Front-end Visual Pathway Reconstruction Method Based on Globally Optimized Streamline Differential Equation

Abstract

A method for reconstructing the front-end visual pathway based on the global optimization streamline differential equation, comprising the following steps: 1) describing the fiber direction distribution based on the hydrodynamic differential equation, assuming that the diffusion movement of water molecules in the white matter of the brain along the nerve fiber direction is a fluid movement, the streamline corresponds to the trajectory of the cranial nerve fiber, the flow field represents the tangent vector of the particle movement trajectory, and the continuous fiber direction distribution in space is described by the flow field distribution function in three-dimensional space; 2) reconstructing the front-end visual pathway based on the global flow field distribution function, estimating the flow field distribution function, and using the fourth-order Runge-Kutta algorithm to calculate the fiber tracking direction at each step, so as to completely reconstruct the front-end visual pathway. The present invention can significantly reduce the reconstruction time and improve the reconstruction accuracy, thereby improving the timeliness and practicality of the front-end visual pathway reconstruction.

Description

Technical Field

[0001] The present invention relates to the fields of medical image processing and artificial intelligence, and is a method for reconstructing the anterior visual pathway based on a globally optimized streamline differential equation. Background Art

[0002] The anterior visual pathway starts from the retina and ends at the lateral geniculate body, and is one of the important pathways for transmitting visual information in the human brain. The anterior visual pathway has complex fiber pathways, including two clusters of crossing fibers and two clusters of non-crossing fibers in a narrow space. In addition, the anterior visual pathway is close to the sphenoid bone, so the diffusion magnetic resonance imaging signal is affected by the partial volume effect, and the result of fiber direction distribution estimation therefore produces many false peaks, so the reconstructed anterior visual pathway has a large error. The above two reasons make the reconstruction of the anterior visual challenging. In addition, at present, most reconstructions of the anterior visual pathway are drawn by neurosurgical experts for regions of interest, which is time-consuming and overly dependent on the subjective experience of experts. And due to the large individual differences among patients, each patient needs to be marked for regions of interest one by one before reconstruction, and this process requires a lot of energy. Therefore, developing an accurate, automatic, and robust anterior visual pathway reconstruction algorithm is still a necessary and challenging task. Summary of the Invention

[0003] In order to overcome the problems that existing fiber tracking algorithms are difficult to track the optic nerve part well and fiber tracking of the anterior visual pathway requires neurosurgical experts to manually draw regions of interest. The present invention proposes a method for reconstructing the anterior visual pathway based on a global streamline differential equation to achieve automatic and accurate reconstruction of the anterior visual pathway. This method can significantly reduce the reconstruction time and improve the reconstruction accuracy, thereby improving the timeliness and practicality of anterior visual pathway reconstruction and making it better applied to medical clinical diagnosis.

[0004] The technical solution adopted by the present invention to solve its technical problems is:

[0005] A method for reconstructing the anterior visual pathway based on a globally optimized streamline differential equation, comprising the following steps:

[0006] 1) Describing the fiber direction distribution based on the hydrodynamic differential equation, assuming that the diffusion movement of water molecules in white matter along the nerve fiber direction is a fluid movement, the streamline corresponds to the nerve fiber trajectory of the brain, the flow field represents the tangent vector of the particle movement trajectory, and the continuous fiber direction distribution in space is described by the flow field distribution function in three-dimensional space;

[0007] 2) Reconstructing the anterior visual pathway based on the global flow field distribution function

[0008] For each part of the anterior visual pathway, global streamline differential equation imaging requires a flow field distribution function; the flow field distribution function of the anterior visual pathway is determined by three parts: the anterior visual pathway mask, the intra-voxel fiber orientation distribution, and the reconstruction termination region; first, the anterior visual pathway mask maps the fibers in the anterior visual pathway atlas to the individual space where the patient's brain fibers are located, marks the voxels in the patient's brain fibers that are included in the atlas mapping, and extracts all the marked voxels; second, for each voxel in the anterior visual pathway reconstruction mask, based on the intra-voxel fiber orientation distribution, calculate the angle between the selected direction and the tangents of all fiber bundles in the current voxel, and retain the one with the smallest angle among the three directions of the current voxel peak image; third, the optic nerve leads from the eyeball to the optic chiasm, and the optic nerve enters the lateral geniculate body from the optic chiasm, so the reconstructed termination region consists of two parts. One part is near the eyeball, and 30 voxels closest to the eyeball segmented from the anterior visual pathway are selected as the termination region. The other part is in the lateral geniculate body, which is defined by the anatomy of the visual system.

[0009] Estimate the flow field distribution function and use the fourth-order Runge-Kutta algorithm to calculate the fiber tracking direction at each step, so as to completely reconstruct the anterior visual pathway.

[0010] Furthermore, in step 1), let Ω be all fiber paths on the diffusion tensor imaging image, and let v(p) = [v X (p), v Y (p), v Z (p)] T be the field vector at point p with spatial coordinates [x, y, z] in the diffusion tensor imaging. The streamline distribution consists of a series of streamline sets S = {s i , i = 1, …, n}. In the streamline set S, the fiber bundle is represented by the streamline that satisfies the following conditions:

[0011] The tangent vector at each coordinate p = [x, y, z] on the fiber path is equal to the field vector v(p), that is

[0012]

[0013] Introduce a streamline differential equation and approximate the field vector with the ternary n-order equation in formula (2)

[0014]

[0015] where a i,j,k represents a polynomial coefficient, and the field vector at each point is expressed as:

[0016] v(p) = [v X (p), v Y (p), vZ (p)] T Equation (3)

[0017] Since the fiber streamline trajectories do not intersect each other and satisfy S i ∩S j = 0, i≠j, which is defined by the streamline differential equation:

[0018]

[0019] Assume that the diffusion displacement of water molecules in the same fiber is continuous. According to the theory of continuous incompressible fluid, the divergence of fiber flow is used to describe the spatial continuity of fiber trajectories

[0020]

[0021] When the fiber bundle reaches the termination region, the divergence satisfies the following equation:

[0022] divΩ = 0 Equation (6)

[0023] The form of the ternary equation aims to use divergence to restrict the estimation of fiber direction distribution, and find the global optimal trajectory through the fitting method. The coefficient matrix A contains all the coefficients in the polynomial, and the expression of A is as follows:

[0024]

[0025] A is calculated using the global minimum loss function based on the diffusion image:

[0026]

[0027] s.t. divΩ = 0 Equation (8)

[0028] where D is the direction at p = [x, y, z].

[0029] Furthermore, in step 2), the flow field distribution function is estimated by Equation (8), and the fiber tracking direction at each step is calculated using the fourth-order Runge-Kutta algorithm according to Equation (3).

[0030] The present invention has developed a new global optimization tracking algorithm, and proposed a ternary n-order differential equation to fit the direction of the global optic nerve, thereby accurately reconstructing the front-end visual pathway. The principle is to define the distribution trend of fibers in the human brain in the way of hydrodynamic equations, and construct a global streamline distribution function according to the hydrodynamic differential equation. It can not only better solve the problem of inaccurate fiber direction distribution at the sphenoid bone, but also accurately estimate the flow field distribution function of the front-end visual pathway through the global optimization algorithm and anatomical knowledge, and then reconstruct an accurate front-end visual pathway. The results show that the front-end visual pathway reconstructed by the method proposed by us is more in line with the known anatomical structure, and this method can automatically and accurately reconstruct a single patient without the participation of medical experts.

[0031] The beneficial effects of the present invention are mainly manifested in: significantly reducing the reconstruction time and improving the reconstruction accuracy, thereby improving the timeliness and practicality of the front-end visual pathway reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of a front-end visual pathway reconstruction method based on global optimization streamline differential equation tracking. DETAILED DESCRIPTION OF THE INVENTION

[0033] The present invention will be further described below with reference to the accompanying drawings.

[0034] Referring to Figure 1 , a front-end visual pathway reconstruction method based on global optimization streamline differential equation includes the following steps:

[0035] 1) Describe the fiber direction distribution based on the hydrodynamic differential equation. Assume that the diffusion movement of water molecules in the white matter of the brain along the nerve fiber direction is a fluid motion, the streamline corresponds to the nerve fiber trajectory of the brain, the flow field represents the tangent vector of the particle motion trajectory, and the continuous fiber direction distribution in space is described by the flow field distribution function in three-dimensional space;

[0036] Furthermore, let Ω be all the fiber paths on the diffusion tensor imaging image, and let v(p)=[v X (p), v Y (p), v Z (p)] T be the field vector at point p with spatial coordinates [x, y, z] in the diffusion tensor imaging. The streamline distribution is composed of a series of streamline sets S={s i , i = 1,..., n}. In the streamline set S, the fiber bundle is represented by the streamline that satisfies the following conditions:

[0037] The tangent vector at each coordinate p = [x, y, z] on the fiber path is equal to the field vector v(p), that is

[0038]

[0039] Introduce a streamline differential equation and approximate the field vector with the ternary n - order equation in formula (2).

[0040]

[0041] where a i,j,k represents a polynomial coefficient, and the field vector at each point is expressed as:

[0042] v(p) = [v X (p), v Y (p), v Z (p)] T Formula (3)

[0043] Since the fiber streamline trajectories do not intersect each other and satisfy S i ∩S j = 0, i ≠ j, which is defined by the streamline differential equation:

[0044]

[0045] Assume that the diffusion displacement of water molecules in the same fiber has continuity. According to the theory of continuous incompressible fluid, the divergence of fiber flow is used to describe the spatial continuity of fiber trajectories

[0046]

[0047] When the fiber bundle reaches the termination region, the divergence satisfies the following equation:

[0048] divΩ = 0 Formula (6)

[0049] The form of the ternary equation aims to use the divergence to restrict the estimation of fiber direction distribution, find the global optimal trajectory through the fitting method, and the coefficient matrix A contains all the coefficients in the polynomial. The expression of A is as follows:

[0050]

[0051] A is calculated based on the diffusion image using the global minimum loss function:

[0052]

[0053] s.t. divΩ = 0 Formula (8)

[0054] where D is the direction at p = [x, y, z];

[0055] 2) Reconstruct the front - end visual pathway based on the global flow field distribution function

[0056] For each part of the front-end visual pathway, global streamline differential equation imaging requires a flow field distribution function; the flow field distribution function of the front-end visual pathway is determined by three parts: the front-end visual pathway mask, the intra-voxel fiber direction distribution, and the reconstruction termination region; first, the mask of the front-end visual pathway maps the fibers in the front-end visual pathway atlas to the individual space where the patient's brain fibers are located, marks the voxels in the patient's brain fibers included in the atlas mapping, and extracts all the marked voxels; second, for each voxel in the front-end visual pathway reconstruction mask, based on the intra-voxel fiber direction distribution, calculate the angle between the selected direction and the tangents of all fiber bundles in the current voxel, and retain the one with the smallest angle among the three directions of the current voxel peak image; third, the optic nerve leads from the eyeball to the optic chiasm, and the optic nerve enters the lateral geniculate body from the optic chiasm, so the reconstruction termination region consists of two parts. One part of the region is near the eyeball, and 30 voxels closest to the eyeball segmented from the front-end visual pathway are selected as the termination region. The other part is in the lateral geniculate body, which is defined by the anatomy of the visual system;

[0057] Estimate the flow field distribution function through Equation (8), and calculate the fiber tracking direction at each step using the fourth-order Runge-Kutta algorithm according to Equation (3), so as to completely reconstruct the front-end visual pathway.

[0058] In this embodiment, for a brand-new patient, after obtaining the dMRI data, calculate the patient's white matter response function, and calculate the fiber direction distribution function of the dMRI using the method of constrained spherical deconvolution based on the white matter response function; perform head motion correction on the DWI data corresponding to the dMRI data and then extract the b0 image to determine the mask region of the brain, and calculate the anisotropy value through local fitting; further, use a U-Net structure to build a parallel deep learning network. Two neurosurgical experts manually annotate the data of the visual pathway, and based on this, train two models. Based on the above models, input the axial slices of the patient's image to achieve automatic and accurate segmentation of the front-end visual pathway region; furthermore, based on the segmented front-end visual pathway, use the unscented Kalman filter method to perform fiber tracking on ten high-quality data (HCP data), and project the fibers of these ten front-end visual pathways into the same space to create a front-end visual pathway fiber atlas.

[0059] Estimate the flow field distribution function through Equation (8), calculate the fiber tracking direction at each step using the fourth-order Runge-Kutta algorithm according to Equation (3), and based on the trend of the visual pathway, match it with the front-end visual pathway fiber atlas to accurately find a pair of crossing fibers and a pair of non-crossing fibers in the optic nerve, so as to completely reconstruct the patient's front-end visual pathway.

Claims

1. A method for reconstructing the anterior visual pathway based on the globally optimized streamline differential equation, characterized in that, the method comprises the following steps: 1) Describe the fiber direction distribution based on the hydrodynamic differential equation. Assume that the diffusion movement of water molecules in the white matter of the brain along the nerve fiber direction is a fluid motion. The streamline corresponds to the nerve fiber trajectory of the brain, and the flow field represents the tangent vector of the particle motion trajectory. The continuous fiber direction distribution in space is described by the flow field distribution function in three-dimensional space; 2) Reconstruct the anterior visual pathway based on the global flow field distribution function For each part of the anterior visual pathway, the globally streamline differential equation imaging requires the flow field distribution function; the flow field distribution function of the anterior visual pathway is determined by three parts: the anterior visual pathway mask, the fiber direction distribution within the voxel, and the reconstruction termination region. First, the mask of the anterior visual pathway maps the fibers in the anterior visual pathway atlas to the individual space where the patient's brain fibers are located, marks the voxels in the patient's brain fibers included in the atlas mapping, and extracts all the marked voxels. Second, for each voxel in the anterior visual pathway reconstruction mask, based on the fiber direction distribution within the voxel, calculate the angle between the selected direction and the tangents of all fiber bundles within the current voxel, and retain the one with the smallest angle among the three directions of the current voxel peak image. Third, the optic nerve leads from the eyeball to the optic chiasm, and the optic nerve enters the lateral geniculate body at the optic chiasm. Therefore, the reconstruction termination region consists of two parts. One part is near the eyeball, and 30 voxels closest to the eyeball segmented from the anterior visual pathway are selected as the termination region. The other part is in the lateral geniculate body, which is defined by the anatomy of the visual system; Estimate the flow field distribution function, and use the fourth-order Runge-Kutta algorithm to calculate the fiber tracking direction at each step, so as to completely reconstruct the anterior visual pathway; In step 1), let Ω be all fiber paths on the diffusion tensor imaging image, and let v(p) = [v X (p), v Y (p), v Z (p)] T be the field vector of the diffusion tensor imaging at point p in the spatial coordinates [x, y, z]. The streamline distribution is composed of a series of streamline sets S = {s i , i = 1, …, n}. In the streamline set S, the fiber bundle is represented by streamlines that satisfy the following conditions: The tangent vector at each coordinate p = [x, y, z] on the fiber path is equal to the field vector v(p), that is Introduce a streamline differential equation, and approximate the field vector with the ternary n-order equation in formula (2) where a i,j,k represents a polynomial coefficient, and the field vector at each point is expressed as: v(p) = [v X (p), v Y (p), v Z (p)] T Equation (3) Since the fiber streamline trajectories do not intersect each other and satisfy S i ∩S j = 0, i ≠ j, which is defined by the streamline differential equation: Assume that the diffusion displacement of water molecules in the same fiber is continuous. According to the theory of continuous incompressible fluid, the divergence of fiber flow is used to describe the spatial continuity of fiber trajectories When the fiber bundle reaches the termination region, the divergence satisfies the following equation: divΩ = 0 Formula (6) The form of the ternary equation aims to use the divergence to limit the estimation of the fiber direction distribution, and find the globally optimal trajectory by the fitting method. The coefficient matrix A contains all the coefficients in the polynomial, and the expression of A is as follows: A is calculated using the global minimum loss function based on the diffusion image: where D is the direction at p = [x, y, z].

2. The method for reconstructing the anterior visual pathway based on the globally optimized streamline differential equation according to claim 1, characterized in that, in the step 2), the flow field distribution function is estimated by equation (8), and the fiber tracking direction at each step is calculated by the fourth-order Runge-Kutta algorithm according to equation (3).

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