WO1995030907A1

WO1995030907A1 - Transverse magnetic gradient coil

Info

Publication number: WO1995030907A1
Application number: PCT/CA1995/000265
Authority: WO
Inventors: Brian K. Rutt; Cynthia K. Maier; Kenneth C. Chu
Original assignee: Victoria/University Hospital Corporation
Priority date: 1994-05-04
Filing date: 1995-05-03
Publication date: 1995-11-16
Also published as: AU2402895A

Abstract

A straight wire gradient coil for magnetic resonance imaging, comprising a cylinder having a radius a, the cylinder being oriented in an axial direction, x, of a three-dimensional reference frame defined by orthogonal coordinates x, ŷ and z, and a plurality of current carrying wires disposed along a circumference of the cylinder at a constant angle, α, to the axial direction, x, wherein current distribution in the wires is defined by the formula (1): J(υ,x) = Jsin(υ-ζ(x)) s, where the formula (2): ζ(x) = xtan(α)/a, and where υ is the azimuthal angle measured from y in a transverse plane defined by coordinates y and z, such that for a small α, the resulting component of the magnetic field along z in the transverse plane is sinusoidal in x, and the direction of the magnetic field in the transverse plane is given by ζ(x).

Description

TRANSVERSE MAGNETIC GRADIENT COIL

Background of the Invention

The present invention relates generally to magnetic resonance imaging (MRI) , and more particularly to a novel transverse gradient coil for magnetic resonance imaging of the breast or head.

Background of the Invention

Magnetic Resonance Imaging (MRI) requires the use of magnetic field gradients to provide spatial information and form an image. Gradients in arbitrary directions can be created by varying the current through three gradient coils, each of which produces a linearly changing magnetic field along one of three orthogonal axes. Important imaging parameters are determined by the characteristics of these gradient coils. Maximum spatial resolution, geometric integrity of the image, and gradient switching time are related to the gradient strength, gradient homogeneity and coil inductance, respectively. Accurate flow velocity and diffusion measurements require very high gradient strength and gradient uniformity. Thus, considerable effort has been expended in the prior art to designing low-inductance gradient coils for producing large gradients which are very uniform over a volume of interest.

Since gradient efficiency (gradient strength/applied current) increases with decreasing gradient coil size, and coil inductance decreases with decreasing coil size, smaller gradient coils which encompass only the part of the body being imaged are preferred where possible. These local gradient coils allow performance of echo-planar imaging and other fast imaging techniques which enable functional imaging of the brain. In addition, the increased efficiency of local coils allows high spatial or velocity resolution imaging provided that gradient uniformity is high over the imaged volume. According to early prior art systems, scaled versions of whole-body gradient coils were used as local gradient coils for head imaging. Both gradient efficiency and inductance of these coils were superior to larger coils, but the gradient uniformity over the whole head suffered. In addition, these coils produced double-valued magnetic fields, particularly in the region of the shoulders, with the potential for creating image artifacts. To produce high-quality images using fast imaging techniques, a local gradient coil is needed which creates a single-valued uniform gradient field everywhere on its interior.

U.S. Patent 4,712,068 (Savelainen) , discloses an RF coil having a cross hatch mesh geometry for sending and receiving radio signals in a uniform magnetic field in a MRI system. The device may be adapted for whole body imaging or local imaging of the head or breast. For each set of parallel wires (i.e. series connected segments comprising respective "turns" of the coil) , the segments are shown lying at respective angles to each other and being "skewed" with respect to the axis of revolution. Nonetheless, the design set forth in this patent is used for high frequency (i.e. radio frequency) signal transmission and reception, and not as a gradient coil, which has a completely different function.

U.S. Patent 5,289,129 (Joseph) discloses a whole body MRI z-axis gradient coil having multiple windings for establishing uniform magnetic field gradients along the z-axis. According to Joseph, a plurality of windings are provided around a cylindrical shape and are equally distributed in azimuthal angle by separating the respective windings in azimuthal angle and by 360°/N, where N is the number of windings. By so distributing the windings progressively improved homogeneity is said to be obtained. According to the system disclosed in Joseph, the axial density of the winding turns is at a minimum at the centre of the cylinder and increases linearly from the centre to each axial end.

The Joseph patent teaches a variation of a standard design for producing a longitudinal gradient, as opposed to a transverse gradient. Although the resulting wire patterns are somewhat helical in nature, the actual gradient field produced is not strictly related to this helical wire pattern, but to the spacing of the wires along the cylinder axis.

Two other patents relating to local gradient coils with improved uniformity of magnetic field gradients are U.S. patent 5,304,933 (Vavrek et al) and 5,293,126 (Schaefer) .

The Vavrek and Schaefer patents discuss transverse gradients, but the designs are variations on the very common "finger-print" transverse gradient designs. U.S. Patent No. 4,646,024 (Schenck) and U.S. Patent 5,177,442 (Roemer) are among the first patents to disclose this prior art "finger-print" design.

U.S. Patent 4,456,881 is also of general interest to the area of gradient coil design.

Summary of the Invention

According to the present invention, "straight wire" and "arcsin" embodiments of a transverse gradient coil are provided which meet the criteria discussed above, and which represent significant advances over the known prior art in applications where a large region of gradient uniformity is required, and where simplicity of the coil wire patterns is deemed important.

According to an additional aspect of the present invention, an "arcsin" coil is provided wherein the coil is effectively bisected for eliminating one half of the coil, so that at the bisected end the magnetic field gradient has the desired direction for head imaging, and is also able to provide images of the breast with high spatial or blood flow velocity resolution. More particularly, according to the preferred embodiment, current return wires are provided which return at the coil ends from a first outer diameter toward the axial centre of the coil cylinder on a second inner diameter, such that a second "twisting sine" current distribution is created.

Brief Description of the Drawings

A detailed description of the prior art and of the preferred embodiment is provided herein below with reference to the following drawings, in which:

Figure 1 is a discrete-wire approximation of surface current density proportional to the sine of the azimuth angle, θ , and flowing in the axial direction, created on the surface of a cylinder according to the prior art;

Figure 2 shows the magnetic field created from the current distribution in the system of Figure 1;

Figure 3 is a discrete-wire approximation of surface current density proportional to the sine of the azimuth angle and flowing at a constant angle to the axial direction, referred to herein as a "straight wire" configuration, according to a first embodiment of the invention; Figure 4 is a discrete-wire approximation of surface current density proportional to the sine of the azimuth angle and flowing at an angle which varies with the axial direction, referred to herein as an "arcsin" configuration, according to a second embodiment of the invention; Figure 5 shows the wire positions for the configuration shown in Figure 4;

Figure 6 shows the wire positions for the configuration shown in Figure 3;

Figure 7 shows comparative contour plots with units of contour in gauss/A, of calculated magnetic field for both the "arcsin" and the "straight-wire" configurations for cross-sections parallel to the x-axis;

Figure 8 shows comparative contour plots of the percentage deviation of bB dx from the average value of dB dx over a small volume at the centre of the coil for the coil configurations and planes given in Figure 7. Figure 9 is a two-dimensional plot of a transverse gradient coil having current return wires near the end of the coil, according to an enhanced aspect of the "arcsin" configuration of Figure 4;

Figure 10 shows the coil of Figure 9 bisected at x=0, where x is the axial direction, so as to eliminate one half of the coil (eg. x < 0) so that B_z=0 at the x=0 end and

B_z=max at x=h/2, where h is the length of the cylinder, according to a further embodiment of the invention;

Figure 11 shows a current distribution created by returning the wires in the embodiment of Figure 10 toward x=h/2 on a second inner diameter;

Figure 12 shows the current return paths formed on a transverse plane closing one end of the cylinder of Figures 10 and 11; Figures 13a, 13b and 13c show contour plots for the percentage deviation of dB dx from the average value of dB dx over a small volume at the centre of a small aspect ratio coil, according to the preferred embodiment.

Detailed Description of the

Prior Art and Preferred Embodiment

It is known that a highly homogeneous magnetic field can be created on the interior of a cylinder if the surface current density, J, which flows in the axial direction, x, is proportional to the sine of the azimuthal angle, θ ,

(defined as the angle measured from the +y-axis as shown in Figure 2) . The direction of the magnetic field for a discrete-wire approximation to this current density using thirty-six wires is shown in Figure l, wherein θ is measured from the positive y-axis such that the positive z- axis is at θ - rr/2 relative to the y-axis. The current density for this configuration is given by:

J( θ) = Jsin(0) x >

The magnetic field, B, from such a current distribution points in a direction transverse to the axis of the cylinder as shown in Figures l and 2 (see E. Mascart and J. Joubert, "Lecons sur l'electricite et le magnetisme", Tome 1, s.357, Corbeil, 1896). In Figure 2, the positive x-axis points out of the page. An ideal sin(0) current density would produce a field which is uniform in the interior of the cylinder, however, the discretization of this current density using a limited number of wires introduces some variation from uniformity near the cylinder periphery.

If one considers the magnetic field in a transverse plane to be due to current flowing at the intersection of this plane with the cylinder only, (i.e. current flowing outside the plane can be assumed to not contribute to the field in the plane) , then for the current configuration described by equation (1), current proportional to the sine of the azimuthal angle flows through the transverse plane at the intersection of the transverse plane with the cylinder. This produces a uniform magnetic field in the transverse plane, pointing along the y-axis as shown in Figure 2.

For an infinite length sin(0) current distribution, symmetry in the axial direction requires that the contributions to the magnetic field from current elements outside the plane result in a net field with the same direction. Thus, an infinite length cylinder with a sin(0) current distribution on its surface has a magnetic field pointing in a direction transverse to its axis that is 5 uniform everywhere on its interior.

If, instead of flowing along the x direction, the current f lows at some constant angle, α, to the x-axis (i.e. the "straight wire" configuration of Fig. 3), the 10 current distribution is given by

J(θ ,x) = Jsin(θ-φ (x) ) $ ^<2)

where

Φ (x) = xtan(α)/a ⁽3⁾

15 and a is the radius of the cylinder and the direction of current flow. If α is small, then the current is mainly along the ^-direction, and the contribution to the component of the magnetic field from current in the ~direction is negligible (

<x cos(o) , where B_τ is the

20 component of the total magnetic field in the plane which is transverse to the coil axis) . Since the magnetic field produced by current flowing in a straight wire falls off as 1/r², where r is the distance from the wire, the field in a

-> transverse plane {x - x₀) is mainly the result of current

25 flowing within a small interval Δx around the plane. In a first approximation, the field in a transverse plane (x - x₀) is due only to current flowing at the intersection of the plane with the cylinder, and current at x ≠ x₀ does not contribute to the field. In this approximation, the

30 magnetic field is uniform within the plane x - x₀, and the direction of the magnetic field vector in this plane is given by φ (x) . Since φ (x) is linear in x, as x increases from -h/2 to +h/2 (where h is the length of the cylinder) , the magnetic field vector will rotate from min (φ (x) ) = -ήtan(α)/2a to max(ø(x) ) = htan(α)/2a, such thatB. is sinusoidal in x. Since most of the contribution to the magnetic field in a transverse plane is from current within a small interval Δx around the plane, this approximation to the field is valid when φ (x) is a slowly varying function of x.

To produce a uniform gradient in B_z along x, that is, a magnetic field vector in the ^-direction whose strength varies linearly with x, the angle must vary as a function of x. Φ (x) must therefore be more complicated than the linear function assumed above. Since for linear φ (x) , the resulting B. is sinusoidal in x, a first approximation to the ideal form of φ (x) is given by:

Φ x) = arcsin(2j_^*/h) ⁽<⁾

This current distribution is shown in Figure 4, using thirty-six wires.

For this form of φ (x) , the angle α is a function of x and is given by:

a (x) = arctarJ a-i- (arcsin(2x/h) ) (5)

=

As before, for small o, |J3_r| « cos(α) , and the field in a transverse plane is mainly due to current flowing perpendicular to the plane at the intersection of the plane with the cylinder. At the center of the cylinder (x=0) , where the current density is that given in Figure 2, the magnetic field is in the Ϋ direction and therefore B_z = 0.

As x increases from zero, the magnetic field vector rotates in the positive sense, and B_z increases along 2. As x decreases from zero, B. increases along -£ . Away from the ends of the coil, B_t is a linear function of x, and is given by:

As the ends of the coil are approached, increases and the projection of the current along the .^-direction decreases rapidly, resulting in a decrease of the primary contribution to B_t from the axial component of the current. Conco itantly, the magnetic field homogeneity in the transverse plane decreases due to a secondary field contribution arising from the increasing component of the current along the azimuthal, or 9, direction. An additional factor affecting the size of the volume of uniform gradient is the finite length of the cylinder. As the ends of the coil are approached, the contribution to Bz from out-of-plane current decreases, resulting in a decrease in dB dx . Near the ends of the coil, the direction of dB_z/dx is reversed and B_z is not uniquely valued in this region.

"Return wires" (i. e. connecting current paths between wires) are necessary to preserve current flow. For large aspect ratio coils, (i.e. coils with large length:diameter ratios) , the return wires can be positioned near the ends of the coil such that their effect on the field near the centre of the coil is minimal, as discussed in greater detail below with reference to Figures 9-13. According to the "arcsin" configuration of Figure 3, the magnetic field from the current distribution described in equations (2) and (4) has been modelled using thirty-six discrete wires. The wire locations are as given in Figure 5. As a comparison, a similar current distribution has been modelled with the wires at a constant angle to the x- axis, as shown in Figure 6.

The results are shown in Figures 7 and 8 and demonstrate the superior gradient uniformity achieved with the arcsin design of the preferred embodiment. In Figure 7, contour plots of B_z are given for both the arcsin design (Figures 7a, 7c and 7e) and the constant α design (Figures 7b, 7d and 7f) . The field strength is given in units of milligauss/Ampere. Figures 7a and 7b show planes of intersection at θ - 0, Figures 7c and 7d show planes at θ - τr/4, and Figures 7e and 7f show planes at β = π/2.

In Figure 8, contour plots of the percentage deviation of dB bx from the central value of B_z/ x are shown.

For a region in which there is no current flowing, and the magnetization is zero, such as in the interior of the cylinder. Maxwell's equation for the curl of B reduces to:

VxB - 0 (8)

This requires that the gradient tensor is symmetric, i.e. G^ - dB db - dB_b/da = G^. This allows the arcsin coil design to be used (a) with its axis transverse to the main field and aligned along x or y to provide G_α or G^, respectively, or (b) with its axis aligned along the main field (z) to provide either G_α or rotated through τr/2 around the z-axis to provide G^. These last two configurations are commonly referred to as "transverse gradients" since they provide gradients in the directions transverse to the main magnetic field.

Figure 9 is a 2-dimensional plot of a coil shown with return wire positions as discussed briefly above. For whole-body, animal, phantom, or specimen imaging (Volume of Interest) is usually located at the center of the coil, and large aspect ratio coils may be used. Therefore, non- idealities introduced by end effects or by current in the return wires are not significant for these applications. This design forms the basis for the coil configurations discussed above with reference to Figures 3 and 4.

A gradient coil has been described above which can be used with its axis along ϋ to produce an x-gradient. The preferred orientation for breast imaging is along Ϋ, where the patient lies prone, with the chest wall supported by the coil and the breast pendulous within the coil. In this orientation, this coil design produces a y-gradient. The same coil can be used aligned with its axis along 2 to produce either a y-gradient or x-gradient. In this orientation, the coil may be used to image the head.

It is not possible to use a scaled version of a large aspect ratio coil for either head or breast imaging. These applications require smaller aspect ratio coils where the VOI is located near one edge of the coil. In this region end effects and return wire effects are significant. In particular, the non-uniqueness of the field inside and beyond the end of the coil will cause image artifacts to occur.

According to the present invention, an improvement to the design described above is provided which is compatible with coil requirements for both head and breast imaging.

End effects cause the magnitude of the magnetic field vector to decrease as the ends of a gradient coil are approached. In the coil design described above, the desired field increases in magnitude as the coil ends are approached. The directions of the desired gradient and the gradient produced by end effects oppose each other, causing the total gradient to reverse directions near the end of the coil and the field to assume non-unique values in this region. It is possible to modify this coil design such that the desired gradient and the gradient introduced by the end effect have the same direction at the end of the coil where the VOI is located. In this case, the end effect still causes non-uniformity of the total gradient field, but the magnetic field decreases monotonically toward the end of the coil.

In the design described above, B.=0 at x=0. Bisecting the coil at x=o and eliminating one half of the coil, x<0 for example, leaves a coil with B.=0 at the x=0 end and B_z=max at x=h/2 (Fig. 10) . If the VOI is located near x=0, the end effect near x=h/2 is not significant. Near x=0, the magnetic field gradient created by the end effect has the same direction as the desired gradient, therefore B. decreases monotonically toward the end of the coil.

One possible configuration for placement of the return wires at the x=0 end is to have the wires return toward x=h/2 on a second, inner layer of current, for example, at a diameter just smaller than the outer layer of current, such that a second "twisting sine" current distribution is created (Fig. 11) . The transverse magnetic field from this second current distribution rotates from ~γ to 2 such that the ^-component of the field is identical to that produced by the outer layer of current. In this way, return wires which contribute in an undesirable way to the magnetic field at x=0 are eliminated. This design can be manufactured either using a double-sided PC board with connecting current paths through the board, or by hand- winding wires into grooves in the surface of a cylinder such that the inner current layer is wound into deeper grooves. At x=^*h/2, the current return paths can be formed on a transverse plane closing this end of the cylinder (Fig. 12) . For either head or breast imaging, it is acceptable to have a cylindrical gradient coil which is closed at one end since the VOI is located near the other end of the coil, and the anatomy of interest will not extend past the x=h/2 end.

Results for a small aspect ratio coil (h/d=1.0) with 36 wires, suitable for breast imaging are shown in Figures 13a, 13b and 13c. Contour plots for B_z and for the percentage deviation of dB x from the average value of dB_z/dx over a small volume at the center of the coil are shown, and demonstrate the large volume of gradient uniformity achieved with this design. Higher aspect ratio coils can be used for head imaging since the coil length is not constrained by space limitations within the imager for this application.

Other embodiments and modifications of the invention possible without departing from the sphere and scope as defined by the claims appended hereto.

Claims

WE CLAIM

1. A straight wire gradient coil for magnetic resonance imaging, comprising a cylinder having a radius a, said cylinder being oriented in an axial direction, x, of a three-dimensional reference frame defined by orthogonal coordinates x, Ϋ and 2 , and a plurality of current carrying wires disposed along a circumference of said cylinder at a constant angle, α, to said axial direction, x, wherein current distribution in said wires is defined by

J( θ ,x) = Jsin ( θ-φ (x) ) S

where

Φ (x) = Jrtan(α)/a

and where θ is the azimuthal angle measured from Ϋ in a transverse plane defined by coordinates f and 2 , such that for a small α, the resulting component of the magnetic field along 2 in said transverse plane is sinusoidal in x, and the direction of said magnetic field in said transverse plane is given by φ (x) .

2. A uniform gradient coil for magnetic resonance imaging, comprising a cylinder having a radius, a, and a length h, said cylinder being oriented in an axial direction, x, of a three-dimensional reference frame defined by orthogonal coordinates, x, Ϋ and 2 , and a plurality of current carrying wires disposed along a circumference of said cylinder at an angle, a, which varies linearly with 2, wherein current distribution in said wires is defined by

J θ ,x) = Jsin ( θ -φ (x) ) § where φ (x) - arcsin (2x/h)

and where θ is the azimuthal angle measured from ^ in a transverse plane defined by coordinates Ϋ and 2 , such that over most of the volume enclosed by said cylinder the resulting component of the magnetic field along 2 is given by

where B_τ is the component of the magnetic field in said transverse plane.

3. The straight wire gradient coil of claim 1, wherein said wires are connected at distal ends of said cylinder to provide return paths for said current.

4. A uniform gradient coil for magnetic resonance imaging, comprising a cylinder having a radius, a, and a length h/2, said cylinder being oriented in an axial direction, 2, of a three-dimensional reference frame defined by orthogonal coordinates, x, _> and 2 , and a plurality of current carrying wires disposed along an outer circumference of said cylinder at an angle, , which varies linearly with , wherein current distribution in said wires is defined by

J( θ ,x) = Jsin(0-ø(x)) £

where

φ (x) = arcsin(2jr/h) and where θ is the azimuthal angle measured from Ϋ in a transverse plane defined by coordinates Ϋ and 2 , such that the resulting component of the magnetic field along 2 , is given by

B_z = \

sin (φ (x) ) = iBrl-Tj**

where B_τ is the component of magnetic field in said transverse plane, and whereby at one end of said cylinder B.=0 and at an opposite end of said cylinder B_z = \ B_T \ .

5. The uniform gradient coil of claim 4, wherein said wires are connected at said one end and said opposite end to provide return paths for said current.

6. The uniform gradient coil of claim 5, wherein said wires return from said one end toward said opposite end along an inner circumference of said cylinder such that the component of the magnetic field in said transverse plane resulting from the current distribution created by said return path rotates from to 2 so that the 2-component of said field is everywhere identical to the field produced by said wires disposed along said outer circumference.

7. The uniform gradient coil of claim 6, wherein said cylinder comprises a double-sided PC board with said return paths connected between said outer circumference and said inner circumference through said PC board.

8. The uniform gradient coil of claim 6, wherein said cylinder comprises a double-sided PC board with said return paths connected between said outer circumference and said inner circumference via respective grooves in an outer surface of said cylinder.

9. The uniform gradient coil of claim 5, wherein said wires return from said opposite end toward said one end via one said transverse plane located at said opposite end.