Automatic digital preemphasis for dynamic NMR-magnetic fields by means of a digital IIR filter

Abstract

A method for driving a power supply (84) of a magnetic field coil (85) for generating a predetermined magnetic field profile B(r,t) in the volume under investigation of a nuclear magnetic resonance (=NMR) apparatus (81), wherein for compensation of distortions caused by the apparatus, an input signal i(t) is predistorted, that predetermines the time behavior of the magnetic field profile, wherein the power supply (84) is driven by the predistorted signal o(t), is characterized in that the predistortion is performed using a transfer function of the form

Description

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 shows a diagram of the intensity behavior with time of a gradient field GR_x in x-direction for a first NMR apparatus during and shortly after the switching ramp of the associated x gradient current, comparing to the desired behavior, measured behavior without pre-distorting measures and measured behavior with inventive predistortion measures;

FIG. 2 shows a diagram like FIG. 1 for a second NMR apparatus which has a tendency towards gradient field oscillations;

FIG. 3 shows a diagram like FIG. 1 for a third NMR apparatus;

FIG. 4 shows a diagram of the time behavior of the B₀ field for a fourth NMR apparatus during and shortly after the switching ramp of the x gradient current for the gradient field GR_x compared to the measured behavior without predistortion measures and measured behavior with inventive predistortion measures with cross-compensation;

FIG. 5 shows a diagram of the time behavior of the B₀ field of FIG. 4 with a longer observation period after the switching ramp;

FIG. 6 shows a diagram of the intensity behavior with time of a gradient field GR_x in x-direction for a fifth NMR apparatus in a time window close to the switching ramp of the associated x gradient flow compared to the measured behavior without predistortion measures and measured behavior with inventive predistortion measures;

FIG. 7 shows a diagram of the intensity behavior with time of the gradient field of FIG. 6 in a larger time window;

FIG. 8 shows a schematic representation of an inventive NMR apparatus.

Claims

1. A method for driving a power supply of a magnetic field coil to generate a predetermined magnetic field profile B(r,t) in a volume under investigation of a nuclear magnetic resonance (=NMR) apparatus, the method comprising the steps of: a) predistorting an input signal i(t) that defines a temporal behavior of the magnetic field profile using a transfer function of the form

2. The method of claim 1, wherein σ=0, O(jω) is a Fourier transform of o(t), and l(jω) is a Fourier transform of i(t).

3. The method of claim 1, wherein the magnetic field coil comprises a gradient coil for generating a magnetic field profile GRx with a magnetic field gradient that is constant in one spatial direction x.

4. The method of claim 1, wherein G(s) is converted into a digital IIR filter (infinite impulse response filter) or into an IIR filter having the following form:

5. The method of claim 1, wherein parameters an, bn are determined as follows: a) a test pulse i*(t) is supplied to the power supply;b) a time behavior of a resulting magnetic field profile o*(t) of the magnetic field coil is measured;c) G−1 is determined through a correlation O*(s)=G−1(s)I*(s) wherein O*(s) is a Laplace transform of o*(t), and I*(s) is a Laplace transform of i*(t);d) G is determined from G−1 through inversion;e) parameters an, bn are determined from G by solving a non-linear compensation problem.

6. The method of claim 5, wherein step e) comprises at least one of a Gauβ-Newton and a Levenberg-Marquardt method.

7. A method for driving power supplies of magnetic field coils of an NMR apparatus, the magnetic field coils being designed for generating a predetermined time varying magnetic field profile B(r,t) in a volume under investigation of the NMR apparatus, wherein each of K power supplies drives one magnetic field coil, with K≧2, the method comprising the steps of: a) predistorting input signals ik(t), with k: channel index between 1 and K, the input signals ik(t) defining a time behavior of magnetic field profile, the predistortion being effected using a transfer matrix G and considering interaction among the magnetic field coils, wherein G is a K×K matrix and O=G·I,  with

8. The method of claim 7, wherein σ=0, Ok(jω) is a Fourier transform of ok(t) and Ik(jω) is a Fourier transform of ik(t).

9. The method of claim 7, wherein at least two magnetic field coils each comprise a gradient coil for generating a magnetic field profile GRk with a magnetic field gradient which is constant in one spatial direction k.

10. The method of claim 9, wherein spatial directions of the magnetic field gradients of different gradient coils are orthogonal.

11. The method of claim 7, wherein G is converted into a system of digital IIR filters (infinite impulse response filter) or into IIR filter having the following form for each channel k:

12. The method of claim 7, wherein parameters an,pq, bn,pq are determined as follows: a) a first test pulse i1*(t) is supplied to a first power supply;b) a time behavior of magnetic field components ok*(t) (k=1 . . . K) of the K magnetic field coils is measured from a resulting magnetic profile;c) entries of a first column of G−1 are determined using a correlation O*=G−1·I* with O*=(O*1, . . . ,O*K) and I*=(I*1, . . . ,I*K) wherein O*k(S) is the Laplace transform of o*k(t) and I*k(s) is a Laplace transform of i*k(t);d) repeating steps a) through c) for channels 2 through K;e) determining G from G−1 through matrix inversion;f) determining the parameters an,pq, bn,pq from G by solving a non-linear compensation problem.

13. The method of claim 12, wherein in step f) comprises at least one of a Gauβ-Newton method and a Levenberg-Marquardt method.

14. A control means for an NMR apparatus the control means being designed to perform the method of claim 1.

15. A controls means for an NMR apparatus designed for performing the method of claim 7.

16. An NMR apparatus comprising a pulse generator means, one or more power supplies and one magnetic field coil for each power supply, wherein the NMR apparatus uses the control means of claim 14 to connect the pulse generator means to the power supply.

17. An NMR apparatus comprising a pulse generator means, one or more power supplies and one magnetic field coil for each power supply, wherein the NMR apparatus uses the control means of claim 15 to connect the pulse generator means to the power supplies.