CN104239642A - Vector solving method for magnetoacoustic coupling direct problem under sinusoidal excitation - Google Patents

Abstract

The invention discloses a vector solving method for a magnetoacoustic coupling direct problem under sinusoidal excitation. The vector solving method comprises a first step: space calculation solving, and a second step: frequency-domain amplitude phase solving, which comprises the following steps: performing space finite element-based solving, calculating the real part and the imaginary part of the complex plane of each subdivision unit, and calculating the real part and the imaginary part of a resultant vector; calculating the amplitude and the phase of a magnetoacoustic signal to realize solving on the magnetoacoustic coupling direct problem. According to the vector solving method for the magnetoacoustic coupling direct problem under the sinusoidal excitation, disclosed by the invention, excitation can be more easily realized, and validation of a theoretical method is easy; meanwhile, as calculation is performed by adopting a vector method, the calculation process of the vector solving method is simpler than that of the traditional calculation method in step, and moreover, error accumulation cannot be generated.

Description

The vector method for solving of magnetosonic coupling direct problem under a kind of sinusoidal excitation

Technical field

The present invention relates to a kind of vector method for solving.Particularly relate to the vector method for solving of magnetosonic coupling direct problem under a kind of sinusoidal excitation.

Background technology

Biological tissue's electrical characteristics reflect the physio-pathological condition of tissue, and especially for the early lesion of tissue, research shows, pathological tissues and normal structure have different conductivity, and the tissue conductivities of different lesions state has difference.Therefore, biological tissue's electrical characteristics are carried out detecting and imaging, is conducive to the early diagnosis of relevant disease.

Magnetosonic coupling imaging is a kind of novel biological tissue's electrical characteristics formation method, and tissue electrical parameters convert information, by applying electric magnetization to medium, is acoustical signal, realizes detection and the imaging of biological tissue's electrical characteristics by it.The harmless functional imaging method of magnetosonic coupling effect, has the feature of high-contrast and high spatial resolution simultaneously, has important researching value to the early diagnosis of the diseases such as tumour.

In magnetosonic coupling imaging, the amplitude of magnetoacoustic signals corresponding frequency band and phase place contain conductivity information and the sound source information of medium, in magnetosonic imaging mathematical model and direct problem research, mainly through being set to impulse function δ (t), then finite element method sound source is utilized to distribute, solved by convolution pumping signal and magnetosonic imaging system function and sensor time characteristic, calculate solution and the magnetoacoustic signals of magnetosonic coupling direct problem, carry out Fourier transform again and calculate magnetoacoustic signals frequency spectrum, and then the amplitude calculated under respective frequencies and phase information.The method calculates and relates to signal convolution, computing and Fourier transform, and process is complicated, easily in multistep calculates, produces the accumulation of error.

In the research of magnetosonic imaging direct problem, the conventional coupling of the magnetosonic based on impulse function δ (t) direct problem Mathematical method, owing to being difficult to the pulse signal realizing unlimited narrow width in reality, affects the checking of theoretical simulation.Carrying out relating to Signal averaging convolution, the calculating such as Fourier transform in direct problem calculating, computation process is complicated, easily produces the accumulation of error simultaneously.

Summary of the invention

Technical matters to be solved by this invention is, the vector method for solving of magnetosonic coupling direct problem under the sinusoidal excitation providing a kind of excitation more easily to realize.

The technical solution adopted in the present invention is: the vector method for solving of magnetosonic coupling direct problem under a kind of sinusoidal excitation, is characterized in that, comprise,

The first step: space calculates and solves

Second step: frequency domain amplitude phase solution, comprises based on Space finite element solution, calculates complex plane real part and the imaginary part of each subdivision unit, calculates real part and the imaginary part of resultant vector; Calculate amplitude and the phase place of magnetoacoustic signals, thus realize magnetosonic coupling direct problem solve.

Space described in the first step calculates to solve and comprises the steps:

1) set the distribution of medium geometric configuration, size and conductivity parameters, set up solving model;

2) utilize Finite Element Method to carry out subdivision to medium, subdivision is n unit, calculates the space length l of i-th subdivision unit _iand current density A _i, wherein, i=1,2 ..., n;

3) result of calculation is stored.

The space length l of each subdivision unit of the calculating described in second step _iand current density A _i, be adopt Comsol finite element simulation platform or ANSYS finite element simulation platform or MATLAB emulation platform to calculate.

Frequency domain amplitude phase solution described in second step comprises the steps:

1) real part and the imaginary part of the corresponding complex plane vector of each subdivision unit in the first step is calculated

Real part is ${\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}=\frac{1}{l_i}f(r,\mathrm{j\ω})A_i\cos (j{\mathrm{\ω}}_1{l}_i/c),$

Imaginary part is ${\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}=\frac{1}{l_i}f(r,\mathrm{j\ω})A_i\sin (j{\mathrm{\ω}}_1{l}_i/c).$

Wherein p _i(r, j ω) is magnetosonic coupling acoustical signal, and r is locus, and ω is angular frequency, and J is current density, B ₀for static magnetic field, δ (t) is impulse excitation, and c is the velocity of sound in medium, and H (j ω) is system function;

2) magnetosonic coupling direct problem solution and resultant vector corresponding to magnetoacoustic signals is calculated

$P(r,\mathrm{j\ω})=\underset{i}{\mathrm{\Σ}}{P}_i(r,\mathrm{j\ω})=\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}+j\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}$

3) corresponding amplitude AMPn and phase place PHAn is calculated

${\mathrm{AMP}}_n=\sqrt{{\left(\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}\right)}^2+{\left(\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}\right)}^2}$

${\mathrm{PHA}}_n=\arctan \left(\frac{\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}}{\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}}\right).$

The vector method for solving of magnetosonic coupling direct problem under a kind of sinusoidal excitation of the present invention, excitation more easily realizes, and is easy to theoretical method checking.Adopt vector method to calculate, its computation process is simple compared to Traditional calculating methods step, and can not produce the accumulation of error simultaneously.

Accompanying drawing explanation

Fig. 1 is the Vector operation schematic diagram of the vector method for solving of magnetosonic coupling direct problem under a kind of sinusoidal excitation of the present invention;

Fig. 2 is the schematic flow sheet of the vector method for solving of magnetosonic coupling direct problem under a kind of sinusoidal excitation of the present invention.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the vector method for solving of magnetosonic coupling direct problem under a kind of sinusoidal excitation of the present invention is described in detail.

First the theory deduction of the coupling of the magnetosonic based on sinusoidal signal excitation direct problem involved in the present invention is provided:

According to the mathematical model wave equation of magnetosonic coupling effect

${\▿}^{2}p(r,t)-\frac{1}{c^2}\frac{\∂}{\∂t^2}p(r,t)=(\▿\·F)\mathrm{\δ}\left(t\right)---\left(1\right)$

Wherein p (r, t) is time domain magnetosonic coupling acoustical signal, and F is the lorentz force density that medium particle is subject to, if set current density as J, static magnetic field is B ₀, then F=J × B ₀, δ (t) is impulse excitation, and c is the velocity of sound in medium.

For function s (t) of arbitrary excitation, be then actuated to the convolution of function and impulse

${\▿}^{2}p(r,t)-\frac{1}{c^2}\frac{\∂}{\∂t^2}p(r,t)=(\▿\·F)\mathrm{\δ}\left(t\right)\⊗s\left(t\right)---\left(2\right)$

The expression formula of frequency domain magnetosonic coupling acoustical signal P (r, j ω) is obtained by Fourier transform,

$P(r,\mathrm{j\ω})=-c\underset{V}{\∫\∫\∫}\mathrm{dv}(\▿\·F)G_k(r,r_0)S\left(\mathrm{j\ω}\right)H\left(\mathrm{j\ω}\right)---\left(3\right)$

Wherein Green function is

$G_k(r,r_0)=\frac{e^{\mathrm{j\ω}|r-r_0|/c}}{4\mathrm{\π}|r_0-r|}---\left(4\right)$

The frequency spectrum that frequency domain S (j ω) is excitation function, the Fourier transform that H (j ω) is magnetosonic imaging system function, ω is angular frequency.According to the separation of variable, time term and space are considered respectively, by the time term in integration

$P(r,\mathrm{j\ω})=-\mathrm{cS}\left(\mathrm{j\ω}\right)H\left(\mathrm{j\ω}\right)\underset{V}{\∫\∫\∫}\mathrm{dv}(\▿\·F)\frac{e^{\mathrm{j\ω}|r-r_0|/c}}{4\mathrm{\π}|r_0-r|}---\left(5\right)$

Wherein r ₀for the spatial position vector of detecting device, r is the corresponding locus of media interior, for medium sound source item, according to constitutive relation Ohm law

J＝σE (6)

E is media interior electric field, and σ is conductivity.From above-mentioned derivation, sound source item contains the conductivity information of medium. for phase term, reflect the delay of the phase place that each particle is formed to detector distance in medium. for amplitude item, i.e. the transmission coefficient of sound wave in distance.Therefore the amplitude solved and phase place, namely contain the parameter distribution of the conductivity of medium.Therefore in order to calculate amplitude and phase place, under a kind of sinusoidal excitation of the present invention, the vector method for solving of magnetosonic coupling direct problem need be realized by following two steps.

As shown in Figure 2, under a kind of sinusoidal excitation of the present invention, the vector method for solving of magnetosonic coupling direct problem, comprises,

The first step: space calculates and solves, the calculating of the electric current distribution of main implementation space, thus obtain the distributed intelligence of sound source, and then substitute into the amplitude phase solution realizing second step; Second step: frequency domain amplitude phase solution, comprises based on Space finite element solution, calculates complex plane real part and the imaginary part of each subdivision unit, calculates real part and the imaginary part of resultant vector; Calculate amplitude and the phase place of magnetoacoustic signals, thus realize magnetosonic coupling direct problem solve.Wherein,

Space described in the first step calculates to solve and comprises the steps:

1) set the distribution of medium geometric configuration, size and conductivity parameters, set up solving model, namely to geometric configuration, the size of medium to be solved, and the conductivity parameters distribution of media interior defines, thus sets up the solving model of medium;

2) utilize Finite Element Method to carry out subdivision to medium, subdivision is n unit, according to set up model, calculate i-th subdivision unit (i=1,2 ..., space length l n) _iand current density A _i, the space length l of each subdivision unit of described calculating _iand current density A _i, be adopt Comsol finite element simulation platform or ANSYS finite element simulation platform or MATLAB emulation platform etc. to calculate;

3) result of calculation is stored.

Frequency domain amplitude phase solution described in second step comprises the steps:

1) real part and the imaginary part of the corresponding complex plane vector of each subdivision unit in the first step is calculated

According to the sine-shaped analytical approach of vector representation in Circuit theory, for a sinusoidal signal,

$s\left(t\right)=A_1\sin ({\mathrm{\ω}}_{1}t+{\mathrm{\ω}}_1{t}_1)\↔A_1{e}^{j{\mathrm{\ω}}_1{t}_1}\mathrm{\δ}(\mathrm{\ω}-{\mathrm{\ω}}_1)---\left(7\right)$

ω ₁for this sinusoidal signal angular frequency, can be A by vector representation ₁+ j ω ₁t ₁, its real part is A ₁cos (ω ₁t ₁), imaginary part is A ₁sin (ω ₁t ₁), therefore for detecting the magnetoacoustic signals amplitude phase place i.e. amplitude of this vector and phase place that obtain.The all point sources of sound of medium are sent to be formed and finally detect the magnetoacoustic signals obtained,

$P(r,\mathrm{j\ω})=\underset{i}{\mathrm{\Σ}}\frac{1}{l_i}f(r,j{\mathrm{\ω}}_1)A_i{e}^{j{\mathrm{\ω}}_1{l}_i/c}=\underset{i}{\mathrm{\Σ}}\frac{1}{|r_i-r_0|}f(r,j{\mathrm{\ω}}_1)A_i{e}^{j{\mathrm{\ω}}_1|r_i-r_0|/c}---\left(8\right)$

Wherein, make

$f(r,t)=-\mathrm{\πc}\▿\·(J\×B_0)\frac{1}{4\mathrm{\π}}\⊗h\left(t\right)---\left(9\right)$

$f(r,\mathrm{j\ω})=-\mathrm{\πc}\▿\·(J\×B_0)\frac{1}{4\mathrm{\π}}H\left(\mathrm{j\ω}\right)---\left(10\right)$

For i-th sound source,

$P_i(r,\mathrm{j\ω})=\frac{1}{l_i}f(r,\mathrm{j\ω})A_i{e}^{j{\mathrm{\ω}}_1{l}_i/c}---\left(11\right)$

Real part is ${\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}=\frac{1}{l_i}f(r,\mathrm{j\ω})A_i\cos (j{\mathrm{\ω}}_1{l}_i/c)---\left(12\right)$

Imaginary part is ${\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}=\frac{1}{l_i}f(r,\mathrm{j\ω})A_i\sin (j{\mathrm{\ω}}_1{l}_i/c)---\left(13\right)$

2) magnetosonic coupling direct problem solution and resultant vector corresponding to magnetoacoustic signals is calculated

P _i(r,jω)＝Re _Pi(r,jω)+jIm _Pi(r,jω) (14)

$\mathrm{AMP}=\sqrt{{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}^2+{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}^2}---\left(15\right)$

PHA＝arctan(Im _Pi(r,jω)/Re _Pi(r,jω)) (16)

(11)-(14) are substituted into (8) then

$P(r,\mathrm{j\ω})=\underset{i}{\mathrm{\Σ}}{P}_i(r,\mathrm{j\ω})=\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}+j\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}---\left(17\right)$

3) corresponding amplitude AMP is calculated _nwith phase place PHA _n

For the summation of n sound source, then as shown in Figure 1, the amplitude obtained by vector method and phase place are respectively

${\mathrm{AMP}}_n=\sqrt{{\left(\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}\right)}^2+{\left(\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}\right)}^2}---\left(18\right)$

${\mathrm{PHA}}_n=\arctan \left(\frac{\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}}{\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}}\right)---\left(19\right)$

If two-layer border sound source, its amplitude and locus are respectively a, b, l _a, l _b, then according to the vector method for solving of magnetosonic coupling direct problem under sinusoidal excitation of the present invention, the amplitude under 10kHz and the 20kHz excitation of calculating and phase place, as shown in table 1.

Table 1

Sound source amplitude	Sound source amplitude	Sound source locus	Sound source locus	10kHz	10kHz	20kHz	20kHz
								a	b	l a	l b	AMP	PHA	AMP	PHA
0.05	0.1	0.1025	0.105	1.405961	337.1319	1.305727	313.8159
								0.1	0.2	0.105	0.11	2.509952	292.92	1.806949	221.0488
0.15	0.3	0.1075	0.115	3.176476	247.9345	1.401363	105.7871
								0.2	0.4	0.11	0.12	3.331632	201.0733	2.027618	310.6557
0.25	0.5	0.1125	0.125	2.99357	149.7409	4.392943	202.6958
								0.3	0.6	0.115	0.13	2.37758	86.88002	6.775146	112.0244
0.35	0.7	0.1175	0.135	2.236123	3.528158	8.131632	25.03596
								0.4	0.8	0.12	0.14	3.372677	286.2953	7.793887	297.8044
0.45	0.9	0.1225	0.145	5.292801	228.5423	5.6297	205.1518
								0.5	1	0.125	0.15	7.451407	179.4532	2.831821	78.57275

Although be described the preferred embodiments of the present invention by reference to the accompanying drawings above, the present invention is not limited to above-mentioned embodiment, and above-mentioned embodiment is only schematic, is not restrictive.Those of ordinary skill in the art is under enlightenment of the present invention, and do not departing under the ambit that present inventive concept and claim protect, can also make a lot of form, these all belong within protection scope of the present invention.

Claims (4)

1. under sinusoidal excitation magnetosonic coupling direct problem a vector method for solving, it is characterized in that, comprise,

The first step: space calculates and solves;

Second step: frequency domain amplitude phase solution, comprises based on Space finite element solution, calculates complex plane real part and the imaginary part of each subdivision unit, calculates real part and the imaginary part of resultant vector; Calculate amplitude and the phase place of magnetoacoustic signals, thus realize magnetosonic coupling direct problem solve.

2. the vector method for solving of magnetosonic coupling direct problem under a kind of sinusoidal excitation according to claim 1, it is characterized in that, space described in the first step calculates to solve and comprises the steps:

1) set the distribution of medium geometric configuration, size and conductivity parameters, set up solving model;

2) utilize Finite Element Method to carry out subdivision to medium, subdivision is n unit, calculates the space length l of i-th subdivision unit _iand current density A _i, wherein, i=1,2 ..., n;

3) result of calculation is stored.

3. under a kind of sinusoidal excitation according to claim 2 magnetosonic coupling direct problem vector method for solving, it is characterized in that, the space length l of each subdivision unit of the calculating described in second step _iand current density A _i, be adopt Comsol finite element simulation platform or ANSYS finite element simulation platform or MATLAB emulation platform to calculate.

4. under a kind of sinusoidal excitation according to claim 1 magnetosonic coupling direct problem vector method for solving, it is characterized in that, the frequency domain amplitude phase solution described in second step comprises the steps:

1) real part and the imaginary part of the corresponding complex plane vector of each subdivision unit in the first step is calculated

Real part is ${\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}=\frac{1}{l_i}f(r,\mathrm{j\ω})A_i\cos (j{\mathrm{\ω}}_1{l}_i/c),$

Imaginary part is ${\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}=\frac{1}{l_i}f(r,\mathrm{j\ω})A_i\sin (j{\mathrm{\ω}}_1{l}_i/c).$

Wherein p _i(r, j ω) is magnetosonic coupling acoustical signal, and r is locus, and ω is angular frequency, and J is current density, B ₀for static magnetic field, δ (t) is impulse excitation, and c is the velocity of sound in medium, and H (j ω) is system function;

2) magnetosonic coupling direct problem solution and resultant vector corresponding to magnetoacoustic signals is calculated

$P(r,\mathrm{j\ω})=\underset{i}{\mathrm{\Σ}}{P}_i(r,\mathrm{j\ω})=\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}+j\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}$

3) corresponding amplitude AMP is calculated _nwith phase place PHA _n

${\mathrm{AMP}}_n=\sqrt{{\left(\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}\right)}^2+{\left(\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}\right)}^2}$

${\mathrm{PHA}}_n=\arctan \left(\frac{\underset{i}{\mathrm{\Σ}}{\mathrm{Im}}_{\mathrm{Pi}(r,\mathrm{j\ω})}}{\underset{i}{\mathrm{\Σ}}{\mathrm{Re}}_{\mathrm{Pi}(r,\mathrm{j\ω})}}\right).$