CN105913458B - A kind of brain white matter integrity imaging method based on group's tracking - Google Patents
A kind of brain white matter integrity imaging method based on group's tracking Download PDFInfo
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Abstract
A kind of brain white matter integrity imaging method based on group's tracking, includes the following steps：1) individual fibers tracking direction is estimated：To observe the sub- voxel grade direction of diffusion signal, while structuring directional information existing for neighboring voxels is made full use of, by obtaining the direction observation to current tracking point to the interpolation of neighboring voxels diffusion directions on individual fibers historical trace direction；2) groups of fibers volume tracing direction estimation：Groups of fibers volume tracing direction estimation uses the multiple targets tracking based on random matrix, it is described with state iteration renewal process based on Bayesian frame, realize that the uncertain filtering come to measuring noise and motion model grass, the model are similar to the simple form of Kalman filter；By carrying out fibre bundle multiple targets status tracking based on this model.The present invention reduces the sensibility to signal noise and model error, reduces dependence, the high stability to local machine direction reconstruction model.
Description
Technical field
The present invention relates to the medical imaging under computer graphics, Nervous System Anatomy field, especially a kind of white matter of brain is fine
Tie up imaging method.
Background technology
Brain is that the control mankind carry out the movable synthesizers of sophisticated functions such as logical thinking, learning and memory, movement and emotion
Official, to human brain working mechanism probe into be contemporary scientific research forward position and hot spot.Brain white matter integrity reconfiguration technique will be by that will have
There is the brain fibre space Microstructure Information of Anatomical significance to be imaged, it has also become brain Mechanism of Cognition probes into, neural class disease
Sick pathological analysis and brain surgery navigation etc. brain sciences research important technical, thus the development of the technology by information,
The common concern of Neuscience related researcher.Diffusion-Weighted MR Imaging (Diffusion Weighted Imaging, DWI) with
Based on Magnetic resonance imaging (Magnetic Resonance Imaging, MRI) technology, applied in a plurality of directions by measuring
Add the Strength Changes that tissue signal generates before and after diffusion gradient field, realizes the observation to water diffusion motion state in tissue.
And the track reconstructing of nerve fibre passes through mould based on portraying the anisotropic directional spreding model of water diffusion in voxel
Intend the fiber tracking process that hydrone is propagated in signal transmission passage to describe.Nerve fibre reconstruct based on DWI scanning signals
Technology has become unique non-invasive methods of the fibr tissue image microstructures in live body brain.
Existing fiber imaging method is the tracking scheme based on single fiber, and the quality of Fiber track result is completely dependent on
In the quality of monomer element local fiber directional spreding reconstruct, since the presence of model error makes the increasing with fiber path length
It is long cause error accumulation and it is uncertain increase, while the very little deviation in local fiber direction may greatly change it is final
Fiber path is distributed, to cause the unstability of reconstruction result.Current fiber imaging algorithm is often through improvement part side
Model error is reduced to realize the raising of tracking accuracy and stability to modeling method, however the influence of signal noise is difficult to lead to
It crosses improvement local fiber direction model to completely eliminate, to unavoidably generate model error.
Invention content
In order to overcome, the sensibility to signal noise and model error of existing brain white matter integrity imaging method is higher, plays a game
The deficiency that the dependence of portion's machine direction reconstruction model is higher, stability is poor, the present invention provide a kind of reduction to signal noise
And model error sensibility, reduce to the dependence of local machine direction reconstruction model, high stability based on group with
The brain white matter integrity imaging method of track.
The technical solution adopted by the present invention to solve the technical problems is：
A kind of brain white matter integrity imaging method based on group's tracking, includes the following steps：
1) individual fibers tracking direction is estimated
For multifilament local direction distributed model, the machine direction of each voxel is distributed during extreme value vector set closes and history
The immediate vector in the direction of propagation is as diffusion principal directionThe corresponding weight value ω of each voxel diffusion principal direction is respectively by distance
Weights ω1With synteny weights ω2It codetermines：
Wherein,For eight diagonal neighboring voxels coordinate point sets of current tracking point, N is the seat of neighboring voxels
It marks [x, y, z], k is the tracking moment, and m is diagonal voxel (in total 8), and i is i-th of individual fibers particle；Apart from weights ω1Profit
It is weighted with trace point and the Euclidean distance of neighboring voxels coordinate points, the side that neighboring voxels are provided is weighed with its distance
To information weight；Synteny weights ω2With the history direction of propagation and neighboring voxels position between the orientation of current tracking point
Synteny size shows that current fibre individual is propagated trend and had with the neighboring voxels on historical trace direction as weight metric
There is stronger correlation；
Historical trace directionAs weighted term to portray the inertial force of fiber propagation, it is based ultimately upon individual fibers
The multi-voxel proton neighbor interpolation direction of historical trace stateIt is obtained by following formula：
Wherein ε1, ε2For vectorial normalization coefficient；
2) groups of fibers volume tracing direction estimation
Pass through two multi-agent synergy action directionsRealize the adjustment to individual fibers tracking trend：Based on fiber beam bundle wheel
The wide group with the constraint of black and white matter frontier distance corrects directionSimilarity constraint direction is moved towards with individual fibers in group
2.1) group's profile state trace model is established
At the k moment by being observed along sub- voxel grade directionPropagated forward, obtain include nkA Point Target position quantity
The fiber beam bundle observation set of surveyAndIndicate that all fibres multiple targets until the k moment are seen
Sequencing row；Using Bayes principle by individual observe under multiple targets state joint probability density function p (xk,Xk|yk) use height
The product of this density function and inverse Wishart density functions indicates：
p(xk,Xk|yk)=p (Yk,nk|xk,Xk)p(xk,Xk|yk-1)
Based on the number n for measuring individualkEqual-probability distribution it is assumed that the k moment observe set YkLikelihood function be simplified to as
Lower formula：
Wherein, N () is Gaussian Profile, and W () is distributed for Wishart, and H is observing matrix, The respectively survey at k moment
It measures mean vector and measures stroll matrix；
It is by prior probability function factorization：
p(xk,Xk|yk-1)=p (xk|Xk,yk-1)p(Xk|yk-1)
=N (xk；xk|k-1,Pk|k-1)IW(Xk；vk|k-1,Xk|k-1)
Wherein, IW () is distributed for inverse Wishart, xk|k-1, Xk|k-1Respectively the scalar parameter of prediction and matrix are joined in next step
Number.N(xk；xk|k-1,Pk|k-1) indicate that obeying vector is desired for xk|k-1, covariance matrix Pk|k-1Gaussian Profile；
Multiple targets state joint posterior probability density function is multiplied to obtain by likelihood function with prior probability function：
p(xk,Xk|yk)∝N(xk；xk|k,Pk|k)IW(Xk；vk|k,Xk|k)
Based on Bayesian model, fiber beam bundle tracking mode includes center of mass motion state and contour feature, uses state respectively
Stochastic variable xkAnd XkExpectation iteration update to obtain；
2.2) constraint of the black and white matter profile to group's direction of motion
Fiber beam bundle profile is weighed fibre bundle in ratio constant conduct always of the front and back moment apart from black and white matter boundary to walk
To the foundation for being parallel to black and white matter boundary, using frontier distance function pair with barycenter direction of primary motionCentered on be uniformly distributed and
Angle is less than the n of predetermined anglepA directionIt is evaluated with the best fibre bundle direction of propagation of determination；
With fibre bundle ellipsoid profile XkThree pairwise orthogonal axis of orientations inThe axis of orientation of angle minimum is as tracking
Axis, remaining two orthogonal direction axis collectively form an elliptic plane, and tracking axis is rotated to candidate direction of primary motion wtOn
Form new elliptic plane；The equal n of adjacent angle is up-sampled in the elliptic planesTo direction vector, and measure these directions
On elliptic contour point at a distance from black and white matter boundaryWherein dt,2j, dt,2j+1Respectively opposite sample direction
On frontier distance；Corresponding frontier distance deviation D (w is calculated to all candidate direction of primary motionst), take the minimum boundary of generation away from
Candidate direction of primary motion from deviation is most preferably moved towards as group, to obtain group orientation
Wherein, δ is that previous moment is most preferably moved towards determining corresponding sample direction frontier distance by group.
2.3) individual fibers move towards similarity constraint in group
According to the space vector of k moment difference Fiber track pointsApart from sizeUtilize parameter rmin,
rmaxDivide three different types of fiber track zones of action：(1) distributing areaIt is fine in this area
Sucking action is shown as between dimension individual, promotes the bunching effect of similar track；(2) repulsive areaWith smaller
Repelling effect is generated between the trace point of space length to ensure the diversity of fiber population at individual；(3) neutral zone domain shows
Independence between the fiber path of larger space distance in evolutionary process；
Wherein, the parameter of τ force strengths in order to control；
2.4) group's separation based on k-means
Judged to realize that group detaches by being clustered based on the k-means of individual fibers tracking direction in group, multiple subgroups point
It is realized from the cluster by class center there are two repeatedly being had, cluster centre number is set as 2, by two cluster centres
Angle is more than when accounting for the 1/3 of group's sum comprising individual amount in given threshold value and each class as the judgement that groups of fibers separation occurs
Condition.
The present invention technical concept be：To observe the sub- voxel grade direction of diffusion signal, while making full use of neighborhood body
Structuring directional information existing for element, by individual fibers historical trace direction to the interpolation of neighboring voxels diffusion directions
Obtain the direction observation to current tracking point.
Groups of fibers volume tracing direction estimation uses the multiple targets tracking based on random matrix, to be based on Bayesian frame
State iteration renewal process describe, realize to measure noise and motion model grass comes it is uncertain filter, the mould
Type is similar to the simple form of Kalman filter；By carrying out fibre bundle multiple targets status tracking based on this model.
Beneficial effects of the present invention are mainly manifested in：The sensibility to signal noise and model error is reduced, reduces and plays a game
Dependence, the high stability of portion's machine direction reconstruction model.
Specific implementation mode
The invention will be further described below.
A kind of brain white matter integrity imaging method based on group's tracking, includes the following steps：
1) individual fibers tracking direction is estimated
Traditional tracking process is using the extremal vector of the current tracking point place voxel directional spreding estimation of individual fibers as biography
Direction is broadcast, however monomer cellulose fiber directional spreding model can only obtain the overall estimation to diffusion profile in entire voxel, without
Directional resolution with sub- voxel grade, i.e., the tracking point change in location in same voxel do not influence the distribution of tracking direction；
To realize that the sub- voxel grade direction to diffusion signal is observed, while making full use of structuring side existing for neighboring voxels
To information, can by individual fibers historical trace direction to the interpolation of neighboring voxels diffusion directions obtain to currently with
The direction of track point is observed；
For multifilament local direction distributed model, the machine direction of each voxel can be distributed during extreme value vector set closes with
The immediate vector in the history direction of propagation is as diffusion principal directionThe corresponding weight value ω of each voxel diffusion principal direction respectively by
Apart from weights ω1With synteny weights ω2It codetermines：
Wherein,For eight diagonal neighboring voxels coordinate point sets of current tracking point, N is the seat of neighboring voxels
It marks [x, y, z], k is the tracking moment, and m is diagonal voxel (in total 8), and i is i-th of individual fibers particle；Apart from weights ω1Profit
It is weighted with trace point and the Euclidean distance of neighboring voxels coordinate points, the side that neighboring voxels are provided is weighed with its distance
To information weight；Synteny weights ω2With the history direction of propagation and neighboring voxels position between the orientation of current tracking point
Synteny size shows that current fibre individual is propagated trend and had with the neighboring voxels on historical trace direction as weight metric
There is stronger correlation.
To promote the flatness of fiber propagated forward, prevent the abnormal conditions that wide-angle shifts from occurring, historical trace directionAlso more bodies of individual fibers historical trace state are based ultimately upon to portray the inertial force of fiber propagation as weighted term
Plain neighbor interpolation directionIt is obtained by following formula：
Wherein ε1, ε2For vectorial normalization coefficient；
2) groups of fibers volume tracing direction estimation
The restriction relation between fibre bundle population mass motion trend is propagated for description individual fibers direction, passes through two
Multi-agent synergy action directionRealize the adjustment to individual fibers tracking trend：Based on fiber beam bundle profile and black and white matter boundary away from
Group from constraint corrects directionSimilarity constraint direction is moved towards with individual fibers in group
2.1) group's profile state trace model is established
It is described with state iteration renewal process based on Bayesian frame, realizes and make an uproar to measuring noise and motion model
The uncertain filtering that vocal cords come, and with the simple form similar to Kalman filter；Will utilize this model based on into
Row fibre bundle multiple targets status tracking；
At the k moment by being observed along sub- voxel grade directionPropagated forward, can obtain including nkA Point Target position
Set the fiber beam bundle observation set of measurementAndIndicate all fibres group until the k moment
Target observation sequence；Under basic thought based on the tracking of random matrix multiple targets will be observed using Bayes principle in individual
Multiple targets state joint probability density function p (xk,Xk|yk) with the product of Gaussian density function and inverse Wishart density functions come
It indicates：
p(xk,Xk|yk)=p (Yk,nk|xk,Xk)p(xk,Xk|yk-1)
Based on the number n for measuring individualkEqual-probability distribution it is assumed that the first item of above formula, that is, k moment observe set YkSeemingly
Right function can be simplified to following formula：
Wherein, N () is Gaussian Profile, and W () is distributed for Wishart, and H is observing matrix, The respectively survey at k moment
It measures mean vector and measures stroll matrix.
For convenience of the calculating and explanation of undated parameter, construct a suitable conjugate gradient descent method so that Posterior distrbutionp and
Prior probability function factorization is by prior distribution form having the same:
p(xk,Xk|yk-1)=p (xk|Xk,yk-1)p(Xk|yk-1)
=N (xk；xk|k-1,Pk|k-1)IW(Xk；vk|k-1,Xk|k-1)
Wherein, IW () is distributed for inverse Wishart, xk|k-1, Xk|k-1The respectively scalar parameter of one-step prediction and matrix ginseng
Number.N(xk；xk|k-1,Pk|k-1) indicate that obeying vector is desired for xk|k-1, covariance matrix Pk|k-1Gaussian Profile；
Multiple targets state joint posterior probability density function is multiplied to obtain by likelihood function with prior probability function：
p(xk,Xk|yk)∝N(xk；xk|k,Pk|k)IW(Xk；vk|k,Xk|k)
Based on above-mentioned Bayesian model, fiber beam bundle tracking mode includes center of mass motion state and contour feature, Ke Yifen
It Yong not state stochastic variable xkAnd XkExpectation iteration update to obtain；
2.2) constraint of the black and white matter profile to group's direction of motion,
To white matter fiber tracts research shows that its track trend is often parallel to black and white matter boundary, thus black and white matter boundary
Provide important information for the trend of fiber, by fiber beam bundle profile ratio of the front and back moment apart from black and white matter boundary always not
Become the foundation that black and white matter boundary is parallel to as measurement fibre bundle trend, using frontier distance function pair with barycenter direction of primary motionCentered on be uniformly distributed and angle is less than 5 ° of npA directionIt is evaluated with the best fibre bundle direction of propagation of determination.
With fibre bundle ellipsoid profile XkThree pairwise orthogonal axis of orientations inThe axis of orientation of angle minimum as tracking axis, remaining
Two orthogonal direction axis collectively form an elliptic plane, and tracking axis is rotated to candidate direction of primary motion wtIt is upper to form newly ellipse
Disk.The equal n of adjacent angle is up-sampled in the elliptic planesTo direction vector, and measure the elliptic wheel on these directions
Exterior feature point is at a distance from black and white matter boundaryWherein dt,2j, dt,2j+1Boundary in respectively opposite sample direction away from
From.Corresponding frontier distance deviation D (w is calculated to all candidate direction of primary motionst), take the time for generating minimum boundary range deviation
Direction of primary motion is selected most preferably to be moved towards as group, to obtain group orientation
Wherein, δ is that previous moment is most preferably moved towards determining corresponding sample direction frontier distance by group.
2.3) individual fibers move towards similarity constraint in group
Based on the fact be distributed there is Similar Track between adjacent fiber individual, interaction that individual fibers in group are tracked
Firmly repel model with interparticle attraction to portray, according to the space vector of k moment difference Fiber track points's
Apart from sizeUtilize parameter rmin, rmaxDivide three different types of fiber track zones of action：1. distributing areaSucking action is shown as between individual fibers in this area, promotes the bunching effect of similar track；2.
Repulsive areaRepelling effect is generated between trace point with smaller space length to ensure fiber population at individual
Diversity；3. neutral zone domain shows the independence in evolutionary process between the fiber path of larger space distance；
The parameter of wherein τ force strengths in order to control.
2.4) group's separation based on k-means
It is influenced due to being broken up by structure of fibrous tissue, it is fine in the region for the complex fiber structures such as with bifurcated, sprawling
The individual direction of propagation of dimension can detach, and further result in the division of fiber tracking group's profile.It is being drilled to portray group direction of motion
Enter more principal direction characteristics that these labyrinth regions occur during changing, the single distributional pattern of group profile is avoided to cause
The space topological continuity of limit needs to judge whether fibre bundle group occurs separation and the multiple targets to there is direction of propagation differentiation
Into line splitting.
Judged to realize that group detaches by being clustered based on the k-means of individual fibers tracking direction in group.Due to multiple sons
Group's separation can be by the cluster at class center there are two repeatedly being had to realize, therefore cluster centre number is set as 2.
It is more than when accounting for the 1/3 of group's sum comprising individual amount in given threshold value and each class as generation fiber using two cluster centre angles
The Rule of judgment of group's separation.
Claims (1)
1. a kind of brain white matter integrity imaging method based on group's tracking, it is characterised in that：Include the following steps：
1) individual fibers tracking direction is estimated
For multifilament local direction distributed model, propagated with history during the machine direction distribution extreme value vector set of each voxel is closed
The immediate vector in direction is as diffusion principal directionThe corresponding weight value ω of each voxel diffusion principal direction is respectively by apart from weights
ω1With synteny weights ω2It codetermines：
Wherein,For eight diagonal neighboring voxels coordinate point sets of current tracking point, N be neighboring voxels coordinate [x,
Y, z], k is the tracking moment, and m is diagonal voxel, 8 in total, and i is i-th of individual fibers particle；Apart from weights ω1Utilize tracking
Point and the Euclidean distance of neighboring voxels coordinate points are weighted, and the directional information that neighboring voxels are provided is weighed with its distance
Weight；Synteny weights ω2With the synteny of the history direction of propagation and neighboring voxels position between the orientation of current tracking point
Size shows that current fibre individual propagates trend and the neighboring voxels on historical trace direction with stronger as weight metric
Correlation；
Historical trace directionAs weighted term with portray fiber propagation inertial force, be based ultimately upon individual fibers history with
The multi-voxel proton neighbor interpolation direction of track stateIt is obtained by following formula：
Wherein ε1, ε2For vectorial normalization coefficient；
2) groups of fibers volume tracing direction estimation
Pass through two multi-agent synergy action directionsRealize the adjustment to individual fibers tracking trend：Based on fiber beam bundle profile with
The group of black and white matter frontier distance constraint corrects directionSimilarity constraint direction is moved towards with individual fibers in group
2.1) group's profile state trace model is established
At the k moment by being observed along sub- voxel grade directionPropagated forward, obtain include nkThe fibre that a Point Target position measures
Tie up beam bundle observation setAndIndicate all fibres multiple targets observation sequence until the k moment
Row；Using Bayes principle by individual observe under multiple targets state joint probability density function p (xk,Xk|yk) close with Gauss
The product of function and inverse Wishart density functions is spent to indicate：
p(xk,Xk|yk)=p (Yk,nk|xk,Xk)p(xk,Xk|yk-1)
Based on the number n for measuring individualkEqual-probability distribution it is assumed that the k moment observe set YkLikelihood function be simplified to following public affairs
Formula：
Wherein, N () is Gaussian Profile, and W () is distributed for Wishart, and H is observing matrix, The measurement at respectively k moment is equal
It is worth vector sum and measures stroll matrix；
It is by prior probability function factorization：
p(xk,Xk|yk-1)=p (xk|Xk,yk-1)p(Xk|yk-1)
=N (xk；xk|k-1,Pk|k-1)IW(Xk；vk|k-1,Xk|k-1)
Wherein, IW () is distributed for inverse Wishart, xk|k-1, Xk|k-1The respectively scalar parameter and matrix parameter of one-step prediction, N
(xk；xk|k-1,Pk|k-1) indicate that obeying vector is desired for xk|k-1, covariance matrix Pk|k-1Gaussian Profile；
Multiple targets state joint posterior probability density function is multiplied to obtain by likelihood function with prior probability function：
p(xk,Xk|yk)∝N(xk；xk|k,Pk|k)IW(Xk；vk|k,Xk|k)
Based on Bayesian model, fiber beam bundle tracking mode includes center of mass motion state and contour feature, random with state respectively
Variable xkAnd XkExpectation iteration update to obtain；
2.2) constraint of the black and white matter profile to group's direction of motion
Fiber beam bundle profile is constant always flat as fibre bundle trend is weighed in ratio of the front and back moment apart from black and white matter boundary
Row is in the foundation on black and white matter boundary, using frontier distance function pair with barycenter direction of primary motionCentered on be uniformly distributed and angle
Less than the n of predetermined anglepA directionIt is evaluated with the best fibre bundle direction of propagation of determination；
With fibre bundle ellipsoid profile XkThree pairwise orthogonal axis of orientations inThe axis of orientation of angle minimum as tracking axis,
Two remaining orthogonal direction axis collectively form an elliptic plane, and tracking axis is rotated to candidate direction of primary motion wtIt is upper to be formed newly
Elliptic plane；The equal n of adjacent angle is up-sampled in the elliptic planesTo direction vector, and measure ellipse on these directions
Circle contour point is at a distance from black and white matter boundaryWherein dt,2j, dt,2j+1Side in respectively opposite sample direction
Boundary's distance；Corresponding frontier distance deviation D (w is calculated to all candidate direction of primary motionst), take the minimum boundary range deviation of generation
Candidate direction of primary motion most preferably walked as group
Wherein, δ is that previous moment is most preferably moved towards determining corresponding sample direction frontier distance by group；
2.3) individual fibers move towards similarity constraint in group
According to the space vector of k moment difference Fiber track pointsApart from sizeUtilize parameter rmin, rmaxIt draws
Divide three different types of fiber track zones of action：(1) distributing areaIndividual fibers in this area
Between show as sucking action, promote the bunching effect of similar track；(2) repulsive areaWith smaller space away from
From trace point between generate repelling effect to ensure the diversity of fiber population at individual；(3) neutral zone domain shows larger sky
Between distance fiber path between independence in evolutionary process；
Wherein, the parameter of τ force strengths in order to control；
2.4) group's separation based on k-means
Judged to realize that group detaches by being clustered based on the k-means of individual fibers tracking direction in group, multiple subgroup separation are logical
The cluster at class center there are two repeatedly being had is crossed to realize, cluster centre number is set as 2, by two cluster centre angles
More than the judgement item as generation groups of fibers separation when accounting for the 1/3 of group's sum comprising individual amount in given threshold value and each class
Part.
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| A swarm tracking approach for stochastic white matter tractography;Yuanjing Feng et al;《2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro》;20110609;803-807 * |
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