CN101216541A - Magnetic resonance image-forming system gradient field spherical harmonic coefficient obtaining method - Google Patents

Abstract

The invention relates to a method for acquiring spherical harmonic coefficient of gradient field of magnetic resonance imaging system, which comprises the following steps of : (a) constructing a water model coordinate system selecting a mark point Pc(u0, v0) closest to the image center as the original point Op, selecting the u axis direction of an MRI image as the c axis direction, selecting the v axis direction in the image as the r axis direction, and selecting the direction forming a right-handed coordinate system with the c and the r axes as the s axis direction; (b) calculating the MRI coordinates of the mark point Pi according to the water model coordinate system by following steps: (1) ignoring the rotation of the water model in the plane thereof and the translation of the original point; (2) considering the rotation by a theta angle in the plane of the water model around the center of Op and a shaft in the direction of a scan layer slice; and (3) considering the translation of the coordination original point of the water model; and (c) obtaining a linear equation group concerning spherical harmonic coefficients a and b if the magnetic field intensity parameters gamma, theta, phi and image coordinates of a certain point are known, and calculating the coefficients a and b by solving the linear equation group.

Description

A kind of acquisition methods of magnetic resonance image-forming system gradient field spherical harmonic coefficient

Technical field

The present invention relates to a kind of acquisition methods of coefficient, particularly a kind of acquisition methods of magnetic resonance image-forming system gradient field spherical harmonic coefficient.

Background technology

In the nuclear resounce system, the non-linear geometry deformation that tends to cause image of gradient fields.No matter be on different MR imaging apparatus or identical MR imaging apparatus and in the different visual field (FOV), the geometry deformation of image is different.Therefore, at the image rectification technology of the nonlinear problem of gradient fields the feasibility of image studies between the precision that improves the magnetic resonance image (MRI) navigating surgery and the many magnetic resonance is judged all have suitable necessity in actual applications.The basic process that gradient deformation of magnetic resonant image is proofreaied and correct is: earlier by obtaining the position offset at limited reference mark in the MR imaging apparatus space someway, next calculate the coordinate of each pixel in the MR imaging apparatus space of image to be corrected, by the side-play amount of interpolation method according to this pixel space of coordinate Calculation of each pixel; Transformational relation according to MR imaging apparatus coordinate system and image coordinate system, this pixel space side-play amount is scaled side-play amount in the image coordinate system, afterwards with this offset compensation in the image coordinate of this pixel, promptly finished the gradient deformation of magnetic resonant image trimming process.

The method of calculating the side-play amount of magnetic resonance imaging space inner control point can be divided into two kinds: first kind is to use 3 D stereo water mould, 3 D stereo water mould provides the reference mark in the three dimensions, by analysis to the magnetic resonance image (MRI) inner control point of three-dimensional water mould, can obtain the anamorphose amount on the finite space reference mark, according to the transformational relation of MR imaging apparatus coordinate system and image coordinate system, the side-play amount in the image coordinate system of this pixel is scaled spatial offset; Another kind method is the side-play amount that the described function-spheric harmonic function of applying a magnetic field is calculated to be limited reference mark in the image space.Because first method relies on three-dimensional water mould, implementation cost is far above second method, and need be to the repeatedly imaging and analyze the position offset that could obtain the reference mark of three-dimensional water mould, so the efficient of enforcement is very low.Use second method, before promptly spheric harmonic function is calculated, at first will provide the correlation-corrected parameter in the spheric harmonic function.Researchist Jorge Jovicich, the SilvesterCzanner of Harvard University is at their paper, Reliability in Multi-Site Structural MRI Studies:Effects of Gradient Non-linearity Correction on Phantom and Human Data, provide the method for calculating the correlation-corrected parameter among the Neuron Image (in press) (multipoint configuration magnetic resonance imaging reliability consideration: gradient non-linear is proofreaied and correct the effect in water mould and human body image, " neural image " Chinese translation).This method is the correction parameter that is used for image rectification according to the calculation of design parameters of gradient coil, but the design parameter of gradient coil is one of principal element of anamorphose, also has other factors not to be considered in addition.So still there is some difference between actual correction parameter and the design parameter.

Summary of the invention

At the problems referred to above, the purpose of this invention is to provide and a kind ofly in image space, get limited some accurate Calculation correction parameter, thereby obtain the acquisition methods of the magnetic resonance image-forming system gradient field spherical harmonic coefficient of real magnetic field gradient parameter at specific gradient coil.

For achieving the above object, the present invention takes following technical scheme: a kind of acquisition methods of magnetic resonance image-forming system gradient field spherical harmonic coefficient, be that basis is got limited point in the real image space, the anti-magnetic resonance correction parameter of asking is spherical harmonic coefficient a and b, and it may further comprise the steps:

(a) set up water mould coordinate system, the MRI image origin is V (x ₀, y ₀, z ₀), with in the water mould image near MRI picture centre V (x _c, y _c, z _c) monumented point P _c(u ₀, v ₀) be water mould coordinate origin O _pWith u direction of principal axis in the MRI image is its c direction of principal axis; With v direction of principal axis in the image is its r direction of principal axis; With the direction with c, r axle formation right-handed coordinate system is the s direction of principal axis; Any monumented point P _iWater mould coordinate system coordinate be (c _i, r _i, s _i); According to O _pImage coordinate calculate its MRI coordinate, obtain

$V_{o_p}(x,y,z)=v_c*{\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="S2008100562041E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_0*p*v_r*v_0*p+V(x_0,{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="S2008100562041E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0,z_0)---\left(1\right)$

Wherein p is the distance between the neighbor.v _c, v _r, v _sBe respectively the axial vector of unit length of c, r and s.

(b) ask the MRI coordinate of monumented point, to monumented point P _i(c _i, r _i, s _i), its MRI coordinate can be divided into following steps by water mould coordinate system:

(i) do not consider the water mould in self plane rotation and the translation of true origin, monumented point P _i(c _i, r _i, s _i) coordinate in the MRI coordinate system is

$V_{p_i}(x,y,z)=c_i*d*v_c+r_i*d*v_r+s_i*d*v_s---\left(2\right)$

(ii) consider in water mould self plane with O _pBeing the center of circle, serves as axle rotation θ angle with the layer direction that scanning is set, monumented point P _iCoordinate in the MRI coordinate system need multiply by rotation matrix T again _Rot

$V_{p_i}=(x^{\&prime;},y^{\&prime;},z^{\&prime;},1)=V_{p_i}(x,y,z,1)*T_{\mathrm{rot}}---\left(3\right)$

$T_{\mathrm{rot}}=\left[\begin{array}{cccc}t*x*x+c& t*x*y+s*z& t*x*z-s*y& 0\\ t*x*y-s*z& t*y*y+c& t*y*z+s*x& 0\\ t*x*z+s*y& t*y*y+c& t*z*z+c& 0\\ 0& 0& 0& 1\end{array}\right]$

c＝cos(θ)，s＝sin(θ)，t＝1-c

X wherein, y, z are the coordinates of layer direction vector;

(iii) consider the translation of water mould true origin, monumented point P _iCoordinate in the MRI coordinate system is

$V_{p_i}=(x^{\&prime;\&prime;},y^{\&prime;\&prime;},z^{\&prime;\&prime;})=V_{p_i}(x^{\&prime;},y^{\&prime;}{z}^{\&prime;})+V_{o_p}(x,y,z)---\left(4\right)$

Wherein, V _Pi(x ", y ", z ") is monumented point P _iActual coordinate in the MRI coordinate system.Magnetic field intensity can be expressed as:

B _r(n，m)(r，θ，_)＝r ⁿ[a _v(n，m)cos(m_)+b _v(n，m)sin(m_)]×P _(n，m)(cosθ) (5)

The magnetic field gradient function:

$G_{v\left(r\right)}\&equiv;\frac{{\&PartialD;\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}}{\&PartialD;v}\&equiv;\frac{\&PartialD;{\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}^L}{\&PartialD;v}+\frac{{\&PartialD;\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}^N}{\&PartialD;v}\&equiv;G_v^L+G_{v\left(r\right)}^L---\left(6\right)$

Department releases by formula (5) (6) (7):

V _x＝∑r ⁿ[a _x(n，m)cos(m_)+b _x(n，m)sin(m_)]×P _(n，m)(cosθ)/a _(1，1)

V _y＝∑r ⁿ[a _y(n，m)cos(m_)+b _y(n，m)sin(m_)]×P _(n，m)(cosθ)/b _(1，1) (8)

V _z＝∑r ⁿ[a _z(n，m)cos(m_)+b _z(n，m)sin(m_)]×P _(n，m)(cosθ)/a _z(1，0)

A wherein _{V (n, m)}, b _{V (n, m)}Be constant, and a _{V (n, m)}, b _{V (n, m)}Be the coefficient that v direction n rank m level is launched item, P _{(n, m)}(cos θ) is Legendre polynomial; Formula (8) left end is monumented point P _iCoordinate figure under the MRI coordinate system;

(c) as mentioned above, as γ, the θ of known certain point, _ and MRI image coordinate, then can obtain system of linear equations about spherical harmonic coefficient a, b, can obtain coefficient a, b by separating system of linear equations.

Described step (c) middle γ, θ, _ be the coordinate of monumented point in the MRI coordinate system.Can be by V _Pi(x ", y ", z ") obtains by following conversion

Contiguous tokens point is provided with for equidistant in the described step (a), and its interval d gets definite value.

In the described step (b), establish P ₁(u ₁, v ₁) be on the water mould on the c direction with P _c(u ₀, v ₀) adjacent monumented point; According to P ₁(u ₁, v ₁) and P _c(u ₀, v ₀) image calculation θ angle, the computing formula at θ angle then

θ＝tg ^-1((v ₁-v ₀)/(u ₁-u ₀))。

The present invention is owing to take above technical scheme, and it has the following advantages: 1, the present invention has overcome the shortcoming that there are differences between gradient coil design parameter and the real magnetic field gradient parameter according to the anti-magnetic field gradient parameter of asking of real image.2, the present invention has considered the influence of water mould putting position to the algorithm degree of accuracy simultaneously in the counter process of asking the magnetic field gradient parameter, has improved the accuracy rate of algorithm.3, the present invention adopts the searching algorithm of gradient field spherical harmonic parameter, has simplified the step that algorithm is implemented greatly, has improved efficiency of algorithm.The inventive method is at being proofreaied and correct by the non-linear anamorphose that causes of gradient fields in magnetic resonance imaging is used, and the feasibility analysis of image studies between the precision that improves the magnetic resonance image (MRI) navigating surgery and the many magnetic resonance is had great importance.

Description of drawings

Fig. 1 is a water mode configuration synoptic diagram of the present invention

Fig. 2 is the side-looking cross-sectional schematic of Fig. 1

Fig. 3 is that the present invention scans the water mould image that obtains and based on the water mould coordinate system synoptic diagram of this foundation

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in detail.

The acquisition methods of magnetic resonance image-forming system gradient field spherical harmonic coefficient provided by the present invention, be according to getting limited point in the real image space, the anti-magnetic resonance correction parameter of asking also is a spherical harmonic coefficient, for taking all factors into consideration of calculated amount and correction accuracy, only carries out the following calculation of parameter in 5 rank.

As shown in Figure 1, 2, gradient calibration water mould is the instrument that is used for gradient calibration, and it both had been used for the search system parameter, also is used for the error after the measurement update.Gradient calibration water mould is a square box body 1, and the cylinder 2 that is arranged in square formation according to the mode of equidistant square formation is set in box body 1, is full of copper-bath in the cylinder 2, can imaging in MR imaging apparatus.

The water mould is placed in the effective imaging space, guarantees that magnetic field center in the water mould, is provided with the water mould image that the plane of scanning motion obtains scanning, as shown in Figure 3.In water mould image near MRI picture centre V (x _c, y _c, z _c) monumented point P _c, its water mould image coordinate is (u ₀, v ₀).The MRI image origin is V (x ₀, y ₀, z ₀), herein V (x, y, the z) x in, y, z are coordinate under the MRI coordinate system.When setting up water mould coordinate system, with monumented point P _cBe coordinate origin O _p, be the c direction of principal axis with u direction of principal axis in the MRI image, be the r direction of principal axis with v direction of principal axis in the image, be the s direction of principal axis with direction with c, r axle formation right-handed coordinate system.Because according to the requirement of described water mould disposing way and scanning, water mould initial point O _pRange image center V (x _c, y _c, z _c) very near, therefore can ignore since the anamorphose that gradient non-linear causes to O _pThe influence of position so can be directly according to O _pImage coordinate to calculate its MRI coordinate as follows

$V_{o_p}(x,y,z)=v_c*{\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="S2008100562041E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_0*p+v_r*v_0*p+V(x_0,{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="S2008100562041E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0,z_0)---\left(1\right)$

Wherein p is the distance between the neighbor, v _c, v _r, v _sBe respectively the axial vector of unit length of c, r and s.

And for any one monumented point P _i,, can't re-use image coordinate and calculate its MRI coordinate, so P because the anamorphose that the gradient non-linear of its position causes is more remarkable _iThe MRI coordinate need calculate by water mould coordinate system.Monumented point P _iWater mould coordinate system coordinate be (c _i, r _i, s _i), contiguous tokens point be spaced apart d, calculating can be divided into following steps:

(i) do not consider the water mould in self plane rotation and the translation of true origin, monumented point P _iCoordinate in the MRI coordinate system is

$V_{p_i}(x,y,z)=c_i*d*v_c+r_i*d*v_r+s_i*d*v_s---\left(2\right)$

(ii) consider in water mould self plane with O _pBeing the center of circle, serves as axle rotation θ angle with the layer slice direction that scanning is set, monumented point P _iCoordinate in the MRI coordinate system need multiply by rotation matrix T again _Rot,

$V_{p_i}=(x^{\&prime;},y^{\&prime;},z^{\&prime;},1)=V_{p_i}(x,y,z,1)*T_{\mathrm{ros}}---\left(3\right)$

$T_{\mathrm{rot}}=\left[\begin{array}{cccc}t*x*x+c& t*x*y+s*z& t*x*z-s*y& 0\\ t*x*y+s*z& t*y*y+c& t*y*z+s*x& 0\\ t*x*z+s*y& t*y*z-s*x& t*z*z+c& 0\\ 0& 0& 0& 1\end{array}\right]$

c＝cos(θ)，s＝sin(θ)，t＝1-c

X wherein, y, z are the coordinates of slice direction vector; If P ₁(u ₁, v ₁) be on the water mould on the c direction with P _c(u ₀, v ₀) adjacent monumented point; According to P ₁(u ₁, v ₁) and P _c(u ₀, v ₀) image calculation θ angle, the computing formula at θ angle then

θ＝tg ^-1((v ₁-v ₀)/(u ₁-u ₀))；

(iii) consider the translation of water mould true origin, monumented point P _iCoordinate in the MRI coordinate system is

$V_{p_i}=(x^{\&prime;\&prime;},y^{\&prime;\&prime;},z^{\&prime;\&prime;})=V_{p_i}(x^{\&prime;},y^{\&prime;}{z}^{\&prime;})+V_{o_p}(x,y,z)---\left(4\right)$

V _Pi, (x ", y ", z ") is monumented point P _iActual coordinate in the MRI coordinate system.

By formula (5) (6) (7) promptly

Magnetic field intensity

B _r(n，m)(r，θ，_)＝r ⁿ[a _v(n，m)cos(m_)+b _v(n，m)sin(m_)]×P _(n，m)(cosθ)(5)

The magnetic field gradient function

$G_{v\left(r\right)}\&equiv;\frac{{\&PartialD;\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}}{\&PartialD;v}\&equiv;\frac{\&PartialD;{\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}^L}{\&PartialD;v}+\frac{{\&PartialD;\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}^N}{\&PartialD;v}\&equiv;G_v^L+G_{v\left(r\right)}^L---\left(6\right)$

Can release by formula (5) (6) (7)

V _x＝∑r ⁿ[a _x(n，m)cos(m_)+b _z(n，m)sin(m_)]×P _(n，m)(cosθ)/a _x(1，1)

V _y＝∑r ⁿ[a _y(n，m)cos(m_)+b _y(n，m)sin(m_)]×P _(n，m)(cosθ)/b _y(1，1) (8)

V _z＝∑r ⁿ[a _z(n，m)cos(m_)+b _z(n，m)sin(m_)]×P _(n，m)(cosθ)/a _z(1，0)

The left end of formula (8) is the coordinate figure of a certain imaging point after distortion under the MRI coordinate system, can calculate by the image coordinate of imaging point.A wherein _{V (n, m)}, b _{V (n, m)}Be constant, a _{V (n, m)}, b _{V (n, m)}Being the coefficient that v direction n rank m level is launched item, is the inherent characteristic of magnetic field nonlinear gradient.P _{(n, m)}(cos θ) is Legendre polynomial.γ in the right-hand member, θ, _ be the coordinate of this point in MRI coordinate system (spherical coordinate system).Can be by V _Pi(x ", y ", z ") converts by formula (9) and obtains.

As mentioned above, the γ of known certain point, θ, _ and image coordinate, then can obtain system of linear equations about a, b, can obtain coefficient a, b by separating system of linear equations.Next can pass through monumented point P _iImage coordinate (u v) calculates the MRI coordinate V after this point deformation _Pi(x, y, z).

$V_{p_i}(x,y,z)=u*v_c*p+v*v_r*p+V(x_0,{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="S2008100562041E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0,z_0)---\left(10\right)$

For taking all factors into consideration of calculated amount and rectification degree of accuracy, only carry out the following calculation of parameter in 5 rank.In spheric harmonic function, parameter a _{V (n, m)}, b _{V (n, m)}Part value non-zero is only arranged below 5 rank, can not consider for zero in calculating, then nonzero term is listed in table 1:

Table 1

X	a	b
			(n＝1，m＝1)	1	0
(n＝3，m＝1)	10 -4	0
			(n＝5，m＝1)	10 -7	0
Y	a	b
			(n＝1，m＝1)	0	1
(n＝3，m＝1)	0	10 -4
			(n＝5，m＝1)	0	10 -7
Z	a	b
			(n＝1，m＝0)	1	0
(n＝3，m＝0)	10 -4	0
			(n＝5，m＝0)	10 -7	0

Annotate: a wherein, b nonzero value are estimated value.

To calculate a _x, b _xBe example, formula (8) can be reduced to:

(11)

Make Lagrangian function

Formula (11) can be write as the form of matrix multiple:

$V_x=\left[\begin{array}{ccc}\cos \left(\mathrm{\&theta;}\right)*\mathrm{\&gamma;}*{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="S2008100562041E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1& \cos \left(\mathrm{\&theta;}\right)*{\mathrm{\&gamma;}}^3*P_3& \cos \left(\mathrm{\&theta;}\right)*{\mathrm{\&gamma;}}^5*P_5\end{array}\right]*\left[\begin{array}{c}{a}_{x\left(\mathrm{1,1}\right)}\\ a_{x(3,1)}\\ a_{x\left(\mathrm{5,1}\right)}\end{array}\right]---\left(12\right)$

With γ, the θ of unlike signal point, _, V _Pi(z) substitution formula (12) can obtain system of linear equations for x, y,

Just can calculate by separating system of linear equations: $\left[\begin{array}{c}{a}_{x\left(\mathrm{1,1}\right)}\\ a_{x\left(\mathrm{3,1}\right)}\\ a_{x\left(\mathrm{5,1}\right)}\end{array}\right].$ Because the calculation method of parameters of y, z direction similarly, so do not repeat them here.

Claims (5)

1. the acquisition methods of a magnetic resonance image-forming system gradient field spherical harmonic coefficient is that basis is got limited point in the real image space, and the anti-magnetic resonance correction parameter of asking is spherical harmonic coefficient a and b, and it may further comprise the steps:

(a) set up water mould coordinate system, the MRI image origin is V (x ₀, y ₀, z ₀), with in the water mould image near MRI picture centre V (x ₀, y ₀, z ₀) monumented point P _c(u ₀, v ₀) be water mould coordinate origin O _pWith u direction of principal axis in the MRI image is its c direction of principal axis; With v direction of principal axis in the image is its r direction of principal axis; With the direction with c, r axle formation right-handed coordinate system is the s direction of principal axis; Any monumented point P _iWater mould coordinate system coordinate be (c _i, r _i, s _i); According to O _nImage coordinate calculate its MRI coordinate, obtain

$V_{o_p}(x,y,z)=v_c*u_0*p+v_r*v_0*p+V\left(x_{0,}{y}_{0,}{z}_0\right)---\left(1\right)$

(b) ask the MRI coordinate of monumented point, to monumented point P _i(c _i, r _i, s _i), its MRI coordinate can be divided into following steps by water mould coordinate system:

(i) do not consider the water mould in self plane rotation and the translation of true origin, monumented point P _i(c _i, r _i, s _i) coordinate in the MRI coordinate system is

$V_{p_i}(x,y,z)=c_i*d*v_c+r_i*d*v_r+s_i*d*v_s---\left(2\right)$

Wherein p is the distance between the neighbor, v _c, v _r, v _sBe respectively the axial vector of unit length of c, r and s;

(ii) consider in water mould self plane with O _pBeing the center of circle, serves as axle rotation θ angle with the layer direction that scanning is set, monumented point P _iCoordinate in the MRI coordinate system need multiply by rotation matrix T again _Rot

$V_{p_i}=(x^{\&prime;},y^{\&prime;},z^{\&prime;},1)=V_{p_i}(x,y,z,1)*T_{\mathrm{rot}}---\left(3\right)$

$T_{\mathrm{rot}}=\left[\begin{array}{cccc}t*x*x+c& t*x*y+s*z& t*x*z-s*y& 0\\ t*x*y-s*z& t*y*y+c& t*y*z+s*y& 0\\ t*x*z+s*y& t*y*z-s*x& t*z*z+c& 0\\ 0& 0& 0& 1\end{array}\right]$

c＝cos(θ)，s＝sin(θ)，t＝1-c

X wherein, y, z are the coordinates of layer direction vector;

(iii) consider the translation of water mould true origin, monumented point P _iCoordinate in the MRI coordinate system is

$V_{p_i}=(x^{\&prime;\&prime;},y^{\&prime;\&prime;},z^{\&prime;\&prime;})=V_{p_i}(x^{\&prime;},y^{\&prime;}{z}^{\&prime;})+V_{o_p}(x,y,z)---\left(4\right)$

Wherein, V _Pi(x ", y ", z ") is monumented point P _iActual coordinate magnetic field intensity in the MRI coordinate system

B _r(n，m)(r，θ，_)＝r ⁿ[a _v(n，m)cos(m_)+b _v(n，m)sin(m_)]×P _(n，m)(cosθ) (5)

The magnetic field gradient function

$G_{v\left(r\right)}\&equiv;\frac{{\&PartialD;\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}}{\&PartialD;v}\&equiv;\frac{\&PartialD;{\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}^L}{\&PartialD;v}+\frac{{\&PartialD;\mathrm{\&Bgr;}}_{\mathrm{zv}\left(r\right)}^N}{\&PartialD;v}\&equiv;G_v^L+G_{v\left(r\right)}^L---\left(6\right)$

Department releases by formula (5) (6) (7)

V _x＝∑r ⁿ[a _x(n，m)cos(m_)+b _x(n，m)sin(m_)]×P _(n，m)(cosθ)/a _(1，1)

V _y＝∑r ⁿ[a _y(n，m)cos(m_)+b _y(n，m)sin(m_)]×P _(n，m)(cosθ)/b _(1，1) (8)

V _z＝∑r ⁿ[a _z(n，m)cos(m_)+b _z(n，m)sin(m_)]×P _(n，m)(cosθ)/a _z(1，0)

A wherein _{V (n, m)}, b _{V (n, m)}Be constant, and a _{V (n, m)}, b _{V (n, m)}Be the coefficient that v direction n rank m level is launched item, P _{(n, m)}(cos θ) is Legendre polynomial; Formula (8) left end is monumented point P _iCoordinate figure under the MRI coordinate system;

(c) as magnetic field intensity parameter γ, the θ of known certain point, _ and MRI image coordinate, then can obtain system of linear equations about spherical harmonic coefficient a, b, can obtain coefficient a, b by separating system of linear equations.

2. the acquisition methods of a kind of magnetic resonance image-forming system gradient field spherical harmonic coefficient as claimed in claim 1 is characterized in that: γ, θ in the described step (c), _ be the coordinate of monumented point in the MRI coordinate system, can be by V _Pi(x ", y ", z ") obtains by following conversion

3. the acquisition methods of a kind of magnetic resonance image-forming system gradient field spherical harmonic coefficient as claimed in claim 1 or 2 is characterized in that: contiguous tokens point is provided with for equidistant in the described step (a), and its interval d gets definite value.

4. the acquisition methods of described a kind of magnetic resonance imaging system gradient field spherical harmonic coefficient as claimed in claim 1 or 2 is characterized in that: in the described step (b), establish P ₁(u ₁, v ₁) be on the water mould on the c direction with P _c(u ₀, v ₀) adjacent monumented point; According to P ₁(u ₁, v ₁) and P _c(u ₀, v ₀) image calculation θ angle, the computing formula at θ angle then

θ＝tg ^-1((v ₁-v ₀)/(u ₁-u ₀))。

5. the acquisition methods of described a kind of magnetic resonance imaging system gradient field spherical harmonic coefficient as claimed in claim 3 is characterized in that: in the described step (b), establish P ₁(u ₁, v ₁) be on the water mould on the c direction with P _c(u ₀, v ₀) adjacent monumented point; According to P ₁(u ₁, v ₁) and P _c(u ₀, v ₀) image calculation θ angle, the computing formula at θ angle then

θ＝tg ^-1((v ₁-v ₀)/(u ₁-u ₀))。

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