WO1996010756A1

WO1996010756A1 - Improvements in nmr investigation

Info

Publication number: WO1996010756A1
Application number: PCT/GB1994/002129
Authority: WO
Inventors: Robert Carter Hawkes; Simon Douglas John Hancorn
Original assignee: Oxford Instruments (Uk) Limited; Herchel Smith Laboratory For Medicinal Chemistry
Priority date: 1994-09-30
Filing date: 1994-09-30
Publication date: 1996-04-11
Also published as: JPH09510017A

Abstract

A method of performing an NMR investigation on a sample comprising: (1) applying a magnetic field across the sample; (2) applying an rf excitation pulse to the sample; (3) applying a plurality of plane rotation adiabatic fast passage (AFP) rf refocussing pulses along an axis at right angles to the magnetic field; and (4) monitoring a characteristic of the response of the sample. Typically the pulse sequence comprises a CPMG pulse sequence with a first 90° excitation pulse followed by a string of 180° pulses. The first 180° pulse is applied a time τ after the 90° pulse and all subsequent 180° are separated by a time 2τ. The pulse sequence is particularly suited to NMR well logging or table top medical applications.

Description

IMPROVEMENTS IN NMR INVESTIGATION FIELD OF THE INVENTION

The present invention relates to methods for investigating a sample using nuclear magnetic resonance (NMR) .

DESCRIPTION OF THE PRIOR ART

Nuclear magnetic resonance (NMR) exploits the fact that nuclei containing odd numbers of protons and/or neutrons, i.e., those with non-zero nuclear spin, have an inherent magnetic moment, μ. This magnetic moment arises in these nuclei because they are spinning charged particles. The simplest nucleus to consider as an illustrative example is the hydrogen nucleus: this is a single proton. The proton has two possible orientations of μ which are degenerate in the absence of an external magnetic field. The nuclear spin states are described by the nuclear spin quantum number, m, which can assume values of +h or -h only. Such nuclei are said to have a nuclear spin, I, of k _' A nucleus with spin I can adopt 21+1 spin orientations. When an ensemble of nuclei with non-zero nuclear spin are placed in a magnetic field, B₀, they separate into non-degenerate distinct energy levels: the largest positive m value corresponding to the lowest energy (most stable) state. This splitting of energy levels in a magnetic field is called the nuclear Zeeman effect. The energy, E_j, of each of these spin states is proportional to both jxi_j and B₀. E, = -m,B₀γ * ( 0. 1)

fc = Planck's constant/2τr γ - magnetogyric ratio; defined as the ratio of the magnetic moment to the angular momentum (μ/J) for the nucleus under study.

Consider the classical description of the motion of a spin in an externally applied magnetic field B. B will produce a torque on the magnetic moment, μ, equal to μ Λ B. However, this torque does not induce a simple rotation; because the nucleus possesses angular momentum (as well as spin) the force results in a precession of μ about B, as is detailed below.

The equation of motion of the magnetic moment is found by equating the torque with the rate of change of angular momentum, J. dJ a

—=μ Λ B (0.2) dt

and, as μ = γJ we have,

—-μ A (γB) (0.3) dt

Thus, as a result of the cross-product in the above equation, any change in μ is perpendicular to both μ and B and we have precession of μ about B at an angle θ. If B is independent of time, θ does not change and μ sweeps out a cone. One can rewrite the equation of motion of the magnetic moment, eqn. 0.3, in terms of a coordinate system rotating at an arbitrary angular velocity ω₀: _ + ω_ Λ μ = μ Λ γ B, or ( 0.4 ) dt

dii a

- ⁼ μ Λ (γ B-i^) (0.5) dt

This tells us that the magnetic field in eqn. 0.3 must be replaced by an effective field, B_eff = B + ω₀/γ, in order that the motion of μ in this new rotating coordinate system obeys the same equation as in the laboratory frame. Therefore, to solve for the motion of the magnetic moment in a static field, B₀, one chooses ω₀ such that

^Beff ^{= B}o ⁺ — ⁼ ° <⁰-⁶>

i.e.

= -Y⁵ ₀ ⁽°'⁷>

In other words, one selects a rotating frame (in which

B₀ appears stationary) with an angular velocity ω₀ = -γB₀ with respect to the laboratory frame. This angular frequency is called the LARMOR FREQUENCY, and the frame of reference is referred to as the rotating frame.

Recalling eqn. 0.1 one can calculate that the energy gap between two spin -h states of a nucleus is ΔE = B₀γ' . Making use of eqn. 0.7 we have; ΔE = >ιω₀ (0.8)

Thus, in order to excite a nucleus from the lower (m=%) to the higher (m=-^) energy level a quantum of energy equal to fcω„ must be supplied. For the majority of nuclei in magnetic fields of the order of Tesla, this corresponds to the radio frequency (r.f.) range of the electromagnetic spectrum (-10s to 100s of MHz) .

In analyzing the effect of applying an r.f. field, B(t) <= 2B₁cosωt, to a magnetic moment it is convenient to consider the alternating field as two counter-rotating components, each of amplitude B₁ as shown in Figure 1.

If B₁ < B₀ the effect of the rotating field on a magnetic moment is negligible unless the frequency of the r.f. field, ω, is in the region of the Larmor frequency, ω₀. Thus, as one of the components of B(t) will be rotating in the same sense as the precession of μ about B, the effect of the other (counter-rotating) vector can be ignored.

Now consider the equation of motion of a spin, including the effects of both B(t) and the static field B₀. From eqn. 0.5,

- =μΛγ [B₀ + B (t) ] (0.9) dt

The time dependence can be eliminated by moving to the rotating frame with angular velocity ω. In this coordinate system, B is static and, as the axis of rotation coincides with B₀, B₀ is also static in this frame. If one takes B(t) to be along the x-axis of the rotating frame we have, from eqns. 0.5 and 0.9

OH = μ Λγ [(B₀ - - ) k + B 1] (0.10) dt Y

where, B,_ff - (B₀-- ) *+B₁i ( 0. 12 )

Y

What eqn. 0.11 means is that, in the rotating frame, the magnetic moment behaves exactly as if it were in a static magnetic field B_βff (recall eqn. 0.3). μ therefore precesses in a cone of fixed angle about the direction of B_eff at angular frequency γB_βff. This is illustrated in Figures 2 and 3.

Note eqn. 0.12 and that if the frequency of the r.f. field (B,) , i.e., ω, is less than the Larmor frequency, ω₀, the effective field has a positive z-component. Similarly if ω<ω₀, B_βff has a negative z-component. The Adiabatic Theorem

Assume one has a magnetic field, B₀, of fixed magnitude, the direction of which can be varied. At t 0, there exists a magnetisation, M, (which is the vector sum of all individual magnetic moments) parallel to the lab. frame z-axis (and therefore B₀ also) . The orientation of

B₀ is then changed smoothly overtime; this motion being characterised by an angular velocity, ω. There exists a theorem which states that if γB₀ » ω, the magnetisation, M, will remain aligned along B₀ as B₀ is rotated through some arbitrary angle θ (relative to the z-axis) .

Proving the Theorem

Let ω be a constant in the z-direction. In this frame of reference, let us also take B₀ to be perpendicular to ω as a component of ω parallel to B₀ produces no effect. M is parallel to B₀ and pointing along the x-axis in the laboratory frame. If one now selects a reference frame rotating at angular velocity ω, B₀ appears static and we have a new effective field,

B_eff=B₀₊" (0.13) This effective field and the magnetisation, M, are shown in Figure 4 at t=0.

M will precess about B_βff making an angle θ such that

tanθ=_f-ϊ- (0.14)

M will therefore remain with an angle 2θ of B₀. From eqn. 0.14 one can see that if

Y*n

M and B₀ remain parallel, as shown in Figure 5. This property of the magnetisation following the direction of the effective field if it is altered sufficiently slowly is described by the term ADIABATIC. Adiabatic Pulses The principle described above may be extended to the case of an applied r.f. field, B at frequency ω applied perpendicular to B₀. If one starts radiating far below resonance, M is essentially parallel to B_eff in the rotating frame where,

³ef " ( (B₀ - - ) ² - B² ) ^ (0.15) v -L

As one approaches resonance (sufficiently below) M will remain parallel to B_eff in the rotating frame. Thus, exactly at resonance, when

the magnetisation will lie along the direction of B,, i.e., at 90° to B₀. This is known as adiabatic excitation. If the frequency sweep continues through resonance to way above the Larmor frequency, M will end up along the z-axis. This is referred to as adiabatic inversion. The term ADIABATIC FAST PASSAGE (AFP) pulses is also used to describe these pulses: adiabatic because the change in direction of B_eff is slow enough to permit the magnetisation to follow and, fast because the duration of the pulse is short compared to the transverse relaxation time, T₂, of the sample under study. The term AFP will be used throughout the remainder of this specification.

The drawback with the standard AFP pulses described up to now is that constant rotations are not induced for magnetisation vectors that are not initially collinear with the longitudinal (z-)axis. This is because any magnetisation initially perpendicular to B_eff will remain in a plane perpendicular to B_eff and fan out during the execution of the pulse. This means that these pulses are unsuitable for plane rotations in, for example, a spin-echo experiment. However, alternative AFP pulses capable of plane rotations have been described in Bendall et al., Magn. Reson. Med. 4 493-499 (1987), Ugirbil et al., J. Magn. Reson. 72 177-185 (1987), Ugurbil et al., J. Magn. Reson. 78 472-497 (1988), Garwood and Ke, J. Magn. Reson. 94 511- 525 (1991) . This "family" of pulses share a common feature in that the effective field undergoes a discontinuous jump of, usually but not always [Journal of Magnetic Resonance: Garwood and Ke, 1991], 180°. This is referred to as the B_e-flip (B_β is B_eff) and uniquely defines this class of pulse. To more fully illustrate and explain the mechanism by which these refocussing pulses operate, it is necessary to briefly introduce the so-called second rotating frame.

During an AFP pulse, in addition to the effective magnetic field, B_eff (which is the vector sum of B₀ - ω/γ and B₁ as previously described) , there exists a small magnetic field due to the rotation of B_eff about say, the y- axis (taking B₀ along z and B₁ along x in the rotating frame) . This magnetic field component is defined as

where dθ / dt is the rate of rotation of B_tff and its direction is given by the axis of rotation of B_βf. The resultant of B_βff and

is denoted b_e, and this is the magnetic field that M will precess around. So, M will always remain within an angle 2α of B_eff. Note however that when the adiabatic condition is satisfied - dθ/dt « γ B_eff - α is small and therefore b_e « B_eff. Thus, one may still consider M to be collinear with B_eff during the pulse.

Ordinarily, AFP pulses are used either for 90° excitation or 180° inversion sequences. The use of a "plane rotation" AFP pulse has also been demonstrated for performing a "spin echo" experiment: this is a 90° excitation pulse followed by a single 180° pulse.

NMR is ideally performed in an extremely uniform magnetic field, with field homogeneity ideally in the region of 1 part in 10 7 -109. An examination region with this quality of field homogeneity is generally only obtainable within a volume defined by for example a polarity of nested co-axial coils. However, in certain applications, such field homogeneity is not possible, for instance in well logging or surface coil medical applications, in which the static B₀ field decreases with distance from the coils. The varying B₀ field causes a variation in Larmor frequency, and subsequently the magnetic spins in the sample under investigation become quickly defocussed before their relaxation time can be measured. This is conventionally overcome by applying a multiple refocussing pulse sequence after the initial excitation pulse. An example is the Carr-Purcell-Meiboo -Gill (CPMG) echo train. The utility of this sequence is that it refocusses any magnetisation decay due to static (spatial and temporal), i.e. all non- time-dependent, magnetic inhomogeneities.

However, a problem of equal concern to the volume of uniform static (B₀) field projection is the corresponding volume of uniform rf (B,) excitation. That is, in certain applications (for instance involving surface coils) the B, field will also decrease with distance from the coils. A conventional refocussing pulse sequence uses "hard" refocussing pulses. However, the conventional non- selective "hard" pulse will tend to result in signal cancellation in particular due to B, inhomogeneity.

In accordance with the present invention, we provide a method of performing an NMR investigation on a sample comprising: (1) applying a magnetic field across the sample;

(2) applying a rf excitation pulse to the sample;

(3) applying a plurality of plane rotation adiabatic fast passage (AFP) rf refocussing pulses along an axis at right angles to the magnetic field; and (4) monitoring a characteristic of the response of the sample.

Typically, the excitation pulse is a 90^β pulse, and the refocussing pulses are 180° pulses.

An AFP pulse involves a sweep in frequency and amplitude which produces a B₁ amplitude insensitive excitation. Each AFP pulse following the excitation pulse will cause the magnetic spins to refocus despite B₀ and B₁ inhomogeneity. A parameter such as the T₂ relaxation term may then be determined from the multiple echoes. Typically, the pulse sequence comprises a CPMG pulse sequence. This involves a 90° excitation pulse followed by a string of 180° pulses applied along an axis at right angles to both the axis of the excitation pulse and the direction of the external magnetic field. If the time interval between the centre of the 90° pulse and the centre of the first 180° pulse is denoted by T, the first echo will form at time r after the centre of the 180° pulse. If all subsequent 180° pulses are spaced by a time 2r, then echoes will also be separated by an interval of duration 2τ.

However, other multiple refocussing pulse sequences may also be used.

A further preferable feature is that the excitation pulse is a 90° AFP pulse.

Modulation of the RF pulses may be optimised for the particular geometry of the applied field. The invention is particularly suitable for applications involving inhomogeneous B₀ and B₁ fields such as NMR well logging or table top medical applications.

This type of pulse sequence has particular application in downhole oil mole technology, whereby the Earth's formation is interrogated at a distance from a "sonde" which is travelling through a borehole. Further uses include medical applications where the object under study is external to the magnet and r.f. coil structure, e.g. non-enclosed under study is external to the magnet and r.f. coil structure, e.g., non-enclosed magnetic resonance imaging (MRI) and spectroscopy machines, or indeed, any application in which a magnetisation refocussing sequence is required.

Examples of the present invention will now be described with reference to the accompanying Figures, in which:-

Figure 1 illustrates a first type of apparatus for carrying out the present invention;

Figure la illustrates a second type of apparatus for carrying out the present invention;

Figure 16 illustrates the r.f. field; Figure 2 illustrates the effective static magnetic field B_βff;

Figure 3 illustrates the precession of the magnetic moment about the effective magnetic field; Figure 4 shows the effective field and the magnetisation M at time t=0;

Figure 5 shows the effective field and magnetisation at the start of an AFP pulse;

Figure 6 illustrates a CPMG pulse sequence according to the present invention;

Figure 7A and 7B illustrate amplitude and phase modulations of the AFP 180° pulses; and.

Figures 8A and 8B illustrate the real and imaginary channel for the amplitude and phase modulated RF excitation.

Figure 9 is a graph of T₂ against pulse power for 4 different AFP sweep widths;

Figure 10 illustrates echo sequences for hard pulses and AFP pulses; Figure 11 illustrates the variation in T₂ with B₀ gradient;

Figure 12 illustrates the echo sequences for hard and AFP pulses at varying distances from the RF coil;

Figure 1 illustrates the B₀ and B, coil arrangement in an enclosed NMR imaging system. The B₀ magnetic field is produced by superconducting solenoid coil windings 1. The rf B, field is produced by saddle coil type rf antennae

2a,2b. As shown, the B₀ and B₁ regions are inside the magnet structure. The present invention may be carried out using the coil arrangement shown in Figure 1. However, the invention is particularly useful in an arrangement such as the one shown in Figure la. Figure la shows a non-enclosed NMR structure, in which the B₀ and B₁ fields are external to the magnet structure. An application of this is table top medical imaging, in which a patient lies on the surface 5.

The B₀ field is produced by permanent magnet pole pieces 3,4. The rf B field is produced by solenoidal rf coil 7. Shims 6 are included to enhance the field homogeneity.

Figure 6 illustrates a CPMG pulse sequence according to the present invention. The RF pulses are indicated at 50 and the response from the sample (which may be detected by the RF coils) is indicated at 51. The pulse sequence commences with a first excitation pulse 52. Preferably, this is an AFP pulse, although it may be a "hard" pulse (i.e. rectangular time envelope, short duration, broad excitation bandwidth) . The subsequent refocussing pulses 53 are separated by a time 2τ and commence at a time r after the excitation pulse 52. The response from the sample comprises a first signal 54 in which the spins dephase over a period τ , followed by a series of echoes (55,56,57 etc.) caused by the refocussing pulses 53 and also separated by a time 2τ. Every other echo is offset slightly, therefore the T₂ characteristic is determined by measuring every other pulse, i.e. (54,56,58 etc) or (55,57,59 etc). Preferably, T₂ measurements are taken from both the odd and even echoes, and the results are averaged. The T₂ measurements are derived from the slope of the decay lines (60 or 61) .

An example of an AFP pulse according to the invention will now be described. When describing these pulses it is useful to think of the total pulse, duration T, as composed of three sections, with discontinuous phase shifts as t=T/4 and 3T/4.

• t=0 to T/4: AFP excitation in reverse

• t=T/4 to 3T/4: AFP inversion • t=3T/4 to T: AFP excitation

Using this idea it is easier to understand the following table, which outlines the modulation functions for a representative AFP refocussing pulse. time (t) amplitude frequency modulation modulation

0 -» T/4 cosine - sine

T/4 → 3T/4 - cosine sine

3T/4 → T cosine - sine 1

Figures 7A and 7B illustrate the amplitude and phase modulations respectively, with respect to time. Figures 8A and 8B illustrate the corresponding real and imagining channels for the amplitude and phase modulated rf excitation.

Note that phase modulation can be considered to be equivalent to frequency modulation. A wide range of modulation schemes are appropriate, including sine, cosine, tangent, hyperbolic secant and hyperbolic tangent functions. The illustrated example shows a combination of sine and cosine functions, but the invention is not limited to this particular example.

Figures 9 to 12 compare and contrast the results from conventional hard pulse CPMG sequences with pulse sequences according to the present invention involving AFP pulses.

Figure 9 shows the variation in T₂ measurement with pulse power. The pulse power of 100 will be close to the coil where the RF pulse will have its highest amplitude, and tends towards zero as the B, amplitude increases with distance from the coil. AFP sweep widths of 4kHz, 10kHz, 15kHz and 20kHz are illustrated. It can be seen that the measured T₂ value remains substantially constant down to a pulse power of approximately 20 units. This shows how the present invention allows T₂ to be measured despite B, inhomogeneity.

Figure 10 illustrates echo trains from a conventional hard pulse CPMG sequence and a 10kHz AFP pulse sequence. It can be seen that there is excellent correspondence between the two methods. Figure 11 illustrates that variation in T₂ measurements over a range of B₀ in homogeneities. It can be seen that the pulse sequence maintains its refocussing performance over a large range of inhomogeneity from a uniform field (B₀ gradient - 0) to a highly inhomogeneous field (B₀ gradient = lOOOHz/cm) .

Figure 12 shows the insensitivity to B₁ magnitude which is indicative of an AFP refocussing sequence. A sequence of echoes are illustrated in the same way as in Figure 7. Echo sequences for both hard and AFP pulses are shown for a sample close to the RF coil (9mm) and further away from the coil (25mm) where the B, field will be lower. It can be seen that there is a marked difference between the echo responses from the hard pulse sequence for the 9mm reading (91) and the 25mm reading (92) . In contrast both readings for the AFP sequence (93,94) are similar.

Claims

1. A method of performing an NMR investigation on a sample comprising:

(1) applying a magnetic field across the sample; (2) applying a rf excitation pulse to the sample;

(3) applying a plurality of plane rotation adiabatic fast passage (AFP) rf refocussing pulses along an axis at right angles to the magnetic field; and

(4) monitoring a characteristic of the response of the sample.

2. A method according to claim 1, wherein the excitation pulse is an AFP pulse.

3. A method according to any of the preceding claims, wherein the rf pulses are optimised for the particular geometry of the applied magnetic field.

4. A method according to any of the preceding claims, wherein the time interval between the excitation pulse and the first refocussing pulse is r, and subsequent refocussing pulses are separated by a time 2τ.

5. A method according to any of the preceding claims, wherein the monitored characteristic is T₂ relaxation time.

6. A method according to any of the preceding claims, wherein the AFP pulses are amplitude and frequency modulated.

7. Apparatus for performing an NMR investigation on a sample, comprising means to apply a magnetic field across the sample; means to apply a rf excitation pulse to the sample; means to apply a plurality of adiabatic fast passage (AFP) rf refocussing pulses along an axis at right angles to the magnetic field; and monitoring means to monitor a characteristic of the response of the sample.

8. Apparatus according to claim 7, wherein the refocussing pulses cause a series of electromagnetic echoes from the sample, and the monitoring means monitors the intensity of the echoes.

9. Apparatus according to claim 8, wherein the monitoring means monitors the T₂ relaxation time of the echoes.

10. Apparatus according to any of claims 7 to 9, for investigation of a sample which is remote from the apparatus, whereby the applied magnetic field and rf pulses are substantially inhomogeneous.