Method for measuring the gradient field of a nuclear magnetic resonance (NMR) system based on the diffusion effect

Abstract

A method for measuring a gradient field of a nuclear magnetic resonance (NMR) system based on a diffusion effect uses a non-uniform field magnet, an NMR spectrometer, a radio frequency (RF) power amplifier, an RF coil, and a standard quantitative phantom with known apparent diffusion coefficient (ADC) and time constant for decay of transverse magnetization after RF-pulse (T2). A plurality of sets of signals are acquired by an NMR sequence with different diffusion-sensitive gradient durations or different echo spacings and the magnitude of the gradient field is calculated by fitting based on the plurality of sets of signals. The method does not require an additional dedicated magnetic field detection device, has a short measurement time, is easy to use with the NMR system, and is convenient to complete gradient field measurement at the installation site, thereby improving the installation and service efficiency of the NMR system.

Claims

1. A method for measuring a gradient field of a nuclear magnetic resonance (NMR) system based on a diffusion effect comprising the following steps: S100: acquiring M sets of echo signals in a non-uniform field NMR system, wherein the echo signal is a four-dimensional array S(m, n, a, p); wherein a first dimension denotes an echo spacing vector τ with a length of M; a second dimension denotes an echo train length N; a third dimension denotes an averaging number A; and a fourth dimension denotes a number of sampling points of a single readout data, wherein the number is P; S200: data preprocessing: converting the echo signal S(m, n, a, p) into a one-dimensional or two-dimensional array S′: S210: performing Fourier transform on the fourth dimension of the echo signal S to acquire frequency domain data and reserving a low-frequency part; S220: averaging data; S230: taking logarithm of all data; and S240: calculating a time series t(m); S300: calculating an equivalent coefficient a by a fitting function:
S′=ƒ(α,T2,t(m)) wherein T2 is a known time constant for decay of transverse magnetization after radio frequency (RF)-pulse on a standard quantitative phantom; and S400: calculating a gradient field by a calculation function: $G=c*\sqrt{\frac{a}{{\gamma }^{2}D}}$ wherein γ denotes the gyromagnetic ratio, D denotes a known apparent diffusion coefficient (ADC) of the standard quantitative phantom, c denotes a constant coefficient, and G denotes the gradient field.

2. The method according to claim 1, wherein in step S100, in the non-uniform field NMR system, an excitation pulse, refocusing pulses, and a constant gradient field are applied; the excitation pulse has a flip angle of θ and is followed by a plurality of refocusing pulses with a flip angle of 2θ; the excitation pulse and a first refocusing pulse have a phase difference of 90° and a time interval of τ/2, and a time interval between the first refocusing pulse and a first acquisition window is τ/2; the time interval between the refocusing pulses is defined as the echo spacing; N echo signals are acquired by one excitation and have an echo spacing τ; and echo signals are acquired for multiple times and are averaged; and the echo spacing τ is changed to perform M measurements to acquire the M sets of echo signals.

3. The method according to claim 2, wherein in step S200, the echo signal S(m, n, a, q) is converted into S′(m, n); step S220 is to average the third dimension; and in step S240, the time series t(m)=[τ(m)].sup.∧2, wherein τ(m) denotes an m-th element in the echo spacing vector τ.

4. The method according to claim 3, wherein step S300 comprises: S310: estimating the equivalent coefficient α: estimating the equivalent coefficient α by fitting S′(m, n): $S^{\prime }\left(m,n\right)=-n\sqrt{t\left(m\right)}\left(\frac{1}{T2}+a*t\left(m\right)\right)+C_1$ wherein C.sub.1 denotes an unknown constant.

5. The method according to claim 4, wherein in step S400, the constant coefficient of the calculation function for the gradient field is expressed as follows:
c=2√{square root over (3)}.

6. The method according to claim 1, wherein in step S100, in the non-uniform field NMR system, an excitation pulse, refocusing pulses, and a constant gradient field are applied; the excitation pulse comprises a first excitation pulse with a flip angle of θ; the refocusing pulses comprise a first refocusing pulse, a second refocusing pulse, . . . , and an n-th refocusing pulse, each with a flip angle of 2θ; a phase difference between the first excitation pulse and the first refocusing pulse is 90°, and a phase difference between the first refocusing pulse and subsequent refocusing pulses is 0°; a time interval between the first excitation pulse and the first refocusing pulse is T, wherein T is defined as a diffusion-sensitive gradient duration; a time interval between the first refocusing pulse and a first acquisition window is T; a time interval between the first acquisition window and the second refocusing pulse is τ/2; a time interval between subsequent refocusing pulses is τ, and a time interval between subsequent acquisition windows is τ; N echo signals are acquired by one excitation; and echo signals are acquired for multiple times and are averaged; and the diffusion-sensitive gradient duration T is changed to perform M measurements to acquire the M sets of echo signals.

7. The method according to claim 6, wherein in step S200, the echo signal S(m, n, a, q) is converted into S′(m); step S220 is to average the third dimension and the second dimension; and in step S240, the time series t(m)=[T(m)].sup.∧2, wherein T(m) denotes an m-th element in the diffusion-sensitive gradient duration series T.

8. The method according to claim 7, wherein step S300 is to calculate the equivalent coefficient α by a fitting function: $S^{\prime }\left(m\right)=-\mathrm{at}\left(m\right)-\frac{2\sqrt{t\left(m\right)}}{T2}+C_2$ wherein C.sub.2 denotes an unknown constant.

9. The method according to claim 8, wherein in step S400, the constant coefficient of the calculation function for the gradient field is expressed as follows: $c=\sqrt{\frac{3}{2}}.$

10. The method according to claim 1, wherein the non-uniform field NMR system comprises a console, an NMR spectrometer, a magnet, an RF system, and the standard quantitative phantom, wherein the console is connected to the NMR spectrometer, and the console is configured to send a command to control parameter selection and region of interest (ROI) positioning of a measurement sequence, receive an NMR signal acquired by the NMR spectrometer, and complete real-time data processing; the magnet is designed as a permanent magnet; the RF system mainly comprises an RF power amplifier, a preamplifier, a transceiver switch, and an RF coil, wherein the RF coil transmits an excitation signal and receives the NMR signal through the transceiver switch; and the standard quantitative phantom is a glass container filled with a solution with known standard ADC and T2.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a magnetic field distribution of a single-sided magnet used for nuclear magnetic resonance (NMR);

(2) FIG. 2 shows an excitation region of a single-sided magnet NMR system;

(3) FIG. 3 is a schematic diagram of a system for measuring a gradient field of an NMR system based on a diffusion effect;

(4) FIG. 4 shows a gradient field measurement sequence, namely a SE-CPMG sequence according to Embodiment 1; and

(5) FIG. 5 shows a gradient field measurement sequence, namely a CPMG sequence according to Embodiment 2.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(6) To make the objectives, technical solutions, and advantages of the present disclosure clearer, the following describes the present disclosure in more detail with reference to the accompanying drawings.

(7) In the present disclosure, some terms used are as follows:

(8) NMR: Nuclear Magnetic Resonance

(9) MRI: Magnetic Resonance Imaging

(10) K-space: a frequency domain space of an NMR signal

(11) DWI: Diffusion-Weighted Imaging

(12) T1: Time constant for regrowth of longitudinal magnetization after RF-pulse

(13) T2: Time constant for decay of transverse magnetization after RF-pulse

(14) TR: Repetition Time

(15) ADC: Apparent diffusion coefficient

(16) EPI: Echo planar imaging

(17) CPMG: an NMR pulse sequence named by several scientists (Carr, Purcell, Meiboom, Gill)

(18) SE-EPI: Spin echo-echo planar imaging

(19) As shown in FIG. 3, a system for measuring a gradient field of an NMR system based on a diffusion effect mainly includes a console, an NMR spectrometer, a magnet, an RF system, and a standard quantitative phantom.

(20) A block diagram of the system is shown in FIG. 3.

(21) The console is connected to the NMR spectrometer and is configured to send a command to control the parameter selection and region of interest (ROI) positioning of a measurement sequence, receive an NMR signal acquired by the NMR spectrometer and complete real-time data processing. The magnet is generally a permanent magnet, such as a single-sided permanent magnet with a highly non-uniform magnetic field within the ROI.

(22) The RF system mainly includes an RF power amplifier, a preamplifier, a transceiver switch, and an RF coil. The RF coil transmits an excitation signal and receives the NMR signal through the transceiver switch.

(23) The standard quantitative phantom is a container made of non-metallic material or a non-conductor and filled with a specific solution with known standard ADC and T2. For example, it could be a glass container filled with pure water or a glass container filled with a 2% copper sulfate solution.

Embodiment 1

(24) FIG. 3 shows the ADC measurement sequence of a non-uniform field NMR system. The sequence is composed of a series of precisely controlled RF pulses, which include a first excitation pulse, a first refocusing pulse, a second refocusing pulse, . . . , and an n-th refocusing pulse. The constant gradient field is a natural gradient field of the magnet and does not require control.

(25) The flip angle of the first excitation pulse is θ, and the flip angle of all the subsequent refocusing pulses is 2θ. The phase difference between the first excitation pulse and the first refocusing pulse is 90°, and the phase difference between the first refocusing pulse and the subsequent refocusing pulses is 0°. The time interval between the first excitation pulse and the first refocusing pulse is T, which is defined as a diffusion-sensitive gradient duration. The time interval between the first refocusing pulse and the first acquisition window is T. The time interval between the first acquisition window and the second refocusing pulse is τ/2. The time interval between the subsequent refocusing pulses is τ, and the time interval between the subsequent acquisition windows is τ. N echo signals are acquired by one excitation. Often, a plurality of excitations and acquisitions are also required to improve the signal-to-noise ratio (SNR) by averaging the signals. To calculate the magnitude of the gradient field, it is necessary to change the diffusion-sensitive gradient duration T for a plurality of measurements to acquire the M sets of echo signals.

(26) Gradient Field Estimating Algorithm

(27) The acquired signal is a 4-dimensional array S(m, n, a, p). The first dimension corresponds to different diffusion-sensitive gradient durations (i.e., T), that is, corresponding to an echo spacing vector τ having M sets of data in total. The second dimension denotes an echo train length N. The third dimension denotes an averaging number A. The fourth dimension denotes the number of sampling points of a single readout data, which is P The estimation of the gradient field based on the four-dimensional array mainly includes the following three steps:

(28) 1. Data preprocessing

(29) Preprocessing step 1: Perform Fourier transform on the fourth dimension of the echo signal S to acquire frequency domain data, reserve only a low-frequency part, and average.

(30) Preprocessing step 2: Average the third dimension.

(31) Preprocessing step 3: Average the second dimension.

(32) Preprocessing step 4: Take the logarithm of all data. Through the preprocessing, the echo signal S(m, n, a, p) is converted into a one-dimensional array S′(m).

(33) Preprocessing Step 5: Calculate a time series t(m)=[T(m)].sup.∧2.

(34) 2. Calculate the equivalent coefficient α by fitting:

(35) $\begin{array}{cc}{S}^{\prime }\left(m\right)=-\mathrm{at}\left(m\right)-\frac{2\sqrt{t\left(m\right)}}{T2}+C_2& \left(1\right)\end{array}$
where T2 denotes a known time constant for decay of transverse magnetization after radio frequency (RF)-pulse on a standard quantitative phantom, S′(m) denotes the one-dimensional data after preprocessing, and C.sub.2 denotes an unknown constant.

(36) 3. Calculate the gradient field

(37) $\begin{array}{cc}G=\sqrt{\frac{3}{2}}*\sqrt{\frac{a}{{\gamma }^{2}D}}& \left(2\right)\end{array}$
where γ denotes the gyromagnetic ratio, D denotes a known ADC of the standard quantitative phantom, and G denotes the measured gradient field magnitude.

Embodiment 2

(38) FIG. 4 shows an ADC measurement sequence of a non-uniform field NMR system, which uses a typical θ-2θ-2θ-2θ. . . RF pulse sequence. A first excitation pulse has a flip angle of 0 and is followed by a plurality of refocusing pulses with a flip angle of 2θ. The phase difference between the first excitation pulse and the first refocusing pulse is 90°. The time interval between the first excitation pulse and the first refocusing pulse is τ/2. The time interval between the first refocusing pulse and the first acquisition window is τ/2. The time interval between the refocusing pulses is τ, which is defined as echo spacing. The constant gradient field is a natural gradient field of the magnet and does not require control. N echo signals are acquired by one excitation. Often, a plurality of excitations and acquisitions are also required to improve the signal-to-noise ratio (SNR) by averaging the signals. To calculate the magnitude of the gradient field, it is necessary to change the echo spacing τ for a plurality of measurements to acquire the M sets of echo signals.

(39) Gradient Field Estimating Algorithm

(40) The acquired signal is a 4-dimensional array S(m, n, a, p). The first dimension corresponds to different echo spacings, that is, corresponding to an echo spacing vector τ having M sets of data in total. The second dimension denotes an echo train length N. The third dimension denotes an averaging number A. The fourth dimension denotes the number of sampling points of a single readout data, which is P. The estimation of the gradient field based on the four-dimensional array mainly includes the following three steps:

(41) 1. Data preprocessing

(42) Preprocessing step 1: Perform Fourier transform on the fourth dimension of the echo signal S to acquire frequency domain data, reserve only a low-frequency part, and average.

(43) Preprocessing step 2: Average the third dimension.

(44) Preprocessing step 3: Take the logarithm of all data. Through the preprocessing, the echo signal S(m, n, a, p) is converted into a two-dimensional array S′(m, n).

(45) Preprocessing Step 4: Calculate a time series t(m)=[τ(m)].sup.∧2.

(46) 2. Estimate the equivalent coefficient α

(47) Calculate the equivalent coefficient α by fitting S′(m, n):

(48) $\begin{array}{cc}{S}^{\prime }\left(m,n\right)=-\frac{n\sqrt{t\left(m\right)}}{\mathrm{at}\left(m\right)+T2}+C_1& \left(3\right)\end{array}$
where τ(m) denotes an m-th element in the echo spacing vector τ, T2 denotes a known time constant for decay of transverse magnetization after radio frequency (RF)-pulse on a standard quantitative phantom, and C.sub.l denotes an unknown constant.

(49) 3. Estimate the gradient field:

(50) $\begin{array}{cc}G=2\sqrt{3}*\sqrt{\frac{a}{{\gamma }^{2}D}}& \left(4\right)\end{array}$
where γ denotes the gyromagnetic ratio, D denotes a known ADC of the standard quantitative phantom, and G denotes the measured gradient field magnitude.

(51) Certainly, the present disclosure may further include other various embodiments. A person skilled in the art can make various corresponding modifications and variations according to the present disclosure without departing from the spirit and essence of the present disclosure, but all these corresponding modifications and variations shall fall within the protection scope defined by the appended claims in the present disclosure.