CN105574849A - Diffusion kurtosis tensor based white matter microstructure feature visualization method - Google Patents

Abstract

The invention discloses a diffusion kurtosis tensor based white matter microstructure feature visualization method. The visualization method comprises the steps of collecting diffusion weighted imaging data; performing preprocessing on the diffusion weighted imaging data; performing tensor fitting on the pre-processed diffusion weighted imaging data; and performing tissue microstructure kurtosis tensor visualization for the result obtained after the tensor fitting is carried out. According to the visualization method, the diffusion weighted imaging data is taken as the original data, and a diffusion kurtosis imaging model is established; two-dimensional and three-dimensional visualization for the brain tissue microstructure is realized through fitting kurtosis tensor and the kurtosis coefficient; the visualization method is more sensitive to non-Gaussian diffusion of water molecules in the tissue, so that more plentiful brain tissue microstructure feature correlation information can be provided; an efficient analysis tool for research on brain mechanisms and brain tissue microstructures is provided; and in addition, the visualized, three-dimensional and actualized display effect enables a user to rapidly and conveniently obtain an analysis result to avoid troublesome operations and redundancy of image parameters.

Description

A kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor

Technical field

The present invention relates to image processing field, particularly relate to a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor.

Background technology

MR diffusion-weighted imaging (MR-DWI, MR-diffusionweightedimaging) cause based on microstructure factor in biological tissue, anisotropy water diffusion is rebuild biological tissue's image and is reflected the imaging technique that its corresponding functional-structural information is emerging.It is the new technology grown up on the magnetic resonance imaging basis of routine, is shown the image of brain tissue microstructure features by the different dispersal patterns rebuilding hydrone in tissue, is research brain tissue microstructure and the important means be connected.

Based on the Single-Index Model of Diffusion-Weighted MR Imaging---diffusion tensor imaging (Diffusiontensorimaging, DTI) is the effective ways that can realize the detection of cerebral white matter non-destructive at present.The second order diffusion tensor obtained by DTI matching can provide that brain white matter nerve fiber moves towards, hydrone white matter Microstructure Information such as Gaussian characteristic in cerebral white matter.DTI becomes the method realizing display white matter Microstructure Information the earliest.But due to the constraint of the stop of myelin, cell membrane and inside and outside shape, the water diffusion probability distribution in cerebral white matter is tending towards non-Gaussian system.Meet the Gaussian DTI for supposed premise with water diffusion probability and can cause uncertainty and deviation for describing cerebral white matter microstructure features.In addition, DTI is subject to the impact of the factor such as partial volume effect (containing Various Tissues such as grey matter, white matter or cerebrospinal fluid in same voxel), path average effect (containing multiple fiber path in same voxel) in white matter microstructure display result, can reduce tissue microstructure specific variations susceptibility.

Therefore need to propose more complicated diffusion model and carry out quantitative description water diffusion characteristic more meticulously.Diffusion kurtosis imaging (Diffusionkurtosisimaging, DKI) introducing quadravalence kurtosis and kurtosis tensor quantize the degree that hydrone actual dispersion departs from Gaussian distribution, and the non-Gaussian system of reflection tissue more can close to the characteristic of the interior water diffusion of tissue.Quadravalence kurtosis tensor is the matrix of the three-dimensional full symmetric of quadravalence on formulation, and the ellipsoid that can solve the reconstruct of second order diffusion tensor cannot move towards with multifilament the difficult problem that matches.The micromechanism information that cerebral white matter enriches is by the tensor representation of quadravalence kurtosis.How to obtain the precise information of water diffusion in voxel from the high order tensor of complexity is be rich in challenging new technology, and this is also the key difficulties of this area research in recent years.This difficult point have impact on the nerve fibre structure three-dimensional reconstruction progress of DKI to a certain extent and applies clinical.

Summary of the invention

The invention provides a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor, the present invention not only can realize the tracking of more reliable white matter nerve fiber by introducing quadravalence kurtosis tensor, and patterned three-dimensional kurtosis tensor is convenient to observe, and the information of abundant brain tissue microstructure can be obtained better in conjunction with quantizating index, described below:

Based on a white matter microstructure features method for visualizing for diffusion kurtosis tensor, described method for visualizing comprises the following steps:

Gather diffusion weighted image data; Pre-service is carried out to diffusion weighted image data;

Tensor matching is carried out to pretreated diffusion weighted image data; To the result after tensor matching, according to observation requirements within the scope of full brain, in mark anisotropic parameters figure, select area-of-interest (comprising some voxels), then tissue microstructure kurtosis tensor carries out one by one to each voxel visual.

Described the step that pretreated diffusion weighted image data carries out tensor matching to be specially:

The imaging of diffusion kurtosis makes up the deficiency of second-order tensor by a quadravalence kurtosis additional in matching;

Build the model of diffusion kurtosis imaging, described model adopts the linear least square of belt restraining.

The model of described diffusion kurtosis imaging is specially:

Wherein, S (0) is signal intensity when not applying diffusion sensitized factor b value; D (n) and K (n) are respectively and are organized in diffusion sensitising gradient direction is apparent diffusion coefficient on n and apparent kurtosis coefficient; Corresponding tensor is diffusion tensor D and kurtosis tensor W, respectively the corresponding real symmetric matrix on two dimension three rank and the real symmetric matrix on the four-dimension three rank.

The linear least square of described belt restraining is specially:

Minimize||AX-B|| ²

CX≤d

Wherein, Minimize is for getting || AX-B|| ²minimum value; A is the matrix that diffusion sensitising gradient weighted direction obtains; B is the attenuation degree of the diffusion-weighted signal of different b value; C is Linear Constraints; D is the vector of constraint kurtosis coefficient range; X is the diffusion coefficient D of demand solution _ijwith kurtosis coefficient V _ijklthe vector of the one dimension 21 × 1 formed.

Described to the result after tensor matching, according to observation requirements within the scope of full brain, in mark anisotropic parameters figure, select area-of-interest, comprise some voxels, then each voxel is carried out one by one to tissue microstructure kurtosis tensor is visual to be specially:

Resampling is carried out to the space that diffusion sensitising gradient direction is formed, obtains, along the kurtosis distribution situation in the space all directions after resampling, kurtosis distribution situation being carried out 3-D display by the matching of kurtosis tensor;

Extract kurtosis tensor cross section, the diffusion tensor in each voxel is carried out diagonalization, obtains eigenwert and characteristic direction, along the planar interception kurtosis tensor that two sub-eigenvalue directions are formed, realize kurtosis tensor two-dimensional visualization.

Describedly obtain being specially along the kurtosis distribution situation in the space all directions after resampling by the matching of kurtosis tensor:

K(X _q)＝g(n)·X _V

Wherein, K (X _q) be X _qkurtosis coefficient on direction; The matrix that the direction vector that g (n) distributes for space uniform is relevant, according to the matching of quadravalence kurtosis tensor; X _vfor the matrix of kurtosis coefficient composition.

Described extraction kurtosis tensor cross section, carries out diagonalization by the diffusion tensor in each voxel, obtains eigenwert and characteristic direction is specially:

D is diffusion tensor; λ _iand v _icharacteristic of correspondence value and proper vector λ ₁>=λ ₂>=λ ₃, and 3 v _ipairwise orthogonal, the respectively direction of corresponding three eigenwerts; T is transposition.

The beneficial effect of technical scheme provided by the invention is: the present invention with Diffusion-Weighted MR Imaging data for raw data, set up diffusion kurtosis imaging model, by matching kurtosis tensor and kurtosis coefficient, realize cerebral tissue microstructure features two dimension, three-dimensional visualization, more traditional diffusion tensor imaging model, method provided by the invention is more responsive to hydrone non-gaussian diffusion in tissue, therefore can provide the information that the cerebral tissue microstructure features of more horn of plenty is relevant.The present invention is for brain mechanism research, brain tissue microstructure study provides efficient analysis tool.As accompanying drawing, be two dimension, three-dimensional visualization design sketch, the display effect of this visualize, three-dimensional, actualization makes user can obtain analysis result quickly and easily, avoids the redundancy of complex operation and image parameters.

Accompanying drawing explanation

Fig. 1 is a kind of process flow diagram of the white matter microstructure features method for visualizing based on diffusion kurtosis tensor;

Fig. 2 is that brain intersection nerve fibre emulates the visual schematic diagram of three-dimensional kurtosis tensor;

It is area-of-interest that Fig. 3 a delineates corpus callosum on full brain mark anisotropic parameters figure;

Fig. 3 b is brain corpus callosum two-dimensional visualization design sketch.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly, below embodiment of the present invention is described further in detail.

The imaging of diffusion kurtosis is by the DWI signals collecting in multiple directions, introducing quadravalence kurtosis and kurtosis tensor quantize the degree that hydrone actual dispersion departs from Gaussian distribution, the non-Gaussian system of reflection tissue more close to the characteristic of water diffusion in tissue, can especially reflect that intercellular spaces and cell membrane are to the interaction of water diffusion.Meanwhile, quadravalence kurtosis tensor is the matrix of the three-dimensional full symmetric of quadravalence on formulation, can solve second order diffusion tensor reconstruct ellipsoid and cannot move towards with multifilament the difficult problem that matches.More general second order diffusion tensor, kurtosis tensor can provide the characteristic information of abundanter tissue microstructure.Therefore, the difficult problem of diffusion tensor at fiber intersection not only can be solved to the visual research of kurtosis tensor, and the quantizating index that kurtosis tensor is relevant can be utilized to obtain such as to tissue microstructure minutias such as neuron, Deiter's cells, dendrons, make high order tensor fully show advantage in the structural research of lossless detection white matter of brain.

The embodiment of the present invention proposes and spreads kurtosis imaging (MR-DKI by the magnetic resonance strong to hydrone non-gaussian diffusion-sensitive, MR-diffusionkurtosisimaging), by the visual display of geometric shape of quadravalence kurtosis tensor and the quantizating index with nerve fibre directional correlation, and then obtain the visual new method of microstructure of people's cranial nerve white matter.Its techniqueflow is: on magnetic resonance imaging platform, gather the diffusion-weighted signal of biological tissue along multiple directions by experimenter, matching obtains reflecting the quadravalence kurtosis tensor of the probability density function feature of water diffusion distribution in tissue, by it is visual, extract the machine direction of kurtosis sign and the quantization parameter of kurtosis tensor geometry form, the information of abundant brain tissue microstructure features can be obtained intuitively, easily.

Embodiment 1

Embodiments provide a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor, see Fig. 1 and Fig. 2, the method comprises the following steps:

101: gather diffusion weighted image data;

On the magnetic resonance imaging platform of 3.0T, single-shot echo planar imaging (SE-EPI) sequence is adopted to carry out diffusion-weighted signals collecting.Wherein, the number in diffusion sensitising gradient direction is 30; 3 diffusion sensitized factor b values (b=0, b=1000 and b=2000s/mm ²); Repetition time TR (timeofrepetition)=10500ms; Echo time TE (timeofehco)=103ms; Multiplicity is 1; Every experimenter's diffusion weighted images obtain T.T. TA (timeofacquisition)=11 point 14 seconds; Noise level is 30; Obtaining image array size is 128 × 128; Visual field FOV=230 × 230mm ²; Thickness is 1.8mm; Full brain gathers 73 layers, interlayer continuously every.

During specific implementation, can also adopt other experiment value, the embodiment of the present invention does not limit this.

102: Image semantic classification;

First brain function diffusion image handling implement bag (FMRIB'sDiffusionToolbox, FDT) of the FSL of Regius professor (theFMRIBSoftwareLibrary) software is adopted to carry out eddy current rectification to diffusion weighted image data and head moves corrective operations; Secondly, before tensor matching, use Gaussian smoothing core, the smoothing windows of 3mm is to the smoothing process of diffusion weighted images.

During specific implementation, the operation steps of this Image semantic classification is conventionally known to one of skill in the art, and the embodiment of the present invention does not repeat this.

103: tensor matching;

Diffusion kurtosis imaging (Diffusionkurtosisimaging) technology is the simple extension of the diffusion tensor imaging (Diffusiontensorimaging) to classics, namely allows many diffusion sensitized factors b value to participate in model fitting process.Classical diffusion tensor imaging model such as formula wherein, S (b) is signal intensity when applying diffusion sensitized factor b value, and b value is the diffusion magnetic susceptibility factor; S (0) is signal intensity when not applying diffusion sensitized factor b value; X is the vector of unit length in gradient sensing direction; T is transposition; D is the diffusion tensor of corresponding tissue, and be the second-order matrix of 3 × 3, spatial shape is an ellipsoid (namely spreading ellipsoid).

In diffusion tensor, element is space coefficient of diffusion, and second-order tensor diagonalization can be tried to achieve eigenwert and characteristic direction.The direction of eigenvalue of maximum, namely spreads ellipsoid major axes orientation and match with the trend of cranial nerve fiber reality, and the direction of sub-eigenvector represents the trend of vertical fibers.Therefore, the ellipsoid of second-order tensor has no idea to solve fiber orientation (now occur sizable eigenwert, cannot the differentiate) problem of fiber intersection.The transition of generation experience from second-order tensor to the fourth-order tenstor of DKI technology, namely DKI makes up the deficiency of second-order tensor by a quadravalence kurtosis additional in models fitting.The model of DKI technology is such as formula (1):

Here D (n) and K (n) is obtained by formula (2) and (3) formula by diffusion tensor and kurtosis tensor,

Wherein, D (n) and K (n) are respectively and are organized in diffusion sensitising gradient direction is apparent diffusion coefficient on n and apparent kurtosis coefficient; Corresponding tensor is diffusion tensor D and kurtosis tensor W, respectively the real symmetric matrix W on a real symmetric matrix D and four-dimension three rank on corresponding two dimension three rank, D _ijand W _ijklfor the element in D and W matrix; MD is the average diffusion coefficient of corresponding tissue site, is got by diffusion tensor matrices D calculating; n _i(or j, k, l) be n i-th (or j, k, l) individual component elements, i, j, k, l scope is all 1 to 3.The linear least square of belt restraining is adopted when estimating DKI model, following formula (4), (5) in this method

Minimize||AX-B|| ²(4)

CX≤d(5)

Wherein, Minimize is for getting || AX-B|| ²minimum value; A is the matrix that diffusion sensitising gradient weighted direction obtains; B is the attenuation degree of the diffusion-weighted signal of different b value; C is Linear Constraints; D is the vector (kurtosis factor v should be limited in 0 to 3) of constraint kurtosis coefficient range; X is the diffusion coefficient D of demand solution _ijwith kurtosis coefficient V _ijklthe vector of the one dimension 21 × 1 formed.

X＝{D ₁₁D ₂₂D ₃₃D ₁₂D ₁₃D ₂₃V ₁₁₁₁……V ₁₁₁₂……V ₁₁₂₂……V ₁₂₁₃} ^T(6)

X is the vector of unknown 21 × 1, and

V _ijkl＝MD ²W _ijkl(7)

Wherein, matrix A is:

Wherein, M is the quantity of non-zero diffusion sensitized factor b value; K is the quantity in diffusion sensitising gradient direction; K row in A with be expressed as follows:

In addition, each diffusion sensitized factor b _ma corresponding specific gradient vector group

Wherein, be M diffusion sensitized factor b _mcorresponding different diffusion sensitising gradient directions.

Therefore the columns of A is provided by following formula:

Vector B is provided by following formula:

B＝[ln(S ₁/S ₀)…ln(S _N/S ₀)] ^T(14)

$S_k=S(n_k^{\left(M\right)},b_M)$ Be the intensity of gradient direction diffusion signal, $k={\mathrm{\Σ}}_{j=1}^{M-1}{N}_j+i.$

In formula (5), Matrix C representative provides linear restriction by following formula

Wherein b _maxfor the maximum diffusion sensitized factor b value collected.

Vector d is provided by following formula

Wherein 0 vector is 1 × N dimension.

104: tissue microstructure kurtosis tensor is visual

Realize in two dimension, three-dimensional visualization process at practical application kurtosis tensor, according to user's needs, at mark anisotropic parameters figure, (Fig. 3 is a) middle selects area-of-interest, comprises some voxels, then analyzes one by one each voxel.First carry out three-dimensional visualization, resampling is carried out to the space that diffusion sensitising gradient direction is formed, is obtained along the kurtosis distribution situation in the space all directions after resampling by the matching of kurtosis tensor, and carried out 3-D display.Then, extract kurtosis tensor cross section, the diffusion tensor in each voxel is carried out diagonalization, obtains eigenwert and characteristic direction, along the planar interception kurtosis tensor that two sub-eigenvalue directions are formed, kurtosis tensor two-dimensional visualization can be realized.

1) kurtosis tensor three-dimensional visualization;

For realizing kurtosis tensor three-dimensional visualization, resampling being carried out to the space that diffusion sensitising gradient direction is formed, needs to produce the equally distributed vector of unit length X of a series of q space angle _q, meet (19) formula,

Wherein, X _q=(X _qx, X _qy, X _qz), θ is position angle, for the elevation angle, Δ θ, represent the constant of fixed intervals.Thus, mikey vector can obtain following formula according to the matching of (3) quadravalence kurtosis tensor,

g(n)＝[X _qx ⁴X _qy ⁴X _qz ⁴4X _qx ³X _qy…64X _qx ²X _qy ²…12X _qxX _qyX _qz ²](20)

Process (20) formula computing obtains the vectorial X that g (n) is formed with 15 elements in the kurtosis tensor matrix W obtained according to 103 models fittings _v=[W ₁₁₁₁w ₁₁₁₂w ₁₁₂₂w ₁₂₁₃] ^t, the matrix X that matrix g (n) that the direction vector distributed by space uniform is relevant forms with kurtosis coefficient _vbe multiplied, namely

K(X _q)＝g(n)·X _V(21)

Wherein, K (X _q) be X _qkurtosis coefficient on direction.Thus, just can obtain the kurtosis coefficient distribution in all directions in space, namely realize kurtosis tensor three-dimensional visualization, as shown in Figure 2.Fig. 2 carries out kurtosis tensor three-dimensional visualization method by emulated data (two decussating fiberss, intersecting angle is respectively 45 °, 60 °, 90 °).Compared to three-dimensional diffusion tensor display result, angle-resolved different fiber crossovers angle that kurtosis tensor visually intersects by outstanding peak-peak (namely 45 °, 60 ° of fiber crossovers time, diffusion tensor shape all shows as spindle, only can reflect the conjunction direction of two fiber crossovers, and the outstanding peak value of kurtosis tensor shows as butterfly-like shape, the angle of intersection be able to reflect the angle of fiber crossovers).

2) three-dimensional kurtosis tensor cross section is extracted

The extraction in kurtosis tensor cross section is conducive to the quantizating index obtaining tissue microstructure, and this cross section is perpendicular to white matter fiber tract direction.Specific practice: first by diffusion tensor matrices, is carried out Diagonalization Decomposition, obtains eigenwert and proper vector, as shown in the formula,

Here, λ _iand v _icharacteristic of correspondence value and proper vector (λ ₁>=λ ₂>=λ ₃), and 3 v _ipairwise orthogonal, the respectively direction of corresponding three eigenwerts; Wherein λ _ithe coefficient of diffusion size on interior three points of directions is organized in representative, and eigenvalue of maximum correspondence direction is the main trend of nerve fibre in tissue, the characteristic of another two eigenwerts reflection Medullary sheath.Along the planar interception kurtosis tensor that two sub-eigenvalue directions are formed, the information (as Fig. 3 b) reflecting the micro mainly moved towards perpendicular to nerve fibre can be obtained.

In sum, the embodiment of the present invention can obtain cerebral nerve tissue microstructure characteristic information intuitively, easily by above-mentioned steps 101-step 104.This invention can improve accuracy, simplicity and the intuitive of studying brain mechanism and white matter of brain microstructure effectively, can obtain about the relevant quantization parameter of cerebral white matter structure simultaneously, avoid the complex operation using science software for calculation research experiment, and obtain considerable Social benefit and economic benefit.

Embodiment 2

Below in conjunction with concrete accompanying drawing 3a and Fig. 3 b, the method in embodiment 1 is carried out to the checking of feasibility, described below:

This method is by second and third proper vector v of diffusion tensor matrices ₂, v ₃place plane YOZ obtains kurtosis tensor cross section, namely perpendicular to the direction of white matter fiber tract.The kurtosis tensor cross section obtained kurtosis value distribution in all directions just shows very clearly, and Fig. 3 is the kurtosis cross section at each position in corpus callosum.

MRI data collection is carried out by adult normal brain, adopt this method to carry out tensor matching and the analysis of white matter microstructure visual analysis method, select brain corpus callosum to be that area-of-interest is (as Fig. 3 a) can estimate and obtains kurtosis tensor cross sectional shape difference (as Fig. 3 b) in different imaging voxel.These differences in shape reflect hydrone in cerebral white matter and spread in a certain direction and be restricted, and difference appears in diffusion displacement, thus implicit fibre diameter, fiber number are different in white matter microstructure.The direction of maximum kurtosis value (namely for the reconstruction radius of fiber tracking) can be found, the direction that namely the limited diffusion of hydrone is maximum by kurtosis cross section.Compared to diffusion tensor imaging, this method finds the direction that the maximum direction of kurtosis value can obtain fibrous bundle more accurately, especially at many white matter fibers infall.

It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the invention described above embodiment sequence number, just to describing, does not represent the quality of embodiment.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1., based on a white matter microstructure features method for visualizing for diffusion kurtosis tensor, it is characterized in that, described method for visualizing comprises the following steps:

Gather diffusion weighted image data; Pre-service is carried out to diffusion weighted image data;

Tensor matching is carried out to pretreated diffusion weighted image data; To the result after tensor matching, according to observation requirements within the scope of full brain, in mark anisotropic parameters figure, select area-of-interest, comprise some voxels, then tissue microstructure kurtosis tensor carries out one by one to each voxel visual.

2. a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor according to claim 1, is characterized in that, is describedly specially the step that pretreated diffusion weighted image data carries out tensor matching:

The imaging of diffusion kurtosis makes up the deficiency of second-order tensor by a quadravalence kurtosis additional in matching;

Build the model of diffusion kurtosis imaging, described model adopts the linear least square of belt restraining.

3. a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor according to claim 2, it is characterized in that, the model of described diffusion kurtosis imaging is specially:

$S(n,b)=S\left(0\right)\exp (-bD(n)+\frac{1}{6}{b}^{2}D{\left(n\right)}^{2}K(n\left)\right)$

Wherein, S (0) is signal intensity when not applying diffusion sensitized factor b value; D (n) and K (n) are respectively and are organized in diffusion sensitising gradient direction is apparent diffusion coefficient on n and apparent kurtosis coefficient; Corresponding tensor is diffusion tensor D and kurtosis tensor W, respectively the corresponding real symmetric matrix on two dimension three rank and the real symmetric matrix on the four-dimension three rank.

4. a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor according to claim 2, it is characterized in that, the linear least square of described belt restraining is specially:

Minimize||AX-B|| ²

CX≤d

Wherein, Minimize is for getting || AX-B|| ²minimum value; A is the matrix that diffusion sensitising gradient weighted direction obtains; B is the attenuation degree of the diffusion-weighted signal of different b value; C is Linear Constraints; D is the vector of constraint kurtosis coefficient range; X is the diffusion coefficient D of demand solution _ijwith kurtosis coefficient V _ijklthe vector of the one dimension 21 × 1 formed.

5. a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor according to claim 1, it is characterized in that, described to the result after tensor matching, according to observation requirements within the scope of full brain, area-of-interest is selected in mark anisotropic parameters figure, comprise some voxels, then each voxel carried out one by one to tissue microstructure kurtosis tensor is visual to be specially:

Resampling is carried out to the space that diffusion sensitising gradient direction is formed, obtains, along the kurtosis distribution situation in the space all directions after resampling, kurtosis distribution situation being carried out 3-D display by the matching of kurtosis tensor;

Extract kurtosis tensor cross section, the diffusion tensor in each voxel is carried out diagonalization, obtains eigenwert and characteristic direction, along the planar interception kurtosis tensor that two sub-eigenvalue directions are formed, realize kurtosis tensor two-dimensional visualization.

6. a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor according to claim 5, is characterized in that, describedly obtains being specially along the kurtosis distribution situation in the space all directions after resampling by the matching of kurtosis tensor:

K(X _q)＝g(n)·X _V

Wherein, K (X _q) be X _qkurtosis coefficient on direction; The matrix that the direction vector that g (n) distributes for space uniform is relevant, according to the matching of quadravalence kurtosis tensor; X _vfor the matrix of kurtosis coefficient composition.

7. a kind of white matter microstructure features method for visualizing based on diffusion kurtosis tensor according to claim 5, it is characterized in that, described extraction kurtosis tensor cross section, carries out diagonalization by the diffusion tensor in each voxel, obtains eigenwert and characteristic direction is specially:

$D={\left[\begin{array}{ccc}{v}_1& v_2& v_3\end{array}\right]}^T\left[\begin{array}{ccc}{\mathrm{\λ}}_1& 0& 0\\ 0& {\mathrm{\λ}}_2& 0\\ 0& 0& {\mathrm{\λ}}_3\end{array}\right]\left[\begin{array}{ccc}{v}_1& v_2& v_3\end{array}\right]$

D is diffusion tensor; λ _iand v _icharacteristic of correspondence value and proper vector λ ₁>=λ ₂>=λ ₃, and 3 v _ipairwise orthogonal, the respectively direction of corresponding three eigenwerts; T is transposition.