CN104352239A - Magnetic resonance human tissue electrical characteristic tomography method - Google Patents

Abstract

The invention relates to a human tissue physical characteristic parameter magnetic resonance tomography method. The method comprises the following steps: (1) calculating B1x(r), B1y(r) and B1z(r) according to B1<+>(r) obtained in a magnetic resonance radiofrequency field and B1<->(r) obtained through magnetic resonance proton density imaging in combination with a reciprocity principle and a magnetic field Gauss theorem; (2) substituting B1x(r), B1y(r) and B1z(r) into a magnetic resonance time-harmonic radiofrequency electromagnetic field FDTD (Finite Difference Time Domain) equation set, and correspondingly setting the initial values of the conductivity sigma(r) and capacity belong to (r) of each tissue in an imaging region as the average conductivity value and average capacity value of human body tissues to obtain E1x(r), E1y(r) and E1z(r); (3) performing repeated iterative operation till algorithm convergence, wherein the distribution of sigma(r) and belong to (r) of each tissue in the imaging region is the evaluated tissue electrical characteristic parameter distribution result; (4) outputting an image according to the tissue electrical characteristic parameter distribution result in the imaging region.

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 method, be specifically related to a kind of power transformation characterisitic parameter Fdtd Method (FDTD) iterative approach formula and solve tissue electrical characteristic parameter (comprising electrical conductivity and dielectric constant), realize the method for tissue electrical characteristic parameter MRT, the tissue electrical characteristic parameter distributed image obtained can be used to instruct clinical tumor extreme early or early diagnosis.

Background technology

Material can be regarded as the build-in attribute of material in the electromagnetic property that elect magnetic field shows, and tissue is no exception.Tissue can show certain electrical characteristics and magnetic characteristic at elect magnetic field.Electrical characteristics, sometimes also referred to as dielectric property (EPs), mainly refer to electrical conductivity and the dielectric constant of tissue, magnetic characteristic refers to the pcrmeability of tissue.Generally speaking, tissue is namagnetic substance, and its pcrmeability, close to the pcrmeability in vacuum, can be counted as constant.Tissue EPs is everywhere relevant with organizing the cell membrane of insulation of interior non-uniform Distribution and the electrolyte of conduction etc., therefore organizes EPs everywhere to distribute and presents heterogeneity, and have frequency dependence.When the physiology of the essential structure unit cell of tissue and pathological state change, the EPs of tissue also will change.Early have in vitro tissue electrical characteristic parameter test experiments to confirm, the EPs of normal structure and tumor tissues often differs greatly, and some difference even reaches more than 10 times.If non-invasively can carry out imaging to the EPs of biological tissue, these EPs images, by the physiology of reflection tissue, organ and pathological state, may provide valuable information for diagnosis.Especially, biological tissue EPs imaging may be used for cancer extreme early or early diagnosis, even may be used for the whole change procedure that tracking monitor normal structure develops to tumor tissues, may have initiative value to the research of cancer and treatment.Visible, human body biological tissue EPs imaging, has very tempting huge potential applicability in clinical practice.

The imaging of noninvasive human body biological tissue electrical characteristics is the sciences problems of not capturing always.Scholar generally believes, in recent years to be suggested and magnetic resonance tissue electrical characteristics fault imaging (MR EPT) technology be rapidly developed has vast potential for future development, likely promote human body biological tissue EPs noinvasive imaging progress to a brand-new stage, producing this expectation is determined by the feature of MR EPT know-why itself.Fundamentally, nuclear magnetic resonance (MRI) is tissue and certain electric magnetic field (i.e. strong static magnetic field, gradient magnetic and radio frequency electromagnetic field) interactional system, therefore, in the MR signal that MRI system detects, the distributed intelligence of tissue electromagnetic property must be carried.Research confirms, the sensor RF coil of human body magnetic resonance (MR) signal, and the RF field distribution of its lateral cross section is strongly depend on the EPs distribution of tissue.Utilize RF field reflection (B ₁etc. Mapping) technology can be measured and obtain RF field distribution, then adopts certain MR EPT algorithm, just can realize biological tissue EPs imaging.

The algorithm of the nuclear magnetic resonance used in existing MR EPT technology is: (1) is supposed obtain the electrical conductivity method for solving based on phase place wherein, φ ⁺r () is each pixel phase place of reconstruction regions, H ⁺r () is each pixel place magnetic intensity vector, ω is angular frequency, and μ is pcrmeability.(2) suppose obtain based on magnetic field amplitude dielectric constant method for solving namely:

As can be seen here, the algorithm used in prior art have employed approximate evaluation method (formula solving σ (r) and ε (r) is all the number of approximating), and error is larger; And owing to being second differnce computing, calculating process and reconstructed results are by the noise (H that measurement obtains ⁺inside (r) value, contain the noise be mixed in measuring process) affect comparatively greatly, imaging resolution is still poor, still needs certain gap in addition with clinical practice.

Summary of the invention

The Algorithm Error that the present invention is directed to the MR EPT used in prior art is larger, affected by noise also larger, the technical problem such as cause EPs imaging resolution poor, proposes a kind ofly can reduce influence of noise, magnetic resonance tissue electrical characteristics tomograph imaging method that imaging resolution is higher.

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

1) according to radio-frequency field corresponding during the radio-frequency transmissions obtained in magnetic resonance radio frequency field and the imaging of magnetic resonance proton density obtain radio frequency reception time corresponding radio-frequency field in conjunction with principle of reciprocity and magnetic field Gauss theorem, calculate x, y, z three axial component B in magnetic resonance radio frequency magnetic field _1x(r), B _1r(r), B _1z(r);

2) B will obtained _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 be electrical conductivity meansigma methods and dielectric constant meansigma methods in tissue by the initial value relative set of imaging region inner tissue conductivityσ (r) and electric permittivity epsilon (r) everywhere, obtain x, y, z three axial component E 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 comprises following (1) ~ (6):

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_x\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1z}\left(r\right)}{\&PartialD;y}-\frac{\&PartialD;B_{1y}\left(r\right)}{\&PartialD;z})---\left(1\right)$

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_y\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1x}\left(r\right)}{\&PartialD;z}-\frac{\&PartialD;B_{1z}\left(r\right)}{\&PartialD;x})---\left(2\right)$

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_z\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1y}\left(r\right)}{\&PartialD;x}-\frac{\&PartialD;B_{1x}\left(r\right)}{\&PartialD;y})---\left(3\right)$

$\mathrm{i\&omega;}{B}_{1x}\left(r\right)=-(\frac{\&PartialD;E_z\left(r\right)}{\&PartialD;y}-\frac{\&PartialD;E_y\left(r\right)}{\&PartialD;z})---\left(4\right)$

$\mathrm{i\&omega;}{B}_{1x}\left(r\right)=-(\frac{\&PartialD;E_x\left(r\right)}{\&PartialD;z}-\frac{\&PartialD;E_z\left(r\right)}{\&PartialD;x})---\left(5\right)$

$\mathrm{i\&omega;}{B}_{1z}\left(r\right)=-(\frac{\&PartialD;E_y\left(r\right)}{\&PartialD;x}-\frac{\&PartialD;E_x\left(r\right)}{\&PartialD;y})---\left(6\right)$

Wherein, σ (r) is the electrical conductivity at radius vector r place, and ε (r) is the dielectric constant at radius vector r place, and i is imaginary symbols, and ω is angular frequency, μ ₀be pcrmeability, x, y, z represents three axis respectively, E _x(r) be the electric field x-axis at radius vector r place to component, E _y(r) be the electric field y-axis at radius vector r place to component, E _z(r) be the electric field z-axis at radius vector r place to component, B _1xr () is the B at radius vector r place ₁magnetic field x-axis to component, B _1yr () is the B at radius vector r place ₁magnetic field y-axis to component, B _1zr () is the B at radius vector r place ₁magnetic field z-axis is to component;

3) E will obtained _1x(r), E _1y(r), E _1zwhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group in (4) ~ (6), again obtain 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 resonance radio frequency 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 electric permittivity epsilon (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 _1zwhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group in (4) ~ (6), again obtain one group of magnetic resonance radio frequency magnetic-field component B upgraded _1x(r), B _1t(r), B _1zr (), so iterates, constantly adjust the numerical value of described conductivityσ (r) and electric permittivity epsilon (r), until the magnetic resonance radio frequency magnetic-field component B that iteration obtains when each interative computation _1x(r), B _1y(r), B _1zr namely () and the difference in magnetic resonance radio frequency magnetic field of actual measurement think algorithmic statement in the range of error set, finishing iteration computing; The distribution of the σ (r) everywhere of imaging region inner tissue now and ε (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 meansigma methods is 0.26S/m, and dielectric constant meansigma methods is 78.

Preferably, the magnetic resonance radio frequency magnetic-field component B that described until iteration obtains _1x(r), B _1y(r), B _1zr () is namely thought with the difference in magnetic resonance radio frequency magnetic field of actual measurement and in the step of finishing iteration computing, being comprised algorithmic statement in the range of error set:

In actual measurement, choose the yardstick of quadratic sum poor before and after the magnetic resonance radio frequency field modulus value iteration of each point in imaging region as magnetic field error size, if the magnetic resonance radio frequency magnetic-field component B that iteration obtains _1x(r), B _1y(r), B _1zr namely the difference of () and this yardstick think algorithmic statement in the range of error allowed.

Preferably, described range of error is within 10%.

Preferably, described range of error is 5%.

Beneficial effect: a kind of magnetic resonance tissue electrical characteristics tomograph imaging method that the present invention proposes, it only relates to first-order difference computing, relative to second differnce computing, effectively can reduce the impact of noise on calculating process and reconstructed results, and can in imaging region global scope the error size of quantified controlling reconstructed results, reconstruction precision error can be set as required, and the reconstructed image resolution obtained and precision significantly improve.

Accompanying drawing explanation

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

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

Detailed description of the invention

For the ease of it will be appreciated by those skilled in the art that the present invention is described further below in conjunction with accompanying drawing and embodiment.

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 achieve with process.

Wherein, represent the radio-frequency field (concrete, to refer to the circular polarisation B1 magnetic field at radius vector r place) that magnetic resonance radio frequency (coil) is corresponding when launching, below use represent that a kth transmitter unit is corresponding when launching accordingly, represent the radio-frequency field that magnetic resonance radio frequency (coil) is corresponding when receiving, below use represent that a jth receiving element is corresponding when receiving also namely with with be respectively conduct with a particular instance, introduce with solution procedure.

With 7T Siemens Erlangen magnetic resonance, being equipped with 16 channel emission receiving array radio-frequency coils is example, refers to Fig. 1 and following steps S100 to step S600.

S100, solve the relative phase that magnetic resonance radio frequency coil transmits and receives each unit:

In time only adopting a radio-frequency coil unit (passage) to launch, obtain the 2D GRE image of a series of 16 little flip angles (flip angle), use 16 radio-frequency coil unit (passage) separately to receive respectively simultaneously.Relative between so different coil unit (coil element) with the phase diagram of (j and k is sequence number, and k represents that, with coil unit k transmitting, j represents with coil unit j reception), just calculated, 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 derived ₀figure, obtains namely follow-uply to use

Wherein, Δ B ₀represent the inhomogeneities of main field (i.e. B0 field); represent the phase place that imaging region each point produces because main field is uneven, this phase place can cause the deviation of flip angle; γ is gyromagnetic ratio, and be a kind of physical constant, TE is the echo time, γ TE Δ B ₀three is multiplied, and what obtain is phase place, and the implication of these parameters and variable is all that those skilled in the art know.

2), suppose

Wherein, be the reservation phase calibration relevant to each passage of spatial points PHASE DISTRIBUTION coil unit, generally ignore.

3), calculate

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

4), calculate wherein

Wherein, " radio-frequency field phase place+received RF field phase is launched " independent of each coil channel.

5) finally obtain require for:

Wherein, it is the relative phase distribution of receiving coil each unitary space; be phase place, oneself the zeroth order phase value respective that the unit of each receiving coil correspond to, " radio-frequency field phase place+received RF field phase is launched " independent of each coil channel, the phase place that imaging region each point produces because main field is uneven, the reservation phase calibration relevant to each passage of spatial points PHASE DISTRIBUTION coil; The implication of these parameters and variable is equally all that those skilled in the art know.

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

1), with unit k launch, receive with all unit, the phase place of the complex data of wherein receiving element j reception is initial data, namely

Wherein, be with unit k launch, receives with all unit time jth receiving element reception the phase place of complex data; the distribution of receiving coil each unitary space relative phase, namely above receiving course the 5th) trying to achieve in item; it is the relative phase distribution of transmitting coil each unitary space; it is oneself the zeroth order phase value respective that the unit of each transmitting coil correspond to; be " launching relative phase+reception relative phase ", be exactly the phase place that imaging region each point produces because main field is uneven, be the reservation phase calibration relevant to each passage of spatial points PHASE DISTRIBUTION coil, the implication of these parameters and variable is equally all that those skilled in the art know.

2), use and above-mentioned receiving element relative phase calculate the Δ B adopted ₀figure, obtains

3), suppose

4) the k unit, to each launched separately, calculates each receiving element

5), remove in the former data obtained these three, obtain

6), when only using a unit to launch, the SNR (i.e. signal to noise ratio) in some region can be very low.Be added to reduce us the phase noise caused, for each transmitter unit k, we are the data of all receiving element j of correspondence, are added according to individual element point correspondence, are used for estimating that phase place is expressed

Correspond to 16 transmitter units to launch separately, those 16 the above-mentioned summations obtained respectively, be more all added, be used for estimating suppose the relative phase item that (similar with received field B1) coil is relevant can cancel out each other in addition, obtain:

Finally, the relative transmission phase place of each transmitter unit

S300, solve and launch Magnetic image figure amplitude

Adopt actual flip angle (Actual Flip Angel) technology, the excitation flip angle obtaining 3D schemes, at this moment all coil units are launched simultaneously, be fused together with the GRE figure of the little flip angle (flip angle) of acquisition before, calculate each coil unit amplitude.

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

2) K transmitting coil unit and J receiving coil unit, when only adopting a kth transmitting coil unit to launch, adopts GE sequence, at the complex signal S that the j receiving coil obtains _kj, the phase place S of compound ratio _k,j÷ S _{1, j}=T _k÷ T ₁(being exactly that two transmitting items are divided by), can be regarded as the phase contrast between each transmitter unit;

3) phase and magnitude for each given passage is arranged, and has measure with all S _k,j, just can produce the map of magnitudes of each coil transmissions passage, that is: $\&ForAll;j:\left|B_{1,k}^{+}\right|=\left\{\right|S_{k,j}|\&divide;{\mathrm{\&Sigma;}}_k|S_{k,j}\left|\right\}\&CenterDot;\left|B_{\mathrm{1,1}~k,\mathrm{all}}^{+}\right|$

S400, based on proton density image:

Finally, all passages are launched together, adopt large flip angle (high SNR), long TR (longitudinal magnetization is probably in balance), short TE (insignificant T2 relaxation), obtain 2D GRE image; Normalization that each image received (totally 16) is used the sine of angle " excitation flip ", produces 16 based on proton density map of magnitudes.

S500, extract proton density and solve:

Based on observation before, launch B1 unit amplitude and with receive unit amplitude and substantially suitable, under about ellipse spherically symmetric all brain structures, and in spherically symmetric situation ellipse along y-axis.Rule of thumb observe, if take y-axis as axis of symmetry upset by the amplitude of launching and (SOM), then the two closer to.Like this, proton density PD _{ratio, est}(magnetizing that Mz is directly proportional to major axis) just can extract:

So obtain: ${\tilde{B}}_{1,j}^{-}{\mathrm{PD}}_{\mathrm{ratio}}\&times;\left|{\tilde{B}}_{1,j}^{-}\right|{\mathrm{PD}}_{\mathrm{ratio},\mathrm{est}}$

In sum, according to the relative transmission phase place of the transmitter unit obtained above with each coil unit amplitude just radio-frequency field corresponding when radio-frequency coil is launched is obtained according to the receiving coil obtained above each unitary space relative phase with the amplitude of each unit of receiving coil just radio-frequency field corresponding when radio-frequency coil receives is obtained (comprising amplitude and phase place).

Above-mentionedly to solve with process, also namely solve in embody rule example with process.

Below just can according to obtain with try to achieve the electrical characteristic parameter value of each point in imaging region, and these electrical characteristic parameter values are shown (key content being the embodiment of the present invention below) with the form of faultage image scattergram, concrete with reference to following steps S600.

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

Refer to Fig. 2, step S600 specifically comprises the following steps L10 to step L40:

L10, according to radio-frequency field corresponding during the radio-frequency transmissions obtained in magnetic resonance radio frequency field and the imaging of magnetic resonance proton density obtain radio frequency reception time corresponding radio-frequency field in conjunction with principle of reciprocity and magnetic field Gauss theorem, calculate x, y, z three axial component B in magnetic resonance radio frequency magnetic field _1x(r), B _1y(r), B _1z(r).

Concrete, in step L10, draw according to above-mentioned with in conjunction with principle of reciprocity ( with $B_1^{-}\left(r\right)={(B_{1x}\left(r\right)-i{B}_{1y}\left(r\right))}^{*}/2$ And magnetic field Gauss theorem $(\frac{{\&PartialD;B}_{1x}}{\&PartialD;x}+\frac{{\&PartialD;B}_{1y}}{\&PartialD;y}+\frac{\&PartialD;B_{1z}}{\&PartialD;z}=0),$ Just x, y, z three axial component B in radio-frequency (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 in (1) ~ (3), and be that in tissue electrical conductivity meansigma methods and dielectric constant meansigma methods be (certainly by the initial value relative set of imaging region inner tissue conductivityσ (r) and electric permittivity epsilon (r) everywhere, also other initial value can be set to), obtain x, y, z three axial component E 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 comprises following (1) ~ (6):

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_x\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1z}\left(r\right)}{\&PartialD;y}-\frac{\&PartialD;B_{1y}\left(r\right)}{\&PartialD;z})---\left(1\right)$

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_y\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1x}\left(r\right)}{\&PartialD;z}-\frac{\&PartialD;B_{1z}\left(r\right)}{\&PartialD;x})---\left(2\right)$

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_z\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1y}\left(r\right)}{\&PartialD;x}-\frac{\&PartialD;B_{1x}\left(r\right)}{\&PartialD;y})---\left(3\right)$

$\mathrm{i\&omega;}{B}_{1x}\left(r\right)=-(\frac{\&PartialD;E_z\left(r\right)}{\&PartialD;y}-\frac{\&PartialD;E_y\left(r\right)}{\&PartialD;z})---\left(4\right)$

$\mathrm{i\&omega;}{B}_{1x}\left(r\right)=-(\frac{\&PartialD;E_x\left(r\right)}{\&PartialD;z}-\frac{\&PartialD;E_z\left(r\right)}{\&PartialD;x})---\left(5\right)$

$\mathrm{i\&omega;}{B}_{1z}\left(r\right)=-(\frac{\&PartialD;E_y\left(r\right)}{\&PartialD;x}-\frac{\&PartialD;E_x\left(r\right)}{\&PartialD;y})---\left(6\right)$

Wherein, σ (r) is the electrical conductivity at radius vector r place, and ε (r) is the dielectric constant at radius vector r place, and i is imaginary symbols, and ω is angular frequency, μ ₀be pcrmeability, x, y, z represents three axis respectively, E _x(r) be the electric field x-axis at radius vector r place to component, E _y(r) be the electric field y-axis at radius vector r place to component, E _z(r) be the electric field z-axis at radius vector r place to component, B _1xr () is the B at radius vector r place ₁magnetic field x-axis to component, B _1yr () is the B at radius vector r place ₁magnetic field y-axis to component, B _1zr () is the B at radius vector r place ₁magnetic field z-axis is to component.

Concrete, in step L20, during magnetic resonance, in humorous radio frequency electromagnetic field FDTD equation group, (1) ~ (6) obtain according to maxwell equation group, and it reflects three component E of electric field respectively _x(r), E _y(r), E _zhow r () obtained by changes of magnetic field, and three of magnetic field component B _1x(r), B _1y(r), B _1zhow r () obtained by electric field change, and the magnetic excitation namely changed produces electric field, the electric field of change excites and produces 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 in (1) ~ (3), and the initial value relative set of conductivityσ (r) and electric permittivity epsilon (r) be in tissue electrical conductivity meansigma methods and dielectric constant meansigma methods (common people soma's average conductivity σ (r) are 0.26S/m, average electrical capacity rate ε _rr () is 78, ε _r(r)=ε (r)/ε ₀(r), ε ₀r () is the dielectric constant in vacuum), just can obtain x, y, z three axial component E in magnetic resonance radio frequency electric field _x(r), E _y(r), E _zr (), owing to being B ₁magnetic 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 in (4) ~ (6), again obtain 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 resonance radio frequency 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 electric permittivity epsilon (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 _1zwhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group in (4) ~ (6), again obtain one group of magnetic resonance radio frequency magnetic-field component B upgraded _1x(r), B _1y(r), B _1zr (), so iterates, constantly adjust the numerical value of described conductivityσ (r) and electric permittivity epsilon (r), until the magnetic resonance radio frequency magnetic-field component B that iteration obtains when each interative computation _1x(r), B _1y(r), B _1zr namely () and the difference in magnetic resonance radio frequency magnetic field of actual measurement think algorithmic statement in the range of error set, finishing iteration computing (it can thus be appreciated that iterations is determined as the case may be); The distribution of the σ (r) everywhere of imaging region inner tissue now and ε (r) is striked organizes electrical characteristic parameter distribution results;

Concrete, the E that step L30 will obtain in step L20 _1x(r), E _1y(r), E _1z(E is substituted into respectively in (4) ~ (6) in humorous radio frequency electromagnetic field FDTD equation group during (r) substitution magnetic resonance _x(r), E _y(r) and E _zin (r)), again obtain one group of new magnetic resonance radio frequency magnetic-field component B _1x(r), B _1y(r), B _1z(r), it is inevitable different from initial magnetic-field component (if identical that this organizes new magnetic-field component, just mean that σ (r) and the ε (r) of institute's assignment are exactly the real EPs value that this place organizes, what give due to assignment at the beginning is even value, and human body is physically uneven, so can not be just equal).

Again by new magnetic resonance radio frequency 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), the numerical value (its range value or phase value can be adjusted) of adjustment conductivityσ (r) and electric permittivity epsilon (r), so iterate, until the magnetic resonance radio frequency magnetic-field component B that iteration obtains _1x(r), B _1y(r), B _1zr namely () and the difference in magnetic resonance radio frequency magnetic field of actual measurement think algorithmic statement in the range of error set, finishing iteration computing.

Concrete, in actual measurement, the yardstick of quadratic sum poor before and after the magnetic resonance radio frequency field modulus value iteration of each point in imaging region as magnetic field error size can be chosen, if the magnetic resonance radio frequency magnetic-field component B that iteration obtains _1x(r), B _1y(r), B _1zr namely the difference of () and this yardstick think algorithmic statement in the range of error allowed.

It is within 10% that concrete range of error can fix on, such as about 5%, greatly can reduce noise interference to result in imaging process.

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

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

Concrete, just according to the distribution results output image of the σ (r) obtained in step L30 and ε (r), image reconstruction can be completed in step L40.

A kind of magnetic resonance tissue electrical characteristics tomograph imaging method that the present embodiment proposes, it only relates to first-order difference computing, relative to second differnce computing, effectively can reduce the impact of noise on calculating process and reconstructed results, and can in imaging region global scope the error size of quantified controlling reconstructed results, reconstruction precision error can be set as required, and the reconstructed image resolution obtained and precision significantly improve.

The above embodiment only have expressed several embodiment of the present invention, and it describes comparatively concrete and detailed, but therefore can not be interpreted as the restriction to the scope of the claims of the present invention.It should be pointed out that for the person of ordinary skill of the art, without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.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, is characterized in that, comprise the following steps:

1) according to radio-frequency field corresponding during the radio-frequency transmissions obtained in magnetic resonance radio frequency field and the imaging of magnetic resonance proton density obtain radio frequency reception time corresponding radio-frequency field in conjunction with principle of reciprocity and magnetic field Gauss theorem, calculate x, y, z three axial component B in magnetic resonance radio frequency magnetic field _1x(r), B _1y(r), B _1z(r);

2) B will obtained _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 be electrical conductivity meansigma methods and dielectric constant meansigma methods in tissue by the initial value relative set of imaging region inner tissue conductivityσ (r) and electric permittivity epsilon (r) everywhere, obtain x, y, z three axial component E 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 comprises following (1) ~ (6):

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_x\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1z}\left(r\right)}{\&PartialD;y}-\frac{\&PartialD;B_{1y}\left(r\right)}{\&PartialD;z})---\left(1\right)$

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_y\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1x}\left(r\right)}{\&PartialD;z}-\frac{\&PartialD;B_{1z}\left(r\right)}{\&PartialD;x})---\left(2\right)$

$(\mathrm{i\&omega;}\&Element;\left(r\right)+\mathrm{\&sigma;}\left(r\right))E_z\left(r\right)=\frac{1}{{\mathrm{\&mu;}}_0}(\frac{\&PartialD;B_{1y}\left(r\right)}{\&PartialD;x}-\frac{\&PartialD;B_{1x}\left(r\right)}{\&PartialD;y})---\left(3\right)$

${\mathrm{i\&omega;B}}_{1x}\left(r\right)=-(\frac{{\&PartialD;E}_z\left(r\right)}{\&PartialD;y}-\frac{{\&PartialD;E}_y\left(r\right)}{\&PartialD;z})---\left(4\right)$

${\mathrm{i\&omega;B}}_{1y}\left(r\right)=-(\frac{{\&PartialD;E}_x\left(r\right)}{\&PartialD;z}-\frac{{\&PartialD;E}_z\left(r\right)}{\&PartialD;x})---\left(5\right)$

${\mathrm{i\&omega;B}}_{1z}\left(r\right)=-(\frac{{\&PartialD;E}_y\left(r\right)}{\&PartialD;x}-\frac{{\&PartialD;E}_x\left(r\right)}{\&PartialD;y})---\left(6\right)$

Wherein, σ (r) is the electrical conductivity at radius vector r place, and ε (r) is the dielectric constant at radius vector r place, and i is imaginary symbols, and ω is angular frequency, μ ₀be pcrmeability, x, y, z represents three axis respectively, E _x(r) be the electric field x-axis at radius vector r place to component, E _y(r) be the electric field y-axis at radius vector r place to component, E _z(r) be the electric field z-axis at radius vector r place to component, B _1xr () is the B at radius vector r place ₁magnetic field x-axis to component, B _1yr () is the B at radius vector r place ₁magnetic field y-axis to component, B _1zr () is the B at radius vector r place ₁magnetic field z-axis is to component;

3) E will obtained _1x(r), E _1y(r), E _1zwhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group in (4) ~ (6), again obtain 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 resonance radio frequency 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 electric permittivity epsilon (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 _1zwhen () substitutes into magnetic resonance r in humorous radio frequency electromagnetic field FDTD equation group in (4) ~ (6), again obtain one group of magnetic resonance radio frequency magnetic-field component B upgraded _1x(r), B _1y(r), B _1zr (), so iterates, constantly adjust the numerical value of described conductivityσ (r) and electric permittivity epsilon (r), until the magnetic resonance radio frequency magnetic-field component B that iteration obtains when each interative computation _1x(r), B _1y(r), B _1zr namely () and the difference in magnetic resonance radio frequency magnetic field of actual measurement think algorithmic statement in the range of error set, finishing iteration computing; The distribution of the σ (r) everywhere of imaging region inner tissue now and ε (r) is striked organizes electrical characteristic parameter distribution results;

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

2. magnetic resonance tissue electrical characteristics tomograph imaging method according to claim 1, it is characterized in that, in described tissue, electrical conductivity meansigma methods is 0.26S/m, and relative permitivity meansigma methods is 78.

3. magnetic resonance tissue electrical characteristics tomograph imaging method according to claim 1, is characterized in that, the magnetic resonance radio frequency magnetic-field component B that described until iteration obtains _1x(r), B _1y(r), B _1zr () is namely thought with the difference in magnetic resonance radio frequency magnetic field of actual measurement and in the step of finishing iteration computing, being comprised algorithmic statement in the range of error set:

In actual measurement, choose the yardstick of quadratic sum poor before and after the magnetic resonance radio frequency field modulus value iteration of each point in imaging region as magnetic field error size, if the magnetic resonance radio frequency magnetic-field component B that iteration obtains _1x(r), B _1y(r), B _1zr namely the difference of () and this yardstick think algorithmic statement in the range of error allowed.

4. magnetic resonance tissue electrical characteristics tomograph imaging method according to claim 1, is characterized in that, the magnetic resonance radio frequency magnetic-field component B that described until iteration obtains _1x(r), B _1y(r), B _1zr namely () and the difference in magnetic resonance radio frequency magnetic field of actual measurement think algorithmic statement in the range of error set, in the step of finishing iteration computing, described range of error is within 10%.

5. magnetic resonance tissue electrical characteristics tomograph imaging method according to claim 4, it is characterized in that, described range of error is 5%.