CN1981700A - Magnetic induction and resonance resistivity imaging method and device - Google Patents

Abstract

A magnetic induction type magnetic resonance resistivity imaging method with low imaging error includes such steps as generating the alternative exciting current by an exciting coil group consisting of 4 planar circular exciting coils arranged symmetrically in pairs, using magnetic resonance to obtain the phase shift caused by the components Bz of total magnetic field in the direction of master magnetic field, obtaining the distribution of Bz from the difference between said phase shift and the phase shift of non-current exciting coil group, and obtaining the resistivity image of the object to be imaged according to the non-linear relation between component Bz and resistivity. Its apparatus is also disclosed.

Description

A kind of magnetic inductive magnetic resonance resistivity imaging method and device

Technical field

The present invention relates to a kind of medical imaging method, particularly a kind of impedance imaging method and device that utilizes mr imaging technique and magnetic induction principle.

Background technology

Traditional magnetic resonance electrical impedance imaging method is (as United States Patent (USP): US6,397,095 B1) utilize exciting electrode to imageable target body injection current, voltage by measurement electrode measurement target body boundary, detect the Distribution of Magnetic Field that injection current produces by mr techniques in the imageable target body, utilize the distribution of impedance image of the Magnetic Field application equipotential line back projection method reestablishment imaging target of surface voltage and imageable target inside.There are the following problems for this magnetic resonance electrical impedance imaging method, mainly is: there is contact impedance in the electrode that place on the imageable target surface (1), and the display case of electrode has influence on the distribution of impedance image to a great extent; (2) if there is current shielding in the imageable target, the skull in the human brain for example, then injection current is difficult to pass through, thereby influences imaging effect.

Deficiency at conventional magnetic resonance electrical impedance imaging technology, CAS Electrical Engineering Research Institute has proposed a patent of invention (a kind of impedance imaging method and device, application number: 200310112963.2), the alternating current that applies by a pair of Helmholtz coil is activated at imageable target body internal induction and goes out electric current, the Distribution of Magnetic Field that electric current produces utilizes mr techniques to record, Distribution of Magnetic Field that utilization records and electromagnetic radiation measuring instrument record the magnetic field and the Electric Field Distribution of excitation coil imaging region when no imageable target, the distribution of impedance image of the integral equation reestablishment imaging target of using electric field intensity and magnetic field intensity.For the conventional magnetic resonance electrical impedance imaging method, utilize the mode of coil stimulating both to avoid using the influence of contact impedance that electrode should rise and putting position to imageable target distribution of impedance image, avoid occurring the problem that the injection current that tissue produces of similar insulator is difficult to pass again, improved the precision of electrical impedance imaging.Yet still there is following deficiency in this method, mainly is: (1) needs to measure with the electromagnetic radiation measuring instrument electric field and the Distribution of Magnetic Field of excitation coil imaging region when no imageable target, stores as systematic parameter; (2) initial magnetic field obtains by the electromagnetic radiation measuring instrument, and the magnetic field when imaging object exists obtains by magnetic resonance, and the measurement error difference of two kinds of different measuring modes causes image error bigger; (3) relate to field type and electric field type dyadic Green's function in the algorithm for reconstructing, its singularity deals with very loaded down with trivial details; (4) adopt a pair of Helmholtz coil as excitation, the conditional number of formed coefficient matrix memory element is bigger in the image reconstruction process, and the pathosis of inverse problem is serious, influences imaging precision.

Summary of the invention

Technical problem to be solved by this invention is:

(1) overcoming prior art needs the loaded down with trivial details and not enough of electromagnetic radiation measuring instrument, avoids the big imaging error of utilizing electromagnetic radiation measuring instrument and two kinds of different measuring modes of magnetic resonance to cause simultaneously;

(2) the loaded down with trivial details and difficulty of avoiding image reconstruction field type and electric field type dyadic Green's function singularity to handle;

The pathosis of image reconstruction process inverse problem when (3) overcoming the excitation of a pair of Helmholtz coil alternating current.

The present invention proposes magnetic inductive magnetic resonance resistivity imaging method and the device thereof that a kind of accurate measurement target body resistivity distributes, carries out in view of the above image reconstruction for this reason.

The inventive method utilizes the excitation coil group to produce the alternating current excitation, at the inner faradic current that produces of imageable target body, the phase shift that utilizes total magnetic field that magnetic resonance obtains comprising real part and imaginary part to cause at the component of main field direction, do not apply the phase shift difference of electric current from this phase shift and excitation coil group, obtain the distribution of the component of total magnetic field main field direction (z direction).Excitation coil group in apparatus of the present invention is made up of four planar rondure excitation coils, and four excitation coils are tangent ground symmetric arrangement in twos, and its central axis has identical angle with the main field direction.The present invention can make the inner faradic current size and Orientation difference that produces of imageable target body, therefore the Given information amount of resistivity distribution that reflects the imaging body is abundanter, reduced the conditional number of image reconstruction coefficient matrix, the inverse problem pathosis obviously improves, and the resistivity precision increases substantially.

The inventive method has been abandoned the method that adopts the electromagnetic radiation measuring instrument to obtain initial magnetic field and Electric Field Distribution, according to the total magnetic field z component of setting up below and the non-linear relation of resistivity, obtains the resistivity image of imageable target body.

The reconstruction principles illustrated is as follows:

Excitation coil excites the alternating magnetic field of angular frequency to satisfy the Maxwell equation group

×E＝-iωB (1)

×B＝μ ₀J (2)

J＝σE (3)

Wherein σ, μ ₀Be respectively electrical conductivity and pcrmeability, E is an electric field intensity, and B is a magnetic flux density, and J is an electric current density, $i=\sqrt{-1}$ Be imaginary unit.

(3) formula two ends with multiply by substitution (1) formula behind the electricalresistivity, are launched

ρ×J+ρ×J＝-iωB (4)

μ is removed at (2) formula two ends together ₀And ask curl, have

$\frac{1}{{\mathrm{\μ}}_0}\▿\×\▿\×B=\▿\×J---\left(5\right)$

(5) formula is utilized vector identity  *  * B=  .B- ²B=- ²B can get

- ²B＝×J (6)

With (6) formula substitution (4) formula, and extract its z component, have

$\frac{\∂\mathrm{\ρ}}{\∂x}{J}_y-\frac{\∂\mathrm{\ρ}}{\∂y}{J}_x-\mathrm{\ρ}\frac{{\▿}^2{B}_Z}{{\mathrm{\μ}}_0}=-\mathrm{i\ω}{B}_z---\left(7\right)$

J wherein _x, J _yBe respectively the x of electric current density, y component, B _zZ component (J for magnetic induction _x, J _yAnd B _ZBe plural number, comprise real component J respectively _XR, J _YR, B _ZRWith imaginary part component J _XI, J _YI, B _ZI).

(7) formula is pressed real part and imaginary part decomposition, then have

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂x}{J}_{\mathrm{yR}}-\frac{\∂\mathrm{\ρ}}{\∂y}{J}_{\mathrm{xR}}-\mathrm{\ρ}\frac{{\▿}^2{B}_{\mathrm{zR}}}{{\mathrm{\μ}}_0}=\mathrm{\ω}{B}_{\mathrm{zI}}\\ \frac{\∂\mathrm{\ρ}}{\∂x}{J}_{\mathrm{yI}}-\frac{\∂\mathrm{\ρ}}{\∂y}{J}_{\mathrm{xI}}-\mathrm{\ρ}\frac{{\▿}^2{B}_{\mathrm{zI}}}{{\mathrm{\μ}}_0}=-\mathrm{\ω}{B}_{\mathrm{zR}}\end{array}\right.---\left(8\right)$

B _ZRAnd B _ZICan utilize magnetic resonance to record, and J _x, J _yDepend on ρ, therefore the described partial differential equations of (8) formula is non-linear, adopts iterative method reconstruct electricalresistivity's distribution.That is:

(1) set up the geometric model of cubical cellular subdivision according to the reconstructed object body, for any one x, the y section, getting discrete steps is Δ x=Δ y=h, x, the y direction comprises L and M unit respectively, and then each section contains L * M unit;

(2) be stored in the regional resistivity unit after giving initial electrical resistivity to subregion;

(3) obtain imageable target volume current density distribution J with 3 D electromagnetic field finite element solving device _xAnd J _y, respectively it is decomposed into real component J _XR, J _YRWith imaginary part component J _XI, J _YI

(4) adopt finite difference discrete to (8) formula,, have for any one unit

$\left\{\begin{array}{c}[\mathrm{\ρ}(i+1,j,k)-\mathrm{\ρ}(i-1,j,k)]J_{\mathrm{yR}}(i,j,k)-[\mathrm{\ρ}(i.j+1,k)-\mathrm{\ρ}(i,j-1,k)]J_{\mathrm{xR}}(i,j,k)-\\ \frac{2\mathrm{h\ρ}(i,j,k)}{{\mathrm{\μ}}_0}{\▿}^2{B}_{\mathrm{zR}}(i,j,k)=2\mathrm{h\ω}{B}_{\mathrm{zI}}(i,j,k)\\ [\mathrm{\ρ}(i+1,j,k)-\mathrm{\ρ}(i-1,j,k)]J_{\mathrm{yI}}(i,j,k)-[\mathrm{\ρ}(i,j+1,k)-\mathrm{\ρ}(i,j-1,k)]J_{\mathrm{xI}}(i,j,k)-\\ \frac{2\mathrm{h\ρ}(i,j,k)}{{\mathrm{\μ}}_0}{\▿}^2{B}_{\mathrm{zI}}(i,j,k)=-2\mathrm{h\ω}{B}_{\mathrm{zR}}(i,j,k)\end{array}\right.---\left(9\right)$

Wherein

$\left\{\begin{array}{c}{\▿}^2{B}_{\mathrm{zR}}(i,j,k)=\frac{1}{6}[B_{\mathrm{zR}}(i+1,j,k)+B_{\mathrm{zR}}(i-1,j,k)+B_{\mathrm{zR}}(i,j+1,k)+B_{\mathrm{ZR}}(i,j-1,k)\\ +B_{\mathrm{zR}}(i,j,k+1)+B_{\mathrm{zR}}(i,j,k-1)-B_{\mathrm{ZR}}(i,j,k)]\\ {\▿}^2{B}_{\mathrm{zI}}(i,j,k)=\frac{1}{6}[B_{\mathrm{zI}}(i+1,j,k)+B_{\mathrm{zI}}(i-1,j,k)+B_{\mathrm{zI}}(i,j+1,k)+B_{\mathrm{zI}}(i,j-1,k)\\ +B_{\mathrm{zI}}(i,j,k+1)+B_{\mathrm{zI}}(i,j,k-1)-B_{\mathrm{zI}}(i,j,k)]\end{array}\right.---\left(10\right)$

L * M unit forms 2 * L * M equation group, and for four motivation models, the dimension of the combination coefficient matrix S of the equation group that forms is P * P, and P=8 * L * M;

(5) combination coefficient matrix S singular value decomposition is obtained generalized inverse matrix S ^-

(6) with the magnetic field B that records _ZRAnd B _ZIPut into the magnetic field vector memory element by the zone;

(7) utilizing multiplier to carry out generalized inverse matrix and magnetic field vector multiplies each other and obtains upgrading the back resistivity distribution;

(8) set stopping criterion for iteration: this resistivity distribution deducts initial electrical resistivity and distributes, and asks its 2 norm, is divided by with 2 norms that initial electrical resistivity distributes, if it is less than precision given in advance, then iterative process stops; Otherwise, upgrade regional resistivity memory element with new resistivity distribution, repeating step (3)～(8);

(9) regional resistivity distribution is carried out pictorial display by the height difference.

Adopt the magnetic resonance electrical impedance imaging device of the invention described above method, it is made up of current excitation coil groups, magnet for magnetic resonant imaging, radio-frequency sending coil and gradient coil, magnetic resonance signal receiving coil, magnetic resonance imaging system, excitation current source and computer.Magnetic resonance imaging system comprises imaging spectrometer, radio-frequency (RF) power amplification and gradient power supply.Radio-frequency sending coil generally adopts planar coil, is installed on the last bottom crown of magnet for magnetic resonant imaging, is used for being encoded in the locus of imageable target.Receiving coil covers on the outside of imageable target, is used to receive the echo-signal of magnetic resonance, and different imageable target can have different receiving coils.Magnet for magnetic resonant imaging, excitation coil group, radio-frequency sending coil, gradient coil and magnetic resonance signal receiving coil place radio shielding indoor, it is outdoor that magnetic resonance imaging system and excitation current source are placed on radio shielding, is connected with radio-frequency sending coil, gradient coil, magnetic resonance signal receiving coil by cable.The excitation coil group is connected by cable with excitation current source.Imaging sequence is input to imaging spectrometer by computer, imaging spectrometer is according to imaging sequence control radio-frequency (RF) power amplification and gradient power supply, thereby realize control to radio-frequency coil and gradient coil, and by the control of control excitation current source realization to the excitation coil group, the magnetic resonance signal receiving coil is delivered to imaging spectrometer with the signal that receives, and is delivered to computer by imaging spectrometer and carries out image reconstruction.

MR imaging apparatus of the present invention is used to produce the excitation coil group of alternating current and is made up of four coils, be installed in the radio-frequency coil top of open type magnetic resonance imaging (MRI) system top crown respectively, the central axis of each coil and main field direction, promptly the z direction has identical angle (10 °～45 °).Coil is by the close coiled hollow cylinder of multiturn copper cash, excitation current source utilizes one tunnel control signal of nuclear magnetic resonance spectrometer to realize through power amplification at the driver element of magnetic resonance imaging system, it is the excitation coil power supply, imposes on the magnetic field that the electric current of each excitation coil should guarantee to produce at imaging region 15～25 Gauss's uneven distributions separately.

The present invention measures B _ZStep be described below:

(1) puts into imageable target, under the situation that excitation coil does not power up, utilize magnetic resonance imaging system and spin-echo imaging sequence, the magnetic resonance signal when not had excitation field can obtain the phase image Φ of imageable target in the case by Fourier transform ₀(x, y).

(2) real part and the imaginary part of note secondary magnetic field z component are respectively B _SZRAnd B _SZI, the z component B of total magnetic field _ZBe the z component B in first magnetic field _PZZ component B with secondary magnetic field _SZSum, its real part B _ZRBe B _SZRZ component B with first magnetic field _PZSum, imaginary part B _ZIBe B _SZIUnder the situation that four excitation coils power up successively, utilize magnetic resonance imaging system and spin-echo imaging sequence, imaging sequence when not powering up is compared, and applies excitation field when difference is phase code, and N time 180 ° of (N for greater than 2 odd number) radio-frequency pulses are applied to B _PZPeak value on, obtain magnetic resonance signal, can obtain the phase image Φ of imageable target in such cases by Fourier transform ₁(x, y).

(3) under the situation that four excitation coils power up, utilize magnetic resonance imaging system and spin-echo imaging sequence, imaging sequence when not powering up is compared, and applies excitation field when difference is phase code, and N 180 ° of radio-frequency pulses (N is the odd number greater than 2) are applied to B _SZIPeak value on, B in each half period _SZIThe phase shift that produces is zero, and B _SZICompare B _ZRLag behind 90 °, obtain magnetic resonance signal, can obtain the phase image Φ of imageable target in such cases by Fourier transform ₂(x, y).

(4) phase place to (1) (2) twice magnetic resonance image (MRI) compares, and obtains the phase difference ΔΦ of magnetic resonance image (MRI) under the both of these case ₁(x, y)=Φ ₁(x, y)-Φ ₀(x, y), according to the equation ΔΦ ₁(x, y)=(1) ^Nγ＜B _SZ(x, y)〉TC (wherein γ, T _C,＜B _SZ(x, y〉be respectively gyromagnetic ratio, current duration and B _SZTime average in the positive half period) calculates total magnetic field in the imageable target at the imaginary part component B of main field direction _ZI

(5) phase place to (1) (3) twice magnetic resonance image (MRI) compares, and obtains the phase difference ΔΦ of magnetic resonance image (MRI) under the both of these case ₂(x, y)=Φ ₂(x, y)-Φ ₀(x, y), according to the equation ΔΦ ₂(x, y)=(1) ^Nγ＜B _RZ(x, y)〉and TC (wherein＜B _RZ(x, y)〉be B _RZTime average in the positive half period) calculates total magnetic field in the imageable target at the real component B of main field direction _ZR

(6) utilize top (4) and (5) to obtain B _Z, according to the resistivity of equation (8) announcement and the relation of total magnetic field distribution, the resistivity distribution image of reestablishment imaging target.

The inventive method has following characteristics:

The inventive method does not need to measure the imageable target surface potential and distributes, the electric field and the Distribution of Magnetic Field of imaging region when not needing to adopt the electromagnetic radiation measuring instrument to measure no imaging object, the metering system that only utilizes the total magnetic field in excitation induced, the magnetic resonance measurement imageable target to distribute along the component of main field direction, the acquisition total magnetic field can be embodied as picture along the distribution of the component of main field direction, has reduced and has used the electromagnetic radiation measuring instrument simultaneously because the resistivity trueness error that different measuring mode difference causes.So both can obtain more the rich data amount, can accurately try to achieve the resistivity distribution of imageable target.

The inventive method is on image reconstructor, no longer utilize field type and electric field type integral equation to rebuild principle, but the non-linear relation of utilizing the total magnetic field to set up along the partial differential equation of the component of main field direction and resistivity rebuilds, and do not need to handle field type and electric field type dyadic Green's function singularity.

Utilize in the data of image reconstruction, the inventive method utilizes four coil stimulatings to obtain the total magnetic field distribution simultaneously, and the total magnetic field had both comprised that real component also comprised the imaginary part component simultaneously, and the rich data amount makes the resistivity precision significantly improve.

Apparatus of the present invention are aspect motivation model, adopt four coils to encourage respectively, the initial magnetic field of encouraging with prior art is uniform magnetic field in imaging region, the situation contrast that the inductive current direction that produces in the imageable target body is close, the present invention can make the inner faradic current size and Orientation difference that produces of imageable target body, therefore the Given information amount that reflects the resistivity distribution of imaging body is enriched, reduced the conditional number of image reconstruction coefficient matrix, the inverse problem pathosis obviously improves, and the resistivity precision that obtains the imageable target body increases substantially.

Apparatus of the present invention have been abandoned the electromagnetic radiation measuring instrument, have avoided the measurement initial magnetic field to distribute and Electric Field Distribution, also need not it is stored as systematic parameter, have overcome the loaded down with trivial details of prior art operation.

Description of drawings

Further specify the present invention below in conjunction with the drawings and specific embodiments.

Fig. 1 is apparatus of the present invention specific embodiment structural representation, among the figure: 10 excitation coil groups, 20 magnet for magnetic resonant imaging, radio-frequency coil and gradient coil, 40 magnetic resonance imaging systems, 50 excitation current sources, 60 computers, 70 image reconstructor;

Fig. 2 is the sketch map of apparatus of the present invention excitation coil group;

Fig. 3 is an image reconstructor theory diagram of the present invention.

Specific embodiment

As shown in Figure 1, magnetic induction magnetic resonance electrical impedance imaging device of the present invention comprises excitation current source 50, magnetic resonance imaging system 40, computer 60, image reconstructor 70.Excitation current source 50, magnetic resonance imaging system 40, computer 60, image reconstructor 70 is linked in sequence successively.20 expression magnet for magnetic resonant imaging, radio-frequency coil and gradient coils.Excitation coil group 10 is installed in the top crown of magnet for magnetic resonant imaging.Excitation coil group 10 is made up of four planar rondure excitation coils 1,2,3,4 as shown in Figure 2, and coil 1,2,3,4 is tangent ground symmetric arrangement in twos, and the hub of a spool axis has identical angle with the main field direction.Each coils from parallel connection of coils is connected on the excitation current source 50, and the terminal voltage of excitation current source 50 is 120V, and maximum output current is 80 amperes.

Magnetic resonance imaging system 40 comprises imaging spectrometer, radio-frequency (RF) power amplification and gradient power supply, and magnetic resonance signal receiving coil 30 is connected with imaging spectrometer in the magnetic resonance imaging system 40, and the main field that places the magnetic resonance magnet to produce.Excitation current source 50 utilizes one tunnel control signal of the nuclear magnetic resonance spectrometer in the magnetic resonance imaging system 40 to realize through power amplification.

In the present embodiment, the interior diameter of each coil is 400mm, and overall diameter is 450mm, highly is 5mm, and close around forming by the copper cash of Φ 5mm, the number of turn is 10.The angle of the axis of each coil and main field direction is 20 °, and exciting current is 70 amperes, then produces the non-uniform magnetic field of 15-25 in imaging region.

The step of induction type magnetic resistance at resonance rate formation method specific embodiment of the present invention is as follows:

(1) initial phase image Φ ₀(x, acquisition y): imageable target 80 is placed in the magnetic field that is produced by magnet for magnetic resonant imaging, and receiving coil 30 covers on the outside of imageable target, is used for receiving the echo-signal of magnetic resonance.Main field strength is 0.25 tesla, and the Rameau frequency is about 10MHz, and magnetic field gradient is 120 Gauss/rice.Utilize magnetic resonance imaging system and spin-echo imaging sequence, the magnetic resonance signal when not had excitation field can obtain the phase image Φ of imageable target in the case by Fourier transform ₀(x, y).

(2) phase image Φ ₁(x, y) acquisition: producing frequency by excitation current source 50 is that 1kHZ, current intensity peak value are the sinusoidal signal of I=70A, input to excitation coil 1,2,3 and 4 respectively, utilize magnetic resonance imaging system, imaging sequence when not powering up is compared, apply excitation field when difference is phase code, N time 180 ° of radio-frequency pulses are applied to the close B of first magnetic _PZPeak value on, in this enforcement in, N gets 39 times, obtains magnetic resonance signal, can obtain the phase image Φ of imageable target in such cases by Fourier transform ₁(x, y).

(3) phase image Φ ₂(x, y): producing frequency by excitation current source 50 is that 1kHZ, current intensity peak value are the sinusoidal signal of I=70A, input to excitation coil 1,2,3 and 4 respectively, imaging sequence when utilizing magnetic resonance imaging system and not powering up is compared, apply excitation field when difference is phase code, N time 180 ° of radio-frequency pulses are applied to the close B of secondary magnetic _PZPeak value on, in this enforcement in, N gets 39 times, obtains magnetic resonance signal, can obtain the phase image Φ of imageable target in such cases by Fourier transform ₂(x, y).

(4) total magnetic field imaginary part component: to phase image Φ ₁(x, y) and Φ ₀(x y) compares, according to the equation ΔΦ ₁(x, y)=(1) ^Nγ＜B _SZ(x, y)〉T _CCalculate total magnetic field in the imageable target at the imaginary part component of main field direction.

(5) total magnetic field real component: to phase image Φ ₂(x, y) and Φ ₀(x y) compares, according to the equation ΔΦ ₂(x, y)=(1) ^Nγ＜B _RZ(x, y)〉T _CCalculate total magnetic field in the imageable target in the real component of main field direction.

(6) image reconstruction: utilize the total magnetic field to realize that according to equation (8) and reconstructor block diagram reconstructs the resistivity distribution image.

Fig. 3 is an image reconstructor theory diagram of the present invention.

As shown in Figure 3, step 1 is set up the geometric model of cube cellular subdivision according to the reconstructed object body, for any one x, and the y section, getting discrete steps is Δ x=Δ y=h, x, the y direction comprises L and M unit respectively, and then each section contains L * M unit;

Step 2 is stored in the regional resistivity unit after giving initial electrical resistivity to subregion;

Step 3 obtains imageable target volume current density distribution J with 3 D electromagnetic field finite element solving device _xAnd J _y, respectively it is decomposed into real component J _XR, J _YRWith imaginary part component J _XI, J _YI

Step 4 adopts finite difference discrete to (8) formula, for any one unit, has

$\left\{\begin{array}{c}[\mathrm{\ρ}(i+1,j,k)-\mathrm{\ρ}(i-1,j,k)]J_{\mathrm{yR}}(i,j,k)-[\mathrm{\ρ}(i,j+1,k)-\mathrm{\ρ}(i,j-1,k)]J_{\mathrm{xR}}(i,j,k)-\\ \frac{2\mathrm{h\ρ}(i,j,k)}{{\mathrm{\μ}}_0}{\▿}^2{B}_{\mathrm{zR}}(i,j,k)=2\mathrm{h\ω}{B}_{\mathrm{zI}}(i,j,k)\\ [\mathrm{\ρ}(i+1,j,k)-\mathrm{\ρ}(i-1,j,k)]J_{\mathrm{yI}}(i,j,k)-[\mathrm{\ρ}(i,j+1,k)-\mathrm{\ρ}(i,j-1,k)]J_{\mathrm{xI}}(i,j,k)-\\ \frac{2\mathrm{h\ρ}(i,j,k)}{{\mathrm{\μ}}_0}{\▿}^2{B}_{\mathrm{zI}}(i,j,k)=-2\mathrm{h\ω}{B}_{\mathrm{zR}}(i,j,k)---\left(9\right)\end{array}\right.$

Wherein

$\left\{\begin{array}{c}{\▿}^2{B}_{\mathrm{zR}}(i,j,k)=\frac{1}{6}[B_{\mathrm{zR}}(i+1,j,k)+B_{\mathrm{zR}}(i-1,j,k)+B_{\mathrm{zR}}(i,j+1,k)+B_{\mathrm{zR}}(i,j-1,k)\\ +B_{\mathrm{zR}}(i,j,k+1)+B_{\mathrm{zR}}(i,j,k-1)-B_{\mathrm{zR}}(i,j,k)]\\ {\▿}^2{B}_{\mathrm{zI}}(i,j,k)=\frac{1}{6}[B_{\mathrm{zI}}(i+1,j,k)+B_{\mathrm{zI}}(i-1,j,k)+B_{\mathrm{zI}}(i,j+1,k)+B_{\mathrm{zI}}(i,j-1,k)\\ +B_{\mathrm{zI}}(i,j,k+1)+B_{\mathrm{zI}}(i,j,k-1)-B_{\mathrm{zI}}(i,j,k)]\end{array}\right.---\left(10\right)$

L * M unit forms 2 * L * M equation group, and for four motivation models, the dimension of the combination coefficient matrix S of the equation group that forms is P * P, and P=8 * L * M;

Step 5 obtains generalized inverse matrix S to combination coefficient matrix S singular value decomposition ^-

Step 6 is with the magnetic field B that records _ZRAnd B _ZIPut into the magnetic field vector memory element by the zone;

Step 7 is utilized multiplier to carry out generalized inverse matrix and magnetic field vector and is multiplied each other and obtain upgrading the back resistivity distribution; Step 8, set stopping criterion for iteration: this resistivity distribution deducts initial electrical resistivity and distributes, and asks its 2 norm, be divided by with 2 norms that initial electrical resistivity distributes, if it is not less than precision given in advance, execution in step 10 is upgraded regional resistivity memory element with new resistivity distribution, return step 3, repeated execution of steps 3～8, up to the judged result of step 8 for being that then iterative process stops, execution in step 9 is carried out pictorial display with regional resistivity distribution by the height difference.

Claims (4)

1, a kind of magnetic inductive magnetic resonance resistivity imaging method, it is characterized in that utilizing excitation coil group [10] to produce the alternating current excitation, at the inner faradic current that produces of imageable target body, utilize magnetic resonance to obtain comprising the component B of the total magnetic field of real part and imaginary part in the main field direction _ZThe phase shift that causes does not apply the phase shift difference of electric current from this phase shift and excitation coil group [10], obtains the component B of total magnetic field in the main field direction _ZDistribute, according to B _ZWith electricalresistivity's non-linear relation, obtain the resistivity image of imageable target body.

2, according to the described magnetic inductive magnetic resonance of claim 1 resistivity imaging method, it is characterized in that B _ZMeasuring process as follows:

(1) puts into imageable target, under the situation that excitation coil does not power up, utilize magnetic resonance imaging system and spin-echo imaging sequence, the magnetic resonance signal when not had excitation field can obtain the phase image Φ of imageable target in the case by Fourier transform ₀(x, y);

(2) real part and the imaginary part of note secondary magnetic field z component are respectively B _SZRAnd B _SZI, the z component B of total magnetic field _ZBe the z component B in first magnetic field _PZZ component B with secondary magnetic field _SZSum, its real part B _ZRBe B _SZRZ component B with first magnetic field _PZSum, imaginary part B _ZIBe B _SZIUnder the situation that four excitation coils power up successively, utilize magnetic resonance imaging system and spin-echo imaging sequence, imaging sequence when not powering up is compared, when being phase code, difference applies excitation field, the radio-frequency pulse of N time 180 ° (N is the odd number greater than 2) is applied on the peak value of BPZ, obtain magnetic resonance signal, can obtain the phase image Φ of imageable target in such cases by Fourier transform ₁(x, y);

(3) under the situation that four excitation coils power up, utilize magnetic resonance imaging system and spin-echo imaging sequence, imaging sequence when not powering up is compared, and applies excitation field when difference is phase code, and N 180 ° of radio-frequency pulses (N is the odd number greater than 2) are applied to B _SZIPeak value on, B in each half period _SZIThe phase shift that produces is zero, and B _SZICompare B _ZRLag behind 90 °, obtain magnetic resonance signal, can obtain the phase image Φ of imageable target in such cases by Fourier transform ₂(x, y);

(4) phase place to (1), (2) twice magnetic resonance image (MRI) compares, and obtains the phase difference ΔΦ of magnetic resonance image (MRI) under the both of these case ₁(x, y)=Φ ₁(x, y)-Φ ₀(x, y), according to the equation ΔΦ ₁(x, y)=(1) ^Nγ＜B _SZ(x, y)〉T _C(wherein γ, T _C,＜B _SZ(x, y〉be respectively gyromagnetic ratio, current duration and B _SZTime average in the positive half period) calculates total magnetic field in the imageable target at the imaginary part component B of main field direction _ZI

(5) phase place to (1), (3) twice magnetic resonance image (MRI) compares, and obtains the phase difference ΔΦ of magnetic resonance image (MRI) under the both of these case ₂(x, y)=Φ ₂(x, y)-Φ ₀(x, y), according to the equation ΔΦ ₂(x, y)=(1) ^Nγ＜B _RZ(x, y)〉T _C(wherein＜B _RZ(x, y)〉be B _RZTime average in the positive half period) calculates total magnetic field in the imageable target at the real component B of main field direction _ZR

(6) utilize top (4) and (5) to obtain B _Z

(7) set up B _ZNon-linear relation with the electricalresistivity:

Excitation coil excites the alternating magnetic field of angular frequency to satisfy the Maxwell equation group

×E＝-iωB (1)

×B＝μ ₀J (2)

J＝σE (3)

Wherein σ, μ ₀Be respectively electrical conductivity and pcrmeability, E is an electric field intensity, and B is a magnetic flux density, and J is an electric current density, $i=\sqrt{-1}$ Be imaginary unit;

(3) formula two ends with multiply by substitution (1) formula behind the electricalresistivity, are launched

ρ×J+ρ×J＝-iωB (4)

μ is removed at (2) formula two ends together ₀And ask curl, have

$\frac{1}{{\mathrm{\μ}}_0}\▿\×\▿\×B=\▿\×J---\left(5\right)$

(5) formula is utilized vector identity  *  * B=  B- ²B=- ²B can get

- ²B＝×J (6)

With (6) formula substitution (4) formula, and extract its z component, have

$\frac{\∂\mathrm{\ρ}}{\∂x}{J}_y-\frac{\∂\mathrm{\ρ}}{\∂y}{J}_x-\mathrm{\ρ}\frac{{\▿}^2{B}_z}{{\mathrm{\μ}}_0}=-\mathrm{i\ω}{B}_z---\left(7\right)$

J wherein _x, J _yBe respectively the x of electric current density, y component, B _ZZ component (J for magnetic induction _x, J _yAnd B _ZBe plural number, comprise real component J respectively _XR, J _YR, B _ZRWith imaginary part component J _XI, J _YI, B _ZI);

(7) formula is pressed real part and imaginary part decomposition, then have

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂x}{J}_{\mathrm{yR}}-\frac{\∂\mathrm{\ρ}}{\∂y}{J}_{\mathrm{xR}}-\mathrm{\ρ}\frac{{\▿}^2{B}_{\mathrm{zR}}}{{\mathrm{\μ}}_0}=\mathrm{\ω}{B}_{\mathrm{zI}}\\ \frac{\∂\mathrm{\ρ}}{\∂x}{J}_{\mathrm{yI}}-\frac{\∂\mathrm{\ρ}}{\∂y}{J}_{\mathrm{xI}}-\mathrm{\ρ}\frac{{\▿}^2{B}_{\mathrm{zI}}}{{\mathrm{\μ}}_0}=-\mathrm{\ω}{B}_{\mathrm{zR}}\end{array}\right.---\left(8\right)$

3, according to the described magnetic inductive magnetic resonance of claim 1 resistivity imaging method, it is characterized in that utilizing B _ZAnd B _ZAs follows with the method step order of electricalresistivity's non-linear relation reconstruct electricalresistivity's distribution:

Step 1 is set up the geometric model of cube cellular subdivision according to the reconstructed object body, for any one x, and the y section, getting discrete steps is Δ x=Δ y=h, x, the y direction comprises L and M unit respectively, and then each section contains L * M unit;

Step 2 is stored in the regional resistivity unit after giving initial electrical resistivity to subregion;

Step 3 obtains imageable target volume current density distribution J with 3 D electromagnetic field finite element solving device _xAnd J _y, respectively it is decomposed into real component J _XR, J _YRWith imaginary part component J _XI, J _YI

Step 4 adopts finite difference discrete to (8) formula, for any one unit, has

$\left\{\begin{array}{c}[\mathrm{\ρ}(i+1,j,k)-\mathrm{\ρ}(i-1,j,k)]J_{\mathrm{yR}}(i,j,k)-[\mathrm{\ρ}(i,j+1,k)-\mathrm{\ρ}(i,j-1,k)]J_{\mathrm{xR}}(i,j,k)-\\ \frac{2\mathrm{h\ρ}(i,j,k)}{{\mathrm{\μ}}_0}{\▿}^2{B}_{\mathrm{zR}}(i,j,k)=2\mathrm{h\ω}{B}_{\mathrm{zI}}(i,j,k)\\ [\mathrm{\ρ}(i+1,j,k)-\mathrm{\ρ}(i-1,j,k)]J_{\mathrm{yI}}(i,j,k)-[\mathrm{\ρ}(i,j+1,k)-\mathrm{\ρ}(i,j-1,k)]J_{\mathrm{xI}}(i,j,k)-\\ \frac{2\mathrm{h\ρ}(i,j,k)}{{\mathrm{\μ}}_0}{\▿}^2{B}_{\mathrm{zI}}(i,j,k)=-2\mathrm{h\ω}{B}_{\mathrm{zR}}(i,j,k)\end{array}\right.---\left(9\right)$

Wherein

$\left\{\begin{array}{c}{\▿}^2{B}_{\mathrm{zR}}(i,j,k)=\frac{1}{6}[B_{\mathrm{zR}}(i+1,j,k)+B_{\mathrm{zR}}(i-1,j,k)+B_{\mathrm{zR}}(i,j+1,k)+B_{\mathrm{zR}}(i,j-1,k)\\ +B_{\mathrm{zR}}(i,j,k+1)+B_{\mathrm{zR}}(i,j,k-1)-B_{\mathrm{zR}}(i,j,k)]\\ {\▿}^2{B}_{\mathrm{zI}}(i,j,k)=\frac{1}{6}[B_{\mathrm{zI}}(i+1,j,k)+B_{\mathrm{zI}}(i-1,j,k)+B_{\mathrm{zI}}(i,j+1,k)+(i,j-1,k)\\ +B_{\mathrm{zI}}(i,j,k+1)+B_{\mathrm{zI}}(i,j,k-1)-B_{\mathrm{zI}}(i,j,k)]\end{array}\right.---\left(10\right)$

L * M unit forms 2 * L * M equation group, and for four motivation models, the dimension of the combination coefficient matrix S of the equation group that forms is P * P, and P=8 * L * M;

Step 5 obtains generalized inverse matrix S to combination coefficient matrix S singular value decomposition ^-

Step 6 is with the magnetic field B that records _ZRAnd B _ZIPut into the magnetic field vector memory element by the zone;

Step 7 is utilized multiplier to carry out generalized inverse matrix and magnetic field vector and is multiplied each other and obtain upgrading the back resistivity distribution;

Step 8, set stopping criterion for iteration: this resistivity distribution deducts initial electrical resistivity and distributes, and asks its 2 norm, be divided by with 2 norms that initial electrical resistivity distributes, if it is not less than precision given in advance, execution in step 10 is upgraded regional resistivity memory element with new resistivity distribution, return step 3, repeated execution of steps 3～8, up to the judged result of step 8 for being that then iterative process stops, execution in step 9 is carried out pictorial display with regional resistivity distribution by the height difference.

4, application rights requires the device of 1 described magnetic inductive magnetic resonance resistivity imaging method, it is characterized in that excitation coil group [10] is made up of four planar rondure excitation coils [1], [2], [3], [4], coil [1], [2], [3], [4] are tangent ground symmetric arrangement in twos, and the hub of a spool axis has identical angle with the main field direction.

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