CN109758149B - Electrical impedance imaging method combining time difference imaging and frequency difference imaging - Google Patents

Electrical impedance imaging method combining time difference imaging and frequency difference imaging Download PDF

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CN109758149B
CN109758149B CN201910049961.4A CN201910049961A CN109758149B CN 109758149 B CN109758149 B CN 109758149B CN 201910049961 A CN201910049961 A CN 201910049961A CN 109758149 B CN109758149 B CN 109758149B
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CN109758149A (en
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杨琳
张学思
代萌
付峰
董秀珍
文治洪
王航
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Fourth Military Medical University FMMU
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Abstract

The invention discloses an electrical impedance imaging method combining time difference imaging and frequency difference imaging, which comprises the steps of performing time difference imaging by adopting two groups of measurement data at the same frequency at two different moments to obtain electrical impedance change of an imaging target (positioned in an imaging area) caused by volume change of the imaging target, performing frequency difference imaging by adopting two groups of measurement data at different frequencies at the same moment to obtain electrical impedance change of the imaging target (positioned in the imaging area) caused by conductivity change of the imaging target, and finally calculating the volume (three-dimensional imaging) of the imaging target or the area (two-dimensional imaging) of the imaging target at a certain moment by combining a time difference reconstruction result and a frequency difference reconstruction result. The invention can calculate the volume (or area) of an imaging target (positioned in an imaging area) at a certain moment by utilizing the respective characteristics of time difference imaging and frequency difference imaging.

Description

Electrical impedance imaging method combining time difference imaging and frequency difference imaging
Technical Field
The invention belongs to the technical field of electrical impedance imaging, and relates to an electrical impedance imaging method combining time difference imaging and frequency difference imaging.
Background
Based on the principle that different biological tissues have different electrical impedance characteristics and the electrical impedance characteristics of the same biological tissue in different physiological and pathological states are different, an Electrical Impedance Tomography (EIT) technology applies certain safety current to electrodes arranged on the surface of a measured body, collects boundary voltage response signals at the same time, and then calculates the electrical impedance distribution or electrical impedance change distribution in the measured body according to an image reconstruction algorithm. The EIT may be classified into static EIT imaging, moveout EIT imaging, and frequency difference EIT imaging, depending on the imaging mode. The static EIT aims at reconstructing absolute electrical impedance distribution inside a measured body, but the imaging result is seriously influenced by the boundary error of the measured body, the position error of an electrode, measurement noise and other factors, so that the static EIT imaging is difficult to realize in practical application.
However, the actual application always requires the absolute impedance distribution inside the measured body, and particularly, the requirement for the absolute impedance distribution (that is, area or volume information) of a certain target inside the measured body at a certain time exists. Although the time difference EIT and the frequency difference EIT respectively use the measurement data at different times and different frequencies to perform differential imaging, which can reflect the distribution change of the electrical impedance at different times and different frequencies inside the measured part of the human body, and has the advantage of obviously reducing the influence of the boundary error, the electrode position error and the measurement noise of the measured body on the imaging result, the time difference EIT and the frequency difference EIT are both the relative change information of the electrical impedance, and cannot directly reflect the absolute impedance (area or volume information) of the imaging target inside the measured part of the human body at a certain time.
Therefore, there is a need for an electrical impedance imaging method capable of calculating an imaging target area or volume using the advantages of the time difference EIT and the frequency difference EIT imaging.
Disclosure of Invention
In order to overcome the disadvantages of the prior art, the invention aims to provide an electrical impedance imaging method combining time difference imaging and frequency difference imaging, which can calculate the volume or area information of an imaging target in a detected part.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
the invention discloses an electrical impedance imaging method combining time difference imaging and frequency difference imaging, which comprises the steps of firstly, carrying out time difference imaging by adopting two groups of measurement data at the same frequency at two different moments to obtain the corresponding relation between the volume change of an imaging target and the electrical impedance change of the imaging target, and obtaining a time difference reconstruction result; then, performing frequency difference imaging by adopting two groups of measurement data at different frequencies at the same moment to obtain the relation between the conductivity change of the imaging target and the electrical impedance change of the imaging target, namely a frequency difference reconstruction result; and finally, calculating the imaging target volume or area at a certain moment by combining the time difference reconstruction result and the frequency difference reconstruction result.
Preferably, the electrical impedance imaging method combining time difference imaging and frequency difference imaging specifically includes the following steps:
1) using two frequencies f1And f2Respectively at two different times t1And t2Exciting to obtain measured data at two frequencies and at two different times
Figure BDA0001950414890000021
And
Figure BDA0001950414890000022
wherein
Figure BDA0001950414890000023
Represents the measurement data at x at the frequency and at the time y;
2) using two different times t1And t2Frequency f1Two sets of measured data of
Figure BDA0001950414890000024
And
Figure BDA0001950414890000025
difference result of (2)
Figure BDA0001950414890000026
Carrying out image reconstruction to obtain frequency f1Electrical impedance change caused by time-dependent change of imaging target volume
Figure BDA0001950414890000027
Solving by
Figure BDA0001950414890000028
Figure BDA0001950414890000029
Wherein S is allergyThe sense matrix is a matrix of the sensed light,
Figure BDA00019504148900000210
for regularization coefficients, L is a regularization matrix,
Figure BDA00019504148900000211
for reconstructing the matrix, T is the transpose of the matrix;
3) using two different times t1And t2Frequency f2Two sets of measured data of
Figure BDA00019504148900000212
And
Figure BDA00019504148900000213
difference result of (2)
Figure BDA00019504148900000214
Carrying out image reconstruction to obtain frequency f2Electrical impedance change caused by time-dependent change of imaging target volume
Figure BDA00019504148900000215
Solving by
Figure BDA00019504148900000216
Figure BDA0001950414890000031
Wherein the content of the first and second substances,
Figure BDA0001950414890000032
to reconstruct the matrix, L is a regularization matrix,
Figure BDA0001950414890000033
is a regularization coefficient;
4) using t1Two frequencies f of time1And f2Two sets of measured data of
Figure BDA0001950414890000034
And
Figure BDA0001950414890000035
difference result of (2)
Figure BDA0001950414890000036
Carrying out image reconstruction to obtain a moment t1Electrical impedance change caused by change of imaging target conductivity along with frequency change
Figure BDA0001950414890000037
Solving by
Figure BDA0001950414890000038
Figure BDA0001950414890000039
Wherein the content of the first and second substances,
Figure BDA00019504148900000310
to reconstruct the matrix, L is a regularization matrix,
Figure BDA00019504148900000311
is a regularization coefficient;
5) using t2Two frequencies f of time1And f2Two sets of measured data of
Figure BDA00019504148900000312
And
Figure BDA00019504148900000313
difference result of (2)
Figure BDA00019504148900000314
Carrying out image reconstruction to obtain a moment t2Electrical impedance change caused by change of imaging target conductivity along with frequency change
Figure BDA00019504148900000315
Solving by
Figure BDA00019504148900000316
Figure BDA00019504148900000317
Wherein the content of the first and second substances,
Figure BDA00019504148900000318
to reconstruct the matrix, L is a regularization matrix,
Figure BDA00019504148900000319
is a regularization coefficient;
6) based on the relationship that the electrical impedance change of an imaging target is in direct proportion to the volume and conductivity characteristics of the imaging target, namely:
Figure BDA00019504148900000320
Figure BDA00019504148900000321
Figure BDA00019504148900000322
Figure BDA00019504148900000323
calculating t from1Temporal imaging target volume
Figure BDA00019504148900000329
Figure BDA00019504148900000324
Then it is determined that,
Figure BDA00019504148900000325
and t2Temporal imaging target volume
Figure BDA00019504148900000326
Wherein the content of the first and second substances,
Figure BDA00019504148900000327
and
Figure BDA00019504148900000328
the sum of the reconstruction results of the imaging region is calculated by the following four formulas:
Figure BDA0001950414890000041
and
Figure BDA0001950414890000042
preferably, the electrical impedance imaging positive problem calculation equation is: s · Δ ρ ═ Δ V;
wherein S is a sensitive matrix, Δ V is a change vector of boundary measurement data to be reconstructed, Δ ρ is an electrical impedance change of the imaging target, and the change vector is associated with a volume C and a conductivity σ of the imaging targetfIs proportional, and expressed as Δ ρ ∈ C · σf。
Preferably, the boundary measurement data to be reconstructed comprise data acquired under various excitation-measurement mode conditions. Four voltage data as described above
Figure BDA0001950414890000043
And
Figure BDA0001950414890000044
in the field of EIT, voltage data can be obtained by a plurality of data acquisition modes, and the method can be suitable for the data obtained in all the acquisition modes.
Preferably, the two different frequencies are two different frequencies within any frequency band.
Preferably, the two different times are two different times at arbitrary intervals.
Preferably, in two-dimensional imaging, the area of the imaging target is calculated; in three-dimensional imaging, a volume of an imaging target is calculated.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides an electrical impedance imaging method combining time difference imaging and frequency difference imaging, which is characterized in that two groups of measurement data at the same frequency at two different moments are adopted for time difference imaging to obtain electrical impedance change of an imaging target (located in an imaging area) caused by volume change of the imaging target; and then, performing frequency difference imaging by adopting two groups of measurement data at different frequencies at the same moment to obtain the relation between the conductivity change of the imaging target and the electrical impedance change of the imaging target, and finally calculating the volume or area (absolute impedance distribution) of the imaging target at a certain moment by combining the time difference reconstruction result and the frequency difference reconstruction result. The prior art can only reconstruct and obtain the volume change of an imaging target between two different moments or the conductivity change of the imaging target between two different frequencies, but cannot obtain the volume of the imaging target at a certain moment. The electrical impedance imaging method combining time difference imaging and frequency difference imaging provided by the invention can flexibly change according to the actual application condition: according to the electrical impedance frequency spectrum characteristics of the imaging target, two different frequencies with different conductivities of the imaging target are selected at will for data acquisition and imaging; and according to the volume change condition of the imaging target, two different moments of the imaging target with volume difference are randomly selected for data acquisition and imaging.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a simulation model of the present invention for calculating simulated measurement data.
FIG. 3 is a simulation reconstruction model of the present invention.
Fig. 4 is a time difference imaging result and a frequency difference imaging result, where 401 and 402 are the time difference imaging results at two frequencies, and 403 and 404 are the frequency difference imaging results at two time instants, respectively.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention is described in further detail below with reference to the accompanying drawings:
referring to fig. 1, in this embodiment, an electrical impedance imaging method combining time difference imaging and frequency difference imaging is provided, in which currents with two different frequencies are respectively adopted to perform excitation at two different times, so as to obtain measurement data at two frequencies and at two different times, and four frames of measurement data are obtained; secondly, respectively reconstructing time difference images at two frequencies and respectively reconstructing frequency difference images at two different moments; and finally, respectively calculating the imaging target volumes at two moments based on the four reconstruction results.
In the present embodiment, two-dimensional imaging is taken as an example, and an imaging portion is assumed to be a circular area with a radius of 12cm, and an imaging target is located in the circular area. Imaging target at a first time t1A first frequency f1Has an electrical conductivity of 1.0S/m atFirst time t1Second frequency f2At a conductivity of 1.05S/m and at a second moment in time a first frequency f1At a conductivity of 1.1S/m, at a second moment in time at a second frequency f2The conductivity of the solution is 1.15S/m; the conductivity in the circular area is 1.0S/m at all times and at all frequencies, as shown in FIG. 2, where 201 in FIG. 2 is the first time t1The simulation model of (2); in FIG. 2, 202 is the second time t1The area of the imaging target changes to 0.873cm at two moments2(the areas of the imaging target at the first and second times are 0.873cm, respectively2And 1.746cm2). After all parameters of the simulation model are set, respectively generating simulation measurement data at two moments and two frequencies according to an electrical impedance imaging principle, and adding certain noise to the simulation data in order to simulate a real situation, so as to finally obtain four frames of measurement data:
Figure BDA0001950414890000061
Figure BDA0001950414890000062
and
Figure BDA0001950414890000063
FIG. 3 is a simulation reconstruction model for reconstructing an image, the model being composed of 12 layers of finite elements, all the finite element meshes being regular triangular mesh, the electrical conductivity in the circular region being uniformly distributed at 1.0S/m.
The invention provides an electrical impedance imaging method combining time difference imaging and frequency difference imaging, which comprises the following steps:
1) using two different times (t)1And t2) Frequency f1Two sets of measured data of
Figure BDA0001950414890000064
And
Figure BDA0001950414890000065
difference result of (2)
Figure BDA0001950414890000066
Image reconstruction is performed at frequency f using the following equation1Electrical impedance change caused by time-dependent change of imaging target volume
Figure BDA0001950414890000067
Figure BDA0001950414890000068
Where S is a sensitivity matrix and L is a regularization matrix (in this embodiment, L ═ diag (S)TS))，
Figure BDA0001950414890000069
Is a regularization coefficient (in this embodiment)
Figure BDA00019504148900000610
)，
Figure BDA00019504148900000611
To a reconstruction matrix.
Figure BDA00019504148900000612
The reconstruction result of (3) is shown as 401 in fig. 4.
2) Using two different times (t)1And t2) Frequency f2Two sets of measured data of
Figure BDA00019504148900000613
And
Figure BDA00019504148900000614
difference result of (2)
Figure BDA0001950414890000071
Carrying out image reconstruction, and solving the reconstruction at the frequency f by using the following formula2Electrical impedance change caused by time-dependent change of imaging target volume
Figure BDA0001950414890000072
Figure BDA0001950414890000073
Where L is a regularization matrix (in this embodiment, L ═ diag (S)TS))，
Figure BDA0001950414890000074
Is a regularization coefficient (in this embodiment)
Figure BDA0001950414890000075
)，
Figure BDA0001950414890000076
To a reconstruction matrix. The reconstruction result of (c) is shown as 402 in fig. 4.
3) Using t1Two frequencies f of time1And f2Two sets of measured data of
Figure BDA0001950414890000077
And
Figure BDA0001950414890000078
difference result of (2)
Figure BDA0001950414890000079
Image reconstruction is performed at time t using the following equation1Electrical impedance change caused by change of imaging target conductivity along with frequency change
Figure BDA00019504148900000710
Figure BDA00019504148900000711
Where L is a regularization matrix (in this embodiment, L ═ diag (S)TS))，
Figure BDA00019504148900000712
Is a regularization coefficient (in this embodiment)
Figure BDA00019504148900000713
)，
Figure BDA00019504148900000714
To a reconstruction matrix. The reconstruction result of (2) is shown as 403 in fig. 4.
4) Using t2Two frequencies f of time1And f2Two sets of measured data of
Figure BDA00019504148900000715
And
Figure BDA00019504148900000716
difference result of (2)
Figure BDA00019504148900000717
Image reconstruction is performed at time t using the following equation2Electrical impedance change caused by change of imaging target conductivity along with frequency change
Figure BDA00019504148900000718
Figure BDA00019504148900000719
Where L is a regularization matrix (in this embodiment, L ═ diag (S)TS))，
Figure BDA00019504148900000720
Is a regularization coefficient (in this embodiment)
Figure BDA00019504148900000721
)，
Figure BDA00019504148900000722
To a reconstruction matrix. The reconstruction result of (a) is shown as 404 in fig. 4.
As can be seen from fig. 4, although the time difference imaging or frequency difference imaging result can reflect the position information of the imaging target, the area (or volume) information of the imaging target cannot be accurately obtained.
5) Based on the relationship that the electrical impedance change of the imaging target is in direct proportion to the volume and conductivity characteristics of the imaging target, t is calculated according to the following formula1Temporal imaging of objectsThe volume of the target volume is marked,
Figure BDA00019504148900000723
and t2Temporal imaging target volume
Figure BDA00019504148900000724
Wherein the content of the first and second substances,
Figure BDA00019504148900000725
and
Figure BDA00019504148900000726
the sum of the reconstruction results of the imaging region is calculated by the following four formulas:
Figure BDA0001950414890000081
Figure BDA0001950414890000082
and
Figure BDA0001950414890000083
through the calculation, the method has the advantages that,
Figure BDA0001950414890000084
Figure BDA0001950414890000085
and
Figure BDA0001950414890000086
then
Figure BDA0001950414890000087
The errors between the imaging target area and the real area at two moments of calculation of the method are respectively 0.8% and 1.03%, and both are less than 5% (within 5% is generally regarded as an acceptable range). Therefore, the electrical impedance imaging method combining the time difference imaging and the frequency difference imaging, which is provided by the invention, can accurately calculate the areas (or volumes) of the imaging target at different moments.
In summary, the method of the present invention performs time difference imaging by using two sets of measurement data at the same frequency at two different times to obtain electrical impedance change of an imaging target (located in an imaging region) caused by volume change of the imaging target, performs frequency difference imaging by using two sets of measurement data at different frequencies at the same time to obtain electrical impedance change of the imaging target (located in the imaging region) caused by conductivity change of the imaging target, and finally calculates the volume of the imaging target (three-dimensional imaging) or the area of the imaging target (two-dimensional imaging) at a certain time by combining a time difference reconstruction result and a frequency difference reconstruction result. The invention can calculate the volume (or area) of an imaging target (positioned in an imaging area) at a certain moment by utilizing the respective characteristics of time difference imaging and frequency difference imaging.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (6)

1. An electrical impedance imaging method combining time difference imaging and frequency difference imaging is characterized in that firstly, time difference imaging is carried out by adopting two groups of measurement data at the same frequency at two different moments to obtain the corresponding relation between the volume change of an imaging target and the electrical impedance change of the imaging target, and then a time difference reconstruction result is obtained; then, performing frequency difference imaging by adopting two groups of measurement data at different frequencies at the same moment to obtain the relation between the conductivity change of the imaging target and the electrical impedance change of the imaging target, namely a frequency difference reconstruction result; finally, calculating the imaging target volume or area at a certain moment by combining the time difference reconstruction result and the frequency difference reconstruction result;
the method comprises the following steps:
1) using two frequencies f1And f2Respectively at two different times t1And t2Exciting to obtain measured data at two frequencies and at two different times
Figure FDA0003386633630000011
And
Figure FDA0003386633630000012
wherein
Figure FDA0003386633630000013
Representing the measurement data at time y at frequency x;
2) using two different times t1And t2Frequency f1Two sets of measured data of
Figure FDA0003386633630000014
And
Figure FDA0003386633630000015
difference result of (2)
Figure FDA0003386633630000016
Carrying out image reconstruction to obtain frequency f1Electrical impedance change caused by time-dependent change of imaging target volume
Figure FDA0003386633630000017
Solving by
Figure FDA0003386633630000018
Figure FDA0003386633630000019
Wherein, S is a sensitive matrix,
Figure FDA00033866336300000110
for regularization coefficients, L is a regularization matrix,
Figure FDA00033866336300000111
for reconstructing the matrix, T is the transpose of the matrix;
3) by using two different phasesMoment t1And t2Frequency f2Two sets of measured data of
Figure FDA00033866336300000112
And
Figure FDA00033866336300000113
difference result of (2)
Figure FDA00033866336300000114
Carrying out image reconstruction to obtain frequency f2Electrical impedance change caused by time-dependent change of imaging target volume
Figure FDA00033866336300000115
Solving by
Figure FDA00033866336300000116
Figure FDA00033866336300000117
Wherein the content of the first and second substances,
Figure FDA00033866336300000118
to reconstruct the matrix, L is a regularization matrix,
Figure FDA00033866336300000119
is a regularization coefficient;
4) using t1Two frequencies f of time1And f2Two sets of measured data of
Figure FDA00033866336300000120
And
Figure FDA00033866336300000121
difference result of (2)
Figure FDA00033866336300000122
Carrying out image reconstruction to obtain a moment t1Electrical impedance change caused by change of imaging target conductivity along with frequency change
Figure FDA00033866336300000123
Solving by
Figure FDA00033866336300000124
Figure FDA0003386633630000021
Wherein the content of the first and second substances,
Figure FDA0003386633630000022
to reconstruct the matrix, L is a regularization matrix,
Figure FDA0003386633630000023
is a regularization coefficient;
5) using t2Two frequencies f of time1And f2Two sets of measured data of
Figure FDA0003386633630000024
And
Figure FDA0003386633630000025
difference result of (2)
Figure FDA0003386633630000026
Carrying out image reconstruction to obtain a moment t2Electrical impedance change caused by change of imaging target conductivity along with frequency change
Figure FDA0003386633630000027
Solving by
Figure FDA0003386633630000028
Figure FDA0003386633630000029
Wherein the content of the first and second substances,
Figure FDA00033866336300000210
to reconstruct the matrix, L is a regularization matrix,
Figure FDA00033866336300000211
is a regularization coefficient;
6) based on the relationship that the electrical impedance change of an imaging target is in direct proportion to the volume and conductivity characteristics of the imaging target, namely:
Figure FDA00033866336300000212
Figure FDA00033866336300000213
Figure FDA00033866336300000214
Figure FDA00033866336300000215
calculating t from1Temporal imaging target volume
Figure FDA00033866336300000216
Figure FDA00033866336300000217
Then it is determined that,
Figure FDA00033866336300000218
and t2Temporal imaging target volume
Figure FDA00033866336300000219
Wherein the content of the first and second substances,
Figure FDA00033866336300000220
and
Figure FDA00033866336300000221
the sum of the reconstruction results of the imaging region is calculated by the following four formulas:
Figure FDA00033866336300000222
and
Figure FDA00033866336300000223
2. an electrical impedance imaging method combining moveout imaging and frequency difference imaging according to claim 1, wherein the electrical impedance imaging positive problem calculation equation is: s · Δ ρ ═ Δ V;
wherein S is a sensitive matrix, Δ V is a change vector of boundary measurement data to be reconstructed, Δ ρ is an electrical impedance change of the imaging target, and the change vector is associated with a volume C and a conductivity σ of the imaging targetfIs proportional, and expressed as Δ ρ ∈ C · σf。
3. A method of electrical impedance imaging combining moveout imaging and frequency difference imaging according to claim 1, wherein the boundary measurement data to be reconstructed comprises data acquired under various excitation-measurement mode conditions.
4. An electrical impedance imaging method incorporating jet lag imaging and frequency difference imaging according to claim 1, wherein the two different frequencies are two different frequencies within any frequency band.
5. A method of electrical impedance imaging combining moveout imaging and frequency difference imaging according to claim 1, wherein the two different times are two different times at arbitrary intervals.
6. An electrical impedance imaging method combining time-of-arrival imaging and frequency-of-arrival imaging according to claim 1, wherein in two-dimensional imaging, the area of the imaged object is calculated; in three-dimensional imaging, a volume of an imaging target is calculated.
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