CN110051352B - Conductivity imaging system based on magneto-acoustic-electric principle - Google Patents

Abstract

A conductivity imaging system based on the magneto-acoustic-electric principle, wherein an imaging platform transmits acquired magneto-acoustic-electric signals to an image reconstruction module. The imaging platform comprises a sound field driving excitation module, a magnetic field excitation module and a detection module; the sound field driving excitation module generates a sound field excitation source; the magnetic field excitation module is an open magnet and is placed near the organism, the generated non-uniform static magnetic field acts on the organism, the organism generates a moving source current under the action of the non-uniform static magnetic field and the sound field, and the detection module collects the moving source current and converts the moving source current into a magneto-acoustic electric voltage signal. The invention detects the magneto-acoustic electric signal by using the electrode, obtains the conductivity distribution image of the imaging body by using the image reconstruction module, and realizes the detection of the conductivity distribution in the target area of the biological tissue.

Description

A Conductivity Imaging System Based on the Principle of Magnetoacoustoelectricity

technical field

The invention relates to an open magnetoacoustic electric conductivity imaging system.

Background technique

Early diagnosis of diseases is of great significance. On the one hand, it can reduce the pain and high medical expenses of patients during treatment, and more importantly, it can improve the survival rate. Studies have shown that changes in electrical properties of tissues are earlier than lesions in tissue structures, so Imaging methods that use electrical parameters as imaging target parameters can achieve early diagnosis of diseases. Magnetoacoustoelectric imaging takes electrical parameters as the imaging target parameters, and has a promising medical imaging method with the advantages of high contrast and high resolution.

In 1998, Han wen et al. proposed Hall effect imaging, and under the excitation of a static magnetic field of a 4.0T magnetic resonance magnetic field, they used electrodes to detect the experimental signal of bacon meat, but the configuration of the experimental system was not mentioned too much. In 2003, Hanwen discussed this imaging system in detail in the patent US6520911B1. During the configuration of the system, a uniform static magnetic field was used as the magnetic field excitation source for magnetoacoustic imaging. In 2007, Y.Xu, S Haider et al. proposed magnetoacoustic imaging based on the reciprocity theorem on the basis of the Hall effect, and obtained the distribution diagram of the reciprocity current density by using the experimental method. Density has been simulated and analyzed, however, no reconstruction method for conductivity has been given. Aiming at the uniform static magnetic field as the magnetic field excitation source of magnetoacoustic electrical imaging, many scholars have done research work on the conductivity reconstruction algorithm. In 2014, Ammari H, Grasland-Mongrain P. from the University of Lyon, France reported the magnetoacoustic electrical imaging Theoretical analysis and simulation research under different SNR conditions (Ammari H et al., 2014). In the same year, Guo Liang of the Institute of Electrical Engineering, Chinese Academy of Sciences used the time-forward method, compressed sensing, and quasi-Newton iterative algorithm to realize the electrical conductivity reconstruction of the electrode-detection magnetoacoustic-electric imaging through simulation analysis (Guo L et al., 2014). Kunyansky L reported the reconstruction algorithm of the conductivity boundary in 2017, designed a 3D scanning platform, detected the magneto-acoustic-electric signal of beef tissue with electrodes, and reconstructed the interface information of beef tissue, which was not obtained through experimental signal reconstruction Conductivity image. The experimental platform reported above is either under the excitation of a uniform static magnetic field, or the target object is a small phantom structure, so it is reasonable to assume that the static magnetic field is uniform.

To sum up, there is no report on the actual medical system. For the actual medical system, there are two solutions to realize the static magnetic field, (1) using a uniform static magnetic field as a magnetic field excitation; (2) using a non-uniform static magnetic field as a magnetic field excitation source. For scheme (1), the realization of the uniform static magnetic field can refer to the design concept of the static magnetic field in magnetic resonance imaging, using permanent magnets, electromagnets or superconducting magnets. The realization of the static magnetic field will greatly increase the cost of the static magnetic field generating device, and further greatly increase the cost of the clinical application equipment of the magnetoacoustic electric imaging. Moreover, the closed environment reduces the imaging area and is not suitable for claustrophobic patients. For scheme (2), a completely uniform static magnetic field generating device is not required, which greatly reduces the cost of the medical system. However, the reconstruction algorithm currently studied is not applicable.

The current magnetoacoustic imaging platform is difficult to transform into a medical imaging system, and has the following disadvantages: (1) the current theoretical model is aimed at a uniform static magnetic field, and the realization of a completely uniform static magnetic field greatly increases the cost of the equipment; (2) non- Uniform static magnetic field as a magnetic field excitation source can reduce the cost of equipment, but there is no corresponding reconstruction algorithm at present.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the prior art and propose a conductivity imaging system based on the principle of magnetoacoustic electricity.

The electrical conductivity imaging system based on the principle of magnetoacoustic electricity of the present invention includes an imaging platform and an image reconstruction module. The imaging platform is connected with the image reconstruction module, and the collected magnetoacoustic electric signal is transmitted to the image reconstruction module through the transmission line.

The imaging platform includes an acoustic field drive excitation module, a magnetic field excitation module and a detection module. The sound field driving excitation module generates the sound field excitation source, that is, ultrasonic waves, which attenuate quickly in the air. In order to better propagate in the living body, a coupling water bag is required. The coupling water bag and the sound field driving excitation module are in complete contact to reduce the Attenuation of sound waves. The non-uniform static magnetic field generated by the magnetic field excitation module acts on the organism. Under the action of the non-uniform static magnetic field and the sound field, the organism will generate a dynamic source current. The detection module collects the dynamic source current and converts it into a magneto-acoustic-electric voltage signal.

The sound field driving excitation module is composed of an ultrasonic driving excitation source, an ultrasonic array and a coupling water bladder. One end of the ultrasonic array is connected to the ultrasonic driving excitation, and the other end of the ultrasonic array is in contact with the coupled water bladder. The ultrasonic driving excitation source excites the ultrasonic array to generate ultrasonic waves. The coupling water bag is filled with water, and the coupling water bag is filled in the space between the ultrasonic array and the living body, so that the ultrasonic wave generated by the ultrasonic array can propagate into the living body.

The magnetic field excitation module is an open magnet placed near the living body.

The detection module is composed of an electrode, a filter circuit, an amplifier circuit and a signal acquisition device. The electrodes are in contact with the organism to detect the voltage signal on the surface of the organism, the filtering and amplification circuit realizes the filtering and amplification of the detection signal, and finally the signal acquisition device realizes the signal acquisition. One end of the electrode is connected to the living body, the other end of the electrode is connected to the input end of the filter circuit, the output end of the filter circuit is connected to the input end of the amplifier circuit, the output end of the amplifier circuit is connected to the input end of the signal acquisition device, and the signal acquisition The output terminal of the device is connected with the image reconstruction module.

The image reconstruction module reconstructs the conductivity distribution according to the magnetoacoustic electric voltage signal of the organism output by the signal acquisition device.

The working process of the conductivity imaging system based on the principle of magnetoacoustic electricity in the present invention is as follows:

The ultrasonic driving excitation source of the sound field driving excitation module generates a pulse excitation signal, which acts on the ultrasonic array, and the ultrasonic array is coupled with the living body through the coupling water bag. Ultrasonic arrays emit ultrasonic waves, which generate ultrasonic vibrations in biological tissues, causing local particle vibrations in biological tissues. The magnetic field excitation module generates a non-uniform static magnetic field in the vibration area of the biological tissue, and the ions vibrating in the biological tissue are subjected to the Lorentz force under the action of the non-uniform static magnetic field to generate charge separation, and then form a local electric field in the biological body, resulting in current distribution. The electrodes attached to the living body measure the electrical signal, and after filtering and amplifying by the filter circuit and amplifier circuit of the detection module, the voltage signal is output to the image reconstruction module by the signal acquisition device. The image reconstruction module utilizes the magnetoacoustic electric voltage signal of the organism and the known non-uniform magnetostatic distribution information, and uses an image reconstruction algorithm to realize the reconstruction of the electrical conductivity distribution.

The image reconstruction module uses two conductivity reconstruction algorithms to reconstruct the conductivity distribution. The first reconstruction algorithm is a direct algebraic iterative conductivity reconstruction algorithm, and the second reconstruction algorithm is an equivalent uniform field algebraic iterative conductivity reconstruction algorithm.

Algorithm 1, direct algebraic iterative conductivity reconstruction algorithm, includes the following three steps:

1. Use the reciprocity theorem to establish the corresponding relationship between the actual measurement process and the physical quantity of the reciprocity process

(1) The actual measurement process is: under the action of the ultrasonic wave generated by the ultrasonic drive excitation module and the non-uniform static magnetic field generated by the magnetic field excitation module, the vibration velocity of the particle is v, and the non-uniform static magnetic field is B ₀ (r), the described The magnetic field is generated by the open magnet of the magnetic field excitation module, and the intensity distribution of the non-uniform static magnetic field B ₀ (r) is known.

(2) The reciprocal process is: close the sound field to drive the excitation module, and make the magnetic field excitation module do not work, feed the direct current of 1 ampere to the electrode in the detection module, and the current density generated by this current in the living body is J _r (r ).

互易过程电流密度J_r(r)，以及磁场激励模块产生的非均匀静磁场B₀(r)之间的关系式：Under the excitation of the non-uniform static magnetic field B ₀ (r) generated by the magnetic field excitation module, the magnetoacoustic electric voltage distribution u(r,t) and the vibration velocity potential can be obtained based on the reciprocity theorem

The relationship between the reciprocal process current density J _r (r) and the non-uniform static magnetic field B ₀ (r) generated by the magnetic field excitation module:

表示振动速度势，ρ₀为生物体的密度，J_r(r)为互易过程中生物体的电流密度，B₀(r)为磁场激励模块产生的非均匀静磁场分布，▽·为散度算符。In formula (1), t represents the propagation time of the ultrasonic wave, Ω represents the area where the organism is located, r represents the field point, that is, the point in the area Ω where the organism is located,

Indicates the vibration velocity potential, ρ ₀ is the density of the organism, J _r (r) is the current density of the organism in the reciprocal process, B ₀ (r) is the non-uniform static magnetic field distribution generated by the magnetic field excitation module, ▽ is the scattered degree operator.

2. According to the magnetoacoustic electric voltage u(r,t) measured in the actual measurement process, the relationship between the reciprocal process current density J _r (r) and the static magnetic field B ₀ (r) is reconstructed according to formula (1)▽ ·(J _r (r)×B ₀ (r))

满足的格林函数为/>

In formula (1), the vibration velocity potential

The Green's function that satisfies is />

According to formula (1) and the symmetry of Green's function, it can be seen that the magnetoacoustic electric voltage u(r,t) satisfies:

In formula (2), r' is the source point, representing the point in the area where the ultrasonic array is located.

Using formula (2), the relationship between the current density J _r (r) of the reciprocal process and the non-uniform static magnetic field B ₀ (r) generated by the open magnet can be obtained. At the same time, since ρ ₀ is a constant, we can get:

In formula (3), c ₀ represents the speed at which the sound field drives the excitation module to generate ultrasonic waves, t _rd =2T ₀ -t+|r-r'|/c ₀ represents the time of inversion field, t represents the propagation time of ultrasonic waves, T ₀ Indicates the moment of reversal u(r,t), r' indicates the point in the area where the ultrasonic array is located, r indicates the point in the area Ω where the organism is located, S indicates the surface of the area Ω where the organism is located, n is the area Ω where the organism is located The unit normal vector at the boundary, u'(r',t _rd ) means the first derivative of u(r',t _rd ), u"(r',t _rd ) means u(r',t _rd ) two order derivative.

The reconstruction of the variable H(r)=▽·(J _r (r)×B ₀ (r)) can be realized by using formula (3).

3. Reconstruct the conductivity distribution according to the variable H(r)

可表示为/>

即：After using formula (3) to realize the distribution of variable H(r)=▽·(J _r (r)×B ₀ (r)), the variable H(r) on each slice z ₀ of biological tissue is

can be expressed as />

Right now:

The brackets (x, y, z ₀ ) in each variable represent the coordinates of the corresponding variable on each fault plane z ₀ inside the organism.

J _r (x,y,z ₀ ) is the current density of the reciprocal process on the z ₀ fault plane. Using Ohm's law, the current density J _r (x,y,z ₀ ) can be expressed as the gradient of the reciprocal process potential and The product between the conductivities, that is:

J _r (x,y,z)=-σ(x,y,z)▽u _r (x,y,z)

So f(x,y,z ₀ ) can be expressed as:

Where u _r (x,y,z ₀ ) is the potential distribution of the reciprocal process on the z ₀ fault plane, and σ(x,y,z ₀ ) represents the distribution of the electrical conductivity of the organism on the z ₀ fault plane.

The potential distribution of the reciprocal process on the z ₀ fault plane satisfies the following relationship:

Wherein I is the direct current of I ampere injected in the reciprocal process, r _A and r _B represent the position of the electrode pair in the detection module, Γ represents the surface of the area Ω where the target body is located, and n represents the unit vector of the outer normal direction of the surface Γ .

的值表示为f(x,y,z₀)，由f(x,y,z₀)重建电导率σ的方法步骤如下：on each fault plane z ₀

The value of is denoted as f(x,y,z ₀ ), the steps of the method for reconstructing conductivity σ from f(x,y,z ₀ ) are as follows:

1) Divide the organism into a series of sub-blocks, consider that the conductivity inside these sub-blocks is uniform, and give the initial value of the conductivity distribution matrix [σ] of the organism, usually choose the initial value of conductivity as 0.1S/m , with a given error precision ε ;

2) Calculate the electric potential u _r (x, y, z ₀ ) of the reciprocal process according to formula (5);

3) Using formula (4) to reconstruct the conductivity distribution of the fault plane where z=z ₀ ;

4) Using the conductivity distribution of each fault obtained in step 3), the conductivity distribution of each sub-block is obtained by linear difference, so as to obtain the conductivity distribution σ ^k of the entire three-dimensional area of the organism at the kth iteration.

5) Calculate the relative error between the biological conductivity distribution σ ^k obtained in the kth iteration and the k+1 biological conductivity distribution σk ⁺¹ , and compare whether the relative error satisfies the given error precision ε , if the given error precision ε is met, stop the iteration. Otherwise, take the conductivity distribution σ ^k of the organism obtained at the kth time as the initial conductivity distribution, and go to step 2), and the above process is iterated in turn until the relative error of the conductivity distribution of the organism obtained by two adjacent calculations satisfies Accuracy requirements.

Using the formulas (1) and (2) can realize the reconstruction of Jian▽·(J _r (r)×B ₀ (r)), and then use the above steps 1) to 5) to realize the reconstruction of the biological conductivity image. The conductivity reconstruction algorithm is called direct algebraic iterative conductivity reconstruction algorithm.

Algorithm 2, the equivalent uniform field algebraic iterative conductivity reconstruction algorithm is as follows:

The equivalent homogeneous field algebraic iterative conductivity reconstruction algorithm is based on the relationship between the magnetoacoustic electric voltage signal and the nonuniform static magnetic field B ₀ (r), and the magnetoacoustic electric voltage with the nonuniform static magnetic field B ₀ (r) as the magnetic field excitation source The principle that the signal is equivalent to a magnetoacoustic electric voltage signal excited by a uniform static magnetic field is as follows: formulas (6)-(14).

Given a three-dimensional model, under the excitation of the non-uniform static magnetic field B ₀ (r), the current I(t) corresponding to the equivalent current source in the living body and the vibration velocity v of the ultrasonic wave in the living body driven by the sound field drive module The relationship is:

I(t)＝ _∫s σv×B ₀ (r)·dS (6)

where S represents the surface element of the surface through which the equivalent current source flows.

According to the acoustic principle, the ultrasonic impulse M and the vibration velocity v need to satisfy:

Where _ρ0 is the density of the organism, and ▽ is the gradient operator.

Substituting formula (7) into formula (6), we can get:

where n represents the unit vector of the normal direction of the surface element of the surface through which the equivalent current source flows.

Further using Stokes formula and vector identity, formula (8) can be simplified as:

Among them, l represents the line of the outer edge of the surface element, and the forward direction of l and the outer normal direction of S conform to the right-hand theorem, and the normal direction of S is n.

When considering practical applications, the frequency range of the energy emitted by the ultrasonic array contains very few DC frequencies, which means that the net momentum of the wave packet generated by the ultrasonic array is zero, so the first term on the right side of the equation (9) is zero.

At the same time, in the actual detection, the electrode can only detect a part of the current of the organism, so the current collected by the signal acquisition device is only a part of the current I(t), and the ratio between the collected voltage and current is defined as α, and the detected magnetic The acoustic-electric voltage U(t) can be expressed as:

Equation (11) is the relationship between the detected magnetoacoustic electric voltage U(t), non-uniform static magnetic field B ₀ (r), electrical conductivity σ, and density ρ ₀ .

为一个小量，忽视此小量，故式(11)可简化为：In practical application, ▽×B ₀ (r) is a very small quantity, so the second term on the right side of the equation (11)

is a small amount, ignore this small amount, so formula (11) can be simplified as:

的方向相同时，式(12)可表示为：In the formula (12), when the direction of the unit vector n of the normal direction of the surface element of the surface through which the equivalent current source flows is the same as

When the directions of are the same, formula (12) can be expressed as:

取此变量的e_x方向分量，则公式(13)可表示为：in

Taking the e _x direction component of this variable, formula (13) can be expressed as:

和B₀(r)之间的夹角。where B _oy and B _oz are respectively the magnetic field distribution θ of B ₀ (r) along the y direction and the z direction.

The angle between and B ₀ (r).

倍。Equation (14) is the theoretical relational expression of the magneto-acoustic-electric voltage signal under the excitation of the non-uniform static magnetic field, which is equivalent to the magneto-acoustic-electric voltage signal under the excitation of the uniform static magnetic field. The magneto-acoustic-electric signal will be amplified or reduced

times.

Algorithm 2, equivalent uniform field algebraic iterative conductivity reconstruction algorithm, the process is:

Firstly, use formula (14) to adjust the magnetoacoustic electric voltage signal u _in (r, t) collected under the excitation of the non-uniform static magnetic field to the equivalent magnetoacoustic electric voltage signal u _ho (r, t) collected under the excitation of the uniform field ;

Then replace all non-uniform static magnetic fields B ₀ (r) in formulas (1)-(5) with uniform static magnetic fields B ₀ ;

Finally, steps 1)-5) of the Algorithm-Direct Algebraic Iterative Conductivity Reconstruction Algorithm are used to realize the reconstruction of the conductivity.

In the equivalent uniform field algebraic iterative conductivity reconstruction algorithm, the magnetoacoustic electric voltage signal u _in (r,t) collected under the excitation of the non-uniform static magnetic field is adjusted to the magnetoacoustic electric voltage signal u _ho collected under the excitation of the uniform static magnetic field After (r, t), not only the direct algebraic iterative conductivity reconstruction algorithm can be used to realize the reconstruction of conductivity, but also the conductivity image can be obtained by using other reconstruction algorithms of conductivity under uniform static magnetic field excitation.

Description of drawings

Fig. 1 is a schematic diagram of the composition of the conductivity imaging system of the present invention;

Fig. 2 is a schematic structural diagram of an embodiment of the conductivity imaging system of the present invention;

Figure 3 The positional relationship between the organism, the coupling water bladder and the ultrasonic array;

In the figure, A1 ultrasonic drive excitation source, A2 ultrasonic array, A3 coupling water bladder, A4 magnetic field excitation module, A5 organism, A6 electrode, A7 amplifier circuit, A8 filter circuit, A9 signal acquisition device, A10 image reconstruction module, A11 single ultrasound Probe, A12 magnetic field generated by the magnetic field excitation module, A13 particle vibration velocity.

Figure 4 is a flow chart of the reconstruction algorithm;

Fig. 5 Flowchart of reconstruction algorithm II.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

The electrical conductivity imaging system based on the principle of magnetoacoustic electricity of the present invention includes an imaging platform and an image reconstruction module. The imaging platform is connected to the image reconstruction module A10, and transmits the magneto-acoustic-electric signals collected by the imaging platform to the reconstruction algorithm module A10.

As shown in Fig. 1 and Fig. 2, the imaging platform includes a sound field driving excitation module, a magnetic field excitation module A4 and a detection module. The sound field excitation source module generates ultrasonic waves. The magnetic field excitation module A4 generates a magnetic field excitation A12 to act on the organism, and the organism generates a dynamic source current under the action of the magnetic field and the sound field. The detection module detects this current signal, and the image reconstruction module A10 reconstructs the conductivity distribution according to the voltage signal.

The sound field driving excitation module is composed of an ultrasonic driving excitation source A1, an ultrasonic array A2 and a coupling water bladder A3. One end of the ultrasonic array A2 is connected to the ultrasonic driving excitation source A1, the other end of the ultrasonic array A2 is in contact with the coupling water bag A3, and the coupling water bag A3 is filled between the ultrasonic array A2 and the organism A5, and is in contact with the ultrasonic array A2 and the organism A5 Good, as shown in FIG. 3 , the ultrasonic wave generated by the ultrasonic driving excitation source A1 exciting the ultrasonic array A2 can propagate into the living body A5 .

The non-uniform static magnetic field A12 generated by the magnetic field excitation module A4 is generated by an open magnet.

The detection module is composed of electrode A6, filter circuit A8, amplifier circuit A7 and signal acquisition device A9. The electrode A6 is in contact with the organism A5 to detect the voltage signal on the surface of the organism. The detected voltage signal is filtered and amplified by the filter circuit A8 and the amplifier circuit A7, and collected by the signal acquisition device A9. One end of the electrode A6 is connected to the organism A5, the other end of the electrode A6 is connected to the input end of the filter circuit A8, the output end of the filter circuit A8 is connected to the input end of the amplifier circuit A7, and the output end of the amplifier circuit A7 is connected to the signal acquisition terminal. The input end of the device A9 and the output end of the signal acquisition device A9 are connected to the image reconstruction module A10.

The image reconstruction module A10 reconstructs the conductivity distribution according to the voltage signal of the organism A5 output by the signal acquisition device A9.

The working process of the electrical conductivity imaging system based on the principle of magnetoacoustic electricity of the present invention is as follows:

The ultrasonic driving excitation source A1 of the sound field driving excitation module generates a pulse excitation signal, which acts on the ultrasonic array A2, and the ultrasonic array A2 is coupled with the living body A5 through the coupling water bladder A3. The ultrasonic array A2 emits ultrasonic waves, which generate ultrasonic vibrations in the tissues of the living body A5, causing local particle vibrations of the living body tissues. The magnetic field excitation module A4 generates a non-uniform static magnetic field A12 in the tissue vibration area of the organism A5, and the ions in the tissue vibration of the organism A5 are subjected to the Lorentz force under the action of the non-uniform static magnetic field A12 to generate charge separation, and then in the organism A5 A local electric field is formed in the medium to generate a current distribution. The electrical signal is measured by the electrode A6 attached to the living body A5, filtered and amplified by the filter circuit A8 and amplifier circuit A7 of the detection module, and the voltage signal is output by the signal acquisition device A9 to the image reconstruction module A10. The image reconstruction module A10 utilizes the voltage signal of the biological body A5 and the known distribution information of the non-uniform magnetostatic A12, and uses an image reconstruction algorithm to realize the reconstruction of the electrical conductivity distribution. The image reconstruction module A10 uses two conductivity reconstruction algorithms to reconstruct the conductivity distribution. The first reconstruction algorithm is a direct algebraic iterative conductivity reconstruction algorithm, and the second reconstruction algorithm is an equivalent uniform field algebraic iterative conductivity reconstruction algorithm.

The process of reconstruction algorithm 1 is shown in Figure 4, and the steps are as follows:

1) Use u(r,t) and formula (2) to reconstruct the distribution of variable H(r);

2) Divide the organism into a series of sub-blocks. It is considered that the electrical conductivity inside these sub-blocks is uniform, and the initial value of the distribution matrix [σ] of the electrical conductivity of the organism is given. Usually, the initial value of the electrical conductivity is selected as 0.1S/ m, given error precision ε;

3) Calculate the electrical potential u _r (x, y, z ₀ ) of the reciprocal process according to formula (5);

4) Using formula (4) to reconstruct the conductivity distribution of the fault plane where z=z ₀ ;

5) Using the conductivity distribution of each fault obtained in step 3), the conductivity distribution of each sub-block is obtained by linear difference, so that the conductivity distribution σ ^k of the entire three-dimensional area of the organism in the k iteration is obtained;

6) Calculate the relative error between the biological conductivity distribution σ ^k obtained in the kth iteration and the k+1 biological conductivity distribution σk ⁺¹ , and compare whether the relative error meets the given error precision ε , if the given error precision ε is met, stop the iteration. Otherwise, take the conductivity distribution σ ^k of the organism obtained at the kth time as the initial conductivity distribution, and go to step 2), and the above process is iterated in turn until the relative error of the conductivity distribution of the organism obtained by two adjacent calculations satisfies Accuracy requirements.

The process of reconstruction algorithm 2 is shown in Figure 5, and the steps are as follows:

1) Using formula (14), firstly adjust the magnetoacoustic electric voltage signal u _in (r,t) collected under the excitation of the non-uniform static magnetic field B ₀ (r) to the equivalent magnetoacoustic electric voltage signal u in (r,t) collected under the excitation of the uniform field B ₀ voltage signal u _ho (r,t);

2) Then replace all non-uniform static magnetic fields B ₀ (r) in formulas (1)-(5) with uniform static magnetic fields B ₀ ;

3) Finally, use steps 1)-6) of Algorithm 1 to realize the reconstruction of electrical conductivity.

In the equivalent uniform field algebraic iterative conductivity reconstruction algorithm, the magnetoacoustic electric voltage signal u _in (r,t) collected under the excitation of the non-uniform static magnetic field B ₀ (r) is adjusted to the one collected under the excitation of the uniform static magnetic field B ₀ After the magnetoacoustic electric voltage signal u _ho (r,t), not only the direct algebraic iterative conductivity reconstruction algorithm can be used to realize the reconstruction of conductivity, but also the conductivity image can be obtained by using other reconstruction algorithms of conductivity under uniform static magnetic field excitation.

Claims (2)

1. The conductivity imaging system based on the magneto-acoustic-electric principle is characterized by comprising an imaging platform and an image reconstruction module; the imaging platform is connected with the image reconstruction module, and the acquired magneto-acoustic-electric signals are transmitted to the image reconstruction module through a transmission line; the imaging platform comprises a sound field driving excitation module, a magnetic field excitation module and a detection module; the sound field driving excitation module generates a sound field excitation source; the magnetic field excitation module is an open magnet and is placed near the organism, the generated non-uniform static magnetic field acts on the organism, the organism generates a moving source current under the action of the non-uniform static magnetic field and the sound field, and the detection module collects the moving source current and converts the moving source current into a magneto-acoustic electric voltage signal;

the sound field driving excitation module consists of an ultrasonic driving excitation source, an ultrasonic array and a coupling water bag; one end of the ultrasonic array is connected with ultrasonic driving excitation, and the other end of the ultrasonic array is contacted with the coupling water bag; the ultrasonic driving excitation source excites the ultrasonic array to generate ultrasonic waves; the coupling water bag is filled with water, and the coupling water bag is filled in a space between the ultrasonic array and the organism, so that ultrasonic waves generated by the ultrasonic array can be transmitted into the organism;

the detection module consists of an electrode, a filter circuit, an amplifying circuit and a signal acquisition device; the electrode contacts with the organism, and detects a voltage signal on the surface of the organism; one end of the electrode is connected with the organism, the other end of the electrode is connected with the input end of the filter circuit, the output end of the filter circuit is connected with the input end of the amplifying circuit, the output end of the amplifying circuit is connected with the input end of the signal acquisition device, and the output end of the signal acquisition device is connected with the image reconstruction module;

the image reconstruction module reconstructs conductivity distribution according to the magneto-acoustic-electric voltage signals of the living body output by the signal acquisition device;

the image reconstruction module utilizes the magneto-acoustic-electric voltage signal of the organism and known non-uniform magnetostatic distribution information to realize the reconstruction of conductivity distribution by adopting an image reconstruction algorithm; the image reconstruction module adopts two conductivity reconstruction algorithms to realize the reconstruction of conductivity distribution, wherein the first reconstruction algorithm is a direct algebraic iterative conductivity reconstruction algorithm, and the second reconstruction algorithm is an equivalent uniform field algebraic iterative conductivity reconstruction algorithm;

the algorithm one is a direct algebraic iterative conductivity reconstruction algorithm, and comprises the following three steps:

(1) Establishing a corresponding relation between an actual measurement process and physical quantity of a reciprocal process by utilizing a reciprocal theorem;

the actual measurement process is as follows: under the action of the ultrasonic wave generated by the ultrasonic driving excitation module and the non-uniform static magnetic field generated by the magnetic field excitation module, the vibration velocity of the particles is v, and the non-uniform static magnetic field is B ₀ (r) the magnetic field is generated by an open magnet of a magnetic field excitation module, and the inhomogeneous static magnetic field B ₀ (r) the distribution of intensity is known;

the reciprocity process is as follows: closing the acoustic field driving excitation module, disabling the magnetic field excitation module, and supplying I ampere direct current to the electrodes in the detection module, wherein the current density generated by the current in the organism is J _r (r)；

Non-uniform static magnetic field B generated by magnetic field excitation module ₀ Under the excitation of (r), the magneto-acoustic-electric voltage distribution u (r, t) and the vibration velocity potential are obtained based on the reciprocity theorem

Reciprocal process current density J _r (r), and a non-uniform static magnetic field B generated by the magnetic field excitation module ₀ The relation between (r) is:

in the formula (1), t represents ultrasonic wavesWhere omega represents the area in which the organism is located, r represents the field point, i.e. the point in the area omega in which the organism is located,

representing the vibration velocity potential ρ ₀ Density of organism, J _r (r) is the current density of the organism in the reciprocal process, B ₀ (r) non-uniform static magnetic field distribution generated by the magnetic field excitation module, < >>

Is a divergence operator;

(2) Reconstructing a reciprocal process current density J according to a formula (1) based on a magneto-acoustic-electric voltage u (r, t) measured in an actual measurement process _r (r) and static magnetic field B ₀ (r) relationship between

Vibration velocity potential

The green's function is satisfied as +.>

Bringing it into formula (1), it can be seen that the magneto-acoustic-electric voltage u (r, t) satisfies:

in the formula (2), r' is a source point and represents a point of an area where the ultrasonic array is located;

obtaining the current density J of the reciprocal process by using the formula (2) _r (r) non-uniform static magnetic field B generated by open magnet ₀ (r) and at the same time due to ρ ₀ Is constant, thus giving:

in the formula (3), c ₀ Representing the speed of ultrasonic wave generated by the sound field driving excitation module, t _rd ＝2T ₀ -t+|r-r'|/c ₀ The time of the reverse field is represented, T represents the propagation time of the ultrasonic wave, T ₀ The moment of inversion u (r, t), r ' represents the point of the region of the ultrasound array, r represents the point in the region Ω of the organism, S represents the surface of the region Ω of the organism, n is the unit normal vector at the outer boundary of the region Ω of the organism, u ' (r ', t) _rd ) Represents u (r', t) _rd ) U "(r', t) _rd ) Represents u (r', t) _rd ) A second derivative;

realizing variable by using (3)

Is reconstructed from the (a);

(3) Reconstructing a conductivity distribution from the variable H (r);

realizing the variable by using the formula (3)

After reconstruction of the distribution of (a) each slice z of the biological tissue ₀ The upper variable H (r) is +.>

Denoted as->

Namely:

wherein the variables are in brackets (x, y, z ₀ ) Representing each fault plane z of the corresponding variable in the organism ₀ Upper coordinates;

J _r (x,y,z ₀ ) Is z ₀ Current density of reciprocal process on fault plane, using ohm's law, the current density J _r (x,y,z ₀ ) Expressed as the product between the gradient of the reciprocal process potential and the conductivity, i.e.:

thus f (x, y, z) ₀ ) Represented as

Wherein u is _r (x,y,z ₀ ) The potential of the reciprocal process is z ₀ Distribution of fault plane, sigma (x, y, z ₀ ) Indicating the conductivity of the organism at z ₀ Distribution of fault planes;

the potential of the reciprocal process is at z ₀ The distribution of fault planes satisfies the following relationship:

wherein I is direct current of I ampere injected in the reciprocal process, r _A And r _B The positions of the electrode pairs in the detection module are represented, Γ represents the surface of the region Ω where the target body is located, and n represents a unit vector in the external normal direction of the surface Γ;

each fault plane z ₀ Upper part of the cylinder

The value of (a) is expressed as f (x, y, z ₀ ) From f (x, y, z ₀ ) The method steps for reconstructing the conductivity σ are as follows:

1) Dividing the organism into a series of sub-blocks, considering that the conductivity inside the sub-blocks is uniform, giving an initial value of a conductivity distribution matrix [ sigma ] of the organism, and generally selecting the initial value of the conductivity to be 0.1S/m and giving error precision epsilon;

2) Electric sign position u of reciprocal process is calculated according to formula (5) _r (x,y,z ₀ )；

3) Reconstructing z=z using equation (4) ₀ The conductivity distribution of the fault plane of (a);

4) Obtaining the conductivity distribution of each sub-block by using the conductivity distribution of each fault obtained in the step 3) and obtaining the conductivity distribution sigma of the whole three-dimensional area of the organism in the kth iteration ^k ；

5) Calculating the organism conductivity distribution sigma obtained by the kth iteration ^k And a k+1th order bioelectric conductivity distribution sigma ^k+1 Comparing whether the relative error meets the given error precision epsilon or not, and stopping iteration if the relative error meets the given error precision epsilon; otherwise, the conductivity distribution sigma of the organism obtained in the kth time is calculated ^k Turning to step 2) as initial conductivity distribution, and sequentially iterating the above processes until the relative error of the organism conductivity distribution obtained by two adjacent times of calculation meets the precision requirement;

using equations (1) and (2) can be achieved

And (3) reconstructing the biological conductivity image by using the steps 1) to 5).

2. The magneto-acoustic-electric principle based conductivity imaging system of claim 1, wherein the algorithmic equivalent uniform field algebraic iterative conductivity reconstruction algorithm is based on magneto-acoustic-electric voltage signals and a non-uniform static magnetic field B ₀ (r) in a non-uniform static magnetic field B ₀ (r) the principle of the magneto-acoustic electric voltage signal equivalent to the magneto-acoustic electric voltage signal excited by the uniform static magnetic field as the magnetic field excitation source is as follows:

given a three-dimensional model, in a non-uniform static magnetic field B ₀ Under the excitation of (r), the relation between the current I (t) corresponding to the equivalent current source in the organism and the vibration velocity v of the ultrasonic wave generated by the sound field driving excitation module in the organism is as follows:

I(t)＝∫ _s σv×B ₀ (r)·dS (6)

wherein S represents the bin of the face through which the equivalent current source flows;

according to the acoustic principle, the ultrasonic impulse M and the vibration velocity v need to satisfy:

wherein ρ is ₀ The density of the organism is such that,

is a gradient operator;

substituting formula (7) into formula (6) yields:

wherein n represents a unit vector of a normal direction of a bin of a face through which the equivalent current source flows;

further using the Stokes equation and vector identity, equation (8) reduces to:

wherein l represents a line of the outer edge of the bin, the forward direction of l and the outer normal direction of S accord with the right-hand theorem, and the normal direction of S is n;

considering that the frequency range of the energy emitted by the ultrasonic array contains very few direct current frequencies in practical application, the net momentum of the wave packet generated by the ultrasonic array is zero, so that the first term on the right of the equal sign of the formula (9) is zero;

meanwhile, in actual detection, only a part of current of an organism can be detected by the electrode, so that the current collected by the signal collection device is only a part of current I (t), the proportion between the collected voltage and the current is defined as alpha, and the detected magneto-acoustic electric voltage U (t) is expressed as:

the magneto-acoustic-electric voltage U (t) and the non-uniform static magnetic field B detected by the formula (11) ₀ (r), conductivity σ, and density ρ ₀ A relation between them;

in the practical application process, the water-based paint can be used,

is a small amount, so that the right second item of the equal sign of formula (11) is +.>

For a small amount, neglecting this small amount, equation (11) is simplified as:

in the formula (12), when the direction of the unit vector n of the normal direction of the face element of the face through which the equivalent current source flows is equal to

When the directions of (2) are the same, formula (12) is expressed as:

wherein the method comprises the steps of

Taking e of this variable _x The directional component, then equation (13) is expressed as:

wherein B is _oy And B _oz Respectively B ₀ (r) a magnetic field distribution in the y-direction and the z-direction,

representation->

And B ₀ (r) an included angle between;

equation (14) is a theoretical relationship that the magneto-acoustic electric voltage signal is equivalent to the magneto-acoustic electric voltage signal under the uniform static magnetic field excitation, and the magneto-acoustic electric signal is amplified or reduced at the position where the conductivity is changed under the non-uniform static magnetic field excitation

Doubling;

the algorithm step of the algorithm two-equivalent uniform field algebraic iterative conductivity reconstruction algorithm is as follows:

firstly, utilizing (14) to collect magneto-acoustic-electric voltage signal u under the excitation of non-uniform static magnetic field _in (r, t) is adjusted to be equivalent to a magneto-acoustic-electric voltage signal u collected under uniform field excitation _ho (r,t)；

Then all of the inhomogeneous static magnetic fields B in the formulas (1) - (5) ₀ (r) substitution with uniform static magnetic field B ₀ ；

And finally, utilizing the step 1) -5) of an algorithm-direct algebraic iterative conductivity reconstruction algorithm to realize conductivity reconstruction.

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