CC BY
5DOI 10.24412/cl-37136-2023-1-25-29
STUDY OF CHANGES IN THE ATTENUATION COEFFICIENT OF TISSUE WITH DEFORMATION ACCORDING TO OCT DATA
EVGENY SHERSTNEV1, ALEXANDER MOISEEV1 AND GRIGORY GELIKONOV1
1A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, Russia
ABSTRACT
Optical coherence tomography (OCT) is an interferometric method for visualizing the structure of objects. One of the implementations of OCT is spectral-domain OCT. In this method, the source light is split into two parts. One of them is directed to the reference mirror, and the second to the object under study. Light reflects off both the mirror and the object. Then the spectrum of the sum of the reflected signals is recorded by a spectrometer, which, as a rule, is based on a diffraction grating (Fig. 1). The constant component is removed from the resulting spectrum. After that, the Fourier transform is performed. The result will be a depth distribution of the reflected signal.
Figure 1: Simplified OCT setup with spectrometer. S—low-coherent light source; C—coupler; M—reference
mirror; O—object.
The main application of OCT is non-invasive imaging of biological tissues in medical applications. OCT is most widely used in ophthalmology, but other applications are being developed. For example, it can be applied in otorhinolaryngology, neurosurgery, dermatology, etc.
One of the additions to OCT is elastographic studies. There are several implementations of optical coherent elastography. One of them is compression OCE (C-OCE). The probe exerts axial pressure on the sample. To determine the pressure, an additional layer of silicone is used, which is placed between the probe and the object. Young's modulus for this silicone is known, its deformation is determined together with the deformation of the object (Fig. 2).
s
probe
tlS^uv.
str
silicone
Figure 2: Standard C-OCE experiment.
Observation of OCT data, which contain amplitude and phase components, is taken as the basis. Firstly, a frame without pressure is recorded, then axial pressure is applied to the sample, and the next frame is recorded. The phase difference between two frames is calculated. The phase difference is linearly related to the local displacement of points in the image. At the same time, the determination of the phase shift makes it possible to detect even small subpixel shifts. Displacement of local points allows you to determine the local relative deformation. Strain and pressure make it possible to evaluate the stiffness of the material. To determine the pressure, an additional layer of silicone is used, which is placed between the probe and the object. Young's modulus for this silicone is known, its deformation is determined together with the deformation of the object from the phase difference in the image (Fig.3)
Structura OCT lmag*,fram* nr>3 Structura OCT imacw.fram« nr*4
4 4 4 0 13 3
InUrfram* Axial ttrjln.frimo nrM frame lJfl"1
SO 100 ISO 200 290
Figure 3: The principle of image processing in C-OCE.
In this case, an assessment of the change in the optical characteristics of an object during its deformation may be of interest as a source of additional information about the object. It is logical to assume that the change in the optical characteristics of an object during deformation is related to its hardness. Thus, the evaluation of changes in optical characteristics has the potential to determine the elastic characteristics of the sample without the use of phase calculations, which require high system stability. The purpose of this work is to evaluate the change in the optical characteristics of several samples with obviously different mechanical properties.
The attenuation coefficient of sample is an optical property of tissue that can be estimated from optical coherence tomography data. The attenuation coefficient calculation is used to study the properties of white matter [1], as well as in ophthalmology to improve the definition of certain pathologies [2]. There are two main methods for estimating the attenuation coefficient of a sample. For homogeneous tissues, the signal attenuation can be approximated by an exponential function. The second method was first proposed in [3]. It allows you to calculate the attenuation coefficient with depth resolution
ri I[i] (1)
where I is the signal intensity, ^est is the attenuation coefficient. The attenuation coefficient is estimated as the ratio of the signal intensity at a point to the sum of the signal intensities at all subsequent points. This method of calculating the attenuation coefficient has a number of requirements for the correctness of the calculation. Firstly, the calculation will be correct if the object under study has a homogeneous directional diagram in
depth. This condition cannot be guaranteed. The second condition is the need for complete attenuation of the signal by the end of the image. If part of the signal does not decay towards the end of the image, then the sum of the intensities in the denominator of eq.1 will be evaluated incorrectly. This causes a calculation error that increases with depth. The fulfillment of this condition can be assessed from the OCT image. The third requirement is the absence of noise in the OCT image. This requirement is not met. To correct the error caused by the presence of noise, the filtering method proposed by our group in [4]:
_ H\i]-SNR^\i] u m
Hrti = 1_ I^i+lWM =1_ (.N)-jimax-i)
L J if=i+1(/m+wm) ij^c/m+wm)
SNR»[i] = X
(2)
mm =__=_^Jn_
where (N) is the mean noise amplitude, SNR^ is the local signal-to-noise ratio, (Ij+Nj) is the measured OCT signal. A - pixel axial size, i - axial measurement number, imax - total number of pixels in axial direction, ^est[i] - attenuation coefficient value, estimated according to [Vermeer].
Four different samples were selected for the study. There are two plastic phantoms and two biological tissues. Chicken skin and chicken muscle tissue were chosen as biological samples.
The experimental scheme is similar to the C-OCE scheme (Fig. 2). The probe was vertically fixed above the sample. The pressure was exerted due to the upward movement of the surface on which the sample was located. A layer of silicone was placed between the probe and the sample to measure the pressure. The same silicone was used in all four experiments. We assumed that the pressure is directly proportional to the deformation of the silicone. At the current stage, we have limited ourselves to measuring the deformation of silicone. As the pressure changed, OCT images were recorded. To assess the change in the attenuation coefficient, regions near the silicone-sample interface were selected. The areas in each image were divided into 64 rectangular pieces of equal size. The attenuation coefficient was averaged over these rectangles. It should be noted that the condition of complete signal attenuation by the end of the image is not met for plastic phantoms, which can cause some error in estimating the attenuation coefficient for these samples. To estimate the magnitude of the change in the attenuation coefficient, a scatterplot of the dependence of the attenuation coefficient on the relative deformation of the additional layer was plotted. A linear approximation of this dependence was carried out according to
[j. = a ■ d+ /3, (3)
where a and P are the coefficients that are determined during the approximation. a is a slope parameter that characterizes the amount of change in the attenuation coefficient. d is deformation of silicone layer, ^ is attenuation coefficient.
The resulting dependencies and their approximation are shown in Fig. 4. The image also shows the value of the slope parameter for each of the samples. The a parameter is 0.26 1/mm for the hard phantom, 0.49 1/mm for the soft phantom, 0.69 1/mm for chicken muscle tissue, and 1.78 1/mm for chicken skin. The rate of change of the attenuation coefficient is the fastest for chicken skin and the lowest slope parameter corresponds to hard plastic.
Tough plastic
Soft plastic
02 04 06 08
Auxiliary layer relative thickness change
Muscle tissue
Auxiliary layer relative thickness change
Skin
01 02 03 04 OS 06 Auxiliary layer relative thickness change
Auxiliary layer relative thickness change
Figure 4: Experimental dependence of the attenuation coefficient on the deformation of the additional layer for four samples: hard and soft phantoms, chicken muscle tissue and chicken skin
The data obtained show that the attenuation coefficient varies differently for objects with different stiffness. The plastic phantoms turn out to be close to each other both in terms of the average damping coefficient and in the rate of change of the damping coefficient under pressure. In this case, the biological samples turn out to be close in terms of the average attenuation coefficient. At the same time, muscle tissue shows a rate of change in the attenuation coefficient closer to phantoms than to skin. The rate of change in the attenuation coefficient for chicken skin is noticeably higher than for all other samples. Two parameters can be selected to differentiate different samples. By using the rate of change of the attenuation factor and the average value of the damping factor, a sample map can be generated containing the magnitude of these two parameters and the margin of error (Fig.5).
Slope parameter [1/mm]
Figure 5: Parameter map. The vertical axis shows the average attenuation coefficient, and the horizontal axis shows the slope of the linear approximation of the experimental data. Plastic samples are shown in red,
biological samples are shown in green.
The obtained results show the possibility of differentiating objects by the rate of change of the attenuation coefficient, however, at the moment it cannot be guaranteed that the rate of change of the damping coefficient is uniquely related to the hardness of the sample. The next step in the study will be to study the stiffness of the samples and compare the characteristics
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