A neuropathological hub node identification method combining pathological and topological information

Abstract

The present invention discloses a method for identifying neuropathological hub nodes by combining pathological and topological information. The method comprises the following steps: firstly, determining a basic mathematical model of a brain network; then defining neuropathological potential and neuropathological potential difference, and then defining the neuropathological potential difference of a whole brain network; constructing an energy function for identifying neuropathological hubs, and determining an optimal method for identifying neuropathological hubs; finally, preprocessing real neuroimaging data, and executing an optimization algorithm to obtain neuropathological hubs; the present invention jointly analyzes the role of neuropathological hubs in the topological structure of a brain network and the characteristic performance of the distribution of neuropathological loads at neuropathological hubs, and identifies hub nodes with high neuropathological potentials, thereby overcoming the limitation that traditional hub identification methods only consider the topological characteristics of hub nodes in a network structure.

Description

Technical Field

[0001] The present invention relates to a method for identifying hub nodes of a brain network, and in particular to a method for identifying neuropathological hub nodes combining pathological and topological information. Background Art

[0002] As a complex neurodegenerative disease, Alzheimer's disease is a syndrome of neuronal disconnection, that is, due to neuropathological damage, the connections between neurons gradually decrease. Usually, neuropathological changes occur long before the onset of AD dementia. Therefore, quantifying the neuropathological burden is crucial for the early diagnosis of AD. Advances in imaging technology enable us to quantify the pathological burden in vivo through positron emission tomography (PET), such as Amyloid-PET (A biomarker), Tau-PET (T biomarker), and other typical AD biomarkers. In order to better understand the pathological mechanism of AD, more and more studies have focused on the spatial pattern of neuropathological burden. At the same time, a large amount of evidence shows that the neuropathological damage of AD spreads along the network pathway in a prion-like pattern.

[0003] The brain is a complex system composed of multiple brain regions, which are structurally interconnected through white matter fibers to form a structured brain network. Like many other real networks, brain networks exhibit the characteristics of small-world and hierarchical network organization. Therefore, there are a small number of key hub brain regions that support most cognitive functions and information interactions in the entire brain network. According to the different roles shared by each hub brain region in the topological structure of the brain network, they are usually classified as provincial hubs and connector hubs. Because connector hubs promote information interaction between multiple local brain groups, it is increasingly believed that compared with damage to provincial hubs, damage to connector hubs is more extensive in the whole brain, and this is even more true for the manifestation of AD pathology. In addition, there is increasing evidence that hub brain regions usually accumulate higher levels of neuropathological loads, such as amyloid and tau proteins, compared with non-hub brain regions, leading to decreased metabolism and anatomical tissue atrophy. Therefore, identifying those hub brain regions with high neuropathological loads is crucial for early prediction and precise treatment of AD.

[0004] Although several hub region identification methods based on brain network topology have been proposed, none of them take into account information about neuropathological load. Current analysis of hub region identification and neuropathological load requires first identifying a set of hub regions and then measuring the neuropathological load within each hub region. Although this two-step approach has the advantage of being intuitive, it ignores the spatial distribution pattern of neuropathological load relative to the topological structure, and in the early stages of AD, there is usually a large difference in neuropathological load between hub regions and their neighboring regions. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a neuropathology hub node identification method combining pathology and topology information.

[0006] The present invention jointly analyzes the role of neuropathological hubs in the topological structure of brain networks and the characteristic manifestations of the distribution of neuropathological loads at neuropathological hubs, identifies hub nodes with high neuropathological potentials, and solves the limitation of traditional hub identification methods that only consider the topological characteristics of hub nodes in the network structure.

[0007] A neuropathological hub node identification method combining pathological and topological information, the steps are as follows:

[0008] Step (1), determine the basic mathematical model of the brain network;

[0009] Step (2), define the neuropathological potential and the neuropathological potential difference:

[0010] The neuropathic potential describes the amount of neuropathic load deposited in one brain region relative to the amount in other brain regions.

[0011] The neuropathic potential difference describes the difference in neuropathic load between a pair of interconnected brain regions. i , v j ) is expressed as:

[0012]

[0013] Step (3), defining the neuropathological potential difference of the whole brain network;

[0014] Step (4), constructing an energy function for neuropathological hub identification;

[0015] Step (5), determining the optimal method for neuropathological hub identification;

[0016] Step (6), preprocessing real neuroimaging data.

[0017] Step (7), executing the optimization algorithm to obtain the neuropathological hub;

[0018] The specific method of step (1) is as follows:

[0019] In neuroscience, each brain network can be represented by a graph Encoding representation. The vertex set V of the brain network is V = {v1,v2,v3,…,v N}, where v iRepresents the i-th vertex (brain region) in the brain network, and N = |V| represents the total number of vertices in each brain network. Anatomical connectivity matrix is an N×N weighted adjacency matrix, w ij Represents a pair of brain regions (v i , v j ), whose value is determined by the number of white matter fibers that achieve physical connection between the corresponding brain regions. For the adjacency matrix W, calculate its symmetric graph Laplacian matrix L = DW, where the diagonal matrix D = diag (d1, d2, ..., d N ), each element on the main diagonal In addition to the topological information dominated by the Laplacian matrix, the characteristic information of the neuropathological load amyloid that causes neurodegeneration is embedded in each node of the brain network, expressed as in Represents brain area v i Neuropathic load within.

[0020] The specific method of step (3) is as follows:

[0021] Given the characteristics of selective attack of neuropathological damage in different regions, the brain networks of samples at different stages of Alzheimer's disease have different neuropathic potentials. Analogous to graph signal theory, the neuropathic potential difference of the whole brain network is equivalent to the total signal variance of a graph:

[0022]

[0023] Here, tr() represents the trace of the matrix.

[0024] The specific method of step (4) is as follows:

[0025] As shown in formula (2), the total neuropathological potential difference of the brain network changes with the change of the network structure. In order to identify the ideal neuropathological node from many brain network nodes, an auxiliary screening matrix is ​​first set:

[0026]

[0027] The matrix S is used to simulate the process of destroying the network topology. s is a binary vector consisting of 0 and 1, where s i =0 means disconnect node v i The connection between its adjacent nodes. Mathematically, the process is described by the following formula:

[0028]

[0029] In formula (4), the superscript T represents the transposition operation of the matrix. From formula (4), we can see that the operation of removing a node from the brain network is to set all elements in the row and column corresponding to the node in the adjacency matrix W to zero. The new adjacency matrix generated by this process is The corresponding Laplace matrix As shown in formula (5),

[0030]

[0031] In the formula The new adjacency matrix A diagonal matrix with elements on the diagonal

[0032] The neuropathological potential difference between the hub node and its adjacent nodes is greater than the neuropathological potential difference between other non-hub nodes. If all the nodes removed from a brain network are hub nodes, the total neuropathological potential difference of the generated residual network should be minimized. Therefore, the identification of neuropathological hubs is transformed into the following optimization process:

[0033]

[0034] In formula (6) Represents the total neuropathological potential difference of the generated residual network. At the same time, the neuropathological hub node is located at the intersection of multiple subgroups in the brain network, so disconnecting the connection between the neuropathological hub node and other nodes will produce the most discrete disconnected subgroups. Based on graph theory, this result is equivalent to the Laplace matrix of the residual network. It has the smallest trace (the sum of eigenvalues), as shown below:

[0035]

[0036] In the above formula represents the smallest k eigenvalues ​​of the Laplacian matrix. represents the low-dimensional embedding of the Laplacian matrix, which is used to characterize the potential topological structure of the brain network and satisfies the orthogonal constraint, that is, F T F=I.

[0037] Considering the above two types of roles of neuropathological hub nodes, the energy function of neuropathological hub identification is constructed by combining equations (6) and (7):

[0038]

[0039] Where β is a scalar weight coefficient.

[0040] Step (5): Determine the optimal method for neuropathological hub identification:

[0041] ① Optimize F. When S = diag(s) is fixed, F has a closed solution, which is given by the matrix It is composed of the eigenvectors corresponding to the smallest k eigenvalues.

[0042] ② Optimize s. When F is fixed, equation (8) can be written as:

[0043]

[0044] In the above formula and are all N×N square matrices, where F i represents the i-th row of the matrix F, F j represents the jth row of the matrix F. Since s is a binary vector consisting of 0 and 1, equation (9) cannot be directly optimized. Therefore, before optimization, a continuous vector p is introduced to relax equation (9) and transform equation (9) into the following equation:

[0045]

[0046] Then, p and s are solved in an alternating manner. To prevent trivial solutions, the number of neuropathological hubs is pre-specified when solving.

[0047] The specific method of step (6) is as follows:

[0048] A total of 131 data samples were selected from the ADNI database, including 45 normal control data samples (NC), 41 mild cognitive impairment data samples (MCI), and 45 Alzheimer's disease data samples (AD). Each data sample has multiple T1-weighted MRI, DWI, and Amyloid-PET scan data. First, all other scan images are aligned with the corresponding T1-weighted MRI using the image registration method. Then, the following steps were performed for processing: ① T1-weighted MRI images were segmented using the FreeSurfer software platform; ② the cortical surface was constructed and the level of amyloid protein in each voxel was calculated; ③ the cortical surface was divided into N = 148 brain regions (V) using the Destrieux brain atlas; ④ a 148 × 148 anatomical connectivity matrix (W) was generated using surface seed-based probabilistic fiber tracing imaging, in which each element (i.e., connectivity strength) was measured by the number of fibers between brain regions; ⑤ the average level of amyloid protein in each brain region was calculated; ⑥ the gray matter of the cerebellum was selected as the reference region, the amyloid protein levels in the 148 brain regions were normalized, and a neuropathological burden (X) of size 148 × 1 was generated.

[0049] The specific method of step (7) is as follows:

[0050] The data preprocessed in step (6): anatomical connectivity matrix (W) and neuropathological load (X) are input into the energy function of neuropathological hub identification obtained in step (4), and the optimization operation in step (5) is performed to obtain the neuropathological hub; the optimization algorithm program is written in MATLAB language.

[0051] The beneficial results of the present invention are as follows:

[0052] 1. As the problem of global population aging becomes increasingly prominent, Alzheimer's disease has gradually become one of the major diseases that cause death. A large number of studies have shown that the neuropathological hub of Alzheimer's disease exhibits more significant pathological characteristics during the development of the disease. Therefore, more accurate identification of the neuropathological hub of Alzheimer's disease is important for the prevention and treatment of the disease.

[0053] 2. The neuropathology hub selected by optimizing the calculation of the neuropathology and topology information of the brain network will achieve consistent distribution of brain network hub nodes and neuropathology load. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a flow chart of a method according to an embodiment of the present invention;

[0055] Figure 2 A flowchart of the method of the present invention for solving the neuropathological hub optimization algorithm;

[0056] Figure 3 This is a comparison chart of the location distribution of hub nodes identified by the method of the present invention and two other traditional methods and the corresponding amyloid protein levels. DETAILED DESCRIPTION

[0057] The method of the present invention is further described below in conjunction with the accompanying drawings.

[0058] like Figure 1 As shown, a neuropathological hub node identification method combining pathological and topological information is provided, and the steps are as follows:

[0059] Step (1): Determine the basic mathematical model of the brain network:

[0060] In neuroscience, each brain network can be represented by a graph Encoding representation. The vertex set V of the brain network is V = {v1, v2, v3, ..., v N}, where v i Represents the i-th vertex (brain region) in the brain network, and N = |V| represents the total number of vertices in each brain network. Anatomical connectivity matrix is an N×N weighted adjacency matrix, w ij Represents a pair of brain regions (v i , v j ), whose value is determined by the number of white matter fibers that achieve physical connection between the corresponding brain regions. For the adjacency matrix W, calculate its symmetric graph Laplacian matrix L = DW, where the diagonal matrix D = diag (d1, d2, ..., d N ), each element on the main diagonal In addition to the topological information dominated by the Laplacian matrix, the characteristic information of the neuropathological load amyloid that causes neurodegeneration is embedded in each node of the brain network, expressed as in Represents brain area v i Neuropathic load within.

[0061] Step (2), define the neuropathological potential and the neuropathological potential difference:

[0062] Based on a widely recognized hypothesis in this research field, that is, the neuropathological load tends to be selectively deposited in the hub brain region, then the neuropathological load in the hub brain region is usually higher than that in the non-hub brain region. In view of the spatial distribution characteristics of the neuropathological load in the brain network, we introduced the concepts of neuropathological potential and neuropathological potential difference.

[0063] The neuropathic potential describes the amount of neuropathic load deposited in one brain region relative to the amount in other brain regions.

[0064] The neuropathic potential difference describes the difference in neuropathic load between a pair of interconnected brain regions. i , v j ) is expressed as:

[0065]

[0066] Step (3), define the neuropathological potential difference of the whole brain network:

[0067] Given the characteristics of selective attack of neuropathological damage in different regions, the brain networks of samples at different stages of Alzheimer's disease have different neuropathic potentials. Analogous to graph signal theory, the neuropathic potential difference of the whole brain network is equivalent to the total signal variance of a graph:

[0068]

[0069] In formula (2), the symbol tr() represents the trace of the matrix.

[0070] Step (4), construct the energy function for neuropathological hub identification:

[0071] As shown in formula (2), the total neuropathological potential difference of the brain network changes with the change of the network structure. In order to identify the ideal neuropathological node from many brain network nodes, an auxiliary screening matrix is ​​first set:

[0072]

[0073] The matrix S is used to simulate the process of destroying the network topology. s is a binary vector consisting of 0 and 1, where s i =0 means disconnect node v i The connection between its adjacent nodes. Mathematically, the process is described by the following formula:

[0074]

[0075] In formula (4), the superscript T represents the transposition operation of the matrix. From formula (4), we can see that the operation of removing a node from the brain network is to set all elements in the row and column corresponding to the node in the adjacency matrix W to zero. The new adjacency matrix generated by this process is The corresponding Laplace matrix As shown in formula (5),

[0076]

[0077] In the formula The new adjacency matrix A diagonal matrix with elements on the diagonal

[0078] The neuropathological potential difference between the hub node and its adjacent nodes is greater than the neuropathological potential difference between other non-hub nodes. If all the nodes removed from a brain network are hub nodes, the total neuropathological potential difference of the generated residual network should be minimized. Therefore, the identification of neuropathological hubs is transformed into the following optimization process:

[0079]

[0080] In formula (6) Represents the total neuropathological potential difference of the generated residual network. At the same time, the neuropathological hub node is located at the intersection of multiple subgroups in the brain network, so disconnecting the connection between the neuropathological hub node and other nodes will produce the most discrete disconnected subgroups. Based on graph theory, this result is equivalent to the Laplace matrix of the residual network. It has the smallest trace (the sum of eigenvalues), as shown below:

[0081]

[0082] In the above formula represents the smallest k eigenvalues ​​of the Laplacian matrix. represents the low-dimensional embedding of the Laplacian matrix, which is used to characterize the potential topological structure of the brain network and satisfies the orthogonal constraint, that is, F T F=I.

[0083] Considering the above two types of roles of neuropathological hub nodes, the energy function of neuropathological hub identification is constructed by combining equations (6) and (7):

[0084]

[0085] Where β is a scalar weight coefficient.

[0086] Step (5): Determine the optimal method for neuropathological hub identification:

[0087] like Figure 2 As shown, the optimization method is as follows

[0088] ① Optimize F. When S = diag(s) is fixed, F has a closed solution, which is given by the matrix It is composed of the eigenvectors corresponding to the smallest k eigenvalues.

[0089] ② Optimize s. When F is fixed, equation (8) can be written as:

[0090]

[0091] In the above formula and are all N×N square matrices, where F i represents the i-th row of the matrix F, F j represents the jth row of the matrix F. Since s is a binary vector consisting of 0 and 1, equation (9) cannot be directly optimized. Therefore, before optimization, a continuous vector p is introduced to relax equation (9) and transform equation (9) into the following equation:

[0092]

[0093] Then, p and s are solved in an alternating manner. To prevent trivial solutions, the number of neuropathological hubs is pre-specified when solving.

[0094] Step (6), preprocessing real neuroimaging data.

[0095] A total of 131 data samples were selected from the ADNI database, including 45 normal control data samples (NC), 41 mild cognitive impairment data samples (MCI), and 45 Alzheimer's disease data samples (AD). Each data sample has multiple T1-weighted MRI, DWI, and Amyloid-PET scan data. First, all other scan images are aligned with the corresponding T1-weighted MRI using the image registration method. Then, the following steps were performed for processing: ① T1-weighted MRI images were segmented using the FreeSurfer software platform; ② the cortical surface was constructed and the level of amyloid protein in each voxel was calculated; ③ the cortical surface was divided into N = 148 brain regions (V) using the Destrieux brain atlas; ④ a 148 × 148 anatomical connectivity matrix (W) was generated using surface seed-based probabilistic fiber tracing imaging, in which each element (i.e., connectivity strength) was measured by the number of fibers between brain regions; ⑤ the average level of amyloid protein in each brain region was calculated; ⑥ the gray matter of the cerebellum was selected as the reference region, the amyloid protein levels in the 148 brain regions were normalized, and a neuropathological burden (X) of size 148 × 1 was generated.

[0096] Step (7), executing the optimization algorithm to obtain the neuropathological hub;

[0097] The data preprocessed in step (6): anatomical connectivity matrix (W) and neuropathological load (X) are input into the energy function of neuropathological hub identification obtained in step (4), and the optimization operation in step (5) is performed to obtain the neuropathological hub; the optimization algorithm program is written in MATLAB language.

[0098] Step (8), verify the performance of the joint information Alzheimer's disease neuropathology hub node identification method

[0099] A comparative analysis is performed with hubs selected by traditional methods (such as betweenness and graph-embedding).

[0100] Figure 3The figure is a comparison chart of the position distribution of hub nodes and the corresponding amyloid protein level identified by the other two traditional methods. The length of the arrow in the figure indicates the size of the amyloid load at the corresponding node, and the direction of the arrow indicates the high and low relationship between the amyloid level at the corresponding node and the average level. The upward arrow indicates that it is higher than the average level, and the downward arrow indicates that it is lower than the average level. In the MCI and AD populations, the amyloid levels at the hub nodes identified by the method of the present invention are mostly higher than the average level. Quantitatively, the average levels of amyloid protein load at the three groups of hub nodes identified by the three methods are 0.41, 0.43, and 0.45, respectively. In addition, the method of the present invention is basically consistent with the hub nodes identified by the traditional graph embedding-based method, confirming the consistency between the distribution of brain network hub nodes and the spatial distribution of neuropathological load, which is consistent with the mainstream inference in this field, that is, neuropathology selectively preferentially attacks the hub brain area.

Claims

1. A neuropathological hub node identification method combining pathological and topological information, characterized in that: Here are the steps: Step (1), determine the basic mathematical model of the brain network; Step (2), define the neuropathological potential and the neuropathological potential difference: The neuropathic potential describes the amount of neuropathic load deposited on one brain region relative to the amount on other brain regions; The neuropathic potential difference describes the difference in neuropathic load between a pair of interconnected brain regions. i , v j ) is expressed as: x i Represents brain area v i Neuropathic load within; x j Represents brain area v j Neuropathic load within; Step (3), defining the neuropathological potential difference of the whole brain network; Step (4), constructing an energy function for neuropathological hub identification; Step (5), determining the optimal method for neuropathological hub identification; Step (6), preprocessing real neuroimaging data; Step (7), executing an optimization algorithm based on the preprocessed data to obtain the neuropathological hub; The specific method of step (1) is as follows: In neuroscience, each brain network can be represented by a graph Encoding representation: The vertex set V of the brain network is V = {v1,v2,v3…,v i …,v N }, where v i represents the i-th vertex in the brain network, N = |V| represents the total number of vertices in each brain network; anatomical connectivity matrix is an N×N weighted adjacency matrix, w ij Represents a pair of brain regions (v i , v j ), whose value is determined by the number of white matter fibers that realize physical connection between the corresponding brain regions; for the adjacency matrix W, calculate its symmetric graph Laplacian matrix L = DW, where the diagonal matrix D = diag(d1, d2, …, d N ), each element on the main diagonal In addition to the topological information dominated by the Laplacian matrix, the characteristic information of the neuropathological load amyloid that causes neurodegeneration is embedded in each node of the brain network, expressed as in Represents brain area v i Neuropathic load within; The specific method of step (3) is as follows: Given the characteristics of selective attack of neuropathological damage in different regions, the brain networks of samples at different stages of Alzheimer's disease have different neuropathic potentials; analogous to the graph signal theory, the neuropathic potential difference of the whole brain network is equivalent to the total signal variance of a graph: Among them, tr() represents the trace of the matrix; The specific method of step (4) is as follows: As shown in formula (2), the total neuropathological potential difference of the brain network changes with the change of the network structure; in order to identify the ideal neuropathological node from many brain network nodes, an auxiliary screening matrix is ​​first set: The matrix S is used to simulate the process of destroying the network topology. s is a binary vector consisting of 0 and 1, where s i =0 means disconnect node v i The connection between its adjacent nodes; mathematically, the process is described by the following formula: In formula (4), the superscript T represents the transposition operation of the matrix. From formula (4), we can see that the operation of removing a node from the brain network is to set all the elements in the rows and columns corresponding to the node in the adjacency matrix W to zero; the new adjacency matrix generated by this process is The corresponding Laplace matrix As shown in formula (5), In the formula The new adjacency matrix A diagonal matrix with elements on the diagonal The neuropathological potential difference between the hub node and its adjacent nodes is greater than the neuropathological potential difference between other non-hub nodes. If all the nodes removed from a brain network are hub nodes, the total neuropathological potential difference of the generated residual network should tend to the minimum value; therefore, the identification of the neuropathological hub is transformed into the following optimization process: In formula (6) Represents the total neuropathological potential difference of the generated residual network; at the same time, the neuropathological hub node is located at the intersection of multiple subgroups in the brain network, so disconnecting the neuropathological hub node from other nodes will produce the most discrete disconnected subgroups. Based on graph theory, this result is equivalent to the Laplace matrix of the residual network. has the smallest trace, as shown below: In the above formula represents the smallest k eigenvalues ​​of the Laplace matrix; represents the low-dimensional embedding of the Laplacian matrix, which is used to characterize the potential topological structure of the brain network and satisfies the orthogonal constraint, that is, F T F = I; The energy function for neuropathological hub identification is constructed by combining equations (6) and (7): Where β is a scalar weight coefficient; The specific method of step (5) is as follows: ① Optimize F. When S = diag(s) is fixed, F has a closed solution, which is given by the matrix It is composed of the eigenvectors corresponding to the smallest k eigenvalues; ② Optimize s. When F is fixed, equation (8) is expressed as: In the above formula and are all N×N square matrices, where F i represents the i-th row of the matrix F, F j represents the jth row of the matrix F; since s is a binary vector consisting of 0 and 1, equation (9) cannot be directly optimized; therefore, before optimization, a continuous vector p is introduced to relax equation (9) and transform equation (9) into the following equation: Then, p and s are solved in an alternating manner; to prevent trivial solutions, the number of neuropathological hubs is pre-specified during the solution.

2. A neuropathology hub node identification method combining pathology and topology information according to claim 1, characterized in that: The specific method of step (6) is as follows: A total of 131 data samples were selected from the ADNI database, including 45 normal control data samples NC, 41 mild cognitive impairment data samples MCI, and 45 Alzheimer's disease data samples AD; each data sample has multiple T1-weighted MRI, DWI, and Amyloid-PET scan data; first, all other scan images are aligned with the corresponding T1-weighted MRI using the image registration method; then, the following steps are performed: ① Tissue segmentation of T1-weighted MRI images is performed using the FreeSurfer software platform; ② Brain Methods:

1. The cerebral cortical surface was divided into N = 148 brain regions V using the Destrieux brain atlas.

2. A 148 × 148 anatomical connectivity matrix W was generated using surface seed-based probabilistic fiber tracing imaging, in which each element was measured by the number of fibers between brain regions.

3. The average level of amyloid protein in each brain region was calculated.

4. The gray matter of the cerebellum was selected as the reference region, and the amyloid protein levels in the 148 brain regions were normalized to generate a neuropathological burden X of size 148 × 1.

3. A neuropathology hub node identification method combining pathology and topology information according to claim 2, characterized in that: The specific method of step (7) is as follows: The data preprocessed in step (6): anatomical connectivity matrix W and neuropathological load X, are input into the energy function of neuropathological hub identification obtained in step (4), and the optimization method in step (5) is executed to obtain the neuropathological hub; the program of the optimization method is written in MATLAB language.

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