WO2008109126A1

WO2008109126A1 - Permanent magnet system

Info

Publication number: WO2008109126A1
Application number: PCT/US2008/002983
Authority: WO
Inventors: Robert Wetservelt; Donhee Ham; Ognjen Ilic; Hakho Lee; Ralph Weissleder
Original assignee: Harvard University Otd (Office Of Technology Development)
Priority date: 2007-03-06
Filing date: 2008-03-06
Publication date: 2008-09-12

Abstract

A magnet system for generating a static magnetic field for NMR analysis includes a first permanent magnet, and a second permanent magnet disposed below the first permanent magnet element and substantially parallel thereto. An upper metallic disc is disposed above the first permanent magnet and a lower metallic disc is disposed below the second permanent magnet. A hollow outer metallic shield encloses the first and second permanent magnets and the upper and lower metallic discs. The upper and lower metallic discs are movable relative to the first and second permanent magnets, respectively, in such a way that the distances between the metallic discs and the respective permanent magnets are optimized so as to render the gradient of a static magnetic field generated by the magnet system sufficiently uniform for use in the NMR analysis.

Description

PERMANENT MAGNET SYSTEM

[001] CROSS-REFERENCE TO RELATED APPLICATIONS

[002] This application is based upon, and claims the benefit of priority under 35 U. S. C. § 119(e) from U.S. Provisional Patent Application Serial No. 60/905,254 filed March 06, 2007, entitled "New Geometry For NMR Devices." The content of this provisional application is incorporated herein by reference in its entirety as though fully set forth.

[003] BACKGROUND

[004] NMR (nuclear magnetic resonance) is a well known analytic technique with a wide range of applications. As one example, there has been a great deal of interest in the last few years in using NMR as a chemical and biological sensor by modulating T₂ via functionalized iron nanoparticles.

[005] NMR is based on the interactions between nuclear spins, and static and time varying external magnetic fields. When a sample (composed of nuclei with a net spin) is placed in a static external magnetic field B₀, the nuclear magnetic moments precess about the axis¹ of the field B₀ at a frequency ^ω° called Larmor frequency. The Larmor frequency depends only on the magnitude of the static field B₀, and a proportionality constant y called the gyromagnetic ratio: ^ω° = γB₀. Since the gyromagnetic ratio ? assumes different values for different nuclei, the Larmor frequency reveals the sample material's chemical composition.

[006] During an NMR analysis, another magnetic field B₁ Js applied, which is time-dependent (typically an RF field), transverse to B₀, and has a frequency matched to the Larmor frequency ^ω° . As a result, the net macroscopic magnetization vector M is excited into a non-equilibrium state, in which the nuclear magnetization vector M is no longer aligned with the static field B₀. Once the RF excitation field Bi is removed, the excited nuclei precess about the axis of the field B₀, while relaxing through relaxation processes, one of

¹ By convention, the Z-axis. which is the spin-spin relaxation.

[007] Spin-spin relaxation is caused by randomly fluctuating fields that result from interactions between the spins, and that cause the spins to get out of phase with each other. The initial phase coherence of the nuclear spins is gradually lost, until eventually the phases are completely disordered and the net transverse (xy) magnetization dies out. The spin-spin relaxation time T₂ is the exponential decay constant for the component of M perpendicular to B₀. T₂ is responsible for the line width of an NMR signal (line width at half-height = 1 / T₂). An accurate measurement of the spin- spin relaxation time, T₂, is therefore important.

[008] Pure spin-spin relaxation assumes that the B₀ field is perfectly uniform. In practice, however, inhomogeneities in B₀ accelerate the dephasing of the spins, since spins experiencing slightly different B₀ field strengths in different parts of the sample precess at slightly different frequencies. The phase coherence of the spins is therefore lost much faster, resulting in a premature relaxation time called T₂*, which is much smaller than the true T₂ due to pure spin-spin interactions. To minimize B₀-field inhomogeneities, large superconducting magnet systems have typically been used to generate the static field B₀. For example, the seminal work in the field of chemical/biological sensing by modulating T₂ via functionalized iron nanoparticles, mentioned above, has been done using large electromagnets or complicated open ended NMR systems.

[009] Such inhomogeneities in B₀ may be more pronounced and harder to avoid with the smaller magnets that are typically used in miniaturized NMR systems,² for which there recently has been a lot of interest. The pronounced field inhomogeneity may cause the NMR signal to be damped far faster than T₂. This may cause difficulty in T₂ relaxometry, i.e. the true T₂ due to spin-spin interactions may be hard to measure, even with a high receiver sensitivity.

² A miniaturized NMR system is described in , the disclosure of which is incorporated herein by reference in its entirety in order to more fully describe the state of the art to which this patent application pertains. [010] Relatively small magnet systems that are capable of generating a static magnetic field that is strong enough and uniform enough to be useful in NMR studies are therefore highly desirable. In particular, portable and/or hand-held magnet systems that can generate such a field would be very useful for miniaturized NMR systems, for which there is increasing interest. Also, these portable, handheld devices would cost a fraction of the large magnet systems that traditionally have been used to generate a strong and uniform static B₀-field for NMR studies.

[011] SUMMARY

[012] A magnet system for generating a static magnetic field for NMR (nuclear magnetic resonance) studies includes a first permanent magnet element, and a second permanent magnet element disposed below the first permanent magnet element and substantially parallel thereto. A top surface of the second permanent magnet is separated from a bottom surface of the first permanent magnet by a distance a, so as to define between the two permanent magnet elements an air gap having a height a.

[013] An upper metallic disc is movably disposed above the first permanent magnet element, and a lower metallic disc is movably disposed below the second permanent magnet element. The bottom surface of the upper disc separated from the top surface of the first permanent magnet element by a distance W_x that is adjustable by moving the upper metallic disc relative to the first permanent magnet element. The top surface of the lower disc separated from the bottom surface of the second permanent magnet element by a distance W₂ that is adjustable by moving the upper metallic disc relative to the first permanent magnet element. A hollow metallic case may enclose the first and second permanent magnet elements and the upper and lower metallic discs.

[014] The distance Wi, the distance W₂, and the distance a are adjustable by moving one or both of the upper and lower metallic discs, so as to reduce the gradient of the static magnetic field generated by the magnet system to a degree sufficient for the magnet system to be usable uniform, so that the . [015] BRIEF DESCRIPTION OF THE DRAWINGS

[016] FIGs. IA and IB illustrate a cross-section view and a side view, respectively, of a permanent magnet system in accordance with one embodiment of the present disclosure.

[017] FIG. 2 illustrates a series of thread on the exterior of the upper steel disc.

[018] FIG. 3A illustrates the field of a magnetic dipole.

[019] FIG. 3B illustrates the field resulting from a superposition of rectangular magnetic dipoles.

[020] FIG. 4A is a plot of the magnetic field when b = 25.4 mm and z = 5 mm.

[021] FIG. 4B is a plot of the magnetic field when z = 15 mm.

[022] FIG. 4C is a plot of the magnetic field when 12.4 mm.

[023] FIG. 5 schematically illustrates the parameters that can be varied and optimized, in a permanent magnet system in accordance with one embodiment of the present disclosure.

[024] FIG. 6 illustrates a substantially uniform magnetic field (having a gradient of only 0.04G/mm) that is generated at an air gap size of 6.1 mm.

[025] DETAILED DESCRIPTION

[026] A magnetic system is disclosed that uses a parallel plate geometry using NdFe permanent magnets. By using an adjustable steel piece in the yoke, the magnetic field gradient can be greatly reduced, leading to field gradients on the order of 0.1G/mm on a IT field. Since the magnetic system described in this disclosure consists only of permanent magnets and metallic (steel) discs, it consumes no extra energy of any form and is cheap to make and easy to use. The magnetic system described in the present disclosure can be used, as just one example, in a handheld T₂ relaxometer that will more easily integrate into benchtop biology and chemistry experiments. [027] The basic components of the magnetic system described in the present disclosure includes an upper and lower permanent magnet, with steel caps above and below. By adjusting the distance between the discs and the magnets, the gradient of the magnetic field generated by the system is reduced to a degree sufficient for use in NMR.

[028] Applicants conducted studies which showed that when there is no steel around the permanent magnets that have dimensions detailed below, a positive gradient is seen at a given z, but when there is some steel around, the steel becomes magnetized and the relative dimensions (i.e. height/width) of the model change, increasing the "effective" z so that the gradient becomes negative. As described below, the pertinent distances and dimensions can be optimized, until a strong static magnetic field having a substantially uniform gradient is generated by the portable-sized magnet system.

[029] FIGs. IA and IB illustrate a permanent magnet system 100 in accordance with one embodiment of the present disclosure. The magnet system 100 is capable of generating a static magnetic field for NMR (nuclear magnetic resonance) analysis, while having a size small enough to be portable and/or handheld.

[030] The magnet system illustrated in FIGs. IA and IB includes an upper (or first) permanent magnet 102, and a lower (or second) permanent magnet element 104 disposed below the first permanent magnet 102 and substantially parallel to the first permanent magnet 102. The first and second permanent magnets are separated by a distance a.

[031] As seen in FIG. IA, an upper metallic disc or cap 120 is disposed above the first permanent magnet 102 and substantially parallel thereto, at a distance Wi from 102, while a lower metallic disc 122 below the second permanent magnet 104 and substantially parallel thereto, at a distance W₂ from 104. Specifically, the bottom surface of the upper disc 120 is separated from the top surface of the first permanent magnet 102 by a distance Wi, while the top surface of the lower disc 122 is separated from the bottom surface of the second permanent magnet 104 by a distance W₂. In this way, air gaps 110 and 111, having a height Wi and W₂ respectively, is defined between each disc and each permanent magnet element.

[032] A hollow outer metallic shield or case 150 encloses the first and second permanent magnets and the upper and lower metallic discs.

[033] The upper and lower metallic discs 120 and 122 are movable relative to the first and second permanent magnet, respectively, in such a way that the heights Wi and W₂ are optimized, so that the gradient of a static magnetic field generated by the magnet system is rendered sufficiently uniform for use in the NMR analysis. Further details of this optimization is provided below in conjunction with FIGs. 3A - 4C. The upper and lower discs are also slidably movable relative to the hollow outer shield that encloses the discs and the magnets.

[034] In one embodiment, a metal ring 510 may be placed between the first permanent magnet and the second permanent magnet (as shown for example in FIG. 5). The ring 510 should be made of a metal having a high magnetic permeability. Examples of suitable metals include, but are not limited to, steel and cobalt. The metal ring concentrates the magnetic field lines.

[035] One or both of the upper and lower permanent magnets may be an NdFe permanent magnet, by way of example, although it should be understood that other embodiments may use different types of permanent magnets and the magnets in the magnet system described in the present disclosure are not limited to NdFe permanent magnets. In an exemplary embodiment, the NdFe permanent magnets may be about 2 inches in diameter, 1 inch thick, and weigh about 13.6 oz. These magnets generate axial magnetization, and the pull force may be about 231 lbs.

[036] In one embodiment, the first and second permanent magnet, the upper and lower discs, and the hollow outer shield may be substantially cylindrical in shape, although other embodiments may include different shapes or forms for the magnets, discs, and outer shield. In the illustrated embodiment, the upper and lower permanent magnets have substantially the same size, and the upper and lower discs also have substantially the same size. Different combinations of shapes and sizes of the magnets and the discs may be used in different embodiments of the present disclosure.

[037] Either or both of the upper and lower metallic discs may be steel discs, in one embodiment, although other types of metal may also be used in different embodiments. In one embodiment, the hollow metallic outer shield may be made of steel. In other embodiments, the outer shield may be made of a metal different from steel. The metal should have a high magnetic permeability.

[038] FIG. 2 illustrates a series of threads 310 on the exterior of the upper steel disc. These threads 310 provide a precise mechanism that causes get the discs to move for only fractions of a millimeter. In one embodiment, these threads offer a resolution of about 1 mm per half turn, greatly facilitating the process the size of the gap

[039] FIGs. 3A-4C provide details regarding how the air gap width a and the distances between the magnets and the discs are optimized, in order to generate the desired uniform magnetic field.

[040] FIG. 3A illustrates the field of a magnetic dipole. The field of a single dipole,

[041]

*" , is given by :

B = V x A

[042]

[043] where

[044] In Cartesian coordinates, these equations become:

μom xy - yx

A =

[045] 4τr (z² + y² + zψ² and

[047] It follows that:

T _ _μom 2z² - p² μ_oπι 1 2 - (f)²

4τr (z2 + _p2)5/2 _{= 4π} z³ (i 4- (fi)²)5/2

[048] where ^P ~ ^{X + y} . (1)

[049] If equation (1) is plotted as a function of p for a fixed z, a negative first derivative is always obtained at p = 0 no matter what the value of z is.

[050] It is useful to consider a rectangle of magnetic dipoles, as shown in FIG. 4B. A single magnetic dipole m, a distance x from the origin, contributes as follows to the field at P:

[052] Letting dm = m_vhΔ dx, where m_v is magnetic moment per unit volume and h, A are the height and depth of one of the rectangles (respectively), the following is obtained:

[054] Equation (3) is much easier to deal with numerically, compared to equation (1), and can be numerically integrated very fast. Equation (3) allows the behavior of the field, resulting from the above-described magnetic system, to be understood, as can be seen from FIGs. 4A - 4C below.

[055] FIG. 4A is a plot of the magnetic field when b = 25.4 mm and z = 5 mm (where the vectors b and z are illustrated in FIG. 3B). As seen from FIG. 4A, the gradient is positive when z is not too large.

[056] FIG. 4B is a plot of the magnetic field when z = 15 mm, while everything else is kept constant. The gradient is negative.

[057] FIG. 4C illustrates a "sweet spot" in which the gradient transitions from positive to negative, in this case at z = 12.4 mm.

[058] The analysis shown in conjunction with FIGs. 3A-4C thus provides an explanation for both limiting cases:

[059] 1. When there is no steel around the permanent magnets, the magnets having the dimensions shown in the figures, a positive gradient is seen at a given z, as seen from FIG. 4A. This is a simpler, but physically similar case.

[060] 2. When there is some steel around, the steel becomes magnetized and the relative dimensions (i.e. height/width) of the model change, increasing the "effective" z so that the gradient becomes negative.

[061] FIGs. 4A-4C thus explains the basic model of the magnetic system described in the present disclosure: steel (or other metallic) discs are provided both above and below the two permanent magnets, and by changing the distances between the discs and the magnets, the absolute value of the gradient of the magnetic field is described.

[062] FIG. 5 schematically illustrates the various distances that can be varied and optimized. By moving the upper and lower magnets can be moved relative to the upper and lower discs, the size W of the air gap (in the illustrated embodiment, it happens that Wi = W₂ = W, i.e. the steel discs are equidistant from the respective magnets) can be varied, so as to be optimized for purpose of minimizing the magnetic field gradient.

[063] As shown in FIG. 5, other parameters that can be varied include: the thickness of the steel ring 510 shown between the magnets, the variation of this thickness changing the gradient. The thickness b of the outer case (or shield) can also be varied. No big difference (except for the fact that the gradient became bigger) was noted when the little steel ring 510 was inserted. On the other hand, the strength of the magnetic field was found to be proportional to the width b of the outer steel case . The main benefit that may be obtained from this variation is possibly having the "sweet-spot" wider, i.e. less susceptible to change under slight variations in w. Both parameters may have to be chosen so as to make the construction as easy as possible. The range of the width of the gap (and the resulting change in gradient) may be enough to compensate for other unwanted effects.

[064] A large number of simulations were run. In the geometry shown in FIG. 5, first the height W of the air gap was varied, while keeping everything also constant. Results are given in Table 1 below, where the range indicates how much the width of the gap was varied.

[065] Table 1

[066] A "sweet-spot" (i.e. a spot where the gradient is minimal because of transition from positive to negative) was found to be for a gap size of w = 6.1mm , in which case the gradient was just 0 04G/mm. This translates to around 0.16G across the entire sample, whose dimensions are about 2 x 4mm. r

[067] FIG. 6 illustrates the resulting substantially uniform magnetic field, having a gradient of only 0.04 G/mm. The transition from positive to negative gradient is clearly seen. In the region 0 mm - 3.5 mm, the entire difference in the magnetic field is only 0.16 G.

[068] In sum, a system of permanent magnets with very low magnetic field inhomogeneity has been described, to make a low cost, hand-held T₂ relaxometer. [069] While certain embodiments have been described of a magnet system for NMR studies, it should be understood that the concepts implicit in these embodiments may be used in other embodiments as well. The protection of this application is limited solely to the claims that now follow.

[070] In these claims, reference to an element in the singular is not intended to mean "one and only one" unless specifically so stated, but rather "one or more." All structural and functional equivalents to the elements of the various embodiments described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference, and are intended to be encompassed by the claims. Moreover, nothing disclosed herein is intended to be dedicated to the public, regardless of whether such disclosure is explicitly recited in the claims. No claim element is to be construed under the provisions of 35 U. S. C. §112, sixth paragraph, unless the element is expressly recited using the phrase "means for" or, in the case of a method claim, the element is recited using the phrase "step for."

Claims

What is claimed is:

1. A magnet system for generating a static magnetic field for NMR (nuclear magnetic resonance) analysis, the magnet system comprising:

a first permanent magnet; a second permanent magnet disposed below the first permanent magnet element and substantially parallel thereto;

an upper metallic disc disposed above the first permanent magnet and substantially parallel thereto, a bottom surface of the upper disc being separated from the top surface of the first permanent magnet by a distance Wi so as to define an air gap having a height Wi;

a lower metallic disc below the second permanent magnet and substantially parallel thereto, a top surface of the lower disc separated from the bottom surface of the second permanent magnet by a distance W₂ so as to define an air gap having a height W₂; and

a hollow outer metallic shield enclosing the first and second permanent magnets and the upper and lower metallic discs;

wherein the upper and lower metallic discs are movable relative to the first and second permanent magnets, respectively, in such a way that the heights W_x and W₂ are optimized so that the gradient of a static magnetic field generated by the magnet system is rendered sufficiently uniform for use in the NMR analysis.

2. The magnet system of claim 1, wherein W_t is equal to W₂.

3. The magnet system of claim 1, wherein the size of the magnet system is sufficiently small to render the magnet system portable.

4. The magnet system of claim 1, wherein the size of the magnet system is sufficiently small so that the magnet system can be hand-held.

5. The magnet system of claim 1, further comprising a series of threads on the exterior of the upper metallic disc to facilitate movement of the upper metallic disc relative to the first permanent magnet; and further comprising a series of threads on the exterior of the lower metallic disc to facilitate movement of the lower metallic disc relative to the second permanent magnet.

6. The magnet system of claim 1, wherein the series of threads have a size chosen so that the upper and lower discs can be accurately movable over a relatively small distance.

7. The magnet system of claim 6, wherein the relatively small distance is on the order of a fraction of a millimeter, and wherein the threads have a resolution of about 1 millimeter per half-turn.

8. The magnet system of claim 1, further comprising a metal ring disposed between the first permanent magnet and the second permanent magnet.

9. The magnet system of claim 8, wherein the metal ring comprises at least one of: a steel ring, and a cobalt ring.

10. The magnet system of claim 1, wherein the hollow outer metallic shield has a thickness b, and wherein the thickness b is chosen to maximize the uniformity of the static magnetic field.

11. The magnet system of claim 1, wherein at least one of the first and the second permanent magnets comprises an NdFe permanent magnet.

12. The magnet system of claim 1, wherein the upper and lower discs are slidably movable relative to the hollow outer shield.

13. The magnet system of claim 1, wherein the first and second permanent magnet, the upper and lower discs, and the hollow outer case are substantially cylindrical in shape.

14. The magnet system of claim 1, wherein the upper metallic disc and the lower metallic disc comprises one of: a steel disc, and a cobalt disc; and wherein the hollow outer shield comprises one of: a steel outer shield, and a cobalt outer shield.

15. The magnet system of claim 1, wherein the first and second magnet elements have substantially equal sizes, and wherein the upper and lower metallic discs have substantially equal sizes.

16. The magnet system of claim 1, wherein Wi is substantially equal to W₂, Wi and W₂ are about 6.1 millimeters, the gradient of the static magnetic field is about 0.04G/mm, and wherein the first and second permanent magnets have a length of about 4 mm.

17. An NMR system for performing an NMR analysis of a sample, the NMR system comprising:

an NMR coil that surrounds the sample ;

an NMR transmitter and an NMR receiver, both coupled to the NMR coil; and

a magnet system configured to generate a static magnetic field B₀ across the sample and the coil;

wherein the magnet system comprises:

a first permanent magnet, and a second permanent magnet disposed below the first permanent magnet and substantially parallel thereto;

an upper metallic disc disposed above the first permanent magnet and a lower metallic disc below the second permanent magnet; and

wherein the upper and lower metallic discs are movable relative to the first and second permanent magnets, respectively, in such a way that the distances between the metallic discs and the respective permanent magnets are optimized so as to render the gradient of a static magnetic field generated by the magnet system sufficiently uniform for use in the NMR analysis.

18. The NMR system of claim 17, wherein the magnet system comprises a portable handheld magnet system, and wherein the NMR system comprises a miniaturized on-chip integrated NMR system.