CN112914543A - Electrical impedance tomography method for detecting lung tumor of human body - Google Patents

Electrical impedance tomography method for detecting lung tumor of human body Download PDF

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CN112914543A
CN112914543A CN202110105328.XA CN202110105328A CN112914543A CN 112914543 A CN112914543 A CN 112914543A CN 202110105328 A CN202110105328 A CN 202110105328A CN 112914543 A CN112914543 A CN 112914543A
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王林浩
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Abstract

The invention discloses an electrical impedance tomography method for detecting lung tumor of a human body, which comprises the following steps: (1) according to the field to be measured, obtaining the boundary measurement voltage required by reconstructionVAnd sensitivity matrixS. (2) And setting initialization parameters. (3) And determining an objective function and minimizing the objective function. (4) A solution model of the objective function is started to be calculated. (5) Judging whether the iteration termination condition is met or not, if so, terminating the iteration, and carrying out the next operation; if not, settingk= k+1And jumping back to the step (4), and continuing to iteratively solve. (6) And imaging according to the gray value obtained by the final solution. Compared with a TV method and a TGV method, the method provided by the invention has an obvious effect on the aspect of improving the image reconstruction quality of electrical impedance tomography.

Description

Electrical impedance tomography method for detecting lung tumor of human body
Technical Field
The invention relates to an electrical impedance tomography image reconstruction technology, in particular to an image reconstruction method for improving background definition and realizing accurate reconstruction of a target object, and belongs to the technical field of electrical impedance tomography.
Background
Electrical Impedance Tomography (EIT) is an imaging technique that reconstructs the Electrical conductivity distribution inside a target without damage. The current excitation voltage measurement is the most common working mode, and applies safe current excitation to the electrodes attached to the surface of an object according to the characteristic of uneven distribution of the electrical conductivity of the internal structure of the object, obtains voltage signals through the rest electrodes, and reversely reconstructs the distribution or changed images of the electrical conductivity in the object by using an effective image reconstruction algorithm. The EIT technology has no radiation, fast response, no damage, low cost, portability and other advantages, and thus the EIT technology is widely applied to the fields of earth object surveying, industrial nondestructive testing, biomedical imaging and the like. Particularly, the EIT technology belongs to a new medical detection technology in the biomedical field, has a very good application prospect, and is also popular in current research.
The EIT technology applies excitation to human bodies by adopting safe current, does not radiate the human bodies and cannot cause damage to the human bodies. The device has simple structure, small volume and low production cost, has no special requirement on detection environment, and is suitable for clinically and continuously monitoring the illness state of a patient in real time for a long time. Furthermore, EIT is a predictive imaging technique that can be used to treat diseases of tissues or organs
The disease can be prevented by changing the state of the disease.
Currently, the most adopted regularization methods comprise a Total Variation (TV) regularization method and a Total Generalized Variation (TGV) regularization method, the TV regularization method has good edge preserving performance, but the TV regularization method brings a step artifact phenomenon; although the TGV regularization method effectively reduces the step effect, artifacts still exist in image reconstruction, and in order to solve the problem of the step artifacts generated in the EIT image reconstruction process, the invention provides an image reconstruction method which improves the background definition and simultaneously realizes the accurate reconstruction of a target object, so that sharp edges can be effectively reserved, and the step artifacts in the image reconstruction process can be well inhibited.
Disclosure of Invention
The invention aims to provide an electrical impedance tomography method for detecting human lung tumors, which can effectively reduce step artifacts, improve background definition of reconstructed images and improve anti-noise performance. Compared with a TV method and a TGV method, the method provided by the invention has an obvious effect on the aspect of improving the image reconstruction quality of electrical impedance tomography.
The technical scheme of the invention is as follows: an electrical impedance tomography method for detecting lung tumor of human body,firstly, a sensitivity matrix S is calculated by combining with a sensitivity theory, the method considers the electrical impedance tomography as a linear ill-posed problem Sg-V, S represents the sensitivity matrix, V is a boundary voltage measurement value, and g is a gray value matrix. Then establishing a first-stage gray value
Figure BDA0002917169080000021
The calculation of (2):
Figure BDA0002917169080000022
in the formula (I), the compound is shown in the specification,
Figure BDA0002917169080000023
is a data fidelity item; λ is a trade-off parameter, γ0And gamma1Are respectively used to balance the first derivative terms
Figure BDA0002917169080000024
And a second derivative term | | epsilon (v) | non-woven phosphor1The first and second order parameters of (a);
Figure BDA0002917169080000025
represents the gradient of the gray value matrix g; v is a field variable, ε (v) is a symmetric gradient operator,
Figure BDA0002917169080000026
the superscript T denotes transpose. And the sensitivity matrix is updated in real time in the solving process, so that the sensitivity of the conductivity change area is improved. Then, by processing the function
Figure BDA0002917169080000027
To pair
Figure BDA0002917169080000028
Further performing clarification treatment to obtain the gray value of the second stage
Figure BDA0002917169080000029
The concrete form of (A) is as follows:
Figure BDA00029171690800000210
wherein μ is a threshold value greater than 0;
Figure BDA00029171690800000211
represents 0 and
Figure BDA00029171690800000212
the maximum value of (a) is,
Figure BDA00029171690800000213
represents 0 and
Figure BDA00029171690800000214
the maximum value of (a) is,
Figure BDA00029171690800000215
the value of (A) is the second stage gray value
Figure BDA00029171690800000216
Then judging whether the iteration termination condition is met, namely whether the maximum iteration times reach 300 times so as to obtain the optimal solution, and then using the obtained second-stage gray value
Figure BDA00029171690800000217
And imaging to obtain a human lung detection image.
The invention has the beneficial effects that: compared with a TV regularization method and a TGV regularization method, the electrical impedance tomography method for detecting the lung tumor of the human body provided by the invention has the best image reconstruction quality. The sensitivity of the conductivity change area is more accurate by updating the sensitivity matrix in real time, and meanwhile, in order to eliminate the repeated influence of information in the conductivity unchanged area, the image definition is updated by adopting a threshold disturbance elimination method.
Drawings
FIG. 1 is a block flow diagram of an electrical impedance tomography method for detecting tumors in the lung of a human subject in accordance with the present invention.
FIG. 2 shows the circular single-section field to be measured, the modes of exciting current and measuring voltage and the electrode distribution of the electrical impedance tomography system of the invention.
FIG. 3 is a schematic image reconstruction diagram of the TV regularization method, TGV regularization method and an electrical impedance tomography method for detecting human lung tumor in the present text when selecting two true healthy lung and tumor lung model distributions.
Fig. 4 shows the relative image error and correlation coefficient of two real models reconstructed by the three methods under the same conditions.
In the figure: 1. electrode 2, field 3 to be measured, measuring voltage 4, excitation current.
Detailed Description
An electrical impedance tomography method for detecting human lung tumor of the invention is described with reference to the accompanying drawings and embodiments.
The invention provides an electrical impedance tomography method for detecting human lung tumor, which aims at the problem of step artifact and unclear background generated by the traditional regularization algorithm, takes the solution result of the first stage as a preliminary condition, combines the proposed image reconstruction method, adopts a bidirectional threshold filter function, solves the gray value of the second stage, and selects an optimal value by adaptively selecting regularization parameters and weight factors, thereby obtaining the gray value of the second stage
Figure BDA0002917169080000039
And imaging to finally obtain a human lung detection image.
Fig. 1 shows a flowchart of an electrical impedance tomography method for detecting lung tumor of a human body according to the present invention. The gray value for imaging can be obtained according to the flow chart, and the specific implementation steps are as follows:
the method comprises the following steps: CT scanning is carried out on the human chest by a spiral CT scanner, and a high-precision human chest CT scanning image is obtained. And analyzing and processing the data of the shape of the chest cavity, and finishing the construction of the human chest cavity model on a computer by combining the electrical impedance information of the normal chest cavity of the human body.
Step two: let the personnel of examining sit and stand on the stool, the upper half of the body is perpendicular to ground. The middle point of the connecting line of the two nipples of the person is taken as a starting point, 16 electrodes are sequentially attached to the skin surface of the human body at equal intervals on a plane parallel to the ground, and the 16 electrodes are uniformly distributed around the circumference of the human body. The internal thorax of the human body surrounded by 16 electrodes is the measurement field. Adopting an adjacent mode to carry out current excitation and voltage measurement on the electrode pairs, taking the end of expiration as a reference point, and obtaining a boundary voltage measurement matrix V at a first moment when the person finishes one inspiration1(ii) a At the end of the next exhalation, a boundary voltage measurement matrix V at a second time is obtained2。V1-V2I.e. the boundary voltage measurement matrix V required for imaging.
Step three: a sensitivity matrix S is calculated. And (4) calculating a sensitivity matrix S by combining a sensitivity theory according to the human chest model constructed in the step one and the current excitation in the step two. The elements in the sensitivity matrix are called sensitivity coefficients, and the calculation formula of the sensitivity coefficients is as follows:
Figure BDA0002917169080000031
in the formula, SmnIs the sensitivity coefficient located in the mth row and column of the sensitivity matrix S, m is the number of boundary voltage measurements, and n is the number of pixels of the reconstruction unit;
Figure BDA0002917169080000032
the excitation current of the ith electrode pair is IiThe potential of the nth pixel within the field is measured,
Figure BDA0002917169080000033
the excitation current of the jth electrode pair is IjThe potential of the nth pixel in the field is measured.
Step four: first stage gray value matrix
Figure BDA0002917169080000034
The calculation of (2):
Figure BDA0002917169080000035
in the formula (I), the compound is shown in the specification,
Figure BDA0002917169080000036
is a data fidelity item; λ is a trade-off parameter, γ0And gamma1Are respectively used to balance the first derivative terms
Figure BDA0002917169080000037
And a second derivative term | | epsilon (v) | non-woven phosphor1The first and second order parameters of (a);
Figure BDA0002917169080000038
represents the gradient of the gray value matrix g; v is a field variable, ε (v) is a symmetric gradient operator,
Figure BDA0002917169080000041
the superscript T denotes transpose.
To solve
Figure BDA0002917169080000042
Writing equation (1) in dual form:
Figure BDA0002917169080000043
in the formula, p and q are dual variables, and P, Q are convex sets corresponding to the dual variables respectively.
The solving step of the minimization problem in the formula (2) is as follows:
1. setting parameter initial values:
Figure BDA0002917169080000044
wherein f is an auxiliary variable,
Figure BDA0002917169080000045
is the optimization variable for v and is,
Figure BDA0002917169080000046
is the first even optimization variable, g0Is the initial value of g. The first projection parameter and the second projection parameter are τ and σ, respectively, τ is 1/L, and σ is 1/L, where L is a normal number. K represents the number of iterations, K has an initial value of 0, KmaxIs the maximum number of iterations. The superscript K or K +1 denotes the Kth or K +1 th iteration of the respective parameter.
2. Update dual variable p:
Figure BDA0002917169080000047
3. updating a dual variable q:
Figure BDA0002917169080000048
4. updating the sensitivity matrix S: and S is SW.
Wherein
W＝diag(wk,k)
Wherein W is an adaptive diagonal matrix; w is ak,kIs an adaptive factor (k is more than or equal to 1 and less than or equal to n), and the specific expression is as follows:
Figure BDA0002917169080000049
where w is a standard parameter and exp represents an exponential function with a natural constant e as the base.
5. Updating an auxiliary variable f:
Figure BDA00029171690800000410
6. let gold＝gK。
7. Updating the gray value matrix g:
Figure BDA00029171690800000411
where div represents the divergence.
8. And v is updated: v. ofK+1＝vK+τ(pK+1+divε(vK)qK+1)。
9. Let vold＝vK。
10. Solving the first-stage gray value matrix
Figure BDA00029171690800000412
11. Updating optimized variables of v
Figure BDA00029171690800000413
12.K＝K+1。
13. When K is equal to KmaxEnding the iterative process to obtain
Figure BDA00029171690800000414
Namely, it is
Figure BDA00029171690800000415
If K<KmaxAnd returns to execution 2.
Step five: by the proposed function
Figure BDA00029171690800000416
To pair
Figure BDA00029171690800000417
Further processing to obtain a second-stage gray value matrix
Figure BDA00029171690800000418
The concrete form of (A) is as follows:
Figure BDA0002917169080000051
wherein μ is a threshold value greater than 0;
Figure BDA0002917169080000052
represents 0 and
Figure BDA0002917169080000053
the maximum value of (a) is,
Figure BDA0002917169080000054
represents 0 and
Figure BDA0002917169080000055
maximum value of (2).
Figure BDA0002917169080000056
The value of (A) is the second stage gray value matrix
Figure BDA0002917169080000057
A value of (i), i.e
Figure BDA0002917169080000058
Step six: using the obtained second-stage gray value matrix
Figure BDA0002917169080000059
And imaging to obtain a human lung detection image.
Fig. 2 is a schematic diagram of a sensor array in electrical resistance tomography, which includes a basic current excitation and voltage measurement portion and sixteen electrode distributions.
The distribution medium models of healthy lung and tumor lung are selected as an embodiment, the real distribution of the lung in the field is shown in the left column of fig. 3, and the other three columns respectively represent a TV regularization method, a TGV regularization method and the regularization algorithm provided by the invention from left to right. In order to better embody the algorithm of the present invention differently from the other two algorithms, the imaging results of the three reconstruction algorithms are shown in fig. 3, respectively. It can be seen that in the distribution of the two lung models, when an algorithm TV regularization method is adopted, sharp edges of the images are well kept, but the images have the phenomena of step effect and artifacts, so that the quality of image reconstruction is seriously influenced; compared with the TV regularization method, although the image reconstruction quality of the TGV regularization method is improved, the image reconstruction quality still has the factors such as artifacts and the like which influence the image, and the algorithm provided by the document has a clearer background on the imaging effect and a more complete target boundary, has a good effect on removing the step effect and the artifacts, and is far superior to the reconstruction results of the TV regularization method and the TGV regularization method.
In electrical resistance tomography, an image Relative Error (RE) and Correlation Coefficient (CC) evaluation algorithm are generally adopted to quantify the image reconstruction quality, and an expression is shown in (i) and (ii), wherein the smaller the image Relative Error is, the larger the Correlation Coefficient is, and the better the image reconstruction quality is.
Figure BDA00029171690800000510
Figure BDA00029171690800000511
Where σ is the calculated conductivity of the reconstructed region, σ*Is the actual conductivity, t represents the number of pixels,
Figure BDA00029171690800000512
and
Figure BDA00029171690800000513
represents sigma and sigma*Average value of (a) ("sigmaiAnd σi *Expressed are σ and σ*The ith triangle cell of (1).
Fig. 4 shows the relative error and the correlation coefficient of the three methods for the reconstructed images of the two models, and it can be seen that compared with the TV regularization method and the TGV regularization method, the electrical impedance tomography method for detecting human lung tumor provided by the present invention has the lowest relative error and the highest correlation coefficient, can accurately reconstruct the distribution in the measured field, and significantly improve the solving precision of the inverse problem of electrical impedance tomography.
The above description is only exemplary of the present invention and should not be taken as limiting the invention, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. An electrical impedance tomography method for detecting human lung tumor is characterized in that the reconstruction process is as follows:
the method comprises the following steps: carrying out CT scanning on the human chest by using a spiral CT scanner to obtain a high-precision human chest CT scanning image, analyzing and processing chest shape data, and completing the construction of a human chest model on a computer by combining electrical impedance information of the normal chest of a human body;
step two: a person to be checked is allowed to sit and stand on a stool, the upper body of the person is perpendicular to the ground, the midpoint of a connecting line of two nipples of the person is taken as a starting point, 16 electrodes are sequentially attached to the skin surface of a human body at equal intervals on a plane parallel to the ground, the 16 electrodes are uniformly distributed around the human body for one circle, the internal thoracic cavity of the human body surrounded by the 16 electrodes is taken as a measurement field, current excitation and voltage measurement are carried out on the electrode pairs in an adjacent mode, the end of expiration is taken as a reference point, and when the person finishes one-time inspiration, a boundary voltage measurement matrix V at a first moment is obtained1(ii) a At the end of the next exhalation, a boundary voltage measurement matrix V at a second time is obtained2，V1-V2The boundary voltage measurement matrix V required by imaging is obtained;
step three: calculating a sensitivity matrix S, and according to the human chest model constructed in the step one and the current excitation in the step two, calculating the sensitivity matrix S by combining a sensitivity theory, wherein elements in the sensitivity matrix are called sensitivity coefficients, and the calculation formula of the sensitivity coefficients is as follows:
Figure FDA0002917169070000011
in the formula, SmnIs the sensitivity coefficient located in the mth row and column of the sensitivity matrix S, m is the number of boundary voltage measurements, and n is the number of pixels of the reconstruction unit;
Figure FDA0002917169070000012
the excitation current of the ith electrode pair is IiThe potential of the nth pixel within the field is measured,
Figure FDA0002917169070000013
the excitation current of the jth electrode pair is IjMeasuring the potential of the nth pixel within the field;
step four: first stage gray value matrix
Figure FDA0002917169070000014
The calculation of (2):
Figure FDA0002917169070000015
in the formula (I), the compound is shown in the specification,
Figure FDA0002917169070000016
is a data fidelity item; λ is a trade-off parameter, γ0And gamma1Are respectively used to balance the first derivative terms
Figure FDA0002917169070000017
And a second derivative term | | epsilon (v) | non-woven phosphor1The first and second order parameters of (a);
Figure FDA0002917169070000018
represents the gradient of the gray value matrix g; v is a field variable, ε (v) is a symmetric gradient operator,
Figure FDA0002917169070000019
superscript T denotes transpose;
to solve
Figure FDA00029171690700000110
Writing equation (1) in dual form:
Figure FDA00029171690700000111
wherein p and q are dual variables, and P, Q are convex sets corresponding to the dual variables respectively;
the solving step of the minimization problem in the formula (2) is as follows:
1. setting parameter initial values:
Figure FDA00029171690700000112
wherein f is an auxiliary variable,
Figure FDA00029171690700000113
is the optimization variable for v and is,
Figure FDA00029171690700000114
is the first even optimization variable, g0Is an initial value of g, the first and second projection parameters are τ and σ, respectively, τ is 1/L, σ is 1/L, where L is a normal number, K represents the number of iterations, K is 0, K is an initial value, K is a number of iterations, andmaxfor the maximum iteration number, the superscript K or K +1 represents the Kth or K +1 th iteration of each parameter;
2. update dual variable p:
Figure FDA0002917169070000021
3. updating a dual variable q:
Figure FDA0002917169070000022
4. updating the sensitivity matrix S: s is SW;
wherein
W＝diag(wk,k)
Wherein W is an adaptive diagonal matrix; w is ak,kIs an adaptive factor (k is more than or equal to 1 and less than or equal to n), and the specific expression is as follows:
Figure FDA0002917169070000023
wherein w is a standard parameter, exp represents an exponential function with a natural constant e as a base;
5. updating an auxiliary variable f:
Figure FDA0002917169070000024
6. let gold＝gK；
7. Updating the gray value matrix g:
Figure FDA0002917169070000025
wherein div represents the divergence;
8. and v is updated: v. ofK+1＝vK+τ(pK+1+divε(vK)qK+1)；
9. Let vold＝vK；
10. Solving the first-stage gray value matrix
Figure FDA0002917169070000026
11. Updating optimized variables of v
Figure FDA0002917169070000027
12.K＝K+1；
13. When K is equal to KmaxEnding the iterative process to obtain
Figure FDA0002917169070000028
Namely, it is
Figure FDA0002917169070000029
If K<KmaxAnd returning to execute 2;
step five: by the proposed function
Figure FDA00029171690700000210
To pair
Figure FDA00029171690700000211
Further processing to obtain a second-stage gray value matrix
Figure FDA00029171690700000212
Figure FDA00029171690700000213
The concrete form of (A) is as follows:
Figure FDA00029171690700000214
wherein μ is a threshold value greater than 0;
Figure FDA00029171690700000215
represents 0 and
Figure FDA00029171690700000216
the maximum value of (a) is,
Figure FDA00029171690700000217
represents 0 and
Figure FDA00029171690700000218
the maximum value of (a) is,
Figure FDA00029171690700000219
the value of (A) is the second stage gray value matrix
Figure FDA00029171690700000220
A value of (i), i.e
Figure FDA00029171690700000221
Step six: using the obtained second-stage gray value matrix
Figure FDA0002917169070000031
And imaging to obtain a human lung detection image.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115251881A (en) * 2022-07-29 2022-11-01 普罗朗生物技术（无锡）有限公司 Tumor risk prediction model based on bioelectrical impedance technology and establishment method thereof
CN117649503A (en) * 2024-01-29 2024-03-05 杭州永川科技有限公司 Image reconstruction method, apparatus, computer device, storage medium, and program product

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115251881A (en) * 2022-07-29 2022-11-01 普罗朗生物技术（无锡）有限公司 Tumor risk prediction model based on bioelectrical impedance technology and establishment method thereof
CN117649503A (en) * 2024-01-29 2024-03-05 杭州永川科技有限公司 Image reconstruction method, apparatus, computer device, storage medium, and program product
CN117649503B (en) * 2024-01-29 2024-05-28 杭州永川科技有限公司 Image reconstruction method, apparatus, computer device, storage medium, and program product

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