CN109528198A - Brain response comparative approach based on low order Multivariate linear model - Google Patents
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- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves
- A61B5/055—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves involving electronic [EMR] or nuclear [NMR] magnetic resonance, e.g. magnetic resonance imaging
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/0033—Features or image-related aspects of imaging apparatus classified in A61B5/00, e.g. for MRI, optical tomography or impedance tomography apparatus; arrangements of imaging apparatus in a room
- A61B5/004—Features or image-related aspects of imaging apparatus classified in A61B5/00, e.g. for MRI, optical tomography or impedance tomography apparatus; arrangements of imaging apparatus in a room adapted for image acquisition of a particular organ or body part
- A61B5/0042—Features or image-related aspects of imaging apparatus classified in A61B5/00, e.g. for MRI, optical tomography or impedance tomography apparatus; arrangements of imaging apparatus in a room adapted for image acquisition of a particular organ or body part for the brain
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
- A61B5/7225—Details of analog processing, e.g. isolation amplifier, gain or sensitivity adjustment, filtering, baseline or drift compensation
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- A—HUMAN NECESSITIES
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- A61B2576/00—Medical imaging apparatus involving image processing or analysis
- A61B2576/02—Medical imaging apparatus involving image processing or analysis specially adapted for a particular organ or body part
- A61B2576/026—Medical imaging apparatus involving image processing or analysis specially adapted for a particular organ or body part for the brain
Abstract
The present invention provides a kind of brain response comparative approach based on low order Multivariate linear model, it is proposed a kind of low order Multivariate linear model first to carry out joint modeling to the reaction of all brain voxels, then regard the parameter Estimation of the model as an optimization problem, the majorized function with penalty term is introduced to guarantee the space-time flatness of Hemodynamics receptance function (HRF) and the sparsity of identified brain region, a kind of effective optimization algorithm is established simultaneously to estimate the brain activity of group, it is proposed a kind of quick selection strategy finally to realize the quick identification of punishment parameter brain region different with reaction.Brain response comparative approach provided by the invention, it not only can flexibly portray the difference of different zones and stimulus type HRF, and information " borrow " between different voxels may be implemented, improve the recognition accuracy of brain region, it is less to compare conventional method parameter simultaneously, computational efficiency is higher, provides a kind of new method for the research of brain activity.
Description
Technical field
The present invention relates to biomedical image analysis technical fields, and in particular to big based on functional magnetic resonance imaging data
The reaction that brain stimulates two kinds is compared
Background technique
Functional mri (functional magnetic resonance imaging, fMRI) is that one kind passes through
Blood oxygen level variation in detection blood vessel measures the technology of brain activity, it is because that its is non-invasive and high spatial resolution is wide
It is general to apply in human brain research.Each fMRI time series usually has hundreds of time points, and the unit time was from 0.5 second
By 2 seconds, the activity condition of brain voxel as time goes by one is shown.Since the brain activity of the mankind is with time, area
The variation of domain, subject and input stimulus and change, therefore by the fMRI data of a variety of Induced by Stimulation not only substantial amounts,
And it is extremely complex, contain huge noise.
In inducing the movable fMRI experiment of human brain using experiment stimulus sequence, research emphasis is normally based on extensively
Adopted linear model (GLM) frame calculates brain to the response situation of every kind of stimulus type, and GLM passes through Hemodynamics receptance function
(HRF) the fMRI time series of each brain voxel and stimulus sequence are linked, has developed one again under this frame
Parametric technique, non-parametric method and half ginseng method of the series to estimate HRF.
HRF estimation method in above-mentioned GLM frame carries out a large amount of univariate analysis, i.e., the once fMRI of one voxel of analysis
Time series.Since the adjacent voxel in space usually has similar function and similar nuclear magnetic resonance data, by voxel
Spatial information be included in it is more effective in HRF modeling and assessment.By assuming that the brain voxel in same block is having the same
Function shape, and document (Chaari et al., 2012；Makni et al., 2005,2008；Vincent et al., 2010)
It proposes to carry out spatially adaptive priori to the HRF height of same block voxel.Using Poisson HRF (Buxton and Frank,
1997；Friston et al., 1994b), document (Zhang et al., 2014a, 2016) establishes and adapts to fMRI time sequence
The bayes method of complicated temporal correlation in column.
As described above, HRF estimation method focuses primarily upon the HRF and drafting of every kind of stimulation of estimation in existing GLM frame
The active regions of brain, and present invention is primarily concerned with the comparisons of HRF.Particularly, in many fMRI experiment, researcher compares
Brain stimulates interest and controls the reaction of stimulation, it is intended to find out the brain region for having differential responses to both stimulations.It is a kind of
Common method is to extract some low-dimensional features (such as height) of HRF, is compared using hypothesis testing.Although this method is simple
It is single intuitive, but have following three defect.First, the HRF estimator of subject due to fMRI data low signal-to-noise ratio (SNR) and have
There is very big changeability, causes its characteristic quantity also unstable.Second, a kind of inspection of HRF feature is possibly can not to identify other HRF
The difference of feature, for example, the t- for comparing HRF height examines the difference that generally can not detect HRF shape.Third, to HRF feature
Detection be substantially monomer element analysis, have ignored the spatial character of fMRI data.Therefore, it is necessary to which it is anti-to invent a kind of new brain
Comparative approach is answered, to solve existing method existing above problem when carrying out brain response and comparing.
Summary of the invention
The purpose of the present invention is being directed to the deficiency of existing method, propose that low order Multivariate linear model comes combined simulation institute
There is reaction of the brain voxel to stimulation, and establish the estimation method of the corresponding HRF of relatively different stimulated a kind of, thus quick and precisely
Identify the brain region with differential responses.Technical solution of the present invention is that the brain based on low order Multivariate linear model is anti-
Comparative approach is answered, is included the following steps:
S1: low order Multivariate linear model is established to fMRI data；
S2: the majorized function with penalty term is introduced；
S3: minimizing punishment majorized function using iterative algorithm and then obtains model parameter estimation amount；
S4: the quick selection of punishment parameter and differential responses brain voxel is realized using the quick selection strategy proposed.
Further, S1 establishes the specific of low order Multivariate linear model to the fMRI time series of all brain voxels
Realize step are as follows:
S1.1: it enablesIt indicates the fMRI time series that subject i is observed in brain voxel j, it is established as follows
GLM model
Wherein, K is the species number that fMRI tests moderate stimulation, and m is the domain of HRF, is assigned a value of 15~25,R=1 T RT/128+1=7,To stimulate function, if by
Examination person i is in the irritating generation of time t, thenOtherwise
S1.2: HRF function in GLM model is indicated with following quadravalence B-spline basic functionbl
It (t) is equidistant 4 rank B-spline basic function on [0, m], spliting node is (t0=0, t1=1 ..., tm=m), L=4+m-1,
S1.3: by the fMRI time series of all brain voxels, stimulus sequence, basic function sequence, coefficient vector and error
Vector merges into matrix form, obtains Multivariate linear modelWhereinIt is that element isT × L tie up matrix；
S1.4: the coefficient matrix in Multivariate linear model is decomposed into the form of two low order battle arrays multiplicationLow order Multivariate linear model is obtained, wherein matrixWithThe temporal information of fMRI data is reflected respectively
And spatial information；
S1.5: consider that two methods acquire group HRF here: first method is to put the difference between individual and totality
Enter in error term, time matrix U and space matrix V in low order Multivariate linear model is kept to keep between Different Individual
It is constant, obtain group's low order Multivariate linear modelThis method can effectively combine all
The fMRI data of body estimate group's brain response (HRF), however it calculates complicated, and it is a large amount of more to handle to need more memories
Individual fMRI data；Second method is individually solved to each individualAgain by formulaGroup HRF is acquired, this method is intended to solve its calculating by the fMRI data of each individual of independent analysis
Problem.
Further, S2 introduces the specific implementation step of the majorized function with penalty term are as follows:
S2.1: matrix is introducedOn time smoothing penalty termTo reflect HRF
Time continuity；
S2.2: matrix is introducedOn space smoothing penalty termTo guarantee adjacent brain
Voxel has similar model parameter, whereinIndicate j andIt is spatially adjacent brain voxel；
S2.3: matrix is introducedOn sparse penalty termTo identify to stimulation
k1、k2Brain region with differential responses；
S2.4: it enablesMerge the penalty term of S2.1-S2.3 introducing and by model
The cost function that error of fitting generatesObtain the majorized function with penalty term
Further, S3 minimizes punishment majorized function using iterative algorithm and then obtains the specific of model parameter estimation amount
Realize step are as follows:
S3.1: given matrix U and d, finding matrix V keeps PSSE (V | U, d) minimum；
S3.2: given matrix V finds matrix U and d keeps PSSE (U, d | V) minimum；
S3.3: the optimal process in continuous iteration S3.1 and S3.2 is until convergence.
Further, S3.1, when giving matrix U and d, PSSE (V | U, d) it is convex not differentiable functions, therefore iteration line can be used
Property approximate gradient method (ALPG) solved, implement step are as follows:
S3.1 I: initialization enables V*, Z1, Z2Indicate null matrix identical with V dimension, G1ForIn Z1The gradient at place；
S3.1 II a: optimization problem is solvedWherein
<,>indicate inner product, ρ=1；
S3.1 II b: Z is calculated2Gradient G2=-G1-ρ(Z2-V*), if Z2Make the value drop of cost function PSSE (V | U, d)
It is low, update V*=Z2；
S3.1 III a: optimization problem is solved
S3.1 III b: Z is calculated1Gradient G1=-G2-ρ(Z1-V*), if Z1Make the value drop of cost function PSSE (V | U, d)
It is low, update V*=Z1；
S3.1 IV: repeating S3.1 II a to S3.1 III b until convergence.
Further, S4 carries out the quick of punishment parameter and differential responses brain voxel using the quick selection strategy of proposition
The specific implementation step of selection are as follows:
S4.1: being e from range to each punishment parameter-1~e10A large amount of candidate values start, utilize iteration in S3 to calculate
Method carries out model parameter estimation to the low order Multivariate linear model with the combination of different punishment parameters, is estimated accordingly
MatrixWith
S4.2: it calculatesIt is wherein that every group of penalty coefficient is corresponding to stimulation k not for 0 item1、k2With different anti-
The brain voxel answered, then selection meets the penalty coefficient combination of following standard, and (1) 5% to 50% brain voxel is selected,
(2) the maximum group variety being selected in brain voxel is accounted for by the 80% of selection voxel total amount；
S4.3: combining each penalty coefficient selected, and it is adjacent thereto unselected to calculate each selected deutocerebrum voxel
The related coefficient (if neighbours' voxel of selected voxel is selected, not calculating) of voxel, is averaged, then selection is average
The smallest penalty coefficient combination of related coefficient, and using its corresponding selected deutocerebrum voxel as to stimulation k1、k2With different anti-
The brain region answered.
Compared with the prior art, the present invention has the following advantages:
1, when multi-voxel proton HRF is indicated with low order form, model parameter quantity is substantially reduced, and computational efficiency greatly improves；
2, the low order expression of multi-voxel proton HRF means that the HRF of different voxels possesses common structure, realizes between voxel
Information " borrow ", and then improve HRF estimated efficiency and brain area domain recognition accuracy；
3, time and the spatial character of brain activity are respectively indicated using time and space matrix, it can be by the time in data
Information and spatial information are separated, to directly solve the problems, such as the computational complexity in functional MRI data analysis.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the brain response comparative approach based on low order Multivariate linear model of the present invention.
Fig. 2 is to establish low order Multivariate linear model flow chart.
Specific embodiment
Below in conjunction with attached drawing, the present invention is further described in detail.
Referring to Fig.1, the present invention includes establishing low order Multivariate linear model to the fMRI data of all brain voxels, is drawn
Enter the majorized function with penalty term, model parameter solved using iterative algorithm, by the quick selection strategy of proposition into
The quick selection of row penalty coefficient brain voxel different with reaction.Specific step is as follows:
One, low order Multivariate linear model is established to fMRI data
Step 1: following GLM model is established to the fMRI time series of each brain voxel
WhereinIndicate the fMRI time series that subject i is observed in brain voxel j, K is that fMRI tests moderate stimulation
Species number, m be HRF domain, be assigned a value of 15~25.r
=1 T RT/128+1=7, T is time span,It is r dimensional vector,It describes in experiment by subject's breathing, the heart
Low frequency wonder caused by jumping,Stimulation function, if subject i in the irritating generation of time t,OtherwiseH (u) is Hemodynamics receptance function (HRF).
Step 2: HRF function in GLM model is indicated with following quadravalence B-spline basic functionbl
It (t) is B-spline basic function equidistant on [0, m], spliting node is (t0=0, t1=1 ..., tm=m), L=4+m-1, simultaneously
It enablesTo meet boundary condition
Step 3: enabling Yi、EiRespectively indicating element isT × J tie up matrix, D is T × r of t behavior D (t)
Tie up matrix, diIt is that jth is classified asR × J tie up matrix,It is that element isT × L tie up matrix,It isCorresponding L × J ties up matrix, then can be to contain all node fMRI time serieses by the GLM model conversation in step 1
Matrix form obtains Multivariate linear model
Step 4: the coefficient matrix in Multivariate linear model is decomposed into the form of two low order battle arrays multiplicationObtain low order Multivariate linear modelWhereinWithIt is L × P and P respectively
× J ties up matrix (P=2), describes time and the spatial character of brain activity.
Step 5: the difference between individual and totality being put into error term, and is kept in low order Multivariate linear model
Time matrix and space matrix remained unchanged between different subjects, obtain group's low order Multivariate linear modelIn actually calculating, if calculating Out of Memory, each individual can individually be solvedAgain by formulaAcquire group HRF.
Two, the majorized function with penalty term is introduced
Step 6: introducing matrixOn time smoothing penalty term
Step 7: introducing matrixOn space smoothing penalty termWhereinIt indicates
J andIt is spatially adjacent brain voxel.
Step 8: introducing matrixOn sparse penalty termTo stimulate first two
Brain response be compared, further, can be by changing in sparse penalty termSubscript k other two kinds stimulations are compared
Compared with
Step 9: enablingModels fitting errorIt is merged with the penalty term that step 6- step 8 introduces, obtains band punishment
The majorized function of item
Three, model parameter is solved using iterative algorithm
Step 10: given matrix U and d, finding matrix V keeps PSSE (V | U, d) minimum:
It 10a) initializes, enables V*, Z1, Z2Indicate null matrix identical as V dimension, G1ForIn Z1The gradient at place；
10b) solve optimization subproblemWherein<,>
Indicate inner product, ρ controls Z2To V*Distance, be assigned a value of 1；
10c) calculate Z2Gradient G2=-G1-ρ(Z2-V*), if Z2Making the value of cost function PSSE (V | U, d) reduces, and updates
V*=Z2；
10d) solve optimization subproblem
10e) calculate Z1Gradient G1=-G2-ρ(Z1-V*), if Z1Making the value of cost function PSSE (V | U, d) reduces, and updates
V*=Z1；
10f) repeat 10b)~10e) until convergence, convergence here refer to iteration twice cost function PSSE (V | U,
D) difference is less than e-4。
Step 11: given matrix V finds matrix U and d keeps PSSE (U, d | V) minimum, at this time majorized function PSSE (U, d |
V) it is quadratic function about U and d, therefore can direct solution.
Step 12: the optimal process in continuous iterative step 10 and step 11 is until convergence, convergence here refer to twice
The majorized function PSSE difference of iteration is less than e-4。
Four, the quick selection of penalty coefficient and the different brain voxels of reaction
Step 13: being e from range to each punishment parameter-1~e10A large amount of candidate values start, utilize iterative algorithm pair
Low order Multivariate linear model with the combination of different penalty coefficients carries out model parameter estimation, obtains corresponding estimated matrixWith
Step 14: every kind of punishment parameter being combined, calculating first two stimulates corresponding space matrix differenceWherein
It is not that different brain voxels is reacted under the punishment parameter for 0 item, simultaneous selection meets the penalty coefficient combination of following standard:
(1) 5% to 50% brain voxel is selected, and (2) are selected the maximum group variety in brain voxel and account for by selection voxel total amount
80%.
Step 15: every group of punishment parameter selected being combined, it is adjacent thereto unselected to calculate each selected deutocerebrum voxel
The related coefficient (if neighbours' voxel of selected voxel is selected, not calculating) of middle voxel, is averaged, then selection is flat
The smallest penalty coefficient combination of related coefficient, and using its corresponding selected deutocerebrum voxel as to first two stimulate the reaction not
Same brain region.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
Anyone skilled in the art within the technical scope of the present disclosure, according to the technique and scheme of the present invention and its
Inventive concept is subject to equivalent substitution or change, should be covered by the scope of protection of the present invention.
Claims (6)
1. a kind of brain response comparative approach based on low order Multivariate linear model, which comprises the following steps:
S1: low order Multivariate linear model is established to fMRI data；
S2: the majorized function with penalty term is introduced；
S3: minimizing punishment majorized function using iterative algorithm and then obtains model parameter estimation amount；
S4: the quick selection of punishment parameter and differential responses brain voxel is realized using the quick selection strategy proposed.
2. a kind of brain response comparative approach based on low order Multivariate linear model according to claim 1, special
Sign is,
S1 establishes the specific implementation step of low order Multivariate linear model to fMRI data are as follows:
S1.1: it enablesIt indicates the fMRI time series that subject i is observed in brain voxel j, establishes following GLM model
Wherein, K is the species number that fMRI tests moderate stimulation, and m is the domain of HRF, is assigned a value of 15~25,R=1T RT/128+1=7,To stimulate function, if tested
Person i is in the irritating generation of time t, thenOtherwise
S1.2: HRF function in GLM model is indicated with following quadravalence B-spline basic functionbl(t) it is
Equidistant B-spline basic function on [0, m], spliting node are (t0=0, t1=1 ..., tm=m), L=4+m-1,
S1.3: by the fMRI time series of all brain voxels, stimulus sequence, basic function sequence, coefficient vector and error vector
Matrix form is merged into, Multivariate linear model is obtainedWhereinIt is that element isT × L tie up matrix；
S1.4: the coefficient matrix in Multivariate linear model is decomposed into the form of two low order battle arrays multiplication?
To low order Multivariate linear model, wherein matrixWithThe temporal information and spatial information of fMRI data are reflected respectively；
S1.5: consider that two methods acquire group HRF here: first method is that the difference between individual and totality is put into mistake
In poor item, time matrix U and space matrix V in low order Multivariate linear model is kept to keep not between Different Individual
Become, obtains group's low order Multivariate linear modelThis method can effectively combine all individuals
FMRI data estimate group's brain response (HRF) that however it calculates complicated, it is a large amount of multiple to handle to need more memories
Body fMRI data；Second method is individually solved to each individualAgain by formulaGroup HRF is acquired, this method is intended to solve its calculating by the fMRI data of each individual of independent analysis
Problem.
3. a kind of brain response comparative approach based on low order Multivariate linear model according to claim 1, special
Sign is,
S2 introduces the specific implementation step of the majorized function with penalty term are as follows:
S2.1: matrix is introducedOn time smoothing penalty termCome reflect HRF when
Between continuity；
S2.2: matrix is introducedOn space smoothing penalty termTo guarantee adjacent brain voxel
With similar model parameter, whereinIndicate j andIt is spatially adjacent brain voxel；
S2.3: matrix is introducedOn sparse penalty termTo identify to stimulation k1、k2
Brain region with differential responses；
S2.4: it enablesMerge the penalty term of S2.1-S2.3 introducing and by models fitting
The cost function that error generatesObtain the majorized function with penalty term
4. a kind of brain response comparative approach based on low order Multivariate linear model according to claim 1, special
Sign is,
S3 minimizes punishment majorized function using iterative algorithm and then obtains the specific implementation step of model parameter estimation amount are as follows:
S3.1: given matrix U and d, finding matrix V keeps PSSE (V | U, d) minimum；
S3.2: given matrix V finds matrix U and d keeps PSSE (U, d | V) minimum；
S3.3: the optimal process in continuous iteration S3.1 and S3.2 is until convergence.
5. a kind of brain response comparative approach based on low order Multivariate linear model according to claim 1, special
Sign is, when giving matrix U and d, finding matrix V makes the smallest specific implementation step of PSSE (V | U, d) are as follows:
S3.1 I: initialization enables V*, Z1, Z2Indicate null matrix identical with V dimension, G1ForIn Z1The gradient at place；
S3.1 II a: optimization problem is solvedWherein<,>
Indicate inner product, ρ=1；
S3.1 II b: Z is calculated2Gradient G2=-G1-ρ(Z2-V*), if Z2Making the value of cost function PSSE (V | U, d) reduces, more
New V*=Z2；
S3.1 III a: optimization problem is solved
S3.1 III b: Z is calculated1Gradient G1=-G2-ρ(Z1-V*), if Z1Making the value of cost function PSSE (V | U, d) reduces,
Update V*=Z1；
S3.1 IV: repeating S3.1 II a to S3.1 III b until convergence.
6. a kind of brain response comparative approach based on low order Multivariate linear model according to claim 1, special
Sign is,
S4 realizes the specific reality of punishment parameter and differential responses brain voxel quickly selected using the quick selection strategy of proposition
Existing step are as follows:
S4.1: being e from range to each punishment parameter-1~e10A large amount of candidate values start, using the iterative algorithm in S3 to band
There is the low order Multivariate linear model of different punishment parameter combinations to carry out model parameter estimation, obtains corresponding estimated matrix
With
S4.2: combining every kind of punishment parameter, calculatesIt is wherein under punishment parameter combination to stimulation not for 0 item
k1、k2Brain voxel with differential responses, the penalty coefficient that then selection meets following standard combine, (1) 5% to 50%
Brain voxel is selected, and (2) are selected the maximum group variety in brain voxel and account for by the 80% of selection voxel total amount；
S4.3: combining every group of punishment parameter selected, calculates each selected deutocerebrum voxel unselected voxel adjacent thereto
Related coefficient (if neighbours' voxel of selected voxel is selected, not calculating), be averaged, then selection is average related
The smallest penalty coefficient combination of coefficient, and using its corresponding selected deutocerebrum voxel as to stimulation k1、k2With differential responses
Brain region.
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| CN110706804A (en) * | 2019-08-23 | 2020-01-17 | 刘雷 | Application method of hybrid expert system in classification of lung adenocarcinoma |
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