Method for predicting human brain function connection
By constructing a higher-order Laplacian matrix and establishing a second-order diffusion model, the problem of inability to effectively characterize the excitability and inhibitory connections in the existing technology is solved, and the positive and negative correlations of functional connections are achieved from structural connections, which is better than the previous model.
Patent Information
- Application Number
- CN202411412044.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-11
- Publication Date
- 2025-03-18
AI Technical Summary
The prior art is difficult to effectively characterize excitatory and inhibitory connections in brain intervals, and cannot directly predict positive and negative correlations of functional connections from the graphical Laplacian representation of brain structural networks.
By constructing the higher-order Laplacian matrix Lp, a second-order diffusion model between the structural connections of the human brain and functional connections is established, the higher-order matrix is used to describe the higher-order nonlinear connection relationship between the brain intervals, and the prediction accuracy of structural connections for functional connections is strengthened through the second-order partial differential equation.
The positive and negative correlations of functional connections are realized directly predicted through structural connections, which is better than the previous Laplacian diffusion model, and can more accurately describe the connection properties of brain intervals.
Smart Images
Figure CN119650075A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of bioinformatics, and in particular relates to a method for predicting human brain functional connections. Background Art
[0002] In brain networks, the gray matter areas of the cerebral cortex are usually defined as brain regions (nodes), and the white matter fiber bundles connecting the gray matter are called connections (edges) between brain regions. In macro-scale networks, edges can be defined as three types of connections: structural connections, functional connections, and causal connections. Since the 1990s, researchers have used structural magnetic resonance imaging to obtain morphological data of the brain, such as gray matter volume, density, thickness, etc., to determine the location of brain regions; and use diffusion magnetic resonance imaging to measure the number and density of connections of white matter fiber bundles in the cerebral cortex, thereby determining the connection information between brain regions, and finally, obtaining the brain structural connection network. In addition, the brain functional connection network can be obtained by indirectly recording the neural activity signals of the cerebral cortex through functional magnetic resonance imaging technology based on blood oxygen level dependence; or by directly recording the neural activity signals of the brain through electroencephalography, magnetoencephalography and other technologies.
[0003] The brain's resting state network is a special functional connection network. The study of this network provides an effective means to explore the relationship between structural connection and functional connection. The resting state refers to a state in which the brain is awake without external stimulation and tasks. Unlike the sleeping state, the brain is conscious and can respond to external stimuli in the resting state. Its brain activity pattern is different from that observed in the sleeping state and the task state. The study found that there is a strong similarity between the brain's resting state network and structural connection, which indicates that functional connection is constrained by structural connection. However, the two are not a simple mapping relationship. There may be functional connection between brain regions without structural connection, and the functional connection is even strong. At the same time, the structural connection obtained by diffusion magnetic resonance imaging cannot characterize the excitatory and inhibitory connections between brain regions, but the functional connection can characterize the positive and negative correlation between brain regions.
[0004] Revealing how the brain's functional network connections are generated by its structural network connections is a very important scientific issue in the field of neuroscience research, and is crucial to understanding the mechanisms of brain cognition and brain diseases. Its detailed mechanism has not been discovered so far. Since the emergence of functional magnetic resonance imaging and diffusion magnetic resonance imaging technology, researchers have begun to use brain function and structural imaging data for computational modeling to explore this mystery. Among them, brain network analysis based on complex network theory and graph theory is currently one of the most commonly used modeling methods internationally. However, the Laplacian representation of the brain's structural network cannot directly describe the interaction between unconnected brain regions in the anatomical structure, that is, the excitability and inhibition between brain regions. Therefore, the current method can only simulate some brain functions and has certain limitations. Summary of the invention
[0005] In view of the above problems existing in the prior art, the present invention proposes a method for predicting human brain functional connections, which has a reasonable design, solves the shortcomings of the prior art and has good effects.
[0006] A method for predicting human brain functional connectivity comprises the following steps:
[0007] Step 1: Based on the attenuation process of signal propagation between brain regions, the Laplacian matrix L is constructed by structural connection;
[0008] Step 2: Solve the high-order Laplacian matrix L based on L p ;
[0009] Step 3: Based on the high-order Laplacian matrix L p , establish a second-order diffusion model between structural and functional connections in the human brain;
[0010] Step 4: Substitute the initial state into the second-order diffusion model to obtain the human brain functional connection matrix.
[0011] Furthermore, the step 1 includes: the Laplacian operator is a second-order differential operator in N-dimensional Euclidean space, which is defined as the divergence of the gradient:
[0012]
[0013] At a point (x, y) in the continuous function f(x, y), take the derivative along the x-axis and y-axis:
[0014] The first-order partial derivative of continuous f(x,y) with respect to x:
[0015]
[0016] Discretize f(x,y) and set Δx = 1, and we get:
[0017]
[0018] The second-order partial derivative of the discretized f(x,y) with respect to x:
[0019]
[0020] The first-order partial derivative of continuous f(x,y) with respect to y:
[0021]
[0022] Discretize f(x,y) and set Δy=1, and we can get:
[0023]
[0024] The second-order partial derivative of the discretized f(x,y) with respect to y:
[0025]
[0026] According to formulas (4) and (7), we can get conclusion 1: the discretized f(x,y) at point (x,y) is It can be regarded as the function value at this point, a measure of the different degrees of the function value in the rectangular neighborhood along the x-axis and y-axis, that is, the gain.
[0027] Furthermore, we extend Conclusion 1 to the human brain. Assuming that the brain has r brain regions, any two brain regions, if connected, have a weight of w. i,j ; otherwise the weight is 0, and the average activity signal in each brain region u=(u 1 ,u 2 ,…,u r );
[0028] First, we analyze the effect of the disturbance in brain area 1 on brain area 2, Δu 1 :
[0029] Δu 1 =βw 1,2 (u 2 -u 1 ); (8)
[0030] Let i = 1, 2..., r, and expand to the i-th brain area. The impact of the disturbance on other brain areas is:
[0031] Δu i =β((w i,1 u 1 +w i,2 u 2 +…+w i,i u i )-(w i,1 u i +w i,2 u i +…+w i,i u i )), i=1,2...,r;(9)
[0032] Convert formula (9) into matrix form:
[0033]
[0034] Then we get the first-order diffusion model:
[0035]
[0036] The solution of formula (11) appears in the form of exponential decay:
[0037] u(t)=e -βLt K i ; (12)
[0038] Where β is the decay rate, L is the Laplacian matrix, L = DW, W is the structural connection matrix, D is the degree matrix of the structural connection construction; K i represents the vector orthogonal to the i-th brain region;
[0039] After regularizing L, we get L = ID -1 / 2 WD -1 / 2 .
[0040] Furthermore, in step 3, the quadratic operator of the Laplacian matrix L is defined as:
[0041]
[0042] Among them, f' is the neural activity signal function, f' i is the neural activity signal function corresponding to the i-th brain region, f' j The neural activity signal function corresponding to the jth brain region;
[0043] High-order Laplacian matrix L p The form is:
[0044]
[0045] L p By the inner product definition, we have:
[0046]
[0047] The function φ p is defined as follows:
[0048] φ p (x)=|x| p-1 sign(x); (17)
[0049] For any given value of p, the high-order Laplacian matrix L is obtained by equation (16): p .
[0050] Furthermore, the step 2 includes:
[0051] At a point (x, y) in the continuous function f(x, y), take the derivative in the clockwise m and counterclockwise n directions:
[0052] The first-order partial derivative of continuous f(x,y) with respect to m:
[0053]
[0054] Discretize f(x,y) and set Δx'=2, and we get:
[0055]
[0056] The first-order partial derivative of continuous f(x,y) with respect to n:
[0057]
[0058] Discretize f(x,y) and set Δy'=2, and we get:
[0059]
[0060] Then we get:
[0061]
[0062] According to formulas (22) and (23), we can get conclusion 2: the discretized f(x,y) at point (x,y) is It can be regarded as a measurement of different degrees of rotation in the clockwise and counterclockwise directions within a rectangular neighborhood with the point as the center, that is, a change in direction.
[0063] Furthermore, we extend Conclusion 2 to the human brain and introduce the high-order Laplacian matrix L p , establish a second-order diffusion model between structural and functional connections in the human brain:
[0064]
[0065] Solving for this yields:
[0066]
[0067] Where x(t) is the second-order description of the neural activity signals of all brain regions, α is the second-order decay rate, a and b are constants, and M i 、N i is a vector orthogonal to the ith brain region.
[0068] Furthermore, the initial state is substituted into u(t) to obtain the human brain functional connection matrix:
[0069]
[0070] Wherein, M and N represent any positive integers.
[0071] Beneficial technical effects brought by the present invention:
[0072] Based on Laplacian, the present invention establishes a high-order Laplacian matrix, which can describe the high-order nonlinear connection relationship between brain regions and characterize the connection properties between brain regions. At the same time, the introduction of the second-order partial differential equation enhances the accuracy of structural connection in predicting functional connection. Therefore, the model proposed by the present invention can directly predict the functional connection reflecting the positive and negative correlation between brain regions only from the structural connection, and the effect is better than the previously proposed graph Laplacian diffusion model. BRIEF DESCRIPTION OF THE DRAWINGS
[0073] Figure 1 A flowchart of a method for predicting human brain functional connectivity in the present invention;
[0074] Figure 2 is a calculation flow chart of an embodiment;
[0075] Where (a) is the structural connection matrix; (b) is the Laplacian matrix; (c) is the high-order Laplacian matrix; (d) is the functional connection matrix;
[0076] Figure 3 Scatter plots between the means of the functional connections predicted by the two models and the means of the true functional connections;
[0077] Where (a) is a scatter plot between the mean of the true functional connectivity and the mean of the functional connectivity of the first-order diffusion model; (b) is a scatter plot between the mean of the true functional connectivity and the mean of the functional connectivity of the second-order diffusion model;
[0078] Figure 4 Matrix diagram of the mean functional connectivity predicted by the two models and the mean actual functional connectivity;
[0079] Among them, (a) is the matrix diagram of the actual functional connectivity mean; (b) is the matrix diagram of the functional connectivity mean predicted by the first-order diffusion model; (c) is the matrix diagram of the functional connectivity mean predicted by the second-order diffusion model. DETAILED DESCRIPTION
[0080] The specific implementation of the present invention is further described below in conjunction with specific embodiments:
[0081] A method for predicting functional connectivity in the human brain, such as Figure 1 As shown, the following steps are included:
[0082] Step 1: Based on the attenuation process of signal propagation between brain regions, the Laplacian matrix L is constructed by structural connection;
[0083] Specifically, the Laplacian operator is a second-order differential operator in N-dimensional Euclidean space, defined as the divergence of the gradient:
[0084]
[0085] At a point (x, y) in the continuous function f(x, y), take the derivative along the x-axis and y-axis:
[0086] The first-order partial derivative of continuous f(x,y) with respect to x:
[0087]
[0088] Discretize f(x,y) and set Δx = 1, and we get:
[0089]
[0090] The second-order partial derivative of the discretized f(x,y) with respect to x:
[0091]
[0092] The first-order partial derivative of continuous f(x,y) with respect to y:
[0093]
[0094] Discretize f(x,y) and set Δy=1, and we can get:
[0095]
[0096] The second-order partial derivative of the discretized f(x,y) with respect to y:
[0097]
[0098] According to formulas (4) and (7), we can get conclusion 1: the discretized f(x,y) at point (x,y) is It can be regarded as the function value at this point, a measure of the different degrees of the function value in the rectangular neighborhood along the x-axis and y-axis, that is, the gain.
[0099] Extending conclusion 1 to the human brain, assuming that the brain has r brain regions, any two brain regions, if connected, have a weight of w i,j ; otherwise the weight is 0, and the average activity signal in each brain region u=(u 1 ,u 2 ,…,u r );
[0100] First, we analyze the effect of the disturbance in brain area 1 on brain area 2, Δu 1 :
[0101] Δu 1 =βw 1,2 (u 1 -u 2 ); (8)
[0102] Let i = 1, 2..., r, and expand to the i-th brain area. The impact of the disturbance on other brain areas is:
[0103] Δu i =β((w i,1 u i +w i,2 u i +…+w i,i u i )-(w i,1 u 1 +w i,2 u 2 +…+w i,i u i )), i=1,2...,r;(9)
[0104] Convert formula (9) into matrix form:
[0105]
[0106] Then we get the first-order diffusion model:
[0107]
[0108] The solution of formula (11) appears in the form of exponential decay:
[0109] u(t)=e -βLt K i ; (12)
[0110] Where β is the decay rate, L is the Laplacian matrix, L = DW, W is the structural connection matrix, D is the degree matrix of the structural connection construction; K i represents the vector orthogonal to the i-th brain region;
[0111] After regularizing L, we get L = ID -1 / 2 WD -1 / 2 .
[0112] Therefore, in the resting state, the dynamic brain functional connectivity can be approximately expressed as
[0113] f(t)=K·e -βLt ; (13)
[0114] Wherein, K represents any positive integer.
[0115] Since the above derivations (1)-(7) only represent the change in size, the calculated f(t) cannot accurately describe the functional connection.
[0116] Step 2: Solve the high-order Laplacian matrix L based on L p ;
[0117] The quadratic operator definition of the Laplacian matrix L is:
[0118]
[0119] Among them, f' is the neural activity signal function, f' i is the neural activity signal function corresponding to the i-th brain region, f' j The neural activity signal function corresponding to the jth brain region;
[0120] High-order Laplacian matrix L p The form is:
[0121]
[0122] L p By the inner product definition, we have:
[0123]
[0124] The function φ p is defined as follows:
[0125] φ p (x)=|x| p-1 sign(x); (17)
[0126] For any given value of p, the high-order Laplacian matrix L is obtained by equation (16): p .
[0127] Step 3: Introduce the high-order Laplacian matrix L p , establish a second-order diffusion model between structural and functional connections in the human brain;
[0128] Specifically, step 3 includes:
[0129] At a point (x, y) in the continuous function f(x, y), take the derivative in the clockwise m and counterclockwise n directions:
[0130] The first-order partial derivative of continuous f(x,y) with respect to m:
[0131]
[0132] Discretize f(x,y) and set Δx'=2, and we get:
[0133]
[0134] The first-order partial derivative of continuous f(x,y) with respect to n:
[0135]
[0136] Discretize f(x,y) and set Δy'=2, and we get:
[0137]
[0138] Then we get:
[0139]
[0140] According to formulas (22) and (23), we can get conclusion 2: the discretized f(x,y) at point (x,y) is It can be regarded as a measurement of different degrees of rotation in the clockwise and counterclockwise directions within a rectangular neighborhood with the point as the center, that is, a change in direction.
[0141] In summary, f(x,y) at (x,y) It can be viewed as the change in size and direction within a rectangular neighborhood centered at the point.
[0142] Extending Conclusion 2 to the human brain, we introduce the high-order Laplacian matrix L p , establish a second-order diffusion model between structural and functional connections in the human brain:
[0143]
[0144] Solving for this yields:
[0145] r 2 +(a+b)αL p r+abα 2 L p 2 =0;(25)
[0146] (r+aαL p )(r+bαL p )=0;(26)
[0147]
[0148] Where x(t) is the second-order description of the neural activity signals of all brain regions, α is the second-order decay rate, a and b are constants, and M i 、N i is a vector orthogonal to the ith brain region.
[0149] Step 4: Substitute the initial state into the second-order diffusion model to obtain the human brain functional connection matrix:
[0150]
[0151] Wherein, M and N represent any positive integers.
[0152] The following uses a sample as an example to illustrate the algorithm calculation process. First, define the adjacency matrix W, that is, the structural connection matrix, as Figure 2 (a) is shown. By L = ID -1 / 2 WD -1 / 2 , and get the Laplacian matrix L, such as Figure 2 (b) As shown. After high-order transformation, the high-order Laplacian matrix L is obtained p ,like Figure 2 Finally, the functional connectivity is predicted by the second-order diffusion model, as shown in (c). Figure 2 In order to clearly show the change process, the diagonal lines in Figures (b), (c), and (d) have been removed.
[0153] Figure 3 The scatter plots between the mean of the true functional connectivity and the mean of the functional connectivity predicted by the first-order diffusion model and the second-order diffusion model in the data set are shown. Since the linearity between the functional connectivity predicted by the second-order diffusion model and the true functional connectivity is higher than that of the first-order diffusion model, the second-order diffusion model proposed in the present invention can better describe the functional connectivity.
[0154] Figure 4 The matrix diagram shows the true functional connectivity mean and the functional connectivity mean predicted by the first-order diffusion model and the second-order diffusion model in the data set. It can be clearly seen that the functional connectivity distribution predicted by the second-order diffusion model is closer to the true functional connectivity distribution than the first-order diffusion model. More importantly, the second-order diffusion model can predict negative correlations in functional connectivity.
[0155] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.
Claims
1. A method for predicting human brain functional connectivity, characterized in that: The following steps are involved: Step 1: Based on the attenuation process of signal propagation between brain regions, the Laplacian matrix L is constructed by structural connection; Step 2: Solve the high-order Laplacian matrix L based on L p ; Step 3: Based on the high-order Laplacian matrix L p , establish a second-order diffusion model between structural and functional connections in the human brain; Step 4: Substitute the initial state into the second-order diffusion model to obtain the human brain functional connection matrix.
2. A method for predicting human brain functional connectivity according to claim 1, characterized in that: The step 1 includes: the Laplacian operator is a second-order differential operator in N-dimensional Euclidean space, which is defined as the divergence of the gradient: At a point (x, y) in the continuous function f(x, y), take the derivative along the x-axis and y-axis: The first-order partial derivative of continuous f(x,y) with respect to x: Discretize f(x,y) and set Δx = 1, and we get: The second-order partial derivative of the discretized f(x,y) with respect to x: The first-order partial derivative of continuous f(x,y) with respect to y: Discretize f(x,y) and set Δy=1, and we can get: The second-order partial derivative of the discretized f(x,y) with respect to y: According to formulas (4) and (7), we can get conclusion 1: the discretized f(x,y) at point (x,y) is It can be regarded as the function value at this point, a measure of the different degrees of the function value in the rectangular neighborhood along the x-axis and y-axis, that is, the gain.
3. A method for predicting human brain functional connectivity according to claim 2, characterized in that: Extending conclusion 1 to the human brain, assuming that the brain has r brain regions, any two brain regions, if connected, have a weight of w i,j ; otherwise the weight is 0, and the average activity signal in each brain region u=(u1,u2,…,u r ); First, analyze the effect of the disturbance in brain area 1 on brain area 2, Δu1: Δu1=βw 1,2 (u2-u1);(8) Let i = 1, 2..., r, and expand to the i-th brain area. The impact of the disturbance on other brain areas is: Δu i =β((in i,1 u1+w i,2 u2+…+in i,i at i )-(In i,1 at i +in i,2 at i +…+in i,i at i )),i=1,2...,r; (9) Convert formula (9) into matrix form: Then we get the first-order diffusion model: The solution of formula (11) appears in the form of exponential decay: u(t)=e -βLt K i ;(12) Where β is the decay rate, L is the Laplacian matrix, L = DW, W is the structural connection matrix, D is the degree matrix of the structural connection construction; K i represents the vector orthogonal to the i-th brain region; After regularizing L, we get L = ID -1 / 2 WD -1 / 2 .
4. A method for predicting human brain functional connectivity according to claim 3, characterized in that: In step 3, the quadratic operator of the Laplacian matrix L is defined as: Among them, f' is the neural activity signal function, f' i is the neural activity signal function corresponding to the i-th brain region, f' j The neural activity signal function corresponding to the jth brain region; High-order Laplacian matrix L p The form is: L p By the inner product definition, we have: The function φ p is defined as follows: φ p (x)=|x p-1 sign(x);(17) For any given value of p, the high-order Laplacian matrix L is obtained by equation (16): p .
5. The method for predicting human brain functional connectivity based on high-order CNNs according to claim 4, characterized in that: The step 2 includes: At a point (x, y) in the continuous function f(x, y), take the derivative in the clockwise m and counterclockwise n directions: The first-order partial derivative of continuous f(x,y) with respect to m: Discretize f(x,y) and set Δx'=2, and we get: The first-order partial derivative of continuous f(x,y) with respect to n: Discretize f(x,y) and set Δy'=2, and we get: Then we get: According to formulas (22) and (23), we can get conclusion 2: the discretized f(x,y) at point (x,y) is It can be regarded as a measurement of different degrees of rotation in the clockwise and counterclockwise directions within a rectangular neighborhood with the point as the center, that is, a change in direction.
6. A method for predicting human brain functional connectivity according to claim 5, characterized in that: Extending Conclusion 2 to the human brain, we introduce the high-order Laplacian matrix L p , establish a second-order diffusion model between structural and functional connections in the human brain: Solving for this yields: Where x(t) is the second-order description of the neural activity signals of all brain regions, α is the second-order decay rate, a and b are constants, and M i 、N i is a vector orthogonal to the ith brain region.
7. A method for predicting human brain functional connectivity according to claim 6, characterized in that: Substitute the initial state into u(t) to obtain the human brain functional connection matrix: Wherein, M and N represent any positive integers.