2.1.

Swept-Source OCT System

We utilized a home-built swept-source OCT system to image the soft tissue samples. The details of the system description are presented in our previous work.^21,22 Briefly, the system utilized a swept laser source (Santec, Inc., Komaki, Aichi, Japan) which has a central wavelength of 1310 nm with a bandwidth of $\sim 150\mathrm{nm}$. The scanning rate over full operating wavelength is 30 kHz, which determines the system temporal resolution of $\sim 33\mu \text{s}$. The OCT system is based on a Mach–Zehnder interferometer, where the light from the reference and the sample arms interference. The fringes are recorded through a balanced photodetector, and the signal is digitized by a high-speed analog to digital convertor (Alazar Tech, Inc., Quebec, Canada). Fast Fourier transform is applied to the $k$-equally spaced interference signals, and the resulted intensity A-lines are presented with dB unit. Depth-resolved two-dimensional (2-D) images of tissue samples can be real-time visualized from the computer. The system can provide an axial resolution of $\sim 15\mu \mathrm{m}$ and an imaging depth of $\sim 9\mathrm{mm}$ (both in air). The transverse resolution of the system is around 15 μm, and the sensitivity is up to 100 dB. During OCT imaging, the focal plane of scan lens was kept at the surface position of the tissue samples for minimizing the effect of the focal function on the computational analysis.

2.2.

Soft Tissue Samples

For the demonstration of our method, pilot experiments were performed on ex vivo human tissues with two types of samples: homogeneous pieces (both normal and abnormal) and tumor margin. For the former, fat, skeletal muscle, well-differentiated liposarcoma (WDLS), and leiomyosarcoma were used in the experiments, and total six pieces of samples from six patients were involved. WDLS is one type of liposarcoma that develops in the tissue of fat, and leiomyosarcoma is a cancer of smooth muscle. For the latter, we conducted our feasibility study on the tissue with the interface between collagen, a normal type of fibrous tissue, and cellular fibrous tumor. All tissue samples were taken from the surgical resection at the University of Texas M.D. Anderson Cancer Center (UTMADCC) Hospital. Sterile phosphate buffered saline was used to keep the samples until the experiments. OCT imaging was performed within 12 h after the surgical resection. The protocols of tissue processing were approved by the UTMDACC and the University of Houston Biosafety Committees. After the experiments, the tissue samples were fixed with formalin, and the hematoxylin and eosin (H&E) stained histology analysis was performed. A UTMADCC sarcoma pathologist conducted the diagnosis and the classification of the samples.

2.3.

Computational Method

The computational analysis is based on individual A-line (with dB unit in log scale) from OCT images. The whole procedure is presented in Fig. 1 with a typical A-line from the OCT imaging of human leiomyosarcoma. Due to the large refractive index change at the air–tissue interface, high reflections of light usually occur at the surface of tissue samples, which can result in relatively large intensity jumps, as shown in Fig. 1(a). To avoid the influence of this effect on the computations, we choose the start of the target region $\sim 40\mu \mathrm{m}$ below the tissue surface. As illustrated in Fig. 1(a), an axial region of $\sim 0.7\mathrm{mm}$ is selected for the A-line processing. The selection of this $\sim 0.7\mathrm{mm}$ depth region is based on our purpose of including as much depth information as possible from the OCT images for computation, and at the same time keeping the size of the depth region constant over the processing for all types of soft tissues. For each extracted A-line, a linear fit is applied to the signal, and the slope value is achieved as the first parameter to characterize the tissue, as shown in Fig. 1(b). Then, the slope information from the A-line is removed by performing a subtraction of the linear fitting function, and thus, resulting in an intensity signal with the mean of approximately zero, as shown in Fig. 1(c). The standard deviation of the intensity signal is calculated as the second parameter for tissue differentiation. A fast Fourier transform is then applied on this intensity signal, and the amplitude information of the spatial frequency spectrum is utilized for an exponential fit with the function of $y=A{e}^{-Bx}$, as shown in Fig. 1(d). The exponential decay coefficient $B$ is obtained as the third parameter for the characterization of tissue. The A-line slope, the standard deviation of slope-removed A-line, and the exponential decay coefficient of its spatial frequency spectrum are finally presented as the indicators of the soft tissue types and are combined together for advanced tissue diagnosis with 3-D information.

Fig. 1

Computational procedure illustrated with A-line from the optical coherence tomography (OCT) imaging of human leiomyosarcoma. (a) Original intensity A-line with the indication of the region for analysis; (b) indication of linear fit of A-line for the slope value; (c) slope-removed A-line for the standard deviation calculation; (d) spatial frequency spectrum presented with the amplitude information for exponential fit to quantify the exponential decay coefficient.

In soft tissues, the intensity of transmitted light, $I$, can be first-order approximated by the Beer–Lambert law, $I=I_0{e}^{-\mu z}$, where $\mu$ is the attenuation coefficient of light, $I_0$ is the incident light intensity, and $z$ is the depth of light traveling inside the tissue.²³ Thus, with the intensity values rescaled in dB unit, the measured slope value is determined by the optical attenuation property of the soft tissue for which a higher slope indicates a larger optical attenuation coefficient of the tissue sample. As OCT detects the backscattered light from the tissue, the mismatch of the refractive index inside the tissue provides the contrast of OCT depth-resolved images.²⁴ With the slope removed, the OCT A-line signal can be a representation of the variations of tissue refractive index (structure) along the depth. Hence, the amplitude and frequency of the intensity fluctuation, characterized by the standard deviation of the slope-removed A-line and the exponential decay coefficient of its spatial frequency spectrum, respectively, are dependent on the structural features of the soft tissues. Specifically, a greater variation of refractive index along the depth will result in a higher value of standard deviation; also, a larger exponential decay coefficient suggests that there exist more of low frequency components in the change of tissue refractive index. Therefore, the combination of these three parameters provides relatively thorough characteristics of the tissue samples.

3.1.

Homogeneous Fat and WDLS

Figure 2 shows the selected H&E histology images [Fig. 2(a) and 2(d)] for fat and WDLS with the corresponding depth-resolved 2-D OCT images [Fig. 2(b) and 2(e)] and typical A-lines [Fig. 2(c) and 2(f)], respectively. By comparing with the histology results, it can be seen that OCT images clearly reveal the morphology of the tissues of fat and WDLS. Specifically, the adipocytes can be easily distinguished with the cell shape presented in OCT images. An important feature can be seen from the OCT images that WDLS involves more nonadipocyte-structure areas compared with fat, which can be explained by the presence of thicker septa in WDLS.²⁵ From the typical A-lines, it is clear that over the 1.8 mm depth differences exist between the fat and WDLS in terms of the slope of the signal and the amplitude and frequency of the intensity fluctuation.

Fig. 2

Selected histology images (a) and (d) for fat and well-differentiated liposarcoma (WDLS), respectively; corresponding OCT images (b) and (e) for fat and WDLS, respectively; typical A-lines (c) and (f) from OCT images of fat and WDLS, respectively. The scale bars in (b) and (e) represent 0.5 mm.

The quantitative representations of these differences are presented in Fig. 3, which shows the statistical results of fat and WDLS with the parameters of the A-line slope, the standard deviation of the slope-removed A-line, and the exponential decay coefficient of its spatial frequency spectrum. Data points from 40,000 and 240,000 recording positions are involved for fat and WDLS, respectively. The slope values of A-line are quantified as $-0.0031\pm 0.0102\mathrm{dB}/\mu \mathrm{m}$ for fat and $-0.0192\pm 0.0100\mathrm{dB}/\mu \mathrm{m}$ for WDLS, as shown in Fig. 3(a). The higher absolute value of the slope from WDLS indicates the tissue of WDLS, compared with fat, attenuates more of the laser light with the same penetration of depth. From Fig. 3(b), the computation of the standard deviation shows $9.4\pm 1.4\mathrm{dB}$ for fat and $8.0\pm 1.2\mathrm{dB}$ for WDLS, which indicates that there exist larger variation of refractive index along the depth in the tissue of fat. We also quantified the exponential decay coefficient of $19.9\pm 4.8$ and $16.8\pm 5.8\mu \mathrm{m}$ for fat and WDLS, respectively, as shown in Fig. 3(c). This suggests that, relative to WDLS, in the tissue of fat more low frequency components exist in the depthwise change of refractive index. For each of the parameters, we performed two-sample unequal-variance Student’s $t$-test and the results indicate all these three parameters can be effective indicators for the differentiation of WDLS from fat.

Fig. 3

Box plots of the quantified results of (a) the A-line slope, (b) the standard deviation of the slope-removed A-line, and (c) the exponential decay coefficient of the spatial frequency spectrum of slope-removed A-line for fat and WDLS. The solid dots and the whiskers represent the mean and the standard deviation of the data, respectively. $N=\mathrm{40,000}$ and 240,000 for the measurements conducted on the tissues of fat and WDLS, respectively. The $P$ values are from the two-sample unequal-variance Student’s $t$-tests.

The combination of the three parameters provides the identification of WDLS and fat in a 3-D space of slope versus standard deviation versus exponential decay coefficient, as shown in Fig. 4. Figure 4(a) indicates the spatial regions occupied by these two types of tissues through the plots of the data points and the 95% confidence ellipsoids. The 2-D projections of the plots are shown in Fig. 4(b)–4(d). Based on the 3-D information, the tissues of WDLS and fat can be clearly distinguished.

Fig. 4

(a) Three-dimensional (3-D) plot of the data points and the confidence ellipsoids (95%) for fat and WDLS in the spatial region composited by the parameters of the A-line slope, the standard deviation of the slope-removed A-line, and the exponential decay coefficient of its spatial frequency spectrum. Two-dimensional (2-D) projections are presented in the spatial plane of (b) exponential decay coefficient versus slope, (c) standard deviation versus slope, and (d) exponential decay coefficient versus standard deviation. $N=\mathrm{40,000}$ and 240,000 for the data points involved for fat and WDLS, respectively.

3.2.

Homogeneous Skeletal Muscle and Leiomyosarcoma

For the tissues of skeletal muscle and leiomyosarcoma, Fig. 5 shows the histology images [Fig. 5(a) and 5(d)], the corresponding OCT images [Fig. 5(b) and 5(e)], and typical A-lines [Fig. 5(c) and 5(f)], respectively. Based on the structural OCT images, the skeletal muscle and the leiomyosarcoma appear similar, because at the scale-level of the system spatial resolution the cells inside both types of the tissues are relatively homogeneous. However, from the intensity A-lines, differences can be clearly observed in the amplitude and frequency of the fluctuation of intensity as well as in the slope of the A-lines.

Fig. 5

Selected histology images (a) and (d) for skeletal muscle and leiomyosarcoma, respectively; corresponding OCT images (b) and (e) for skeletal muscle and leiomyosarcoma, respectively; typical A-lines (c) and (f) from OCT images of skeletal muscle and leiomyosarcoma, respectively. The scale bars in (b) and (e) represent 0.5 mm.

Similar to Fig. 3, for quantifying the differences between skeletal muscle and leiomyosarcoma, we present the statistical results of the A-line slope, the standard deviation of the slope-removed A-line, and the exponential decay coefficient of its spatial frequency spectrum in Fig. 6. Our computations involve a total of 40,000 and 80,000 data points from different measurement positions on the tissues of skeletal muscle and leiomyosarcoma, respectively. From Fig. 6(a), the skeletal muscle has a slope value of $-0.0285\pm 0.0089\mathrm{dB}/\mu \mathrm{m}$, while the slope value for leiomyosarcoma is $-0.0351\pm 0.0073\mathrm{dB}/\mu \mathrm{m}$. This difference indicates, with respect to the wavelength range from the laser source, the tissue of leiomyosarcoma has a relatively higher optical attenuation coefficient compared with skeletal muscle. In Fig. 6(b), our computations show a larger standard deviation of $6.2\pm 0.8\mathrm{dB}$ for skeletal muscle than $5.7\pm 0.5\mathrm{dB}$ for leiomyosarcoma, which suggests the variation of refractive index along the depth appears to be relatively lower in the tissue of leiomyosarcoma. Also, the exponential decay coefficients are quantified as $10.8\pm 3.5\mu \mathrm{m}$ for skeletal muscle and $4.9\pm 1.9\mu \mathrm{m}$ for leiomyosarcoma, as shown in Fig. 6(c). Compared with skeletal muscle, the lower value of exponential decay coefficient indicates that for the tissue of leiomyosarcoma, there are fewer of low frequency components existing in the refractive index change over depth. Similar to the study with fat and WDLS, we conducted the two-sample unequal-variance Student’s $t$-test for all three parameters, and the differences between skeletal muscle and leiomyosarcoma have been found to be statistically significant.

Fig. 6

Box plots of the quantified results of (a) the A-line slope, (b) the standard deviation of the slope-removed A-line, and (c) the exponential decay coefficient of the spatial frequency spectrum of slope-removed A-line for skeletal muscle and leiomyosarcoma. The solid dots and the whiskers represent the mean and the standard deviation of the data, respectively. $N=\mathrm{40,000}$ and 80,000 for the measurements conducted on the tissues of skeletal muscle and leiomyosarcoma, respectively. The $P$ values are from the two-sample unequal-variance Student’s $t$-tests.

The 3-D plots of the data points and the 95% confidence ellipsoids are presented in Fig. 7(a) indicating the relative positions of skeletal muscle and leiomyosarcoma in the spatial region composited by the three parameters. Figure 7(b)–7(d) show the corresponding 2-D projections for both the types of tissues. It can be clearly seen that the differentiation of leiomyosarcoma from the tissue of skeletal muscle can be achieved based on our 3-D computational method.

Fig. 7

(a) 3-D plot of the data points and the confidence ellipsoids (95%) for skeletal muscle and leiomyosarcoma in the spatial region composited by the parameters of the A-line slope, the standard deviation of the slope-removed A-line, and the exponential decay coefficient of its spatial frequency spectrum. 2-D projections are presented in the spatial plane of (b) exponential decay coefficient versus slope, (c) standard deviation versus slope, and (d) exponential decay coefficient versus standard deviation. $N=\mathrm{40,000}$ and 80,000 for the data points involved for skeletal muscle and leiomyosarcoma, respectively.

3.3.

Cellular Fibrous Tumor Margin with Collagen

Our method is also demonstrated on the soft tissue sample with tumor margin. The histology result and the corresponding OCT image from the same location of the tissue are shown in Fig. 8(a) and 8(b), respectively. The vertical margin between the tissues of collagen and cellular fibrous tumor can be clearly visualized from the histology image. The 3-D computational method was performed for every individual A-line from the OCT image, and the quantified values are color-coded and plotted below the OCT image at the corresponding A-line positions. The color of red, green, and yellow are utilized to represent the parameters of the A-line slope, the standard deviation of the slope-removed A-line, and the exponential decay coefficient of its spatial frequency spectrum, respectively. For all of them, darker regions represent larger values, while brighter regions indicate smaller values. Figure 8(c) is the combination of the three parameters with the overlap of three colors. It can be seen that the part of cellular fibrous tumor is relevant to the brighter regions of all three colors, suggesting the tissue of cellular fibrous tumor has higher attenuation of the light from the system laser, smaller variation of the refractive index and fewer of low frequency components for the refractive index change inside the tissue. The estimated position of the vertical tumor margin based on the 3-D computational method is indicated with blue arrows in Fig. 8. The good agreement with the histology results demonstrates the feasibility of our method in the accurate delineation of the vertical margin between cellular fibrous tumors and the tissue of collagen.

Fig. 8

Vertical tumor margin between collagen and cellular fibrous tumor presented with (a) histology image, (b) OCT image, and (c) color-coded plot combining the parameters of the A-line slope, the standard deviation of the slope-removed A-line, and the exponential decay coefficient of its spatial frequency spectrum. The arrows point at the estimated position of the vertical tumor margin. The scale bars represent 0.5 mm.