CN101266289B - Deformation Space Design Method for Transverse Gradient Coils in Open MRI System - Google Patents

Abstract

The invention discloses a deformation space design method of a transverse gradient coil in an open MRI system, which is applied to the design of a double-plane symmetrical transverse gradient coil. First add control parameters to variate the shape of the cockle wire, and use a series of deformed cockle wires to represent the current-carrying wire of the coil. These parameters define the layout of the entire coil system. The overall closed curve can use these parameters to control the deformation; if you are interested The constrained target point is selected in the spherical space of the imaging area; according to the design requirements and the constrained target point, the gradient field distribution of the initial coil is calculated using the Biot-Savat theorem, and the error function formula is established; the optimal parameters are obtained through the least square method optimization, and the The goal of the design is to obtain a suitable uniform gradient field; according to the obtained optimal parameter set, draw each deformed cockle line to obtain the style of the coil. The method is simple and effective, and the optimization process naturally includes size constraints; it can be used to design transverse gradient coils with more complex shapes.

Description

The distortion space design method of horizontal gradient loop in the open MRI systems

Technical field

The present invention relates to the distortion space design method of horizontal gradient loop in a kind of open MRI systems.

Background technology

In the magnetic resonance imaging field,,, carried out a large amount of work for obtaining uniform gradient magnetic about gradient coil.Mainly contain two kinds of methods for designing.A kind of method for designing that is based on fourier space is such as target field method (R.Turner, " A target field approach to optimal coil design; " Journal ofPhysics D:Applied Physics, vol.19, pp.L147-L151,1986.); Another kind is based on the method for the real space, such as simulated annealing (S.Crozier and D.M.Doddrell, " Gradient-coil design bysimulated annealing, " J.Magn.Reson.A, vol.103, pp.354-357,1993.).Two kinds of methods respectively have relative merits.

Method for designing based on fourier space is, expresses current density on the coil plane with analytic expression or series expansion.As the target field method, represent current density on the coil plane with the Fourier analytic expression, distribute according to the target field of hope then and find the solution current density with Fourier transform.Utilize FFT to realize this process easily very rapidly, and do not need to set in advance the pattern of coil.But unique inverse transformation is arranged for Fourier is changed, need the infinity of hypothesis coil, to the outer electric current of regulation limited range be zero when therefore finding the solution actual coil, need carry out ' change mark ' (J.M.Jin, Electromagnetic Analysis and Design inMagnetic Resonance Imaging.Boca Raton, Florida:CRC Press, 1998.) or approximate, this can cause the impairment of gradient fields homogeneity range; For the coil of design rule shape, be very effective simultaneously, but be difficult to be applied to the situation of arbitrary shape, because the parsing expansion of distribution of current is difficult to try to achieve.

And all be earlier at coil space supposition current-carrying element (annular or arc) based on the method for designing of the real space, utilize the random optimization method to adjust the current-carrying positions of elements then to reach designing requirement.As simulated annealing, Crozier etc. are mapped to deformation space with circle, form the egg deltoid, are used for representing current carrying conductor, adjust the position of lead then with simulated annealing, electric current, loop shape etc.Tomasi etc. have proposed fast simulated annealing method (FSA) (D.Tomasi, E.C.Caparelli, H.Panepucci, and B.Foerster, " FastOptimization of a Biplanar Gradient Coil Set, " J.Magn.Reson., vol, 140, pp.325-339,1999.).This method can be set limited dimension line circle naturally, but just uses simple shape at present, as straight line or loop wire, can not construct complicated coil pattern, adapts to more complex gradients field distribution requirement.

Summary of the invention

The distortion space design method that the purpose of this invention is to provide horizontal gradient loop in a kind of open MRI systems, can design the plane gradient coil shape of more complicated, be mainly used in the design of biplane horizontal gradient loop in the open type magnetic resonance imaging (MRI) system.

The technical solution used in the present invention is:

The present invention represents current carrying conductor at coil space with a series of curves, utilize deformation technology, these curves can come controlled deformation with several simple parameters, utilize the least square method optimization method to adjust coil parameter, finally obtain the coil curve that adheres to specification.This method comprises following each step:

1) according to the limacon fundamental formular, under rectangular coordinate system, the controlled variable that increases the limacon curve is out of shape, and sets up new parametric equation, and limacon is carried out the shape variation;

2) pre-placement is out of shape limacons as initial coil for 4 groups on two coil planes;

3) at the selected constrained objective point of imaging area spherical space interested;

4) according to designing requirement and constraint impact point, utilize Bi Ao-Sa to cut down the gradient fields distribution that theorem is calculated initial coil, set up the error function formula;

5) set up the least square method optimization problem, utilize least square method optimization method iteration to seek the optimized parameter set;

6) according to the set of the optimized parameter that obtains, obtain the expression formula of each limacon, each bar limacon that draws can obtain the pattern of coil.

Described limacon fundamental formular (1) is:

r＝a+bcosθ，

(1)

θ∈[0，2π]

In the formula, r represents the limacon radial coordinate, and θ represents the limacon angle coordinate, and a, b represent the controlled variable of limacon curve shape;

Under rectangular coordinate system, the controlled variable that increases curve is out of shape, and obtains following parametric equation (2)

x(θ)＝(a+bcosθ)cosθ+k

y(θ)＝(c+dcosθ)sinθ (2)

θ∈[0，2π]

In the formula, θ represents the perspective curve coordinate, x (θ) represents the x component of deformation curve in rectangular coordinate system, is the function about θ, and y (θ) represents the y component of deformation curve in rectangular coordinate system, it also is function about θ, a, b, k are the controlled variable of curve x component, c, d are the controlled variable of curve y component;

Described 4 groups of distortion limacons placing at two coil planes are as initial coil, symmetry based on coil, two groups of distortion limacon left-right symmetric on each plane, distortion limacon group on two planes is identical, on behalf of whole coil, therefore only set up the parametric equation group of one group of distortion limacon promptly distribute, if whole parameter sets vectors of selected limacon group are Γ, utilize this parameter sets vector, just can release the distribution of whole coil;

Described selected constrained objective point, according to extreme value theory, magnetic induction density is got maximal value or minimum value on the border of closed interval, gets final product so the constrained objective point is taken to choose on the sphere of imaging area interested; Again based on the symmetry of coil, get point on a certain quadrant on the xz plane as representative;

Described according to designing requirement and obligatory point, utilize Bi Ao-Sa to cut down the gradient fields distribution that theorem is calculated initial coil, set up error function formula (3):

$f\left(\mathrm{\Γ}\right)=\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{\[G(x_t,y_t,z_t)-G^t(x_t,y_t,z_t)]}^2---\left(3\right)$

G ^t(x _t, y _t, z _t) representing that the desired value at constrained objective point place is the gradient fields intensity of designing requirement, N is that selected constrained objective is counted, wherein G (x _t, y _t, z _t) represent and utilize Bi Ao-Sa to cut down the Grad of the initial coil of theorem calculating at constrained objective point place;

Setting up the least square method optimization problem is

Minimize：f(Γ)

Utilize least square method optimization method iteration,, error function is minimized, seek optimized parameter set vector Γ in conjunction with the practical project restriction;

According to the optimized parameter that obtains set vector Γ, substitution parametric equation (2) obtains the expression formula of each limacon, and according to coil symmetry, each bar limacon that draws can obtain the pattern of whole coil.

The beneficial effect that the present invention has is:

Be in " the change mark " that need not carry out for the coil that obtains finite size, size be limited in very natural having included in the optimizing process; Do not need to find the solution ill-condition equation.In addition, select suitable curve parametric equation, can obtain various special loop geometries, the present invention can be used to design the gradient coil that has than complicated shape.

Description of drawings

The difformity curve of Fig. 1 limacon, trisection of an angle line chart.

The difformity curve of Fig. 2 limacon, heart-curve diagram.

The difformity curve of Fig. 3 limacon, ripples shape limacon figure.

The limacon figure of Fig. 4 distortion.

Fig. 5 coil space and imaging space of interest figure.

Fig. 6 presets the synoptic diagram of 16 distortion limacons.

The sample graph of Fig. 7 constrained objective point.

Fig. 8 optimizes process flow diagram.

Fig. 9 horizontal gradient loop design result---go up the coil pattern diagram on right side, plane.

The distribution pattern diagram of Figure 10 horizontal gradient loop design result---whole biplane coil.

The coil gradient fields of Figure 11 design is at the distribution situation figure of xz central plane.

Embodiment

Designing requirement of the present invention is that the goal gradient field strength is 6.25mT/m, and DSV is 0.38m, and two interplanar spacings are 0.5m, and coil size is limited in the circle that radius is 0.43m.

Select for use the polar coordinates formula of curve limacon to be (1):

r＝a+bcosθ，

(1)

θ∈[0，2π]

In the formula, r represents the limacon radial coordinate, and θ represents the limacon angle coordinate, a, b represents the controlled variable of limacon curve shape, a, and the situation that b is different can form different curve shapes, during such as a＜b, form inner ring, during special circumstances a=b/2, form three angular bisectors, be illustrated in figure 1 as a=1/2, the situation during b=1; During a=b, form cardioid, as shown in Figure 2 the situation during a=b=1; During 2b＞a＞b, limacon forms ripples, is illustrated in figure 3 as a=3/2, the situation during b=1.By learning also shown in Fig. 1,2,3 that limacon is axisymmetric about x;

Under rectangular coordinate system, the controlled variable that increases curve is out of shape, and obtains following parametric equation (2)

x(θ)＝(a+bcosθ)cosθ+k

y(θ)＝(c+dcosθ)sinθ (2)

θ∈[0，2π]

θ represents the perspective curve coordinate in the formula, x (θ) represents the x component of deformation curve in rectangular coordinate system, it is function about θ, y (θ) represents the y component of deformation curve in rectangular coordinate system, also is the function about θ, a, b, k is the controlled variable of curve x component, and c, d are the controlled variable of curve y component.As shown in Figure 4, shown a kind of limacon curve that has been out of shape, wherein parameter value is a=0.2113, b=0.1570, c=0.4212, d=0.0170, k=0.0763.

4 groups two coil planes placements are out of shape limacons as initial coil, as shown in Figure 5, represent one group with a limacon among the figure, the dot-dash coil is represented the maximum constraints scope of coil, the black ball is represented imaging area interested, generally represent, show that the gradient intensity in this scope requires evenly with sphere diameter DSV.Because what the present invention paid close attention to is symmetric coil, symmetry based on coil, distortion limacon group on each plane two groups distortion limacon left-right symmetric, two planes is identical, therefore can only set up the parametric equation group of one group of distortion limacon and can represent whole coil to distribute.If whole parameter sets vectors of selected limacon group are Γ, utilize this parameter sets vector, just can release the distribution of whole coil.The selected distortion limacon group that goes up the right side, plane makes up the parametric equation group, be provided with 16 sealing limacons altogether, because the distortion limacon remains axisymmetric about x, as shown in Figure 6, only illustrate 16 to seal limacons, 1,2 among the figure with the curve distribution of the first half,, 16 have represented the numbering of each bar distortion limacon.Wherein the corresponding Deformation control parameter of i bar distortion limacon is a _i, b _i, c _i, d _i, k _i(i=1,2 ... 16), Γ=(a then ₁, b ₁, c ₁, d ₁, k ₁..., a _i, b _i, c _i, d _i, k _i... a ₁₆, b ₁₆, c ₁₆, d ₁₆, k ₁₆).

Setting the constrained objective point at imaging area sphere interested, is imaging area interested in DSV (the diameter of spherevolume) scope as shown in Figure 5.According to extreme value theory, magnetic induction density is got maximal value or minimum value on the border of closed interval, so constrained objective point district gets final product on the DSV sphere; Based on the symmetry of coil, the point on a certain quadrant on the desirable xz plane just can be used as representative again.As shown in Figure 7, evenly chosen 20 sample points on the first quartile as the constrained objective point in the DSV scope of xz plane, angle intervals is

Solid dot on the first quartile circumference has been represented the constrained objective point of being got, and wherein has any to fall into the 4th quadrant, and this is to make institute's reconnaissance the processing that the too small unfavorable calculating of coordinate figure is done not occur for being avoided.

Calculate the field intensity value of initial coil on these constrained objective points, again according to the designing requirement value, can set up error function on these aspects, error function is expressed as

$f\left(\mathrm{\Γ}\right)=\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{\[G(x_t,y_t,z_t)-G^t(x_t,y_t,z_t)]}^2---\left(3\right)$

(x wherein _t, y _t, z _t) in represent the constrained objective point, subscript t represents t constrained objective point G (x _t, y _t, z _t), N is that total selected constrained objective is counted, and is 20 in this example; Utilize Bi Ao-Sa to cut down the Grad of the initial coil of theorem calculating at constrained objective point place, G ^t(x _t, y _t, z _t) represent that the desired value at constrained objective point place is the gradient fields intensity of designing requirement, the error function that f (Γ) representative is set up is the function about Γ, Γ represents the parameter sets vectors of whole 16 distortion limacons.

Set up the least square method optimization problem

Minimize：f(Γ)

According to engineering restriction as two interplanar spacings is 0.5m, and coil size is limited in the circle that radius is 0.43m. utilize least square method optimization method iteration to seek optimized parameter set vector Γ, error function is minimized.Optimization step as shown in Figure 8.In optimizing process, the magnetic induction density that calculates on each constrained objective point is because every limacon all is a closed curve, can adopt the one dimension Gauss integration easily.

According to the optimized parameter set that obtains, obtain the expression formula of each limacon, each parametric equation of substitution (2), each bar limacon draws; According on the unified plane about coil to becoming, with gained limacon sets of curves left mirror image promptly obtain a coil distribution on the plane; And then whole plane copied to the pattern that the lower plane position promptly obtains whole coil.As shown in Figure 9, be the distortion limacon group pattern of going up the right side, plane, Figure 10 is the distribution pattern of whole biplane coil.Figure 11 shows the distribution situation of gradient fields on the xz central plane that designed coil produces, the zone line of outline line represent gradient intensity error 5% with interior scope, the dot-and-dash line circle is represented the gradient homogeneity range of designing requirement, be the DSV scope, visible design result has met the DSV size requirements well among the figure.

Claims (1)

1. the distortion space design method of horizontal gradient loop in the open MRI systems, it is characterized in that: design biplane gradient coil shape, be applied to symmetric transverse gradients coil in the open type magnetic resonance imaging (MRI) system, this method comprises following each step:

1) according to the limacon fundamental formular, under rectangular coordinate system, the controlled variable that increases the limacon curve is out of shape, and sets up new parametric equation, and limacon is carried out the shape variation;

2) pre-placement is out of shape limacons as initial coil for 4 groups on two coil planes;

3) at the selected constrained objective point of imaging area spherical space interested;

4) according to designing requirement and constraint impact point, utilize Bi Ao-Sa to cut down the gradient fields distribution that theorem is calculated initial coil, set up the error function formula;

5) set up the least square method optimization problem, utilize least square method optimization method iteration to seek the optimized parameter set;

6) according to the set of the optimized parameter that obtains, obtain the expression formula of each limacon, each bar limacon that draws promptly obtains the pattern of coil;

Described limacon fundamental formular (1) is:

r＝a+bcosθ，(1)

θ∈[0，2π]

In the formula, r represents the limacon radial coordinate, and θ represents the limacon angle coordinate, and a, b represent the controlled variable of limacon curve shape;

Under rectangular coordinate system, the controlled variable that increases curve is out of shape, and obtains following parametric equation (2)

x(θ)＝(a+bcosθ)cosθ+k

y(θ)＝(c+dcosθ)sinθ (2)

θ∈[0，2π]

In the formula, θ represents the perspective curve coordinate, x (θ) represents the x component of deformation curve in rectangular coordinate system, is the function about θ, and y (θ) represents the y component of deformation curve in rectangular coordinate system, it also is function about θ, a, b, k are the controlled variable of curve x component, c, d are the controlled variable of curve y component;

Described 4 groups of distortion limacons placing at two coil planes are as initial coil, symmetry based on coil, two groups of distortion limacon left-right symmetric on each plane, distortion limacon group on two planes is identical, on behalf of whole coil, therefore only set up the parametric equation group of one group of distortion limacon promptly distribute, if whole parameter sets vectors of selected limacon group are Г, utilize this parameter sets vector, just can release the distribution of whole coil;

Described selected constrained objective point, according to extreme value theory, magnetic induction density is got maximal value or minimum value on the border of closed interval, gets final product so the constrained objective point is taken to choose on the sphere of imaging area interested; Again based on the symmetry of coil, get point on a certain quadrant on the xz plane as representative;

Described according to designing requirement and obligatory point, utilize Bi Ao-Sa to cut down the gradient fields distribution that theorem is calculated initial coil, set up error function formula (3):

$f\left(\mathrm{\Γ}\right)=\underset{t=1}{\overset{N}{\∑}}{[G(x_t,y_t,z_t)-G^t(x_t,y_t,z_t)]}^2---\left(3\right)$

G ' (x _t, y _t, z _t) representing that the desired value at constrained objective point place is the gradient fields intensity of designing requirement, N is that selected constrained objective is counted, wherein G (x _t, y _t, z _t) represent and utilize Bi Ao-Sa to cut down the Grad of the initial coil of theorem calculating at constrained objective point place;

Setting up the least square method optimization problem is

Minimize：f(Г)

Utilize least square method optimization method iteration,, error function is minimized, seek optimized parameter set vector Г in conjunction with the practical project restriction;

According to the optimized parameter that obtains set vector Г, substitution parametric equation (2) obtains the expression formula of each limacon, and according to coil symmetry, each bar limacon that draws can obtain the pattern of whole coil.

Images