A method for constructing a heterogeneous whole brain model based on linearization theory and fusing connection-nonconnection effects

Abstract

The application belongs to the technical field of biomedical engineering and brain science, and particularly relates to a heterogeneous whole brain model construction method based on linearization theory and fusing connection-nonconnection effects, which constructs a heterogeneous whole brain model, uses real structural connections obtained through fiber bundle tracking as model input, compresses heterogeneous parameters based on real neural image data, introduces the influence of nonconnection effects on the whole brain model after completing parameter optimization, and solves the nonconnection effects through mathematical simplification, thereby providing a specific method for constructing individual-level heterogeneous whole brain models. The application introduces real neural image data, overcomes the difficulty of high-dimensional parameter optimization, and enhances the biological rationality of heterogeneous parameters, and simultaneously significantly improves the speed and stability of parameter optimization through the linearization method.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of biomedical engineering and brain science, specifically involving a method for constructing a heterogeneous whole-brain model based on the fusion of connectivity and non-connectivity effects using linearization theory. Background Technology

[0002] Whole Brain Modeling (WBM) is a key research area in computational neuroscience, aiming to approximate the neural activity of the entire brain using numerical methods. WBM can reproduce neural activity at a macroscopic scale and can be directly compared with experimental data acquired in the human brain using non-invasive neuroimaging techniques (such as MEG, EEG, and fMRI). The human brain is a highly complex dynamic system composed of hundreds of functional and structural regions. WBM typically employs network modeling, representing the brain as a system of interconnected nodes, where each node represents a specific brain region, and the edges connecting nodes are defined by anatomical connectivity (i.e., "connection sets") to determine their existence and connection strength. Within this framework, commonly used neurodynamic models include neural oscillation models, neural population models, and mean-field models. These models, by integrating anatomical connections between different brain regions, local neurodynamic characteristics, and the influence of external stimuli, can simulate multi-scale brain activity patterns and their complex network behavior. Constructing whole-brain neural computational models that encompass the interactions between multiple brain regions, tailored to specific cognitive functions or brain states, not only helps to reveal the brain's information processing mechanisms but also provides a novel information science perspective and methodological approach for the diagnosis and intervention of brain diseases.

[0003] In recent years, an increasing number of experimental studies have shown that different brain regions exhibit significant fragmentation and heterogeneity in terms of cellular composition, anatomical structure, gene expression, and functional characteristics. That is, there are significant differences between different brain regions, while each region exhibits relatively consistent structural and functional attributes. This heterogeneity has important biological significance and demonstrates a high degree of correspondence between structure and function. Furthermore, heterogeneity between brain regions is also reflected in their response patterns to external stimuli, neurodynamic characteristics, and connections with other brain regions. Against this backdrop, current whole-brain modeling research is gradually shifting towards a "heterogeneity" framework that more closely reflects real biological characteristics. By introducing differentiated neurodynamic parameters between brain regions, personalized connection weights, and multimodal data fusion strategies, novel whole-brain models can more accurately simulate brain activity patterns and demonstrate higher fit and predictive ability when compared with actual neuroimaging data. This not only improves the physiological rationality of the models but also helps to deepen the understanding of the mechanisms behind complex brain functions, providing a theoretical basis and technical support for personalized medicine and precision intervention for brain diseases. However, incorporating heterogeneity into whole-brain models also brings significant modeling and computational challenges. First, heterogeneity parameter optimization is essentially a high-dimensional optimization problem. Traditional numerical simulation methods are easily affected by random noise during the solution process and have extremely high computational costs. As the number of brain regions increases, the dimensionality of model parameters rises rapidly, leading to an exponential increase in computational resource consumption. This high time and resource cost limits the application and promotion of such models at the individual level. Furthermore, most current heterogeneity-based whole-brain models still rely primarily on structural connections between brain regions as the driving factor, assuming that functional synchronization is mainly determined by anatomical connections. However, increasing research shows that functional consistency between brain regions is not solely derived from structural connections but is also influenced by the structural similarity, functional characteristics, and molecular factors (such as neurotransmitter receptor distribution and gene expression profiles) of the brain regions themselves. Therefore, heterogeneity models based solely on connectivity-driven approaches are insufficient to comprehensively characterize the complex dynamic activities of the brain. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the prior art by providing a method for constructing a heterogeneous whole-brain model based on linearization theory that integrates connectivity and non-connectivity effects, thereby rapidly establishing an individual-level heterogeneous whole-brain model while simultaneously considering connectivity and non-connectivity effects.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for constructing a heterogeneous whole-brain model based on linearization theory, incorporating connectivity-nonconnectivity effects, includes the following steps:

[0007] S1, Obtain structural connectivity data, which is used to represent the connection strength between different brain regions;

[0008] S2, Construct a heterogeneous whole-brain model, which includes an input module, a neurodynamic module, and an output module;

[0009] S3, input the structural connection data as the initial weights of the model into the input module and preprocess it;

[0010] S4, based on the preprocessed structural connectivity data, uses a neurodynamics module to describe the electrical activity of different brain regions. The specific process is as follows:

[0011] S41 uses the DMF model to describe the electrical activity of different brain regions through a neurodynamic model. The specific expression of the neurodynamic model is as follows:

[0012]

[0013] Among them, S i H(x) represents the average synaptic gating variable. i ) represents the population firing rate of brain region i, x i The total current input to brain region i, v i (t) represents the external driving force for each brain region i, where the dynamic parameter τ s =0.1s, γ=0.641, the activation function parameters a=270(n / C), b=108(Hz), d=0.154(s), synaptic coupling parameter J N =0.3(nA), G represents the coupling scaling parameter, C ij The output of the input module represents the connection weights between brain regions i and j; w i This indicates the intensity of self-feedback in each brain region. w represents the average intensity of noncortical interconnection conduction currents in various brain regions. i and Together, these two parameters constitute the heterogeneity parameters describing brain region activity. Their values ​​differ between different brain regions. For a whole-brain model containing N brain regions, there are a total of 2N such parameters. Since these 2N parameters need to be determined independently through data fitting or optimization processes, they are also free parameters in the model.

[0014] S42, considering computational difficulty and biological rationality, adopts a parameter simplification strategy, compressing the number of free parameters from 2N to 6 by establishing a mapping relationship between heterogeneous parameters and the inherent characteristics of brain regions;

[0015] S43, Linearize and simplify the parametrically compressed neurodynamic model to obtain the covariance matrix expression for brain region activity:

[0016]

[0017] Where J is the system Jacobian matrix; Q is the input covariance matrix, which is a unit diagonal matrix in the current module; W is the system variable transfer matrix; I is the identity matrix; Re represents the real part; π is pi; j is the imaginary unit; f represents the response frequency; and each element in J is calculated using the following formula:

[0018]

[0019] Where * represents the steady-state value of each variable;

[0020] W ij To be calculated according to the following formula:

[0021] W ij =w i J N +GJ N C ij ;

[0022] S44, Optimize model parameter a for each individual subject. w b w c w a I b I c I Connecting matrix FC based on individual real functions emp To minimize the simulation function connection matrix. With FC emp The mean squared error (MSE) is calculated as follows:

[0023]

[0024] Where N represents the total number of connections in the matrix;

[0025] After optimization, individual fixed parameters are obtained, and the Jacobian matrix J is calculated accordingly. sub and variable transfer matrix W sub Substitute it into the covariance matrix Cov I In the calculation formula, while keeping the noise covariance matrix Q a diagonal matrix, the simulated functional connectivity matrix generated entirely by connectivity effects is obtained.

[0026] S45, Based on the neurodynamic model in step S41, in the functional connectivity matrix FC emp In the model fitting formula, besides Q sub All other parameters are fixed values, and their expressions are as follows:

[0027]

[0028] By numerically approximating the spectral response of this formula and analyzing the comparison of the contributions of the imaginary and real parts, it is further simplified to the following formula:

[0029]

[0030] Where A is (j2πfI-J) sub ) -1 The real part of the equation is used to solve for the covariance matrix Q of the external driving force of each brain region i in reverse order based on the simplified formula. sub ;

[0031] S46. After completing the above process, all parameters of the neurodynamics module have been determined as known quantities. After substituting them into the neurodynamics module, the neurodynamics model of each individual is obtained. Subsequently, numerical simulation is performed using the Dragon Tower method to obtain the brain region activity signal output generated by the output module for the neural activity of each brain region.

[0032] Furthermore, the structural connection data in step S1 is obtained by using a fiber bundle tracking algorithm to obtain the structural connection matrix.

[0033] Furthermore, step S3 involves preprocessing the received structural connectivity data, specifically: normalizing the structural connectivity moments to a maximum value of 1 to unify the structural connectivity strength across different individuals; and simultaneously setting diagonal elements to zero to remove self-connections. Further, in step S42, a parameter simplification strategy is employed to compress the number of free parameters from 2N to 6 by establishing a mapping relationship between heterogeneous parameters and inherent brain region features.

[0034] Set the heterogeneity parameter w i and It can be represented as a linear combination of the myelin ratio and functional connectivity gradient of known neuroanatomical features of the brain region:

[0035] w i =a w Myelin i +b w Grad i +c w ;

[0036]

[0037] Among them, Myelin i The myelin ratio of brain region i; Grad i The functional connectivity gradient for brain region i is given; this parameter, along with the myelin ratio, was obtained from neural influence data. w b w c w aI b I c I These are the model's free parameters;

[0038] By using the above linear combination, the free parameters of the brain neurodynamic model are transformed from 2N to only 6 global parameters that need to be optimized.

[0039] This invention constructs a heterogeneous whole-brain model, using structural connections obtained from real fiber tract tracking as model input. It compresses heterogeneous parameters based on real neuroimaging data, and after parameter optimization, introduces the influence of non-connectivity effects on the whole-brain model, solving for these effects through mathematical simplification. This provides a concrete method for constructing individual-level heterogeneous whole-brain models. The introduction of real neuroimaging data overcomes the difficulties of high-dimensional parameter optimization and enhances the biological rationality of heterogeneous parameters. Simultaneously, the use of linearization significantly improves the speed and stability of parameter optimization.

[0040] Compared to existing models that rely entirely on connectivity, this embodiment introduces the influence of non-connectivity effects through step S45, significantly improving the model's performance and biological interpretability, and providing a new direction for the construction of personalized whole-brain models. This model is more flexible and adaptable, helping to reveal the deep connections between brain function, structural connectivity, and non-structural connectivity, and providing more efficient technical support for brain science research. Attached Figure Description

[0041] Figure 1 A flowchart illustrating an embodiment of a method for constructing a heterogeneous whole-brain model based on linearization theory that integrates connectivity-nonconnectivity effects;

[0042] Figure 2 This is a schematic diagram of the static functional connection simulation in the embodiment;

[0043] Figure 3 This is a schematic diagram of the dynamic simulation of functional connections in the embodiment. Detailed Implementation

[0044] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] like Figure 1 As shown in the figure, this embodiment provides a method for constructing a heterogeneous whole-brain model based on linearization theory that integrates connectivity-nonconnectivity effects. Figure 1 As shown, it includes the following steps:

[0046] S1. Acquiring structural connectivity data and constructing a heterogeneous whole-brain model: This data represents the connection strength between different brain regions. In this embodiment, the structural connectivity data is obtained by using a fiber tract tracking algorithm to obtain the structural connectivity matrix. A heterogeneous whole-brain model is constructed, which is based on the mean-field model of a spiking neural network and uses simulated neural activity as the output. It includes an input module, a neurodynamics module, and an output module.

[0047] S2, Structural Connection Data Preprocessing: The structural connection data is used as the initial weights of the model and input to the input module, and then preprocessed. Specifically, the structural connection matrix is ​​normalized to a maximum value of 1 to unify the structural connection strength of different individuals. At the same time, the diagonal elements are set to zero to remove self-connections.

[0048] S3, Selecting the heterogeneity parameters of the model: Input the preprocessed structural connectivity matrix into the neurodynamics module, which uses the DMF model to describe the electrical activity of different brain regions. The specific expression of the neurodynamics model is as follows:

[0049]

[0050] Among them, S i H(x) represents the average synaptic gating variable. i ) represents the population firing rate of brain region i, x i The total current input to brain region i, v i (t) represents the external driving force for each brain region i, where the dynamic parameter τ s =0.1s, γ=0.641, the activation function parameters a=270(n / C), b=108(Hz), d=0.154(s), synaptic coupling parameter J N =0.3(nA), G represents the coupling scaling parameter, C ij The output of the input module represents the connection weights between brain regions i and j; w i This indicates the intensity of self-feedback in each brain region. This represents the average intensity of noncortical interconnection conduction currents within each brain region.

[0051] In the above neurodynamic learning model, w i and These parameters collectively constitute the heterogeneous parameters describing brain region activity, and their values ​​differ between different brain regions. For a whole-brain model containing N brain regions, there are a total of 2N such parameters. Since these 2N parameters need to be determined independently through data fitting or optimization processes, they are also free parameters in the model.

[0052] S4. Considering computational difficulty and biological rationality, this embodiment adopts a parameter simplification strategy. By establishing a mapping relationship between heterogeneous parameters and inherent characteristics of brain regions, the number of free parameters is compressed from 2N to 6. The implementation method is as follows:

[0053] Set the heterogeneity parameter w i and It can be represented as a linear combination of the myelin ratio and functional connectivity gradient of known neuroanatomical features of the brain region:

[0054] w i =a w Myelin i +b w Grad i +c w ;

[0055]

[0056] Among them, Myelin i The myelin ratio of brain region i; Grad i The functional connectivity gradient for brain region i is given; this parameter, along with the myelin ratio, was obtained from neural influence data. w b w c w a I b I c I These are the model's free parameters;

[0057] By using the above linear combination, the free parameters of the brain neurodynamic model are transformed from 2N to only 6 global parameters that need to be optimized, and the number of parameters does not increase with the number of brain regions.

[0058] S5. After parameter compression, the above neurodynamic model is still a system of differential equations, which is difficult to solve directly. Therefore, this embodiment linearizes and simplifies the parameter-compressed neurodynamic model to obtain the covariance matrix expression of brain region activity:

[0059]

[0060] Where J is the system Jacobian matrix; Q is the input covariance matrix, which is a unit diagonal matrix in the current module; W is the system variable transfer matrix; I is the identity matrix; Re represents the real part; π is pi; j is the imaginary unit; f represents the response frequency; and each element in J is calculated according to the following formula:

[0061]

[0062] The definitions of each variable are consistent with those stored in S3, and * represents the steady-state value of each variable;

[0063] W ij To be calculated according to the following formula:

[0064] W ij =w i J N +GJ N C ij ;

[0065] The definitions of each variable are consistent with those saved in S3.

[0066] S6. Optimize model parameter a for each individual subject. w b w c w a I b I c I Connecting matrix FC based on individual real functions emp To minimize the simulation function connection matrix. With FC emp The mean squared error (MSE) is calculated as follows:

[0067]

[0068] Where N represents the total number of connections in the matrix.

[0069] After optimization, individual fixed parameters are obtained, and the Jacobian matrix J is calculated accordingly. sub and variable transfer matrix W sub Substitute it into the covariance matrix Cov I In the calculation formula, while keeping the noise covariance matrix Q a diagonal matrix, the simulated functional connectivity matrix generated entirely by connectivity effects is obtained.

[0070] S7, Based on the neurodynamic model in step S3, in the functional connectivity matrix FC emp In the model fitting formula, besides Q sub All other parameters are fixed values, and their expressions are as follows:

[0071]

[0072] By numerically approximating the spectral response of this formula and analyzing the comparison of the contributions of the imaginary and real parts, it is further simplified to the following formula:

[0073]

[0074] Where A is (j2πfI-J) sub ) -1The real part of the equation is used to solve for the covariance matrix Q of the external driving force of each brain region i in reverse order based on the simplified formula. sub .

[0075] S8. After completing the above process, all parameters of the neurodynamics module have been determined as known quantities. These are then input into the neurodynamics module to calculate the neurodynamics model for each individual. Subsequently, numerical simulation is performed using the Dragon Tower method to obtain the brain region activity signal output generated by the output module for each brain region's neural activity.

[0076] In this embodiment, step S9 is also included, which evaluates the model performance, as follows:

[0077] Figure 2 This section describes the static functional connections generated based on this model, and compares them with real data. The model's static properties are as follows: Figure 2 As shown: The static properties of the model are evaluated by comparing the static functional connectivity of brain regions generated by the computational model with the static functional connectivity of individual brain regions. Evaluation criterion: The mean squared error (MSE) of both is used; the smaller the MSE value, the better the static properties of the model.

[0078] Figure 3 To generate the dynamic probability density distribution of functional connections based on this model, and to compare it with real data. The model's dynamic properties are as follows: Figure 3 As shown: The dynamic properties of the model are evaluated by comparing the dynamics of brain region activity generated by the computational model with the dynamics of brain region activity in individuals. The evaluation metric is the KL divergence between the two. When the KL divergence is sufficiently small, it indicates that the model can generate dynamic patterns that are highly consistent with real data. There is no hard and fast standard for this evaluation.

[0079] In summary, this embodiment overcomes the difficulties of high-dimensional parameter optimization by introducing real neuroimaging data and enhances the biological rationality of heterogeneous parameters. Simultaneously, the linearization method employed significantly improves the speed and stability of parameter optimization. Compared to existing models that rely entirely on connectivity, this embodiment introduces the influence of non-connectivity effects, significantly improving model performance and biological interpretability, and providing a new direction for the construction of personalized whole-brain models. This model possesses greater flexibility and adaptability, helping to reveal the deep connections between brain function, structural connectivity, and non-structural connectivity, providing more efficient technical support for brain science research.

[0080] It should be noted that those skilled in the art will recognize that the embodiments described herein are for the purpose of helping the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

[0081] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A method for constructing a heterogeneous whole-brain model based on linearization theory and incorporating connectivity-nonconnectivity effects, characterized in that, Includes the following steps: S1, Obtain structural connectivity data, which is used to represent the connection strength between different brain regions; S2, Construct a heterogeneous whole-brain model, which includes an input module, a neurodynamic module, and an output module; S3, input the structural connection data as the initial weights of the model into the input module and preprocess it; S4, based on the preprocessed structural connectivity data, uses a neurodynamics module to describe the electrical activity of different brain regions. The specific process is as follows: S41 uses the DMF model to describe the electrical activity of different brain regions through a neurodynamic model. The specific expression of the neurodynamic model is as follows: Among them, S i H(x) represents the average synaptic gating variable. i ) represents the population firing rate of brain region i, x i The total current input to brain region i, v i (t) represents the external driving force for each brain region i, where the dynamic parameter τ s =0.1s, γ=0.641, the activation function parameters a=270(n / C), b=108(Hz), d=0.154(s), synaptic coupling parameter J N =0.3(nA), G represents the coupling scaling parameter, C ij The output of the input module represents the connection weights between brain regions i and j; w i This indicates the intensity of self-feedback in each brain region. w represents the average intensity of noncortical interconnection conduction currents in various brain regions. i and Together, they constitute the heterogeneity parameters describing brain region activity, and are also free parameters in the model, totaling 2N. S42 employs a parameter simplification strategy, compressing the number of free parameters from 2N to 6 by establishing a mapping relationship between heterogeneous parameters and the inherent characteristics of brain regions; S43, Linearize and simplify the parametrically compressed neurodynamic model to obtain the covariance matrix expression for brain region activity: Where J is the system Jacobian matrix; Q is the input covariance matrix, which is a unit diagonal matrix in the current module; W is the system variable transfer matrix; I is the identity matrix; Re represents the real part; π is pi; j is the imaginary unit; f represents the response frequency; and each element in J is calculated using the following formula: Where * represents the steady-state value of each variable; W ij To be calculated according to the following formula: IN ij =in i J N +GJ N C ij ; S44, Optimize model parameter a for each individual subject. w b w c w a I b I c I Connecting matrix FC based on individual real functions emp The objective is to minimize the simulation function connection matrix. With FC emp The mean squared error (MSE) is calculated as follows: Where N represents the total number of connections in the matrix; After optimization, individual fixed parameters are obtained, and the Jacobian matrix J is calculated accordingly. sub and variable transfer matrix W sub Substitute it into the covariance matrix Cov I In the calculation formula, while keeping the noise covariance matrix Q a diagonal matrix, the simulated functional connectivity matrix generated entirely by connectivity effects is obtained. S45, Based on the neurodynamic model in step S41, in the functional connectivity matrix FC emp In the model fitting formula, besides Q sub All other parameters are fixed values, and their expressions are as follows: By numerically approximating the spectral response of this formula and analyzing the comparison of the contributions of the imaginary and real parts, it is further simplified to the following formula: Where a is (j2πfI-J) sub ) -1 The real part of the equation is used to solve for the covariance matrix Q of the external driving force of each brain region i in reverse order based on the simplified formula. sub ; S46. After completing the above process, all parameters of the neurodynamics module have been determined as known quantities. After substituting them into the neurodynamics module, the neurodynamics model of each individual is obtained. Subsequently, numerical simulation is performed using the Dragon Tower method to obtain the brain region activity signal output generated by the output module for the neural activity of each brain region.

2. The method for constructing a heterogeneous whole-brain model based on linearization theory and incorporating connectivity-disconnectivity effects, as described in claim 1, is characterized in that... The structural connection data in step S1 is obtained by using a fiber bundle tracking algorithm to obtain the structural connection matrix.

3. The method for constructing a heterogeneous whole-brain model based on linearization theory and incorporating connectivity-disconnectivity effects, as described in claim 1, is characterized in that... Step S3 is a process of preprocessing the received structural connection data. Specifically, the structural connection moments are normalized to a maximum value of 1 to unify the structural connection strength of different individuals; at the same time, the diagonal elements are set to zero to remove self-connections.

4. The method for constructing a heterogeneous whole-brain model based on linearization theory and incorporating connectivity-disconnectivity effects, as described in claim 3, is characterized in that... Step S42 employs a parameter simplification strategy. By establishing a mapping relationship between heterogeneous parameters and inherent features of brain regions, the process of compressing the number of free parameters from 2N to 6 includes: Set the heterogeneity parameter w i and It can be represented as a linear combination of the myelin ratio and functional connectivity gradient of known neuroanatomical features of the brain region: w i =a w Myelin i +b w Grad i +c w ; I meani =a I Myelin i +b I Grad i +c I ; Among them, Myelin i The myelin ratio of brain region i; Grad i The functional connectivity gradient for brain region i is given; this parameter, along with the myelin ratio, was obtained from neural influence data. w b w c w a I b I c I These are the model's free parameters; By using the above linear combination, the free parameters of the brain neurodynamic model are transformed from 2N to only 6 global parameters that need to be optimized.

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