5.4.

Limitations

The catheter-related terms were not considered in this work. As far as we know, even in the most recently published studies in the literature of the experimental optical measurements, the catheter-related term was reported to be calibrated either with OCT measurements in a weakly scattering media,¹⁹ or a particular phantom.⁴⁴ Since we had access only to the image data and not the used catheter, the catheter specific calibration could not be done. However, as it has been discussed in the work of Vermeer et al., the maximum bias caused by the confocal function to the estimated DR attenuation is $\pm 1/(4z_R)$ at depth $z=z_0\pm 2z_R$ where $z_0$ is the focus position and the $z_R$ is the Rayleigh length. Calculating with $z_R=2\mathrm{mm}$ used in the work of Ughi et al.,³² the maximum bias is expected to be around $\pm 0.125{\mathrm{mm}}^{-1}$, which is relatively small compared to the scale for the estimated DR attenuation coefficient with IVOCT images.

Another potential issue could be that different tissue types have different refractive indices. This is not taken into account during the reconstruction process. This could lead to a difference in image resolution in different tissue types, while a fixed resolution is used. Ideally, different refractive indices should be applied for different types of tissues during the reconstruction. However, it requires prior knowledge of tissue compositions, which is almost impossible in practice.

When the resolution term is modeled as a function related to depth and tissue type, the impact on the accuracy of estimated optical coefficients can vary. Equation (4) will become

For the sake of real-time computing, a median filter is applied rather than a more complex speckle noise removal filter such as the iwhTV denoising published recently³⁴ or the entropy filter used by Jimenez et al.⁴⁵ A fixed window size has been selected as around $60\mu \mathrm{m}$. As it was discussed, the median filter blurs only the attenuation at the border of different tissues, and it affects the local statistical numbers minimally.

The statistical numbers for different tissue types have been calculated within the manually delineated regions. Other tissue types such as loose connective tissue, proteoglycans, calcified nodules, and smooth muscle cell-rich fibrous tissue were not assessed in this study because of the limited study sample size and the absence of specific staining.⁴² Artifacts would inevitably affect the light property analysis. These points can be limitations in the future for tissue classification and subjects for a further investigation.

5.5.

Future Directions

Generating a distribution map indicating the probability of each type of plaque is one of the interesting directions in future work. Toward this goal as it has been proposed in the literature,²⁶ the following works need to be done. Enough features should be extracted, including the first- and second-order statistical features²⁷ of intensities, attenuation coefficient, backscatter term, the power spectrum parameters, etc. Feature selection should be used to remove strongly linear-related features, which can result in a noninvertible covariance matrix. Then, a likelihood density map can be generated for each type of tissue. For a fair comparison between tissue types to determine the most likely tissue type for each pixel, the prior probabilities are necessary to be obtained in advance. Usually, manually reviewing a pullback series is time-consuming and points of interest easily cannot be overlooked due to the huge amount of data (up to over 1000 images). Integrated with the automated lumen detection in QCU-CMS,⁴⁶ carpet views as shown in Figs. 13 and 14 can be generated robust and fast without the need of predefining the segmentation of the lumen tissue. This overview of the examined coronary vessel wall can potentially improve the abnormality determination and further help with the treatment decision^47,48 for coronary diseases, e.g., for stent placement and risk assessment of the patient in an automated way which is lacking in the current clinical practice.