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
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
(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
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
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:
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.
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
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
(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,
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
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
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).
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:
Make Lagrangian function
Formula (11) can be write as the form of matrix multiple:
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:
Because the calculation method of parameters of y, z direction similarly, so do not repeat them here.