Electricity: measuring and testing – Particle precession resonance – Spectrometer components
Reexamination Certificate
2000-04-10
2003-03-04
Lefkowitz, Edward (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Spectrometer components
C324S322000
Reexamination Certificate
active
06529003
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to a method of manufacturing a gradient coil, a gradient coil unit, a gradient coil and an MRI (magnetic resonance imaging) apparatus, and more particularly to a method of manufacturing a gradient coil, a gradient coil unit, a gradient coil and an MRI apparatus which can provide good linearity without reducing efficiency in generating a magnetic field.
In “Method of Manufacturing Gradient Coil, Gradient Coil unit and Gradient Coil” disclosed in Japanese Patent Application Laid Open No. 6-14900, a winding pattern of a gradient coil is basically determined as follows:
(1) A winding pattern is assumed to have a plurality of bow-shaped spirals as shown in
FIG. 1
, and its electric current distribution in the r-direction is expressed by Eq. (2) below and that in the &phgr;-direction is expressed by Eq. (3):
J
r
=
-
R
0
r
{
∑
n
S
n
·
sin
(
n
π
r
R
0
)
+
∑
m
C
m
·
cos
(
2
m
π
r
R
0
)
}
sin
φ
,
and
(
2
)
J
φ
=
{
-
∑
n
S
n
·
n
π
·
cos
(
n
π
r
R
0
)
+
∑
m
C
m
·
2
m
π
·
sin
(
2
m
π
r
R
0
)
}
cos
φ
,
(
3
)
wherein r is a position in the radial direction, &phgr; is a position in the angular direction, R
0
is a maximum radius, and S
n
, n, C
m
and m are parameters to be manipulated for optimization.
(2) Optimum values for S
n
, n, C
m
and m are obtained at &phgr;=0. Specifically, appropriate values for S
n
, n, C
m
and m are assumed to calculate an linearity error of a magnetic field in a required region, and S
n
, n, C
m
and m are manipulated so that the linearity error falls within an allowable value, to obtain the optimum values.
(3) An electric current distribution profile on a line &phgr;=0 is obtained from Eq. (3) with the resulting S
n
, n, C
m
and m substituted. A
p
, which is the sum of the areas of small regions enclosed by a line J
&phgr;
=0 and a positive part of the electric current distribution profile from the line J
101
=0, is divided by the number N of positions at which the windings of the gradient coil intersect the line &phgr;=0, and the resulting value is defined as &Dgr;A
p
.
(4) The entire region enclosed by the line J
&phgr;
=0 and the positive part of the electric current distribution profile from the line J
&phgr;
=0 is separated by &Dgr;A
p
into sub-regions. An r-position in the middle of each sub-region is defined as a position at which each of the windings intersects the line &phgr;=0.
(5) The steps (3)-(4) are repeated while sequentially varying the value of &phgr; within a first quadrant to obtain a winding pattern in the first quadrant as shown in FIG.
2
.
(6) The resulting winding pattern in the first quadrant is duplicated symmetrically with respect to the x-axis (the line &phgr;=0) to obtain a winding pattern for a fourth quadrant with the direction of electric current inverted. Moreover, a pattern for connecting the winding patterns in the first and fourth quadrants is added, considering the direction of electric current, so that one coil is formed as a whole. A winding pattern on one side is thus obtained.
(7) The winding pattern on one side is duplicated symmetrically with respect to the y-axis (an axis orthogonal to the x-axis). A winding pattern of a gradient coil unit is thus obtained.
(8) A plurality of the gradient coil units are combined.
In the conventional winding pattern of the gradient coil as above (cf. FIGS.
1
and
2
), some adjacent paths carry electric current flowing in the opposite directions at some locations (in
FIG. 2
, at four locations).
For this reason, although good linearity can be obtained, efficiency in generating a magnetic field is reduced.
SUMMARY OF THE INVENTION
It is therefore an object of the present invention to provide a method of manufacturing a gradient coil, a gradient coil unit, a gradient coil and an MRI apparatus which can provide good linearity without reducing efficiency in generating a magnetic field.
In accordance with a first aspect of the invention, there is provided a method of manufacturing a gradient coil, comprising the steps of:
(1) assuming a winding pattern of one semicircular spiral, and expressing its x-axis electric current distribution by the following electric current distribution equation:
J
x
(
x
)
=
∑
n
A
n
·
sin
(
π
2
n
x
R
0
)
+
∑
m
B
m
·
sin
(
π
2
m
x
R
0
)
,
wherein the x-axis is an axis dividing the semicircular spiral into two equal parts, R
0
is a maximum radius, and A
n
, n, B
m
and m are parameters to be manipulated for optimization;
(2) assuming appropriate values for A
n
, n, B
m
and m so that an x-axis electric current distribution profile expressed by the electric current distribution equation with the values for A
n
, n, B
m
and m substituted does not lie in both the positive and negative polarities, calculating a linearity error of a magnetic field at a plurality of magnetic field measurement points, and manipulating A
n
, n, B
m
and m so that the linearity error falls within an allowable value, to obtain optimum values for A
n
, n, B
m
and m;
(3) dividing an area A
p
of a region enclosed by the electric current distribution profile and a line J
x
=0 by the number N of positions at which line members constituting a straight-line portion of the semicircular spiral intersect the x-axis, and defining the resulting value as &Dgr;A
p
;
(4) separating the region enclosed by the electric current distribution profile and the line J
x
=0 by &Dgr;A
p
into sub-regions, and defining an x-position in the middle of each sub-region as a position at which each line member of the straight-line portion of the semicircular spiral intersects the x-axis;
(5) forming an arc-shaped portion of the semicircular spiral as a semicircle having a radius of R
0
, thereby generating a winding pattern on one side;
(6) symmetrically duplicating the winding pattern on one side with the respective straight-line portions adjacent to each other, thereby generating a winding pattern of a gradient coil unit; and
(7) combining a plurality of the gradient coil units.
In the method of manufacturing a gradient coil of the first aspect, a winding pattern of one semicircular spiral is assumed; its electric current distribution is expressed by a continuous function such that an x-axis electric current distribution profile does not lie in both the positive and negative polarities; parameters of the continuous function are optimized so that desired linearity can be obtained; and a position of each line member constituting a straight-line portion of the semicircular spiral is determined so that the electric current distribution profile given by the optimized continuous function is fulfilled. Then, the resulting pattern is symmetrically duplicated to generate a gradient coil unit, and a plurality of the gradient coil units are combined to form a gradient coil. This provides good linearity, and avoids reduction in efficiency in generating a magnetic field because employing a winding pattern of a semicircular spiral provides only two locations at which adjacent paths carry electric current flowing in the opposite directions, and besides the paths are well apart from each other.
In accordance with a second aspect of the invention, there is provided the method of manufacturing a gradient coil as described regarding the first aspect, wherein the plurality of magnetic field measurement points are points on a sphere that does not contain an electric current element.
In the method of manufacturing a gradient coil of the second aspect, the linearity is inspected selecting as magnetic field measurement points a plurality of points
Goto Takao
Inoue Yuji
GE Yokogawa Medical Systems Limited
Kojima Moonray
Lefkowitz Edward
Vargas Dixomara
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