CN109270107A - Multi-dimensional nmr measurement method - Google Patents
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Abstract
The invention proposes a kind of analysis methods that the multi-dimensional nmr data for material tests are acquired and handled.This method is suitable for the magnetic resonance detection instrument under the configuration of different field strength differences.This method is related to a variety of nuclear magnetic resonance pulse sequences, by carrying out corresponding data processing to obtained three-dimensional data structure body, it can analyze to obtain the porosity of detection material, pore structure, be full of the important parameters such as type of fluid, skeleton susceptibility and heterogeneity.
Description
It is on March 27th, 2017 that the present invention, which is the Chinese applying date, application No. is 2017101862466, entitled " multidimensional core
The divisional application of magnetic resonance measurement method ".
Technical field
The present invention relates to the realization process of nuclear magnetic resonance field more particularly to a kind of multi-dimensional nmr measurement method and its
The process of data processing.
Technical background
Nuclear magnetic resonance technique is as a kind of advanced lossless detection means, in medicine, the energy, material, agricultural, food, peace
The multiple fields such as full monitoring, chemical industry have extremely wide application.The common characterisitic parameter of nuclear magnetic resonance includes longitudinal relaxation
Time T1, lateral relaxation time T2, the diffusion coefficient D or solid bone of molecule can be quickly obtained additionally by nuclear magnetic resonance technique
The susceptibility χ of frame.It, can be in multiple dimensions by editing corresponding characteristic nmr in the different time sections of pulse train
Upper these characteristic nmrs of association.Hole medium character can comprehensively be studied, be obtained more by these TIME CORRELATION EXPERIMENTSs
Add information abundant.Nmr Relaxation Properties are applied to the pore structure of detection pore media, pore communication, hole sky
Between structure composition；Diffusion coefficient be used to understand the internal component etc. for being full of type of fluid and crude oil.Therefore pass through spatial nuclei
Mr techniques can be in higher dimension to the molecule of the pore-size of pore media, internal field gradient and complex fluid
Composition carries out comprehensive study.
NMR relaxation or diffusion response in pore media meet multi-exponential decay rule.It is obtained by measurement result inverting
It is an ill-conditioning problem to interstitial space relaxation or diffusion profile.The solution of the refutation process is not unique, and small in measurement result
Disturbance solving result will be affected greatly.By introducing regularization term in solution procedure, refutation process is carried out
Stablize processing.The data volume of three-dimensional NMR is big, carries out inverting according to one-dimensional data roadmap and takes a long time.By to core
Function carries out tensor product after compressing respectively, carries out singular value decomposition to obtained new kernel function, interception meets setting condition number
Singular value, while using interception after orthogonal matrices three-dimensional data is compressed, accelerate inversion speed.
Summary of the invention
The purpose of the present invention is illustrate three kinds of multidimensional cores for being used for analysis of material pore structure and internal fill fluid characteristic
Magnetic resonance measurement method, and corresponding multi-dimensional nmr flow chart of data processing.
The first multi-dimensional nmr measurement method, which comprises
Step 1 applies 90 ° of radio-frequency pulses for the macroscopic magnetization strength vector M to sample090 ° of switching；
After step 2, waiting time τ, apply second 90 ° of pulse to sample, a certain amount of magnetization arrow will be restored
Amount is from along magnetostatic field B0Identical direction 90 ° of switching again；
Step 3 is waiting TEAfter/2 time, apply 180 ° of radio-frequency pulses, identical waiting time to sample
TEAfter/2, it can be acquired in the channel ACQ and generate spin echo signal；
Step 4 repeats to apply 180 ° of radio-frequency pulses, can acquire generation in the channel ACQ and repeat multiple spin echo signals, obtain
To echo string signal；
Step 5 changes waiting time τ, and repeating said steps 2-4 is generated under several different waiting time τ with acquiring respectively
Echo string signal；
Step 6 carries out nuclear magnetic resonance data processing according to the collected echo string signal.
Wherein, echo string signal magnetization vector matrix caused by step 5 are as follows:
M(τ,nTE,mts)=∫ ∫ ∫ K1K2K3F(T1,T2,Δχ)dT1·dT2·dΔχ
Wherein, τ is the waiting time, and n is 180 ° of pulse numbers, and m is FID acquisition points, tsBetween the time of the collection point FID
Every F (T1,T2, Δ x) is the three-dimensional T of sample1–T2Δ χ feature matrix, T1For longitudinal relaxation time, T2For transverse relaxation
Time, Δ χ are the susceptibility difference of sample and internal fill fluid, K1, K2, K3For three kernel functions, concrete form
Are as follows:
K1=1-exp (- τ/T1)
K2=exp (- nTE/T2)
K3=exp (- γ Δ χ B0·mts)
Wherein, γ is the gyromagnetic ratio of proton, B0For static magnetic field strength.
The step 6 is led to specifically, using quick three-dimensional data processing algorithm to the progress inverting of multi-dimensional nmr data
It crosses and chooses suitable regularization factors, obtain the three-dimensional T of sample1–T2Δ chi square distribution information.Specifically:
Step 1: using mathematics tensor product by the first two nuclear matrix function K1And K2It is coupled as a new kernel matrix
K12:
Step 2: the three-dimensional NMR data that measurement obtains are re-expressed as:
M=K12FK3
Step 3: to above-mentioned kernel matrix K12And K3Carry out SVD decomposition and singular value interception, and then to acquisition data into
Row compression processing, carrying out singular value decomposition to kernel matrix can obtain:
K12=U12·S12·V′12
K3=U3·S3·V3′
Wherein S12And S3Diagonal entry value arranges from big to small, and is diagonal matrix, and size is respectively s12×s12And s3
×s3, wherein s12For K12Non-zero singular value number, s3For K3Non-zero singular value number；U12、V12And U3、V3For Orthogonal Units battle array；
To diagonal matrix S12And S3It is intercepted, so that the conditional number of kernel matrix meets setting value C, it may be assumed that
Assuming that C is 1000；WithRespectively correspond K12And K3Maximum singular value, i.e. diagonal matrix S12And S3?
One diagonal entry,Indicate K12I-th of singular value,Indicate K3J-th of singular value；
Step 4: echo string signal magnetization vector matrix M being pressed with the unit matrix of the singular value decomposition after interception
Contracting reduces datarams, compressed magnetization vector are as follows:
Wherein,For compressed magnetization vector matrix,For two kernel function K12And K3It is decomposed by SVD and odd
Remaining matrix after different value interception, U '12、V′12Respectively K12Matrix U after SVD is decomposed and singular value intercepts12、V12's
Transposition, V3' it is K3Matrix V after SVD is decomposed and singular value intercepts3Transposition；
Step 5: after data compression is completed, inverting being carried out to data matrix using Tikhonov regularization method, wherein
Regularization term are as follows:
Wherein, α is regularization factors, related to the acquisition signal-to-noise ratio of data, and K is the general of the nuclear matrix in refutation process
Form, | | | | item represents the Frobenius norm of matrix；
Step 6: by choosing optimal regularization factors α, obtaining last solution fr, solution formula is as follows:
Wherein,The tensor product matrix of remaining matrix after being intercepted for compression,ForTransposed matrix, αoptFor it is optimal just
Then changing the factor, I is cell matrix,For compressed magnetization vector matrixOne-dimensional matrix form, wherein
Second of multi-dimensional nmr measurement method, which comprises
Step 1 applies 90 ° of radio-frequency pulses for the macroscopic magnetization strength vector M to sample in the channel TRS0Switching
90°；
Step 2 applies the gradient pulse that a duration is δ in the channel GRD；
Step 3, then after the channel TRS applies 180 ° of radio-frequency pulses, applying second duration in the channel GRD is δ
Gradient pulse.Gradient pulse initial time in this step differs delta time with the gradient pulse starting in step 2；
Step 4, after the time that whole system waits the first two radio-frequency pulse interval equal, to sample apply 90 °
Radio-frequency pulse, by a certain amount of magnetization vector from vertical magnetostatic field B090 ° of identical direction switching；
Step 5 applies small-angle radio frequency pulse, acquires free damping signal in the channel ACQ；
Step 6, waiting time taAfterwards, it repeats to apply small-angle radio frequency pulse, it can be in the channel ACQ repeated acquisition to freely declining
Cut signal；
Step 7, change the channel GRD in two gradient pulses intensity value, repeating said steps 4-6 to acquire not respectively
With the free damping signal generated under pulse strength；
Step 8 carries out nuclear magnetic resonance data processing according to the collected free damping string signal.
The free damping signal magnetization vector matrix that the step 7 obtains are as follows:
M(g,nta,mts)=∫ ∫ ∫ K1K2K3F(D,T1,Δχ)dD·dT1·dΔχ
Wherein, g is magnetostatic field gradient value, and n is 180 ° of pulse numbers, taFor the waiting time, m is FID acquisition points, tsFor
The collection point FID time interval, F (D, T1, Δ χ) be sample three-dimensional D-T1Δ χ feature matrix, T1When for longitudinal relaxation
Between, D is sample self-diffusion coefficient, and Δ χ is the susceptibility difference of sample and internal fill fluid, K1, K2, K3For
Three kernel functions, concrete form are as follows:
K1=exp (- D γ2g2δ2(Δ-δ/3))
K2=exp (- nta/T1)
K3=exp (- γ Δ χ B0·mts)
By change D edit in pulsed gradient intensity g, T1Low-angle pulse number n and Δ χ in editor are edited
In acquisition points m obtain three-dimensional data.Inverting is carried out to it using quick three-dimensional data processing algorithm, it is suitable by choosing
Regularization factors obtain the three-dimensional D-T of sample1Δ chi square distribution information.Specifically:
2.1, using mathematics tensor product by the first two nuclear matrix function K1And K2It is coupled as a new kernel matrix
K12:
2.2, the echo string signal magnetization vector matrix that measurement obtains is re-expressed as:
M=K12FK3
2.3, to above-mentioned kernel matrix K12And K3SVD decomposition and singular value interception are carried out, and then acquisition data are carried out
Compression processing, carrying out singular value decomposition to kernel matrix can obtain:
K12=U12·S12·V′12
K3=U3·S3·V3′
Wherein S12And S3Diagonal entry value arranges from big to small, and is diagonal matrix, and size is respectively s12×s12And s3
×s3, wherein s12For K12Non-zero singular value number, s3For K3Non-zero singular value number；U12、V12And U3、V3For Orthogonal Units battle array；
To diagonal matrix S12And S3It is intercepted, so that the conditional number of kernel matrix meets setting value C, it may be assumed that
Assuming that C is 1000；WithRespectively correspond K12And K3Maximum singular value, i.e. diagonal matrix S12And S3's
First diagonal entry,Indicate K12I-th of singular value,Indicate K3J-th of singular value；
2.4: echo string signal magnetization vector matrix M being pressed with the unit matrix of the singular value decomposition after interception
Contracting reduces datarams, compressed magnetization vector are as follows:
Wherein,For compressed magnetization vector matrix,For two kernel function K12And K3It is decomposed by SVD and odd
Remaining matrix after different value interception, U '12、V′12Respectively K12Matrix U after SVD is decomposed and singular value intercepts12、V12's
Transposition, V3' it is K3Matrix V after SVD is decomposed and singular value intercepts3Transposition；
2.5: after data compression is completed, inverting being carried out to data matrix using Tikhonov regularization method, wherein just
Then change item are as follows:
Wherein, α is regularization factors, related to the acquisition signal-to-noise ratio of data, and K is the general of the nuclear matrix in refutation process
Form, | | | | item represents the Frobenius norm of matrix；
2.6: by choosing optimal regularization factors α, obtaining last solution fr, solution formula is as follows:
Wherein,The tensor product matrix of remaining matrix after being intercepted for compression,ForTransposed matrix, αoptFor it is optimal just
Then changing the factor, I is cell matrix,For compressed magnetization vector matrixOne-dimensional matrix form, wherein
The third multi-dimensional nmr measurement method, which comprises
Step 1 applies 90 ° of pulses for macroscopic magnetization strength vector M to sample090 ° of switching；
After step 2, waiting time τ, system applies second 90 ° of pulse to sample, will restore a certain amount of magnetic
Change vector from along magnetostatic field B0Identical direction 90 ° of switching again；
Step 3 applies the gradient pulse that a duration is δ in the channel GRD；
Step 4, then after the channel TRS applies 180 ° of radio-frequency pulses, applying second duration in the channel GRD is δ
Gradient.Gradient pulse initial time in this step differs delta time with the gradient pulse starting in step 2；
Step 5 waits T in whole systemEAfter/2 time, apply 180 ° of radio-frequency pulses to sample, it is identical
Waiting time TEAfter/2, it can be acquired in the channel ACQ and generate spin echo signal；
Step 6 repeats to apply 180 ° of radio-frequency pulses, can acquire generation in the channel ACQ and repeat multiple spin echo signals, claim
Be echo string signal, record echo signal peaks value；
Step 7, change the channel GRD in two gradient pulses intensity value, repeating said steps 4-6 to acquire not respectively
With the echo signal peaks value generated under pulse strength；
Step 8 changes waiting time τ, and repeating said steps 7 to acquire the echo generated under the different waiting time respectively
Signal peaks value；
Step 9 carries out nuclear magnetic resonance data processing according to the collected free damping string signal.
The echo signal peaks value magnetization vector matrix that step 8 obtains are as follows:
M(τ,g,nTE)=∫ ∫ ∫ K1K2K3F(T1,D,T2)dT1·dD·dT2
Wherein, τ is the waiting time, and g is magnetostatic field gradient value, and n is 180 ° of pulse numbers, TEFor echo sounding, F (T1,D,
T2) be sample three-dimensional T1-D-T2Feature matrix, T1For longitudinal relaxation time, T2For lateral relaxation time, D is detected sample
Product self-diffusion coefficient, K1, K2, K3For three kernel functions, concrete form are as follows:
Wherein γ is the gyromagnetic ratio of proton, and g is pulsed field gradient gradient intensity value, and δ is single pulse gradient duration.
By changing T1Edit session τ, D edit in pulsed gradient intensity g and T2180 ° of pulse number n in editor obtain three dimensions
According to.Inverting is carried out to it using quick three-dimensional data processing algorithm, by choosing suitable regularization factors, obtains sample
Three-dimensional T1-D-T2Distributed intelligence.Specifically:
2.1, using mathematics tensor product by the first two nuclear matrix function K1And K2It is coupled as a new kernel matrix
K12:
2.2, the echo string signal magnetization vector matrix that measurement obtains is re-expressed as:
M=K12FK3
2.3, to above-mentioned kernel matrix K12And K3SVD decomposition and singular value interception are carried out, and then acquisition data are carried out
Compression processing, carrying out singular value decomposition to kernel matrix can obtain:
K12=U12·S12·V′12
K3=U3·S3·V3′
Wherein S12And S3Diagonal entry value arranges from big to small, and is diagonal matrix, and size is respectively s12×s12And s3
×s3, wherein s12For K12Non-zero singular value number, s3For K3Non-zero singular value number；U12、V12And U3、V3For Orthogonal Units battle array；
To diagonal matrix S12And S3It is intercepted, so that the conditional number of kernel matrix meets setting value C, it may be assumed that
Assuming that C is 1000；WithRespectively correspond K12And K3Maximum singular value, i.e. diagonal matrix S12And S3's
First diagonal entry,Indicate K12I-th of singular value,Indicate K3J-th of singular value；
2.4, echo string signal magnetization vector matrix M is pressed with the unit matrix of the singular value decomposition after interception
Contracting reduces datarams, compressed magnetization vector are as follows:
Wherein,For compressed magnetization vector matrix,For two kernel function K12And K3It is decomposed by SVD and odd
Remaining matrix after different value interception, U '12、V′12Respectively K12Matrix U after SVD is decomposed and singular value intercepts12、V12's
Transposition, V3' it is K3Matrix V after SVD is decomposed and singular value intercepts3Transposition；
2.5, after data compression is completed, inverting is carried out to data matrix using Tikhonov regularization method, wherein just
Then change item are as follows:
Wherein, α is regularization factors, related to the acquisition signal-to-noise ratio of data, and K is the general of the nuclear matrix in refutation process
Form, | | | | item represents the Frobenius norm of matrix；
2.6, by choosing optimal regularization factors α, last solution f is obtainedr, solution formula is as follows:
Wherein,The tensor product matrix of remaining matrix after being intercepted for compression,ForTransposed matrix, αoptFor it is optimal just
Then changing the factor, I is cell matrix,For compressed magnetization vector matrixOne-dimensional matrix form, wherein
It is measured compared to conventional one-dimensional nuclear magnetic resonance, the multi-dimensional nmr of the application is measured due to being capable of providing more
Relaxation and diffusion profile information abundant, thus be widely used in multiple fields.Multi-dimensional nmr technology can
For detecting the pore structure of pore media, identifying different types of fluid and determining the saturation infromation of preservation fluid.
Detailed description of the invention
Fig. 1 is the pulse sequence diagram of one nuclear magnetic resonance measuring method of the embodiment of the present invention；
Fig. 2 is the pulse sequence diagram of two nuclear magnetic resonance measuring method of the embodiment of the present invention；
Fig. 3 is the pulse sequence diagram of three nuclear magnetic resonance measuring method of the embodiment of the present invention；
Fig. 4 is the inversion process figure that the embodiment of the present invention four handles multi-dimensional nmr data.
Wherein, TRS represents the impulse ejection channel of NMR system, and the signal that ACQ represents NMR system receives
Channel, the channel GRD represent gradient pulse transmission channel.
Specific embodiment
Illustrate a specific embodiment of the invention in conjunction with Figure of description.It should be noted that for these implementations
The explanation of example mode is used to help understand the present invention, but and does not constitute a limitation of the invention.
Following introduction is done in definition and its physical significance first to relevant technical terms involved in the present invention.
Magnetostatic field B0.Magnetostatic field is provided by magnet, determines the signal-to-noise ratio of NMR signal.Sample is placed in magnetostatic field
In, energy level splitting occurs in spin system, a macroscopic magnetization vector M can be generated along magnetostatic field direction0。M0By magnetostatic field strength
Spend B0, the decision of the parameters such as temperature.
RF magnetic field B1With radio-frequency pulse.Radio-frequency pulse is electromagnetic signal, is usually generated by coil.What radio-frequency pulse generated
Magnetic field is RF magnetic field.The direction of RF magnetic field is vertical with magnetostatic field direction, realizes to the magnetization vector formed in magnetostatic field
Switching operation, switching angle are as follows: θ=γ B1tp.Wherein B1For RF magnetic field intensity, tpFor the duration of radio-frequency pulse.Cause
This can achieve the purpose that change switching angle by the amplitude or duration for controlling radio-frequency pulse.Nuclear magnetic resonance pulse sequence is not by
With the radio-frequency pulse of quantity and frequency attribute according to setting timing composition.By adjusting inter-pulse time interval, pulse angle and
The frequency selectivity of pulse is realized and is measured relaxation, diffusion of spin system etc..
Magnetic field gradient.Magnetic field gradient can recorde molecule in certain time and be displaced along gradient direction average diffusion, thus
Calculate the self-diffusion coefficient of molecule.The method is measured as a kind of effective self-diffusion coefficient, is applied to type of fluid and is identified
And the fields such as sample calibration.Pulsed magnetic field gradients are generated by gradient coil, and pulsed gradient coil is usually considered during application
With the eddy current effect of radio-frequency coil, shield effectiveness is paid attention to.
Spin echo.Spin echo is Nuclear Magnetic Resonance Measurement one of the most common type signal.90 ° are applied to sample first
Pulse, by magnetization vector M0Switching is to perpendicular on the transverse plane of magnetostatic field direction.Diffusion and magnetostatic field due to molecule
The reasons such as spatial heterogeneity, magnetization vector M0Dephasing occurs.If this period of time opening signal acquisition channel to signal into
Row acquisition, obtains free damping signal.After undergoing certain time τ, apply 180 ° of pulses.Magnetization vector after dephasing can be same
Reunion is realized after equal times τ, forms an echo-signal.Change echo-signal and is referred to as spin echo signal.Spin echo exists
Mainly there are following three aspects in nuclear magnetic resonance application: (1) by applying a series of 180 ° of pulses, being concatenated to form from cycle
Wave, records echo string signal, this pulse train is CPMG pulse sequence.The signal is special for the transverse relaxation for studying pore media
Property is particularly important, under certain condition available pore-size relevant information；(2) by changing gradient width under gradient magnetic
Value or gradient duration record the variation of spin echo amplitude, the self-diffusion coefficient of available fluid molecule；(3) pass through
The frequency coding or phase encoding gradient being applied to pair parse the spatial spin density information of sample, realize nuclear magnetic resonance
Imaging.
Relaxation.Spin system restores from resonance state to the process of thermal equilibrium state.The process is in different directions by indulging
To relaxation time T1Or lateral relaxation time T2Characterization.T1Also known as spin-lattice relaxation time, reflection spin system and outside
The energy exchange of environment.T2Also known as spin spin relaxation time reflects spin system internal energy loss.Spin system relaxes
Henan process can be described by Bloch equation.Longitudinal relaxation time T1Saturation recovery pulse train can be used to measure.Pass through
Change the time interval τ between two pulses, tracer signal amplitude reflects longitudinal magnetization vector drilling under different edit sessions
Change process:
Lateral relaxation time T2Measurement completed by CPMG pulse sequence.Emit spin echo series impulse sequence, observes
The amplitude attenuation of spin echo string, the evolutionary process of reflection longitudinal magnetization vector at any time:
Wherein n is the echo number of acquisition, TEFor echo sounding.
Self-diffusion coefficient D.Reflect the diffusion speed degree of molecule.Since the diffusion process of molecule is random motion, one
Diffusive transport function or spreading probability density after fixing time meet Gaussian Profile.When molecule is spread in gradient magnetic,
The change of signal is related with the average diffusion displacement of molecule in certain time, and expanding certainly for molecule can be calculated by this rule
Dissipate coefficient.It generallys use pulsed magnetic field gradients or magnetostatic field gradient realizes the measurement of diffusion coefficient.With self-rotary echo-pulse series
For, utilize influence of the integral calculation gradient in specific time to magnetization vector phase.Magnetization vector with pulse parameter change
Law are as follows:
Wherein, γ is the gyromagnetic ratio of proton, and 2 π × 42.58MHz/T, g are magnetostatic field gradient value, and Δ is pulsed gradient pair
Interval, δ are single pulse gradient duration.Therefore, the attenuation rate by measurement magnetization vector in the presence of magnetic field gradient, can
To obtain fluid molecule relaxation in a free state and diffusion characteristic.
Susceptibility χ.Susceptibility reflects influence situation of the material to distribution of static magnetic field itself.The FID of pore media believes
Number reflection is that magnetization vector by relaxation and magnetic field non-uniformity is influenced attenuation process, attenuation rate 1/T in hole2 *By following formula
It can obtain:
By standard water sample to relaxation T2And external static magnetic field heterogeneity γ Δ B0After being demarcated, so that it may obtain by
The susceptibility discrepancy delta χ of sample and internal fill fluid.After the susceptibility of known fluid, solid skeletal can be acquired
The susceptibility of material.
The pulse train of multi-dimensional nmr technology is made of several editors, and the editor by changing several windows joins
Number, collects multi-dimensional nmr data.Multi-dimensional nmr data attenuation law is determined by nuclear matrix.Kernel function is usually
Exponential function characterizes changing rule of the magnetization vector on different dimensions.By carrying out data processing to acquisition data, can obtain
To the distribution function of multi-dimensional nmr characteristic.
Embodiment one
According to measurement sample longitudinal relaxation time T1, lateral relaxation time T2With the susceptibility χ-parameter of solid skeletal
Rule designs nuclear magnetic resonance pulse sequence as shown in Figure 1, specific as follows:
Step 1 applies 90 ° of pulses for the macroscopic magnetization strength vector M to sample090 ° of switching；
After step 2, waiting time τ, system applies second 90 ° of pulse to sample, will restore a certain amount of magnetic
Change vector from along magnetostatic field B0Identical direction 90 ° of switching again；
Step 3 waits T in whole systemEAfter/2 time, apply 180 ° of radio-frequency pulses to sample, it is identical
Waiting time TEAfter/2, it can be acquired in the channel ACQ and generate spin echo signal；
Step 4 repeats to apply 180 ° of radio-frequency pulses, can acquire generation in the channel ACQ and repeat multiple spin echo signals, claim
Be echo string signal；
Step 5 changes waiting time τ, and repeating said steps 2,3 and 4 are produced under several different waiting time τ with acquiring respectively
Raw echo；
Step 6 carries out nuclear magnetic resonance data processing according to the collected echo string signal.
Following response formula can be obtained by acquiring signal:
M(τ,nTE,mts)=∫ ∫ ∫ K1K2K3F(T1,T2,Δχ)dT1·dT2·dΔχ
Three kernel function K1, K2, K3Concrete form are as follows:
K1=1-exp (- τ/T1)
K2=exp (- nTE/T2)
K3=exp (- γ Δ χ B0·mts)
By changing T1Edit session τ, T2180 ° of pulse number n and Δ χ in editor edit in acquisition points m obtain
Take three-dimensional data.Inverting is carried out to it using quick three-dimensional data processing algorithm, by choosing suitable regularization factors, is obtained
The three-dimensional T of sample1-T2Δ chi square distribution information.
Embodiment two
On the basis of example 1, according to measurement sample self-diffusion coefficient D, longitudinal relaxation time T1And solid bone
The susceptibility χ-parameter rule of frame, designs nuclear magnetic resonance pulse sequence as shown in Figure 2, specifically:
Step 1 applies 90 ° of pulses for the macroscopic magnetization strength vector M to sample in the channel TRS090 ° of switching；
Step 2 applies the gradient pulse that a duration is δ in the channel GRD；
Step 3, then after the channel TRS applies 180 ° of radio-frequency pulses, applying second duration in the channel GRD is δ
Gradient.Gradient pulse initial time in this step differs delta time with the gradient pulse starting in step 2；
Step 4, after the time that whole system waits the first two radio-frequency pulse interval equal, to sample apply 90 °
Radio-frequency pulse, by a certain amount of magnetization vector from vertical magnetostatic field B090 ° of identical direction switching；
Step 5 applies small-angle radio frequency pulse, acquires free damping signal in the channel ACQ；
Step 6, waiting time taAfterwards, it repeats to apply small-angle radio frequency pulse, it can be in the channel ACQ repeated acquisition to freely declining
Cut signal；
Step 7, change the channel GRD in two gradient pulses intensity value, repeating said steps 4,5 and 6 to adopt respectively
Collect the free damping signal generated under different pulse strengties；
Step 8 carries out nuclear magnetic resonance data processing according to the collected free damping string signal.
Following response formula can be obtained by acquiring signal:
M(g,nta,mts)=∫ ∫ ∫ K1K2K3F(D,T1,Δχ)dD·dT1·dΔχ
Three kernel function K1, K2, K3Concrete form are as follows:
K1=exp (- D γ2g2δ2(Δ-δ/3))
K2=exp (- nta/T1)
K3=exp (- γ Δ χ B0·mts)
By change D edit in pulsed gradient intensity g, T1Low-angle pulse number n and Δ χ in editor are edited
In acquisition points m obtain three-dimensional data.Inverting is carried out to it using quick three-dimensional data processing algorithm, it is suitable by choosing
Regularization factors obtain the three-dimensional D-T of sample1Δ chi square distribution information.
Embodiment three
On the basis of the above embodiments, according to measurement sample longitudinal relaxation time T1, self-diffusion coefficient D and transverse direction
Relaxation time T2Parameter regularity designs nuclear magnetic resonance pulse sequence as shown in Figure 3, specific as follows:
Step 1 applies 90 ° of pulses for the macroscopic magnetization strength vector M to sample090 ° of switching；
After step 2, waiting time τ, system applies second 90 ° of pulse to sample, will restore a certain amount of magnetic
Change vector from along magnetostatic field B0Identical direction 90 ° of switching again；
Step 3 applies the gradient pulse that a duration is δ in the channel GRD；
Step 4, then after the channel TRS applies 180 ° of radio-frequency pulses, applying second duration in the channel GRD is δ
Gradient.Gradient pulse initial time in this step differs delta time with the gradient pulse starting in step 2；
Step 5 waits T in whole systemEAfter/2 time, apply 180 ° of radio-frequency pulses to sample, it is identical
Waiting time TEAfter/2, it can be acquired in the channel ACQ and generate spin echo signal；
Step 6 repeats to apply 180 ° of radio-frequency pulses, can acquire generation in the channel ACQ and repeat multiple spin echo signals, claim
Be echo string signal, record echo string signal kurtosis；
Step 7, change the channel GRD in two gradient pulses intensity value, repeating said steps 4-6 to acquire not respectively
With the echo signal peak generated under pulse strength；
Step 8 changes waiting time τ, and repeating said steps 7 to acquire the echo generated under the different waiting time respectively
Signal peak；
Step 9 carries out nuclear magnetic resonance data processing according to the collected free damping string signal.
Following response formula can be obtained by acquiring signal:
M(τ,g,nTE)=∫ ∫ ∫ K1K2K3F(T1,D,T2)dT1·dD·dT2
Three kernel function K1, K2, K3Concrete form are as follows:
Wherein γ is the gyromagnetic ratio of proton, and g is pulsed field gradient gradient intensity value.By changing T1Edit session τ, D volume
Pulsed gradient intensity g and T in volume2180 ° of pulse number n in editor obtain three-dimensional data.Using quick three-dimensional data processing
Algorithm carries out inverting to it, by choosing suitable regularization factors, obtains the three-dimensional T of sample1-D-T2Distributed intelligence.
Example IV
On the basis of embodiment one arrives embodiment three, the obtained multi-dimensional nmr data of above-described embodiment are carried out
Processing.It is illustrated in conjunction with Processing Algorithm of the Fig. 4 to the multi-dimensional nmr data of proposition:
Step 1: using mathematics tensor product by the first two nuclear matrix function K1And K2It is coupled as a new kernel matrix
K12:
Step 2: the three-dimensional NMR data that measurement obtains are re-expressed as:
M=K12FK3
Step 3: SVD decomposition is carried out to obtained two kernel matrixes and singular value intercepts, and then to acquisition data into
Row compression processing.Before carrying out data compression, first the Degree of Ill Condition of nuclear magnetic resonance data refutation process is analyzed.Matrix
Degree of Ill Condition is related with singular value.Data rapidly decay to zero, and the diagonal element in the singular value matrix of kernel matrix is also fast
Speed decays to zero.If still considering whole singular values in refutation process, the conditional number of entire kernel matrix can be very
Greatly, cause the severity of inversion problem morbid state higher.Therefore singular value is intercepted using the conditional number that setting needs, reduces core letter
Several Degree of Ill Condition.Carrying out singular value decomposition to kernel matrix can obtain:
K12=U12·S12·V′12
K3=U3·S3·V3′
Wherein S12And S3Diagonal entry value arranges from big to small, and is diagonal matrix, and size is respectively s12×s12And s3
×s3.Wherein s12For K12Non-zero singular value number, s3For K3Non-zero singular value number.U12, V12And U3, V3For Orthogonal Units battle array.
To diagonal matrix S12And S3It is intercepted, so that the conditional number of kernel matrix meets setting value C, it may be assumed that
Assuming that C is 1000；WithRespectively correspond K12And K3Maximum singular value, i.e. diagonal matrix S12And S3?
One diagonal entry,Indicate K12I-th of singular value,Indicate K3J-th of singular value；
Step 4: measured data being compressed with the unit matrix of the singular value decomposition after interception, is reduced in data
It deposits.Since using unit matrix, the data after compression are compared with initial data, information is not lost.After compression
Magnetization vector are as follows:
Step 5: after data compression is completed, introducing regularization term and inverting is carried out to data matrix.Stable standard in order to obtain
True solution f generallys use Tikhonov regularization method, introduces regularization term item come by measuring obtained nuclear magnetic resonance data
Matrix M obtains characteristic nmr matrix F:
Wherein, α is regularization factors, related to the acquisition signal-to-noise ratio of data, | | | | item represents the Frobenius of matrix
Norm, K represent the rule of NMR signal decaying, that is, the general type of the nuclear matrix in refutation process.It introduces just
Then change stability and accuracy that item determines solving result.Regularization factors selection is excessive, although it is more steady to solve obtained distribution
It is fixed, but the accuracy solved is poorer, i.e., it is so-called excessively smooth；Regularization factors selection is too small, and seeking for solution is more accurate, but solves
Stability reduce, the false signal of appearance is more, that is, owes smooth.Therefore, the stability for comprehensively considering the authenticity reconciliation of solution, makes
It is the emphasis of this method with reasonable regularization factors.By under the available specific regularization factors α of nonnegativity restrictions step
Nonnegativity restrictions solution f, obtained solution obtain the residual distribution of solving result and measurement result by following formula:
χ (α)=| | M-Kf (α) | |2
The selection standard of usually optimal regularization factors α is
Step 6: by obtaining optimal regularization factors α, obtaining last solution fr, solution formula is as follows:
Wherein,For the tensor product matrix of remaining matrix after compression interception；For remaining square after compression interception
The tensor product matrix of battle arrayTransposed matrix, I is cell matrix.For compressed magnetization vector matrixOne-dimensional rectangular
Formula.
The advantages of multi-dimensional nmr data processing algorithm proposed by the present invention be according to kernel function size to data into
Row processing, is effectively utilized matrix information, while simplifying the inverting difficulty of high dimensional data, ensure that the speed of inverting.
As described above, the present invention can be realized preferably.Without departing from the principles and spirit of the present invention to these
Embodiment is changed, modifies, replacing, integrating and modification is still fallen in protection scope of the present invention.
Claims (5)
1. a kind of multi-dimensional nmr measurement method, the method is special for analysis of material pore structure and internal fill fluid
Property, which is characterized in that the described method includes:
(1) design of multi-dimensional nmr pulse train and the acquisition of multi-dimensional nmr data；
(2) inverting and explanation are carried out to multi-dimensional nmr data.
2. a kind of multi-dimensional nmr measurement method according to claim 1, which is characterized in that the step (1) includes
Following steps:
1.1, apply 90 ° of radio-frequency pulses for macroscopic magnetization strength vector M to sample in the channel TRS090 ° of switching；
1.2, apply the gradient pulse that a duration is δ in the channel GRD；
1.3, then after the channel TRS applies 180 ° of radio-frequency pulses, apply the gradient that second duration is δ in the channel GRD
Pulse, wherein the gradient pulse initial time in step 1.3 differs delta time with the gradient pulse starting in step 1.2；
1.4, after the time for waiting the first two radio-frequency pulse interval equal, apply 90 ° of radio-frequency pulses to sample, it will be a certain amount of
Magnetization vector from vertical magnetostatic field B090 ° of identical direction switching；
1.5, apply small-angle radio frequency pulse, acquire free damping signal in the channel ACQ；
1.6, waiting time taAfterwards, it repeats to apply small-angle radio frequency pulse, it can be in the channel ACQ repeated acquisition to free damping signal；
1.7, change the intensity value of two gradient pulses in the channel GRD, repeating said steps 1.4-1.6 to acquire difference respectively
The free damping signal generated under pulse strength.
3. a kind of multi-dimensional nmr measurement method according to claim 2, which is characterized in that the step 1.7 obtains
Free damping signal magnetization vector matrix are as follows:
M(g,nta,mts)=∫ ∫ ∫ K1K2K3F(D,T1,Δχ)dD·dT1·dΔχ
Wherein, g is magnetostatic field gradient value, and n is 180 ° of pulse numbers, taFor the waiting time, m is FID acquisition points, tsIt is adopted for FID
Collection point time interval, F (D, T1, Δ χ) be sample three-dimensional D-T1Δ χ feature matrix, T1For longitudinal relaxation time, D is
Sample self-diffusion coefficient, Δ χ are the susceptibility difference of sample and internal fill fluid, K1, K2, K3For three cores
Function, concrete form are as follows:
K1=exp (- D γ2g2δ2(Δ-δ/3))
K2=exp (- nta/T1)
K3=exp (- γ Δ χ B0·mts)
Wherein, γ is the magnetic rotaion comparison of proton, B0For static magnetic field strength.
4. a kind of multi-dimensional nmr measurement method according to claim 1, which is characterized in that the step (2) uses
Quick three-dimensional data processing algorithm carries out inverting to multi-dimensional nmr data.
5. a kind of multi-dimensional nmr measurement method according to claim 3, which is characterized in that the step (2) is specific
Are as follows:
2.1, using mathematics tensor product by the first two nuclear matrix function K1And K2It is coupled as a new kernel matrix K12:
2.2, the echo string signal magnetization vector matrix that measurement obtains is re-expressed as:
M=K12FK3
2.3, to above-mentioned kernel matrix K12And K3SVD decomposition and singular value interception are carried out, and then acquisition data are compressed
Processing, carrying out singular value decomposition to kernel matrix can obtain:
K12=U12·S12·V′12
K3=U3·S3·V′3
Wherein S12And S3Diagonal entry value arranges from big to small, and is diagonal matrix, and size is respectively s12×s12And s3×s3,
Wherein s12For K12Non-zero singular value number, s3For K3Non-zero singular value number；U12、V12And U3、V3For Orthogonal Units battle array；To diagonal
Matrix S12And S3It is intercepted, so that the conditional number of kernel matrix meets setting value C, it may be assumed that
Assuming that C is 1000；WithRespectively correspond K12And K3Maximum singular value, i.e. diagonal matrix S12And S3First
Diagonal entry,Indicate K12I-th of singular value,Indicate K3J-th of singular value；
2.4: echo string signal magnetization vector matrix M being compressed with the unit matrix of the singular value decomposition after interception, is dropped
Low datarams, compressed magnetization vector are as follows:
Wherein,For compressed magnetization vector matrix,For two kernel function K12And K3By SVD decomposition and singular value
Remaining matrix after interception, U '12、V′12Respectively K12Matrix U after SVD is decomposed and singular value intercepts12、V12Transposition,
V′3For K3Matrix V after SVD is decomposed and singular value intercepts3Transposition；
2.5: after data compression is completed, inverting being carried out to data matrix using Tikhonov regularization method, wherein regularization
Are as follows:
Wherein, α is regularization factors, related to the acquisition signal-to-noise ratio of data, and K is the general shape of the nuclear matrix in refutation process
Formula, | | | | item represents the Frobenius norm of matrix；
2.6: by choosing optimal regularization factors α, obtaining last solution fr, solution formula is as follows:
Wherein,The tensor product matrix of remaining matrix after being intercepted for compression,ForTransposed matrix, αoptFor optimal regularization
The factor, I are cell matrixs,For compressed magnetization vector matrixOne-dimensional matrix form, wherein
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