CN109270107B - Multi-dimensional nuclear magnetic resonance measurement method - Google Patents

Multi-dimensional nuclear magnetic resonance measurement method Download PDF

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CN109270107B
CN109270107B CN201811251294.XA CN201811251294A CN109270107B CN 109270107 B CN109270107 B CN 109270107B CN 201811251294 A CN201811251294 A CN 201811251294A CN 109270107 B CN109270107 B CN 109270107B
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刘化冰
宗芳荣
汪正垛
孙哲
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Beijing Limecho Technology Co ltd
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Abstract

The invention provides an analysis method for acquiring and processing multidimensional nuclear magnetic resonance data for material detection. The method is suitable for nuclear magnetic resonance detection instruments with different field strengths and different configurations. The method relates to various nuclear magnetic resonance pulse sequences, and important parameters such as porosity, pore structure, saturated fluid type, framework magnetization coefficient, heterogeneity and the like of a detection material can be analyzed and obtained by carrying out corresponding data processing on an obtained three-dimensional data structure.

Description

Multi-dimensional nuclear magnetic resonance measurement method
The invention relates to a divisional application named as a multi-dimensional nuclear magnetic resonance measurement method, which is applied in China at 27.3.2017 and under the application number of 2017101862466.
Technical Field
The invention relates to the field of nuclear magnetic resonance, in particular to a realization process of a multi-dimensional nuclear magnetic resonance measurement method and a data processing process thereof.
Technical Field
The nuclear magnetic resonance technology is used as an advanced nondestructive detection means, and has extremely wide application in a plurality of fields such as medicine, energy, materials, agriculture and forestry, food, safety monitoring, chemical industry and the like. Common characteristic parameters of NMR include the longitudinal relaxation time T1Transverse relaxation time T2In addition, the diffusion coefficient D of the molecule or the magnetic susceptibility x of the solid skeleton can be rapidly obtained by the nuclear magnetic resonance technology. These nuclear magnetic resonance properties can be correlated in multiple dimensions by editing the corresponding nuclear magnetic resonance properties over different time periods of the pulse sequence. The properties of the pore medium can be comprehensively researched by the related experimentsAnd richer information is obtained. The nuclear magnetic resonance relaxation characteristic is applied to detecting the pore structure, pore connectivity and pore space structure composition of a pore medium; the diffusion coefficient is used to understand the internal saturated fluid species as well as the composition of the crude oil, etc. Therefore, the pore size of the pore medium, the internal magnetic field gradient and the molecular composition of the complex fluid can be comprehensively researched in a higher dimension by the three-dimensional nuclear magnetic resonance technology.
The nuclear magnetic resonance relaxation or diffusion response within the porous medium satisfies the multiexponential decay law. Pore space relaxation or diffusion distributions obtained by inversion of measurements are a pathological problem. The solution of the inversion process is not unique, and small disturbance in the measurement result can cause great influence on the solution result. And (4) stabilizing the inversion process by introducing a regularization term in the solving process. The data volume of the three-dimensional nuclear magnetic resonance is large, and the time consumption for inversion according to the one-dimensional data processing idea is long. The kernel functions are compressed respectively and then subjected to tensor product, singular value decomposition is carried out on the obtained new kernel functions, singular values meeting set condition numbers are intercepted, meanwhile, three-dimensional data are compressed by adopting the intercepted orthogonal unit matrix, and the inversion speed is accelerated.
Disclosure of Invention
The invention aims to illustrate three multidimensional nuclear magnetic resonance measuring methods for analyzing the pore structure and the internal filling fluid characteristics of a material and corresponding multidimensional nuclear magnetic resonance data processing flows.
A first multi-dimensional nuclear magnetic resonance measurement method, the method comprising:
step 1, applying 90-degree radio frequency pulse to a tested sample to enable the macroscopic magnetization vector M0Turning for 90 degrees;
step 2, after waiting for the time T, applying a second 90-degree pulse to the sample to be measured to recover a certain amount of magnetization vector along the static magnetic field B0Turning again in the same direction by 90 degrees;
step 3, waiting for TEAfter the time of/2, applying 180 DEG radio frequency pulse to the tested sample, and waiting for the same time TEAfter the/2, acquiring and generating a spin echo signal in an ACQ channel;
step 4, repeatedly applying 180-degree radio frequency pulses, and collecting and generating a plurality of repeated spin echo signals in an ACQ channel to obtain echo train signals;
step 5, changing the waiting time tau, and repeating the steps 2-4 to respectively collect echo string signals generated under a plurality of different waiting times tau;
and 6, processing nuclear magnetic resonance data according to the acquired echo train signals.
Wherein, the echo train signal magnetization vector matrix generated in step 5 is:
M(τ,nTE,mts)＝∫∫∫K1K2K3F(T1,T2,Δχ)dT1·dT2·dΔχ
wherein tau is waiting time, n is 180 DEG pulse number, m is FID collection point number, tsFID acquisition Point time Interval, F (T)1,T2Δ x) is the three-dimensional T of the sample being measured1–T2- Δ χ characteristic matrix, T1For longitudinal relaxation time, T2Δ χ, the transverse relaxation time, is the difference in the susceptibility of the sample being measured and the fluid filling the interior, K1，K2，K3Is a specific form of three kernel functions:
K1＝1-exp(-τ/T1)
K2＝exp(-nTE/T2)
K3＝exp(-γ·Δχ·B0·mts)
wherein gamma is the gyromagnetic ratio of proton, B0The static magnetic field strength.
The step 6 is specifically that a rapid three-dimensional data processing algorithm is adopted to invert the multi-dimensional nuclear magnetic resonance data, and a proper regularization factor is selected to obtain the three-dimensional T of the detected sample1–T2- Δ χ distribution information. The method specifically comprises the following steps:
step 1: using the product of the mathematical tensors to carry out the first two kernel matrix functions K1And K2Coupled as a new kernel function matrix K12：
Figure BDA0001841758960000021
Step 2: the measured three-dimensional nuclear magnetic resonance data is re-expressed as:
M＝K12FK3
and step 3: for the kernel function matrix K12And K3SVD decomposition and singular value interception are carried out, further compression processing is carried out on the collected data, and singular value decomposition is carried out on the kernel function matrix to obtain:
K12＝U12·S12·V′12
K3＝U3·S3·V3′
wherein S12And S3The diagonal element values are arranged from large to small and are diagonal matrixes with the sizes of s12×s12And s3×s3Wherein s is12Is K12Number of non-zero singular values, s3Is K3The number of non-zero singular values; u shape12、V12And U3、V3Is an orthogonal unit array; for diagonal matrix S12And S3Intercepting is carried out, so that the condition number of the kernel function matrix meets a set value C, namely:
Figure BDA0001841758960000022
assume C is 1000;
Figure BDA0001841758960000023
and
Figure BDA0001841758960000024
respectively correspond to K12And K3Maximum singular value, i.e. diagonal matrix S12And S3The first diagonal element of (a) is,
Figure BDA0001841758960000025
represents K12The (i) th singular value of (a),
Figure BDA0001841758960000026
represents K3The jth singular value of (a);
and 4, step 4: and compressing the echo string signal magnetization vector matrix M by using the intercepted singular value decomposed identity matrix to reduce the data memory, wherein the compressed magnetization vector is as follows:
Figure BDA0001841758960000031
Figure BDA0001841758960000032
Figure BDA0001841758960000033
wherein the content of the first and second substances,
Figure BDA0001841758960000034
for the matrix of the compressed magnetization vectors,
Figure BDA0001841758960000035
as two kernel functions K12And K3Residual matrix, U 'after SVD decomposition and singular value interception'12、V′12Are each K12Matrix U after SVD decomposition and singular value interception12、V12Transpose of (V)3Is' K3Matrix V after SVD decomposition and singular value interception3Transposing;
and 5: after data compression is completed, inverting the data matrix by adopting a Tikhonov regularization method, wherein the regularization item is as follows:
Figure BDA0001841758960000036
wherein, alpha is a regularization factor and is related to the signal-to-noise ratio of the acquired data, K is a general form of a kernel matrix in the inversion process, and the term of | · | | represents the Frobenius norm of the matrix;
step 6: obtaining a final solution f by selecting an optimal regularization factor alpharThe solving formula is as follows:
Figure BDA0001841758960000037
wherein the content of the first and second substances,
Figure BDA0001841758960000038
to compress the tensor product matrix of the truncated residual matrix,
Figure BDA0001841758960000039
is composed of
Figure BDA00018417589600000310
Transposed matrix of alphaoptFor optimal regularization factor, I is the cell matrix,
Figure BDA00018417589600000311
as a matrix of compressed magnetization vectors
Figure BDA00018417589600000312
In the form of a one-dimensional matrix of (a), wherein,
Figure BDA00018417589600000313
a second multi-dimensional nuclear magnetic resonance measurement method, the method comprising:
step 1, applying 90-degree radio frequency pulse to a measured sample in a TRS channel to enable the macroscopic magnetization vector M to be subjected to measurement0Turning for 90 degrees;
step 2, applying a gradient pulse with the duration delta to the GRD channel;
step 3, followed by applying a 180 RF pulse at the TRS channel, and then applying a second gradient pulse of duration δ at the GRD channel. The gradient pulse starting time in the step is different from the gradient pulse starting time in the step 2 by delta time;
step 4, after the whole system waits for the time when the interval of the first two radio frequency pulses is equal, applying 90-degree radio frequency pulses to the sample to be measured, and enabling a certain amount of magnetization vectors to be perpendicular to the static magnetic field B0Turning in the same direction for 90 degrees;
step 5, applying small-angle radio frequency pulses, and collecting free attenuation signals in an ACQ channel;
step 6, waiting time taThen, repeatedly applying small-angle radio frequency pulses, and repeatedly acquiring free attenuation signals in an ACQ channel;
step 7, changing the intensity values of two gradient pulses in the GRD channel, and repeating the steps 4-6 to respectively collect free attenuation signals generated under different pulse intensities;
and 8, processing nuclear magnetic resonance data according to the acquired free attenuation string signals.
The free attenuation signal magnetization vector matrix obtained in the step 7 is as follows:
M(g,nta,mts)＝∫∫∫K1K2K3F(D,T1,Δχ)dD·dT1·dΔχ
wherein g is the gradient value of static magnetic field, n is the number of 180 DEG pulses, taFor latency, m is the FID collection point number, tsFID acquisition Point time Interval, F (D, T)1Δ χ) is the three-dimensional D-T of the sample being measured1- Δ χ characteristic matrix, T1The longitudinal relaxation time, D is the self-diffusion coefficient of the measured sample, Delta chi is the difference of the magnetic coefficients of the measured sample and the internal filling fluid, and K1，K2，K3Is a specific form of three kernel functions:
K1＝exp(-Dγ2g2δ2(Δ-δ/3))
K2＝exp(-nta/T1)
K3＝exp(-γ·Δχ·B0·mts)
by varying the pulse gradient strength g, T in D editing1And acquiring three-dimensional data by using the number n of small-angle pulses in editing and the number m of acquisition points in delta x editing. Inverting the three-dimensional data by adopting a rapid three-dimensional data processing algorithm, and obtaining the three-dimensional D-T of the measured sample by selecting a proper regularization factor1- Δ χ distribution information. The method specifically comprises the following steps:
2.1 taking the product of the mathematical tensors to carry out the matrix function K on the first two kernels1And K2Coupled as a new kernel function matrix K12：
Figure BDA0001841758960000041
2.2, the measured echo train signal magnetization vector matrix is expressed again as:
M＝K12FK3
2.3 for the kernel function matrix K12And K3SVD decomposition and singular value interception are carried out, further compression processing is carried out on the collected data, and singular value decomposition is carried out on the kernel function matrix to obtain:
K12＝U12·S12·V′12
K3＝U3·S3·V3′
wherein S12And S3The diagonal element values are arranged from large to small and are diagonal matrixes with the sizes of s12×s12And s3×s3Wherein s is12Is K12Number of non-zero singular values, s3Is K3The number of non-zero singular values; u shape12、V12And U3、V3Is an orthogonal unit array; for diagonal matrix S12And S3Intercepting is carried out, so that the condition number of the kernel function matrix meets a set value C, namely:
Figure BDA0001841758960000042
assume C is 1000;
Figure BDA0001841758960000043
and
Figure BDA0001841758960000044
respectively correspond to K12And K3Maximum singular value, i.e. diagonal matrix S12And S3The first diagonal element of (a) is,
Figure BDA0001841758960000045
represents K12The (i) th singular value of (a),
Figure BDA0001841758960000046
represents K3The jth singular value of (a);
2.4: and compressing the echo string signal magnetization vector matrix M by using the intercepted singular value decomposed identity matrix to reduce the data memory, wherein the compressed magnetization vector is as follows:
Figure BDA0001841758960000047
Figure BDA0001841758960000048
Figure BDA0001841758960000049
wherein the content of the first and second substances,
Figure BDA00018417589600000410
for the matrix of the compressed magnetization vectors,
Figure BDA00018417589600000411
as two kernel functions K12And K3Residual matrix, U 'after SVD decomposition and singular value interception'12、V′12Are each K12Matrix U after SVD decomposition and singular value interception12、V12Transpose of (V)3Is' K3Matrix V after SVD decomposition and singular value interception3Transposing;
2.5: after data compression is completed, inverting the data matrix by adopting a Tikhonov regularization method, wherein the regularization item is as follows:
Figure BDA0001841758960000051
wherein, alpha is a regularization factor and is related to the signal-to-noise ratio of the acquired data, K is a general form of a kernel matrix in the inversion process, and the term of | · | | represents the Frobenius norm of the matrix;
2.6: obtaining a final solution f by selecting an optimal regularization factor alpharThe solving formula is as follows:
Figure BDA0001841758960000052
wherein the content of the first and second substances,
Figure BDA0001841758960000053
to compress the tensor product matrix of the truncated residual matrix,
Figure BDA0001841758960000054
is composed of
Figure BDA0001841758960000055
Transposed matrix of alphaoptFor optimal regularization factor, I is the cell matrix,
Figure BDA0001841758960000056
as a matrix of compressed magnetization vectors
Figure BDA0001841758960000057
In the form of a one-dimensional matrix of (a), wherein,
Figure BDA0001841758960000058
a third multi-dimensional nuclear magnetic resonance measurement method, the method comprising:
step 1, applying 90-degree pulse to a tested sample to enable macroscopic magnetization vector M0Turning for 90 degrees;
step 2, after waiting for the time T, the system applies a second 90-degree pulse to the measured sample to recover a certain amount of magnetization vector along the static magnetic field B0Turning again in the same direction by 90 degrees;
step 3, applying a gradient pulse with the duration delta to the GRD channel;
step 4, followed by applying a 180 RF pulse at the TRS channel, a second gradient of duration δ is applied at the GRD channel. The gradient pulse starting time in the step is different from the gradient pulse starting time in the step 2 by delta time;
step 5, waiting for T in the whole systemEAfter the time of/2, applying 180 DEG radio frequency pulse to the tested sample, and waiting for the same time TEAfter the/2, acquiring and generating a spin echo signal in an ACQ channel;
step 6, repeatedly applying 180-degree radio frequency pulses, collecting and generating a plurality of repeated spin echo signals in an ACQ channel, namely echo train signals, and recording echo train signal peak values;
step 7, changing the intensity values of two gradient pulses in the GRD channel, and repeating the steps 4-6 to respectively collect echo train signal peak values generated under different pulse intensities;
step 8, changing the waiting time tau, and repeating the step 7 to respectively collect peak values of echo string signals generated under different waiting times;
and 9, processing nuclear magnetic resonance data according to the acquired free attenuation string signals.
The magnetization vector matrix of the peak value of the echo train signal obtained in the step 8 is as follows:
M(τ,g,nTE)＝∫∫∫K1K2K3F(T1,D,T2)dT1·dD·dT2
wherein tau is waiting time, g is static magnetic field gradient value, n is 180 degree pulse number, TEFor echo spacing, F (T)1,D,T2) Three-dimensional T for a sample to be measured1-D-T2Characteristic matrix, T1For longitudinal relaxation time, T2Transverse relaxation time, D is self-diffusion coefficient of the measured sample, K1，K2，K3Is a specific form of three kernel functions:
Figure BDA0001841758960000061
Figure BDA0001841758960000062
Figure BDA0001841758960000063
where γ is the gyromagnetic ratio of protons, g is the pulse gradient field gradient strength value, and δ is the single pulse gradient duration. By varying T1Editing time τ, pulse gradient strength g and T in D editing2The number n of 180 ° pulses in the editing acquires three-dimensional data. Inverting the three-dimensional data by adopting a rapid three-dimensional data processing algorithm, and obtaining the three-dimensional T of the tested sample by selecting a proper regularization factor1-D-T2And distributing the information. The method specifically comprises the following steps:
2.1 taking the product of the mathematical tensors to carry out the matrix function K on the first two kernels1And K2Coupled as a new kernel function matrix K12：
Figure BDA0001841758960000064
2.2, the measured echo train signal magnetization vector matrix is expressed again as:
M＝K12FK3
2.3 for the kernel function matrix K12And K3SVD decomposition and singular value interception are carried out, further compression processing is carried out on the collected data, and singular value decomposition is carried out on the kernel function matrix to obtain:
K12＝U12·S12·V′12
K3＝U3·S3·V3′
wherein S12And S3The diagonal element values are arranged from large to small and are diagonal matrixes with the sizes of s12×s12And s3×s3Wherein s is12Is K12Number of non-zero singular values, s3Is K3The number of non-zero singular values; u shape12、V12And U3、V3Is an orthogonal unit array; for diagonal matrix S12And S3Intercepting is carried out, so that the condition number of the kernel function matrix meets a set value C, namely:
Figure BDA0001841758960000065
assume C is 1000;
Figure BDA0001841758960000066
and
Figure BDA0001841758960000067
respectively correspond to K12And K3Maximum singular value, i.e. diagonal matrix S12And S3The first diagonal element of (a) is,
Figure BDA0001841758960000068
represents K12The (i) th singular value of (a),
Figure BDA0001841758960000069
represents K3The jth singular value of (a);
and 2.4, compressing the echo string signal magnetization vector matrix M by using the intercepted singular value decomposed unit matrix, and reducing the data memory, wherein the compressed magnetization vector is as follows:
Figure BDA00018417589600000610
Figure BDA00018417589600000611
Figure BDA00018417589600000612
wherein the content of the first and second substances,
Figure BDA00018417589600000613
for the matrix of the compressed magnetization vectors,
Figure BDA00018417589600000614
as two kernel functions K12And K3Residual matrix, U 'after SVD decomposition and singular value interception'12、V′12Are each K12Matrix U after SVD decomposition and singular value interception12、V12Transpose of (V)3Is' K3Matrix V after SVD decomposition and singular value interception3Transposing;
2.5, after data compression is completed, inverting the data matrix by adopting a Tikhonov regularization method, wherein the regularization item is as follows:
Figure BDA0001841758960000071
wherein, alpha is a regularization factor and is related to the signal-to-noise ratio of the acquired data, K is a general form of a kernel matrix in the inversion process, and the term of | · | | represents the Frobenius norm of the matrix;
2.6, obtaining a final solution f by selecting an optimal regularization factor alpharSolving the formula asThe following:
Figure BDA0001841758960000072
wherein the content of the first and second substances,
Figure BDA0001841758960000073
to compress the tensor product matrix of the truncated residual matrix,
Figure BDA0001841758960000074
is composed of
Figure BDA0001841758960000075
Transposed matrix of alphaoptFor optimal regularization factor, I is the cell matrix,
Figure BDA0001841758960000076
as a matrix of compressed magnetization vectors
Figure BDA0001841758960000077
In the form of a one-dimensional matrix of (a), wherein,
Figure BDA0001841758960000078
compared with conventional one-dimensional nuclear magnetic resonance measurement, the multi-dimensional nuclear magnetic resonance measurement can provide richer relaxation and diffusion distribution information, so that the multi-dimensional nuclear magnetic resonance measurement is widely applied to multiple fields. The multidimensional nuclear magnetic resonance technology can be used for detecting the pore structure of a pore medium, identifying different types of fluids and determining saturation information of existing fluids.
Drawings
FIG. 1 is a pulse sequence diagram of a nuclear magnetic resonance measurement method according to an embodiment of the present invention;
FIG. 2 is a pulse sequence diagram of a second NMR measurement method according to an embodiment of the invention;
FIG. 3 is a pulse sequence chart of a three-NMR measurement method according to an embodiment of the invention;
FIG. 4 is a flowchart illustrating inversion of four-process multi-dimensional NMR data according to an embodiment of the invention.
Wherein, TRS represents a pulse emission channel of a nuclear magnetic resonance system, ACQ represents a signal receiving channel of the nuclear magnetic resonance system, and GRD channel represents a gradient pulse emission channel.
Detailed Description
The embodiments of the invention are described in conjunction with the drawings. It should be noted that the description of the embodiments is provided to help understanding of the present invention, but the present invention is not limited thereto.
First, definitions of related art terms and their physical meanings referred to in the present invention will be described as follows.
Static magnetic field B0. The static magnetic field is provided by a magnet and determines the signal-to-noise ratio of the nuclear magnetic resonance signal. The sample to be measured is placed in a static magnetic field, energy level splitting occurs in a spinning system, and a macroscopic magnetization vector M is generated along the direction of the static magnetic field0。M0From static magnetic field strength B0Temperature, etc.
Radio frequency magnetic field B1And radio frequency pulses. The radio frequency pulses are electromagnetic signals, typically generated by a coil. The magnetic field generated by the radio frequency pulse is a radio frequency magnetic field. The direction of the radio frequency magnetic field is vertical to the direction of the static magnetic field, so that the wrenching operation of the magnetization vector formed in the static magnetic field is realized, and the wrenching angle is as follows: theta ═ gamma B1tp. Wherein B is1Is the RF magnetic field strength, tpThe duration of the radio frequency pulse. Therefore, the purpose of changing the pulling angle can be achieved by controlling the amplitude or the duration of the radio frequency pulse. The nuclear magnetic resonance pulse sequence is composed of radio frequency pulses with different numbers and frequency attributes according to a set time sequence. The relaxation, diffusion and other measurements of the spin system are realized by adjusting the time interval between pulses, the pulse angle and the frequency selectivity of the pulses.
A magnetic field gradient. The magnetic field gradient can record the average diffusion displacement of the molecule along the gradient direction in a certain time, thereby calculating the self-diffusion coefficient of the molecule. The method is used as an effective self-diffusion coefficient measurement and is applied to the fields of fluid type identification, sample calibration and the like. Pulsed magnetic field gradients are generated by gradient coils, usually taking into account the eddy current effects of the pulsed gradient coils and the radio frequency coil during application, taking care of the shielding effect.
Spin echo. Spin echo is one of the most common signals for nuclear magnetic resonance measurements. Firstly, a 90-degree pulse is applied to a sample to be measured, and a magnetization vector M is applied0Is switched to a transverse plane perpendicular to the direction of the static magnetic field. The magnetization vector M is due to the diffusion of molecules and the spatial non-uniformity of the static magnetic field0Phase dispersion occurs. And if the signal acquisition channel is opened to acquire the signal in the period of time, obtaining a free attenuation signal. After a certain time τ, a 180 pulse is applied. The magnetization vector after dephasing can realize reunion after the same time tau, and an echo signal is formed. The echo signal is referred to as a spin echo signal. Spin echo has three main aspects in nuclear magnetic resonance applications: (1) the echo train signal is recorded by applying a series of 180 ° pulses, which are CPMG pulse sequences, to repeatedly form spin echoes. The signal is extremely important for researching the transverse relaxation property of the pore medium, and the pore size related information can be obtained under a certain condition; (2) recording the change of the amplitude of the spin cycle wave by changing the gradient amplitude or the gradient duration under the gradient magnetic field, so as to obtain the self-diffusion coefficient of the fluid molecules; (3) and analyzing the spatial spin density information of the tested sample by applying paired frequency coding or phase coding gradients to realize the nuclear magnetic resonance imaging.
And (6) relaxation. The process of the spin system returning from the resonance state to the thermal equilibrium state. The process is based on the longitudinal relaxation time T in different directions1Or transverse relaxation time T2And (5) characterizing. T is1Also known as spin-lattice relaxation time, reflects the energy exchange of the spin system with the external environment. T is2Also known as spin-spin relaxation time, reflects the energy loss inside the spin system. The spin system relaxation process can be described by the Bloch equation. Longitudinal relaxation time T1Measurements can be made using a saturation recovery pulse sequence. By changing the time interval tau between two pulses, the signal amplitude is recorded, and the evolution process of the longitudinal magnetization vector under different editing times is reflected：
Figure BDA0001841758960000081
Transverse relaxation time T2The measurement of (2) is performed by a CPMG pulse sequence. And (3) transmitting a spin echo train pulse sequence, observing the amplitude attenuation of the spin echo train, and reflecting the evolution process of the longitudinal magnetization vector along with time:
Figure BDA0001841758960000082
where n is the number of echoes acquired, TEIs the echo spacing.
Self-diffusion coefficient D. Reflecting how fast the molecules diffuse. Since the diffusion process of the molecules is random motion, the diffusion propagation function or diffusion probability density after a certain time follows gaussian distribution. When the molecule diffuses in the gradient magnetic field, the change of the signal in a certain time is related to the average diffusion displacement of the molecule, and the self-diffusion coefficient of the molecule can be calculated by the law. Measurement of diffusion coefficients is typically achieved using pulsed or static magnetic field gradients. Taking the spin echo pulse sequence as an example, the influence of the gradient on the magnetization vector phase in a specific time is calculated by integration. The change rule of the magnetization vector along with the pulse parameters is as follows:
Figure BDA0001841758960000083
wherein gamma is the gyromagnetic ratio of proton, 2 pi is 42.58MHz/T, g is the static magnetic field gradient value, delta is the interval of pulse gradient pair, delta is the single pulse gradient duration. Therefore, by measuring the decay rate of the magnetization vector in the presence of a magnetic field gradient, the relaxation and diffusion characteristics of the fluid molecules in the free state can be obtained.
The magnetic susceptibility χ. The susceptibility reflects the effect of the material itself on the static magnetic field distribution. The FID signal of the pore medium reflects that the magnetization vector in the pore is subjected to relaxation and magnetic fieldThe non-uniformity affects the decay process, the decay rate is 1/T2 *This is obtained from the following equation:
Figure BDA0001841758960000091
relaxation by standard water sample pair T2And external magnetostatic field inhomogeneity γ Δ B0After calibration, the difference Δ χ between the magnetic susceptibility of the sample to be measured and the internal filling fluid can be obtained. When the magnetic susceptibility of the fluid is known, the magnetic susceptibility of the solid framework material can be obtained.
The pulse sequence of the multi-dimensional nuclear magnetic resonance technology consists of a plurality of editing windows, and multi-dimensional nuclear magnetic resonance data are acquired by changing editing parameters of the windows. The attenuation law of the multi-dimensional nuclear magnetic resonance data is determined by a nuclear matrix. The kernel function is usually an exponential function, and represents the change rule of the magnetization vector in different dimensions. The distribution function of the multidimensional nuclear magnetic resonance characteristics can be obtained by processing the acquired data.
Example one
According to the measurement of the longitudinal relaxation time T of the measured sample1Transverse relaxation time T2And a magnetic susceptibility χ parameter rule of the solid skeleton, and designing a nuclear magnetic resonance pulse sequence shown in figure 1 as follows:
step 1, applying 90-degree pulse to a tested sample to enable macroscopic magnetization vector M to be subjected to measurement0Turning for 90 degrees;
step 2, after waiting for the time T, the system applies a second 90-degree pulse to the measured sample to recover a certain amount of magnetization vector along the static magnetic field B0Turning again in the same direction by 90 degrees;
step 3, waiting for T in the whole systemEAfter the time of/2, applying 180 DEG radio frequency pulse to the tested sample, and waiting for the same time TEAfter the/2, acquiring and generating a spin echo signal in an ACQ channel;
step 4, repeatedly applying 180-degree radio frequency pulses, and collecting and generating a plurality of repeated spin echo signals in an ACQ channel, wherein the signals are called echo train signals;
step 5, changing the waiting time tau, and repeating the steps 2, 3 and 4 to respectively collect echo strings generated under a plurality of different waiting times tau;
and 6, processing nuclear magnetic resonance data according to the acquired echo train signals.
By collecting the signal, the following response equation can be obtained:
M(τ,nTE,mts)＝∫∫∫K1K2K3F(T1,T2,Δχ)dT1·dT2·dΔχ
three kernel functions K1，K2，K3The concrete form of (A) is as follows:
K1＝1-exp(-τ/T1)
K2＝exp(-nTE/T2)
K3＝exp(-γ·Δχ·B0·mts)
by varying T1Edit time τ, T2The number n of 180-degree pulses in editing and the number m of acquisition points in delta x editing are used for acquiring three-dimensional data. Inverting the three-dimensional data by adopting a rapid three-dimensional data processing algorithm, and obtaining the three-dimensional T of the tested sample by selecting a proper regularization factor1-T2- Δ χ distribution information.
Example two
Based on the first embodiment, the self-diffusion coefficient D and the longitudinal relaxation time T of the measured sample are measured1And a magnetic susceptibility χ parameter rule of the solid framework, and designing a nuclear magnetic resonance pulse sequence shown in figure 2, wherein the nuclear magnetic resonance pulse sequence specifically comprises the following steps:
step 1, applying 90-degree pulse to a tested sample in a TRS channel to enable macroscopic magnetization vector M to be subjected to measurement0Turning for 90 degrees;
step 2, applying a gradient pulse with the duration delta to the GRD channel;
step 3, followed by applying a 180 RF pulse at the TRS channel, applies a second gradient of duration δ at the GRD channel. The gradient pulse starting time in the step is different from the gradient pulse starting time in the step 2 by delta time;
step 4, after the whole system waits for the time when the interval of the first two radio frequency pulses is equal, applying 90-degree radio frequency pulses to the sample to be measured, and enabling a certain amount of magnetization vectors to be perpendicular to the static magnetic field B0Turning in the same direction for 90 degrees;
step 5, applying small-angle radio frequency pulses, and collecting free attenuation signals in an ACQ channel;
step 6, waiting time taThen, repeatedly applying small-angle radio frequency pulses, and repeatedly acquiring free attenuation signals in an ACQ channel;
step 7, changing the intensity values of two gradient pulses in the GRD channel, and repeating the steps 4, 5 and 6 to respectively collect free attenuation signals generated under different pulse intensities;
and 8, processing nuclear magnetic resonance data according to the acquired free attenuation string signals.
By collecting the signal, the following response equation can be obtained:
M(g,nta,mts)＝∫∫∫K1K2K3F(D,T1,Δχ)dD·dT1·dΔχ
three kernel functions K1，K2，K3The concrete form of (A) is as follows:
K1＝exp(-Dγ2g2δ2(Δ-δ/3))
K2＝exp(-nta/T1)
K3＝exp(-γ·Δχ·B0·mts)
by varying the pulse gradient strength g, T in D editing1And acquiring three-dimensional data by using the number n of small-angle pulses in editing and the number m of acquisition points in delta x editing. Inverting the three-dimensional data by adopting a rapid three-dimensional data processing algorithm, and obtaining the three-dimensional D-T of the measured sample by selecting a proper regularization factor1- Δ χ distribution information.
EXAMPLE III
Based on the above embodiment, the longitudinal relaxation time T of the tested sample is measured1Self diffusion coefficientD and transverse relaxation time T2The nuclear magnetic resonance pulse sequence shown in fig. 3 is designed according to the parameter rule, and specifically comprises the following steps:
step 1, applying 90-degree pulse to a tested sample to enable macroscopic magnetization vector M to be subjected to measurement0Turning for 90 degrees;
step 2, after waiting for the time T, the system applies a second 90-degree pulse to the measured sample to recover a certain amount of magnetization vector along the static magnetic field B0Turning again in the same direction by 90 degrees;
step 3, applying a gradient pulse with the duration delta to the GRD channel;
step 4, followed by applying a 180 RF pulse at the TRS channel, a second gradient of duration δ is applied at the GRD channel. The gradient pulse starting time in the step is different from the gradient pulse starting time in the step 2 by delta time;
step 5, waiting for T in the whole systemEAfter the time of/2, applying 180 DEG radio frequency pulse to the tested sample, and waiting for the same time TEAfter the/2, acquiring and generating a spin echo signal in an ACQ channel;
step 6, repeatedly applying 180-degree radio frequency pulses, collecting and generating a plurality of repeated spin echo signals in an ACQ channel, wherein the spin echo signals are called echo string signals, and recording the peak values of the echo string signals;
step 7, changing the intensity values of two gradient pulses in the GRD channel, and repeating the steps 4-6 to respectively collect echo train signal peaks generated under different pulse intensities;
step 8, changing the waiting time tau, and repeating the step 7 to respectively collect the echo string signal peak values generated under different waiting times;
and 9, processing nuclear magnetic resonance data according to the acquired free attenuation string signals.
By collecting the signal, the following response equation can be obtained:
M(τ,g,nTE)＝∫∫∫K1K2K3F(T1,D,T2)dT1·dD·dT2
three kernel functions K1，K2，K3The concrete form of (A) is as follows:
Figure BDA0001841758960000111
Figure BDA0001841758960000112
Figure BDA0001841758960000113
wherein gamma is the gyromagnetic ratio of proton, and g is the gradient strength value of the pulse gradient field. By varying T1Editing time τ, pulse gradient strength g and T in D editing2The number n of 180 ° pulses in the editing acquires three-dimensional data. Inverting the three-dimensional data by adopting a rapid three-dimensional data processing algorithm, and obtaining the three-dimensional T of the tested sample by selecting a proper regularization factor1-D-T2And distributing the information.
Example four
On the basis of the first to third embodiments, the multi-dimensional nuclear magnetic resonance data obtained in the above embodiments are processed. The proposed processing algorithm for multi-dimensional nmr data is explained with reference to fig. 4:
step 1: using the product of the mathematical tensors to carry out the first two kernel matrix functions K1And K2Coupled as a new kernel function matrix K12：
Figure BDA0001841758960000114
Step 2: the measured three-dimensional nuclear magnetic resonance data is re-expressed as:
M＝K12FK3
and step 3: and performing SVD decomposition and singular value interception on the two obtained kernel function matrixes, and further compressing the acquired data. Before data compression, the ill-conditioned degree of the nuclear magnetic resonance data inversion process is analyzed. The degree of matrix morbidity is related to the singular values. The data decays rapidly to zero, as do the diagonal elements in the singular value matrix of the kernel function matrix. If all singular values are still considered in the inversion process, the condition number of the whole kernel function matrix is very large, and the severity of inversion problem ill-conditioned is high. Therefore, the singular value is intercepted by setting the required condition number, and the ill-conditioned degree of the kernel function is reduced. Singular value decomposition is performed on the kernel function matrix to obtain:
K12＝U12·S12·V′12
K3＝U3·S3·V3′
wherein S12And S3The diagonal element values are arranged from large to small and are diagonal matrixes with the sizes of s12×s12And s3×s3. Wherein s is12Is K12Number of non-zero singular values, s3Is K3Number of non-zero singular values. U shape12，V12And U3，V3Is an orthogonal unit array. For diagonal matrix S12And S3Intercepting is carried out, so that the condition number of the kernel function matrix meets a set value C, namely:
Figure BDA0001841758960000121
assume C is 1000;
Figure BDA0001841758960000122
and
Figure BDA0001841758960000123
respectively correspond to K12And K3Maximum singular value, i.e. diagonal matrix S12And S3The first diagonal element of (a) is,
Figure BDA0001841758960000124
represents K12The (i) th singular value of (a),
Figure BDA0001841758960000125
represents K3The jth singular value of (a);
and 4, step 4: and compressing the actually measured data by using the intercepted singular value decomposed identity matrix, thereby reducing the data memory. Because the unit matrix is adopted, the compressed data is compared with the original data, and no information is lost. The compressed magnetization vector is:
Figure BDA0001841758960000126
Figure BDA0001841758960000127
Figure BDA0001841758960000128
and 5: after data compression is completed, a regularization item is introduced to invert the data matrix. In order to obtain a stable and accurate solution F, a Tikhonov regularization method is generally adopted, and a regularization term is introduced to obtain a nuclear magnetic resonance characteristic matrix F by measuring an obtained nuclear magnetic resonance data matrix M:
Figure BDA0001841758960000129
wherein α is a regularization factor, and is related to the signal-to-noise ratio of the acquired data, the term of | · | | | represents the Frobenius norm of the matrix, and K represents the law of nuclear magnetic resonance signal attenuation, that is, the general form of the kernel matrix in the inversion process. The introduced regularization term determines the stability and accuracy of the solution result. The regularization factor is selected too large, and although the distribution obtained by solving is more stable, the accuracy of the solution is poorer, namely, the solution is over-smooth; if the regularization factor is selected to be too small, the solution is more accurate to obtain, but the stability of the solution is reduced, and the more pseudo signals appear, namely the solution is not smooth. Therefore, it is the focus of the method to use a reasonable regularization factor, taking into account the authenticity of the solution and the stability of the solution. Through the non-negative constraint step, a non-negative constraint solution f under a specific regularization factor alpha can be obtained, and the obtained solution obtains the residual distribution of the solution result and the measurement result through the following formula:
χ(α)＝||M-K·f(α)||2
the generally optimal regularization factor α is selected as
Figure BDA0001841758960000131
Step 6: obtaining the final solution f by obtaining the optimal regularization factor alpharThe solving formula is as follows:
Figure BDA0001841758960000132
wherein the content of the first and second substances,
Figure BDA0001841758960000133
compressing a tensor product matrix of the intercepted residual matrix;
Figure BDA0001841758960000134
tensor product matrix for compressing truncated residual matrix
Figure BDA0001841758960000135
I is a cell matrix.
Figure BDA0001841758960000136
As a matrix of compressed magnetization vectors
Figure BDA0001841758960000137
In the form of a one-dimensional matrix.
The multidimensional nuclear magnetic resonance data processing algorithm provided by the invention has the advantages that the data are processed according to the size of the kernel function, the matrix information is effectively utilized, the inversion difficulty of high-dimensional data is simplified, and the inversion speed is ensured.
As described above, the present invention can be preferably realized. Variations, modifications, substitutions, integrations and variations of these embodiments may be made without departing from the principle and spirit of the invention, and still fall within the scope of the invention.

Claims (4)

1. A multi-dimensional nmr measurement method for analyzing material pore structure and internal fill fluid characteristics, comprising:
(1) designing a multi-dimensional nuclear magnetic resonance pulse sequence and acquiring multi-dimensional nuclear magnetic resonance data;
(2) inverting and interpreting the multi-dimensional nuclear magnetic resonance data; wherein the content of the first and second substances,
the step (1) comprises the following steps:
1.1 applying 90 deg. radio frequency pulse to tested sample in TRS channel to make macroscopic magnetization vector M0Turning for 90 degrees;
1.2, applying a gradient pulse with the duration delta to the GRD channel;
1.3, subsequently applying a 180 ° rf pulse on the TRS channel, applying a second gradient pulse of duration δ on the GRD channel, wherein the gradient pulse start time in step 1.3 differs from the gradient pulse start in step 1.2 by a Δ time;
1.4, after waiting the same time interval between the first two radio-frequency pulses, applying 90-degree radio-frequency pulses to the tested sample to make a certain amount of magnetization vector from the vertical static magnetic field B0Turning in the same direction for 90 degrees;
1.5, applying small-angle radio frequency pulse, and collecting a free attenuation signal in an ACQ channel;
1.6, waiting time taThen, repeatedly applying small-angle radio frequency pulses, and repeatedly acquiring free attenuation signals in an ACQ channel;
1.7, changing the intensity value of two gradient pulses in the GRD channel, and repeating the steps 1.4-1.6 to respectively collect free attenuation signals generated under different pulse intensities.
2. The method of claim 1, wherein the free decay signal magnetization vector matrix obtained in step 1.7 is:
M(g，nta，mts)＝∫∫∫K1K2K3F(D，T1，Δχ)dD·dT1·dΔχ
wherein g is the gradient value of static magnetic field, n is the number of 180 DEG pulses, taFor latency, m is the FID collection point number, tsFID acquisition Point time Interval, F (D, T)1Δ χ) is the three-dimensional D-T of the sample being measured1- Δ χ characteristic matrix, T1The longitudinal relaxation time, D is the self-diffusion coefficient of the measured sample, Delta chi is the difference of the magnetic coefficients of the measured sample and the internal filling fluid, and K1，K2，K3Is a specific form of three kernel functions:
K1＝exp(-Dγ2g2δ2(Δ-δ/3))
K2＝exp(-nta/T1)
K3＝exp(-γ·Δχ ·B0·mts)
wherein gamma is the magnetic rotation ratio of proton, B0The static magnetic field strength.
3. The multi-dimensional nmr measurement method of claim 1, wherein step (2) uses a fast three-dimensional data processing algorithm to invert the multi-dimensional nmr data.
4. The method according to claim 2, wherein the step (2) is specifically:
2.1 taking the product of the mathematical tensors to carry out the matrix function K on the first two kernels1And K2Coupled as a new kernel function matrix K12：
Figure FDA0003117530540000021
2.2, the measured echo train signal magnetization vector matrix is expressed again as:
M＝K12FK3
2.3 for the kernel function matrix K12And K3SVD decomposition and singular value interception are carried out, further compression processing is carried out on the collected data, and singular value decomposition is carried out on the kernel function matrix to obtain:
K12＝U12·S12·V′12
K3＝U3·S3·V′3
wherein S12And S3The diagonal element values are arranged from large to small and are diagonal matrixes with the sizes of s12×s12And s3×s3Wherein s is12Is K12Number of non-zero singular values, s3Is K3The number of non-zero singular values; u shape12、V12And U3、V3Is an orthogonal unit array; for diagonal matrix S12And S3Intercepting is carried out, so that the condition number of the kernel function matrix meets a set value C, namely:
Figure FDA0003117530540000022
assume C is 1000;
Figure FDA0003117530540000023
and
Figure FDA0003117530540000024
respectively correspond to K12And K3Maximum singular value, i.e. diagonal matrix S12And S3The first diagonal element of (a) is,
Figure FDA0003117530540000025
represents K12The (i) th singular value of (a),
Figure FDA0003117530540000026
represents K3The jth singular value of (a);
2.4: and compressing the echo string signal magnetization vector matrix M by using the intercepted singular value decomposed identity matrix to reduce the data memory, wherein the compressed magnetization vector is as follows:
Figure FDA0003117530540000027
Figure FDA0003117530540000028
Figure FDA0003117530540000029
wherein the content of the first and second substances,
Figure FDA00031175305400000210
for the matrix of the compressed magnetization vectors,
Figure FDA00031175305400000211
as two kernel functions K12And K3Residual matrix, U 'after SVD decomposition and singular value interception'12、V′12Are each K12Matrix U after SVD decomposition and singular value interception12、V12Transpose of, V'3Is K3Matrix V after SVD decomposition and singular value interception3Transposing;
2.5: after data compression is completed, inverting the data matrix by adopting a Tikhonov regularization method, wherein the regularization item is as follows:
Figure FDA0003117530540000031
wherein, alpha is a regularization factor and is related to the signal-to-noise ratio of the acquired data, K is a general form of a kernel matrix in the inversion process, and the term of | · | | represents the Frobenius norm of the matrix;
2.6: obtaining a final solution f by selecting an optimal regularization factor alpharThe solving formula is as follows:
Figure FDA0003117530540000032
wherein the content of the first and second substances,
Figure FDA0003117530540000033
to compress the tensor product matrix of the truncated residual matrix,
Figure FDA0003117530540000034
is composed of
Figure FDA0003117530540000035
Transposed matrix of alphaoptFor optimal regularization factor, I is the cell matrix,
Figure FDA0003117530540000036
as a matrix of compressed magnetization vectors
Figure FDA0003117530540000037
In the form of a one-dimensional matrix of (a), wherein,
Figure FDA0003117530540000038
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