JPH0359690B2 - - Google Patents

Description

[Detailed Description of the Invention] [Industrial Field of Application] This invention is applicable to magnetic resonance imaging (MRI).
This relates to a radial (X, Y) gradient magnetic field coil used in

[Conventional technology]

Figure 4 shows, for example, the literature "Cxogenics"
(1973), pages 554 onwards; shows the conventional X-gradient magnetic field coil shown in VAZABRODIN et al. The Y gradient magnetic field coil can be realized by rotating the X gradient magnetic field coil by 90° about the Z axis. In the figure, 4 is a saddle-shaped coil, and the absolute value of each position in the Z direction of the circular arc current of the saddle-shaped coil is Z ₁ =0.3893×a, Z ₁ ′=2.5687×a, arc angle from -60° to +60° centering on the X axis
2 ₁ = 120°, has the value of current I ₁ . Four of these saddle-shaped coils are arranged symmetrically in shape and direction of current with respect to the X-Y plane, and symmetrically in shape and symmetrically in the direction of current with respect to the Y-Z plane.

FIG. 5 shows the output magnetic field of the X gradient magnetic field coil, and shows the magnetic field Bz in the Z direction that increases linearly in the X direction.

FIG. 6 shows a circular arc current on the Z=Zi plane, and shows the radius a, the circular arc angle, and the current I.

Next, the operation will be explained. For magnetic resonance imaging (MRI), a spatially uniform magnetic field
It is necessary to further superimpose on B _z0 a B _z gradient magnetic field that increases linearly with distance as shown in FIG. 5 (FIG. 5 shows an example of an X gradient magnetic field).
In order to obtain a good NMR image, the X and Y gradient magnetic fields should be placed at the center of the coil (X = 0 in Figure 4,
In the vicinity of the point Y=0, Z=0), the magnetic field is highly linear, that is, it generates only the magnetic field components linearly proportional to the distance of X or Y (∂B _z /∂X, ∂B _z /∂Y, etc.). (for example, a magnetic field component cubically proportional to the distance in X or Y (∂ ³ B _z /∂X ³ , ∂ ³ B _z /∂Y ^3, etc.), and the gradient magnetic field strength ∂B _z /∂X is 0.5
×10 ^-2 T/m to approximately 1.0 × 10 ^-2 T/m,
Two points are required. In order to obtain an X gradient magnetic field having only ∂B _z /∂X components near the center of the coil, the coil has a shape called an X gradient magnetic field coil shown in FIG. 4, and the positions Z ₁ and Z ₁ ' are respectively described later. As in Z ₁ = 0.3893×a, Z ₁ ′=2.5687×a, ₁ =
It is necessary to take a value of 60°. In addition, the Y gradient magnetic field coil can be replaced with the X gradient magnetic field coil shown in FIG.
This can be achieved by rotating 90 degrees around the axis.

Next, we will discuss how to design an X gradient magnetic field coil that generates only the ∂B _z /∂X component near the center of the gradient magnetic field coil described above. (Since they are exactly the same except for rotating them by 90 degrees, only the X gradient magnetic field coil will be described below.)

(a) In the X gradient magnetic field coil shown in FIG. 4, the saddle-shaped coil 4 consists of a circular arc current and a linear current parallel to the Z axis, but the linear current does not produce a _Bz component. Therefore, only the arc current is considered. By the way, the magnetic field created by the arc current at the measurement point (X, Y, Z) is the arc current (as shown in Figure 6, the arc angle is 2 from - to + around the X axis, the radius is a, When a current (having a current value I) exists on the Z= _Z0 plane, it can be expressed as follows using the Biot-Savart equation.

B _z (X, Y, Z)=μ ₀ Ia/4π∫ B _z (X, Y, Z)=μ ₀ Ia/4π∫ −(a−Xcosα−Ysinα)dα/{(X−acosα) ² +
(Y−asinα) ² + (Z−Z ₀ ) ² } ^3/2 …(1) (b) Next, when the gradient magnetic field coil has the shape shown in Figure 4, the magnetic field differential component ∂ ^{2m+1+ 2n+2l} B _z ／∂X ^2m +1∂Y ²ⁿ ∂Z ^2l (However, m=0, 1, 2...; n=0, 1, 2
... ; l = 0, 1, 2, ...) becomes zero at the gradient magnetic field coil center (hereinafter, the coil center will be referred to as the origin). In the gradient magnetic field coil having the shape shown in Fig. 4, the saddle-shaped coil arrangement and coil current are
It is symmetrical about the Z plane. Therefore, from equation (1), B _z becomes an odd function with respect to X and becomes zero in the Y-Z plane, that is, the X=0 plane (including the origin). Similarly, the 2nth order differential component with respect to X also becomes an odd function from equation (1), and becomes zero on the YZ plane, that is, the X=0 plane (including the origin). Therefore, at the origin, the next differential components (coefficients) are all zero.

∂ ^2m+n+l B _z /∂X ^2m ∂Y ⁿ ∂Z ^l =0 (2) The saddle-shaped coil arrangement is symmetrical with respect to the X-Z plane, but the current is antisymmetrical. Therefore, (1)
From the equation, B _z becomes an even function of Y, but the first-order differential component of B _z with respect to Y becomes an odd function and becomes zero in the X-Z plane, that is, the Y=0 plane (including the origin). Similarly, the (2n+1) order differential component of B _z with respect to Y is also an odd function, and the X-Z plane, that is, Y=
It becomes zero within the 0 plane (including the origin). Therefore, at the origin, the next differential components are all zero.

∂ ^m ′ ⁺²ⁿ ′ ^+1+l ′B _z ／∂X ^m ′∂Y ²ⁿ ′ ⁺¹ ∂Z ^l ′＝
0...(3) The saddle-shaped coil arrangement and coil current are symmetrical with respect to the X-Y plane. Therefore, from equation (1),
B _z is an even function of Z, but 1 of B _z with respect to Z
The next differential component becomes an odd function and becomes zero in the XY plane, that is, the Z=0 plane (including the origin). Similarly, the (2n+1)th order differential component of B _z with respect to Z is also an odd function and becomes zero in the XY plane, that is, the Z=0 plane (including the origin). Therefore, at the origin, the next differential components are all zero.

∂ ^m ″ ⁺ⁿ ″ ^+2l ″ ⁺¹ B _z ／∂X ^m ″∂Y ⁿ ″∂Z ^2l ″ ⁺¹ ＝
0...(4) From the above equations (2) to (4), the differential components that do not become zero at the origin are limited to those shown by the following equation.

∂ ^2m+1+2n+2l B _z /∂X ^2m+1 ∂Y ²ⁿ ∂Z ^2l =0...(5) From equation (5), writing the differential components from the lowest order becomes as follows.

∂B _z /∂X, ∂ ³ B _z /∂X ³ , ∂ ³ B _z /∂X∂Y ² , ∂ ³ B _z /
∂X∂Z ² , ∂ ⁵ B _z /∂X ⁵ , ∂ ⁵ B _z /∂X ³ ∂Y ² , ∂ ⁵ B _z /∂ ³ X∂Z ² , ∂ ⁵ B _z /∂X∂Y ⁴ ... (c) In (b) above, it was stated that in the gradient magnetic field coil having the shape shown in FIG. 4, the differential components other than equation (5) become zero. There are an infinite number of odd-order unnecessary differential components other than ∂B _z /∂X, but here we will discuss how to make three types of third-order differential components, which are unnecessary differential components, zero at the origin (unnecessary differential components of fifth order or higher This component is extremely small compared to the third-order unnecessary differential component, and can be approximated to almost zero to the extent that it can be ignored).

To make the third-order differential component zero, from equation (1), 3
The next differential component is calculated, and the Z-direction coordinates Z ₁ and Z ₁ ' of the arc current in FIG. 4 and the arc angle are determined so that the third-order differential component becomes zero. When the first-order differential component and the third-order differential component at the origin are calculated from equation (1), they are expressed by the following equations (6) to (9), respectively.

∂B _z (0, 0, 0)/∂X=μ ₀ Ia/2π・(2a ²
−Z ² / ₁ ) / (Z ² / ₁ ∂ ² ) ^5/2・sin…(6) ∂ ³ B _z (0, 0, 0) / ∂X ³ = 9μ0Ia / 8π [4Z
⁴ / ₁ −27a ² Z ² / ₁ +4a ⁴ / (Z ² / ₁ + a ² ) ^9/2 sin−5a ² −
(3Z ² / ₁ −4a ² ) / 9 (Z ² / ₁ + a ² ) ^9/2 sin3]…(7) ∂ ³ B _z (0, 0, 0) / ∂Y ² = 3μ ₀ Ia / 8π [ 4Z
^4/1 27a ² Z ^2/1 +4a ⁴ /(Z ^2/1 +a ² ) ^9/2 _sin + _5a ² ( _3Z
² / ₁ −4a ² ) / 3 (Z ² / ₁ + a ² ) ^9/2 sin〕…(8) ∂ ³ B _z (0, 0, 0) / ∂X∂Z ² = −6μ ₀ Ia/4
π [4Z ⁴ / ₁ −27a ² Z ² / ₁ +4a ⁴ / (Z ² / ₁ + a ² ) ^9/2 sin
]...(9) Furthermore, β=Z0/a, F/(β)=4β ⁴ −27β ² +4/(
β ² +1) ^9/2 , F ₂ (β) = 3β ² -4/(β ² +1) ^9/2 , then equations (7), (8), and (9) can be transformed into the following equations (7): ′,
(8)′ and (9)′.

∂ ³ B _z (0, 0, 0)/∂X ³ =9μ ₀ I/8πa ⁴ [F
1(β)sin5/9F ₂ (β)sin3〕…(7)′ ∂ ³ B _z (0, 0, 0)/∂X∂Y ² =3μ ₀ I/8πa ⁴
[F ₁ (β) sin−5/9F ₂ (β) sin3]…(8)′ ∂ ³ B _z (0, 0, 0)/∂X∂Z ² =−6μ ₀ I/4
πa ⁴ F ₁ (β)sin…(9)′ The solution that makes equations (7)′, (8)′, and (9)′ zero at the same time is
= 60°, β ₁ = Z ₁ /a = ± which is the solution of F ₁ (β) = 0
0.3893, β ₁ =Z ₁ ′/a=±2.5687. That is, in the gradient magnetic field coil having the shape shown in FIG. 4, the eight arc currents are Z ₁ =±0.3893×a, Z ₁ '=
When taking the value of ±2.5687×a,=60°, it is possible to generate only the ∂B _z /∂X component near the origin.

The method for designing the X gradient magnetic field coil has been described above. By the way, as mentioned above, the gradient magnetic field strength ∂B _z /∂X is required to be about 0.5T ⁻² /m1.0T ² /m. Next, calculate the number of amperes [AT] required to generate a gradient magnetic field of approximately 0.5 ^-2 T/m to 1.0 T ^-2 /m. Since there are eight arcuate currents, the ∂B _z /∂X component produced by the eight arcuate currents at the origin can be expressed by the following equation by taking into account the direction of the current and using equation (1).

(∂B _z (0, 0, 0)/∂X)T ₀ tal=4μ ₀ Ia/2π[2a ²
−Z ² / ₁ / (Z ² / ₁ + a ² ) ^5/2 −2a ² Z′ ² / ₁ / (Z ² / ₁ + a ²
) ^5/2 ] sin...(6)′ In equation (6)′, Z ₁ = ±0.3893×a, Z′ ₁ = ±
Substituting 2.5687×a, = 60° and μ ₀ = 4π×10 ^-7 , we get
Equation (6)' becomes the following equation.

∂B _z (0, 0, 0)/∂X920×10 ^-7 I/a ² …(6)″ Using equation (6), ∂B _z (0, 0, 0)/∂X=1.0× Calculating the number of amperes required to generate a gradient magnetic field with a magnitude of 10 ^-2 T/m, a = 0.3 [m]
In the case of
1000AT is required.

By the way, the coil winding that can flow about 1000 AT,
The shape shown in Fig. 4 (i.e.,
Z ₁ = 0.3893 × a, Z ₁ ′ = 2.5687 × a, = 60°) It is extremely difficult to concentrate and accurately wind the coil, and even if it were possible to wind it, the Since there is a width in , = 60°, Z ₁ = 0.3893×a,
The coil current flows to a position shifted from the position of Z ₁ ′=2.5687×a, and the 3 components other than ∂B _z /∂X component
The following odd differential component occurs, causing deterioration of linearity.

[Problem that the invention seeks to solve]

As mentioned above, the conventional radial gradient magnetic field coil is
The position of the arc current in the Z-axis direction is Z ₁ =0.3983×a,
Z ₁ ' = 2.5687 Even if it were possible, the coil width would become wider and the coil current would flow at a position deviated from the above position, and a third-order odd differential component other than the ∂B _z /∂X component would occur, deteriorating the linearity and decreasing the magnetic field. There was a problem that it could not be used for resonance imaging.

The present invention was made in order to solve the above-mentioned problems, and an object of the present invention is to provide a radial gradient magnetic field coil for magnetic resonance imaging that can be easily wound and that linearity can be improved.

(Means for solving the problem) The radial gradient magnetic field coil, which is the premise of this invention, carries two arc currents on a plane perpendicular to the Z-axis and two DC currents parallel to the Z-axis. Four basic hollow-shaped coils are arranged so that both the shape and the direction of the current are symmetrical with respect to the X-Y plane, and the shape is symmetrical with respect to the Y-Z plane, but the direction of the current is antisymmetrical. This is what was placed.

In this invention, this radial gradient magnetic field coil is
Another 2N (N = integer of 1, 2, i, ...) saddle-shaped coil has 4 i-th weighted saddle coils arranged in the same way as the basic saddle-shaped coil. The arc angle of the coil and the arc angle of the i-th saddle-shaped coil are determined by two arbitrary absolute positions in the Z-axis direction of the arc current of both the saddle-shaped coils, an arbitrary arc radius, and an arbitrary arc current value. The present invention has been improved to have a predetermined angle determined by

This gradient magnetic field coil includes an X-axis and a Y-axis gradient magnetic field coil, and the Y-axis gradient magnetic field coil can be realized by rotating the X-axis gradient magnetic field coil by 90 degrees around the Z-axis.

[Effect]

In this invention, even a gradient magnetic field coil with a very large amperage can be divided and wound, so the coil width of each saddle-shaped coil can be reduced, and the coil width can be reduced from the position where only the ∂B _z /∂X component is generated. As a result of the reduction of the coil windings present in the position 3
The next odd differential component is reduced and linearity is improved.

[Embodiments of the invention]

An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 shows an example of an X gradient magnetic field coil, which has a double structure, unlike the conventional example shown in FIG. 4, which has a single structure. The saddle-shaped coil 1 is the first layer, and the saddle-shaped coil 2 is the second layer. Each of the four basic hollow-shaped coils 1 has an arbitrary value Z ₁ and Z ₁ ' for the absolute value of the position of the arc current in the Z-axis direction, an arbitrary radius a ₁ , and a value for the arc angle of the arc current 2 ₁ . and has an arbitrary current value _I1 . These four saddle-shaped coils 1 are arranged symmetrically in shape and direction of current with respect to the X-Y plane, and symmetrically in shape with respect to the Y-Z plane, but antisymmetrically in direction of current. .

In addition, each of the saddle-shaped coils 2 has Z of circular arc current.
The absolute value of the position in the axial direction has arbitrary values Z ₂ and Z ₂ ′, the arbitrary radius a ² , the arc angle of the arc current has a value of 2 ₂ ,
and has an arbitrary current value _I2 . These four saddle-shaped coils 2, like the saddle-shaped coils 2, are arranged symmetrically with respect to the X-Y plane, and the shape is symmetrical with respect to the Y-Z plane, but the direction of the current is arranged symmetrically. Note that the Y gradient magnetic field coil rotates the X gradient magnetic field coil at 90° with respect to the Z axis.
This can be achieved by rotating.

The split-wound type X gradient magnetic field coil shown in FIG. 1 has a double structure. In this gradient magnetic field coil, like the conventional X gradient magnetic field coil, various parameters (coil position, current, radius) are determined to eliminate unnecessary third-order magnetic field components, but because it has a double structure, The coil width of each saddle-shaped coil can be made narrower than that of the conventional X-gradient magnetic field coil, which makes winding easier and eliminates the position of the coil that generates only the ∂B _z /∂X component. The coil current flowing through the position is reduced, and as a result, the occurrence of third-order odd differential components is reduced, and linearity is also improved. The method for determining these parameters will be described below.

The third-order unnecessary magnetic field component is given by equations (7), (8), and (9), and this is an unnecessary magnetic field component created by one circular arc current. In FIG. 1, since there are eight saddle-shaped coils, there are actually 16 arc currents. Therefore, the unnecessary magnetic field component created by the 16 arc currents near the origin is expressed by the following equation using equations (7), (8), and (9) and taking into account the direction of the current.

∂ ³ B _z (0, 0, 0)/∂X ³ =4・9μ ₀ /8π [{(G _3
1 (Z ₁ , a ₁ ) − G ₃₁ (Z ₁ ′, a ₁ )) I, sin ₁ + (G ₃₁ (Z ₂ , a ₂ ) − G ₃₁ (Z′ ₂ , a ₂ )) I ₂ sin ₂ }
−5/9 {(G ₃₂ (Z ₁ , a ₁ ) −G ₃₂ Z ₁ ′, a ₁ )) I ₁ sin3 ₁ + (G ₃₂ (Z ₂ , a ₂ )−G
₃₂ (Z ₂ ′, a ₂ )) I ₂ sin3 ₂ }]…(10) ∂ ³ B _z (0, 0, 0) / ∂X∂Y ² =4・3μ ₀ /8π [{
(G ₃₁ (Z ₁ , a ₁ ) − G ₃₁ (Z ₁ ′, a ₁ )) I ₁ sin ₁ + (G ₃₁ (Z ₂ , a ₂ ) − G ₃₁ (Z′ ₂ , a ₂ )) I ₂ sin ₂ }
+5/3 {(G ₃₂ (Z ₁ , a ₁ ) −G ₃₂ (Z ₁ , a ₁ )) I ₁ sin ₁ + (G ₃₂ (Z ₂ , a ₂ )−G _3
2 (Z ₂ , a ₂ )) I ₂ sin3 ₂ }]…(11) ∂ ³ B _z (0, 0, 0)/∂X∂Z ² =4・(−6μ ₀ /4π[
(G ₃₁ (Z ₁ , a ₁ ) − G ₃₁ (Z ₁ ′, a ₁ )) I ₁ , sin ₁ + (G ₃₁ (Z ₂ , a ₂ )−G ₃₁ (Z′ ₂ , a ₂ )) I ₂ sin ₂ 〕
…(12) Here, G ₃₁ (Zn, an) = 4an (Zn ⁴ −27an ² Zn ² 4an ⁴ ) / (Zn ² + an ²
) ^9/2 G ₃₂ (Zn, an)=an ³ (3Zn ² −4an ² )/(Zn ² +an ² ) ^9/2 (10) To make equations (11) and (12) zero at the same time,
The following formula must hold.

(Z ₃₁ (Z ₁ , a ₁ ) − G ₃₁ (Z ₁ ′a ₁ )) I, sin ₁ + (G ₃₁
(Z ₂ , a ₂ )−G ₃₁ (Z ₂ ′, a ₂ )) I ₂ sin ₂ =0…(13) (G ₃₂ (Z ₁ , a ₁ )−G ₃₂ (Z ₁ ′a ₁ )I ₁ , sin3 ₁ + (G ₃₂ (
Z ₂ , a ₂ )−G ₃₂ (Z ₂ ′, a ₂ )) I ₂ sin3 ₂ = 0…(14) Each variable Z ₁ , Z ₁ ′, Z ₂ , Z ₂ ′ is adjusted to satisfy the above formula. ,
I ₁ , I ₂ , a ₁ , a ₂ , ₁ , and ₂ must be determined, which can be easily done in the following way.

If Z ₁ , Z ₁ ′, Z ₂ , Z ₂ ′, I ₁ , I ₂ , a ₁ , a ₂ are given completely arbitrarily in advance, (G ₃₁ (Z ₁ , a ₁ )−G ₃₁ (Z ₁ ′ −a ₁ )) I ₁ = A (G ₃₁ (Z ₂ , a ₂ ) − G ₃₁ (Z ₂ ′− a ₂ )) I ₂ = B (G ₃₂ (Z ₁ , a ₁ ) − G ₃₂ (Z ₁ ′-a ₁ )) I ₁ = C (G ₃₂ (Z ₂ , a ₂ )-G ₃₂ (Z ₂ ′-a ₂ )) I ₂ = D, so equations (13) and (14) are It can be rewritten as follows.

Asin ₁ + Bsin ₂ = 0 Csin3 ₁ + Dsin3 ₂ = 0 … (15) If you solve equation (15) using the formula sin3 = −4 sin + 3 sin, However, 0<n90° (n=1) The condition for the existence of a solution to equation (15) is 0n90°
(n=1, 2), _03B2 (DA-CB)/4( ^DA3 - ^CB3 )1 and 0(-A/B)1. Thus, arbitrarily Z ₁ , Z ₁ ′, Z ₂ , Z ₂ ′,
By setting a ₁ , a ₂ , I ₁ , and I ₂ and then calculating ₁ and ₂ , a split-wound gradient magnetic field coil can be easily designed.

The method for determining 1 and ₂ when Z ₁ , Z ₁ ′Z ₂ , Z ₂ ′, a ₁ , a _{2 ,} I ₁ , and I ₂ take arbitrary values has been described above. Although there are countless solutions that satisfy equation (15),
An example of the solution is shown in Figure 2. Figure 2 shows I ₁ −0.5, I ₂
=1, β=Z ₁ /a ₁ =0.3, β ₁ ′=Z ₁ ′/a ₁ =2.2, β ₂ ′
When we set = Z ₂ ′/a ₂ = 1.8, a ₁ = 1, and a ₂ = 1, ₁ , ₂
The value of is plotted using β ₂ =(=Z ₂ /a ₂ ) as a parameter.

As described above, the position in the Z direction, arc angle, radius, and current value of the arc current of 16 2×8 saddle-shaped coils are set so as to satisfy equation (15) (however, Z ₁ , Z ₁ ′ , Z ₂ ,
(Z ₂ ′, a ₁ , a ₂ , I ₁ , I ₂ can be set arbitrarily) If the coil windings are wound in a concentrated manner, only the first-order differential component is generated and the third-order higher-order differential component is generated. It is possible to realize an X-gradient magnetic field coil that does not generate any magnetic field. Further, since the above-mentioned coil can be divided into two parts and wound, even in a coil having a large coil width, the coil width of each saddle-shaped coil can be made smaller than that of a conventional X-gradient magnetic field coil. As a result, the number of coil windings existing at positions that do not satisfy equation (15) is reduced, so the third-order odd differential component is reduced, and linearity is improved.

In addition, although a double structure was adopted in the above embodiment,
N X gradient magnetic field coils shown in FIG. 1 may be stacked to form a 2N stack. That is, if a combination of double saddle-shaped coils is used, the position of the arc current in the Z direction, the arc angle, and the radius can be arbitrarily set. Therefore,
When there are N double gradient magnetic field coils, it is possible to arrange the saddle-shaped coils so that they do not overlap.

FIG. 3 shows an example of a gradient magnetic field coil in the case of a 2N load. 3 represents one (i-th) of the 2N-fold saddle-shaped coils, and the two circular arc currents of the saddle-shaped coil each have an arbitrary value Zi, the absolute value of the position in the Z direction, Zi′, arbitrary radius ai,
It has an arc angle 2i and an arbitrary current value Ii. Four of these saddle-shaped coils are arranged symmetrically in shape and current direction with respect to the There is a saddle-shaped coil).

〔Effect of the invention〕

As described above, according to the present invention, since the coil winding wire is divided and wound, winding becomes easier and linearity is improved. Also, the Z-axis direction position of the arc current Z ₁ , Z ₁ ′, Z ₂ , Z ₂ ′, radius a ₁ ,
There is also the advantage that a ₂ and current values I ₁ and I ₂ can be set arbitrarily.

[Brief explanation of drawings]

FIG. 1 is a schematic diagram of an X-gradient magnetic field coil according to an embodiment of the present invention, FIG. 2 is a diagram giving numerical values for the coil of the present invention, and FIG. 3 is a diagram showing an X-gradient magnetic field coil according to another embodiment of the present invention. Schematic diagram, Figure 4 is the conventional X
A schematic diagram of a gradient magnetic field coil, Fig. 5 is a diagram showing the generated magnetic field near the origin of the gradient magnetic field coil, and Fig. 6 is a diagram showing the radius a of the arc current on the Z=Zi plane, the arc,
FIG. 3 is a diagram of current I etc. viewed from the Z direction. In the figure, numeral 1 indicates the first hollow-shaped coil, 2 indicates the second hollow-shaped coil, and 3 indicates the i-th hollow coil. In each figure, the same reference numerals indicate the same or equivalent parts.

Claims (1)

[Claims] 1. Four basic hollow-shaped coils that flow two arc currents on a plane perpendicular to the Z-axis and two direct currents parallel to the Z-axis, each having a shape with respect to the X-Y plane. 2N (N =1,
2, ... i, ... integers) are arranged in the same manner as the above-mentioned hollow-shaped coils, and the four i-th hollow-shaped coils are arranged in the same manner as the above-mentioned hollow-shaped coils, and the arc angle of the base hollow-shaped coil and the above-mentioned The arc angle of the i-weighted hollow coil is
Magnetic resonance characterized in that the arc currents of both said saddle-shaped coils have a predetermined angle determined by two arbitrary absolute positions in the Z-axis direction, an arbitrary arc radius, and an arbitrary arc current value. Radial gradient coil for imaging. 2. The gradient magnetic field coil includes an X-axis and a Y-axis gradient magnetic field coil, and the Y-axis gradient magnetic field coil
The radial gradient magnetic field coil for magnetic resonance imaging according to claim 1, which is an axial gradient magnetic field coil rotated by 90° about the Z-axis.