A conductivity visualization method for electrical impedance tomography of the brain

Abstract

The application discloses a conductivity visualization method for brain electrical impedance tomography, which combines a Tikhonov regularization method with a denoising algorithm to realize brain imaging. According to the relative boundary voltage measurement and the sensitivity matrix required for reconstruction of a measured field, the Tikhonov regularization method is used to solve an initial conductivity change, and then the denoising algorithm is combined to obtain an optimized conductivity change. The specific process is as follows: a minimum objective function is designed; initialization parameters are set; an alternating minimization method is used to update the value of the solution; it is judged whether the parameters meet the limited conditions; it is judged whether the iteration is ended; and according to the finally obtained conductivity change and coordinate position information, an image is reconstructed. The method can effectively improve the spatial resolution of the reconstructed image, and then improve the imaging quality, and has wide applicability and great application potential in brain electrical impedance tomography.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of electrical tomography, and particularly relates to a conductivity visualization method for brain electrical impedance tomography. BACKGROUND

[0002] Medical imaging is a key part of clinical procedures, which provides the possibility for diagnosis, monitoring and treatment of human diseases. At present, many medical imaging techniques have been developed, among which, computed tomography (CT) and magnetic resonance imaging (MRI) are commonly used for clinical diagnosis. However, CT is radioactive, and MRI is expensive. In recent years, electrical impedance tomography (EIT) has attracted considerable research interest of scholars. Compared with CT and MRI, EIT has the characteristics of portability, non-invasiveness and low cost, and is more suitable for bedside monitoring of patients. Due to its various advantages, EIT shows great potential in medical applications, such as breast cancer detection, chest tomography and brain imaging.

[0003] As a devastating brain disease, intracranial hemorrhage is known for its high mortality rate and poor prognosis. In order to reduce the mortality rate of patients and improve the effect of prognosis, accurate imaging examination is crucial in clinical treatment. It is well known that the change of pathological tissue will lead to the change of conductivity distribution, which provides the possibility for monitoring brain hemorrhage with EIT technology. In brain imaging based on EIT technology, a pair of opposite electrodes attached to the scalp are injected with a safe current, and the boundary voltage between the remaining electrode pairs is measured to recover the conductivity distribution in the detection area. However, the inverse problem of electrical impedance tomography is severely ill-conditioned, which will lead to poor reconstruction quality. Especially in brain imaging, due to the low conductivity of the skull, it becomes more difficult to reconstruct the conductivity distribution. In order to solve this problem, the regularization method has proved to be an effective method, by adding a regularization term in the objective function, the solution of the inverse problem can be stabilized. For example, Haoting Li et al. published in Physiological Measurement, Vol. 38, pp. 1776-1790, in 2017, the article name is Unveiling the development of intracranial injury using dynamic brain EIT: an evaluation of current reconstruction algorithms. Among various regularization-based reconstruction methods, Tikhonov method is simple, stable and fast, and has been widely used. However, the image clarity reconstructed by Tikhonov method is not high, which will lead to inaccurate information of the target object in reconstruction. At present, there are some methods combined with Tikhonov method to improve the image reconstruction quality, such as F. Margotti published in Inverse Problem, Vol. 32, document number 125012, in 2016, the article name is Mixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in banach spaces. However, the above Tikhonov combination method is mainly around the reconstruction of conductivity distribution in the field with simple structure and regular boundary, and there is less research on the target area of head with complex structure.

[0004] In order to improve the spatial resolution of the reconstructed image, especially to improve the quality of brain imaging, the application provides a conductivity visualization method for brain electrical impedance tomography, which combines the Tikhonov regularization method with the denoising algorithm, and can effectively improve the image reconstruction quality. SUMMARY

[0005] The technical problem solved by the application is to provide a conductivity visualization method for brain electrical impedance tomography, which improves the spatial resolution of the reconstructed image by combining the Tikhonov regularization method with the denoising algorithm, and improves the imaging quality.

[0006] The application adopts the following technical scheme to solve the above technical problem, a conductivity visualization method for brain electrical impedance tomography, characterized by the following specific steps:

[0007] Step S1, according to the shape information of the brain target field and the conductivity information in the field, a standard model is constructed on the computer;

[0008] Step S2, the relative boundary voltage measurement value b and the sensitivity matrix A required for reconstruction of the four typical models are obtained respectively, and the specific process is as follows:

[0009] Step S201, 16 electrodes are uniformly distributed outside the measured field, a mode of relative current excitation adjacent voltage measurement and non-measurement excitation electrode is adopted, the boundary voltage under the cycle excitation cycle measurement is sequentially collected, a total of 192 measurement values are obtained, the relative boundary voltage measurement value b is the difference between the boundary voltage measurement value b0 of the empty field without inclusions and the boundary voltage measurement value b1 of the field with inclusions, that is, the relative boundary voltage measurement value b = b1-b0;

[0010] Step S202, the sensitivity matrix A is calculated according to the boundary voltage measurement value of the empty field without inclusions, combined with the sensitivity theory, and the calculation formula is as follows: Wherein, A ij is the sensitivity coefficient of the jth electrode pair to the ith electrode pair, φ i , φ j are the field potential distributions of the ith electrode pair and the jth electrode pair when the excitation currents are I i , I j , respectively, s N represents the measurement field; is a gradient operator;

[0011] Step S3, the electrical tomography is regarded as a linear ill-posed problem b≈A·g, and the Tikhonov regularization algorithm objective function is constructed: The solution is: g=(A T A+λI)-1 A T b, where λ is a regularization parameter, g is the conductivity change, and I is an identity matrix;

[0012] Step S4, the minimization objective function is designed as:

[0013]

[0014] where ξ e is an auxiliary variable, S is a ill-conditioned matrix, g * is the conductivity change obtained by the Tikhonov regularization algorithm in step S3, g * is the optimized conductivity change, h(g * ) is a fidelity term, and h(g * ) is a prior term;

[0015] Step S5, the pseudo-inverse matrix is introduced into the minimization objective function, and the transformation is:

[0016]

[0017] where is a semi-norm;

[0018] Step S6, the unconstrained problem in the minimization objective function is converted into a constrained problem minimization form:

[0019]

[0020] The constraint condition is replaced by and is replaced by Then, the minimization form of the constrained problem of the minimization objective function is:

[0021]

[0022] where δ is a design parameter;

[0023] Step S7, the alternating minimization method is adopted to solve the minimization objective function, and the following is obtained:

[0024]

[0025] Step S701, the closed solution of is solved, and the following is obtained: where I n is an identity matrix, and k is the iteration number;

[0026] Step S702, the fast Fourier transform is adopted to solve and the following is obtained: where ω is a regulation factor, F{·} is a fast Fourier transform operator;

[0027] In step S8, the parameters δ and ω should satisfy the following conditions:

[0028]

[0029] The conditions can be obtained by using the fast Fourier transform as follows:

[0030]

[0031] In step S9, the optimized conductivity change g is solved. * The iteration solving process is as follows:

[0032] In step S901, the initial parameters are set: the initial iteration number k=0, and the maximum iteration number is k max The initial conductivity change is g The design parameter δ, the regulation factor ω, and the regulation factor step size Δω are set.

[0033] In step S902, g is updated.

[0034] In step S903, g is updated.

[0035] In step S904, it is judged whether δ and ω satisfy the conditions in step S8 and k>1, if yes, the next operation is performed; if not, the iteration process is restarted: k=0, ω=ω+Δω, and g and g

[0036] In step S905, it is judged whether the iteration satisfies the iteration termination condition k≤k max , if yes, the iteration is terminated; if not, k=k+1 is set, and the iteration solving is continued by returning to step S902.

[0037] In step S906, the conductivity change g is updated. The updated conductivity change is used for image reconstruction according to the coordinate position information.

[0038] Compared with the prior art, the present application has the following beneficial effects: the present application proposes a conductivity visualization method for brain electrical impedance tomography, the initial conductivity change is calculated by the Tikhonov regularization method, and then the optimized conductivity change is obtained by combining the denoising algorithm, and finally the image reconstruction of the brain region is realized. The method can effectively improve the spatial resolution of the reconstructed image, and then improve the imaging quality, and the method has great application potential in brain medical imaging. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 A flow chart of a conductivity visualization method for brain electrical impedance tomography provided by the present application;

[0040] Figure 2 A model of a single section of a skull model measured field, electrode distribution, excitation current and measured voltage of the present application, in which: 1-measured field, 2-measured voltage, 3-electrode, 4-excitation current;

[0041] Figure 3 A graph of image reconstruction results of the Tikhonov method and the method provided by the present application under noise-free conditions for four models;

[0042] Figure 4 A schematic diagram of image reconstruction results of the Tikhonov method and the method provided by the present application under noise conditions for four models;

[0043] Figure 5 A blur radius (BR) of reconstruction results of four models, in which: (a) is the BR value under noise-free conditions; (b) is the BR value under noise conditions. DETAILED DESCRIPTION

[0044] The present application provides a conductivity visualization method for brain electrical impedance tomography in detail in combination with the drawings and examples.

[0045] The conductivity visualization method for brain electrical impedance tomography provided by the present application aims to improve the quality of brain imaging reconstruction, and improves the spatial resolution of the reconstructed image by combining the Tikhonov regularization method with a denoising algorithm to effectively improve the quality of the reconstructed image in view of the problems of image artifacts and unclear image background.

[0046] As shown in Figure 1 The specific steps of the conductivity visualization method for brain electrical impedance tomography provided by the present application are as follows:

[0047] Step S1, according to the shape information of the brain target field and the conductivity information in the field, the standard model construction is completed on the computer;

[0048] Step S2, the relative boundary voltage measurement value b and the sensitivity matrix A required for reconstruction of four typical models are obtained, and the specific process is as follows:

[0049] Step S201, 16 electrodes are uniformly distributed outside the measured field at equal intervals, a mode of adjacent voltage measurement and excitation electrode non-measurement is adopted, and the boundary voltage under cyclic excitation and cyclic measurement is collected in sequence, 192 measurement values are obtained, and the relative boundary voltage measurement value b is the difference between the empty field boundary voltage measurement value b0 without inclusions and the boundary voltage measurement value b1 of the field with inclusions, that is, the relative boundary voltage measurement value b = b1-b0;

[0050] Step S202, the sensitivity matrix A is calculated according to the empty field boundary voltage measurement value without inclusions combined with the sensitivity theory, and the calculation formula is: Wherein, A ij is the sensitivity coefficient of the jth electrode pair to the ith electrode pair, φ i , φ j are the field potential distributions of the ith electrode pair and the jth electrode pair when the excitation currents are I i , I j respectively; s N represents the measurement field; is a gradient operator;

[0051] Step S3, regarding the electrical tomography as a linear ill-posed problem b≈A·g, a Tikhonov regularization algorithm target function is constructed: Its solution is: g=(A T A+λI) -1 A T b, wherein λ is a regularization parameter, g is the conductivity change, and I is a unit matrix;

[0052] Step S4, the minimum target function is designed as:

[0053]

[0054] Wherein, ξ e is an auxiliary variable, S is a pathological matrix, is the conductivity change obtained by the Tikhonov regularization algorithm in step S3, g * is the optimized conductivity change, is a fidelity term, and h(g * ) is a priori term;

[0055] Step S5, the pseudo-inverse matrix is introduced into the minimum target function, which is transformed into:

[0056]

[0057] Wherein, is a semi-norm;

[0058] Step S6, the unconstrained problem in the minimization objective function is converted into a constrained problem minimization form:

[0059]

[0060] The constraint condition is replaced by and is replaced by Then the minimization form of the constrained problem of the minimization objective function is:

[0061]

[0062] Wherein, δ is a design parameter;

[0063] Step S7, the alternating minimization method is adopted to solve the minimization objective function, and the following is obtained:

[0064]

[0065] Step S701, the closed solution of is solved, and the following is obtained: Wherein I n is a unit matrix, and k is the iteration number;

[0066] Step S702, the fast Fourier transform is adopted to solve and the following is obtained: Wherein ω is an adjustment factor, and F{·} is a fast Fourier transform operator;

[0067] Step S8, parameter selection, the design parameter δ and the adjustment factor ω should satisfy the following limited conditions:

[0068]

[0069] The limited condition for adopting the fast Fourier transform is:

[0070]

[0071] Step S9, the optimized conductivity change g * is solved, and the iteration solving process is as follows:

[0072] Step S901, setting the initial parameters: the initial iteration number k = 0, the maximum iteration number is k max , the initial conductivity change is set as the design parameter δ, the adjustment factor ω, and the adjustment factor step size Δω;

[0073] Step S902, updating

[0074] Step S903, updating

[0075] Step S904, judge whether satisfies the condition in step S8 and k>1, if yes, proceed to the next step; if not, restart the iteration process: k=0, ω=ω+Δω, update and

[0076] Step S905, judge whether the iteration satisfies the iteration termination condition k≤k max , if yes, the iteration is terminated; if not, set k=k+1, and return to step S902 to continue the iteration solution;

[0077] Step S906, update the conductivity change The updated conductivity change is reconstructed according to the coordinate position information.

[0078] As Figure 2 shown, it is a single section of the skull model measured field 1, excitation current 4, measurement voltage 2 mode and electrode 3 distribution, 16 electrodes 3 are evenly distributed outside the field.

[0079] Four typical skull models are selected as examples, and the real distribution of the inclusions in the field is shown in the first row. Figure 3 The first row shows that the COMSOL Multiphysics and MATLAB R2018a are used for simulation modeling in this embodiment, the simulation parameters are set according to the real human tissue parameters, the brain background conductivity is set to the brain cerebrospinal fluid conductivity 0.15 S / m, and the conductivity of the bleeding target inclusion is set to 0.8 S / m. Figure 3 The second row is the reconstructed image obtained by using the Tikhonov method, and it can be seen that there are many artifacts in the background, and the reconstructed inclusion is blurred. Especially for model B, the reconstruction quality is relatively poor, which is due to the fact that the sensitivity of the field center is much lower than that of the field boundary. In contrast, Figure 3 The third row is the reconstructed image obtained by using the method provided by the present application, for the four models A, B, C and D, the inclusion can be well reconstructed, and there is almost no artifact in the background. The results show that the method provided by the present application can effectively improve the image quality of brain imaging.

[0080] As Figure 4As shown in the figure, the image reconstruction results of the Tikhonov method and the method provided in the application under the condition that the system has noise are shown for four models. Under the influence of noise, the inclusions reconstructed by the Tikhonov method are further deformed, and more obvious artifacts are generated in the background. Compared with the noise-free condition, the reconstructed image of the method provided in the application is almost not affected by noise, the inclusions can be well reconstructed, and the image background is clear. The results show that the method provided in the application has good anti-noise performance. In general, the application provides an alternative method for brain imaging, which can effectively improve the image quality of brain imaging and improve the spatial resolution of the reconstructed image.

[0081] As Figure 5 shown, the blur radius (Blur Radius, BR) of the reconstruction results of the Tikhonov method and the method provided in the application for four models is shown. Wherein (a) is the BR value under the noise-free condition, (b) is the BR value under the noise condition. The expression is as shown in the following formula, and the smaller the blur radius value of the reconstructed image, the better the quality of the reconstructed image.

[0082]

[0083] In the formula, A S is the area of the target region, and A0 is the area of the entire field.

[0084] It can be seen that the blur radius of the reconstructed image of the method provided in the application is much smaller than the blur radius of the reconstructed image of the Tikhonov algorithm, which further confirms the superiority of the method provided in the application, which can effectively improve the quality of the reconstructed image. Even under the condition of noise, it can also show good performance.

[0085] The above only describes the preferred embodiments of the application and is not used to limit the application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A method for visualizing electrical conductivity in brain electrical impedance tomography, characterized in that... The specific steps are as follows: Step S1: Based on the shape information of the target field in the brain and the conductivity information within the field, complete the standard model construction on the computer. Step S2 involves obtaining the relative boundary voltage measurement value b and sensitivity matrix A required for reconstruction for each of the four typical models. The specific process is as follows: Step S201: Sixteen electrodes are evenly distributed at equal intervals outside the field to be measured. The boundary voltage under cyclic excitation and cyclic measurement is collected sequentially using the mode of relative current excitation and adjacent voltage measurement without excitation electrode measurement. A total of 192 measurement values ​​are obtained. The relative boundary voltage measurement value b is the difference between the boundary voltage measurement value b0 of the empty field without inclusions and the boundary voltage measurement value b1 of the field with inclusions, that is, the relative boundary voltage measurement value b = b1 - b0. Step S202, the sensitivity matrix A is calculated based on the measured value of the empty field boundary voltage without inclusions, combined with sensitivity theory. The calculation formula is as follows: Among them, A ij Let φ be the sensitivity coefficient of the j-th electrode pair to the i-th electrode pair. i φ j The excitation currents for the i-th electrode pair and the j-th electrode pair are respectively I. i I j Time-domain electric potential distribution; s N Represents the measurement field; For gradient operators; Step S3: Treating electrical tomography as a linear ill-posed problem b≈A·g, construct the objective function of the Tikhonov regularization algorithm: The solution is: g = (A T A+λI) -1 A T b, where λ is the regularization parameter, g is the change in conductivity, and I is the identity matrix; Step S4, design the objective function to be minimized as follows: Where, ξ e As auxiliary variables, S is the ill-conditioned matrix. Let g be the change in conductivity obtained by the Tikhonov regularization algorithm in step S3. * This represents the optimized change in conductivity. To ensure fidelity, h(g) * ) is a priori; Step S5: Introduce a pseudo-inverse matrix into the minimization objective function. Transformed into: in, It is a seminorm; Step S6: Transform the unconstrained problem in the objective function into a constrained problem minimization form: Constraints Replace with And Replace with The minimization form of the objective function constraint problem is: Where δ is the design parameter; Step S7: Solve the objective function using the alternating minimization method, and obtain: Step S701, Solve The closed solution is obtained. Among them I n Let k be the identity matrix and k be the number of iterations. Step S702: Solve using Fast Fourier Transform. get in ω is the adjustment factor, and F{·} is the Fast Fourier Transform operator; Step S8, parameter selection: The design parameter δ and adjustment factor ω should meet the following constraints: Using the Fast Fourier Transform, we can obtain the following constraints: Step S9, solve for the optimized change in conductivity g. * The iterative solution process is as follows: Step S901, set initialization parameters: initial iteration count k = 0, maximum iteration count is k max Change in initial conductivity Design parameters δ, adjustment factor ω, adjustment factor step size Δω; Step S902, Update Step S903, Update Step S904: Determine whether δ and ω satisfy the constraints in step S8 and k > 1. If yes, proceed to the next step; otherwise, restart the iteration process: k = 0, ω = ω + Δω, and update according to steps S902 and S903 respectively. and Step S905: Determine whether the iteration satisfies the iteration termination condition k≤k max If yes, the iteration terminates; otherwise, set k = k + 1 and return to step S902 to continue iterating. Step S906, update the change in conductivity. The updated conductivity change is used to reconstruct the image based on the coordinate location information.

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