CN112630712A - Simple and convenient nuclear magnetic resonance gradient waveform distortion pre-correction method - Google Patents

Abstract

The invention provides a simple and convenient nuclear magnetic resonance gradient waveform distortion pre-correction method, which comprises the following steps: first correction, the ideal gradient waveform, i.e. S, is loaded in a gradient generator_gg(i＝1,t)＝S_ideal(t), the gradient waveform is distorted after passing through a gradient system, and a gradient waveform S in an imaging space is obtained through a sequence method_vol(i 1, t) according to S_vol(i ═ 1, t) and S_ideal(t) estimating the response of the gradient system to obtain the system impulse response h (t); correction S_vol(i-1, t) vs_ideal(t) distortion, next iteration, update of the output gradient waveform S_gg(i +1, t); multiple iterations until S_volAnd (i-1, t) is the minimum distortion, and the steps are repeated to obtain a predistortion gradient waveform database. The invention does not need to specially measure the frequency response of the gradient system, is more stable and reliable, does not need to be prescan, and can adapt to the scanning of any geometric orientation.

Description

Simple and convenient nuclear magnetic resonance gradient waveform distortion pre-correction method

Technical Field

The invention relates to the technical field of magnetic resonance imaging, in particular to a simple and convenient pre-correction method for nuclear magnetic resonance gradient waveform distortion.

Background

Gradient pulses are of great importance in Magnetic Resonance Imaging (MRI). In one aspect, in combination with the radio frequency pulses, it determines the excitation profile of the tissue; on the other hand, although current MRI introduces the concepts of RF encoding and coil sensitivity encoding, gradient encoding remains the most important spatial encoding approach. However, due to the inductive nature of the gradient coil and the bandwidth limitations of the gradient amplifier, the conductor structure in the magnet space, etc., the magnetic field gradient actually generated in the imaging space always deviates from the ideal gradient waveform designed in the MRI imaging sequence by a certain amount, i.e., so-called gradient waveform distortion or waveform distortion. Gradient waveform distortion causes changes in the excitation/sampling k-space trajectory, which may cause artifacts such as excitation profile distortion, image deformation, and aliasing. Modern magnetic resonance imaging equipment is usually corrected by using self-shielding coils, gradient pre-emphasis and other techniques to alleviate the influence of gradient waveform distortion. However, in some cases, such as two-dimensional radio frequency pulse design, VERSE pulse design, and non-cartesian sampling, where the fidelity requirements for the gradient waveforms are higher, additional correction means are typically required.

For the case of high requirement on the fidelity of the gradient waveform, the current correction methods can be divided into two types: one is to estimate the gradient waveform. The method considers that the gradient system can be approximate to a linear time-invariant system, the frequency response function of the gradient system is measured by a certain method, then the distorted gradient pulse generated in the imaging space after the ideal gradient waveform passes through the gradient system is estimated, or conversely, the predistortion gradient pulse required for generating the ideal gradient waveform in the imaging space can also be estimated; the other is measuring gradient waveform, and this method adds one pre-scan before each scan to measure distorted gradient pulse in imaging space. By the two methods, gradient waveforms actually generated in an imaging space can be obtained, and radio frequency pulses or reconstructed images are designed according to the gradient waveforms, so that the influence of gradient deformation can be corrected.

For the two methods, the first gradient waveform distortion correction method needs to measure the frequency response of the gradient system, the process is complex, the measurement time is long, and accurate measurement is often difficult in practice; the second method extends the scanning time, and in practical applications, the accuracy of measuring the gradient waveform is also easily affected by the geometry of the subject, so that there is a certain risk of measurement failure. In addition, in some cases, such as the half-pulse design of two-dimensional ultrashort echo time imaging, the slice selection gradient must approach the ideal waveform, and the second method cannot be applied.

Disclosure of Invention

In view of the shortcomings of the prior art, the present invention provides a simple pre-correction method for nuclear magnetic resonance gradient waveform distortion to correct the influence of gradient distortion, which does not need to specially measure the frequency response of the gradient system and increase the pre-scanning time, and can be applied to all the above mentioned situations, especially the advantage is more obvious when correcting the gradient pulse involved in the radio frequency pulse design.

The technical scheme of the invention is realized as follows: a simple pre-correction method for nuclear magnetic resonance gradient waveform distortion comprises the following steps:

(1) in the first step of correction, the ideal gradient waveform is first loaded in the gradient generatorI.e. S_gg(i＝1,t)＝S_ideal(t), ideal gradient waveform S_ideal(t) generating distortion after passing through a gradient system, and measuring by a sequence method to obtain a gradient waveform S in an imaging space_vol(i 1, t) according to S_vol(i ═ 1, t) and S_ideal(t) estimating the gradient system response to obtain an approximate system impulse response h (t);

(2) for correcting the actually measured gradient waveform S in the imaging space_vol(i-1, t) with respect to an ideal waveform S_ideal(t) in the next iteration, updating the gradient waveform S output by the gradient generator_gg(i +1, t) is:

S_gg(i+1,t)＝S_gg(i,t)+ΔS_gg(i,t) (1)

wherein, Delta S_gg(i, t) should satisfy:

H*ΔS_gg(i,t)＝S_ideal(t)-S_vol(i,t) (2)

h is the matrix expression of impulse response H (t);

(3) repeating the step (2) for a plurality of iterations until S_vol(i is 1, t) until the distortion is minimized.

Further, in the step (2), the formula (2) is substituted into the formula (1), and the gradient waveform S_gg(i +1, t) is:

S_gg(i+1,t)＝S_gg(i,t)+lr*(H^TH+λI)H^T(S_ideal(t)-S_vol(i,t)) (3)

wherein, H is the matrix expression of impulse response H (t), I is the unit matrix, lambda is the regularization factor, and lr is the updating step length.

(4) And (4) repeating the steps (1) to (3) for the three X/Y/Z physical axes of the gradient system respectively, and storing the corrected gradient waveform to form a pre-corrected gradient waveform database.

(5) When in actual scanning, the data is read from the predistortion gradient waveform database according to the geometric orientation of the slice (i.e. the selected direction of the slice), and the required predistortion gradient waveform can be synthesized.

Further, in step (1), according to S_vol(i ═ 1, t) and S_ideal(t) estimating the response of the gradient system, and for the trapezoidal wave, carrying out differential operation on the gradient waveform to obtain h (t) as follows:

h(t)≈c_arb*D(S_vol(i＝1,t＜T_ramp)) (4)

wherein, c_arbTo normalize constant, T_rampThe time of the gradient plateau after the rising edge of the trapezoidal wave is selected.

Further, in step (1), according to S_vol(i ═ 1, t) and S_ideal(t) estimating the gradient system response, and using the Linear Time Invariant (LTI) characteristic of the gradient system to obtain h (t) as:

wherein, F and F^-1Respectively representing a fourier transform and an inverse fourier transform.

Further, in step (3), the gradient system response may also be estimated at each iteration to obtain the system impulse response h (t).

The invention has the beneficial effects that:

(1) the method does not need to specially measure the frequency response of the gradient system, is simple and easy to implement, and has more stable and reliable results;

(2) the method finally generates the gradient predistortion waveform of each physical axis, directly synthesizes the required input gradient waveform according to the geometric orientation during actual scanning, does not need pre-scanning, shortens the scanning time, is more stable and reliable, and can adapt to scanning in any geometric orientation.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a flow chart of a gradient waveform distortion predistortion method of the present invention;

FIG. 2 is a diagram illustrating the effect of predistortion of gradient waveform according to the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.

Example one

Referring to fig. 1, a flow chart of the gradient waveform distortion predistortion method of the present invention is shown in fig. 1, which is essentially an iterative optimization process.

A simple pre-correction method for nuclear magnetic resonance gradient waveform distortion comprises the following steps:

(1) in the first step of the correction (iteration number i equal to 1), the ideal gradient waveform, i.e., S, is initially loaded in the gradient generator_gg(i＝1,t)＝S_ideal(t), the gradient waveform is distorted after passing through a gradient system, and the gradient waveform S in the imaging space is measured by a nuclear magnetic resonance imaging sequence method_vol(i 1, t) according to S_vol(i ═ 1, t) and S_ideal(t) the system response of the gradient system over a certain frequency band can be roughly estimated to obtain an approximate system impulse response h (t), and by using the Linear Time Invariant (LTI) characteristic of the gradient system, the system response can be estimated by equation (5):

wherein, F and F^-1Respectively representing a fourier transform and an inverse fourier transform;

(2) for correcting the actually measured gradient waveform S in the imaging space_vol(i-1, t) with respect to an ideal waveform S_idealDistortion between (t) atIn one iteration, the gradient waveform S output by the gradient generator is updated_gg(i +1, t) is:

S_gg(i+1,t)＝S_gg(i,t)+ΔS_gg(i,t) (1)

wherein, Delta S_gg(i, t) should satisfy:

H*ΔS_gg(i,t)＝S_ideal(t)-S_vol(i,t) (2)

h is the matrix expression of impulse response H (t); for example, if h (t) is expressed as a vector of N × 1, i.e.:

h(t)＝[h(0) h(1) ...... h(N-2) h(N-1)] (6)

then H can be expressed as:

thus, h (t) and Δ S_ggThe convolution operation of (i, t) is converted into matrix multiplication, the formula (2) is substituted into the formula (1), and the least square method is applied to estimate S_gg(i+1,t)：

S_gg(i+1,t)＝S_gg(i,t)+lr*(H^TH+λI)H^T(S_ideal(t)-S_vol(i,t)) (3)

Wherein, H is the matrix expression of impulse response H (t), I is the unit matrix, lambda is the regularization factor, and lr is the updating step length.

(3) Repeating the step (2) for a plurality of iterations until S_volThe distortion of (i ═ 1, t) is minimized, and in practice, convergence is achieved in 3 to 5 steps. A simple example of a gradient waveform distortion correction is shown in fig. 2, where it can be seen that the corrected gradient waveform is closer to the ideal gradient waveform.

(4) The three physical axes of X/Y/Z of the gradient system are respectively corrected by adopting the steps (1) - (3), and generally speaking, a plurality of groups of waveforms with different gradient strengths need to be corrected, and finally, the corrected gradient waveforms are stored in a computer to form a pre-correction gradient waveform database. During actual scanning, data are read from the predistortion gradient waveform database according to the geometric orientation of the slice, and the required predistortion gradient waveform can be synthesized, so that the predistortion gradient waveform can be suitable for scanning in any geometric orientation.

Example two

This embodiment is substantially the same as the first embodiment, except that in step (1), according to S_vol(i ═ 1, t) and S_ideal(t) the system response of the gradient system on a certain frequency band can be roughly estimated, and for the trapezoidal wave, the difference operation can be directly carried out on the gradient waveform, namely:

h(t)≈c_arb*D(S_vol(i＝1,t＜T_ramp)) (4)

wherein, c_arbTo normalize constant, T_rampIn the time of a certain gradient platform after the rising edge can be selected according to the actual situation, only the influence of the gradient falling edge needs to be avoided, and h (t) is the approximate system impulse response. The estimation method is more accurate when the gradient climbing rate is higher and the gradient platform time is longer.

EXAMPLE III

This embodiment is substantially the same as the first or second embodiment, except that: in the step (3), the gradient system response is estimated in each iteration to obtain the system impulse response h (t).

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (5)

1. A simple pre-correction method for nuclear magnetic resonance gradient waveform distortion is characterized by comprising the following steps:

(1) in the first step of correction, the ideal gradient waveform, i.e., S, is first loaded in the gradient generator_gg(i＝1,t)＝S_ideal(t), the gradient waveform is distorted after passing through a gradient system, and the gradient waveform S in the imaging space is measured by a sequence method_vol(i 1, t) according to S_vol(i ═ 1, t) and S_ideal(t) estimating the gradient system response to obtain an approximate system impulse response h (t);

(2) for correcting the actually measured gradient waveform S in the imaging space_vol(i-1, t) with respect to an ideal waveform S_ideal(t) in the next iteration, updating the gradient waveform S output by the gradient generator_gg(i +1, t) is:

S_gg(i+1,t)＝S_gg(i,t)+ΔS_gg(i,t) (1)

wherein, Delta S_gg(i, t) should satisfy:

H*ΔS_gg(i,t)＝S_ideal(t)-S_vol(i,t) (2)

h is the matrix expression of impulse response H (t);

(3) repeating the step (2) for a plurality of iterations until S_vol(i is 1, t) until the distortion is minimized.

(4) And (4) repeating the steps (1) to (3) for the three X/Y/Z physical axes of the gradient system respectively, and storing the corrected gradient waveform to form a pre-corrected gradient waveform database.

(5) When in actual scanning, the data is read from the predistortion gradient waveform database according to the geometric orientation of the slice, and the needed predistortion gradient waveform can be synthesized.

2. A simple nmr gradient waveform predistortion method as claimed in claim 1, wherein in step (2), the formula (2) is substituted into the formula (1), and the gradient waveform S is_gg(i +1, t) is:

S_gg(i+1,t)＝S_gg(i,t)+lr*(H^TH+λI)H^T(S_ideal(t)-S_vol(i,t)) (3)

wherein, H is the matrix expression of impulse response H (t), I is the unit matrix, lambda is the regularization factor, and lr is the updating step length.

3. A simple predistortion method of nuclear magnetic resonance gradient waveform according to claim 1 or 2, characterized in that in step (1), according to S_vol(i ═ 1, t) and S_ideal(t) estimating the gradient system response, for trapezoidal waves, performing a difference operation on the gradient waveforms,h (t) is obtained as:

h(t)≈c_arb*D(S_vol(i＝1,t<T_ramp)) (4)

wherein, c_arbTo normalize constant, T_rampThe time of the gradient plateau after the rising edge of the trapezoidal wave is selected.

4. A simple predistortion method of nuclear magnetic resonance gradient waveform according to claim 1 or 2, characterized in that in step (1), according to S_vol(i ═ 1, t) and S_ideal(t) estimating the gradient system response, in practice, optionally also using the linear time-invariant property of the gradient system, to obtain h (t) as:

wherein, F and F^-1Respectively representing a fourier transform and an inverse fourier transform.

5. A simple nmr gradient waveform predistortion method as set forth in claim 1, wherein in step (3), the system impulse response h (t) is obtained by estimating the gradient system response for each iteration.

Images