A Compensation Method for the Change of Single-Electrode Contact Impedance in Electrical Impedance Tomography of the Brain

Abstract

The present invention discloses a compensation method for the change of single - electrode contact impedance in electrical impedance tomography of the brain. This method completes modeling based on the three - layer brain structure information and the conductivity information of each layer; obtains the boundary voltage values and the sensitivity matrix required for reconstruction according to the measured field; simultaneously obtains the change amount of the boundary voltage value when the electrode contact impedance changes and the boundary voltage value when the electrode contact impedance does not change without inclusions; uses the sensitivity matrix obtained when the electrode contact impedance does not change in the forward problem, and according to the compensated boundary voltage value when the electrode contact impedance changes, adopts the L1 regularization method to invert the change value of the conductivity inside the field to achieve image reconstruction. The present invention can effectively suppress the influence of the change of electrode contact impedance on the conductivity distribution, improve the spatial resolution of the reconstructed image, improve the imaging quality, and has great application prospects in electrical impedance tomography when the electrode contact impedance changes.

Description

Technical Field

[0001] The present invention belongs to the technical field of electrical impedance tomography, and particularly relates to a compensation method for the change of single-electrode contact impedance in brain electrical impedance tomography. Background Technique

[0002] Electrical impedance tomography (EIT), as a novel medical imaging technology that can reflect the internal structure and tissue organ function of organisms, has the advantages of being harmless to the human body, capable of multiple measurements, portable device, low cost, and can be used for continuous monitoring in clinical applications compared with traditional imaging examination methods such as computed tomography (CT) and magnetic resonance imaging technology (MRI). Based on the unique superiority of EIT technology, it can play a role in many medical fields, so it is a non-invasive medical imaging technology with great application prospects.

[0003] EIT technology is based on the physical principle that different tissues in the human body have different electrical conductivities. By injecting a safe current into the human body and measuring the potential information on the surface of the measured object, the electrical conductivity distribution or the image of the change in the electrical conductivity distribution inside the human body is reconstructed. Since the electrical conductivity of normal tissues and diseased tissues varies greatly, the location of the lesion and the progress of the disease can be observed based on EIT technology. In EIT measurement, a limited number of electrodes are used for current injection and voltage measurement. The contact impedance between the electrode and the measured object generates an error in the measured boundary voltage value, which in turn affects the image reconstruction. However, the change of contact impedance is a common phenomenon in clinical applications. When brain electrical impedance tomography is used for human dynamic monitoring, with the extension of the monitoring time, the electrode contact impedance will not only change due to the change in the water content of the conductive paste / coupling agent, but also be affected by the change in the human body measurement position and the patient's head movement. Since EIT estimates the unknown electrical conductivity distribution based on the measured boundary voltage value, the boundary voltage value with errors due to the change of electrode contact impedance leads to errors in the reconstructed electrical conductivity distribution. Moreover, in brain EIT imaging, the low-electrical-conductivity skull greatly hinders the current injection into the brain area, making the boundary voltage very small. The influence of electrode contact impedance change on image reconstruction poses a greater challenge than other medical applications.

[0004] Due to the change in electrode contact impedance, it will further affect the measurement of the boundary voltage value, thereby reducing the image reconstruction quality. Currently, various methods have been proposed to solve the problems caused by the change in electrode contact impedance. For example, G. Boverman et al. published in the IEEE Transactions on Biomedical Engineering, Vol. 56, pp. 2762-2772 in 2009, with the article title "Methods for compensating for variable electrode contact in EIT"; Ma Hang et al. published in IEEE Acess, Vol. 7, pp. 95186-95196 in 2019, with the article title "Real-time monitoring of contact impedance from multiple electrode–scalp interfaces during cerebral electrical impedance tomography". In the case of changes in electrode contact impedance, these studies do not involve dealing with the error of the measured boundary voltage value.

[0005] In order to reduce the error introduced by the change in electrode contact impedance in brain electrical impedance tomography to the measurement of the boundary voltage value, and thus improve the image reconstruction quality, the present invention aims at the problems that it is difficult to accurately identify the target due to the change in electrode contact impedance and there are many artifacts in the image background in brain electrical impedance tomography, and proposes a method for compensating the change in single-electrode contact impedance in brain electrical impedance tomography, which effectively suppresses the influence of the change in electrode contact impedance on brain electrical impedance tomography. Summary of the Invention

[0006] The technical problem solved by the present invention is to propose a method for compensating the change in single-electrode contact impedance in brain electrical impedance tomography. This method compensates the boundary voltage value when the electrode contact impedance changes, and performs image reconstruction based on the compensated boundary voltage value. This method can effectively suppress the influence of the change in electrode contact impedance on the conductivity distribution, improve the spatial resolution of the reconstructed image, and thus effectively improve the imaging quality.

[0007] The present invention adopts the following technical solutions to solve the above technical problems. A method for compensating the change in single-electrode contact impedance in brain electrical impedance tomography is characterized in that the specific steps are as follows:

[0008] Step 1: Based on the structural information of the brain target field and the conductivity information of each layer in the field, complete the construction of a three-layer brain model on a computer;

[0009] Step 2: Place 16 electrodes equidistantly and uniformly outside the field to be measured. The electrodes are numbered 1, 2, …, 16 in counterclockwise order. Adopt the mode of relative current excitation, adjacent voltage measurement and non - measurement of the excitation electrode, and collect the boundary voltages under cyclic excitation and cyclic measurement in sequence.

[0010] Step 3: According to the boundary voltage value of the empty field obtained in Step 2, when there is no inclusion in the field, obtain the boundary voltage value U' measured when the contact impedance of a single arbitrary electrode changes. Except for the electrode with the changed contact impedance, the contact impedances of other electrodes do not change. Further obtain the change amount ΔU of the boundary voltage value U' when the contact impedance of a single electrode changes and the boundary voltage value U when the contact impedance of this electrode does not change, expressed as ΔU = U' - U, where represents a matrix, and Y is the number of measured voltage values;

[0011] Step 4: When there is no inclusion in the field, according to Step 3, within the pre - set contact impedance change range, change the contact impedance value at a fixed change rate Δ N and measure the boundary voltage values ΔU at N groups of contact impedance change values N , and establish a prior matrix U N composed of Δ N and ΔU P , where Y is the number of voltage values in one frame, and N is the number of contact impedance value changes;

[0012] Step 5: When there is an inclusion in the field, determine the electrodes with changed contact impedance. The specific steps are as follows:

[0013] Step 5.1: Uniformly paste 16 electrodes on the surface of the real measurement field. When the contact impedances of 15 of these electrodes do not change and only the contact impedance value of any single electrode changes, according to Step 3, in the voltage values measured in one frame, the number of relevant voltage values when each electrode serves as a measurement electrode is 24. Taking electrode No. 1 as an example, calculate the number of relevant voltage values when electrode No. 1 serves as a measurement electrode: When sinusoidal excitation currents are injected into electrode No. 1 and electrode No. 9, electrode No. 1 cannot serve as a measurement electrode, that is, there are no relevant voltage values, and the number of relevant voltage values is 0; when sinusoidal excitation currents are injected into electrode No. 2 and electrode No. 10, electrode No. 1 serves as a measurement electrode, and the voltage value between electrode No. 16 and electrode No. 1 can be collected, but the voltage value between electrode No. 1 and electrode No. 2 cannot be collected, that is, the number of relevant voltage values is 1; when sinusoidal excitation currents are injected into electrode No. 3 and electrode No. 11, electrode No. 1 serves as a measurement electrode, and the voltage values between electrode No. 16 and electrode No. 1 and between electrode No. 1 and electrode No. 2 can be collected, that is, the number of relevant voltage values is 2; and so on. Finally, the total number of relevant voltage values when electrode No. 1 serves as a measurement electrode is 24. According to the above method, it can be known that the number of relevant voltage values when other electrodes serve as measurement electrodes is the same as that when electrode No. 1 serves as a measurement electrode;

[0014] Step 5.2: Calculate the average relative change of the 24 relevant voltage values when each electrode serves as a measurement electrode according to Step 5.1. The calculation formula is:

[0015]

[0016] In the formula, ARCM represents the average relative change, is the voltage value after the contact impedance changes, represents the voltage value when the contact impedance does not change, n = 1, 2, 3,..., 24;

[0017] Step 5.3: Calculate the average relative change of the 24 relevant voltage values when each of the 16 electrodes serves as a measurement electrode in turn. By comparison, the electrode with the changed contact impedance is the most affected, and it is the electrode with the largest average relative change of the relevant voltage values. According to this method, the electrode with the changed contact impedance is judged;

[0018] Step Six: Calculate the degree of change of the electrode contact impedance. When there are inclusions in the field and the electrodes with changed contact impedance have been determined, it is necessary to judge the degree of change of the electrode contact impedance. The specific steps are as follows:

[0019] When there are inclusions in the field, obtain the boundary voltage value of one frame when the contact impedance of a single arbitrary electrode changes And obtain the boundary voltage value of one frame when the contact impedance does not change Boundary voltage change The calculation formula is:

[0020]

[0021] To find the average relative change in the boundary voltage change per frame, the calculation formula is:

[0022]

[0023] From this, the relationship between the average relative change in the boundary voltage change and the corresponding change in contact impedance is obtained. A linear fit is performed on this relationship to further determine the degree of change in the electrode contact impedance;

[0024] Step 7: After obtaining the electrodes with changed contact impedance and the degree of their change through Step 5 and Step 6, according to the calculated degree of change in contact impedance and the prior matrix U P , extract the boundary voltage value ΔU corresponding to this degree of change for one frame N , and the compensated boundary voltage value can be obtained:

[0025] U c = U i - U0 - ΔU N

[0026] In the formula, U i is the boundary voltage value measured when the contact impedance changes under actual conditions, and U0 is the boundary voltage value measured when the contact impedance does not change and there are no inclusions;

[0027] Step 8: Image reconstruction. In electrical impedance tomography of the brain, the inverse problem is ill-posed and ill-conditioned. To overcome this problem, an image reconstruction strategy using the L1 regularization method is selected. Let b = U c , and the conductivity distribution is obtained by minimizing the objective function:

[0028]

[0029] In the formula, represents the estimated conductivity, α is a regularization parameter that balances the weights between the fidelity term and the regularization term, is the fidelity term, ||g||1 is the penalty term, C is the sensitivity matrix, and g is the change in conductivity;

[0030] Using the Alternating Direction Method of Multipliers (ADMM) algorithm to constrain the objective function, its Lagrangian augmented function is expressed as:

[0031]

[0032] In the formula, L Ais the Lagrangian augmented function, where m and h are the constraint functions of g and Cg - b respectively, β and γ represent the augmented Lagrangian multipliers, χ1 and χ2 represent the penalty parameters for balancing weights. Then, the optimization problem is divided into several sub - problems for solution to obtain the optimized conductivity distribution, and the conductivity distribution information obtained is used for image reconstruction.

[0033] Further defined, the specific process of collecting the boundary voltage under cyclic excitation and cyclic measurement in step one is as follows: First, inject a sinusoidal excitation current through electrode 1 and electrode 9, measure the voltage values between other adjacent electrodes, then measure the voltage value between electrode 2 and electrode 3, measure the voltage value between electrode 3 and electrode 4, and so on. A total of 12 voltage values can be obtained. Then, change the excitation electrode pair, inject a sinusoidal excitation current through electrode 2 and electrode 10, measure the voltage values between other adjacent electrodes, and obtain 12 voltage values. Cycle the excitation 16 times, and a total of 192 voltage values are obtained as one frame. According to the boundary voltage value of the empty field without inclusions, the sensitivity matrix C can be calculated. The calculation formula is:

[0034]

[0035] In the formula, C ij is the sensitivity coefficient of the j - th electrode pair to the i - th electrode pair, Ω represents the measured field domain, ▽ is the gradient operator, φ i and φ j are the potential distributions of the i - th electrode pair and the j - th electrode pair in the field domain when the excitation currents are I i and I j respectively.

[0036] The beneficial effects of the present invention are as follows: The present invention proposes a compensation method for the change of single - electrode contact impedance in brain electrical impedance tomography. First, a priori matrix between the boundary voltage change and the contact impedance change rate is obtained from the theoretical basis, then the relative average change of 24 relevant voltage values when each electrode is used as a measurement electrode is calculated to determine the electrode with the changed contact impedance, and finally, the boundary voltage values with errors are compensated. This method can effectively suppress the influence of electrode contact impedance change on the conductivity distribution, improve the spatial resolution of the reconstructed image, and thus effectively improve the imaging quality, having great potential in brain electrical impedance tomography under the change of electrode contact impedance. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flow chart of a compensation method for the change of single - electrode contact impedance in brain electrical impedance tomography provided by the present invention;

[0038] Figure 2 is the three - layer structure of the circular brain of the electrical resistance tomography system of the present invention, the mode of excitation current and measurement voltage, and the electrode distribution;Figure 2 In: 1 - excitation current, 2 - measured voltage, 3 - electrode, 4 - inclusion, 5 - scalp layer, 6 - skull layer, 7 - brain tissue layer;

[0039] Figure 3 It is the reconstructed image when the electrode contact impedance of Model A and Model B does not change.

[0040] Figure 4 It is a schematic diagram of the image reconstruction results before compensating the boundary voltage value and after compensating the boundary voltage value by the method proposed in the present invention when the single - electrode contact impedance of Model A changes to different degrees.

[0041] Figure 5 It is a schematic diagram of the image reconstruction results before compensating the boundary voltage value and after compensating the boundary voltage value by the method proposed in the present invention when the single - electrode contact impedance of Model B changes to different degrees. Specific embodiments

[0042] Combined with the accompanying drawings and embodiments, a compensation method for single - electrode contact impedance change in brain electrical impedance tomography provided by the present invention will be described in detail.

[0043] A compensation method for single - electrode contact impedance change in brain electrical impedance tomography according to the present invention reduces the error introduced by measuring the boundary voltage value in brain electrical impedance tomography, improves the image reconstruction quality, and compensates the boundary voltage value under the change of electrode contact impedance to suppress the influence of electrode contact impedance change on the quality of the reconstructed image, aiming at the problems that it is difficult to accurately identify the target due to the change of electrode contact impedance and there are many artifacts in the image background.

[0044] As Figure 1 shown, it is a flow chart of a compensation method for single - electrode contact impedance change in brain electrical impedance tomography provided by the present invention, which is divided into the following steps:

[0045] Step 1: Based on the structural information of the brain target field and the conductivity information of each layer in the field, complete the construction of a three - layer brain model on a computer.

[0046] Step 2: Place 16 electrodes equidistantly and uniformly outside the field to be measured. The electrodes are numbered 1, 2, …, 16 in counterclockwise order. Adopt the mode of relative current excitation, adjacent voltage measurement, and non-measurement of the excitation electrodes, and sequentially collect the boundary voltages under cyclic excitation and cyclic measurement. Specifically: First, inject a sinusoidal excitation current through electrode No. 1 and electrode No. 9, and measure the voltage values between other adjacent electrodes. For example, measure the voltage value between electrode No. 2 and electrode No. 3, measure the voltage value between electrode No. 3 and electrode No. 4, and so on. A total of 12 voltage values can be obtained. Then, change the excitation electrode pair, inject a sinusoidal excitation current through electrode No. 2 and electrode No. 10, and measure the voltage values between other adjacent electrodes to obtain 12 voltage values. Cycle through the excitation 16 times, and a total of 192 voltage values are obtained as one frame. According to the boundary voltage values of the empty field without inclusions, the sensitivity matrix C can be calculated. The calculation formula is:

[0047]

[0048] In the formula, C ij is the sensitivity coefficient of the jth electrode pair to the ith electrode pair. Ω represents the field to be measured, ▽ is the gradient operator, and φ i , φ j are the potential distributions in the field when the excitation currents of the ith electrode pair and the jth electrode pair are I i , I j respectively.

[0049] Step 3: According to the boundary voltage values of the empty field obtained in Step 2, when there are no inclusions in the field, obtain the boundary voltage value U' measured when the contact impedance of a single arbitrary electrode changes. Except for the electrode with the changed contact impedance, the contact impedances of other electrodes do not change. Further obtain the change amount ΔU of the boundary voltage value U' when the contact impedance of a single electrode changes and the boundary voltage value U when the contact impedance of this electrode does not change, expressed as ΔU = U' - U. In the formula represents the matrix, and Y is the number of measured voltage values.

[0050] Step 4: When there are no inclusions in the field, according to Step 3, within the preset range of contact impedance changes, change the contact impedance value at a fixed change rate Δ N , and measure the boundary voltage values ΔU N at N sets of contact impedance change values. Establish a priori matrix U N composed of Δ N and ΔU P . Among them, Y is the number of voltage values in one frame, and N is the number of contact impedance value changes.

[0051] Step 5. When inclusions are present in the field, determine the electrode with a changed contact impedance. The specific steps are as follows:

[0052] Step 5.1. Uniformly paste 16 electrodes on the surface of the actual measurement field. When the contact impedances of 15 of these electrodes do not change and only the contact impedance value of any single electrode changes. According to Step 3, in the voltage values measured in one frame, the number of relevant voltage values when each electrode is used as a measurement electrode is 24. Taking electrode No. 1 as an example, calculate the number of relevant voltage values when electrode No. 1 is used as a measurement electrode: When a sinusoidal excitation current is injected between electrode No. 1 and electrode No. 9, electrode No. 1 cannot be used as a measurement electrode, that is, there is no relevant voltage value, and the number of relevant voltage values is 0; when a sinusoidal excitation current is injected between electrode No. 2 and electrode No. 10, electrode No. 1 is used as a measurement electrode, and the voltage value between electrode No. 16 and electrode No. 1 can be collected, but the voltage value between electrode No. 1 and electrode No. 2 cannot be collected, that is, the number of relevant voltage values is 1; when a sinusoidal excitation current is injected between electrode No. 3 and electrode No. 11, electrode No. 1 is used as a measurement electrode, and the voltage values between electrode No. 16 and electrode No. 1 and between electrode No. 1 and electrode No. 2 can be collected, that is, the number of relevant voltage values is 2; and so on. Finally, the total number of relevant voltage values when electrode No. 1 is used as a measurement electrode is 24. According to the above method, it can be known that the number of relevant voltage values when other electrodes are used as measurement electrodes is the same as that when electrode No. 1 is used as a measurement electrode.

[0053] Step 5.2. Calculate the average relative change of the 24 relevant voltage values when each electrode is used as a measurement electrode according to Step 5.1. The calculation formula is:

[0054]

[0055] In the formula, ARCM represents the average relative change, is the voltage value after the contact impedance changes, represents the voltage value when the contact impedance does not change, and n = 1, 2, 3,..., 24.

[0056] Step 5.3. Calculate the average relative change of the 24 relevant voltage values when each of the 16 electrodes is used as a measurement electrode in turn. By comparison, the electrode with a changed contact impedance is the one most affected, and it is the electrode with the largest average relative change of the relevant voltage values. According to this method, the electrode with a changed contact impedance can be judged.

[0057] Step 6. Calculate the degree of change in the electrode contact impedance. When inclusions are present in the field and the electrode with a changed contact impedance has been determined, it is necessary to judge the degree of change in the electrode contact impedance. The specific steps are as follows:

[0058] When inclusions are present in the field, obtain the boundary voltage value of one frame when the contact impedance of a single arbitrary electrode changes and obtain the boundary voltage value of one frame when the contact impedance remains unchanged Boundary voltage change The calculation formula is as follows:

[0059]

[0060] To find the average relative change of the boundary voltage change of one frame, the calculation formula is as follows:

[0061]

[0062] Thus, the relationship between the average relative change of the boundary voltage change and its corresponding contact impedance change is obtained. Linear fitting is performed on this relationship, and then the degree of change in the electrode contact impedance can be determined.

[0063] Step 7. The electrodes with changed contact impedance and the degree of their change are obtained through Step 5 and Step 6. According to the prior matrix U P obtained in Step 4 from the calculated degree of change in contact impedance, extract the boundary voltage value ΔU corresponding to one frame of this degree of change N , and the compensated boundary voltage value can be obtained:

[0064] U c = U i - U0 - ΔU N

[0065] where U i is the boundary voltage value measured when the contact impedance changes under actual conditions, and U0 is the boundary voltage value measured when the contact impedance has no change and no inclusions are present.

[0066] Step 8. Image reconstruction. In electrical impedance tomography of the brain, the inverse problem is ill-posed and ill-conditioned. To overcome this problem, an image reconstruction strategy using the L1 regularization method is selected. Let b = U c , and the conductivity distribution is obtained by minimizing the objective function:

[0067]

[0068] where represents the estimated conductivity, α is a regularization parameter that balances the weights between the fidelity term and the regularization term, is the fidelity term, ||g||1 is the penalty term, C is the sensitivity matrix, and g is the conductivity change.

[0069] Furthermore, the alternating direction multiplier method (ADMM) algorithm is adopted. The objective function is constrained, and its Lagrangian augmented function is expressed as:

[0070]

[0071] In the formula, L A is the Lagrangian augmented function, m and h are the constraint functions of g and Cg-b respectively, β and γ represent the augmented Lagrange multipliers, and χ1 and χ2 represent the penalty parameters for balancing weights. Then, the optimization problem is divided into several sub-problems for solution to obtain the optimized conductivity distribution, and the conductivity distribution information obtained is used for image reconstruction.

[0072] As Figure 2 shown, for the scalp layer 5, skull layer 6, and brain tissue layer 7 of the circular brain in the electrical impedance tomography system, the modes of the excitation current 1 and the measured voltage 2, the inclusions 4 are inside the field area, and 16 electrodes 3 are evenly distributed on the outer wall of the field area.

[0073] As Figure 3 shown, image reconstructions were performed on two models without contact impedance changes. The true distribution of the inclusions in the brain is as Figure 3 shown in the first row, and the second row is the reconstructed image when the electrode contact impedance does not change. It can be clearly seen that when the electrode contact impedance does not change, the circular inclusions are well reconstructed. And the reconstruction quality of model A is better than that of model B because the sensitivity of brain EIT around the boundary is stronger than that in the center and the resolution is higher.

[0074] As Figure 4 shown, it is a schematic diagram of the image reconstruction results before compensating the boundary voltage value and after compensating the boundary voltage value by the method proposed in the present invention when the contact impedance of electrode No. 1 in model A changes to different degrees. The electrode contact impedance is changed to: 540Ω, 690Ω, 750Ω, 850Ω, and 960Ω respectively. It can be seen that without compensating the boundary voltage value, the greater the change degree of the electrode contact impedance, the more distorted the inclusion shape, and obvious artifacts can be observed in the reconstructed image; while after compensating the boundary voltage value, the reconstructed image has been greatly improved. It can be seen that the method proposed in the present invention effectively improves the quality of image reconstruction.

[0075] As Figure 5As shown, it is a schematic diagram of the image reconstruction results before compensating the boundary voltage value and after compensating the boundary voltage value by the method proposed in the present invention when the contact impedance of electrode No. 10 in Model B changes to different degrees. The electrode contact impedance is changed to: 450Ω, 510Ω, 570Ω, 660Ω, and 750Ω respectively. It can be seen that without compensating the boundary voltage value, the change in electrode contact impedance has a greater impact on Model B. When the degree of change in contact impedance increases, the inclusions become increasingly blurred and even disappear within the field, and serious artifacts are observed in the entire reconstructed image; while after compensating the boundary voltage value, the clear inclusions and background image are restored in the reconstructed image, effectively improving the quality of image reconstruction. Even when the inclusions disappear due to a large change in electrode contact impedance, the inclusions can still be effectively reconstructed. It can be seen that the method proposed in the present invention can effectively reduce the influence of the change in electrode contact impedance on the quality of image reconstruction.

[0076] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for compensating for changes in single - electrode contact impedance in electrical impedance tomography of the brain, characterized in that The specific steps are as follows: Step 1: Based on the structural information of the brain target field and the conductivity information of each layer within the field, construct a three-layer brain model on a computer; Step 2: Place 16 electrodes evenly at equal distances outside the measured field. The electrodes are numbered 1, 2, …, 16 in counterclockwise order. Adopt the mode of relative current excitation, adjacent voltage measurement, and non-measurement of the excitation electrode, and sequentially collect the boundary voltages under cyclic excitation and cyclic measurement; Step 3: According to the empty-field boundary voltage value obtained in Step 2, when there are no inclusions in the field domain, the boundary voltage value U' measured when the contact impedance of a single arbitrary electrode changes is obtained. Except for the electrode with the changed contact impedance, the contact impedances of other electrodes do not change. Further, the change amount ΔU of the boundary voltage value U' when the contact impedance of a single electrode changes and the boundary voltage value U when the contact impedance of this electrode does not change is obtained, expressed as ΔU = U' - U, where represents a matrix, and Y is the number of measured voltage values; Step 4. When there are no inclusions in the field, according to Step 3, within the preset contact impedance change range, with a fixed change rate Δ N change the contact impedance value, and measure the boundary voltage values ΔU at N groups of contact impedance change values N , and establish a prior matrix U N composed of Δ N and ΔU P , where Y is the number of voltage values in one frame, and N is the number of contact impedance value changes; Step 5: When there are inclusions within the field, determine the electrodes with changed contact impedance. The specific steps are as follows: Step 5.1: Paste 16 electrodes evenly on the surface of the actual measurement field. When the contact impedances of 15 of these electrodes do not change and only the contact impedance value of any single electrode changes, according to Step 3, in the voltage values measured in one frame, the number of relevant voltage values when each electrode is used as a measurement electrode is 24. Taking the 1st electrode as an example, calculate the number of relevant voltage values when the 1st electrode is used as a measurement electrode: Inject sinusoidal excitation current between the 1st electrode and the 9th electrode. The 1st electrode cannot be used as a measurement electrode, that is, there is no relevant voltage value, and the number of relevant voltage values is 0; Inject sinusoidal excitation current between the 2nd electrode and the 10th electrode. The 1st electrode is used as a measurement electrode, and the voltage value between the 16th electrode and the 1st electrode can be collected, but the voltage value between the 1st electrode and the 2nd electrode cannot be collected, that is, the number of relevant voltage values is 1; Inject sinusoidal excitation current between the 3rd electrode and the 11th electrode. The 1st electrode is used as a measurement electrode, and the voltage values between the 16th electrode and the 1st electrode and between the 1st electrode and the 2nd electrode can be collected, that is, the number of relevant voltage values is 2; and so on. Finally, the total number of relevant voltage values when the 1st electrode is used as a measurement electrode is 24. According to the above method, it can be known that the number of relevant voltage values when other electrodes are used as measurement electrodes is the same as that when the 1st electrode is used as a measurement electrode; Step 5.2: Calculate the average relative change of the 24 relevant voltage values when each electrode is used as a measurement electrode according to Step 5.

1. The calculation formula is: where ARCM represents the average relative change, is the voltage value after the contact impedance changes, represents the voltage value when the contact impedance does not change, and n = 1, 2, 3,..., 24; Step 5.3: Calculate the average relative change of the 24 relevant voltage values when each of the 16 electrodes is used as a measurement electrode in turn. By comparison, the electrode with changed contact impedance is most affected, and it is the electrode with the largest average relative change of relevant voltage values. According to this method, determine the electrodes with changed contact impedance; Step 6: Calculate the degree of change in electrode contact impedance. When there are inclusions within the field and the electrodes with changed contact impedance have been determined, it is necessary to judge the degree of change in electrode contact impedance. The specific steps are as follows: When inclusions are contained in the field, obtain the boundary voltage value of one frame when the contact impedance of a single arbitrary electrode changes And obtain the boundary voltage value of one frame when the contact impedance does not change Boundary voltage change amount The calculation formula is as follows: Find the average relative change of the boundary voltage change amount in one frame. The calculation formula is: Thus, obtain the relationship between the average relative change of the boundary voltage change amount and its corresponding contact impedance change amount, perform linear fitting on this relationship, and further determine the degree of change in electrode contact impedance; Step 7: From the electrode with the changed contact impedance and the degree of its change obtained in Steps 5 and 6, according to the degree of contact impedance change obtained by calculation, and based on the prior matrix U obtained in Step 4 P , extract a frame of boundary voltage value ΔU corresponding to the degree of change N , and the compensated boundary voltage value can be obtained: U c = U i - U0 - ΔU N where U i is the boundary voltage value measured when the contact impedance changes under actual conditions, and U0 is the boundary voltage value measured when the contact impedance does not change and no inclusions are included; Step 8, Image reconstruction. In electrical impedance tomography of the brain, the inverse problem is ill-posed and ill-conditioned. To overcome this problem, an image reconstruction strategy using the L1 regularization method is selected. Let b = U c , and the conductivity distribution is obtained by minimizing the objective function as follows: wherein represents the estimated conductivity, α is a regularization parameter that balances the weights between the fidelity term and the regularization term, is the fidelity term, ||g||1 is the penalty term, C is the sensitivity matrix, and g is the change in conductivity; Adopt the Alternating Direction Method of Multipliers (ADMM) algorithm to constrain the objective function. Its Lagrangian augmented function is expressed as: where L A is the Lagrangian augmented function, m and h are the constraint functions of g and Cg - b respectively, β and γ represent the augmented Lagrangian multipliers, χ1 and χ2 represent the penalty parameters for balancing weights. Then, the optimization problem is divided into several sub - problems for solution to obtain the optimized conductivity distribution, and the image reconstruction is carried out based on the obtained conductivity distribution information.

2. The method for compensating the change of single electrode contact impedance in electrical impedance tomography of the brain according to claim 1, characterized in that: The specific process of collecting the boundary voltage under cyclic excitation and cyclic measurement in Step 1 is as follows: First, a sinusoidal excitation current is injected through the 1st electrode and the 9th electrode, and the voltage values between other adjacent electrodes are measured. Then, the voltage value between the 2nd electrode and the 3rd electrode is measured, and the voltage value between the 3rd electrode and the 4th electrode is measured, and so on. A total of 12 voltage values can be obtained. Next, the excitation electrode pair is changed, and a sinusoidal excitation current is injected through the 2nd electrode and the 10th electrode, and the voltage values between other adjacent electrodes are measured to obtain 12 voltage values. By performing this cyclic excitation 16 times, a total of 192 voltage values are obtained as one frame. Based on the boundary voltage values of the empty field without inclusions, the sensitivity matrix C can be calculated, and the calculation formula is: where C ij is the sensitivity coefficient of the j-th electrode pair to the i-th electrode pair, Ω represents the measured field domain, is the gradient operator, φ i and φ j are the potential distributions in the field domain when the excitation currents of the i-th electrode pair and the j-th electrode pair are I i and I j respectively.

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