CN105913480B - A kind of brain fiber microstructure reconstructing method based on space structure consistency - Google Patents

Abstract

A kind of brain fiber microstructure reconstructing method based on space structure consistency, includes the following steps：Step 1, using the bivalve basic function based on spherical surface dictionary deconvolution, step 2 establishes space structure consistency model, is based on separable space domain

Description

A kind of brain fiber microstructure reconstructing method based on space structure consistency

Technical field

The present invention relates to the medical imaging under computer graphics, Nervous System Anatomy field, especially a kind of brain fiber is micro- Structural remodeling method.

Background technology

With the development of the times, the progress of Medical Imaging Technology, diffusion tensor imaging is in the research of Neuscience Increasing influence power is accounted for, it is that this epoch is indispensable to possess advanced neuroimaging technology；Diffusion tensor imaging is made For a kind of method of emerging description brain structure, while being also a kind of unique method of In vivo detection human brain structure, in nerve Medical domain is mainly the research to brain tissue structure feature；Currently, diffusion tensor imaging is just widely used in essence The supplementary means of refreshing section's disease and diagnosis, it might even be possible to be used for the formulation of pre-operative surgical scheme, it may be said that it is in medical domain Contribution has the advantage that can not be substituted；So having great meaning for brain science to the algorithm research based on diffusion tensor.

Brain white matter integrity directional spreding Model Reconstruction is one of the significant process of brain fiber imaging, is provided for fibre bundle tracking Accurate machine direction estimation.The constraints of conventional method tends to rely on the machine direction information of priori, limits calculating The raising of efficiency and precision.It is proposed that new more advanced brain white matter integrity directional spreding model is the hot spot of research.

Invention content

The computational efficiency of existing brain fiber microstructure reconstructing method is relatively low, the lower deficiency of precision in order to overcome, the present invention A kind of promotion computational efficiency, the higher brain fiber microstructure reconstructing method based on space structure consistency of precision are provided.

The technical solution adopted by the present invention to solve the technical problems is：

A kind of brain fiber microstructure reconstructing method based on space structure consistency, includes the following steps：

Step 1, using the bivalve basic function based on spherical surface dictionary deconvolution：

In rotating vectorAnd center vectorOn fiber probability-distribution function f (v | u) be known as fODF, Middle m_vIndicate Spatial Dimension, the m of rotating vector group_uWhat is indicated is the Spatial Dimension of center vector group, passes through spherical surface the Method of Deconvolution Fiber morphology structure is described as to the convolution of kernel function, in diffusion gradient g ∈ S²On measuring signal s (g | u)：

Wherein r (g, v) indicates kernel function, and μ (v) is in S²On Haar estimate；For the sake of convenient, s (g | u) signal can be by equal The even discrete sampling μ being distributed in unit sphere is indicated：

Define fiber receptance function：

Wherein It is the diagonal matrix for characterizing diffusion tensor D, λ_maxIt is this to angular moment Principal eigenvector in battle array, l indicate diffusion-sensitive coefficient and the influence degree that anisotropy interaction decays to signal；With This expands the estimation of the fiber receptance function on more shell sampling plans：

Wherein J=1 ..., q refers to j-th spherical shell,Correspondence is distributed in b_JGradient vector collection g on shell,Indicate J B under a spherical shell_JThe l that a diffusion-sensitive coefficient is referred to；To push away a kind of new machine direction distribution function form：

d(v,u_i) indicate Vector Groups v and u_iOne group of excessively complete directional spreding basic function under a direction, w_iIt is base letter Several relative weightings,It is w_iThe number of middle nonzero element；Apparent diffusion coefficient can be by approximate evaluation：

g^TDg≈λ_maxg^T(vv^T) g=λ_maxcos²θ(g,v)

θ (g, v) indicates included angle cosine function, and D is indicated by all d (v, u_i) constitute one group of basic function dictionary；For Dictionary base distribution under description spherical coordinate, we are by d (v, u under original rectangular coordinate system_i) be described as under spherical coordinate 's

It is the minimum angle cosine on discrete set, κ₁Machine direction distribution function is normalized to unit ball, κ₂It is for adjusting The parameter of whole peak value, τ indicate even power；The estimation of basic function coefficient w in machine direction distribution function fODF：

Φ is observing matrix, and s is signal vector；To avoid pseudo- peak and complicated algorithm and the extensive morbid state of higher order The calculating of inverse problem directly acquires the estimation of basic function coefficient w by non-negative least square method：

w^*Indicate the optimal solution of w；

Step 2 establishes space structure consistency model：

Using Bayesian formula, obtain：

P(x|s)∝P(s|x)P(x)

Posterior probability density P (x | s) is proportional to multiplying for data likelihood function P (s | x) and priori probability density function P (x) Product；It is rewritten as later：

U^InIt is internal energy,It is external energy, β_jIt is the hyper parameter of prior distribution；The maximization of posterior probability converts For the minimum of total energy function：

P (x | s) it is posterior probability density, U^InIt is internal energy,It is external energy, β_jIt is the hyper parameter of prior distribution； Wherein internal energy：

S is measuring signal collection, and S ' expressions are signals to be estimated, and W is w coefficient sets, and Θ is the block based on observing matrix Diagonal matrix；External energy：

Indicate external energy,Indicate that the arithmetic average of machine direction distribution function, M pass through down-sampled direction v_t One dictionary base of training is gone to obtain, w_cIndicate the coefficient of c-th of voxel, c ∈ Ω；The estimation of W：

s_cIt is coefficient of the measuring signal in c-th of voxel, w_cIt is coefficient of the dictionary in c-th of voxel；Body in order to obtain The structure of plain decussating fibers defines global cost function：

By calculating w_cAnd w_cThe coefficient COS distance of surrounding neighbors obtains, α₁An artificially defined parameter, Q be by Training dictionary obtains on basic function；The local linear approximate evaluation of space structure consistency model：

T is iteration index, δ_ξIt is predefined aiding constant,It is the extension Lagrange multiplier vector of the t times iteration, Above formula is divided into two parts：

It is optimized for a separable space domain, is solved, is obtained with enhancing Lagrangian method：

Wherein I indicates unit matrix；

Based on separable space domainThe distribution that machine direction Distribution Value is fitted using the soft MATLAB emulation of mathematics, is led to The extreme point crossed in search machine direction Distribution Value obtains the principal direction of fiber.

The present invention technical concept be：Apparent, more flexible, more effective spherical shape bivalve basic function, and it is basic herein It is upper to form an excessively complete dictionary to characterize the machine direction distribution function (abbreviation fODF) of more shell basic function weightings.

Beneficial effects of the present invention are mainly manifested in：It is higher to promote computational efficiency, precision.

Specific implementation mode

The invention will be further described below.

A kind of brain fiber microstructure reconstructing method based on space structure consistency, includes the following steps：

Step 1, using the bivalve basic function based on spherical surface dictionary deconvolution：

In rotating vectorAnd center vectorOn fiber probability-distribution function f (v | u) be known as fODF, Middle m_vIndicate Spatial Dimension, the m of rotating vector group_uWhat is indicated is the Spatial Dimension of center vector group, passes through spherical surface the Method of Deconvolution Fiber morphology structure is described as to the convolution of kernel function, in diffusion gradient g ∈ S²On measuring signal s (g | u)：

Wherein r (g, v) indicates kernel function, and μ (v) is in S²On Haar estimate；For the sake of convenient, s (g | u) signal can be by equal The even discrete sampling μ being distributed in unit sphere is indicated：

Define fiber receptance function：

Wherein It is the diagonal matrix for characterizing diffusion tensor D, λ_maxIt is this to angular moment Principal eigenvector in battle array, l indicate diffusion-sensitive coefficient and the influence degree that anisotropy interaction decays to signal；With This expands the estimation of the fiber receptance function on more shell sampling plans：

Wherein J=1 ..., q refers to j-th spherical shell,Correspondence is distributed in b_JGradient vector collection g on shell,Indicate J B under a spherical shell_JThe l that a diffusion-sensitive coefficient is referred to；To push away a kind of new machine direction distribution function form：

d(v,u_i) indicate Vector Groups v and u_iOne group of excessively complete directional spreding basic function under a direction, w_iIt is base letter Several relative weightings,It is w_iThe number of middle nonzero element；Apparent diffusion coefficient can be by approximate evaluation：

g^TDg≈λ_maxg^T(vv^T) g=λ_maxcos²θ(g,v)

θ (g, v) indicates included angle cosine function, and D is indicated by all d (v, u_i) constitute one group of basic function dictionary；For Dictionary base distribution under description spherical coordinate, we are by d (v, u under original rectangular coordinate system_i) be described as under spherical coordinate 's

It is the minimum angle cosine on discrete set, κ₁Machine direction distribution function is normalized to unit ball, κ₂It is for adjusting The parameter of whole peak value, τ indicate even power；The estimation of basic function coefficient w in machine direction distribution function (fODF)：

Φ is observing matrix, and s is signal vector；To avoid pseudo- peak and complicated algorithm and the extensive morbid state of higher order The calculating of inverse problem directly acquires the estimation of basic function coefficient w by non-negative least square method：

w^*Indicate the optimal solution of w；

Step 2 establishes space structure consistency model：

Using Bayesian formula, obtain：

P(x|s)∝P(s|x)P(x)

Posterior probability density P (x | s) is proportional to multiplying for data likelihood function P (s | x) and priori probability density function P (x) Product；It is rewritten as later：

U^InIt is internal energy,It is external energy, β_jIt is the hyper parameter of prior distribution；The maximization of posterior probability converts For the minimum of total energy function：

P (x | s) it is posterior probability density, U^InIt is internal energy,It is external energy, β_jIt is the hyper parameter of prior distribution； Wherein internal energy：

S is measuring signal collection, and S ' expressions are signals to be estimated, and W is w coefficient sets, and Θ is the block based on observing matrix Diagonal matrix；External energy：

Indicate external energy,Indicate that the arithmetic average of machine direction distribution function, M pass through down-sampled direction v_t One dictionary base of training is gone to obtain, w_cIndicate the coefficient of c-th of voxel, c ∈ Ω；The estimation of W：

s_cIt is coefficient of the measuring signal in c-th of voxel, w_cIt is coefficient of the dictionary in c-th of voxel；Body in order to obtain The structure of plain decussating fibers defines global cost function：

By calculating w_cAnd w_cThe coefficient COS distance of surrounding neighbors obtains, α₁An artificially defined parameter, Q be by Training dictionary obtains on basic function；The local linear approximate evaluation of space structure consistency model：

T is iteration index, δ_ξIt is predefined aiding constant,It is the extension Lagrange multiplier vector of the t times iteration, Above formula is divided into two parts：

It is optimized for a separable space domain, is solved, is obtained with enhancing Lagrangian method：

Wherein I indicates unit matrix；

Based on separable space domainThe distribution that machine direction Distribution Value is fitted using the soft MATLAB emulation of mathematics, is led to The extreme point crossed in search machine direction Distribution Value obtains the principal direction of fiber.

Claims (1)

1. a kind of brain fiber microstructure reconstructing method based on space structure consistency, it is characterised in that：The reconstructing method includes Following steps：

Step 1, using the bivalve basic function based on spherical surface dictionary deconvolution：

In rotating vectorAnd center vectorOn fiber probability-distribution function f (v | u) be known as fODF, wherein m_v Indicate Spatial Dimension, the m of rotating vector group_uWhat is indicated is the Spatial Dimension of center vector group, will by spherical surface the Method of Deconvolution Fiber morphology structure is described as the convolution of kernel function, in diffusion gradient g ∈ S²On measuring signal s (g | u)：

Wherein r (g, v) indicates kernel function, and μ (v) is in S²On Haar estimate；For the sake of convenient, s (g | u) signal can be by uniformly dividing Discrete sampling μ of the cloth in unit sphere is indicated：

Define fiber receptance function：

Wherein It is the diagonal matrix for characterizing diffusion tensor D, λ_maxIt is in the diagonal matrix Principal eigenvector, l indicate diffusion-sensitive coefficient and the influence degree that anisotropy interaction decays to signal；Expanded with this Put on display the estimation of the fiber receptance function on more shell sampling plans：

Wherein J=1 ..., q refers to j-th spherical shell,Correspondence is distributed in b_JGradient vector collection g on shell,Indicate j-th ball B under shell_JThe l that a diffusion-sensitive coefficient is referred to；To push away a kind of new machine direction distribution function form：

d(v,u_i) indicate Vector Groups v and u_iOne group of excessively complete directional spreding basic function under a direction, w_iIt is basic function Relative weighting, m_uIt is w_iThe number of middle nonzero element；Apparent diffusion coefficient can be by approximate evaluation：

g^TDg≈λ_maxg^T(vv^T) g=λ_maxcos²θ(g,v)

θ (g, v) indicates included angle cosine function, and D is indicated by all d (v, u_i) constitute one group of basic function dictionary；In order to describe Dictionary base distribution under spherical coordinate, we are by d (v, the u under original rectangular coordinate system_i) be described as under spherical coordinate

It is the minimum angle cosine on discrete set, κ₁Machine direction distribution function is normalized to unit ball, κ₂It is for adjusting peak The parameter of value, τ indicate even power；The estimation of basic function coefficient w in machine direction distribution function fODF：

Φ is observing matrix, and s is signal vector；To avoid the algorithm at pseudo- peak and complexity and the extensive morbid state of higher order from inverse asking The calculating of topic directly acquires the estimation of basic function coefficient w by non-negative least square method：

w^*Indicate the optimal solution of w；

Step 2 establishes space structure consistency model：

Using Bayesian formula, obtain：

P(x|s)∝P(s|x)P(x)

Posterior probability density P (x | s) is proportional to the product of data likelihood function P (s | x) and priori probability density function P (x)；It After be rewritten as：

U^InIt is internal energy,It is external energy, β_jIt is the hyper parameter of prior distribution；The maximization of posterior probability is converted into always The minimum of energy function：

P (x | s) it is posterior probability density, U^InIt is internal energy,It is external energy, β_jIt is the hyper parameter of prior distribution；Wherein Internal energy：

S is measuring signal collection, and S ' expressions are signals to be estimated, and W is w coefficient sets, and Θ is that the block based on observing matrix is diagonal Matrix；External energy：

Indicate external energy,Indicate that the arithmetic average of machine direction distribution function, M pass through down-sampled direction v_tIt goes to instruct Practice dictionary base to obtain, w_cIndicate the coefficient of c-th of voxel, c ∈ Ω；The estimation of W：

s_cIt is coefficient of the measuring signal in c-th of voxel, w_cIt is coefficient of the dictionary in c-th of voxel；Voxel is handed in order to obtain The structure of fiber is pitched, global cost function is defined：

By calculating w_cAnd w_cThe coefficient COS distance of surrounding neighbors obtains, α₁It is an artificially defined parameter, Q is by base Training dictionary obtains on function；The local linear approximate evaluation of space structure consistency model：

T is iteration index, δ_ξIt is predefined aiding constant,It is the extension Lagrange multiplier vector of the t times iteration, above formula It is divided into two parts：

It is optimized for a separable space domain, is solved, is obtained with enhancing Lagrangian method：

Wherein I indicates unit matrix；

Based on separable space domainThe distribution that machine direction Distribution Value is fitted using perceptive construction on mathematics emulation, by searching Extreme point in rope machine direction Distribution Value obtains the principal direction of fiber.