CN102509282A - Efficiency connection analysis method fused with structural connection for each brain area - Google Patents

Abstract

The invention discloses an efficiency connection analysis method fused with structural connection for each brain area. The method comprises the following steps of: extracting and analyzing a brain structural network of an interested area, and converting obtained structural information into a prior probability distribution space of an efficiency connection parameter; establishing an efficiency connection model based on a variational Bayesian framework; and evaluating efficiency connection of each brain area through ensemble learning and an EM (Expectation Maximization) algorithm. Compared with other methods, the method has the advantages that: 1, structural connection is mapped to the prior probability space of the efficiency connection parameter, and a model parameter is optimized in subsequent ensemble learning, so that a relation between the structural connection and the efficiency connection is reflected truly; and 2, structural connection information is combined, so that a result of brain activity analysis is more reliable, and convenience is brought to the discuss of the practical situation of an individual.

Description

The interval usefulness of each brain that a kind of fusion structure connects connects analytical approach

Technical field

The present invention relates to the usefulness connection computing method that a kind of fusion structure connects, belong to fields such as medical image methodology and medical image signal Processing, be applicable to the analysis and the research of brain activity.

Background technology

Previously discover that mental illnesses such as comprising depression, schizophrenia, epilepsy is all relevant with the impaired or functional disorder of the structure of brain.The structural information of brain (structure connection) and function information (function is connected, usefulness connect) have reflected the situation of whole brain, and the exploration and the research of the pathomechanism of various mental illnesses is played an important role.And structure connects and to have close contact between connecting with merit (effect), and merit (effect) can be connected and reflect the structure connection on certain degree, but not exclusively depends on the structure connection.Research in the past seldom combines them and studies, if be connected with function from multi-modal angle fusion structure connection, bring great help will for the research of various mental illnesses.

Connect with usefulness about integrated structure and to be connected the research of carrying out brain activity, have some primary method and exploration but have some problems.Method 1: utilize DTI (dispersion tensor magnetic resonance imaging diffusion tensor imaging) and MEG (magneticencephalogram magnetoencephalography) advantage separately, research and analyse separately from different angles, then analysis-by-synthesis.But do not inquire into the two relation, do not relate to the fusion between them.Method 2: the result that the analysis that utilization connects structure connects function retrains and optimizes.Though this method utilization has also been analyzed relation between the two, still not having can be really with both fusion.Method 3: the experimental data of utilizing structure to connect is come the function of extensive simulation brain, or studies the nervous activity that the network structure of what type can produce specific function.This method can be got up both fusions, but still just focuses on discussion contact between the two.

Summary of the invention

In order to solve the weak point in the existing method, the present invention proposes the interval usefulness connection analytical approach of each brain that a kind of new fusion structure connects, concrete technical scheme is following:

The interval usefulness of each brain that fusion structure connects connects analytical approach, and basic thought is: extract and analyze the brain structure network of region of interest, and convert the structural information that obtains into prior probability distribution space that usefulness connects parameter; Set up usefulness link model then based on the variation Bayesian frame; Through integrated study (Ensemble Learning) and EM algorithm (Expectation-Maximization Algorithm), ask for the interval usefulness of each brain and connect at last.

The concrete steps of this method comprise:

1, a kind of fusion structure connects with usefulness and is connected the method for carrying out the cerebration analysis, it is characterized in that step comprises:

1) nerve fibre that at first utilizes dispersion tensor magnetic resonance imaging DTI data to carry out full brain is followed the trail of, and sets up the structure connection network of whole brain; In addition, the magneticencephalogram MEG signal that collects being carried out the 3D source rebuilds; The 3D source of MEG rebuilds the method for having used MSP (Multiple Sparse Priors), this step mainly be want SPM8 ( Http:// www.fil.ion.ucl.ac.uk/spm/) software handles.This method is a kind of method of using layering Bayes and experience Bayes to carry out distributed dipole source reconstruction, and its advantage is can under simple priori, carry out a plurality of sparse cortexes to be derived from moving choosing.

2) area-of-interest of analyzing as required extracts the core network in the said connection network, and core network is converted into figure;

If the brain any interested district in the core network is i, each the region of interest ROI (i) in the core network all is regarded as a node i, and the cortex area of the area-of-interest of node i representative is S (i);

(i, j), the length and the weight on limit are respectively nerve fibre ROI (i) and the ROI (j) that connects two brain district i and j in the core network corresponding to the limit E of connected node i and j

With

Wherein, E _fBe all fibres of connected node i and j, l _fBe the length of these fibers, N _fNumber for nerve fibre; So l is the average length of all nerve fibres in connection two zones, what w reflected is the Connection Density in two zones;

3) (the structural information here refers to the length and the weight on limit to the structural information of each region of interest of gained; Length and density corresponding to the nerve fibre that connects region of interest) carry out normalization; And be transformed into the prior probability distribution space that usefulness connects, transformation model is: ${\mathrm{\Σ}}_{\mathrm{Ij}}=\frac{{\mathrm{\Σ}}_0}{1+{\mathrm{\Σ}}_0{e}^{a-{\mathrm{Bs}}_{\mathrm{Ij}}}}={\mathrm{\α}}_{\mathrm{Ij}}^{-1}={\mathrm{\α}}_0+e^{a-{\mathrm{Bs}}_{\mathrm{Ij}}};$

Usefulness connection Gaussian distributed N between any brain district i and the j (0, ∑ _Ij), s _IjBe the structure link information after the normalization, ∑ ₀, a, b be the customized parameter of model;

4) the usefulness link model based on the variation Bayesian frame is Y=XW+E, and among the model Y, the interval usefulness of the corresponding expression of W brain connects parameter matrix, and this matrix W is the autoregressive coefficient parameter matrix;

E is that average is zero, the precision matrix is the Gaussian noise of Λ, and Λ～Γ (b, c); X, Y is the area-of-interest signal after rebuilding through the 3D source, for given data set D={X, Y} has: $p\left(D\right|W,\mathrm{\Λ})={\left(2\mathrm{\π}\right)}^{-\mathrm{DN}/2}{\left|\mathrm{\Λ}\right|}^2{e}^{-\frac{1}{2}\mathrm{Tr}\left(\mathrm{\Λ}{E}_D\left(W\right)\right)};$ For the ease of the analysis of model Y, it is vectorial w that W is elongated, and the distribution of w is following:

$p\left(w\right|\left\{{\mathrm{\α}}_k\right\})=\underset{k=1}{\overset{n}{\mathrm{\Π}}}{\left(\frac{{\mathrm{\α}}_k}{2\mathrm{\π}}\right)}^{1/2}{e}^{-{\mathrm{\α}}_k{E}_k\left(w\right)};$ Wherein, d is the number of brain district signal, and N is the length of brain district burst, and w is the vector that matrix W stretches, and n is the number that usefulness connects parameter, $E_k\left(w\right)=\frac{1}{2}{w}^T{I}_{k}w;$

Said parameter w, Λ and α Gaussian distributed N (0, ∑ _Ij);

5), ask for the interval usefulness of each brain and connect Y through integrated study method and greatest hope EM algorithm.

Beneficial effect

The present invention has the following advantages with respect to additive method: 1, structure is connected the prior probability space that is mapped to usefulness connection parameter by transformation model; And in follow-up integrated study the Optimization Model parameter, the relation that makes structure connect to be connected with usefulness is reflected really; 2, combine the structure link information, the result who makes cerebration analyze is more reliable, and is convenient to individuality is carried out the discussion of actual conditions.

Description of drawings

Fig. 1: the basic procedure synoptic diagram of this method;

Fig. 2: structure link information treatment scheme synoptic diagram;

Fig. 3: structural information transformation model diagram intention;

Fig. 4: usefulness connects synoptic diagram as a result.

Embodiment

Combine accompanying drawing that the present invention is done further description at present:

Whole flow process of the present invention can be with reference to accompanying drawing 1, and concrete implementation step is following:

1, brain structure connects the foundation of network and the pre-service and the source reconstruction of brain magnetic signal

The generation that high-precision configuration from nuclear magnetic resonance disperse image DTI to whole brain connects network needs following step: (1) diffusion-weighted treatment of picture; Like eddy current correction, a NMO correction; The calculating of the match of dispersion tensor model, dispersion tensor and anisotropy value, and the conversion of normed space etc.; (2) albocinereous cutting apart; (3) white matter nerve fiber bundles is followed the trail of imaging; (4) cutting apart of cerebral cortex structure and choosing of area-of-interest; (5) core network that the area-of-interest of analyzing as required extracts, and be translated into figure.Each region of interest ROI (i) in the network all can be considered a node i, and the cortex area in the zone of its representative is S (i).(i, j), the length and the weight on limit are respectively corresponding to the limit E of connected node i and j to connect the nerve fibre of ROI (i) and ROI (j) in the network $l=\frac{1}{N_f}{\mathrm{\Σ}}_{f\∈E_f}{l}_f,$ $w=\frac{2}{S\left(i\right)+S\left(j\right)}{\mathrm{\Σ}}_{f\∈E_f}\frac{1}{l_f}.$ Wherein, E _fBe all fibres of connected node i and j, l _fBe the length of these fibers, N _fBe the number of nerve fibre, so l refers to the average length of all nerve fibres that connect two zones, what w reflected is the Connection Density in two zones.This treatment scheme can be with reference to accompanying drawing 2.

After the pre-service of brain magnetic signal (comprise conversion, cut apart, filtering, removal artefact, equalization), carry out the 3D source and rebuild, this treatment scheme has been used the method for MSP (Multiple Sparse Priors), this method step mainly be want SPM8 ( Http:// www.fil.ion.ucl.ac.uk/spm/) software handles.This method is a kind of method of using layering Bayes and experience Bayes to carry out distributed dipole source reconstruction, and its advantage is can under simple priori, carry out a plurality of sparse cortexes to be derived from moving choosing.

2, the conversion of structure link information

The structural information of each region of interest of above-mentioned gained is carried out normalization, and it is transformed into the prior probability distribution space that usefulness connects, transformation model is:

${\mathrm{\Σ}}_{\mathrm{ij}}=\frac{{\mathrm{\Σ}}_0}{1+{\mathrm{\Σ}}_0{e}^{a-{\mathrm{bs}}_{\mathrm{ij}}}}={\mathrm{\α}}_{\mathrm{ij}}^{-1}={\mathrm{\α}}_0+e^{a-{\mathrm{bs}}_{\mathrm{ij}}}$

Usefulness connection Gaussian distributed N between any brain district i and the j (0, ∑ _Ij), s _IjBe the structure link information after the normalization, ∑ ₀, a, b be the customized parameter of model, in follow-up integrated study, step by step they is optimized, make structure connect the relation that is connected with usefulness and reflected really.The functional arrangement of this transformation model is shown in accompanying drawing 3.

3, based on the analysis of the usefulness link model of variation Bayesian frame

Usefulness link model based on the variation Bayesian frame is Y=XW+E.W is the autoregressive coefficient matrix in the model, and the usefulness interval corresponding to brain connects parameter matrix, and these parameter Gaussian distributed N (0, ∑ _Ij); E is that average is zero, and the precision matrix is the Gaussian noise of Λ, and Λ～Γ (b, c).X, Y are the area-of-interest signal after rebuilding through the source, and for given data set D={X, Y} has:

$p\left(D\right|W,\mathrm{\Λ})={\left(2\mathrm{\π}\right)}^{-\mathrm{dN}/2}{\left|\mathrm{\Λ}\right|}^2{e}^{-\frac{1}{2}\mathrm{Tr}\left(\mathrm{\Λ}{E}_D\left(W\right)\right)}$

For the ease of the analysis of model, it is that it distributes as follows with vectorial w that coefficient parameter matrix W is elongated:

$p\left(w\right|\left\{{\mathrm{\α}}_k\right\})=\underset{k=1}{\overset{n}{\mathrm{\Π}}}{\left(\frac{{\mathrm{\α}}_k}{2\mathrm{\π}}\right)}^{1/2}{e}^{-{\mathrm{\α}}_k{E}_k\left(w\right)}$

The number of d brain district signal wherein; N is the length of burst; W is that usefulness connects the vector that parameter matrix W stretches; N is the number that usefulness connects parameter,

4, finding the solution of model provides the algorithm of a kind of improved EM in this example:

For data set D given above and parameter θ={ w, α, Λ }, the logarithm argument of model m does

log?p(D|m)＝F(θ)+KL(q(θ|D)||p(θ|D，m))

F (θ) is the negative free energy of model, when q (θ | D)=p (θ | D, m), model logarithm argument obtained lower limit F (θ) when promptly the approximate posterior probability of model parameter distributed and is equal to true posterior probability and distributes, the parameter of this moment is requirements of model parameter just also.Yet directly finding the solution parameter through equality is difficulty very, with F (θ) further decompose obtain F (θ)=∫ q (θ | D) log p (D | θ, m) d θ-KL (q (and θ | D) || p (θ | m)).The initial value of given parameter θ is also fixed α and Λ wherein, can proper q (w|D)=e through simplifying ^{I (w)}The time, F (θ) obtains maximal value, wherein I (w)=∫ ∫ q (Λ | D) q (α | D) log (p (D|w, Λ) p (w| α)) d α d Λ.Undated parameter w and fixedly w and Λ in like manner can solve α, and also fixedly α and w solve Λ to undated parameter α then.Through the algorithm of this improved EM (Expectation-Maximization), constantly carry out iteration until convergence, the usefulness of obtaining between the parameter He Genao district of model connects (result sees accompanying drawing 4).

Claims (3)

1. the interval usefulness of each brain of a fusion structure connection connects analytical approach, it is characterized in that step comprises:

1) nerve fibre that at first utilizes dispersion tensor magnetic resonance imaging DTI data to carry out full brain is followed the trail of, and sets up the structure connection network of whole brain; In addition, the magneticencephalogram MEG signal that collects being carried out the 3D source rebuilds;

2) area-of-interest of analyzing as required extracts the core network in the said connection network, and core network is converted into figure;

If the brain any interested district in the core network is i, each the region of interest ROI (i) in the core network all is regarded as a node i, and the cortex area of the area-of-interest of node i representative is S (i);

(i, j), the length and the weight on limit are respectively nerve fibre ROI (i) and the ROI (j) that connects two brain district i and j in the core network corresponding to the limit E of connected node i and j

With

Wherein, E _fBe all fibres of connected node i and j, l _fBe the length of these fibers, N _fNumber for nerve fibre; So l is the average length of all nerve fibres in connection two zones, what w reflected is the Connection Density in two zones;

3) structural information of each region of interest of gained is carried out normalization, and be transformed into the prior probability distribution space that usefulness connects, transformation model is: ${\mathrm{\Σ}}_{\mathrm{Ij}}=\frac{{\mathrm{\Σ}}_0}{1+{\mathrm{\Σ}}_0{e}^{a-{\mathrm{Bs}}_{\mathrm{Ij}}}}={\mathrm{\α}}_{\mathrm{Ij}}^{-1}={\mathrm{\α}}_0+e^{a-{\mathrm{Bs}}_{\mathrm{Ij}}};$ Said structural information refers to the length and the weight on said limit, corresponding to the length and the density of the nerve fibre that connects region of interest;

Usefulness connection Gaussian distributed N between any brain district i and the j (0, ∑ _Ij), s _IjBe the structure link information after the normalization, ∑ ₀, a, b be the customized parameter of model;

4) the usefulness link model based on the variation Bayesian frame is Y=XW+E, and among the model Y, the interval usefulness of the corresponding expression of W brain connects parameter matrix, and this matrix W is the autoregressive coefficient parameter matrix;

E is that average is zero, the precision matrix is the Gaussian noise of Λ, and Λ～Γ (b, c); X, Y is the area-of-interest signal after rebuilding through the 3D source, for given data set D={X, Y} has: $p\left(D\right|W,\mathrm{\Λ})={\left(2\mathrm{\π}\right)}^{-\mathrm{DN}/2}{\left|\mathrm{\Λ}\right|}^2{e}^{-\frac{1}{2}\mathrm{Tr}\left(\mathrm{\Λ}{E}_D\left(W\right)\right)};$ For the ease of the analysis of model Y, it is vectorial w that W is elongated, and the distribution of w is following:

$p\left(w\right|\left\{{\mathrm{\α}}_k\right\})=\underset{k=1}{\overset{n}{\mathrm{\Π}}}{\left(\frac{{\mathrm{\α}}_k}{2\mathrm{\π}}\right)}^{1/2}{e}^{-{\mathrm{\α}}_k{E}_k\left(w\right)};$ Wherein, d is the number of brain district signal, and N is the length of brain district burst, and w is the vector that matrix W stretches, and n is the number that usefulness connects parameter, $E_k\left(w\right)=\frac{1}{2}{w}^T{I}_{k}w;$

Said parameter w, Λ and α Gaussian distributed N (0, ∑ _Ij);

5), ask for the interval usefulness of each brain and connect Y through integrated study method and greatest hope EM algorithm.

2. method according to claim 1 is characterized in that in the said step 1), and the step of setting up the structure connection network of whole brain comprises:

101) the DTI image is handled, and comprising:

Eddy current correction and the calculating of match, dispersion tensor and the anisotropy value of a NMO correction, dispersion tensor model and the conversion of normed space;

102) albocinereous cutting apart;

103) white matter nerve fiber bundles is followed the trail of imaging;

104) cutting apart of cerebral cortex structure and choosing of area-of-interest.

3. method according to claim 1 is characterized in that in the said step 5), for said data set D and parameter θ={ w, α; Λ }, the logarithm argument of model Y is: log p (D|m)=F (θ)+KL (q (θ | D) || p (θ | D, m)); Wherein F (θ) is the negative free energy of model Y, when q (θ | D)=p (θ | D, m); Be that the approximate posterior probability of model parameter distributes when being equal to true posterior probability and distributing, when model Y logarithm argument obtained lower limit F (θ), parameter θ model Y just required parameter;

F (θ) is obtained further the decomposition:

F(θ)＝∫q(θ|D)logp(D|θ，m)dθ-KL(q(θ|D)||p(θ|m))；

The initial value of given parameter θ is also fixed α and Λ wherein, obtains through simplification: as q (w|D)=e ^{I (w)}The time, F (θ) obtains maximal value, wherein I (w)=∫ ∫ q (Λ | D) q (α | D) log (p (D|w, Λ) p (w| α)) d α d Λ; Undated parameter w and fixedly w and Λ in like manner solve α, and also fixedly α and w of undated parameter α solves Λ then;

Through this algorithm, constantly carry out iteration until convergence, the usefulness of obtaining between the parameter He Genao district of model connects.

Images