Detection of Abnormal Blood Flow Region Based on Near Infrared Correlation Spectroscopy

Abstract

Blood flow measurement of microvessels in human tissues is of vital importance for the diagnosis and treatment of many diseases. In this paper, the detection method of abnormal blood flow regions based on near-infrared correlation spectroscopy is studied. We used the NL-Bregman-TV imaging algorithm to realize Blood flow imaging. However, due to the limitation of the number and distribution of detectors, the pixels obtained from images are extremely low, which cannot meet the practical requirements of the visual and the abnormal blood flow range measurement. In this paper, the bicubic interpolation method is used to improve the resolution of low-pixel blood flow images. The parameter index of the normalized similarity was proposed to help judge the effect of the interpolation method on the resolution of this kind of image. Aiming at the extraction of abnormal regions, a threshold segmentation algorithm based on the histogram difference method and a morphological processing algorithm is proposed to extract the contour of abnormal blood flow. The method proposed in this paper can be used to accurately locate and extract the clear and smooth contour of abnormal blood flow.

1. Introduction

Blood flow measurement of microvessels in human tissues is of vital importance for the diagnosis and treatment of many diseases [1]. Studies have shown that cerebral ischemia lasting for a few minutes can lead to stroke or other irreversible nerve damage [2]. Breast Tumors may have abnormal metabolic functions. The hemodynamic manifestations are the abnormal increase in tissue blood flow and decrease in tissue blood oxygen level [3]. Sleep apnea may lead to accelerated blood flow turbulence [4,5]. Relative to static indexes such as blood oxygen, blood flow, as a dynamic indicator of brain function, is more sensitive to pathological responses. According to the literature, in brain excited states and tumor tissues, the change (or contrast) in blood flow is much higher than that in blood oxygen [6,7]. Therefore, the measurement of blood flow in human tissues and the monitoring of its state will contribute to the early diagnosis and treatment assessment of a variety of diseases [8,9,10] and for those with functional degradation earlier than measurable pathological changes, such as Alzheimer’s disease [11] and sleep apnea [4]. Accordingly, in order to realize the measurement and monitoring of human tissue blood flow, it is very important to study effective measurement technology and abnormal region extraction algorithms.

Near-infrared diffuse correlation tomography (NIR-DCT) uses near-infrared diffuse light as a detection means to analyze the influence of the diffusion movement of red blood cells in microvessels on the light field correlation function [12,13], and obtains the spatial distribution of blood flow by means of image reconstruction (blood flow imaging, BFI), to measure the spatial blood flow contrast of the tissue. The technology, which has the characteristics of being non-invasive, continuous, portable and low cost, has enough sensitivity to detect superficial positions of the human body such as the brain, neck and breast [14], and can quickly obtain the spatial blood flow contrast of tissues to monitor abnormal blood flow. Due to the influence of detector volume and detection depth, only a limited number of light source detector (S-D) pairs can be set. Since the number of S-D pairs is much smaller than the number of unknown voxels in the image, the blood flow imaging can be achieved by solving the non-adaptation problem in mathematics. We used the NL algorithm to extract tissue blood flow parameters. The Split–Bregman algorithm is combined with the TV sparse model for real-time image reconstruction. Thus we obtained the spatial blood flow contrast of tissues [15]. But the resolution of the image is very low, which can not meet the actual requirements of the visual and the abnormal blood flow contour measurement. This paper studied two aspects which are increasing the resolution of the low pixel blood flow images and extracting the abnormal blood flow contours. The bicubic interpolation method is used to improve the resolution of low-pixel blood flow images. Aiming at the extraction of abnormal regions, a contour extraction method of abnormal blood flow was constructed by combining histogram-based threshold segmentation and morphological processing. The clear and smooth image contour can provide favorable conditions for subsequent blood flow abnormal localization.

2. Principle of NIR-DCT Blood Flow Imaging and Extracting Abnormal Blood Flow Contours

NIR light [16] is used for measuring the physiological parameters of the human body. A waveband with a wavelength range of 650–950 nm is selected, in which photons propagate in a diffusion mode in tissues, and the absorption coefficients of hemoglobin and water in tissues are very low [17]. Several S-D pairs are oppositely arranged on the skin surface of the tissue to be measured. Photons are scattered by tissue scatterers (such as organelles and mitochondria), and a part of photons return to the skin surface and are received by a single-mode optical fiber and recorded by a single-photon detector [18,19,20]. The movement of red blood cells in the tissue causes fluctuations in light intensity. Light intensity fluctuations carry information about the dynamic characteristics of moving red blood cells. By collecting photons on the tissue surface using a single photon detector, we can measure the fluctuation of light intensity over time [21] as shown in Figure 1.

The measured light intensity autocorrelation function and the electric field autocorrelation function are correlated through the Siegert relation [22], to calculate the electric field autocorrelation function $g_1\left(\tau \right)$, which correlates the measured signal with the movement of red blood cells. The blood flow value can be obtained using the NL algorithm model so that the blood flow value can be determined [23,24]. When the DCS technology is used to monitor the change value of blood flow with time, which is affected by the detector volume and detection depth, only a few or dozens of light S-D pairs can be set, so the number of S-D pairs is much smaller than the number of unknown voxels in the image. Therefore, blood flow imaging can be realized by solving the non-adaptation problem in mathematics. The reconstruction method is vital for the image quality of hemodynamic reconstruction. The TV (Total Variation) regularization is intended to sparsely represent the image by minimizing the $L_1$ norm of the image gradient amplitude transformation. As far as TV minimization is concerned, the Split–Bregman algorithm has been proven to be an effective method for DCT reconstruction [15]. Therefore, this method is named as the NL-Bregman-TV algorithm for real-time imaging of blood flow data. The resolution of the image obtained by this method is very low. It is difficult to observe the image details. Therefore, we use the image interpolation technology to improve the resolution. In this paper, the DCT image is interpolated by bicubic interpolation. Then we used the histogram difference algorithm to extract the effective abnormal region, and then the morphological method was used to extract the contour to obtain a clear and smooth abnormal blood flow image contour. The DCT blood flow imaging and abnormal blood flow contour extraction method flow diagram is shown in Figure 2.

3. DCT Imaging Algorithm

3.1. DCT Imaging Modeling

The DCT blood flow imaging model is based on a novel Nth-order linear (NL) algorithm, and the concept of this imaging model comes from the normalized form of light field autocorrelation $G_1(\overrightarrow{r},\tau )$, which satisfies the following integral expression [23,24]

$$G_1\left(\tau \right)=G_1(\overrightarrow{r},\tau )/G_1(\overrightarrow{r},0)=\underset{0}{\overset{\infty }{\int }}P\left(s\right)exp(-2k_o^2\alpha D_B\tau {\displaystyle \frac{s}{l^{*}}})ds$$

(1)

In this equation, $\tau$ is the delay time of the autocorrelation function, $G_1(\overrightarrow{r},\tau )$ is the correlation function of the light field, $P\left(s\right)$ is the normalized distribution of the path lengths s of photons transmitted in a tissue. $k_o$ is the wave-vector value of the light in the medium and it has a value equal to ${\displaystyle \frac{2\pi ·n}{\lambda }}$. $l^{*}$ is the total distance of photons in the organization and it has a value equal to ${\displaystyle \frac{1}{u_s^{\prime }}}$, $u_s^{\prime }$ is the scattering coefficient of the tissue, and s is the substep length.

Due to the complex integration form of the variable $\alpha D_B$ to be solved, it is difficult to directly solve Equation (1). Through the analysis of Equation (2), a high-order nonlinear model of the autocorrelation of the light field is designed to separate the blood flow information and the photon transmission paths. After a series of mathematical derivations, we can obtain:

$$G_1(\tau ,j)-1=\tau \sum _{i=1}^{n}A(i,j)\alpha D_B\left(i\right)$$

(2)

$$G_1(\tau ,j)-1-\sum _{k=2}^N{\displaystyle \frac{{\displaystyle \sum _{p=1}^Q}w(p,j){[-2{\displaystyle \sum _{i=1}^n}{k}_0^2\left(i\right)\alpha D_B\left(i\right)s(i,p,j){\mu }_s^{\prime }\left(i\right)]}^k}{k!}}{\tau }^k=\tau \sum _{i=1}^{n}A(i,j)\alpha D_B\left(i\right)$$

(3)

Equations (2) and (3) are referred to as the first- and the Nth-order linear algorithms, respectively, where $\alpha D_B\left(i\right)$ is the blood flow value of the i-th spatial unit. When the tissue morphology image information can be obtained, the transmission path $s(i,j,p)$ of a photon within the tissue can be obtained through MC simulation of photons, thereby further obtaining the coefficient matrix:

$$A(i,j)=\sum _{P=1}^Q-2w(p,j)k_0^2\left(i\right)s(i,p,j){\mu }_s^{\prime }\left(i\right)$$

(4)

Equation (4) specifically describes how the morphological information and the internal component information of the organ are incorporated into the DCT modeling.

Note, that when the order $N>1$, there is an unknown quantity $\alpha D_B\left(i\right)=[\alpha D_B\left(1\right),\dots ,$$\alpha D_B{\left(n\right)]}^T$ on the left side of Equation (3), so the calculation of blood flow value is gradually obtained through an iterative solution, and the final form of the solution is as follows:

$$G_1(\tau ,j)-1-\sum _{k=2}^N{\displaystyle \frac{{\displaystyle \sum _{p=1}^Q}w(p,j){[-2{\displaystyle \sum _{i=1}^n}{k}_0^2\left(i\right)\alpha D_B^{N-1}s(i,p,j){\mu }_s^{\prime }\left(i\right)]}^k}{k!}}{\tau }^k=\tau S{l}^N\left(j\right)$$

(5)

$$A^T\alpha D_B^{\left(N\right)}=S{l}^{\left(N\right)}$$

(6)

The blood flow value $\alpha D_B$ of each spatial unit can be obtained through an image reconstruction algorithm. Thus, blood flow imaging can be achieved. So, the main process is to solve Equations (3) and (5).Thus, NIR diffuse light imaging is simplified to solve a system of linear equations.

3.2. Calculating the Nth-Order Blood Flow Value $\alpha D_B$ and Image Reconstruction

In this process, the solution of the linear Equations (5) and (6) is the key link. Because the number of the measured data is far less than that of the image voxel to be reconstructed; the corresponding linear equations are seriously ill-conditioned. Therefore, the TV regularization is introduced for constraint, and the Split–Bregman algorithm is adopted to realize image reconstruction [15].

Let $v=\alpha D_B^{\left(N\right)}$ and $b=S{l}^{\left(N\right)}$. The reconstruction Equation (6) after the TV regularization becomes Equation (7):

$$\begin{array}{c}{v}^{*}={argmin\left|\right|v\left|\right|}_{TV}+{\displaystyle \frac{\mu }{2}}\left|\right|Av-{b\left|\right|}_2^2\\ s.t.v_i\ge 0(i=1,\dots ,n)\end{array}$$

(7)

The TV norm form of the anisotropic gradient transformation based on three-dimensional (3D) images can be expressed as:

$${\left|\right|v\left|\right|}_{TV}={\left|\right|\nabla v(x,y,z)\left|\right|}_1=\left|\right|{\nabla }_x{v\left|\right|}_1+\left|\right|{\nabla }_y{v\left|\right|}_1+\left|\right|{\nabla }_{z}v{\left|\right|}_1$$

(8)

where,

$$\begin{array}{c}\hfill {\left({\nabla }_{x}v\right)}_{i,j,k}=v_{i+1,j,k}-v_{i,j,k}\\ \hfill {\left({\nabla }_{y}v\right)}_{i,j,k}=v_{i,j+1,k}-v_{i,j,k}\\ \hfill {\left({\nabla }_{z}v\right)}_{i,j,k}=v_{i,j,k+1}-v_{i,j,k}\end{array}$$

(9)

By variable substitution, the optimization algorithm of Equation (7) is as in Equation (10)

$$\begin{array}{c}\underset{v,d_x,d_y,d_z}{min}\left|\right|d_x{\left|\right|}_1+\left|\right|d_y{\left|\right|}_1+\left|\right|d_z{\left|\right|}_1+{\displaystyle \frac{\mu }{2}}\left|\right|Av-{b\left|\right|}_2^2\\ s.t.d_x={\nabla }_{x}v,y={\nabla }_{y}v,z={\nabla }_{z}v\end{array}$$

(10)

Equation (10) can be obtained by the Split–Bregman algorithm:

$$\underset{v,d_x,d_y,d_z}{min}\left|\right|d_x{\left|\right|}_1+\left|\right|d_y{\left|\right|}_1+\left|\right|d_z{\left|\right|}_1+{\displaystyle \frac{\mu }{2}}\left|\right|Av-{b\left|\right|}_2^2+{\displaystyle \frac{\lambda }{2}}\left|\right|d_x-{\nabla }_{x}v-b_x^k{\left|\right|}_2^2+{\displaystyle \frac{\lambda }{2}}\left|\right|d_y-{\nabla }_{y}v-b_y^k{\left|\right|}_2^2+{\displaystyle \frac{\lambda }{2}}\left|\right|d_z-{\nabla }_{z}v-b_z^k{\left|\right|}_2^2$$

(11)

The Split–Bregman algorithm is as follows [15]:

Step 1: Use Equation (12) to iterate and optimize to obtain $v^{k+1}$:

$$v^{k+1}=arg\underset{v}{min}{\displaystyle \frac{\mu }{2}}\left|\right|Av-{b\left|\right|}_2^2+{\displaystyle \frac{\lambda }{2}}\left|\right|d_x^k-{\nabla }_{x}v-b_x^k{\left|\right|}_2^2+{\displaystyle \frac{\lambda }{2}}\left|\right|d_y^k-{\nabla }_{y}v-b_y^k{\left|\right|}_2^2+{\displaystyle \frac{\lambda }{2}}\left|\right|d_z^k-{\nabla }_{z}v-b_z^k{\left|\right|}_2^2$$

(12)

Because the actual blood flow index is non-negative, a non-negative constraint is applied:

$$v^{k+1}=\left\{\begin{array}{ccc}& v^{k+1}\hfill & \hfill v^{k+1}\ge 0\\ & 0\hfill & \hfill v^{k+1}<0\end{array}\right.$$

(13)

Step 2: Use Equation (14) to iterate and optimize to obtain $d{x}^{k+1},d{y}^{k+1},d{z}^{k+1}$:

$$\begin{array}{c}(d_x^{k+1},d_y^{k+1},d_z^{k+1})=arg\underset{d_x,d_y,d_z}{min}\left|\right|d_x{\left|\right|}_1+\left|\right|d_y{\left|\right|}_1+\left|\right|d_z{\left|\right|}_1+\\ {\displaystyle \frac{\lambda }{2}}\left|\right|d_x-{\nabla }_x{v}^{k+1}-b_x^k{\left|\right|}_2^2+{\displaystyle \frac{\lambda }{2}}\left|\right|d_y-{\nabla }_y{v}^{k+1}-b_y^k{\left|\right|}_2^2+{\displaystyle \frac{\lambda }{2}}\left|\right|d_z-{\nabla }_z{v}^{k+1}-b_z^k{\left|\right|}_2^2\end{array}$$

(14)

Step 3: Use Equation (15) to iterate and optimize $d{x}^{k+1},d{y}^{k+1},d{z}^{k+1}$:

$$\begin{array}{c}\hfill b_x^{k+1}=b_{x}k+({\nabla }_x{v}^{k+1}-d_x^{k+1})\\ \hfill b_y^{k+1}=b_{y}k+({\nabla }_y{v}^{k+1}-d_y^{k+1})\\ \hfill b_z^{k+1}=b_{z}k+({\nabla }_z{v}^{k+1}-d_z^{k+1})\end{array}$$

(15)

The stopping condition is shown in Equation (16), and if the condition is not met, repeat steps 1–3.

$$\left|\right|v^{k+1}-v^k{\left|\right|}_2<ϵ$$

(16)

In the first step, v is updated using a bi-conjugate gradient algorithm [25,26]. In the second step, d is calculated by the shrinking algorithm:

$$\begin{array}{c}\hfill d_x^{k+1}=shrink\left(\right|{\nabla }_x{v}^{k+1}+b_x^k|,{\displaystyle \frac{1}{\lambda }})\\ \hfill d_y^{k+1}=shrink\left(\right|{\nabla }_y{v}^{k+1}+b_y^k|,{\displaystyle \frac{1}{\lambda }})\\ \hfill d_z^{k+1}=shrink\left(\right|{\nabla }_z{v}^{k+1}+b_z^k|,{\displaystyle \frac{1}{\lambda }})\end{array}$$

(17)

where,

$$shrink(t,\gamma )={\displaystyle \frac{t}{\left|t\right|}}\ast max\left(\right|t|-\gamma ,0)$$

(18)

The imaging experiments are carried out by using a breast phantom and the above method. We used a cross-shaped solid gel heterogeneity to simulate abnormal breast tissue, it was shown in Figure 3e. And four tomographic images are obtained as shown in Figure 3.

It can be seen from the figure that the shape and size of the heterogeneous bodies are similar to those of the actual phantom, and the reconstruction position is accurate. However, the resolution of the imaging pattern is extremely low; therefore, the image cannot be directly used to distinguish the change in blood flow or extract the abnormal blood flow area. Therefore, it is necessary to interpolate the image to improve its resolution to obtain a more actual blood flow image. Besides, the extraction of abnormal blood flow contours is studied to create conditions for the extraction of abnormal blood flow areas.

4. Image Interpolation Method

Due to the limitations of the light source and detector volumes and other factors, the resolution of the imaging pattern is extremely low and it is difficult to observe its details. The depth learning (DL) method is a popular image processing method that can also improve image resolution but needs a large amount of simulation and measured data to form a sample set. At present, near-infrared blood flow imaging technology has not been applied in clinics, and there are not enough datasets, so this method is difficult to realize. Therefore, we use image interpolation technology, which is inexpensive and convenient, to improve the image resolution to present more details. Bicubic interpolation, also called cubic convolution interpolation [27], can create image edges that are smoother than that of bilinear interpolation. Bicubic interpolation algorithms are often used in image or video scaling and can preserve better detail quality than dominant bilinear filtering algorithms. Such an algorithm uses the gray values of 16 points around a point to be sampled for cubic interpolation, which considers not only the influence of the gray values of four directly adjacent points but also the influence of the change rate of the gray values among the adjacent points [27]. Three operations can obtain a magnification effect closer to a high-resolution image. This algorithm needs to select an interpolation basis function to fit the data. In this paper, the function shown in Equation (19) is used as the basis function.

$$\begin{array}{c}\hfill h_c\left(x\right)=\left\{\begin{array}{ccc}& {1.5\left|x\right|}^3-2.5{\left|x\right|}^2+1\hfill & \hfill \left|x\right|\le 1\\ & -{0.5\left|x\right|}^3+{2.5\left|x\right|}^2-4\left|x\right|+2\hfill & \hfill 1<\left|x\right|\le 2\\ & 0\hfill & \hfill others\end{array}\right.\end{array}$$

(19)

The bicubic interpolation method considers 4 × 4 adjacent points around the coordinate $(i+u,j+v)$ of the point to be interpolated as the reference point. Let i and j be the integer parts and u and v be the decimal parts, respectively. Then, the pixel value $f(i+u,j+v)$ at the point $(i+u,j+v)$ can be obtained from the following interpolation formula:

$$f(i+u,j+v)=ABC$$

(20)

where, A, B and C are all matrices:

$$A=\left[S\right(u+1\left)S\right(u+0\left)S\right(u-1\left)S\right(u-2\left)\right]$$

(21)

$$\begin{array}{c}\hfill B=\left[\begin{array}{cccc}f(i-1,j-1)& f(i-1,j+0)& f(i-1,j+1)& f(i-1,j+2)\\ f(i+0,j-1)& f(i+0,j+0)& f(i+0,j+1)& f(i+0,j+2)\\ f(i+1,j-1)& f(i+1,j+0)& f(i+1,j+1)& f(i+1,j+2)\\ f(i+2,j-1)& f(i+2,j+0)& f(i+2,j+1)& f(i+2,j+2)\end{array}\right]\end{array}$$

(22)

$$\begin{array}{c}\hfill C=\left[\begin{array}{c}S(v+1)\\ S(v+0)\\ S(v-1)\\ S(v-2)\end{array}\right]\end{array}$$

(23)

We used rectangle solid gel heterogeneity to simulate diseased abnormal tissues and used the above method to generate DCT images and perform bi-cubic interpolation. The DCT images of strip tissues and interpolation results are shown in Figure 4. It can be seen that the image after interpolation shows the basic shape and distribution of the simulated blood flow.

Because the resolution of the image before and after the image interpolation has changed, it is no longer suitable to evaluate the interpolation effect by the traditional image quality grading parameters such as mean square error, root mean square error, signal-to-noise ratio and peak signal-to-noise ratio. The histogram can reflect the probability distribution of pixel gray values of an image. It is convenient to calculate the similarity between the interpolated image and the original image by histogram normalization correlation coefficients. The algorithm measures the similarity of the images based on the difference between the mathematical vectors and can reflect the probability distribution of the pixel gray values of the whole image. Based on subjective observation, this paper proposes to use the correlation of normalized histogram, i.e., histogram similarity, to judge the structural similarity of the original image and the interpolated image, to evaluate the interpolation effect.

The method comprises the following steps: firstly, calculate image histogram H1 before interpolation and H2 after interpolation; then obtain normalized histograms by using Equation (24); finally, calculate the correlation coefficient between H1 and H2 by using Equation (25). The two images are considered identical when the correlation coefficient is 1, and the larger the correlation coefficient is, the larger the similarity degree of the histograms before and after interpolation is, therefore, the more the interpolated image can represent the information of the original image.

$$p\left(k\right)={\displaystyle \frac{n_k}{MN}}$$

(24)

where k is the grayscale level of the pixel, $n_k$ is the number of pixels with grayscale k, and $MN$ is the total number of pixels in the figure.

$$d(H_1,H_2)={\displaystyle \frac{{\sum }_I(H_1\left(I\right)-\overline{H_1})(H_2\left(I\right)-\overline{H_2})}{\sqrt{{\sum }_I{(H_1\left(I\right)-\overline{H_1})}^2{\sum }_I{(H_2\left(I\right)-\overline{H_2})}^2}}}$$

(25)

where

$$\overline{H_k}={\displaystyle \frac{1}{N}}{\sum }_J{H}_k\left(J\right)$$

(26)

The Normalized histogram of “Rectangular” shape blood flow original Image is shown in Figure 4d. The histogram of the interpolation Image is shown in Figure 4e. The similarity between the interpolated image and the original image was calculated to be 0.9488 by using the histogram normalization correlation coefficient.

5. Extraction of Abnormal Blood Flow Areas

5.1. Image Segmentation

The detection of the abnormal blood flow area and its size change has important significance for the clinical judgment of the change in tumors or nodules and can provide a certain basis for the next treatment plan. In order to extract the abnormal blood flow region, image edge detection can be used to identify the set of pixels with sharp brightness change in the image, which eliminates the information irrelevant to the target, retains the important structural attributes of the image, and realizes the segmentation and location of the object in the image. The traditional image edge detection is achieved by detecting the area in which the pixel gray value changes suddenly, and then determining the edge position of the image according to the first or second-order differential values. There are mainly three kinds of edge detection methods. The first type detects the edges of an image by calculating its gradient values, such as the Sobel operator [28], Prewitt operator [29], Roberts operator [30], etc., the second type detects the edge by seeking the zero crossing point in the second derivative, such as Laplacian operator, Laplacian of Gaussian operator, Canny operator, etc., the third type comprehensively utilizes the characteristics of the first-order differential and the second-order differential, such as Marr–Hildreth edge detection operator, etc. If an operator is used to segment the image, because the sensitivity of the operator to changes is strong, more regions of interest will be segmented. In terms of the actual requirement, edges, outlines and other features of the target image are selectively highlighted for the convenience of display, observation, or further analysis and processing. Therefore, the method of histogram difference is used to extract the effective abnormal region, and then the morphological method is used to extract the contour to obtain a clear and smooth image contour.

Through the research of the interpolated DCT gray images, it was found that the gray value of the images was also small; the abnormal blood flow in the dark background area was difficult to distinguish, but the gray level of the abnormal blood flow images, with some edge features, was still higher than that of most background images. Therefore, binary segmentation can be conducted on the original images to achieve enhancement goals and suppress the effect of the background, under the condition of the original contour of the abnormal blood flow images. The key to binary segmentation is to select a proper gray threshold. The number of gray-level pixels in an image is usually counted by histograms. The proper gray level threshold can be found by analyzing the histogram characteristics. The histogram threshold segmentation algorithm is to find a suitable threshold according to the histogram to realize binary segmentation of the image.

The number of pixel points with gray level distribution within the range of 85–97 formed a peak corresponding to the main gray level of the background image in the dark area. The abnormal blood flow image occupied a small number of pixels and the gray level was higher than most of the background image, and should be located on the right side of the peak. The gray level of the abnormal blood flow image was similar to the gray level corresponding to the peak, but there was a gap in the number of pixels, so that the crest appeared as a steep foreslope, and the steepest position of the foreslope corresponded to the optimal gray threshold for segmenting the heterogeneous bodies and the background. Therefore, a threshold segmentation algorithm based on the histogram difference method was proposed in this paper. First-order difference was calculated for pixel points within 85–97 gray level range, and the gray level of the maximum point of first-order difference was used as the threshold value to segment the original image.The interpolation image of the 400 mL/h blood flow phantom generated by a peristaltic pump, and the histogram of the interpolated image is shown in Figure 5. The result shown in Figure 6 demonstrates that the abnormal blood flow image was effectively enhanced.

5.2. Contour Extraction of Abnormal Blood Flow by Morphological Processing Algorithm

Morphological processing, which is a non-linear image processing algorithm based on image structure and geometry analysis, modifies the geometric features of the image to be processed quantitatively by structuring elements. It has good noise reduction performance and simple algorithm structure and has been widely used in noise suppression and image recognition [31]. The basic operations of morphology processing are expansion and corrosion. The expansion operation is an expansion process, which can fill the concave part with unsmooth boundaries; the corrosion operation is a contraction process, which can eliminate the convex part with uneven boundaries. In this paper, a circular structuring element was used to smooth the binary image first and then open to effectively filter the noise at the edge of the image, reduce the interference of the noise on the target image, smooth the edge burr of the abnormal blood flow image and fill the internal tiny gaps. The processing result is shown in Figure 7. Then, the contour of the image was extracted. The clear and smooth image contour can provide favorable conditions for subsequent blood flow abnormal localization. Meanwhile, image noise is further eliminated, and the abnormal blood flow contour map is obtained and presented in Figure 7. The contour of the abnormal blood flow image was well preserved, and the results were in line with the actual situation.

6. Experiments

According to clinical experience, the blood flow index (BFI) of tumors such as breast tumors is higher than the surrounding normal tissues [3]. Therefore, a peristaltic pump was designed to generate “tubular” heterogeneous bodies with different flow rates to simulate the BFIs in tumors. Whereas for some calcified tumors and post-operative necrotic tissues and even nodules, the blood flow index is much smaller than the normal tissues. So, we used “cross” and “strip” shaped solid gel heterogeneous bodies to simulate this type of diseased tissue.

In experiments, an NIR diffuse light contact measurement mode was adopted. An NIR laser light source was used for emitting coherent light, photons were scattered in tissues, and the scattered photons were detected by a plurality of S-D detection pairs at the same time. The weak light scattering signal was extracted from noise by using correlation detection, and the blood flow value was calculated according to the autocorrelation function transformation relation of the light field and the electric field. The blood flow data were collected by the eight-channel blood flow tester (DCS acquisition instrument) set up by the experimental group. As shown in Figure 8, the DCS acquisition instrument was mainly composed of a long coherent infrared laser, a single photon detector, a digital correlator, a data acquisition card, an 8 × 8 optical switch, and a notebook computer with control software interface.

In order to realize continuous real-time monitoring and data acquisition, our research group developed a computer data acquisition software based on Visual Basic. The user interface is shown in Figure 8b. The software interface has three graphical display areas. The first displays autocorrelation curves of the collected data, the second displays real-time information about relative blood flow values, and the third displays blood information. In the “Manual” area, there are eight control switches for each light source. After the user selects the option of a specific light source and clicks the “Sequence Scan” button, the six boxes in the “Status” area will record the photon count result of the corresponding detector. The data will be updated every 0.2 s. When all eight light sources are finished, the user can click the “Quit” button on the interface to terminate the data collection program.

An optical probe having a specific S-D configuration was placed on the surface of the tissue under test to emit and collect photon signals from the tissue. The optical probe was composed of eight source optical fibers and 48 detector optical fibers, covering an area of $80*80$ mm² on the tissue model. The source optical fibers and the detector optical fibers were crossly distributed in the array (Figure 8c). Six S-D sensing arrays with different colors can be seen in the Figure 8d. The dots represent the light sources and are indicated by. The stars represent the detectors. The detectors with the same color as the light source belonged to the same group and were responsible for collecting the escaped photons indicated by $S_i(i=1,\dots 8;j=1,\dots 6)$, which was from the light emitted by the light source and scattered by $D_{ij}(i=1,\dots 8;j=1,\dots 6)$ the tissue. Take the first group of light sources and detectors (pink, $S_1$ denotes the light source, $D_{11}$–$D_{16}$ denote six detectors) as an example. The distance from $D_{11}$, $D_{13}$, and $D_{15}$ to $S_1$ light source was 2.83 cm, and the detection depth was about $1.4$ cm; The distance from $D_{12}$, $D_{14}$, and $D_{16}$ to the light source was $2.00$ cm, and the detection depth was about 1 cm. This array can have up to 384 (i.e., $8\ast 48$) S-D pairs with a maximum penetration depth of $1.414$ cm. For the convenience of adjustment and fixation, a PVC panel with small holes and a bracket was manufactured by using 3D printing technology. The optical fiber probe was arranged on the PVC panel. The panel was supported by the bracket, and the height of the panel was adjustable. The aperture (about $2.62$ mm) was slightly larger than the diameter (about $2.62$ mm) of the optical fiber lantern ring to ensure the fixation of the optical fiber position, and the photons vertically entered the phantom solution. One end of the fiber ferrule was in contact with the target tissue and the other end (FC connector) was linked to a light source or detector in the optical switch. The “tubular” heterogeneous body was fixed by melt adhesive to the middle beam of the bracket, at a distance of $0.5$ cm from the optical fiber probe. One end of the “tubular” heterogeneous body was connected with the peristaltic pump through a rubber pipe, and the other end was extended into a waste liquid collecting tank through a rubber pipe. The solid heterogeneous body was lifted by an acupuncture needle of a $0.25$ mm diameter inserted in the bulge of the beam in the chassis. The distance from the upper surface to the optical fiber probe was about $0.5$ cm.

For the phantom experiments, the optical parameters of the background solution and the abnormal region were obtained by Monte Carlo simulation. The background solution was placed in a rectangular glass jar, which was formed by mixing distilled water, fat emulsion and India ink. India ink was used to control the absorption coefficient $\mu$ of the phantom solution, where $\lambda$ is the laser wavelength (e.g., 785 nm). First, dilute the ink with distilled water to $1\%$ and calibrate its absorption coefficient with a spectrometer to be $28.57$ cm⁻¹. The fat emulsion solution was used to control the reduced scattering coefficient ${\mu }_s^{\prime }$$\left(\lambda \right)$ of the phantom solution, and the internal particles in the fat emulsion solution were used to simulate the movement of red blood cells, i.e., the blood flow of microvessels. Equation (27) gives the ratio of the reduced scattering coefficient to distilled water and fat emulsion.

$${\displaystyle \frac{8{\mathrm{cm}}^{-1}}{{\mu }_s}}={\displaystyle \frac{23.35}{V_{water}}}$$

(27)

We prepared a phantom solution that requires optical parameters of (${\mu }_a\left(\lambda \right)=0.05$ cm⁻¹ and ${\mu }_s^{\prime }$$\left(\lambda \right)$$=8.0$ cm⁻¹), a background solution with an absorption coefficient of $0.05$ cm⁻¹. After preparation, the solution was mixed well and left to stand for at least 30 min to reduce interference from other movements. A kind of “strip” and “cross” shaped heterogeneous bodies were prepared by mixing transparent silica gel, fat emulsion and ink, followed by air-drying. So, we obtained a solid heterogeneous body with the same optical parameters (${\mu }_a\left(\lambda \right)=0.05$ cm⁻¹ and ${\mu }_s^{\prime }$$\left(\lambda \right)$$=8.0$ cm⁻¹) as the background solution and basically zero flow rate ($BFI\approx 0{\mathrm{cm}}^{-1}/\mathrm{s}$). Experiments were carried out by using the established data acquisition platform, as in Figure 8 imaging calculation was performed by the NL-Bregman-TV algorithm; the interpolation results are shown in Figure 9.

For “tubular” heterogeneous bodies, fill a glass tube with $0.8$ mm OD (outside diameter) and $0.4$ cm ID (inside diameter) with a background solution and many solid heterogeneous bodies (used to simulate the complex scattering environment inside the tissue) and steadily increase output from 0 mL/h to 600 mL/h in an increment of 100 mL/h using a peristaltic pump.

The experiments were carried out by using the established data acquisition platform, as Figure 8, and the imaging calculation by using the NL-Bregman-TV algorithm and interpolation results are shown in Figure 10. We used the histogram similarity formula to calculate the similarity between the interpolated image and the original generated image. The histogram similarity formula is mentioned in section four Formula (25). The calculation result of the similarity of the interpolated images of the solid and “tubular” heterogeneous bodies is shown in

Table 1. Image similarity comparison.

	Cross	Strip	100 mL/h	200 mL/h	300 mL/h	400 mL/h	500 mL/h	600 mL/h	Average
bicubic interpolation	0.9780	0.9602	0.9313	0.9418	0.9556	0.9076	0.9145	0.8763	0.9332

, and the average value of the similarity reached $0.9332$.

Contour extraction was performed on the image interpolated from the reconstructed images of the solid and “tubular” flowing heterogeneous bodies. The results are shown in Figure 11 and Figure 12, and the area of the heterogeneous bodies was calculated, and the results are presented in

Table 2. Normalized results of heterogeneous objects regional area.

	Cross	Strip	100 mL/h	200 mL/h	300 mL/h	400 mL/h	500 mL/h	600 mL/h	Maximum Deviation	Mean Square Error
original image	1	1	1	1	1	1	1	1	0	0
bicubic interpolation	0.9498	1.0177	0.8291	0.8318	0.7932	1.0171	0.8805	0.9714	0.1181	0.0069

. We normalized the area of the abnormal blood flow region calculated on the original abnormal blood flow profile extraction method and the interpolated image. The results are shown in Table 2. It can be seen from the table that the mean deviation of this set of data is $0.1181$ and the mean variance is $0.0069$.

Based on the above discussion and experiments, the DCT image obtained by the NL-Bregman-TV imaging algorithm can be interpolated by the bicubic interpolation method to obtain a high-resolution image. Such an image can be processed by the histogram-based threshold segmentation and morphological method to obtain the abnormal blood flow contour which is very close to the original image.

7. Discussion

Through the above analysis and experiments, it can be seen that the abnormal blood flow outline obtained by our proposed method was very close to the original image.

In the experiment, we used cross-shaped solid gel heterogeneous bodies to simulate the abnormal lesions tissue. The blood flow of the heterogeneous bodies can be considered to be zero. For “tubular” heterogeneous materials, a peristaltic pump is used to change the flow rate of the Imitation solution in the tube to simulate abnormal changes in blood flow in the blood vessels within the tissue. The experimental results show that the solid gel heterogeneous bodies image’s similarity between the low-pixel original image and the interpolated image of the abnormal tissue is higher than “tubular” heterogeneous bodies.

In terms of the area calculated by the abnormal blood flow contour obtained by the histogram based threshold segmentation and morphology method proposed in this paper, the area contained in the contour of the solid gel heteroplasm is closer to the area contained in the original image contour.

Therefore, we believe that our proposed method of abnormal blood flow contour extraction for DCT images can locate the abnormal blood flow and extract the contour. It is more accurate to extract the contour of a heterogeneous object with a blood flow velocity of basically zero. So, it is more suitable for the location and contour calculation of the areas such as nodules in similar tissues which abnormal blood flow is near zero.

At present, the blood flow measurement often adopts ultrasonic Doppler and laser Doppler technology [32,33,34]. The former measures blood flow in large blood vessels, while the latter measures blood flow in microvessels and the monitoring depth is about 1–3 mm. Other technologies with the function of human deep blood flow imaging [35,36] (such as magnetic resonance perfusion imaging technology, computerized tomography, etc.) require large and expensive equipment, and it is difficult to achieve dynamic and continuous blood flow imaging. According to the changes in different optical parameters in biological tissues, NIR diffuse light technology can detect and characterize the changes in tissue function from the metabolic level. The technology allows for convenient, fast and real-time measurements of human tissue. DCT uses more combination of light source and detector to obtain more measurement data and reconstruct the three-dimensional spatial distribution of blood flow, which can obtain the spatial blood flow contrast of tissues (such as the contrast between tumors and surrounding normal tissues). It provides more comprehensive and accurate blood flow information, which is more conducive to the clinical diagnosis of doctors.

The disadvantage of using NIR diffused light technology to obtain blood flow is that it is unable to obtain deeper (larger than 2 cm) blood flow changes. In addition, the technology calculates the movement status of red blood cells in the tissue by detecting the change in scattered light on the tissue surface. Therefore, the displacement deviation between the optical probe and the measured tissue will introduce noise to the BFI fitting. Thus blood flow detection is more sensitive to movement changes.

8. Summary

The spatial distribution of blood flow can be obtained by means of near-infrared diffuse light correlation tomography (blood flow imaging), and the spatial blood flow contrast of tissues can be quickly obtained to monitor abnormal blood flow. Due to the impact of detector volume and detection depth, only a limited number of light source-detector (S-D) pairs can be set, and blood flow imaging can be realized by the NL-Bregman-TV imaging algorithm. In this paper, an image interpolation technique was proposed to solve the problem that the pixels of the image were too low to meet the practical requirements. The parameter index of the normalized similarity was proposed to help judge the effect of the interpolation method on the resolution of this kind of image. Aiming at the extraction of abnormal regions, a contour extraction method of abnormal blood flow was constructed by combining histogram-based threshold segmentation and morphological processing. The clear and smooth image contour can provide favorable conditions for subsequent blood flow abnormal localization. The simulation results of solid and “tubular” flowing heterogeneous body phantoms showed that the abnormal blood flow contours can be accurately located and extracted by the proposed method.