Lymphography method based on time-autocorrelated optical coherence tomography

Yi Lian; Yi Lian; Tingfeng Li; Tingfeng Li; Nanshou Wu; Jiayi Wu; Zhilie Tang; Zhilie Tang

doi:10.1364/BOE.470390

1. Introduction

The lymphatic vasculature is an important part of the human circulatory and immune system, where lymph fluid collects excess tissue fluid, transports lymphocytes and other white blood cells, and clears cellular debris. Several physiological and pathological processes can alter these lymphatic vessels, such as skin inflammation [1], skin wound healing, and lymphedema after cancer surgery [2]. Current lymphangiographic techniques that can observe these physiological and pathological processes include blue dye staining [3], fluorescence optical imaging [4], computed tomography (CT) [5], magnetic resonance imaging (MRI) [6], ultrasound imaging [7], photoacoustic imaging (PAI) [8], positron emission tomography (PET) [9], multi-modal imaging [10] and so on. These methods usually require the injection of exogenous contrast agents to label lymphatic vessels [11], which increases cost, safety concerns, and diagnostic time.

Related study has found that water accounts for 94% of the lymphatic fluid, and only 6% is solid with the scattering effect on light [12]. Lymph is largely transparent to light in the visible and near-infrared spectra [13], so the OCT signal of lymphatic vessels is usually comparable to the background noise level. Researchers have used OCT imaging systems to extract lymphatic vessels based on this feature of the lymph signal. A Hessian filter method has been adopted to segment lymphatic vessels in OCT structural images [14]. The contrast of OCT structure maps was first improved using attenuation compensation algorithm, and finally the lymphatic vessels in the volumetric data were mapped using sorted mini-mum intensity projection (sMIP) technique [15]. Nevertheless, these image intensity-based threshold segmentation methods are greatly affected by noise (especially the motion noise of the sample), and it is difficult to accurately separate lymphatic vessels. A deep learning method was proposed to extract the lymphatic vessels, which requires ensuring the accuracy of the pre-training samples and sufficient datasets. The accurate segment can be obtained after a large number of trainning, and the accuracy of the results is also influenced by human factors [16]. The speckle decorrelation method was utilized to obtain human skin lymphatic vessels image by exploiting the low scattering properties of lymphatic vessels [17]. However, the speckle decorrelation algorithm is essentially an improvement based on the correlation mapping algorithm [18], which is also widely used in vascular imaging. Although it can visualize the lymphatic and blood vessel networks simultaneously, the two are easily confused and require additional correlation algorithms to separate them. It also requires complex motion correction to obtain a better imaging result. In addition, this method obtains contrast maps by sacrificing image resolution, which is disadvantageous for lymphangiography.

Aiming at the problems of lymphography methods above, we propose a lymphography method based on time-autocorrelated optical coherence tomography (OCT), which segments lymphatic vessels from surrounding tissues by using their difference in the decayed minimum value of the time-autocorrelation function of the interference signal varying time. The time-autocorrelated method allows non-invasive and high-sensitivity lymphography without sacrificing image resolution, avoiding the disturbance of vascular signals on lymphatic vessel signals, and reducing the influence of sample motion on the results.

2. Methods

In the OCT structural image, the lymphatic vessel is a low-scattering area, the interference signal intensity is very low, and its time-varying signal is a broadband random signal. The autocorrelation function of the broadband random signal decays rapidly over a short period of time, which is markedly different from time-varying signals in blood vessel and tissue area. According to the characteristics of lymphatic vessels, this paper uses the attenuation difference of the autocorrelation signals of broadband random signals and other signals to extract lymphatic vessels. The autocorrelation properties of different signals are discussed in detail below.

The sine signal can be expressed as:

(1)$$X(t) = X\sin (2\pi {f_0}t + \theta ),$$

where $f_0$ is the frequency of the sine signal. According to the definition of the autocorrelation function, the autocorrelation function of the sine function can be derived by:

(2)$${R_X}(\tau ) =\frac{{{X^2}}}{{2\pi }}\int_{-\infty }^{+\infty} {\sin (2\pi {f_0}t + \theta )} \sin [2\pi {f_0}(t + \tau ) + \theta] dt =\frac{{{X^2}}}{2}\cos (2\pi {f_0}\tau ).$$

The spectral range of the broadband random process is much larger than that of the narrowband random process, whose signal is formed by the superposition of many frequency signals. So the expression of the broadband random signal can be obtained by changing and expanding the distribution range of the narrowband random process. According to the definition of the narrowband random signal, the width $\Delta f$ of the significant region of its spectral density is small compared to the center frequency $f_0$ of that region, and satisfies $f_{0} \gg \Delta f$, then the narrowband random can be written as [19]:

(3)$$\begin{aligned} X(t) & = A(t)\cos [2\pi {f_0}t + \varphi (t)]\\ & = A(t)\cos \varphi (t)\cos 2\pi {f_0}t - A(t)\sin \varphi (t)\sin 2\pi {f_0}t\\ & = X(t)\cos 2\pi {f_0}t - Y(t)\sin 2\pi {f_0}t, \end{aligned}$$

where $X(t)$ is the in-phase component, and $Y(t)$ is the quadrature component, and they are all low-frequency band limiting processes. $A(t)$ and $\varphi (t)$ can be defines as:

(4)$$A(t) = \sqrt {{X^2}(t) + {Y^2}(t)},$$

(5)$${\varphi (t) = \arctan \left[ {\frac{{Y(t)}}{{X(t)}}} \right].}$$

Two random processes $A(t)$ and $\varphi (t)$ respectively represent the envelope and phase of the narrowband process. Based on the expression of $X(t)$, we can calculate its autocorrelation function:

(6)$$\begin{aligned} {R_X}(\tau ) = {R_a}(\tau )\cos (2\pi{f_0}t)\cos (2\pi{f_0}(t + \tau )) - {R_{ba}}(\tau )\sin (2\pi{f_0}t)\cos (2\pi{f_0}(t + \tau ))\\ {\rm{ }} - {R_{ab}}(\tau )\cos (2\pi{f_0}t)\sin (2\pi{f_0}(t + \tau )) + {R_b}(\tau )\sin (2\pi{f_0}t)\sin (2\pi{f_0}(t + \tau )). \end{aligned}$$

From the property of the narrowband random process, it can be known that:

(7)$${R_a}(\tau ) = {R_b}(\tau ),{R_{ab}}(\tau ) ={-} {R_{ba}}(\tau ).$$

Therefore,

(8)$${R_X}(\tau ) = {R_a}(\tau )\cos (2\pi{f_0}\tau ) + {R_{ba}}(\tau )\sin (2\pi{f_0}\tau ).$$

As a result, the expression of the broadband random signal can be expressed by expanding the distribution range of $f_{0}$ according to the Eq. 3.

Autocorrelations of different signals have obvious difference in the decayed minimum value. The autocorrelation of the sine function is a cosine function, as shown in Fig. 1(a)-Fig. 1(b). The sine wave is added with a low frequency noise and a random noise, as shown in Fig. 1(c), and its autocorrelation function is shown in Fig. 1(d). When the sinusoidal signal is mixed with a low frequency noise and a random noise, its autocorrelation function reaches the maximum when the time delay is zero, and the waveform at other times is approximately the same as that of the sinusoidal wave. For a narrowband random signal, as shown in Fig. 1(e), the autocorrelation function decays slowly with the envelope, as shown in Fig. 1(f). Compared with the autocorrelation of the narrowband random signal, the autocorrelation of the broadband random signal (Fig. 1(g)) decays more rapidly in a short time, as shown in Fig. 1(h). Under the influence of a low frequency noise and a random noise, the waveform of a constant function will fluctuate, as shown in Fig. 1(i). Its autocorrelation signal will slowly decay to a negative value from the maximum value, as shown in Fig. 1(j), and the minimum value after decay is obviously smaller than that in Fig. 1(h). It can be discovered from the comparison chart that the minimum values of the autocorrelation functions of different signals after attenuation have obvious difference. The attenuation speed of broadband random signals is significantly faster, and the minimum values after attenuation are larger than those of other signals. This paper exploits the feature to separate lymphatic vessels from surrounding tissues.

Fig. 1. Comparison between autocorrelation function graphs of different signals. (a), (c), (e), (g), (i) Waveforms of the sinusoidal function, the sinusoidal function mixed with random noise, narrowband random signal, the broadband random signal and the constant function under the influence of low-frequency noise, respcetively. (b), (d), (f), (h), (j) Autocorrelation signals corresponding to the above waveforms.

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At the optical path difference $z$, the light intensity of interference signal $I(k,t)$ collected by the linear CCD can be expressed as:

(9)$$I(k,t) = {I_0}\cos (2kz + 2\pi ft),$$

where $k$ is the wave number, $f$ is the Doppler frequency shift. By performing Fourier transform on $I(k,t)$ according to $k$, the interference light intensity information $\hat {I} (z,t)$, in the depth direction can be demodulated, and its expression is:

(10)$$\mathop I^ \wedge (z,t) = FT[I(k,t)].$$

In order to compare the time-autocorrelated curves of different tissues, a scale shrinkage operation similar to normalization was performed. $H(z,t_{i})$ can be obtained as:

(11)$$H(z,t_{i}) = \frac{ |\hat{I}(z,t_{i})| - \frac{1}{N} \sum_{i=1}^{N} |\hat{I}(z,t_{i})|}{ |\hat{I}(z,t_{i})|_{max}- \frac{1}{N} \sum_{i=1}^{N} |\hat{I}(z,t_{i})|},\quad i=1,2,3,\ldots,N,$$

where $N$ is the integer, $|\hat {I}(z,t_{i})|$ is the complex modulus of the interference light intensity at time $t_{i}$. In order to extract the lymphatic vessel signal from blood vessels and tissue sites, the autocorrelation operation needs to be done on $H(z,t_{i})$. The equation for the autocorrelation function $R(z,\tau )$ can be written as:

(12)$$R(z,\tau ) = \sum_{i=1}^{N}{H(z,t_{i})H(z,t_{i} + \tau )},\quad i=1,2,3,\ldots,N.$$

In the lymphatic vessel area, the autocorrelation function decays rapidly because the lymphatic interferometric intensity over time is expressed as a broadband random signal. The minimum value after the autocorrelation decay is taken for imaging, and the image of lymphatic vessels can be obtained.

3. Setup

The lymphatic imaging system in this paper is a spectral-domain OCT system, which is shown in Fig. 2. SD-OCT system uses a broadband light source (DL-BX9-CS3307A, Denselight) with a central wavelength of 1310nm and a bandwidth of 55nm. After passing through a 2 $\times$ 2 fiber coupler, the beam is split into the reference arm and the sample arm in a ratio of 50:50. The light reflected from the sample and the mirror is returned to the fiber coupler for interference. The output interference signal was received by a spectrometer composed of a grating (1145lines/mm, f=50mm, 1004-2, Thorlabs) and a linear CCD (SU1024-LDH2, Goodrich). The acquisition speed of the linear CCD is adjusted to 46.816kHz. Data were acquired by M-scan mode, with 500 A-scans repeated at each point.

Fig. 2. Schematic of the lymphatic imaging system.

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4. Experiment

To verify the feasibility of the method proposed in this paper, a simulation experiment was carried out using two tubes filled with liquid embedded in a gel mixed with agar and milk. One of them was filled with water, the other was filled with milk, both of which were connected to a syringe through a thin hose. The syringe connected to milk is injected forward at a certain rate, while the syringe connected to water remains stationary. The acquisition process used M-scan mode which was repeated 2 times in a B-scan. In M-scan mode, 500 A-scans were repeated at the same point. The result is shown in Fig. 3. In OCT structure (Fig. 3(a)), the left tube contained stationary water to simulate lymphatic vessels, and the right tube contained flowing milk which was a high scattering fluid to simulate blood vessels. Figure 3(b) is the result obtained by using the optical micro-angiography (OMAG) technique [20] based on the data collected by repeated B-scans. Only the flow signal can be seen in the figure, and the background signal is regarded as the static signal which is suppressed or even removed. Figure 3(c) shows the result exploiting the time-autocorrelated lymphography algorithm proposed in this paper. It can be seen that the signal in the low scattering region is significantly higher than that in the high scattering region, and the flow signal is also suppressed. The time-autocorrelated lymphography method can eliminate the influence of the vascular flow on the results, and the simulated lymphatic signal intensity is higher than that in other parts of the tissue. This result indicates that the proposed method in this paper can indeed extract the signal in the low scattering region.

Fig. 3. (a) OCT structure cross section image of simulated sample. There are two tubes embedded in a gel mixed with agar and milk. On the left, the tube filled with water to simulate the lymphatic vessel. While on the right, there is flowing milk to simulate the blood vessel. (b) OMAG can only extract the flowing and scattering blood vessel. (c) The time-autocorrelated method can be used to extract the image of low scattering area. Scale bar = 500 µm.

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The time-varying signals of interference intensity at the positions marked I (simulated blood vessel), II (simulated lymphatic vessel), III (simulated tissue), and IV (the background above the simulated tissue) in Fig. 3(a) after normalization and their autocorrelation signals are taken for analysis, and the analysis result is shown in Fig. 4. Figure 4(a) - (b) show the original signal and its autocorrelation signal at the simulated blood vessel respectively. The signal at the simulated lymphatic vessel is a broadband random signal as shown in Fig. 4(c), and the minimum value of its autocorrelation function is close to zero as shown in Fig. 4(d). The mixed gel was used to simulate tissue, and its interference signal fluctuates under the influence of noise, as shown in Fig. 4(e). Its autocorrelation waveform (Fig. 4(f)) slowly attenuates to a negative value after getting the maximum value, and its minimum value is far less than that of Fig. 4(d). Figure 4(g)-(h) show the original signal and its autocorrelation signal at the background above the simulated tissue, respectively. Compared with Fig. 4(c)-(d), it is found that the interference signal waveforms of both are broadband random signals. We can clearly discover the difference in the minimum value after the attenuation after comparing the autocorrelation curves above. The attenuation speed of the autocorrelation of the lymphatic vessel is significantly faster than that of other signals, and its minimum is the largest among all the curves. Using this difference, we can extract lymphatic vessels from the tissue for lymphography imaging.

Fig. 4. The time-varying interference signal intensity of the simulated sample and its autocorrelation function. (a), (c), (e), (g) are the time-varying signals of the normalized interference signal intensity at the positions marked I (simulated blood vessel), II (simulated lymphatic vessel), III (simulated tissue), and IV (the background above the simulated tissue) in Fig. 3(a), respectively. (b), (d), (f), (h) are the autocorrelation signals of (a), (c), (e), (g), respectively.

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The above experiment proved the feasibility of time-autocorrelated lymphography in simulated samples. In order to further prove its feasibility in biological imaging, SD rat ears were used for imaging. The rat used in the experiment was female and weighed 230 g. Before imaging, the rat was anesthetized with vaporized isoflurane for 5 min, and then injected with 5% chloral hydrate at the dose of 0.004 ml/g for further anesthesia. The body temperature was maintained between 35.5$^\circ$C and 36.5$^\circ$C by a heating pad during the experiment. The ear was depilated and flattened for imaging. The time-autocorrelation method was applied to the imaging of rat ear lymphangiography. Then 1ml of a 0.5% solution of Evans blue dye was injected intradermally at the inner surface of the rim of the ear to verify lymphatic vessels. The injection of Evans blue is a standard method to macroscopically visualize cutaneous lymphatic vessels and lymphatic drainage from the skin [21]. All animal experiment procedures are approved by the Animal Care and Use Committee of South China Normal University. The result of the experiment is shown in Fig. 5. Figure 5(a) shows the rat ear before the injection. Figure 5(b) shows the photograph of the rat ear after injection of Evans blue dye, the area indicated by a blue box is the scanning area, the white arrows point to the stained lymphatic vessels, and the photographing time is 1 min after injection. From Fig. 5(a)-(b), it can be seen that the blue dye spread along the lymphatic vessels from the injection site in the imaging area, where lymphatic vessels that cannot be observed with the naked eye before the injection were stained blue. Figure 5(c) shows the OMAG angiography image of the scanning area. Figure 5(d) shows the lymphangiography image obtained by the time-autocorrelation method. The distribution of lymphatic vessels can be clearly observed in the figure without the appearance of blood vessels and tissue images, and the differentiation of lymphatic vessels from blood vessels and tissues is successfully achieved. Figure 5(e) shows the fusion image of lymphography and angiography images. The lymphatic vessels are marked green and the blood vessels are marked red. Figure 5(f) shows the fusion image of lymphatic vessels and angiography, and the comparison with the image of SD rats after staining. The comparison result can show that the contrast image of lymphatic vessels is consistent with the staining result after the injection of Evans blue dye, which proves that the proposed method can achieve the imaging of lymphatic vessels in living organisms.

Fig. 5. (a), (b) The photograph of rat ear before and after injection of Evans blue dye. (c) The angiography image obtained by OMAG algorithm. (d) The lymphography image obtained by time-autocorrelated method. (e) The fusion image of lymphography and angiography images. Scale bar = 500 µm. (f) The lymphography image is consistent with the staining result.

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The difference between lymphatic vessels and blood vessels can also be observed in the OCT cross-sectional view, which is shown in Fig. 6. The cross-sectional location is marked in Fig. 5(e). Figure 6(a) shows the OCT cross-sectional view of the ear of the rat. Figure 6(b) and Fig. 6(c) show the cross-sectional view of lymphatic vessels and blood vessels respectively. Figure 6(d) is the composite image of the OCT cross-sectional image and the lymphangiography image, with the lymphatic region in green. Figure 6(e) shows the fusion image of lymphatic vessels and blood vessels, where green is the lymphatic vessels and red is the blood vessels. From Fig. 6, the structure and location of the lymphatic vessels are different from those of the blood vessels, and the location of the lymphatic vessels is exactly in the low-scattering region of the cross-sectional view of the ear of the rat in Fig. 6(a), which also proves the low-scattering property of lymphatic vessels.

Fig. 6. (a) Cross-sectional OCT structure image of the rat ear. (b) and (c) The cross-sectional image of lymphatic vessels and blood vessels. (d) The location of the lymphatic vessels is exactly in the low-scattering region of the cross-sectional view of the ear of the rat in (a). (e) The structure and location of the lymphatic vessels are different from those of the blood vessels.

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Compared with the speckle decorrelation and threshold segmentation methods based on OCT, the time-autocorrelated lymphography method proposed in this paper has obvious advantages, and the comparison results are shown in Fig. 7. Figure 7(a) shows the lymphography image obtained by the time-autocorrelated method. From the figure, it can be discovered that the time-autocorrelated method has a strong noise suppression ability and can separate the low-scattering signal from the stationary high-scattering tissue and the flowing vascular signal without losing the original signal resolution. Figure 7(b) is the lymphatic angiography image obtained by the threshold segmentation method, from which the distribution of lymphatic vessels can be faintly seen, but is extremely affected by motion noise. Figure 7(c) shows the image obtained by speckle decorrelation. Due to the low sensitivity of imaging, the lymphatic distribution at the same location as in Fig. 7(a) is barely discernible at the dashed line in Fig. 7(c). It contains not only lymphatic vessels but also blood vessels, and the two cannot be distinguished from the projection image alone. Additional algorithms are needed to further separate lymphatic vessels from the cross-sectional image (B-scan image) according to the scattering characteristics, which increase the complexity of data processing. In addition, the speckle decorrelation method calculates the spatial correlation of two adjacent B-scan images through a specific small window, which loses the axial and lateral spatial resolution of the images. As the cross-correlation window increases and the influence of various jitter factors in live samples, it is not conducive to microlymphatic vessels imaging. Therefore, compared with the threshold segmentation method, the time-autocorrelated method has strong noise suppression ability, and has obvious advantage in imaging sensitivity compared with the speckle decorrelation method.

Fig. 7. Comparison of the time-autocorrelated method, the threshold segmentation method and the speckle decorrelation method. (a) The projection image by using time-autocorrelated method. (b) The projection image by using the threshold segmentation method. (c) The projection image by using the speckle decorrelation method. Scale bar = 500 µm.

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Although the time-autocorrelated method can achieve high sensitivity imaging of lymphatic vessels, there is still room for improvement in practical applications. In the experiments of this paper, the image acquisition process performed 500 A-scans at each point for the time autocorrelation. In fact, the number of A-scans can be appropriately reduced to improve the time of data acquisition and image processing while taking into account the image quality and the time of data acquisition and processing. The imaging system used for the experiments in this paper is not sufficient to resolve capillary lymphatic vessels. The visualization of capillary lymphatic vessels can be further achieved by increasing the imaging resolution of the system.

5. Conclusions

In summary, based on the difference in the decay characteristics of the autocorrelation function of different signals, a time-autocorrelated lymphography method is proposed. The interference intensity of the lymphatic vessels is significantly lower than that of the surrounding tissue. The time-varying signal of the normalized interference intensity is a broadband random signal, and the minimum value of its autocorrelation function after attenuation is significantly larger than that of blood vessels and the surrounding tissue. So this difference can be exploited to separate lymphatic vessels from blood vessels and the surrounding tissue. The experimental results show that the time-autocorrelated lymphography method has stronger noise suppression ability than the threshold segmentation method, and higher imaging sensitivity than the speckle decorrelation method, and it can be non-invasive and high-resolution. This rapid visualization of lymphatic vessels provides a technical reference and has potential application value in the diagnosis and treatment of lymph-related diseases.

Funding

National Natural Science Foundation of China (61575067).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Lymphography method based on time-autocorrelated optical coherence tomography

Abstract

1. Introduction

2. Methods

3. Setup

4. Experiment

5. Conclusions

Funding

Disclosures

Data Availability

Supplemental document

References

Supplementary Material (1)

Data Availability

Cited By

Figures (7)

Equations (12)

Biomedical Optics Express