CN114601443B - Electrical impedance tomography method for correcting offset mismatch of single electrode - Google Patents
Electrical impedance tomography method for correcting offset mismatch of single electrode Download PDFInfo
- Publication number
- CN114601443B CN114601443B CN202210175973.3A CN202210175973A CN114601443B CN 114601443 B CN114601443 B CN 114601443B CN 202210175973 A CN202210175973 A CN 202210175973A CN 114601443 B CN114601443 B CN 114601443B
- Authority
- CN
- China
- Prior art keywords
- electrode
- offset
- value
- angle
- electrodes
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 58
- 238000002593 electrical impedance tomography Methods 0.000 title claims abstract description 34
- 239000011159 matrix material Substances 0.000 claims abstract description 35
- 230000033001 locomotion Effects 0.000 claims abstract description 29
- 230000035945 sensitivity Effects 0.000 claims abstract description 23
- 230000008859 change Effects 0.000 claims abstract description 15
- 238000012937 correction Methods 0.000 claims abstract description 12
- 238000003384 imaging method Methods 0.000 claims abstract description 9
- 238000006073 displacement reaction Methods 0.000 claims abstract description 6
- 230000005284 excitation Effects 0.000 claims description 28
- 238000005259 measurement Methods 0.000 claims description 27
- 230000008569 process Effects 0.000 claims description 13
- 238000009826 distribution Methods 0.000 claims description 10
- 238000004070 electrodeposition Methods 0.000 claims description 7
- 238000004364 calculation method Methods 0.000 claims description 6
- 125000004122 cyclic group Chemical group 0.000 claims description 6
- 238000004458 analytical method Methods 0.000 claims description 3
- 238000010276 construction Methods 0.000 claims description 3
- 238000002347 injection Methods 0.000 claims description 3
- 239000007924 injection Substances 0.000 claims description 3
- 239000000243 solution Substances 0.000 claims description 3
- 230000005477 standard model Effects 0.000 claims description 3
- 238000004422 calculation algorithm Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000002591 computed tomography Methods 0.000 description 2
- 238000013135 deep learning Methods 0.000 description 2
- 230000006870 function Effects 0.000 description 2
- 238000010030 laminating Methods 0.000 description 2
- 238000012544 monitoring process Methods 0.000 description 2
- 238000003325 tomography Methods 0.000 description 2
- 238000002940 Newton-Raphson method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000006399 behavior Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000000747 cardiac effect Effects 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000002059 diagnostic imaging Methods 0.000 description 1
- 201000010099 disease Diseases 0.000 description 1
- 208000037265 diseases, disorders, signs and symptoms Diseases 0.000 description 1
- 230000005684 electric field Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000030136 gastric emptying Effects 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 239000012535 impurity Substances 0.000 description 1
- 230000002401 inhibitory effect Effects 0.000 description 1
- 238000002595 magnetic resonance imaging Methods 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000036285 pathological change Effects 0.000 description 1
- 231100000915 pathological change Toxicity 0.000 description 1
- 230000004796 pathophysiological change Effects 0.000 description 1
- 230000035790 physiological processes and functions Effects 0.000 description 1
- 230000002685 pulmonary effect Effects 0.000 description 1
- 230000005855 radiation Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 238000009827 uniform distribution Methods 0.000 description 1
- 238000009423 ventilation Methods 0.000 description 1
- 238000012800 visualization Methods 0.000 description 1
Classifications
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves
- A61B5/053—Measuring electrical impedance or conductance of a portion of the body
- A61B5/0536—Impedance imaging, e.g. by tomography
Landscapes
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
- Biomedical Technology (AREA)
- Medical Informatics (AREA)
- Biophysics (AREA)
- Pathology (AREA)
- Engineering & Computer Science (AREA)
- Radiology & Medical Imaging (AREA)
- Heart & Thoracic Surgery (AREA)
- Physics & Mathematics (AREA)
- Molecular Biology (AREA)
- Surgery (AREA)
- Animal Behavior & Ethology (AREA)
- General Health & Medical Sciences (AREA)
- Public Health (AREA)
- Veterinary Medicine (AREA)
- Apparatus For Radiation Diagnosis (AREA)
- Measurement And Recording Of Electrical Phenomena And Electrical Characteristics Of The Living Body (AREA)
Abstract
The invention discloses an electrical impedance tomography method for single electrode offset mismatch correction, which is characterized in that boundary voltage and sensitivity matrix required by reconstruction are obtained according to a detected field, a priori matrix between boundary voltage variation and offset angle is obtained by theoretically calculating potential values on the boundary of the detected field when the single electrode is offset, meanwhile, a moving electrode can be determined by combining with a jacobian matrix of electrode displacement, the azimuth and angle of electrode offset are obtained, and mismatched voltage data are corrected. And inverting the conductivity change value in the field area by a regularization method by utilizing a sensitivity matrix obtained in the forward problem when the electrode is not deviated and combining the boundary voltage data corrected when the single electrode is deviated, so as to realize image reconstruction. The invention can effectively overcome model parameter errors generated when the single electrode moves, inhibit the influence of the single electrode movement on the image reconstruction quality, improve the spatial resolution of the reconstructed image and improve the imaging quality.
Description
Technical Field
The invention belongs to the technical field of electrical tomography, and particularly relates to an electrical impedance tomography method for single electrode offset mismatch correction.
Background
Electrical Impedance Tomography (EIT), ELECTRICAL IMPEDANCE, is a potential non-invasive medical imaging technique that measures induced voltages at boundaries by injecting a safe current into a specific part of the human body. Based on these voltage data, the conductivity distribution in the region to be measured can be visually displayed. It is well known that pathological changes are associated with changes in conductivity distribution, and therefore human diseases can be diagnosed using EIT techniques. Compared with traditional Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), EIT has the advantages of portability, non-invasiveness, no radiation, low cost, high time resolution and the like. EIT is of great interest today in various medical applications.
For EIT techniques, visualization may be achieved by developing various image reconstruction algorithms. Sensitivity-based algorithms such as regularization, landweber and Newton-Raphson methods, and the like. In this type of approach, the sensitivity matrix is an essential element obtained in the forward mapping. It is well known that the sensitivity distribution is affected not only by the change in the shape of the boundary, but also by the position of the electrode. In solving the EIT problem, an EIT model of the uniform distribution of the electrodes is usually built, so that the calculated sensitivity matrix is reliable with the electrodes fixed on the boundary, and the reconstructed conductivity distribution is accurate. However, in medical application of EIT, the position of the electrode may be different, on one hand, when the EIT is used for monitoring in clinical application, physiological functions such as pulmonary ventilation, gastric emptying, cardiac cycle and the like of the patient can affect the change of the electrode position, on the other hand, when the EIT is used for monitoring at the bedside for a long time, the patient cannot be kept still for a long time, and the change of the body posture of the patient can also cause the movement of the electrode position. In this case the sensitivity matrix will change and if the image reconstruction is still performed with the previously calculated sensitivity matrix, the reconstructed image will be heavily distorted or even severely distorted. Thus, accurate detection of human pathophysiological changes presents a significant challenge.
At the same time, it is very difficult to determine the position of the electrode on the surface of the human body very accurately. If the electrode movement direction can be determined in the reconstruction process, the accuracy of model parameters is improved, and the quality of EIT reconstructed images is improved very effectively. Currently, various methods have been proposed to solve the problems caused by the movement of the electrodes. For example, m.soleimani et al, 2006, volume 27, pages 103-113, physiological measurements (Physiological Measurement), entitled image reconstruction of conductivity changes and electrode movement in electrical impedance imaging (Imaging of conductivity CHANGES AND electrode movement in EIT); smyl et al, 2020, published in journal of IEEE instruments and measurements (IEEE Transactions on Instrumentation and Measurement), volume 69, pages 6030-6044, entitled "optimizing electrode position in two-dimensional Electrical impedance tomography Using deep learning" (Optimizing electrode positions in-D ELECTRICAL IMPEDANCE tomograph using DEEP LEARNING). Most of the researches are to optimize EIT technology around algorithms, inhibit the influence of electrode movement on a reconstructed image through a more stable algorithm, and ensure the accuracy of the reconstructed image. In the case of an electrode position shift, little is studied to process mismatched voltage data.
In order to overcome model parameter errors generated during electrode movement, inhibit the influence of electrode movement on image reconstruction quality and improve the spatial resolution of reconstructed images, the invention provides an electrical impedance tomography method for single electrode offset mismatch correction, which can effectively overcome the influence of electrode movement on image reconstruction quality and further effectively improve the quality of reconstructed images, aiming at the problems of artifact caused by electrode movement, unclear image background and the like.
Disclosure of Invention
The invention solves the technical problem of providing an electrical impedance tomography method for correcting the offset mismatch of a single electrode, which corrects voltage data during electrode offset and then reconstructs an image according to the corrected data and a sensitivity matrix with conductivity change. The method can effectively overcome model parameter errors generated when the electrodes move, inhibit the influence of the electrode movement on the image reconstruction quality, improve the spatial resolution of the reconstructed image and improve the imaging quality.
The invention adopts the following technical proposal to solve the technical problems, and is an electrical impedance tomography method for correcting single electrode offset mismatch, which is characterized by comprising the following specific steps:
Step S1, uniformly distributing M electrodes on a field to be measured, numbering the M electrodes as 1,2, … and M according to anticlockwise respectively, completing standard model construction on a computer, adopting a mode of measuring current excitation voltage and not measuring excitation electrodes, and collecting boundary voltage under cyclic excitation and cyclic measurement, wherein the specific process is as follows: step S101, injecting sinusoidal excitation current between the electrode I and the electrode II, measuring voltage values between other M-2 adjacent electrodes, namely injecting sinusoidal excitation current between the electrode I and the electrode II, measuring voltage values between the electrode III and the electrode IV, measuring voltage values between the electrode IV and the electrode V, and the like, and finally measuring voltage values between the electrode M-1 and the electrode M to obtain M-3 voltage values in total; step S102, the injection electrode is converted from the original electrode I and electrode II to the electrode II and electrode III, the measurement voltage is the voltage value between M-2 adjacent electrodes except the electrode II and electrode III, M-3 voltage values are obtained in total, M (M-3) measurement values are obtained in total by the same, M (M-3)/2 independent measurement values are obtained by the reciprocity theorem, the sensitivity matrix S is calculated according to the boundary measurement voltage of an empty field without inclusion, and the calculation formula is:
Where S jk is the sensitivity coefficient of the kth electrode pair to the jth electrode pair, The field potential distribution of the jth electrode pair and the kth electrode pair when the excitation current is I j、Ik respectively; /(I)Is a gradient operator;
Step S2, establishing a polar coordinate system, and calculating potential values of all places on the boundary when a single electrode is deviated by adopting an analytic method under the condition that the field does not contain inclusions, wherein the potential values are as follows:
Wherein phi (ρ, θ) is the potential value of any place on the measured field, ρ is the polar diameter, θ is the polar angle, I is the excitation current, σ is the conductivity, δ is the angle of the electrode relative to the center of the circle, θ s+1 and θ s are the polar angles corresponding to two adjacent excitation electrodes respectively, and Δ ζ is the angle of single electrode movement;
Step S3: according to the potential values of the boundary obtained in the step S2, calculating to obtain a boundary voltage value U 1 when the single electrode moves under the condition of no inclusion in the field, and further obtaining the variation delta U m, namely delta U m＝U1-U0, of the boundary voltage value U 1 when the single electrode moves relative to the boundary voltage value U 0 when the electrodes are uniformly distributed, wherein H is the number of measurement, M is the number of the electrodes, and M is more than or equal to 1 and less than or equal to M;
Step S4, when the field does not contain inclusions, the positions of the M electrodes are changed one by one along the boundary of the field, the direction of position offset is divided into clockwise and anticlockwise, wherein the offset angle of the mth electrode is delta m, and the prior matrix P m between the delta U m and the offset angle delta m is obtained by further calculation by combining the delta U m obtained in the step S3, wherein the prior matrix P m is P m＝ΔUm/Δm, and the offset angle of the mth electrode is delta m W is the number of offset angles;
step S5, when the field contains inclusions, determining the offset azimuth and the offset angle of the single electrode, wherein the specific process is as follows:
step S501, setting a range of a single electrode offset angle, and attaching M electrodes on the surface of a real measurement object, wherein M-1 electrode positions are the same as the attachment positions of the electrodes in the step S1, and the rest 1 electrodes are electrodes with offset positions, wherein the range of the electrode offset angle is 0.5-10 degrees;
Step S502, calculating the electrode offset angle, obtaining a group of boundary voltage measurement values Y when single electrodes are offset under the mode of adjacent current excitation at the moment t, The offset Δx can be obtained according to Tikhonov regularization:
The solution is as follows:
Δx＝(Jx TJx+λxI)-1Jx TY
In the formula, the offset Lambda x is the regularization parameter, J x is the jacobian matrix of electrode displacement,I is an identity matrix;
In order to adjust the relation between the calculated value delta of the offset angle and the actual value delta * of the offset angle, a scale factor omega is introduced, and delta=omega.Deltax, and the scale factor omega is adjusted to ensure that delta is approximately equal to delta *, wherein positive signs and negative signs in the calculated results respectively represent the anticlockwise movement and the clockwise movement of the electrode;
Step S503, preliminarily determining the azimuth and angle of the single electrode offset, taking the mth electrode offset as an example: based on the calculated value delta of the offset angle calculated in step S502, With the lower limit of 3/4 times the maximum absolute value, i.e.Wherein, delta i is the i-th calculated value in M calculated values delta of the offset angle, i is more than or equal to 1 and less than or equal to M, the offset electrode is the M-th or M-1-th according to the limiting condition, and the offset azimuth and angle of any single electrode are preliminarily determined according to the method;
step S504, accurately determining the direction and angle of the single electrode offset, calculating the variation Δu m＝Pm·Δm of the boundary voltage value when the single electrode moves relative to the boundary voltage value when the electrode is uniformly distributed according to the prior matrix P m obtained in step S4 and the direction and angle of the electrode offset preliminarily determined in step S503, for the differential imaging method, comparing the value of the modified boundary voltage difference b ' =u eσ-ΔUm-U0 with the value of the boundary voltage difference b when the electrode does not offset, wherein U eσ is the boundary voltage value when the field contains inclusions and the single electrode offset, U 0 is the boundary voltage value when the field does not contain inclusions and the electrode offset does not exist, calculating the modified boundary voltage difference b m ' when the electrode of m number is offset and the modified boundary voltage difference b m-1 ' when the electrode of m number is offset respectively based on the prior information of the electrode offset of m number or m-1 preliminarily determined in step S503, and quantizing the value of b m ' with the value of b m-1 ' and the boundary voltage difference b when the electrode does not offset respectively, and selecting the value of b m ' to be the closest to the value b m ', i.e. the position of the electrode offset;
step S6: image reconstruction, which regards electrical impedance tomography as a linear uncertainty problem, minimizes the objective function as:
In the method, in the process of the invention, G (G) is a penalty term, and lambda is a regularization parameter; and (3) obtaining a corrected boundary voltage difference value b m 'according to the step S504, setting b=b m', solving the change amount of the conductivity by using the regularization method, and reconstructing an image of the obtained change amount of the conductivity according to the coordinate information.
Further defined, the electrode M has a value in the range of 8, 16 or 32.
Further defined, the sensitivity matrix is specifically: the method comprises the steps of performing subdivision modeling on a detected area by using a finite element method, dividing the detected area into a limited number of small grid units, wherein each small grid unit is a pixel point, and calculating a sensitivity matrix by combining a sensitivity theory.
Further defined, the specific process of image reconstruction is: and inverting the conductivity change value in the field area by a regularization method by utilizing a sensitivity matrix obtained in the forward problem when the electrode is not deviated and combining the boundary voltage difference value data corrected when the electrode is deviated, so as to realize image reconstruction.
The invention has the beneficial effects that: the invention provides an electrical impedance tomography method for single electrode offset mismatch correction, which comprises the steps of firstly, theoretically calculating to obtain a priori matrix between boundary voltage variation and offset angle, and simultaneously, combining with a jacobian matrix of electrode displacement, determining a movable electrode and correcting mismatched voltage data. The method can effectively overcome model parameter errors generated when the electrode moves, inhibit the influence of the electrode movement on the image reconstruction quality, improve the spatial resolution of the reconstructed image, further improve the imaging quality, and has great application potential in the electric conductivity distribution imaging of unavoidable electrode movement.
Drawings
FIG. 1 is a block flow diagram of a single electrode offset mismatch corrected electrical impedance tomography method provided by the present invention;
FIG. 2 is a circular single-section field under test, excitation current and measurement voltage pattern and electrode distribution for a resistive tomography system of the present invention; in fig. 2: 1-field to be measured, 2-measuring voltage, 3-electrode, 4-exciting current and 5-electric field line;
FIG. 3 is a reconstructed image of two models A and B with electrodes uniformly distributed;
FIG. 4 is a schematic diagram of the image reconstruction results before correction of mismatch data and in the method according to the present invention, in the case where the single electrode in model A is shifted counterclockwise by different angles and the single electrode in model B is shifted clockwise by different angles;
FIG. 5 shows the Relative Blur Radii (RBR) of the reconstructed results for two models A and B at different angles of single electrode deflection.
Detailed Description
The invention provides an electrical impedance tomography method for single electrode offset mismatch correction, which is described in detail with reference to the accompanying drawings and embodiments.
The electrical impedance tomography method for correcting the single electrode offset mismatch aims at inhibiting the influence of electrode movement on the image reconstruction quality, aims at solving the problems of artifact problem caused by electrode movement, unclear image background and the like, and overcomes model parameter errors caused by electrode movement by correcting voltage data during electrode offset, thereby effectively improving the quality of reconstructed images.
As shown in fig. 1, a flow chart of an electrical impedance tomography method for single electrode offset mismatch correction provided by the invention comprises the following specific steps:
And S1, uniformly distributing M electrodes on a detected field, numbering the M electrodes as 1,2, … and M according to anticlockwise directions, and completing standard model construction on a computer. The boundary voltage under the cyclic excitation cyclic measurement is collected by adopting a mode that the current excitation voltage is measured and the excitation electrode is not measured, and the specific process is as follows: step S101, injecting sinusoidal excitation current between the electrode I and the electrode II, measuring voltage values between other M-2 adjacent electrodes, namely injecting sinusoidal excitation current between the electrode I and the electrode II, measuring voltage values between the electrode III and the electrode IV, measuring voltage values between the electrode IV and the electrode V, and the like until the voltage values between the electrode M-1 and the electrode M are measured, so as to obtain M-3 voltage values in total; step S102, the injection electrode is converted from the original electrode I and electrode II to the electrode II and electrode III, the measurement voltage is the voltage value between M-2 adjacent electrodes except the electrode II and the electrode III, and M-3 voltage values are obtained in total. And so on to obtain M (M-3) measured values in total, and M (M-3)/2 independent measured values are obtained by the reciprocity theorem. The sensitivity matrix S can be calculated according to the boundary measurement voltage of the empty field without inclusion, and the calculation formula is as follows:
Where S jk is the sensitivity coefficient of the kth electrode pair to the jth electrode pair, The field potential distribution of the jth electrode pair and the kth electrode pair when the excitation current is I j、Ik respectively; /(I)Is a gradient operator.
Step S2, establishing a polar coordinate system, and calculating potential values of all places on the boundary when a single electrode is deviated by adopting an analytic method under the condition that the field does not contain inclusions, wherein the potential values are as follows:
Wherein phi (ρ, θ) is the potential value of any place on the measured field, ρ is the polar diameter, θ is the polar angle, I is the excitation current, σ is the conductivity, δ is the angle of the electrode relative to the center of the circle, θ s+1 and θ s are the polar angles corresponding to two adjacent excitation electrodes respectively, and Δ ζ is the angle of single electrode movement.
And step S3, calculating the boundary voltage value U 1 when the single electrode moves under the condition that the field does not contain impurities according to the potential values of the various places on the boundary obtained in the step S2, and further obtaining the variation delta U m, namely delta U m＝U1-U0, of the boundary voltage value U 1 when the single electrode moves relative to the boundary voltage value U 0 when the electrodes are uniformly distributed. Wherein the method comprises the steps of H is the number of measurement, M is the number of the electrodes, and M is more than or equal to 1 and less than or equal to M.
And S4, when the field does not contain inclusions, changing the positions of the M electrodes one by one along the boundary of the field, and dividing the direction of position offset into clockwise and anticlockwise. The m-th electrode offset angle is delta m, and the prior matrix P m between the delta U m and the offset angle delta m is calculated by combining the delta U m obtained in the step three, wherein the prior matrix P m＝ΔUm/Δm is obtained. Wherein the method comprises the steps ofW is the number of offset angles.
Step S5, when the field contains inclusions, determining the offset azimuth and the offset angle of the single electrode, wherein the specific process is as follows:
Step 501 sets a range of individual electrode offset angles. Laminating M electrodes on the surface of a real measurement object, wherein the positions of the M-1 electrodes are the same as the laminating positions of the electrodes in the step one, the rest 1 electrodes are electrodes with position deviation, and the angle range of the electrode deviation is as follows: 0.5-10 deg.
Step 502, calculating an angle of electrode offset. In the adjacent current excitation mode, at time t, a set of boundary voltage measurements Y at single electrode offset are obtained,The offset Δx can be obtained according to Tikhonov regularization:
The solution is as follows:
Δx＝(Jx TJx+λxI)-1Jx TY
In the formula, the offset Lambda x is regularization parameter, J x is Jacobian matrix of electrode displacement,/>I is an identity matrix.
In order to adjust the relation between the calculated value Δ of the offset angle and the true value Δ * of the offset angle, a scale factor ω is introduced, and Δ=ω·Δx. By adjusting the scale factor ω such that Δ≡Δ *, the positive and negative signs in the calculation represent the counter-clockwise and clockwise movement of the electrode, respectively.
In step 503, the orientation and angle of the individual electrode offset is initially determined. Taking the electrode shift of the m-th electrode as an example: calculated value delta of offset angle calculated according to step S502With the lower limit of 3/4 times the maximum absolute value, i.e.Wherein Delta i is the i-th calculated value (i is more than or equal to 1 is less than or equal to M) in M calculated values of the offset angle Deltaand the offset electrode is the M-th or M-1-th according to the limiting condition. According to the method, the offset azimuth and angle of any single electrode can be preliminarily determined when the single electrode is offset.
The orientation and angle of the individual electrode offset is accurately determined, step 504. According to the prior matrix P m obtained in step S4 and the offset electrode orientation and angle preliminarily determined in step S503, the variation Δu m＝Pm·Δm of the boundary voltage value when the single electrode moves relative to the boundary voltage value when the electrodes are uniformly distributed can be calculated. For the differential imaging method, the modified boundary voltage difference is b' =u eσ-ΔUm-U0, which is approximately equal to the boundary voltage difference b when the electrodes are not offset, where U eσ is the boundary voltage value when the field contains inclusions and the individual electrodes are offset, and U 0 is the boundary voltage value when the field contains no inclusions and the electrodes are not offset. Based on the a priori information of the electrode shift of the m-number or m-1 number preliminarily determined in step S503, the boundary voltage difference b m 'after correction when the electrode shift of the m-number occurs and the boundary voltage difference b m-1' after correction when the electrode shift of the m-1 number occurs are respectively obtained. Further, the value of b m ' is quantitatively compared with the value of b m-1 ' and the boundary voltage difference b when the electrodes are not offset, and the value closest to b is selected from the two values, namely b m ', and the corresponding electrode is the electrode with offset position.
Step S6, reconstructing an image, namely regarding electrical impedance tomography as a linear uncertainty problem, wherein the minimization objective function is as follows:
In the method, in the process of the invention, G (G) is a penalty term, and lambda is a regularization parameter; and (3) obtaining a corrected boundary voltage difference value b m 'according to the step S504, setting b=b m', solving the change amount of the conductivity by using the regularization method, and reconstructing an image of the obtained change amount of the conductivity according to the coordinate information.
As shown in fig. 2, for the circular single-section measured field 1, exciting current 4 and measuring voltage 2 of the electrical impedance tomography system, the electric field lines 5 and the electrodes 3 are distributed, and the electrodes 3 are uniformly distributed on the outer wall of the field by adopting 16.
Two typical medium models are selected as an embodiment, the real distribution of objects in a field is shown in the first row of fig. 3, and the embodiment uses COMSOL Multiphysics and MATLAB R2018a to carry out simulation modeling in combination, wherein simulation parameters are set as follows, the field background conductivity is 0.3S/m, and the conductivity of inclusions is 0.6S/m. The reconstructed image of the second behavior electrodes when uniformly distributed can be obviously seen that the images of the two models can be reconstructed well when the electrodes are uniformly distributed.
As shown in fig. 4, the image reconstruction results before the mismatch data correction and in the method according to the present invention are shown in the schematic diagram of the case that the electrode No. 2 in the model a is offset counterclockwise by different angles and the electrode No. 13 in the model B is offset clockwise by different angles. The angle of the electrode offset is 0.5 degrees, 1 degrees, 2 degrees, 4 degrees and 10 degrees, and it can be seen that the quality of the reconstructed image is affected by the electrode motion, and with the increase of the offset angle, it is difficult or even impossible to reconstruct the inclusion image clearly, and in addition, obvious artifacts can be seen in the background. After the mismatched voltage data is corrected by the method provided by the invention, the quality of the reconstructed image when the electrode is deviated can be effectively improved. Under the condition of small angle offset of the electrode, clear inclusion and background images can be reconstructed. Even when the electrodes are offset at a large angle, the inclusion images can be effectively reconstructed. In general, the invention provides an alternative method for image reconstruction under the condition of clockwise and anticlockwise deflection of the single electrode, can effectively inhibit the influence of the single electrode movement on the image reconstruction quality, and improves the quality of the reconstructed image.
As shown in fig. 5, the relative blur radius (Relative Blur Radius, RBR) is the reconstructed result at different angles of single electrode offset for the two models a and B. The expression is shown in the following formula, and the closer the relative blur radius value of the image is to the reference value 1, the better the reconstructed image quality is.
Where BR 1 is the blur radius at electrode deflection and BR 0 is the true radius of the model.
It can be seen that after the invention corrects the mismatched voltage data, the RBR values of all models under the small-angle displacement of the electrode are close to the reference value 1, and even if the electrode is offset at a large angle, the change of the RBR is obviously smaller than that of the non-corrected RBR. The method has good performance in overcoming the reconstruction problem caused by electrode movement, and can effectively inhibit the influence of electrode movement on the image reconstruction quality, thereby effectively improving the quality of the reconstructed image.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather to enable any modification, equivalent replacement, improvement or the like to be made within the spirit and principles of the invention.
Claims (4)
1. An electrical impedance tomography method for correcting offset mismatch of a single electrode is characterized by comprising the following specific steps:
Step S1, uniformly distributing M electrodes on a field to be measured, numbering the M electrodes as 1,2, … and M according to anticlockwise respectively, completing standard model construction on a computer, adopting a mode of measuring current excitation voltage and not measuring excitation electrodes, and collecting boundary voltage under cyclic excitation and cyclic measurement, wherein the specific process is as follows: step S101, injecting sinusoidal excitation current between the electrode I and the electrode II, measuring voltage values between other M-2 adjacent electrodes, namely injecting sinusoidal excitation current between the electrode I and the electrode II, measuring voltage values between the electrode III and the electrode IV, measuring voltage values between the electrode IV and the electrode V, and the like, and finally measuring voltage values between the electrode M-1 and the electrode M to obtain M-3 voltage values in total; step S102, the injection electrode is converted from the original electrode I and electrode II to the electrode II and electrode III, the measurement voltage is the voltage value between M-2 adjacent electrodes except the electrode II and electrode III, M-3 voltage values are obtained in total, M (M-3) measurement values are obtained in total by the same, M (M-3)/2 independent measurement values are obtained by the reciprocity theorem, the sensitivity matrix S is calculated according to the boundary measurement voltage of an empty field without inclusion, and the calculation formula is:
Where S jk is the sensitivity coefficient of the kth electrode pair to the jth electrode pair, The field potential distribution of the jth electrode pair and the kth electrode pair when the excitation current is I j、Ik respectively; /(I)Is a gradient operator;
Step S2, establishing a polar coordinate system, and calculating potential values of all places on the boundary when a single electrode is deviated by adopting an analytic method under the condition that the field does not contain inclusions, wherein the potential values are as follows:
Wherein phi (ρ, θ) is the potential value of any place on the measured field, ρ is the polar diameter, θ is the polar angle, I is the excitation current, σ is the conductivity, δ is the angle of the electrode relative to the center of the circle, θ s+1 and θ s are the polar angles corresponding to two adjacent excitation electrodes respectively, and Δ ζ is the angle of single electrode movement;
Step S3: according to the potential values of the boundary obtained in the step S2, calculating to obtain a boundary voltage value U 1 when the single electrode moves under the condition of no inclusion in the field, and further obtaining the variation delta U m, namely delta U m＝U1-U0, of the boundary voltage value U 1 when the single electrode moves relative to the boundary voltage value U 0 when the electrodes are uniformly distributed, wherein H is the number of measurement, M is the number of the electrodes, and M is more than or equal to 1 and less than or equal to M;
Step S4, when the field does not contain inclusions, the positions of the M electrodes are changed one by one along the boundary of the field, the direction of position offset is divided into clockwise and anticlockwise, wherein the offset angle of the mth electrode is delta m, and the prior matrix P m between the delta U m and the offset angle delta m is obtained by further calculation by combining the delta U m obtained in the step S3, wherein the prior matrix P m is P m＝ΔUm/Δm, and the offset angle of the mth electrode is delta m W is the number of offset angles;
step S5, when the field contains inclusions, determining the offset azimuth and the offset angle of the single electrode, wherein the specific process is as follows:
step S501, setting a range of a single electrode offset angle, and attaching M electrodes on the surface of a real measurement object, wherein M-1 electrode positions are the same as the attachment positions of the electrodes in the step S1, and the rest 1 electrodes are electrodes with offset positions, wherein the range of the electrode offset angle is 0.5-10 degrees;
Step S502, calculating the electrode offset angle, obtaining a group of boundary voltage measurement values Y when single electrodes are offset under the mode of adjacent current excitation at the moment t, The offset Δx can be obtained according to Tikhonov regularization:
The solution is as follows:
In the formula, the offset Lambda x is regularization parameter, J x is Jacobian matrix of electrode displacement,/>I is an identity matrix;
In order to adjust the relation between the calculated value delta of the offset angle and the actual value delta * of the offset angle, a scale factor omega is introduced, and delta=omega.Deltax, and the scale factor omega is adjusted to ensure that delta is approximately equal to delta *, wherein positive signs and negative signs in the calculated results respectively represent the anticlockwise movement and the clockwise movement of the electrode;
Step S503, preliminarily determining the azimuth and angle of the single electrode offset, taking the mth electrode offset as an example: based on the calculated value delta of the offset angle calculated in step S502, With the lower limit of 3/4 times the maximum absolute value, i.e.Wherein, delta i is the i-th calculated value in M calculated values delta of the offset angle, i is more than or equal to 1 and less than or equal to M, the offset electrode is the M-th or M-1-th according to the limiting condition, and the offset azimuth and angle of any single electrode are preliminarily determined according to the method;
step S504, accurately determining the direction and angle of the single electrode offset, calculating the variation Δu m＝Pm·Δm of the boundary voltage value when the single electrode moves relative to the boundary voltage value when the electrode is uniformly distributed according to the prior matrix P m obtained in step S4 and the direction and angle of the electrode offset preliminarily determined in step S503, for the differential imaging method, comparing the value of the modified boundary voltage difference b ' =u eσ-ΔUm-U0 with the value of the boundary voltage difference b when the electrode does not offset, wherein U eσ is the boundary voltage value when the field contains inclusions and the single electrode offset, U 0 is the boundary voltage value when the field does not contain inclusions and the electrode offset does not exist, calculating the modified boundary voltage difference b m ' when the electrode of m number is offset and the modified boundary voltage difference b m-1 ' when the electrode of m number is offset respectively based on the prior information of the electrode offset of m number or m-1 preliminarily determined in step S503, and quantizing the value of b m ' with the value of b m-1 ' and the boundary voltage difference b when the electrode does not offset respectively, and selecting the value of b m ' to be the closest to the value b m ', i.e. the position of the electrode offset;
step S6: image reconstruction, which regards electrical impedance tomography as a linear uncertainty problem, minimizes the objective function as:
In the method, in the process of the invention, G (G) is a penalty term, and lambda is a regularization parameter; and (3) obtaining a corrected boundary voltage difference value b m 'according to the step S504, setting b=b m', solving the change amount of the conductivity by using the regularization method, and reconstructing an image of the obtained change amount of the conductivity according to the coordinate information.
2. A single electrode offset mismatch corrected electrical impedance tomography method as defined in claim 1, wherein: the value range of the electrode M is 8, 16 or 32.
3. The electrical impedance tomography method of single electrode offset mismatch correction of claim 1, wherein the sensitivity matrix is specifically: the method comprises the steps of performing subdivision modeling on a detected area by using a finite element method, dividing the detected area into a limited number of small grid units, wherein each small grid unit is a pixel point, and calculating a sensitivity matrix by combining a sensitivity theory.
4. The electrical impedance tomography method of single electrode offset mismatch correction according to claim 1, wherein the specific process of image reconstruction is: and inverting the conductivity change value in the field area by a regularization method by utilizing a sensitivity matrix obtained in the forward problem when the electrode is not deviated and combining the boundary voltage difference value data corrected when the electrode is deviated, so as to realize image reconstruction.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210175973.3A CN114601443B (en) | 2022-02-25 | 2022-02-25 | Electrical impedance tomography method for correcting offset mismatch of single electrode |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210175973.3A CN114601443B (en) | 2022-02-25 | 2022-02-25 | Electrical impedance tomography method for correcting offset mismatch of single electrode |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114601443A CN114601443A (en) | 2022-06-10 |
| CN114601443B true CN114601443B (en) | 2024-05-14 |
Family
ID=81859473
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210175973.3A Active CN114601443B (en) | 2022-02-25 | 2022-02-25 | Electrical impedance tomography method for correcting offset mismatch of single electrode |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114601443B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116269303B (en) * | 2023-03-09 | 2024-09-20 | 南京航空航天大学 | Conductivity solving method considering electrode abnormality, imaging method and storage medium |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102961136A (en) * | 2012-11-29 | 2013-03-13 | 中国人民解放军第四军医大学 | Calibration device for electric impedance tomography system |
| EP2762062A1 (en) * | 2013-02-05 | 2014-08-06 | Dräger Medical GmbH | Electro-impedance tomography device and method |
| CN104739407A (en) * | 2013-12-30 | 2015-07-01 | 中国医学科学院生物医学工程研究所 | Electrical impedance tomography method for reducing influence of boundary deformation |
| CN109919844A (en) * | 2019-02-28 | 2019-06-21 | 河南师范大学 | A kind of high-resolution electricity tomography distribution of conductivity method for reconstructing |
-
2022
- 2022-02-25 CN CN202210175973.3A patent/CN114601443B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102961136A (en) * | 2012-11-29 | 2013-03-13 | 中国人民解放军第四军医大学 | Calibration device for electric impedance tomography system |
| EP2762062A1 (en) * | 2013-02-05 | 2014-08-06 | Dräger Medical GmbH | Electro-impedance tomography device and method |
| CN104739407A (en) * | 2013-12-30 | 2015-07-01 | 中国医学科学院生物医学工程研究所 | Electrical impedance tomography method for reducing influence of boundary deformation |
| CN109919844A (en) * | 2019-02-28 | 2019-06-21 | 河南师范大学 | A kind of high-resolution electricity tomography distribution of conductivity method for reconstructing |
Non-Patent Citations (1)
| Title |
|---|
| 电阻抗断层成像中抑制电极移动伪影方法的研究进展;陈荣庆;徐灿华;董秀珍;付峰;;中国医疗设备;20171025(第10期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114601443A (en) | 2022-06-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN101564294B (en) | Method for structural information fused electrical impedance tomography | |
| Harikumar et al. | Electrical impedance tomography (EIT) and its medical applications: A review | |
| Soleimani et al. | Imaging of conductivity changes and electrode movement in EIT | |
| JP5419717B2 (en) | System and method for correcting non-uniform fields | |
| CN110859636B (en) | Dynamic bladder volume measurement method insensitive to urine conductivity | |
| Kauppinen et al. | Sensitivity distribution visualizations of impedance tomography measurement strategies | |
| CN114601444B (en) | Electrical impedance tomography method for inhibiting influence of movement of two electrodes | |
| CN111616708A (en) | Image reconstruction method for accurately identifying cerebral apoplexy intracranial lesion area | |
| CN114601443B (en) | Electrical impedance tomography method for correcting offset mismatch of single electrode | |
| Dimas et al. | Electrical impedance tomography image reconstruction for adjacent and opposite strategy using FEMM and EIDORS simulation models | |
| Dehghani et al. | Incorporating a priori anatomical information into image reconstruction in electrical impedance tomography | |
| Li et al. | Electrical-impedance-tomography imaging based on a new three-dimensional thorax model for assessing the extent of lung injury | |
| CN116869504A (en) | Data compensation method for cerebral ischemia conductivity distribution reconstruction | |
| Shi et al. | A mismatch correction method for electrode offset in electrical impedance tomography | |
| CN112450910B (en) | Boundary measuring device and method for electrical impedance tomography | |
| CN114708350A (en) | Conductivity visualization method for electrical impedance tomography of brain | |
| CN117523089B (en) | Method for solving reconstruction matrix based on discrete training set, three-dimensional imaging method and storage medium | |
| CN116824048B (en) | Sensor, jacobian matrix solving method, three-dimensional imaging system and three-dimensional imaging method | |
| CN109946388B (en) | Electrical/ultrasonic bimodal inclusion boundary reconstruction method based on statistical inversion | |
| Cao et al. | 2D image reconstruction of a human chest by using Calderon's method and the adjacent current pattern | |
| Baysal et al. | Use of a priori information in estimating tissue resistivities-a simulation study | |
| Husain et al. | A neural network-based local decomposition approach for image reconstruction in electrical impedance tomography | |
| Zhang et al. | Survey of EIT image reconstruction algorithms | |
| Kotre | Studies of image reconstruction methods for electrical impedance tomography | |
| Eyuboglu et al. | Limitations to SV determination from APT images |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |