CN110051352B - Conductivity imaging system based on magneto-acoustic-electric principle - Google Patents
Conductivity imaging system based on magneto-acoustic-electric principle Download PDFInfo
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- A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves
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- A61B5/053—Measuring electrical impedance or conductance of a portion of the body
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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
Technical Field
The invention relates to an open type magneto-acoustic electric conductivity imaging system.
Background
The early diagnosis of the disease is significant, on one hand, pain in the treatment process of a patient can be reduced, and high medical cost is realized, and more importantly, the survival rate can be improved, and the research shows that the change of the electrical characteristics of the tissue is earlier than the pathological change of the tissue structure, so that the early diagnosis of the disease can be realized by using the imaging method with the electrical parameters as imaging target parameters. The magneto-acoustic-electric imaging uses the electric parameter as the imaging target parameter, and the medical imaging method with good application prospect has the advantages of high contrast and high resolution.
In 1998 Han wen et al proposed hall effect imaging and detected experimental signals of bacon meat with electrodes under excitation of a 4.0T magnetic resonance field static magnetic field, but the configuration of the experimental system was not so much mentioned. In 2003, hanwen in patent US6520911B1 discussed in detail this imaging system, during configuration of the system, utilizes a uniform static magnetic field as the magnetic field excitation source for magnetoacoustic imaging. In 2007, Y.xu, S Haider et al propose magneto-acoustic-electric imaging based on the Hall effect, and obtain a distribution diagram of reciprocal current density by using an experimental method, and simultaneously do simulation analysis on the current density in the reciprocal process, but do not provide a conductivity reconstruction method. For a uniform static magnetic field as a magnetic field excitation source for magneto-acoustic-electric imaging, a plurality of students have made research work on a conductivity reconstruction algorithm, and in 2014, ammari H, grasland-Mongarain P. Et al report theoretical analysis of magneto-acoustic-electric imaging and simulation research under different signal-to-noise ratio conditions (Ammari H et al, 2014). In the same year, guo Liang of institute of electrical and electronics of China academy of sciences utilizes time transfer method, compressed sensing and quasi-Newton iterative algorithm, and reconstruction of electrode detection type magneto-acoustic-electric imaging conductivity is achieved through simulation analysis (Guo L et al, 2014). The Kunyansky L2017 reports a reconstruction algorithm of a conductivity boundary, designs a 3D scanning platform, detects a magneto-acoustic-electric signal of a beef tissue by using an electrode, reconstructs interface information of the beef tissue, and does not reconstruct an image of the conductivity through experimental signals. The experimental platform reported above is either under the excitation of a uniform static magnetic field or the targeted target is a small-sized imitative structure, so it is reasonable to assume that the static magnetic field is uniform.
In summary, no practical medical system has been reported. There are two solutions for practical medical systems to achieve a static magnetic field, (1) using a uniform static magnetic field as the magnetic field excitation; (2) using a non-uniform static magnetic field as a magnetic field excitation source. The realization of the uniform static magnetic field in the scheme (1) can be referred to the design concept of the static magnetic field in the magnetic resonance imaging, the realization of the permanent magnet, the electromagnet or the superconducting magnet is adopted, the reconstruction of the conductivity can be referred to the earlier research results, but the realization of the static magnetic field with high uniformity can greatly improve the cost of a static magnetic field generating device, and further greatly improve the cost of magneto-acoustic-electric imaging clinical application equipment. And the closed environment reduces the imaging area and is not suitable for claustrophobic patients. The scheme (2) does not need a completely uniform static magnetic field generating device, so that the manufacturing cost of a medical system is greatly reduced, but the reconstruction algorithm studied at present is not applicable.
The existing magneto-acoustic-electric imaging platform is difficult to convert into a medical imaging system, and has the following defects: (1) The current theoretical model realizes a completely uniform static magnetic field aiming at the uniform static magnetic field, thereby greatly improving the manufacturing cost of equipment; (2) The non-uniform static magnetic field is used as a magnetic field excitation source to reduce the manufacturing cost of equipment, but no corresponding reconstruction algorithm exists at present.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a conductivity imaging system based on the magneto-acoustic-electric principle.
The invention discloses a conductivity imaging system based on a magneto-acoustic-electric principle, which comprises an imaging platform and an image reconstruction module. The imaging platform is connected with the image reconstruction module, and the acquired magneto-acoustic and 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, namely ultrasonic waves, the ultrasonic waves attenuate rapidly in the air, and in order to better propagate in organisms, the coupling water bag is required to be completely contacted with the sound field driving excitation module so as to reduce the attenuation of the sound waves. The non-uniform static magnetic field generated by the magnetic field excitation module acts on the living body, the living body can generate 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 magnetic field excitation module is an open magnet and is placed near the living body.
The detection module consists of an electrode, a filter circuit, an amplifying circuit and a signal acquisition device. The electrode contacts with the organism, detects the voltage signal on the surface of the organism, the filtering and amplifying circuit realizes the filtering and amplifying of the detection signal, and finally the signal acquisition device realizes the acquisition of the signal. 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 invention relates to a conductivity imaging system based on a magneto-acoustic-electric principle, which comprises the following working processes:
the ultrasonic driving excitation source of the sound field driving excitation module generates pulse excitation signals which act on the ultrasonic array, and the ultrasonic array is coupled with the organism through the coupling water bag. The ultrasonic array emits ultrasonic waves, and generates ultrasonic vibrations in the living tissue, causing local particle vibrations of the living tissue. The magnetic field excitation module generates a non-uniform static magnetic field in a biological tissue vibration area, ions vibrating in the biological tissue are subjected to the action of Lorentz force under the action of the non-uniform static magnetic field to generate charge separation, and then a local electric field is formed in the biological body to generate current distribution. The electrode attached to the organism measures the electric signal, the electric signal is filtered and amplified by the filter circuit and the amplifying circuit of the detection module, and the voltage signal is output to the image reconstruction module by the signal acquisition device. The image reconstruction module uses the magneto-acoustic-electric voltage signal of the organism and the known non-uniform magnetostatic distribution information to reconstruct the conductivity distribution by adopting an image reconstruction algorithm.
The image reconstruction module adopts two conductivity reconstruction algorithms to reconstruct 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 first algorithm, the direct algebraic iterative conductivity reconstruction algorithm, comprises the following three steps:
1. establishing the corresponding relation between the actual measurement process and the physical quantity of the reciprocal process by utilizing the reciprocal theorem
(1) 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 The distribution of (r) intensities is known.
(2) Reciprocal crossingThe 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 can be 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):
in the formula (1), t represents the propagation time of the ultrasonic wave, Ω represents the region where the living body is located, r represents the field point, i.e., the point in the region Ω where the living body 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) is the non-uniform static magnetic field distribution generated by the magnetic field excitation module, and v is the 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 Relation between (r) (J) r (r)×B 0 (r))
Vibration velocity potential in (1)
The green's function is satisfied as +.>
From the symmetry of equation (1) and green's function, it can be seen that the magneto-acoustic-electric voltage u (r, t) satisfies:
in formula (2), r' is a source point and represents a point of the region where the ultrasound array is located.
The current density J of the reciprocal process can be obtained 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 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 ) And a second derivative.
The variable H (r) =.v· (J) can be achieved using equation (3) r (r)×B 0 (r)) reconstruction.
3. Reconstructing the conductivity distribution from the variable H (r)
The variable H (r) =.v (J) is implemented using equation (3) r (r)×B 0 (r)) after the distribution of the tissue of the organism at each fault plane z 0 The upper variable H (r) is
Can be expressed 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 And (5) 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 ) Can be expressed as the product between the gradient of the reciprocal process potential and the conductivity, i.e.:
J r (x,y,z)＝-σ(x,y,z)▽u r (x,y,z)
thus f (x, y, z) 0 ) Can be expressed 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 position of the electrode pair in the detection module is represented by Γ, the surface of the region Ω where the target is located, and n represents the 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 ) Square for reconstructing conductivity sigmaThe method comprises the following steps:
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 And (3) 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 the initial conductivity distribution, the above process is iterated in sequence until the relative error of the organism conductivity distribution obtained by two adjacent calculations meets the accuracy requirement.
By using the formulas (1) and (2), the V (J) can be built r (r)×B 0 (r)) and then using the above steps 1) to 5) to realize the reconstruction of the biological conductivity image, the conductivity reconstruction algorithm is called a direct algebraic iterative conductivity reconstruction algorithm.
The second algorithm, the equivalent uniform field algebraic iterative conductivity reconstruction algorithm is as follows:
equivalent uniform field algebraic iteration conductivity reconstruction algorithm is based on magneto-acoustic-electric voltage signals and 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 uniform static magnetic field excitation as the magnetic field excitation source is as follows formulas (6) - (14).
Given a three-dimensional model, in a non-uniform static stateMagnetic 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)
where 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, and the sign of the gradient.
Substituting formula (7) into formula (6) yields:
where n represents the unit vector of the normal direction of the bin of the face through which the equivalent current source flows.
Further using the Stokes equation and vector identity, equation (8) reduces to:
where l denotes the line of the outer edge of the bin, and the forward direction of l conforms to the right-hand theorem with the outer normal direction of S, which is n.
Considering that the frequency range of the energy emitted by the ultrasonic array contains very little direct current frequency, the net momentum of the wave packet generated by the ultrasonic array is zero, so the first term to the right of the equal sign of 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) can be 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 And a relational expression between the two.
In practical application, ×B 0 (r) is a small amount, so the second term to the right of the sign of formula (11)
To a small amount, neglecting this small amount, equation (11) can be 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) can be expressed as:
wherein the method comprises the steps of
Taking e of this variable x The directional component, equation (13) can be expressed as:
wherein B is oy And B oz Respectively B 0 (r) the magnetic field distribution θ in the y-direction and the z-direction is represented
And B 0 And (r) an included angle between them.
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
Multiple times.
Algorithm two, equivalent uniform field algebraic iteration conductivity rebuilding algorithm, the flow is:
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.
In the equivalent uniform field algebraic iterative conductivity reconstruction algorithm, the magneto-acoustic-electric voltage signal u collected under the excitation of the non-uniform static magnetic field is obtained in (r, t) is adjusted to be a magneto-acoustic-electric voltage signal u collected under the excitation of a uniform static magnetic field ho After (r, t), the conductivity reconstruction can be realized by using a direct algebraic iterative conductivity reconstruction algorithm, and the conductivity image can be obtained by using other conductivity reconstruction algorithms under uniform static magnetic field excitation.
Drawings
FIG. 1 is a schematic diagram of the composition of the conductivity imaging system of the present invention;
FIG. 2 is a schematic diagram of an embodiment of the conductivity imaging system of the present invention;
FIG. 3 positional relationship between an organism and a coupling water bladder and an ultrasound array;
in the figure, an A1 ultrasonic driving excitation source, an A2 ultrasonic array, an A3 coupling water sac, an A4 magnetic field excitation module, an A5 organism, an A6 electrode, an A7 amplifying circuit, an A8 filter circuit, an A9 signal acquisition device, an A10 image reconstruction module, an A11 single ultrasonic probe, a magnetic field generated by an A12 magnetic field excitation module and an A13 particle vibration speed.
FIG. 4 is a flowchart of a reconstruction algorithm;
FIG. 5 is a second flowchart of the reconstruction algorithm.
Detailed Description
The invention is further described below with reference to the drawings and detailed description.
The invention discloses a conductivity imaging system based on a magneto-acoustic-electric principle, which comprises an imaging platform and an image reconstruction module. The imaging platform is connected with the image reconstruction module A10, and the acquired magneto-acoustic-electric signals of the imaging platform are transmitted to the reconstruction algorithm module A10.
As shown in fig. 1 and 2, the imaging platform comprises 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 magnetic field excitation A12 to act on organisms, the organisms generate a moving source current under the action of magnetic field and sound field, the detection module detects the current signal, and the image reconstruction module A10 reconstructs conductivity distribution according to the voltage signal.
The sound field driving excitation module consists of an ultrasonic driving excitation source A1, an ultrasonic array A2 and a coupling water sac A3. One end of the ultrasonic array A2 is connected with an ultrasonic driving excitation source A1, the other end of the ultrasonic array A2 is in contact with a coupling water bag A3, the coupling water bag A3 is filled between the ultrasonic array A2 and a biological body A5 and well contacts with the ultrasonic array A2 and the biological body A5, and as shown in FIG. 3, ultrasonic waves generated by exciting the ultrasonic array A2 by the ultrasonic driving excitation source A1 can be transmitted into the biological body A5.
The inhomogeneous static magnetic field a12 generated by the magnetic field excitation module A4 is generated by an open magnet.
The detection module consists of an electrode A6, a filter circuit A8, an amplifying circuit A7 and a signal acquisition device A9. The electrode A6 is contacted with the organism A5, the voltage signal on the surface of the organism is detected, the detected voltage signal is filtered and amplified by the filter circuit A8 and the amplifying circuit A7, and the voltage signal is collected by the signal collecting device A9. One end of the electrode A6 is connected with the organism A5, the other end of the electrode A6 is connected with the input end of the filter circuit A8, the output end of the filter circuit A8 is connected with the input end of the amplifying circuit A7, the output end of the amplifying circuit A7 is connected with the input end of the signal acquisition device A9, and the output end of the signal acquisition device A9 is connected with the image reconstruction module A10.
The image reconstruction module a10 reconstructs a conductivity distribution from the voltage signal of the living body A5 output from the signal acquisition device A9.
The working process of the conductivity imaging system based on the magneto-acoustic-electric principle is as follows:
the ultrasonic driving excitation source A1 of the sound field driving excitation module generates pulse excitation signals which act on the ultrasonic array A2, and the ultrasonic array A2 is coupled with the organism A5 through the coupling water bag A3. The ultrasonic array A2 emits ultrasonic waves, and generates ultrasonic vibrations in the tissue of the living body A5, thereby causing local mass point vibrations of the living body tissue. The magnetic field excitation module A4 generates a non-uniform static magnetic field a12 in the tissue vibration region of the living body A5, and ions vibrating in the tissue of the living body A5 are subjected to the lorentz force under the action of the non-uniform static magnetic field a12 to generate charge separation, so that a local electric field is formed in the living body A5, and current distribution is generated. The electrode A6 attached to the organism A5 measures the electric signal, the electric signal is filtered and amplified by the filter circuit A8 and the amplifying circuit A7 of the detection module, and the voltage signal is output to the image reconstruction module A10 by the signal acquisition device A9. The image reconstruction module A10 uses the biological A5 voltage signal and the known non-uniform static magnetic A12 distribution information to realize conductivity distribution reconstruction by adopting an image reconstruction algorithm. The image reconstruction module A10 adopts two conductivity reconstruction algorithms to reconstruct 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 first reconstruction algorithm is shown in fig. 4, and includes the following steps:
1) Reconstructing by using u (r, t) and a formula (2) to obtain the distribution of a variable H (r);
2) 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 distribution matrix [ sigma ] of the conductivity of the organism, and generally selecting the initial value of the conductivity to be 0.1S/m, giving an error precision epsilon;
3) Electric sign position u of reciprocal process is calculated according to formula (5) r (x,y,z 0 )；
4) Reconstructing z=z using equation (4) 0 The conductivity distribution of the fault plane of (a);
5) 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 ；
6) Calculating the organism conductivity distribution sigma obtained by the kth iteration k And a k+1th order bioelectric conductivity distribution sigma k+1 And (3) 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 the initial conductivity distribution, the above process is iterated in sequence until the relative error of the organism conductivity distribution obtained by two adjacent calculations meets the accuracy requirement.
The second reconstruction algorithm is shown in fig. 5, and comprises the following steps:
1) First, the inhomogeneous static magnetic field B is generated by using the method (14) 0 (r) magneto-acoustic-electric voltage signal u collected under excitation in (r, t) is adjusted to an equivalent uniform field B 0 Magneto-acoustic electric voltage signal u collected under excitation ho (r,t)；
2) Then all of the inhomogeneous static magnetic fields B in the formulas (1) - (5) 0 (r) substitution with uniform static magnetic field B 0 ；
3) Finally, the step 1) -6) of the algorithm I is utilized to realize the reconstruction of the conductivity.
In the equivalent uniform field algebraic iterative conductivity reconstruction algorithm, the non-uniform static magnetic field B 0 (r) magneto-acoustic-electric voltage signal u collected under excitation in (r, t) is adjusted to a uniform static magnetic field B 0 Magneto-acoustic electric voltage signal u collected under excitation ho After (r, t), the conductivity reconstruction can be realized by using a direct algebraic iterative conductivity reconstruction algorithm, and the conductivity image can be obtained by using other conductivity reconstruction algorithms 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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