CN104352239B - A kind of magnetic resonance tissue electrical characteristics tomograph imaging method - Google Patents

Abstract

The present invention relates to a kind of tissue physical characteristic parameter MRT method, comprising: 1) according to what magnetic resonance radio frequency field obtainedAnd magnetic resonance proton density imaging obtainsIn conjunction with principle of reciprocity and magnetic field Gauss theorem, it is calculated B_1x(r)、B_1y(r)、B_1z(r)；By B_1x(r)、B_1y(r)、B_1zWhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group, and be electrical conductivity mean value and capacitivity mean value in tissue by the initial value relative set of imaging region inner tissue conductivityσ (r) everywhere He capacitivity ∈ (r), obtain E_1x(r)、E_1y(r)、E_1z(r)；3) carry out iterating computing, until algorithmic statement, the now distribution of imaging region inner tissue σ (r) everywhere and ∈ (r) is striked tissue electrical characteristic parameter distribution results；4) according to imaging region inner tissue electrical characteristic parameter distribution results output image.

Description

A kind of magnetic resonance tissue electrical characteristics tomograph imaging method

Technical field

The invention belongs to magnetic resonance imaging arts, relate to a kind of tissue physical characteristic parameter MRT side Method, is specifically related to a kind of power transformation characterisitic parameter Fdtd Method (FDTD) iterative approach formula and solves tissue electrical characteristic parameter (including electrical conductivity and capacitivity), it is achieved the method for tissue electrical characteristic parameter MRT, the human body group obtained Knit electrical characteristic parameter distributed image to can be used to instruct clinical tumor extreme early or early diagnosis.

Background technology

The electromagnetic property that material shows in electromagnetic field can be regarded as the build-in attribute of material, and tissue is the most not Exception.Tissue can show certain electrical characteristics and magnetic characteristic in electromagnetic field.Electrical characteristics, otherwise referred to as dielectric property (EPs), being primarily referred to as electrical conductivity and the capacitivity of tissue, magnetic characteristic refers to the magnetic conductivity of tissue.It is said that in general, tissue is Namagnetic substance, its magnetic conductivity, close to the magnetic conductivity in vacuum, is regarded as constant.Tissue EPs everywhere and tissue The cell membrane of the insulation of interior non-uniform Distribution and the electrolyte of conduction etc. are relevant, therefore organize everywhere EPs distribution present non-all Even property, and there is frequency dependence.When the physiology of essential structure unit cell of tissue and pathological state change, The EPs of tissue also will change.Early in vitro tissue electrical characteristic parameter test experiments is had to confirm, normal structure and tumor tissues EPs often differs greatly, and some difference has been even up to more than 10 times.If able to non-invasively the EPs of biological tissue is carried out Imaging, these EPs images, by reflection tissue, the physiology of organ and pathological state, may provide valuable information for diagnosis.Special Not, biological tissue EPs imaging is possibly used for cancer extreme early or early diagnosis, in some instances it may even be possible to for tracking monitor normal structure The whole change procedure developed to tumor tissues, research and treatment to cancer are likely to be of initiative value.Visible, human body Biological tissue EPs imaging, has the most tempting huge potential applicability in clinical practice.

The sciences problems that noninvasive human body biological tissue electrical characteristics imaging is not always captured.Scholar is it is believed that in recent years Before magnetic resonance tissue electrical characteristics fault imaging (MR EPT) technology being suggested and being rapidly developed has wide development Scape, it is possible to promoting the human body noninvasive imaging progress of biological tissue EPs to the brand-new stage, producing this expectation is by MR The feature of EPT know-why itself determines.Fundamentally, magnetic resonance imaging (MRI) is tissue and certain electric magnetic field The system that (i.e. strong static magnetic field, gradient magnetic and radio frequency electromagnetic field) interacts, therefore, the MR signal that MRI system detects In, necessarily carry tissue electromagnetic property distributed intelligence.Research confirms, the sensor of detection human body magnetic resonance (MR) signal RF coil, the RF field distribution of its lateral cross section is strongly depend on the EPs distribution of tissue.RF field is utilized to video (B₁Etc. Mapping) technology can be measured and obtain RF field distribution, then uses certain MR EPT algorithm, can be achieved with biological tissue EPs imaging.

The algorithm of the magnetic resonance imaging used in existing MR EPT technology is: (1) is assumed Obtain electrical conductivity method for solving based on phase placeWherein, φ⁺R () is reconstruction regions each pixel phase Position, H⁺R () is magnetic intensity vector at each pixel, ω is angular frequency, and μ is magnetic conductivity.(2) assume Obtain capacitivity method for solving based on magnetic field amplitude i.e.:

As can be seen here, the algorithm used in prior art have employed approximate evaluation method and (solves the formula of σ (r) and ∈ (r) All numbers of being about equal to), error is bigger；And owing to being that second differnce computing, calculating process and reconstructed results (are measured by noise The H arrived⁺Inside (r) value, the noise being mixed into during containing measurement) impact is relatively big, imaging resolution is the most poor, still with face Bed is actually needed also certain gap.

Summary of the invention

The present invention is directed to the Algorithm Error of the MR EPT of use in prior art relatively big, affected by noise the biggest, cause The technical problems such as EPs imaging resolution is poor, propose a kind of can to reduce influence of noise, magnetic resonance people that imaging resolution is higher Soma's electrical characteristics tomograph imaging method.

A kind of magnetic resonance tissue electrical characteristics tomograph imaging method that the present invention proposes, it comprises the following steps:

1) according to radiofrequency field corresponding during the radio-frequency transmissions obtained in magnetic resonance radio frequency fieldAnd magnetic resonance proton Radiofrequency field corresponding during the radio frequency reception that density imaging obtainsIn conjunction with principle of reciprocity and magnetic field Gauss theorem, it is calculated Three axial component B of x, y, z in magnetic resonance radio frequency magnetic field_1x(r)、B_1y(r)、B_1z(r)；

2) B that will obtain_1x(r)、B_1y(r)、B_1z(r) substitute into magnetic resonance time humorous radio frequency electromagnetic field FDTD equation group in (1)～ (3) in, and it is tissue by the initial value relative set of imaging region inner tissue conductivityσ (r) everywhere He capacitivity ∈ (r) Middle electrical conductivity mean value and capacitivity mean value, obtain three axial component E of x, y, z in magnetic resonance radio frequency electric field_1x(r)、E_1y (r)、E_1z(r)；

During described magnetic resonance, humorous radio frequency electromagnetic field FDTD equation group includes following (1)～(6):

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_x\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1z}\left(r\right)}{\∂y}-\frac{\∂B_{1y}\left(r\right)}{\∂z})---\left(1\right)$

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_y\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1x}\left(r\right)}{\∂z}-\frac{\∂B_{1z}\left(r\right)}{\∂x})---\left(2\right)$

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_z\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1y}\left(r\right)}{\∂x}-\frac{\∂B_{1x}\left(r\right)}{\∂y})---\left(3\right)$

${\mathrm{i\ωB}}_{1x}\left(r\right)=-(\frac{\∂E_z\left(r\right)}{\∂y}-\frac{\∂E_y\left(r\right)}{\∂z})---\left(4\right)$

${\mathrm{i\ωB}}_{1y}\left(r\right)=-(\frac{\∂E_x\left(r\right)}{\∂z}-\frac{\∂E_z\left(r\right)}{\∂x})---\left(5\right)$

${\mathrm{i\ωB}}_{1z}\left(r\right)=-(\frac{\∂E_y\left(r\right)}{\∂x}-\frac{\∂E_x\left(r\right)}{\∂y})---\left(6\right)$

Wherein, σ (r) is the electrical conductivity at radius vector r, and ∈ (r) is the capacitivity at radius vector r, and i is imaginary symbols, and ω is angle Frequency, μ₀Magnetic conductivity, x, y, z represent respectively three axially, E_xR () is that the electric field x-axis at radius vector r is to component, E_yR () is to vow Electric field y-axis at the r of footpath is to component, E_zR () is that the electric field z-axis at radius vector r is to component, B_1xR () is the B at radius vector r₁Magnetic field x-axis To component, B_1yR () is the B at radius vector r₁Magnetic field y-axis is to component, B_1zR () is the B at radius vector r₁Magnetic field z-axis is to component；

3) E that will obtain_1x(r)、E_1y(r)、E_1z(r) substitute into magnetic resonance time humorous radio frequency electromagnetic field FDTD equation group in (4)～ (6), in, one group of new magnetic resonance radio frequency magnetic-field component B is retrieved_1x(r)、B_1y(r)、B_1z(r), then by described new magnetic resonance RF magnetic field component B_1x(r)、B_1y(r)、B_1zWhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group in (1)～(3), And adjust the numerical value of described conductivityσ (r) and capacitivity ∈ (r), obtain one group of new magnetic resonance radio frequency electric field component E_1x(r)、 E_1y(r)、E_1z(r), then by new magnetic resonance radio frequency electric field component E_1x(r)、E_1y(r)、E_1zHumorous radio frequency electrical when () substitutes into magnetic resonance r In the FDTD equation group of magnetic field in (4)～(6), retrieve one group of magnetic resonance radio frequency magnetic-field component B updated_1x(r)、B_1y(r)、 B_1zR (), so iterates, constantly adjust the numerical value of described conductivityσ (r) and capacitivity ∈ (r) when each interative computation, Until magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1zThe difference in the magnetic resonance radio frequency magnetic field of (r) and actual measurement Different in the error range set, i.e. think algorithmic statement, terminate interative computation；The σ everywhere of imaging region inner tissue now R the distribution of () and ∈ (r) is this striked region inner tissue electrical characteristic parameter distribution results；

4) according to described imaging region inner tissue electrical characteristic parameter distribution results output image.

Concrete, in described tissue, electrical conductivity mean value is 0.26S/m, and capacitivity mean value is 78.

Preferably, described until magnetic resonance radio frequency magnetic-field component B that obtains of iteration_1x(r)、B_1y(r)、B_1z(r) and actual measurement The difference in magnetic resonance radio frequency magnetic field i.e. thinks algorithmic statement in the error range set, and terminates in the step of interative computation, bag Include:

In actual measurement, choose in imaging region the quadratic sum of the magnetic resonance radio frequency field modulus value iteration pre-post difference of each point as magnetic The yardstick of field error size, if magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1z(r) and this measurement The difference of yardstick i.e. thinks algorithmic statement in the error range allowed.

Preferably, within described error range is 10%.

Preferably, described error range is 5%.

Beneficial effect: a kind of magnetic resonance tissue electrical characteristics tomograph imaging method that the present invention proposes, it only relates to one Rank calculus of differences, relative to second differnce computing, it is possible to effectively reduce noise to calculating process and the impact of reconstructed results, and Can in imaging region global scope the error size of quantified controlling reconstructed results, make the reconstruction precision error can be as required Setting, the reconstructed image resolution and the precision that obtain significantly improve.

Accompanying drawing explanation

Fig. 1 is a kind of magnetic resonance tissue electrical characteristics tomograph imaging method embodiment flow process signal that the present invention proposes Figure.

Fig. 2 is the magnetic resonance tissue electrical characteristics tomography rebuilding step calculating electromagnetic method in Fig. 1 based on FDTD Decomposition step schematic flow sheet.

Detailed description of the invention

The present invention is carried out further below in conjunction with accompanying drawing and embodiment for the ease of it will be appreciated by those skilled in the art that Describe.

A kind of magnetic resonance tissue electrical characteristics tomograph imaging method that the present invention proposes, embodiment is as follows:

First, introduction is tried to achieveWithProcess.

Wherein,Represent corresponding radiofrequency field when magnetic resonance radio frequency (coil) is launched (concrete, refer at radius vector r Circular polarisation B₁Magnetic field), below useRepresent that kth transmitter unit is corresponding when launchingAccordingly,Represent The radiofrequency field that magnetic resonance radio frequency (coil) is corresponding when receiving, below usesRepresent that jth receives when unit receives correspondingNamely withWithIt is respectively conductWithA particular instance, introduceWithAsk Solution preocess.

With the Erlangen magnetic resonance of 7T Siemens, as a example by being equipped with 16 channel emission receiving array radio-frequency coils, refer to Fig. 1 And following steps S100 are to step S600.

S100, solve magnetic resonance radio frequency coil launch and receive each unit relative phase:

When launching only with a radio-frequency coil unit (passage) when, obtain a series of 16 little flip angles The 2D GRE image of (flip angle), separately receives with 16 radio-frequency coil unit (passage) respectively simultaneously.The most collinear Relative between coil unit (coil element)With(j and k is sequence number, and k represents with coil unit k transmitting, j Represent with coil unit j receive) phase diagram, just calculate, concrete calculation procedure is as follows:

1), from the phase place of the compound ratio of the two width images of 10ms and 6ms echo time, Δ B is derived₀Figure, obtains

Follow-up use

Wherein, Δ B₀Represent main field (i.e. B₀) inhomogeneities；Represent that imaging region each point is because of main field Uneven and the phase place that produces, this phase place can cause the deviation of flip angle；γ is gyromagnetic ratio, is a kind of physical constant, and TE is Echo time, γ TE Δ B₀Three is multiplied, and obtain is phase place, and the implication of these parameters and variable is all known to those skilled in the art Dawn.

2), assume

Wherein,It is the reservation phase calibration relevant to spatial points phase distribution each passage of coil unit, one As ignore.

3), calculate

Wherein,It it is oneself the zeroth order phase value respective that correspond to of the unit of each coil；It it is spatial points The original complex value of pixel MRI image.

4), calculateWherein

Wherein,It is independently of " the launching radiofrequency field phase place+reception radiofrequency field phase place " of each coil channel.

5), requirement is finally obtainedFor:

Wherein,It is to receive the relative phase distribution of coil each unit space；It isPhase place,It is every Oneself the zeroth order phase value respective that the unit of individual reception coil all correspond to,It is independently of " sending out of each coil channel Penetrate radiofrequency field phase place+reception radiofrequency field phase place ",It is the phase place that produces because main field is uneven of imaging region each point,It is the reservation phase calibration relevant to spatial points each passage of phase distribution coil；Containing of these parameters and variable Justice is the most all that those skilled in the art are known.

S200, calculating magnetic resonance radio frequency coil launch each unit relative phase difference, and process is as follows:

1), launching with unit k, receive with all of unit, the phase place wherein receiving the complex data that unit j receives is original Data, i.e.

Wherein,When being to launch with unit k, receive with all of unit, jth receives the phase of the complex data that unit receives Position；It is to receive the distribution of coil each unit space relative phase, receives the 5th of process i.e. above) being tried to achieve in item 's；It it is the relative phase distribution of transmitting coil each unit space；It is that the unit of each transmitting coil correspond to Oneself zeroth order phase value respective；It is " launching relative phase+reception relative phase ", it is simply that It is the phase place that produces because main field is uneven of imaging region each point,It is each with spatial points phase distribution coil The reservation phase calibration that individual passage is relevant, the implication of these parameters and variable is the most all that those skilled in the art are known.

2) the Δ B used with the calculating of above-mentioned reception unit relative phase, is used₀Figure, obtains

3), assume

4) k cell, to each independent transmitting, calculates each and receives unit

5), remove in the former data obtainedThese three, obtain

6), when only using a unit to launch, the SNR (i.e. signal to noise ratio) in some region can be the lowest.In order to reduce us Being added the phase noise that causes, for each transmitter unit k, we are the data of corresponding all of reception unit j, according to by Individual pixel correspondence is added, and is used for estimating that phase place is expressed

Correspond to 16 transmitter units individually launch, those 16 the above-mentioned summations respectively obtained, be more all added, be used for EstimateAssume (with received field B1 is similar to) relative phase item that coil is relevantAddition can mutually be supported Disappear, obtain:

Finally, the relative transmission phase place of each transmitter unit

S300, solve transmitting Magnetic image figure amplitude

Use actual flip angle (Actual Flip Angel) technology, obtain the excitation flip angle figure of 3D, at this moment institute Some coil units are launched simultaneously, are fused together with the GRE figure of the little flip angle (flip angle) of acquisition before, calculate Each coil unitAmplitude.

1) all transmitter units are launched simultaneously, and all unit receive, and obtain

2) K transmitting coil unit and J reception coil unit, when launching only with kth transmitting coil unit, adopt Use GE sequence, receive, at the j, complex signal S that coil obtains_kj, phase place S of compound ratio_k,j÷S_1,j=T_k÷T₁(it is exactly two to send out Penetrate item to be divided by), can be regarded as the phase difference between each transmitter unit；

3) phase and magnitude for each given passage is arranged, and has Measure/B1,1～k, all+/and all of Sk, j, it is possible to produce the map of magnitudes of each coil transmissions passage, That is:

S400, based on proton densityImage:

Finally, all of passage is launched together, uses big flip angle (high SNR), and (longitudinal magnetization is general for long TR It is in balance), short TE (insignificant T2 relaxation), obtain 2D GRE image；Each image received (totally 16) With the sine of flip angle " excitation " normalization, produce 16 based on proton densityMap of magnitudes.

S500, extract proton density andSolve:

Based on observation before, launch the unit of B1 amplitude andWidth with the unit received Degree andSubstantially suitable, under the most ellipse spherically symmetric all brain structures, and along the ellipse spherically symmetric situation of y-axis Under.Rule of thumb observe, if by launch amplitude and (SOM) with y-axis for symmetry axis overturn if, then the two closer to.This Sample, proton density PD_ratio,est(being directly proportional to major axis magnetization Mz) just can extract:

Then obtain:

In sum, according to the relative transmission phase place of transmitter unit derived aboveWith each coil unitAmplitudeJust radiofrequency field corresponding when radio-frequency coil is launched has been obtainedEach according to reception coil derived above Unitary space relative phaseWith the amplitude receiving coil each unitJust obtained when radio-frequency coil receives corresponding Radiofrequency field(including amplitude and phase place).

Above-mentioned solveWithProcess, namely solve in concrete application exampleWithProcess.

Below just can be according to obtainingWithTry to achieve the electrical characteristic parameter value of each point in imaging region, and will These electrical characteristic parameter values show (the following is the key content of the embodiment of the present invention) with the form of faultage image distribution map, With specific reference to following steps S600.

S600, magnetic resonance tissue electrical characteristics fault imaging (MR EPT) based on FDTD calculating electromagnetic method are rebuild:

Referring to Fig. 2, step S600 specifically includes following steps L10 to step L40:

L10, according to radiofrequency field corresponding during the radio-frequency transmissions obtained in magnetic resonance radio frequency fieldAnd magnetic resonance matter Radiofrequency field corresponding during the radio frequency reception that sub-density imaging obtainsIn conjunction with principle of reciprocity and magnetic field Gauss theorem, calculate Three axial component B of x, y, z in magnetic resonance radio frequency magnetic field_1x(r)、B_1y(r)、B_1z(r)。

Concrete, in step L10, draw according to above-mentionedWithIn conjunction with principle of reciprocity WithAnd magnetic field Gauss theorem Just three axial component B of x, y, z in RF magnetic field can be calculated_1x(r)、B_1y(r)、B_1z(r)。

L20, the B that will obtain_1x(r)、B_1y(r)、B_1zWhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group (1) ～in (3), and it is human body group by the initial value relative set of imaging region inner tissue conductivityσ (r) everywhere He capacitivity ∈ (r) Knit middle electrical conductivity mean value and capacitivity mean value (it is of course also possible to being set to other initial value), obtain magnetic resonance radio frequency Three axial component E of x, y, z in electric field_1x(r)、E_1y(r)、E_1z(r)；

During described magnetic resonance, humorous radio frequency electromagnetic field FDTD equation group includes following (1)～(6):

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_x\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1z}\left(r\right)}{\∂y}-\frac{\∂B_{1y}\left(r\right)}{\∂z})---\left(1\right)$

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_y\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1x}\left(r\right)}{\∂z}-\frac{\∂B_{1z}\left(r\right)}{\∂x})---\left(2\right)$

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_z\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1y}\left(r\right)}{\∂x}-\frac{\∂B_{1x}\left(r\right)}{\∂y})---\left(3\right)$

${\mathrm{i\ωB}}_{1x}\left(r\right)=-(\frac{\∂E_z\left(r\right)}{\∂y}-\frac{\∂E_y\left(r\right)}{\∂z})---\left(4\right)$

${\mathrm{i\ωB}}_{1y}\left(r\right)=-(\frac{\∂E_x\left(r\right)}{\∂z}-\frac{\∂E_z\left(r\right)}{\∂x})---\left(5\right)$

${\mathrm{i\ωB}}_{1z}\left(r\right)=-(\frac{\∂E_y\left(r\right)}{\∂x}-\frac{\∂E_x\left(r\right)}{\∂y})---\left(6\right)$

Wherein, σ (r) is the electrical conductivity at radius vector r, and ∈ (r) is the capacitivity at radius vector r, and i is imaginary symbols, and ω is angle Frequency, μ₀Magnetic conductivity, x, y, z represent respectively three axially, E_xR () is that the electric field x-axis at radius vector r is to component, E_yR () is to vow Electric field y-axis at the r of footpath is to component, E_zR () is that the electric field z-axis at radius vector r is to component, B_1xR () is the B at radius vector r₁Magnetic field x-axis To component, B_1yR () is the B at radius vector r₁Magnetic field y-axis is to component, B_1zR () is the B at radius vector r₁Magnetic field z-axis is to component.

Concrete, in step L20, during magnetic resonance, in humorous radio frequency electromagnetic field FDTD equation group, (1)～(6) is according to Max Wei equation group obtains, and it reflects three component E of electric field respectively_x(r)、E_y(r)、E_zR () be how to be obtained by changes of magnetic field , and three component B in magnetic field_1x(r)、B_1y(r)、B_1zHow r () obtained by electric field change, and the magnetic field i.e. changed is swashed Send out and produce electric field, the electric field of change excites generation magnetic field.

The B that step L10 is obtained_1x(r)、B_1y(r)、B_1zWhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group (1)～in (3), and the initial value relative set of conductivityσ (r) and capacitivity ∈ (r) is electrical conductivity mean value in tissue (common people soma's average conductivity σ (r) are 0.26S/m, average capacitance rate ∈ with capacitivity mean value_rR () is 78, ∈_r(r) =∈ (r)/∈₀(r),∈₀R () is the capacitivity in vacuum), just can get x, y, z three in magnetic resonance radio frequency electric field and axially divide Amount E_x(r)、E_y(r)、E_zR (), owing to being B₁Magnetic field produces, and is therefore designated as E_1x(r)、E_1y(r)、E_1z(r)。

L30, the E that will obtain_1x(r)、E_1y(r)、E_1zWhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group (4) ～in (6), retrieve one group of new magnetic resonance radio frequency magnetic-field component B_1x(r)、B_1y(r)、B_1z(r), then by described new magnetic altogether Shake RF magnetic field component B_1x(r)、B_1y(r)、B_1zWhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group (1)～(3) In, and adjust the numerical value of described conductivityσ (r) and capacitivity ∈ (r), obtain one group of new magnetic resonance radio frequency electric field component E_1x (r)、E_1y(r)、E_1z(r), then by new magnetic resonance radio frequency electric field component E_1x(r)、E_1y(r)、E_1zR () is humorous when substituting into magnetic resonance penetrates In frequency electromagnetic field FDTD equation group in (4)～(6), retrieve one group of magnetic resonance radio frequency magnetic-field component B updated_1x(r)、B_1y (r)、B_1zR (), so iterates, constantly adjust described conductivityσ (r) and capacitivity ∈ (r) when each interative computation Numerical value, until magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1z(r) and the magnetic resonance radio frequency magnetic field surveyed Difference in the error range set, i.e. think algorithmic statement, terminate interative computation (it can thus be appreciated that iterations is according to specifically Depending on situation)；The distribution of the σ (r) everywhere of imaging region inner tissue now and ∈ (r) is striked tissue electrical characteristics ginseng Number distribution results；

Concrete, that step L30 will obtain in step L20 E_1x(r)、E_1y(r)、E_1zHumorous radio frequency electrical when () substitutes into magnetic resonance r Magnetic field FDTD equation group (substitutes into E in (4)～(6) respectively_x(r)、E_y(r) and E_zIn (r)), retrieve one group of new magnetic altogether Shake RF magnetic field component B_1x(r)、B_1y(r)、B_1z(r), the inevitable and initial magnetic-field component of this new magnetic-field component of group different (as If the most identical, it is meant that the σ (r) and ∈ (r) of institute's assignment is exactly the real EPs value of tissue at this, owing to composing at the beginning What value was given is uniform value, and human body is physically uneven, so will not be the most equal).

Again by new magnetic resonance radio frequency magnetic-field component B_1x(r)、B_1y(r)、B_1zHumorous radio frequency electromagnetic field when () substitutes into magnetic resonance r In FDTD equation group in (1)～(3), the numerical value adjusting conductivityσ (r) and capacitivity ∈ (r) (can adjust its range value or phase Place value), so iterate, until magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1zR () is with real The difference in the magnetic resonance radio frequency magnetic field surveyed i.e. thinks algorithmic statement in the error range set, and terminates interative computation.

Concrete, in actual measurement, the flat of the magnetic resonance radio frequency field modulus value iteration pre-post difference of each point in imaging region can be chosen Side and the yardstick as magnetic field error size, if magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1z R the difference of () and this yardstick i.e. thinks algorithmic statement in the error range allowed.

Concrete error range can be scheduled within being 10%, and such as about 5%, noise can be substantially reduced in imaging Interference to result in journey.

After determining algorithmic statement, the distribution of imaging region inner tissue σ (r) everywhere and ∈ (r) is striked group Knit electrical characteristic parameter distribution results.

L40, according to described imaging region inner tissue electrical characteristic parameter distribution results output image.

Concrete, step L40 just can export image according to the distribution results of the σ (r) obtained in step L30 and ∈ (r), Complete image reconstruction.

A kind of magnetic resonance tissue electrical characteristics tomograph imaging method that the present embodiment proposes, it only relates to first-order difference fortune Calculate, relative to second differnce computing, it is possible to effectively reduction noise is on calculating process and the impact of reconstructed results, and can become As the error size of quantified controlling reconstructed results in region global scope, make reconstruction precision error can as desired to set, The reconstructed image resolution and the precision that obtain significantly improve.

Embodiment described above only have expressed the several embodiments of the present invention, and it describes more concrete and detailed, but also Therefore the restriction to the scope of the claims of the present invention can not be interpreted as.It should be pointed out that, for those of ordinary skill in the art For, without departing from the inventive concept of the premise, it is also possible to make some deformation and improvement, these broadly fall into the guarantor of the present invention Protect scope.Therefore, the protection domain of patent of the present invention should be as the criterion with claims.

Claims (5)

1. a magnetic resonance tissue electrical characteristics tomograph imaging method, it is characterised in that comprise the following steps:

1) according to radiofrequency field corresponding during the radio-frequency transmissions obtained in magnetic resonance radio frequency fieldAnd magnetic resonance proton density becomes Radiofrequency field corresponding during the radio frequency reception that picture obtainsIn conjunction with principle of reciprocity and magnetic field Gauss theorem, it is calculated magnetic resonance Three axial component B of x, y, z in RF magnetic field_1x(r)、B_1y(r)、B_1z(r)；

2) B that will obtain_1x(r)、B_1y(r)、B_1zWhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group (1)～(3) In, and be in tissue by the initial value relative set of imaging region inner tissue conductivityσ (r) everywhere He capacitivity ∈ (r) Electrical conductivity mean value and capacitivity mean value, obtain three axial component E of x, y, z in magnetic resonance radio frequency electric field_1x(r)、E_1y(r)、 E_1z(r)；

During described magnetic resonance, humorous radio frequency electromagnetic field FDTD equation group includes following (1)～(6):

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_x\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1z}\left(r\right)}{\∂y}-\frac{\∂B_{1y}\left(r\right)}{\∂z})---\left(1\right)$

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_y\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1x}\left(r\right)}{\∂z}-\frac{\∂B_{1z}\left(r\right)}{\∂x})---\left(2\right)$

$(i\mathrm{\ω}\∈(r)+\mathrm{\σ}(r\left)\right)E_z\left(r\right)=\frac{1}{{\mathrm{\μ}}_0}(\frac{\∂B_{1y}\left(r\right)}{\∂x}-\frac{\∂B_{1x}\left(r\right)}{\∂y})---\left(3\right)$

${\mathrm{i\ωB}}_{1x}\left(r\right)=-(\frac{\∂E_z\left(r\right)}{\∂y}-\frac{\∂E_y\left(r\right)}{\∂z})---\left(4\right)$

${\mathrm{i\ωB}}_{1y}\left(r\right)=-(\frac{\∂E_x\left(r\right)}{\∂z}-\frac{\∂E_z\left(r\right)}{\∂x})---\left(5\right)$

${\mathrm{i\ωB}}_{1z}\left(r\right)=-(\frac{\∂E_y\left(r\right)}{\∂x}-\frac{\∂E_x\left(r\right)}{\∂y})---\left(6\right)$

Wherein, σ (r) is the electrical conductivity at radius vector r, and ∈ (r) is the capacitivity at radius vector r, and i is imaginary symbols, and ω is angular frequency, μ₀Magnetic conductivity, x, y, z represent respectively three axially, E_xR () is that the electric field x-axis at radius vector r is to component, E_yR () is at radius vector r Electric field y-axis to component, E_zR () is that the electric field z-axis at radius vector r is to component, B_1xR () is the B at radius vector r₁Magnetic field x-axis is to dividing Amount, B_1yR () is the B at radius vector r₁Magnetic field y-axis is to component, B_1zR () is the B at radius vector r₁Magnetic field z-axis is to component；

3) E that will obtain_1x(r)、E_1y(r)、E_1zWhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group (4)～(6) In, retrieve one group of new magnetic resonance radio frequency magnetic-field component B_1x(r)、B_1y(r)、B_1z(r), more described new magnetic resonance is penetrated Frequently magnetic-field component B_1x(r)、B_1y(r)、B_1zWhen () substitutes into magnetic resonance r, humorous penetrating is in frequency electromagnetic field FDTD equation group in (1)～(3), And adjust the numerical value of described conductivityσ (r) and capacitivity ∈ (r), obtain one group of new magnetic resonance radio frequency electric field component E_1x(r)、 E_1y(r)、E_1z(r), then by new magnetic resonance radio frequency electric field component E_1x(r)、E_1y(r)、E_1zHumorous radio frequency electrical when () substitutes into magnetic resonance r In the FDTD equation group of magnetic field in (4)～(6), retrieve one group of magnetic resonance radio frequency magnetic-field component B updated_1x(r)、B_1y(r)、 B_1zR (), so iterates, constantly adjust the numerical value of described conductivityσ (r) and capacitivity ∈ (r) when each interative computation, Until magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1zThe difference in the magnetic resonance radio frequency magnetic field of (r) and actual measurement Different in the error range set, i.e. think algorithmic statement, terminate interative computation；The σ everywhere of imaging region inner tissue now R the distribution of () and ∈ (r) is striked tissue electrical characteristic parameter distribution results；

4) according to described imaging region inner tissue electrical characteristic parameter distribution results output image.

Magnetic resonance tissue electrical characteristics tomograph imaging method the most according to claim 1, it is characterised in that described human body In tissue, electrical conductivity mean value is 0.26S/m, and relative permitivity mean value is 78.

Magnetic resonance tissue electrical characteristics tomograph imaging method the most according to claim 1, it is characterised in that described until Magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1zR () exists with the difference in the magnetic resonance radio frequency magnetic field of actual measurement I.e. think algorithmic statement in the error range set, terminate in the step of interative computation, including:

In actual measurement, choose in imaging region the quadratic sum of the magnetic resonance radio frequency field modulus value iteration pre-post difference of each point as magnetic field by mistake The yardstick of difference size, if magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1z(r) and this yardstick Difference in the error range allowed, i.e. think algorithmic statement.

Magnetic resonance tissue electrical characteristics tomograph imaging method the most according to claim 1, it is characterised in that described until Magnetic resonance radio frequency magnetic-field component B that iteration obtains_1x(r)、B_1y(r)、B_1zR () exists with the difference in the magnetic resonance radio frequency magnetic field of actual measurement I.e. think algorithmic statement in the error range set, terminate in the step of interative computation, within described error range is 10%.

Magnetic resonance tissue electrical characteristics tomograph imaging method the most according to claim 4, it is characterised in that described error Scope is 5%.