CN105842642A - Fractional anisotropy microstructure characteristic extraction method based on kurtosis tensor and apparatus thereof - Google Patents

Abstract

The invention relates to the image processing and medical instrument technology field and provides a burgeoning parameter extraction method of biological tissue anisotropy detection, wherein the method is used for clinic application. An analysis method of reconstructing and quantizing a clear, refine and highly-stable biological-tissue microcosmic anisotropy characteristic and a correlation apparatus are obtained. In a technical scheme used in the invention, based on the kurtosis-tensor fractional anisotropy microstructure characteristic extraction method, a subject collects multiple b value diffusion weight images of tissues along a plurality of diffusion sensitivity gradient directions on a magnetic resonance scanner; after the diffusion weight images are preprocessed, in an individual space, a second-order diffusion tensor and a fourth-order kurtosis tensor matrix reflecting a water molecule diffusion distribution probability density function characteristic in the tissues are acquired through fitting; through matrix operation, the corresponding fractional anisotropy FA and kurtosis tensor fractional anisotropy KTFA are acquired; and combining a characteristic parameter, a nerve fiber microstructure characteristic is acquired. The method and the apparatus are mainly used in medical equipment designing and manufacturing.

Description

Based on kurtosis tensor mark anisotropic microstructure feature extracting method and device

Technical field

The present invention relates to image procossing, technical field of medical instruments, specifically, relate to based on kurtosis tensor mark respectively to different Property microstructure features extracting method and device.

Background technology

Cerebral white matter is to be assembled by the nerve fiber of turnover cerebral hemisphere and contact brain both sides hemisphere and formed, in it The nerve tract of various difference in functionality is contained in portion.Therefore, brain white matter nerve fiber is the important medium of information transmission and coding, control Making neuron signal to share, coordinate the properly functioning of communication for information between brain district, there is pathological changes or will be serious by infringement in it Big brain cognitive function is hindered to grow or cause functional deterioration and pathological changes.White matter fiber integrity deteriorate relevant presenile dementia, Depression, schizophrenia and with the alzheimer's disease with neurofibrillary tangles as main pathological basis, to affect brain white The cranial nerve diseases such as the cerebral tumor of matter normal outcome distribution are all relevant to the close structure of cerebral white matter.

At present, the method that can nondestructively carry out brain white matter nerve fiber reconstruction is mostly based on diffusion mark anisotropy (factional anisotropy, FA) parameter.FA is the biological tissue being commonly used to quantify to be obtained by diffusion magnetic resonance data The parameter index of microstructure features.But, although kinetics of diffusion has an obvious dependence of angle, but FA even disappears can diminish Lose in some position, at decussating fibers.Additionally, FA is affected greatly by volume effect, also include as close in orientational dispersion and neurite The interference to FA value of degree.Accordingly, it would be desirable to consider that other are used for weighing the index that diffusion anisotropy stability is stronger.

Diffusion kurtosis imaging (diffusion kurtosis imaging, DKI) is at the base of traditional diffusion tensor imaging Introduce quadravalence kurtosis on plinth, by the diffusion-weighted signals collecting in multiple directions, obtain the diffusion profile of the interior hydrone of tissue Situation, and then the microcosmos structure characteristic that postgraduate's fabric texture is the finest.Along with DKI proposes, domestic and international researcher has pointed out one The series measurement anisotropic index of water diffusion based on kurtosis tensor, but a lot of index comes from integrating diffusion tensor Information obtains, and not yet makes up the as above defect of FA.

Summary of the invention

For overcoming the deficiencies in the prior art, it is contemplated that propose a kind of emerging detection biology group for clinical practice Knit anisotropic parameter extracting method.Be can get by the mark anisotropic parameters index extracted based on high-order kurtosis tensor Rebuild and quantify biological tissue microscopic anisotropy feature clearly, refine and the strong analysis method of stability, and relevant apparatus. The technical solution used in the present invention is, based on kurtosis tensor mark anisotropic microstructure feature extracting method, passes through experimenter Magnetic resonance scanner gathers the tissue many b value diffusion weighted images along multiple diffusion sensitising gradient directions, by diffusion-weighted After Image semantic classification, in individual space matching obtain reflection tissue in water diffusion distribution probability density function feature two Rank diffusion tensor and quadravalence kurtosis tensor matrix, obtain corresponding mark anisotropy FA by matrix operations and kurtosis tensor divide Number anisotropy KTFA, in conjunction with characteristic parameter, it is thus achieved that nerve fiber microstructure features.

Diffusion weighted magnetic resonance images collection uses 3.0T magnetic resonance scanner and 32 channel head coils, and acquisition sequence is to make Single-shot spin echo-echo planar imaging sequence (SE-EPI, the single shot read with Echo-plane imaging (EPI) Spin echo-echo planar imaging), diffusion-weighted signal correction experiment acquisition parameter: repetition time TR (repetition time)=10500ms, echo time TE (echo time)=103ms, partial Fourier transform 75%, depending on Open country is 256 × 256mm², it is thus achieved that image array is 128 × 128, and thickness is 2mm, full brain gather 73 layers, interlayer continuously every；Diffusion Sensitive factor b value selects b=1000s/mm²And b=2000s/mm², have the diffusion-weighted of 30 gradient directions, simultaneously volume respectively An outer b=0 of collection without diffusion-weighted benchmark image, obtaining a size is the matrix data of 128 × 128 × 73 × 61 Collection, acquisition time is about 8 points 40 seconds, and signal noise ratio (snr) of image is 2.03.

Diffusion weighted images pretreatment comprises the concrete steps that, all tested diffusion weighted magnetic resonance images need advanced wardrobe to move Artifact checks, if being wherein translating beyond 1mm or rotating over the image of 4 ° by disallowable, should not carry out follow-up tensor estimation； Then, use the dtiInit module in mrDiffusion tool kit that data carry out eddy current correction and head dynamic(al) correction operation, with BET module in Shi Yunyong FSL software carries out shelling brain；By the image obtained before entering tensor and estimating, gaussian kernel is used to smooth Process, and full width at half maximum value is gather image voxel 1.25～1.5 times.

Tensor is estimated, the gradient pulse resonance gradient magnetic field strength using standard is g, Pulse duration is the calibration pulse gradient fields of the time interval Δ at δ and diffusion-sensitive gradient pulses center, is spread In kurtosis imaging model, diffusion kurtosis with the prevailing relationship of diffusion signal is,

$ln\[\frac{S\left(b\right)}{S\left(0\right)}\]=-{\mathrm{bD}}_{app}+\frac{1}{6}{b}^2{D_{app}}^2{K}_{app}$

Wherein S (b) is the signal intensity that with the addition of gradient magnetic, b=1000,2000s/mm²；S (0) is not apply diffusion The intensity of the magnetic resonance reference signal of sensitive gradient pulses；B value is the diffusion magnetic susceptibility factor；D_appIt it is the apparent expansion in certain direction Dissipate coefficient, K_appBeing the apparent diffusion kurtosis along certain direction, diffusion tensor D is the real symmetric matrix of a two-dimensional third-order, it Calculate and at least need 6 gradient directions；Diffusion kurtosis tensor K is the real symmetric matrix on the four-dimension three rank, and its calculating needs At least two non-zero b value and 15 gradient directions, for any direction, apparent diffusion coefficient and apparent diffusion kurtosis estimator Expression formula is written as,

$D\left(\hat{n}\right)={\mathrm{\Σ}}_{ij}{n}_i{n}_j{D}_{ij}$

$K\left(\hat{n}\right)=\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}{\mathrm{\Σ}}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Wherein,WithIt is respectively hydrone to existApparent diffusion coefficient on direction and apparent coefficient of kurtosis,It is Diffusion sensitising gradient direction, n_i,n_j,n_k,n_l, it isI-th or j, k, l component elements；Average diffusion coefficientWith diffusion kurtosisObtained by all directions are averaging,

$\stackrel{\‾}{D}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}D\left(\hat{n}\right)$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}K\left(\hat{n}\right)$

Order:

$W\left(\hat{n}\right)={\mathrm{\Σ}}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Then the expression formula of average kurtosis tensor is,

$\stackrel{\‾}{W}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}W\left(\hat{n}\right)$

Mark can be asked to draw by D matrix, λ_iFor matrix D eigenvalue, represent and organize the diffusion coefficient on interior three points of directions big Little, and eigenvalue of maximum correspondence direction extremely organizes the main trend of interior nerve fiber, another two eigenvalue reflection nerve fiber The characteristic of myelin,

$\stackrel{\‾}{D}=\frac{Tr\left(D\right)}{3}=\frac{{\mathrm{\λ}}_1+{\mathrm{\λ}}_2+{\mathrm{\λ}}_3}{3}$

Average kurtosis tensor is represented by,

$\stackrel{\‾}{W}=\frac{W_{1111}+W_{2222}+W_{3333}+2W_{1122}+2W_{1133}+2W_{2233}}{5}$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}W\left(\hat{n}\right)$

It isApproximation, in the two is equal and if only if tissue, water diffusion is isotropic diffusion.

FA Yu KTFA parametric estimation step, FA is defined as

$FA\≡\sqrt{\frac{3}{2}}\frac{\left|\right|D-\stackrel{\‾}{D}{I}^{\left(2\right)}|{|}_F}{\left|\right|D|{|}_F}$

Wherein,For standardized constant, the span of FA is made to be limited between 0 to 1；D is diffusion tensor, is one The two-dimensional matrix of 3 × 3；I⁽²⁾For symmetrical second-order matrix,δ_ijFor Kronecker function, i, j desirable 1,2, 3；‖…‖_FFor the F norm of matrix, kurtosis tensor mark anisotropy (KTFA), it is defined as

$KTFA=\frac{\left|\right|W-\stackrel{\‾}{W}{I}^{\left(4\right)}|{|}_F}{\left|\right|W|{|}_F}$

Wherein, W is kurtosis tensor；I⁽⁴⁾For symmetrical,δ_ij, δ_kl,δ_ik,δ_jl For Kronecker function, i, j, k, l desirable 1,2,3；‖…‖_FFor the F norm of matrix, KTFA easily by each diffusion group divide between difference The impact of the opposite sex, rather than as FA depends on the direction of each diffusion component.

Based on kurtosis tensor mark anisotropic microstructure feature deriving means, including: diffusion weighted magnetic resonance images is adopted Acquisition means, and computer；Be provided with diffusion weighted images pretreatment module in computer, tensor is estimated and characteristic extracting module.

Diffusion weighted magnetic resonance images harvester is 3.0T magnetic resonance scanner and 32 channel head coils, and acquisition sequence is Use single-shot spin echo-echo planar imaging sequence (SE-EPI, single shot that Echo-plane imaging (EPI) reads spin echo-echo planar imaging)。

Diffusion weighted images pretreatment module is used for carrying out head and moves artifact inspection, if being wherein translating beyond 1mm or rotation Image more than 4 °, by disallowable, should not carry out follow-up tensor estimation；Then, diffusion weighted images pretreatment module uses DtiInit module in mrDiffusion tool kit carries out eddy current correction and head dynamic(al) correction operation to data, uses FSL simultaneously BET module in software carries out shelling brain；By the image obtained before entering tensor and estimating, diffusion weighted images pretreatment module is adopted Use gaussian kernel smoothing processing, and full width at half maximum value is gather image voxel 1.25～1.5 times.

Tensor is estimated and characteristic extracting module, and the gradient pulse resonance gradient magnetic field strength using standard is g, arteries and veins Rush the calibration pulse gradient fields of the time interval Δ that the persistent period is δ and diffusion-sensitive gradient pulses center, obtain spreading peak In degree imaging model, diffusion kurtosis with the prevailing relationship of diffusion signal is,

$ln\[\frac{S\left(b\right)}{S\left(0\right)}\]=-{\mathrm{bD}}_{app}+\frac{1}{6}{b}^2{D_{app}}^2{K}_{app}$

Wherein S (b) is the signal intensity that with the addition of gradient magnetic, b=1000,2000s/mm²；S (0) is not apply diffusion The intensity of the magnetic resonance reference signal of sensitive gradient pulses；B value is the diffusion magnetic susceptibility factor；D_appIt it is the apparent expansion in certain direction Dissipate coefficient, K_appBeing the apparent diffusion kurtosis along certain direction, diffusion tensor D is the real symmetric matrix of a two-dimensional third-order, it Calculate and at least need 6 gradient directions；Diffusion kurtosis K is the real symmetric matrix on the four-dimension three rank, and its calculating needs at least Two non-zero b values and 15 gradient directions, for any direction, apparent diffusion coefficient and the expression of apparent diffusion kurtosis estimator Formula is written as,

$D\left(\hat{n}\right)={\mathrm{\Σ}}_{ij}{n}_i{n}_j{D}_{ij}$

$K\left(\hat{n}\right)=\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}{\mathrm{\Σ}}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Wherein,WithIt is respectively hydrone to existApparent diffusion coefficient on direction and apparent coefficient of kurtosis,Depend on It is so diffusion sensitising gradient direction, n_i,n_j,n_k,n_l, it isI-th or j, k, l component elements；Average diffusion coefficientAnd diffusion KurtosisObtained by all directions are averaging,

$\stackrel{\‾}{D}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}D\left(\hat{n}\right)$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}K\left(\hat{n}\right)$

Order:

$W\left(\hat{n}\right)={\mathrm{\Σ}}_{iikl}{n}_i{n}_i{n}_k{n}_l{W}_{ijkl}$

Then the expression formula of average kurtosis tensor is,

$\stackrel{\‾}{W}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}W\left(\hat{n}\right)$

Mark can be asked to draw by D matrix, λ_iFor matrix D eigenvalue, represent and organize the diffusion coefficient on interior three points of directions big Little, and eigenvalue of maximum correspondence direction extremely organizes the main trend of interior nerve fiber, another two eigenvalue reflection nerve fiber The characteristic of myelin,

$\stackrel{\‾}{D}=\frac{Tr\left(D\right)}{3}=\frac{{\mathrm{\λ}}_1+{\mathrm{\λ}}_2+{\mathrm{\λ}}_3}{3}$

Average kurtosis tensor is represented by,

$\stackrel{\‾}{W}=\frac{W_{1111}+W_{2222}+W_{3333}+2W_{1122}+2W_{1133}+2W_{2233}}{5}$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}W\left(\hat{n}\right)$

It isApproximation, in the two is equal and if only if tissue, water diffusion is isotropic diffusion, W₁₁₁₁, W₂₂₂₂, W₃₃₃₃, W₁₁₂₂, W₁₁₃₃, W₂₂₃₃, subscript represents this element position in kurtosis tensor matrix W.

FA Yu KTFA parameter estimation module, uses following steps to obtain FA Yu KTFA parameter: FA is defined as

$FA\≡\sqrt{\frac{3}{2}}\frac{\left|\right|D-\stackrel{\‾}{D}{I}^{\left(2\right)}|{|}_F}{\left|\right|D|{|}_F}$

Wherein,For standardized constant, the span of FA is made to be limited between 0 to 1；D is diffusion tensor, is one The two-dimensional matrix of 3 × 3；I⁽²⁾For symmetrical second-order matrix,δ_ijFor Kronecker function, i, j desirable 1,2, 3；‖…‖_FFor the F norm of matrix, kurtosis tensor mark anisotropy KTFA, it is defined as

$KTFA=\frac{\left|\right|W-\stackrel{\‾}{W}{I}^{\left(4\right)}|{|}_F}{\left|\right|W|{|}_F}$

Wherein, W is kurtosis tensor；I⁽⁴⁾For symmetrical,δ_ij,δ_kl,δ_ik,δ_jl For Kronecker function, i, j, k, l desirable 1,2,3；‖…‖_FFor the F norm of matrix, KTFA easily by each diffusion group divide between difference The impact of the opposite sex, rather than as FA depends on the direction of each diffusion component.

The feature of the present invention and providing the benefit that:

The present invention proposes a kind of mark anisotropic parameters index KTFA extracted based on high-order kurtosis tensor, it is intended to obtain Take clear and definite, the stable analysis method that can be used for rebuilding and quantifying biological tissue's microscopic anisotropy feature.Utilize this parameter, can By obtaining the obvious sign of white matter degree of degeneration based on voxel statistical analysis, the analysis of multivariate voxel, sorting algorithm etc., especially Being in neurodegenerative diseases, white matter fiber number of crossovers is the most less, and when the phenomenon that puppet increases occurs in FA, KTFA can be bright Present white matter fiber micro structure pathological changes aobviously and cause the attenuation trend of parameter index.Can be characterized increasingly complex big by KTFA The diffusing phenomenon of hydrone in brain, have in the research exploring cerebral white matter micro structure and are of great significance.Fig. 3 chooses one 27th layer and the 19th layer of KTFA and FA parametric image contrast of 22 years old normal male brain of name.By parametric image, reality can be realized Border crowd and the statistical analysis of pathology, identify, classify and explore people's brain structure of various disease or various disease pathology In the scientific research of feature.

Accompanying drawing illustrates:

Fig. 1 Technology Roadmap.

Fig. 2 nerve fiber infall KTFA and FA Property comparison.

Fig. 3 people brain KTFA and the contrast of FA parametric image.

Detailed description of the invention

The present invention proposes an emerging index kurtosis tensor mark for describing anisotropic degree respectively to different Property (kurtosis-tensor-based factional anisotropy, KTFA).This index is to utilize kurtosis to open purely The parameter index that the attributes extraction of amount obtains, is considered as FA naturally extending in diffusion tensor implication.KTFA compared to FA, The information such as water diffusion direction that is that more uniqueness can be provided and that supplement and diffusion size, thus the preferably biological group of reflection Knit the microscopic property of structure.

The present invention propose based on kurtosis tensor (kurtosis tensor, KT) extract in brain water diffusion respectively to Opposite sex degree, thus rebuild and quantify parametric image extraction and the method for analysis of biological tissue's microscopic anisotropy.Its technical flow Cheng Shi: gather tissue on magnetic resonance scanner by experimenter diffusion-weighted along many b values in multiple diffusion sensitising gradient directions Signal, after diffusion weighted images pretreatment, water diffusion distribution probability in matching obtains reflection tissue in individual space The second order diffusion tensor of density function feature and quadravalence kurtosis tensor matrix, obtain corresponding mark respectively to different by matrix operations Property FA and kurtosis tensor mark anisotropy KTFA, in conjunction with characteristic parameter, can obtain brain white matter nerve fiber microstructure features, Can also be used for exploring brain white matter integrity pathological changes external performance in neurodegenerative diseases.

Based on kurtosis mark anisotropic cerebral white matter microstructure features extracting method idiographic flow as shown in Figure 1.Whole Body flow process is: first gather the diffusion weighted magnetic resonance images of 2 b values, diffusion sensitising gradient side on magnetic resonance imaging platform It it is 30 to quantity；Then diffusion weighted images is used software carry out, and head moves, eddy current corrects；Last at tested individual space Inside carry out tensor estimation (including diffusion tensor and kurtosis tensor), after carrying out a series of mathematical operation, estimate obtain FA and KTFA parametric image, can obtain cerebral white matter microstructure features and information, and compare and be applied to research.

1 diffusion weighted magnetic resonance images collection

Diffusion weighted magnetic resonance images collection uses 3.0T magnetic resonance scanner and 32 channel head coils, and acquisition sequence is to make Single-shot spin echo-echo planar imaging sequence (SE-EPI, the single shot read with Echo-plane imaging (EPI) spin echo-echo planar imaging).Diffusion-weighted signal correction experiment acquisition parameter: repetition time TR (repetition time)=10500ms, echo time TE (ehco time)=103ms, partial Fourier transform 75%, depending on Open country is 256 × 256mm², it is thus achieved that image array is 128 × 128, and thickness is 2mm, full brain gather 73 layers, interlayer continuously every；Diffusion Sensitive factor b value selects b=1000s/mm²And b=2000s/mm², have the diffusion-weighted of 30 gradient directions, simultaneously volume respectively An outer b=0 of collection without diffusion-weighted benchmark image, obtaining a size is the matrix data of 128 × 128 × 73 × 61 Collection, acquisition time is about 8 points 40 seconds, and signal noise ratio (snr) of image is 2.03.

2 diffusion weighted images pretreatment

All tested diffusion weighted magnetic resonance images need advanced wardrobe move artifact inspection, if be wherein translating beyond 1mm or Person rotates over the image of 4 ° by disallowable, should not carry out follow-up tensor estimation.Then, use in mrDiffusion tool kit DtiInit module data are carried out eddy current correction and head dynamic(al) correction operation, use the BET module in FSL software to carry out simultaneously Stripping brain (i.e. removing other the non-brain regions beyond image deutocerebrum).By the image obtained before entering tensor and estimating, adopt By widely used gaussian kernel smoothing processing, and full width at half maximum value is gather image voxel 1.25～1.5 times.

3 tensors are estimated and feature extraction

Diffusion kurtosis imaging DKI is the new technique of a kind of non-gaussian diffusing phenomenon rebuilding hydrone, is to classical expansion Dissipate tensor imaging modelSimple extension.It is assumed that due to cell membrane and cellularity shape The diffusion being strapped in Water Proton molecule is restricted.And the non-gaussian diffusion of hydrone provides mechanics of biological tissue The information the most useful with pathobiology.The gradient pulse resonance gradient magnetic field strength of employing standard is g, and pulse is held The continuous time is the calibration pulse gradient fields of the time interval Δ at δ and diffusion-sensitive gradient pulses center, can obtain spreading kurtosis In imaging model, diffusion kurtosis with the prevailing relationship of diffusion signal is,

$ln\[\frac{S\left(b\right)}{S\left(0\right)}\]=-{\mathrm{bD}}_{app}+\frac{1}{6}{b}^2{D_{app}}^2{K}_{app}$

Wherein S (b) is signal intensity (b=1000, the 2000s/mm that with the addition of gradient magnetic²)；S (0) is not apply to expand Dissipate the intensity of the magnetic resonance reference signal of sensitive gradient pulses；B value is the diffusion magnetic susceptibility factor.D_appIt is the apparent of certain direction Diffusion coefficient, K_appBeing the apparent diffusion kurtosis along certain direction, they are for matching diffusion tensor, necessity of diffusion kurtosis Parameter.Diffusion tensor D is the real symmetric matrix of a two-dimensional third-order, and its calculating at least needs 6 gradient directions；Diffusion kurtosis Tensor K is the real symmetric matrix on the four-dimension three rank, and its calculating needs at least two non-zero b value and 15 gradient directions.Right In any direction, the expression formula of apparent diffusion coefficient and apparent diffusion kurtosis estimator can be written as,

$D\left(\hat{n}\right)={\mathrm{\Σ}}_{ij}{n}_i{n}_j{D}_{ij}$

$K\left(\hat{n}\right)=\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}{\mathrm{\Σ}}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Wherein,WithIt is respectively hydrone to existApparent diffusion coefficient on direction and apparent coefficient of kurtosis,Depend on It is so diffusion sensitising gradient direction, x_i(or j, k, l) it isI-th component elements, W is kurtosis tensor, W_ijklMiddle subscript represents This element position in a matrix, average diffusion coefficientWith diffusion kurtosisObtained by all directions are averaging,

$\stackrel{\‾}{D}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}D\left(\hat{n}\right)$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}K\left(\hat{n}\right)$

Order:

$W\left(\hat{n}\right)={\mathrm{\Σ}}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Then the expression formula of average kurtosis tensor is,

$\stackrel{\‾}{W}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}W\left(\hat{n}\right)$

For differential term, integral sign before correspondence,Mark can be asked to draw by D matrix, λ_iFor matrix D eigenvalue, represent Organize the diffusion coefficient size on interior three points of directions, and eigenvalue of maximum correspondence direction extremely organizes mainly walking of interior nerve fiber To, the characteristic of another two eigenvalue reflection Medullary sheath,

$\stackrel{\‾}{D}=\frac{Tr\left(D\right)}{3}=\frac{{\mathrm{\λ}}_1+{\mathrm{\λ}}_2+{\mathrm{\λ}}_3}{3}$

Average kurtosis tensor is represented by,

$\stackrel{\‾}{W}=\frac{W_{1111}+W_{2222}+W_{3333}+2W_{1122}+2W_{1133}+2W_{2233}}{5}$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}W\left(\hat{n}\right)$

It isApproximation, in the two is equal and if only if tissue, water diffusion is isotropic diffusion, W₁₁₁₁, W₂₂₂₂, W₃₃₃₃, W₁₁₂₂, W₁₁₃₃, W₂₂₃₃, subscript represents this element position in kurtosis tensor matrix W.

4FA Yu KTFA parameter estimation

Mark anisotropy FA is the most most common extraction from diffusion tensor matrices for weighing diffusion anisotropy Parameter index.Initially, the physical significance of FA is diffusion tensor is decomposed into anisotropy component and isotropism component, because of This, FA can be defined as

$FA\≡\sqrt{\frac{3}{2}}\frac{\left|\right|D-\stackrel{\‾}{D}{I}^{\left(2\right)}|{|}_F}{\left|\right|D|{|}_F}$

Wherein,For standardized constant, the span of FA can be made to be limited between 0 to 1；D is diffusion tensor, is one The two-dimensional matrix of individual 3 × 3；I⁽²⁾For symmetrical second-order matrix,δ_ijFor Kronecker function, i, j desirable 1,2, 3；‖…‖_FF norm for matrix.The definition of FA may be interpreted as the F norm of anisotropy component and the F norm ratio of diffusion tensor Value.In real brain, the diffusing phenomenon of hydrone are gained knowledge according to diffusion kinetics, have the spy of obvious dependence of angle Levy, but when water diffusion direction number is more than or equal to 2, FA can diminish and even disappear.Additionally, FA is by image volume effect shadow Ring bigger.In sum, the present invention propose that a kind of stability is strong, be not easily affected by environmental factors based on high-order kurtosis tensor Mark anisotropic parameters New Set kurtosis tensor mark anisotropy (KTFA), is defined as

$KTFA=\frac{\left|\right|W-\stackrel{\‾}{W}{I}^{\left(4\right)}|{|}_F}{\left|\right|W|{|}_F}$

Wherein, W is kurtosis tensor；I⁽⁴⁾For symmetrical,δ_ij,δ_kl,δ_ik,δ_jl For Kronecker function, i, j, k, l desirable 1,2,3；‖…‖_FF norm for matrix.KTFA easily by each diffusion group divide between difference The impact of the opposite sex, rather than as FA depends on the direction of each diffusion component.KTFA Yu FA is at the Character Comparison of nerve fiber infall As in figure 2 it is shown, KTFA demonstrates higher stability, i.e. along with the increase of nerve fiber intersecting angle, KTFA numerical value shows as Minor fluctuations；FA is easily affected by fiber crossovers angle, and stability is slightly worse.Fig. 3 chooses the of 22 years old normal male brain 27 layers and the contrast of the 19th layer of KTFA and FA parametric image, KTFA parametric image can position compared with FA accurate cerebral white matter nervous tissue Position and feature.The purport of the present invention is to propose a kind of emerging anisotropic parameters KTFA based on kurtosis tensor, by expanding Dissipate nuclear magnetic resonance collection and diffusion kurtosis measured, with provide about brain white matter nerve fiber morphological characteristic and micro structure respectively to The additional information of the opposite sex.This invention can be effectively improved the Stability and veracity exploring cerebral white matter microstructure features, and Obtain considerable Social benefit and economic benefit.Optimum implementation is intended using invention transfer, technological cooperation or product development.Base Product in this technological development can be applicable to actual crowd and the statistical analysis of pathology, identifies, classify and explore various disease Or in the scientific research of people's brain architectural feature of various disease pathology.

Claims (10)

1., based on a kurtosis tensor mark anisotropic microstructure feature extracting method, it is characterized in that, by experimenter at magnetic The tissue many b value diffusion weighted images along multiple diffusion sensitising gradient directions are gathered, by diffusion weighted images in resonance scanner After pretreatment, in individual space, matching obtains reflection tissue, the second order of water diffusion distribution probability density function feature expands Dissipate tensor and quadravalence kurtosis tensor matrix, obtain corresponding mark anisotropy FA by matrix operations and kurtosis tensor mark is each Anisotropy KTFA, in conjunction with characteristic parameter, it is thus achieved that nerve fiber microstructure features.

2. as claimed in claim 1 based on kurtosis tensor mark anisotropic microstructure feature extracting method, it is characterized in that, expand Dissipating weighted magnetic resonance images collection and use 3.0T magnetic resonance scanner and 32 channel head coils, acquisition sequence is to use echo planar imaging Single-shot spin echo-echo planar imaging sequence (SE-EPI, single shot spin echo-that imaging (EPI) is read Echo planar imaging), diffusion-weighted signal correction experiment acquisition parameter: repetition time TR (repetition time) =10500ms, echo time TE (echo time)=103ms, partial Fourier transform 75%, the visual field is 256 × 256mm², Obtain image array be 128 × 128, thickness is 2mm, full brain gather 73 layers, interlayer continuously every；Diffusion sensitized factor b value selects b =1000s/mm²And b=2000s/mm², there is the diffusion-weighted of 30 gradient directions respectively, b=0's of the most extra collection Without diffusion-weighted benchmark image, obtaining the matrix data collection that size is 128 × 128 × 73 × 61, acquisition time is about 8 Dividing 40 seconds, signal noise ratio (snr) of image is 2.03.

3. as claimed in claim 1 based on kurtosis tensor mark anisotropic microstructure feature extracting method, it is characterized in that, expand Dissipating weighted image pretreatment to comprise the concrete steps that, all tested diffusion weighted magnetic resonance images need advanced wardrobe to move artifact inspection, If being wherein translating beyond 1mm or rotating over the image of 4 ° by disallowable, follow-up tensor estimation should not be carried out；Then, use DtiInit module in mrDiffusion tool kit carries out eddy current correction and head dynamic(al) correction operation to data, uses FSL simultaneously BET module in software carries out shelling brain；By the image obtained before entering tensor and estimating, use gaussian kernel smoothing processing, and half High overall with value is gather image voxel 1.25～1.5 times.

4., as claimed in claim 1 based on kurtosis tensor mark anisotropic microstructure feature extracting method, it is characterized in that, Amount is estimated, the gradient pulse resonance gradient magnetic field strength using standard is g, during pulse persistance Between be the calibration pulse gradient fields of time interval Δ at δ and diffusion-sensitive gradient pulses center, obtain spreading kurtosis imaging mould In type, diffusion kurtosis with the prevailing relationship of diffusion signal is,

$ln\[\frac{S\left(b\right)}{S\left(0\right)}\]=-{\mathrm{bD}}_{app}+\frac{1}{6}{b}^2{D_{app}}^2{K}_{app}$

Wherein S (b) is the signal intensity that with the addition of gradient magnetic, b=1000,2000s/mm²；S (0) is not apply diffusion-sensitive The intensity of the magnetic resonance reference signal of gradient pulse；B value is the diffusion magnetic susceptibility factor；D_appIt it is the apparent diffusion system in certain direction Number, K_appBeing the apparent diffusion kurtosis along certain direction, diffusion tensor D is the real symmetric matrix of a two-dimensional third-order, its calculating At least need 6 gradient directions；Diffusion kurtosis tensor K is the real symmetric matrix on the four-dimension three rank, and its calculating needs at least Two non-zero b values and 15 gradient directions, for any direction, apparent diffusion coefficient and the expression of apparent diffusion kurtosis estimator Formula is written as,

$D\left(\hat{n}\right)={\Σ}_{ij}{n}_i{n}_j{D}_{ij}$

$K\left(\hat{n}\right)=\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}{\Σ}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Wherein,WithIt is respectively hydrone to existApparent diffusion coefficient on direction and apparent coefficient of kurtosis,It it is diffusion Sensitising gradient direction, n_i,n_j,n_k,n_l, it isI-th or j, k, l component elements；Average diffusion coefficientWith diffusion kurtosisBy

All directions are averaging and obtain,

$\stackrel{\‾}{D}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}D\left(\hat{n}\right)$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}K\left(\hat{n}\right)$

Order:

$W\left(\hat{n}\right)={\Σ}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Then the expression formula of average kurtosis tensor is,

$\stackrel{\‾}{W}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}W\left(\hat{n}\right)$

Mark can be asked to draw by D matrix, λ_iFor matrix D eigenvalue, represent the diffusion coefficient size organized on interior three points of directions, And eigenvalue of maximum correspondence direction extremely organizes the main trend of interior nerve fiber, another two eigenvalue reflection Medullary sheath Characteristic,

$\stackrel{\‾}{D}=\frac{Tr\left(D\right)}{3}=\frac{{\mathrm{\λ}}_1+{\mathrm{\λ}}_2+{\mathrm{\λ}}_3}{3}$

Average kurtosis tensor is represented by,

$\stackrel{\‾}{W}=\frac{W_{1111}+W_{2222}+W_{3333}+2W_{1122}+2W_{1133}+2W_{2233}}{5}$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}W\left(\hat{n}\right)$

It isApproximation, in the two is equal and if only if tissue, water diffusion is isotropic diffusion.

5. as claimed in claim 1 based on kurtosis tensor mark anisotropic microstructure feature extracting method, it is characterized in that, FA With KTFA parametric estimation step, FA is defined as:

$FA\≡\sqrt{\frac{3}{2}}\frac{{||D-\stackrel{\‾}{D}{I}^{\left(2\right)}||}_F}{{||D||}_F}$

Wherein,For standardized constant, the span of FA is made to be limited between 0 to 1；D is diffusion tensor, is one 3 × 3 Two-dimensional matrix；I⁽²⁾For symmetrical second-order matrix,For Kronecker function, i, j desirable 1,2,3；‖…‖_FFor The F norm of matrix, kurtosis tensor mark anisotropy (KTFA), it is defined as

$KTFA=\frac{{||W-\stackrel{\‾}{W}{I}^{\left(4\right)}||}_F}{{||W||}_F}$

Wherein, W is kurtosis tensor；I⁽⁴⁾For symmetrical,δ_ij,δ_kl,δ_ix,δ_jlFor gram Magnesium carbonate gram function, i, j, k, l desirable 1,2,3；‖…‖_FFor the F norm of matrix, KTFA easily by each diffusion group divide between diversity Impact, rather than as FA depends on the direction of each diffusion component.

6., based on a kurtosis tensor mark anisotropic microstructure feature deriving means, it is characterized in that, including: diffusion-weighted magnetic Resonance image harvester, and computer；Be provided with diffusion weighted images pretreatment module in computer, tensor is estimated and feature Extraction module.

7. as claimed in claim 6 based on kurtosis tensor mark anisotropic microstructure feature deriving means, it is characterized in that, expand Dissipating weighted magnetic resonance images harvester is 3.0T magnetic resonance scanner and 32 channel head coils, and acquisition sequence is to use plane to return Single-shot spin echo-echo planar imaging sequence (SE-EPI, single shot spin echo-that ripple imaging (EPI) is read echo planar imaging)。

8. as claimed in claim 6 based on kurtosis tensor mark anisotropic microstructure feature deriving means, it is characterized in that, expand Scattered weighted image pretreatment module is used for carrying out head and moves artifact inspection, if being wherein translating beyond 1mm or rotating over the figure of 4 ° As by disallowable, follow-up tensor estimation should not be carried out；Then, diffusion weighted images pretreatment module uses mrDiffusion work DtiInit module in tool bag carries out eddy current correction and head dynamic(al) correction operation to data, uses the BET mould in FSL software simultaneously Block carries out shelling brain；By the image obtained before entering tensor and estimating, diffusion weighted images pretreatment module uses gaussian kernel to smooth Process, and full width at half maximum value is gather image voxel 1.25～1.5 times.

9., as claimed in claim 6 based on kurtosis tensor mark anisotropic microstructure feature deriving means, it is characterized in that, Amount is estimated and characteristic extracting module, and the gradient pulse resonance gradient magnetic field strength using standard is g, the pulse duration For the calibration pulse gradient fields of the time interval Δ at δ and diffusion-sensitive gradient pulses center, obtain spreading kurtosis imaging model Middle diffusion kurtosis with the prevailing relationship of diffusion signal is,

$ln\[\frac{S\left(b\right)}{S\left(0\right)}\]=-{\mathrm{bD}}_{app}+\frac{1}{6}{b}^2{D_{app}}^2{K}_{app}$

Wherein S (b) is the signal intensity that with the addition of gradient magnetic, b=1000,2000s/mm²；S (0) is not apply diffusion-sensitive The intensity of the magnetic resonance reference signal of gradient pulse；B value is the diffusion magnetic susceptibility factor；D_appIt it is the apparent diffusion system in certain direction Number, K_appBeing the apparent diffusion kurtosis along certain direction, diffusion tensor D is the real symmetric matrix of a two-dimensional third-order, its calculating At least need 6 gradient directions；Diffusion kurtosis K is the real symmetric matrix on the four-dimension three rank, and its calculating needs at least two Non-zero b value and 15 gradient directions, for any direction, the expression formula of apparent diffusion coefficient and apparent diffusion kurtosis estimator is write For,

$D\left(\hat{n}\right)={\Σ}_{ij}{n}_i{n}_j{D}_{ij}$

$K\left(\hat{n}\right)=\frac{{\stackrel{\‾}{D}}^2}{D\left(\hat{n}\right)}{\Σ}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Wherein,WithIt is respectively hydrone to existApparent diffusion coefficient on direction and apparent coefficient of kurtosis,It is still that Diffusion sensitising gradient direction, n_i,n_j,n_k,n_l, it isI-th or j, k, l component elements；Average diffusion coefficientWith diffusion kurtosisObtained by all directions are averaging,

$\stackrel{\‾}{D}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}D\left(\hat{n}\right)$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}K\left(\hat{n}\right)$

Order:

$W\left(\hat{n}\right)={\Σ}_{ijkl}{n}_i{n}_j{n}_k{n}_l{W}_{ijkl}$

Then the expression formula of average kurtosis tensor is,

$\stackrel{\‾}{W}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}W\left(\hat{n}\right)$

Mark can be asked to draw by D matrix, λ_iFor matrix D eigenvalue, represent the diffusion coefficient size organized on interior three points of directions, And eigenvalue of maximum correspondence direction extremely organizes the main trend of interior nerve fiber, another two eigenvalue reflection Medullary sheath Characteristic,

$\stackrel{\‾}{D}=\frac{Tr\left(D\right)}{3}=\frac{{\mathrm{\λ}}_1+{\mathrm{\λ}}_2+{\mathrm{\λ}}_3}{3}$

Average kurtosis tensor is represented by,

$\stackrel{\‾}{W}=\frac{W_{1111}+W_{2222}+W_{3333}+2W_{1122}+2W_{1133}+2W_{2233}}{5}$

$\stackrel{\‾}{K}=\frac{1}{4\mathrm{\π}}\∫d\hat{n}\frac{{\stackrel{\‾}{D}}^2}{D{\left(\hat{n}\right)}^2}W\left(\hat{n}\right)$

It isApproximation, in the two is equal and if only if tissue, water diffusion is isotropic diffusion, W₁₁₁₁, W₂₂₂₂, W₃₃₃₃, W₁₁₂₂, W₁₁₃₃, W₂₂₃₃, subscript represents this element position in kurtosis tensor matrix W.

10., as claimed in claim 6 based on kurtosis tensor mark anisotropic microstructure feature deriving means, it is characterized in that, FA Yu KTFA parameter estimation module, uses following steps to obtain FA Yu KTFA parameter: FA is defined as

$FA\≡\sqrt{\frac{3}{2}}\frac{{||D-\stackrel{\‾}{D}{I}^{\left(2\right)}||}_F}{{||D||}_F}$

Wherein,For standardized constant, the span of FA is made to be limited between 0 to 1；D is diffusion tensor, is one 3 × 3 Two-dimensional matrix；I⁽²⁾For symmetrical second-order matrix,For Kronecker function, i, j desirable 1,2,3；‖…‖_FFor The F norm of matrix, kurtosis tensor mark anisotropy KTFA, it is defined as

$KTFA=\frac{{||W-\stackrel{\‾}{W}{I}^{\left(4\right)}||}_F}{{||W||}_F}$

Wherein, W is kurtosis tensor；I⁽⁴⁾For symmetrical,δ_ij,δ_kl,δ_ik,δ_jlFor gram Magnesium carbonate gram function, i, j, k, l desirable 1,2,3；‖…‖_FFor the F norm of matrix, KTFA easily by each diffusion group divide between diversity Impact, rather than as FA depends on the direction of each diffusion component.