CN110710972A - Information processing method of coil detection type magnetoacoustic tomography - Google Patents

Information processing method of coil detection type magnetoacoustic tomography Download PDF

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CN110710972A
CN110710972A CN201911002203.3A CN201911002203A CN110710972A CN 110710972 A CN110710972 A CN 110710972A CN 201911002203 A CN201911002203 A CN 201911002203A CN 110710972 A CN110710972 A CN 110710972A
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樊晓曦
宫礼坤
陈距文
王兴伟
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China University of Petroleum East China
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Abstract

The invention discloses an information processing method of coil detection type magneto-acoustic tomography, relates to the technical field of magneto-acoustic imaging, solves by applying a vector field equation or an inverse problem integral equation, further reconstructs conductivity, has the advantages of accuracy, rapidness and high analysis efficiency, and has high development potential in the field of medical imaging.

Description

Information processing method of coil detection type magnetoacoustic tomography
Technical Field
The invention relates to the technical field of electromagnetic acoustic imaging, in particular to an information processing method of coil detection type electromagnetic acoustic tomography.
Background
Medical research has shown that the electrical properties of biological tissues are particularly important for the early diagnosis of cancer. Electrical impedance imaging methods for non-invasively detecting electrical properties of biological tissue, such as electrical impedance tomography EIT, have been disclosed in the prior art. The EIT is limited by the number of sensors detected and the spatial resolution is low. Therefore, in order to improve the resolution, the electromagnetic field and the ultrasonic wave are combined to study the conductivity imaging of the electromagnetic field, and a simplified image signal is processed.
In the conventional electrode detection of electromagnetic field, if a pair of electrodes is used to detect a magnetoacoustic signal, the electrodes must be closely attached to the surface of the target to be measured, and the change in contact resistance between the electrodes and the target directly affects the accuracy of measurement. In addition, if the electrodes are physically connected to the target volume, the vibrations of the electrodes will also generate magnetoacoustic electrical signals when ultrasound propagates within the target volume, if the electrodes are still in the static magnetic field. This can interfere with the normal magnetoacoustic electrical signal, resulting in measurement errors. Therefore, a non-contact coil detection method is needed to solve the corresponding problems.
Coil-detection magnetoacoustic-electrical imaging, also known as magnetic induction magnetoacoustic-electrical imaging (MAET-MI), is a non-contact magnetoacoustic-electrical imaging method that uses coils to detect changes in current in a target body. In the magnetoacoustic-electric process, the change of the current density in the target body can cause the change of a space magnetic field, and the coil outside the target body induces the change of the space magnetic field to generate induced voltage, which is similar to electrode detection and can also reflect the information of the internal conductivity of the target body. However, how to rapidly reconstruct the conductivity through each magnetoacoustic signal detected by the coil for the convenience of biological tissue detection is not related in the prior art.
Disclosure of Invention
In order to overcome the problems in the prior art, the information processing method of the coil detection type magnetoacoustic tomography is provided, the image contrast is high, the information processing method is not in direct contact with a target body, the accurate detection of the electric signal of the target body can be realized, and the development potential in the field of medical imaging is very large.
The invention provides a coil detection type magneto-acoustic tomography information processing method, and the specific positive problem processing flow of the magnetic induction type magneto-acoustic tomography comprises the following steps:
1) performing a coil detection mode: ultrasonic transducer is used for emitting ultrasonic waves into an imaging region omega, and the boundary of the region omega is used
Figure BDA0002241669630000021
Showing the dynamic source current density J of the vibration velocity v excited in the static magnetic fielde1Is composed of
Je1＝σv×B0(1)，
Wherein, B0Is a static magnetic field vector, with units of Tesla T;
2) at Je1In response to the excitation of (2) to generate a response electric field E1And a varying magnetic field H1Due to a varying magnetic field H1Changes along with the propagation of the ultrasound, so that an induced voltage u (t) is obtained in the coil;
3) in the coil detection mode, the relationship between the magnetic field and the electric field is, according to Faraday's law of electromagnetic induction (2a) and Ampere's law (2b)
Figure BDA0002241669630000022
Wherein, the subscript 1 represents the field quantity in the actual physical process of the induction type magnetoacoustic electrography,is a particle vibration velocity vector with the unit of m/s; region omega Total electric field of
Figure BDA0002241669630000025
Since ultrasound is a conservative field, it is not possible to detect,
Figure BDA0002241669630000026
rotation is zero, thereforeIn response to the electric field E1Is the total electric field intensity of the imaging area and the varying magnetic field H1Is the total magnetic field strength of the imaging region; μ is the dielectric permeability, t is the time, σ is the electrical conductivity,
Figure BDA0002241669630000031
is a gradient operator, expressed in Cartesian coordinates as
Figure BDA0002241669630000032
xyz are three coordinate values respectively, e is a natural constant;
4) due to response to electric field E1Is rotating so that an induced voltage can be detected by a coil, the induced voltage in the coil can be expressed as the following line integral
Figure BDA0002241669630000033
Wherein lcirRepresenting vectors along the coil, dlcirA minute line element along the detection coil;
5) and (3) solving by adopting vector field equation direct coupling: dividing the conductivity sigma on the right side of the formula (2b) to the left, solving the rotation degrees at two ends, and combining the two ends with the formulas (1) and (2a) to obtain a vector field equation which is solved by taking the magnetic field as an unknown quantity:
Figure BDA0002241669630000034
preferably, under the condition of infinite boundary, a numerical solution of the vector field equation formula (4) can be obtained by using a finite element or edge element method; obtaining the changing magnetic field H by calculating the formula (4)1Then, the electric field strength can be obtained by substituting the equations (2a) and (2 b).
The invention also provides an information processing method for magnetic acoustic tomography of coil detection, which utilizes the reciprocity process of induction type magnetic acoustic tomography to solve an inverse problem integral equation to obtain the space component of the reciprocity current density or the rotation thereof as the basis for reconstructing the conductivity; the specific treatment process preferably comprises:
1) performing a coil detection mode: ultrasonic transducer is adopted to emit ultrasonic waves into the imaging area to obtain the current density J of the live sourcee1Expression (1), varying magnetic field H1And in response to the electric field E1Relations (2a) (2b), and induced voltage u (t) in the coil are expressed by expression (3);
2) carrying out a corresponding reciprocity mode: using ultrasonic transducers directed at the imaging zoneUltrasonic waves are emitted in the field, and a pulse current density J which changes along with time is introduced into a coil near a target bodye2Inducing an eddy current density J in the imaging area2And electric field E2(ii) a From current density J in the coile2And the distributed current density J in the target body2Co-excitation generating a magnetic field H2；
3) The detection coil is assumed to be a wire loop with a cross-sectional area of 0, wherein the applied pulse current density is introduced
Je2＝δ(r-rcir)s(t)ee2(r) (5)
Wherein r represents a field point, rcirRepresenting a point on the coil, δ (-) representing a Dirac function in three-dimensional space, s (t) being the applied current Je2Time item of (c). e.g. of the typee2Denotes Je2A unit vector along a circumferential direction of the coil; selectivity according to Dirac function, δ (r-r)cir) Represents the applied current density Je2Only applied to the coil, and no value elsewhere;
4) according to Faraday's law of electromagnetic induction (6a) and Ampere's law (6b), the relationship between the magnetic and electric fields excited by an applied current in the process of reciprocity is
Figure BDA0002241669630000041
Wherein the subscript 2 denotes the field magnitude in the reciprocal process, E2And H2Vortex electric field intensity and vortex magnetic field intensity respectively; the effect of displacement current is neglected due to low excitation frequency;
5) in the actual physical process, the two sides of the ampere law relation formula (2b) are opposite to E2Do inner product
Figure BDA0002241669630000043
Wherein the operator<A,B>Representing spatial domainsInner product of (2)Omega is the whole calculation region, including the measured imaging region and the region where the coil is located, and r belongs to omega, which means that a field point r belongs to the whole calculation region omega;
6) according to vector identityFormula (7) rewritten on the left as
Figure BDA0002241669630000053
By the principle of Gauss's law, to obtain
Figure BDA0002241669630000054
Wherein n represents a boundary
Figure BDA0002241669630000055
A unit vector in the outer normal direction; under the condition of infinite boundary with enough solving area, E2Or H10 at the boundary, thereby (E)2×H1) N has a boundary integral of 0;
7) substituting the formula (10) into the formula (7) to obtain
Figure BDA0002241669630000056
For the two pairs E of formula (6b)1Do inner product
Figure BDA0002241669630000057
8) Taking Fourier transform on two sides of the formulas (11) and (12) to obtain a frequency domain expression of
Figure BDA0002241669630000061
Where ω is angular frequency, j is an imaginary unit, and the wavy line above the variable represents the corresponding field magnitude in the frequency domain; due to the fact that
Figure BDA0002241669630000062
And
Figure BDA0002241669630000063
if the result is constant, the formula (13b) is subtracted from the formula (13a)
Figure BDA0002241669630000064
Since the variables in equation (14) are functions of the spatial point r and the angular frequency ω, they are detailed as
Figure BDA0002241669630000065
9) Substituting equation (1) into the left hand portion of (15), and based on
Figure BDA0002241669630000066
To obtain
Figure BDA0002241669630000067
Substituting the formulas (3) and (5) into the right part of (15) to obtain
Wherein the content of the first and second substances,
Figure BDA0002241669630000069
and
Figure BDA00022416696300000610
fourier transforms of s (t) and u (t), respectively; the Dirac function divides the volume of the three-dimensional space intoConverting to a line integral along the coil;
10) according to equations (15) to (17), the frequency domain expression of the induced voltage detected by the coil satisfies
Figure BDA0002241669630000071
Wherein except the static magnetic field B0Regardless of frequency, all field quantities are functions of angular frequency ω and spatial point r,
Figure BDA0002241669630000072
also, the velocity potential function satisfies (19) and the vector identity (8), and the formula (18) is rewritten as
Figure BDA0002241669630000073
Wherein the content of the first and second substances,
Figure BDA0002241669630000074
representing a function of velocity potential
Figure BDA0002241669630000075
A Fourier transform of (1); equation (20) is split into a volume fraction and a surface fraction;
11) the current density in reciprocal process is determined by wrapping the target with non-conductive insulating fluid medium, preferably insulating oil or distilled water
Figure BDA0002241669630000076
The value at the boundary is 0; therefore, the second term boundary integral on the right side of equation (20) is equal to 0; from an acoustically homogeneous medium, equation (20) reduces to
Figure BDA0002241669630000077
In the reciprocity process, because the electrical conductivity of the target body is low, the induced eddy current will satisfy approximately the same time law at each point in space, i.e. in the low-conductivity target body, the time term and the space term of the induced eddy current can be separated, and then the space term and the frequency term of the induced eddy current can be separated. Therefore, the temperature of the molten metal is controlled,
12) will be provided with
Figure BDA0002241669630000081
Is rewritten as
Figure BDA0002241669630000082
And
Figure BDA0002241669630000084
respectively representing a spatial term and a temporal term of induced eddy currents in a reciprocity process;
13) in a low conductivity medium, neglecting the secondary magnetic field, the time term of the induced electric field or current should be the induced magnetic field H2The first derivative of the time term; therefore, should satisfy in the frequency domain
Figure BDA0002241669630000085
14) Substituting the formulas (23) and (22) into (21) to obtain
Figure BDA0002241669630000086
Order to
Figure BDA0002241669630000087
Is constant, i.e., s (t) equals δ (t), equation (24) reduces to
Figure BDA0002241669630000088
Generally speaking, as long as
Figure BDA0002241669630000089
In that
Figure BDA00022416696300000810
Non-zero in the non-zero spectral range,
Figure BDA00022416696300000811
can be reduced in equation (24). In inductive magneto-acoustic imaging (MAT-MI),
Figure BDA00022416696300000812
is determined by the actual physical process, e.g. assuming s (t) is a step function, equivalent to assumingHowever, in MAET-MI, as long as
Figure BDA00022416696300000814
In thatThe non-zero frequency spectrum range has no zero value, so that the frequency spectrum can be adjusted to be zero
Figure BDA00022416696300000816
The excitation in the reciprocity process is selected and reduced in equation (21). For the sake of simplicity, s (t) is preferably chosen to be δ (t), i.e. s (t) is preferably chosen to beEquation (22) also illustrates that the magneto-acoustic electrical signal is related to the spatial component of the current density rotation in the reciprocal process, and also related to the ultrasonic velocity potential function.
15) In some preferred embodiments of the invention, the inverse Fourier transform of equation (22) is applied to obtain a time domain integral expression in degrees of rotation of the reciprocal current density
Figure BDA0002241669630000092
Wherein the content of the first and second substances,
Figure BDA0002241669630000093
representing a function of velocity potential
Figure BDA0002241669630000094
The first derivative is taken with respect to time.
In other preferred embodiments of the present invention, equations (22) and (23) are substituted into equation (18) to approximate both sides
Figure BDA0002241669630000095
And solving the Fourier inverse transformation to obtain a time domain integral expression expressed by reciprocal current density vector
Figure BDA0002241669630000096
Further, the magnetoacoustic signal measured in the coil detection mode is the induced voltage in the coil, or, as described above, the induced voltage signal is calculated by forward modeling from the reciprocity theorem.
Wherein the inverse problem integral equation (26) is a calculation formula based on the reciprocal current density curl in the coil detection mode, and the inverse problem integral equation (27) is a calculation formula based on the reciprocal current density in the coil detection mode.
More preferably, in the coil-detecting magnetoacoustic-electrography, the inverse problem integral equation (26) is regarded as a solution to the following wave equation
Figure BDA0002241669630000097
The field quantity u (r, t) of the wave equation is generated by exciting any wave field source H (r ') with delta' (t); under the condition of infinite boundary, the solution of the wave equation is expressed by the integral of the derivative of the Greens function
Figure BDA0002241669630000101
Wherein r 'represents a source point, r represents a field point, and H (r') represents a field source distribution function; g (r, t | r ',0) still represents the Green's function of the field magnitude u (r, t) under point source excitation, which still satisfies the wave equation (20);
Figure BDA0002241669630000102
wherein r 'represents a source point, r represents a field point, and H (r') represents a field source distribution function; g (r, t | r ',0) represents the Green's function of the field magnitude u (r, t) under point source excitation, which satisfies the wave equation (20), let the wave field source H (r ')
Figure BDA0002241669630000103
The inverse problem of coil-detection magnetoacoustic-electroimaging can be converted into an inverse source reconstruction problem of the wave equation (28), wherein the distributed sources satisfy the formula (31); in a subsequent step of the inverse problem reconstruction, the conductivity distribution is reconstructed from the spatial components of the reciprocal current density or its curl, preferably by a quasi-newton method or a finite difference-damped least squares method.
Compared with the prior art, the invention has the beneficial effects that:
the method comprises the steps of (1) establishing a mathematical physical model of MAET-MI and carrying out positive problem analysis, and firstly obtaining a numerical solution by combining a vector field equation with a finite element or edge unit method so as to obtain the electric field intensity; (2) the method of solving the inverse problem integral equation firstly and then reconstructing the conductivity according to the space component integral formula of the reciprocal current density or the rotation degree thereof is adopted, so that the conductivity information of the target imaging area is accurately and efficiently obtained, and a foundation is laid for medical imaging application.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
In the drawings:
FIG. 1 is a schematic diagram comparing detection models of the information processing method of coil detection type magneto-acoustic tomography of the present invention: (a) actual physical processes, (b) reciprocal processes corresponding thereto.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
Example 1
A coil detection type magneto-acoustic tomography information processing method is disclosed, wherein the positive problem processing specific flow of the magnetic induction type magneto-acoustic tomography comprises the following steps:
1) performing a coil detection mode: ultrasonic transducer is used for emitting ultrasonic waves into an imaging region omega, and the boundary of the region omega is used
Figure BDA0002241669630000111
Showing the dynamic source current density J of the vibration velocity v excited in the static magnetic fielde1Is composed of
Je1＝σv×B0(1)，
Wherein, B0Is a static magnetic field vector, with units of Tesla T;
2) at Je1In response to the excitation of (2) to generate a response electric field E1And a varying magnetic field H1Due to a varying magnetic field H1Changes along with the propagation of the ultrasound, so that an induced voltage u (t) is obtained in the coil;
3) in the coil detection mode, the relationship between the magnetic field and the electric field is, according to Faraday's law of electromagnetic induction (2a) and Ampere's law (2b)
Figure BDA0002241669630000121
Figure BDA0002241669630000122
Wherein the subscript 1 represents the actual physical process of the inductive magnetoacoustic-electroimagingThe amount of field in (a) is,
Figure BDA0002241669630000123
is a particle vibration velocity vector with the unit of m/s; region omega Total electric field of
Figure BDA0002241669630000124
Since ultrasound is a conservative field, it is not possible to detect,
Figure BDA0002241669630000125
rotation is zero, therefore
Figure BDA0002241669630000126
In response to the electric field E1Is the total electric field intensity of the imaging area and the varying magnetic field H1Is the total magnetic field strength of the imaging region; μ is the dielectric permeability, t is the time, σ is the electrical conductivity,
Figure BDA0002241669630000127
is a gradient operator, expressed in Cartesian coordinates as
Figure BDA0002241669630000128
xyz are three coordinate values respectively, e is a natural constant;
4) due to response to electric field E1Is rotating so that an induced voltage can be detected by a coil, the induced voltage in the coil can be expressed as the following line integral
Figure BDA0002241669630000129
Wherein lcirRepresenting vectors along the coil, dlcirA minute line element along the detection coil;
5) and (3) solving by adopting vector field equation direct coupling: dividing the conductivity sigma on the right side of the formula (2b) to the left, solving the rotation degrees at two ends, and combining the two ends with the formulas (1) and (2a) to obtain a vector field equation which is solved by taking the magnetic field as an unknown quantity:
Figure BDA00022416696300001210
under the condition of an infinite boundary, a numerical solution of the vector field equation formula (4) can be obtained by using a finite element or edge unit method; obtaining the changing magnetic field H by calculating the formula (4)1Then, the electric field strength can be obtained by substituting the formula (2a,2 b).
However, relying solely on the vector field equation is equivalent to satisfying the equation in x, y, z directions simultaneously, andthe method is different at different moments and different angles, and the solving process is long in time consumption and low in efficiency. It is difficult to achieve fast processing of electrical characteristics for imaging detection applications. Therefore, the temperature of the molten metal is controlled,
example 2
The embodiment provides an information processing method for magnetic acoustic tomography (MAGE), which is used for coil detection, and comprises the steps of solving by using a reciprocity process of induction type MAGE, solving an inverse problem integral equation in the first step, and reconstructing the conductivity according to a space component of reciprocity current density or rotation of the reciprocity current density in the second step; the specific processing flow comprises the following steps:
1) performing a coil detection mode: ultrasonic transducer is adopted to emit ultrasonic waves into the imaging area to obtain the current density J of the live sourcee1Expression (1), varying magnetic field H1And in response to the electric field E1Relations (2a) (2b), and induced voltage u (t) in the coil are expressed by expression (3);
2) carrying out a corresponding reciprocity mode: ultrasonic transducer is adopted to emit ultrasonic waves into an imaging area, and pulse current density J which changes along with time is introduced into a coil near a target bodye2Inducing an eddy current density J in the imaging area2And electric field E2(ii) a From current density J in the coile2And the distributed current density J in the target body2Co-excitation generating a magnetic field H2；
3) The detection coil is assumed to be a wire loop with a cross-sectional area of 0, wherein the applied pulse current density is introduced
Je2＝δ(r-rcir)s(t)ee2(r) (5)
Wherein r represents a field point, rcirRepresenting a point on the coil, δ (-) representing a Dirac function in three-dimensional space, s (t) being the applied current Je2Time item of (c). e.g. of the typee2Denotes Je2A unit vector along a circumferential direction of the coil; selectivity according to Dirac function, δ (r-r)cir) Represents the applied current density Je2Only applied to the coil, and no value elsewhere;
4) according to Faraday's law of electromagnetic induction (6a) and Ampere's law (6b), the relationship between the magnetic and electric fields excited by an applied current in the process of reciprocity is
Figure BDA0002241669630000141
Figure BDA0002241669630000142
Wherein the subscript 2 denotes the field magnitude in the reciprocal process, E2And H2Vortex electric field intensity and vortex magnetic field intensity respectively; the effect of displacement current is neglected due to low excitation frequency;
5) in the actual physical process, the two sides of the ampere law relation formula (2b) are opposite to E2Do inner product
Figure BDA0002241669630000143
Wherein the operator<A,B>Representing the inner product of a spatial domain
Figure BDA0002241669630000144
Omega is the whole calculation region, including the measured imaging region and the region where the coil is located, and r belongs to omega, which means that a field point r belongs to the whole calculation region omega;
6) according to vector identity
Figure BDA0002241669630000145
Formula (7) rewritten on the left as
Figure BDA0002241669630000146
By the principle of Gauss's law, to obtain
Figure BDA0002241669630000147
Wherein n represents a boundaryA unit vector in the outer normal direction; under the condition of infinite boundary with enough solving area, E2Or H10 at the boundary, thereby (E)2×H1) N has a boundary integral of 0;
7) substituting the formula (10) into the formula (7) to obtain
Figure BDA0002241669630000151
For the two pairs E of formula (6b)1Do inner product
Figure BDA0002241669630000152
8) Taking Fourier transform on two sides of the formulas (11) and (12) to obtain a frequency domain expression of
Figure BDA0002241669630000153
Figure BDA0002241669630000154
Where ω is angular frequency, j is an imaginary unit, and the wavy line above the variable represents the corresponding field magnitude in the frequency domain; due to the fact thatAnd
Figure BDA0002241669630000156
if the result is constant, the formula (13b) is subtracted from the formula (13a)
Figure BDA0002241669630000157
Since the variables in equation (14) are functions of the spatial point r and the angular frequency ω, they are detailed as
Figure BDA0002241669630000158
9) Substituting equation (1) into the left hand portion of (15), and based onTo obtain
Figure BDA00022416696300001510
Substituting the formulas (3) and (5) into the right part of (15) to obtain
Figure BDA0002241669630000161
Wherein the content of the first and second substances,
Figure BDA0002241669630000162
and
Figure BDA0002241669630000163
fourier transforms of s (t) and u (t), respectively; as shown in equation (17), the Dirac function converts the volume fraction of the three-dimensional space into a line integral along the coil;
10) according to equations (15) to (17), the frequency domain expression of the induced voltage detected by the coil satisfies
Wherein except the static magnetic field B0Regardless of frequency, all field quantities are functions of angular frequency ω and spatial point r,
Figure BDA0002241669630000165
also, the velocity potential function satisfies (19) and the vector identity (8), and the formula (18) is rewritten as
Figure BDA0002241669630000166
Wherein the content of the first and second substances,
Figure BDA0002241669630000167
representing a function of velocity potential
Figure BDA0002241669630000168
A Fourier transform of (1); equation (20) is split into a volume fraction and a surface fraction;
11) the target body is wrapped by non-conductive insulating fluid medium in the detection process and is insulating oil or distilled water, and the current density in the reciprocal process
Figure BDA0002241669630000171
The value at the boundary is 0; therefore, the second term boundary integral on the right side of equation (20) is equal to 0; from an acoustically homogeneous medium, equation (20) reduces to
Figure BDA0002241669630000172
In the reciprocity process, because the electrical conductivity of the target body is low, the induced eddy current will satisfy approximately the same time law at each point in space, i.e. in the low-conductivity target body, the time term and the space term of the induced eddy current can be separated, and then the space term and the frequency term of the induced eddy current can be separated. Therefore, the temperature of the molten metal is controlled,
12) will be provided with
Figure BDA0002241669630000173
Is rewritten as
Figure BDA0002241669630000174
Figure BDA0002241669630000175
Andrespectively representing a spatial term and a temporal term of induced eddy currents in a reciprocity process;
13) in a low conductivity medium, neglecting the secondary magnetic field, the time term of the induced electric field or current should be the induced magnetic field H2The first derivative of the time term; therefore, should satisfy in the frequency domain
Figure BDA0002241669630000177
14) Substituting the formulas (23) and (22) into (21) to obtain
Figure BDA0002241669630000178
Order to
Figure BDA0002241669630000179
Is constant, i.e., s (t) equals δ (t), equation (24) reduces to
Figure BDA0002241669630000181
Generally speaking, as long asIn that
Figure BDA0002241669630000183
Non-zero in the non-zero spectral range,
Figure BDA0002241669630000184
can be reduced in equation (24). In the case of inductive magneto-acoustic imaging,
Figure BDA0002241669630000185
is determined by the actual physical process, e.g. assuming s (t) is a step function, equivalent to assuming
Figure BDA0002241669630000186
However, in MAET-MI, as long asIn that
Figure BDA0002241669630000188
The non-zero frequency spectrum range has no zero value, so that the frequency spectrum can be adjusted to be zeroThe excitation in the reciprocity process is selected and reduced in equation (21). For the sake of simplicity, s (t) is chosen to be δ (t), i.e. s (t) is1. Equation (22) also illustrates that the magneto-acoustic electrical signal is related to the spatial component of the current density rotation in the reciprocal process, and also related to the ultrasonic velocity potential function.
15) In this embodiment, the inverse fourier transform of equation (22) is performed to obtain a time domain integral expression expressed in degrees of rotation of reciprocal current density
Figure BDA00022416696300001811
Wherein the content of the first and second substances,representing a function of velocity potential
Figure BDA00022416696300001813
The first derivative is taken with respect to time.
16) The magneto-acoustic electrical signal measured in the coil detection mode is the induced voltage in the coil.
Wherein, the inverse problem integral equation (26) is a calculation formula based on the reciprocal current density curl in the coil detection mode.
Example 3
This example was carried out using the treatment method of example 2, except that,
15) in this embodiment, substituting equations (22) and (23) into equation (18) results in two edges being eliminated
Figure BDA00022416696300001814
And solving the Fourier inverse transformation to obtain a time domain integral expression expressed by reciprocal current density vector
Figure BDA0002241669630000191
16) And obtaining the induction voltage signal by forward calculation according to a reciprocity theorem.
Wherein, the inverse problem integral equation (27) is a calculation formula based on the reciprocal current density in the coil detection mode.
Example 4
The embodiment is implemented by using the processing method of embodiment 2, and the difference is that the spatial component of the reciprocal current density or the rotation thereof is reconstructed by using filtered back projection,
in coil-sensing magnetoacoustic-electrical imaging, the inverse problem integral equation (26) is considered to be a solution to the following wave equation
The field quantity u (r, t) of the wave equation is generated by exciting any wave field source H (r ') with delta' (t); under the condition of infinite boundary, the solution of the wave equation is expressed by the integral of the derivative of the Greens function
Figure BDA0002241669630000193
Wherein r 'represents a source point, r represents a field point, and H (r') represents a field source distribution function; g (r, t | r ',0) still represents the Green's function of the field magnitude u (r, t) under point source excitation, which still satisfies the wave equation (20);
Figure BDA0002241669630000194
wherein r 'represents a source point, r represents a field point, and H (r') represents a field source distribution function; g (r, t | r ',0) represents the Green's function of the field magnitude u (r, t) under point source excitation, which satisfies the wave equation (20), let the wave field source H (r ')
Figure BDA0002241669630000201
The inverse problem of coil-detection magnetoacoustic-electroimaging can be converted into an inverse source reconstruction problem of the wave equation (28), where the distributed source satisfies equation (31).
In a second step of the inverse problem reconstruction, the conductivity distribution is reconstructed from the spatial components of the reciprocal current density or its rotation, in particular by the quasi-newton method or the finite difference-damped least squares method. Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. 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 (9)

1. An information processing method of coil detection type magneto-acoustic tomography is characterized in that: the positive problem processing specific flow of the magnetic induction type magnetoacoustic-electric imaging comprises the following steps:
1) performing a coil detection mode: ultrasonic transducer is used for emitting ultrasonic waves into an imaging region omega, and the boundary of the region omega is used
Figure FDA0002241669620000011
Showing the dynamic source current density J of the vibration velocity v excited in the static magnetic fielde1Is composed of
Je1＝σv×B0(1)，
Wherein, B0Is a static magnetic field vector, with units of Tesla T;
2) at Je1In response to the excitation of (2) to generate a response electric field E1And a varying magnetic field H1Due to a varying magnetic field H1Changes along with the propagation of the ultrasound, so that an induced voltage u (t) is obtained in the coil;
3) in the coil detection mode, the relationship between the magnetic field and the electric field is, according to Faraday's law of electromagnetic induction (2a) and Ampere's law (2b)
Figure FDA0002241669620000012
Figure FDA0002241669620000013
Wherein, the subscript 1 represents the field quantity in the actual physical process of the induction type magnetoacoustic electrography,
Figure FDA0002241669620000014
is a particle vibration velocity vector with the unit of m/s; region omega Total electric field of
Figure FDA0002241669620000015
Since ultrasound is a conservative field, it is not possible to detect,
Figure FDA0002241669620000016
rotation is zero, therefore
Figure FDA0002241669620000017
In response to the electric field E1Is the total electric field intensity of the imaging area and the varying magnetic field H1Is the total magnetic field strength of the imaging region; μ is the dielectric permeability, t is the time, σ is the electrical conductivity;
Figure FDA0002241669620000018
is a gradientAn operator, expressed in Cartesian coordinates as
Figure FDA0002241669620000019
xyz are three coordinate values respectively, e is a natural constant;
4) due to response to electric field E1Is rotating so that an induced voltage can be detected by a coil, the induced voltage in the coil can be expressed as the following line integral
Figure FDA0002241669620000021
Wherein lcirRepresenting vectors along the coil, dlcirA minute line element along the detection coil;
5) and (3) solving by adopting vector field equation direct coupling: dividing the conductivity sigma on the right side of the formula (2b) to the left, solving the rotation degrees at two ends, and combining the two ends with the formulas (1) and (2a) to obtain a vector field equation which is solved by taking the magnetic field as an unknown quantity:
Figure FDA0002241669620000022
2. the information processing method of coil-based magnetoacoustic tomography according to claim 1, characterized in that: under the condition of an infinite boundary, obtaining a numerical solution of the vector field equation formula (4) by using a finite element or edge unit method; obtaining the changing magnetic field H by calculating the formula (4)1Then, the electric field strength can be obtained by substituting the formula (2a,4.2 b).
3. An information processing method of coil detection type magneto-acoustic tomography is characterized in that: and solving an inverse problem integral equation by utilizing a reciprocity process of the induction type magneto-acoustic-electric imaging to obtain a space component of the reciprocity current density or the rotation degree of the reciprocity current density as a basis for reconstructing the conductivity.
4. The information processing method of coil-based magnetoacoustic tomography according to claim 3, characterized in that: the specific processing flow comprises the following steps:
1) performing a coil detection mode: ultrasonic transducer is adopted to emit ultrasonic waves into the imaging area to obtain the current density J of the live sourcee1Expression (1), varying magnetic field H1And in response to the electric field E1Relations (2a) (2b), and induced voltage u (t) in the coil are expressed by expression (3);
2) carrying out a corresponding reciprocity mode: ultrasonic transducer is adopted to emit ultrasonic waves into an imaging area, and pulse current density J which changes along with time is introduced into a coil near a target bodye2Inducing an eddy current density J in the imaging area2And electric field E2(ii) a From current density J in the coile2And the distributed current density J in the target body2Co-excitation generating a magnetic field H2；
3) The detection coil is assumed to be a wire loop with a cross-sectional area of 0, wherein the applied pulse current density is introduced
Je2＝δ(r-rcir)s(t)ee2(r) (5)
Wherein r represents a field point, rcirRepresenting a point on the coil, δ (-) representing a Dirac function in three-dimensional space, s (t) being the applied current Je2The time item of (c); e.g. of the typee2Denotes Je2A unit vector along a circumferential direction of the coil; selectivity according to Dirac function, δ (r-r)cir) Represents the applied current density Je2Only applied to the coil, and no value elsewhere;
4) according to Faraday's law of electromagnetic induction (6a) and Ampere's law (6b), the relationship between the magnetic and electric fields excited by an applied current in the process of reciprocity is
Figure FDA0002241669620000032
Wherein the subscript 2 represents the reciprocity processAmount of field in, E2And H2Vortex electric field intensity and vortex magnetic field intensity respectively; the effect of displacement current is neglected due to low excitation frequency;
5) in the actual physical process, the two sides of the ampere law relation formula (2b) are opposite to E2Do inner product
Figure FDA0002241669620000033
Wherein the operator<A,B>Representing the inner product of a spatial domain
Figure FDA0002241669620000034
Omega is the whole calculation region, including the measured imaging region and the region where the coil is located, and r belongs to omega, which means that a field point r belongs to the whole calculation region omega;
6) according to vector identityFormula (7) rewritten on the left asBy the principle of Gauss's law, to obtain
Wherein n represents a boundary
Figure FDA0002241669620000043
A unit vector in the outer normal direction; under the condition of infinite boundary with enough solving area, E2Or H10 at the boundary, thereby (E)2×H1) N has a boundary integral of 0;
7) substituting the formula (10) into the formula (7) to obtain
Figure FDA0002241669620000044
For the two pairs E of formula (6b)1Do inner product
Figure FDA0002241669620000045
8) Taking Fourier transform on two sides of the formulas (11) and (12) to obtain a frequency domain expression of
Figure FDA0002241669620000046
Figure FDA0002241669620000047
Where ω is angular frequency, j is an imaginary unit, and the wavy line above the variable represents the corresponding field magnitude in the frequency domain; due to the fact that
Figure FDA0002241669620000048
Andif the result is constant, the formula (13b) is subtracted from the formula (13a)
Figure FDA0002241669620000051
Since the variables in equation (14) are functions of the spatial point r and the angular frequency ω, they are detailed as
Figure FDA0002241669620000052
9) Substituting equation (1) into the left hand portion of (15), and based on
Figure FDA0002241669620000053
To obtain
Figure FDA0002241669620000054
Substituting the formulas (3) and (5) into the right part of (15) to obtain
Figure FDA0002241669620000055
Wherein the content of the first and second substances,
Figure FDA0002241669620000056
and
Figure FDA0002241669620000057
fourier transforms of s (t) and u (t), respectively; as shown in equation (17), the Dirac function converts the volume fraction of the three-dimensional space into a line integral along the coil;
10) according to equations (15) to (17), the frequency domain expression of the induced voltage detected by the coil satisfies
Figure FDA0002241669620000058
Wherein except the static magnetic field B0Regardless of frequency, all field quantities are functions of angular frequency ω and spatial point r,
Figure FDA0002241669620000061
also, the velocity potential function satisfies (19) and the vector identity (8), and the formula (18) is rewritten as
Figure FDA0002241669620000062
Wherein the content of the first and second substances,
Figure FDA0002241669620000063
representing a function of velocity potential
Figure FDA0002241669620000064
A Fourier transform of (1); equation (20) is split into a volume fraction and a surface fraction;
11) the target body is wrapped by non-conductive insulating fluid medium in the detection process, and the current density in the reciprocal processThe value at the boundary is 0; therefore, the second term boundary integral on the right side of equation (20) is equal to 0; from an acoustically homogeneous medium, equation (20) reduces to
12) In the process of reciprocity, because the time term and the space term of the induced eddy current can be separated, the space term and the frequency term of the induced eddy current can also be separated; therefore, will
Figure FDA0002241669620000067
Is rewritten as
Figure FDA0002241669620000069
And
Figure FDA00022416696200000610
respectively representing a spatial term and a temporal term of induced eddy currents in a reciprocity process;
13) in a low conductivity medium, neglecting the secondary magnetic field, the time term of the induced electric field or current should be the induced magnetic field H2The first derivative of the time term; therefore, should satisfy in the frequency domain
14) Substituting the formulas (23) and (22) into (21) to obtain
Figure FDA0002241669620000071
Order to
Figure FDA0002241669620000072
Is constant, i.e., s (t) equals δ (t), equation (24) reduces to
Figure FDA0002241669620000073
5. The information processing method of coil-based magnetoacoustic tomography according to claim 4, characterized in that: taking the inverse Fourier transform of equation (22) to obtain the time domain integral expression expressed by the rotation of reciprocal current density
Figure FDA0002241669620000074
Wherein the content of the first and second substances,
Figure FDA0002241669620000075
representing a function of velocity potential
Figure FDA0002241669620000076
The first derivative is taken with respect to time, and the inverse problem integral equation (26) is a calculation formula based on the reciprocal current density curl in the coil detection mode.
6. The information processing method of coil-based magnetoacoustic tomography according to claim 4, characterized in that: substituting equations (22) and (23) into equation (18) results in two-sided rounding
Figure FDA0002241669620000077
And solving the Fourier inverse transformation to obtain a time domain integral expression expressed by reciprocal current density vector
Figure FDA0002241669620000078
The inverse problem integral equation (27) is a calculation formula based on the reciprocal current density in the coil detection mode.
7. The information processing method of coil-detection type magneto-acoustic tomography according to claim 5 or 6, characterized in that: the magnetoacoustic electrical signal measured in the coil detection mode is the induced voltage in the coil, or the induced voltage signal is calculated by forward modeling from the reciprocity theorem.
8. The information processing method of coil-detection-type magneto-acoustic tomography according to claim 5, characterized in that: in coil-sensing magnetoacoustic-electrical imaging, the inverse problem integral equation (26) is considered to be a solution to the following wave equation
The field quantity u (r, t) of the wave equation is generated by exciting any wave field source H (r ') with delta' (t); under the condition of infinite boundary, the solution of the wave equation is expressed by the integral of the derivative of the Greens function
Figure FDA0002241669620000082
Wherein r 'represents a source point, r represents a field point, and H (r') represents a field source distribution function; g (r, t | r ',0) still represents the Green's function of the field magnitude u (r, t) under point source excitation, which still satisfies the wave equation (20);
wherein r 'represents a source point, r represents a field point, and H (r') represents a field source distribution function; g (r, t | r ',0) represents the Green's function of the field magnitude u (r, t) under point source excitation, which satisfies the wave equation (20), let the wave field source H (r ')
Figure FDA0002241669620000084
The inverse problem of coil-detection magnetoacoustic-electroimaging can be converted into an inverse source reconstruction problem of the wave equation (28), wherein the distributed sources satisfy the formula (31); in a subsequent step of the inverse problem reconstruction, the conductivity distribution is reconstructed from the spatial components of the reciprocal current density or its rotation.
9. The information processing method of coil-based magnetoacoustic tomography according to claim 8, characterized in that: the conductivity distribution is reconstructed by quasi-newton method or finite difference-damped least squares method from the spatial component of the reciprocal current density or its rotation.
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