Alzheimer's pathological oscillation electrical stimulation signal screening method based on a description function

Abstract

The application provides an Alzheimer's pathological oscillation electric stimulation signal screening method based on a description function, which comprises the following steps: constructing a virtual cortex network comprising a plurality of virtual neurons to simulate an Alzheimer's state of a patient's brain nerve; then performing linearization processing on the virtual cortex network model by using a description function method to obtain an equivalent linear closed loop system; generating a plurality of initial electric stimulation signals according to a range of electric stimulation parameters that can be borne by the patient, and inputting the initial electric stimulation signals into the equivalent linear closed loop system; and screening out candidate electric stimulation signals capable of making the system out of the Alzheimer's state by analyzing the response state of the system when the system is affected by each initial electric stimulation signal. The above scheme solves the problem that the existing linear system theoretical model is difficult to intuitively restore the dynamic regulation and control effect of electric stimulation on a biological neural network; and the effective electric stimulation signal can be efficiently screened out within the range of electric stimulation parameters that can be borne by the patient, thereby avoiding the disadvantages of blind attempts of different frequency and amplitude electric signals.

Description

Technical Field

[0001] This invention generally relates to the field of computer pathology simulation technology, and specifically to a method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions. Background Technology

[0002] Alzheimer's disease (AD) is a typical neurodegenerative disease, initially characterized by progressive cognitive decline, which gradually develops into large-scale neuronal degeneration in specific brain regions such as the hippocampus and temporal cortex. Studies have shown that an imbalance in the excitation-inhibition balance in the cerebral cortex is one of the core pathological features of early Alzheimer's disease, typically manifested as an abnormal enhancement of theta-band (4-8 Hz) EEG oscillations. This abnormal neural rhythm is considered an important biomarker of cognitive impairment.

[0003] It is currently known that electrical stimulation can stimulate neurons and help the brain recover from Alzheimer's disease. However, not all electrical signals of any frequency and amplitude can help the brain recover from Alzheimer's disease.

[0004] Due to the extreme complexity of the brain, existing linear system theory models cannot intuitively recreate the regulatory effect of electrical stimulation on the dynamics of biological neural networks. As a result, the mechanism by which existing electrical stimulation therapies can help the brain get rid of Alzheimer's disease remains unclear. Consequently, it is still impossible to know which frequencies and amplitudes of electrical signals can effectively help the brain get rid of Alzheimer's disease. Summary of the Invention

[0005] In view of the above-mentioned defects or deficiencies in the prior art, it is desirable to provide a method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions.

[0006] This invention provides a method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions, including: S1: Construct a virtual cortical network containing multiple virtual neurons; the synaptic coupling strength between the virtual neurons is consistent with the synaptic coupling strength between the patient's neurons, in order to simulate the Alzheimer's state of the patient's brain. S2: The virtual cortical network model is linearized using the describing function method to obtain an equivalent linear closed-loop system; the equivalent linear closed-loop system is used to equivalently characterize the Alzheimer's pathological oscillation state of the virtual cortical network model. S3: Generate multiple initial electrical stimulation signals based on the range of electrical stimulation parameters; the range of electrical stimulation parameters is the range of electrical stimulation signals that the patient can tolerate. S4: Input the multiple initial electrical stimulation signals into the equivalent linear closed-loop system respectively to obtain the response state of the equivalent linear closed-loop system when affected by each initial electrical stimulation signal; the response state includes: being in the Alzheimer's state and being out of the Alzheimer's state; S5: Select candidate electrical stimulation signals from multiple initial electrical stimulation signals corresponding to the exit from Alzheimer's state.

[0007] According to the technical solution provided by the present invention, the virtual cortical network model is linearized using the describing function method to obtain an equivalent linear closed-loop system, including: S2-1: Obtain multiple nonlinear functions and multiple second-order transfer functions of various virtual neurons; the nonlinear functions are used to simulate the input and output of electrical signals of virtual neurons; the second-order transfer functions are used to simulate the dynamic characteristics of virtual neurons under electrical stimulation. S2-2: Obtain the describing function; the describing function is the ratio of the output fundamental frequency of the nonlinear function to the complex value of the electrical stimulation signal input to the nonlinear function; S2-3: Replace the nonlinear function in the corresponding virtual neuron with the described function, and calculate the equivalent transfer function of the virtual neuron after replacement; S2-4: Recombine multiple description functions, multiple equivalent transfer functions and corresponding second-order transfer functions into multiple virtual neurons to obtain the equivalent linear closed-loop system.

[0008] According to the technical solution provided by the present invention, obtaining a description function includes: An electrical stimulation signal is provided to represent the input nonlinear function; the electrical stimulation signal is a sinusoidal signal and contains unknown frequency and amplitude. The electrical stimulation signal is input into a nonlinear function, and the output periodic signal of the nonlinear function is expanded into a Fourier series to obtain the Fourier series output signal. The output fundamental frequency is obtained by calculating the Fourier series signal using Fourier integration; The description function is obtained by calculating the complex value ratio of the electrical stimulation signal to the output fundamental wave.

[0009] According to the technical solution provided by the present invention, the nonlinear function includes a linear part and a nonlinear part; The describing function replaces the nonlinear part of the nonlinear function; the equivalent transfer function replaces the linear part of the nonlinear function.

[0010] According to the technical solution provided by the present invention, multiple initial electrical stimulation signals are respectively input into the equivalent linear closed-loop system to obtain the response state of the equivalent linear closed-loop system under the influence of each initial electrical stimulation signal, including: Calculate the Nyquist curve of the equivalent linear closed-loop system; Multiple initial electrical stimulation signals are respectively input into the equivalent linear closed-loop system, and the negative reciprocal function curves of the descriptive functions in various virtual neurons of the equivalent linear closed-loop system under the action of the initial electrical stimulation signals are calculated. If the Nyquist curve intersects the negative reciprocal function curve, the equivalent linear closed-loop system is determined to be in the Alzheimer's state; otherwise, the equivalent linear closed-loop system is determined to be out of the Alzheimer's state.

[0011] According to the technical solution provided by the present invention, the range of electrical stimulation parameters includes: frequency range and amplitude range; The generation of multiple initial electrical stimulation signals based on the range of electrical stimulation parameters includes: By iterating through all the values ​​within the specified frequency range, multiple reference frequency values ​​are obtained; By iterating through all the values ​​within the range of amplitude, multiple reference amplitudes are obtained; Multiple reference frequency values ​​and multiple reference amplitude values ​​are combined to obtain multiple parameter sets; Multiple initial electrical stimulation signals are generated based on multiple sets of parameters.

[0012] According to the technical solution provided by the present invention, screening candidate electrical stimulation signals from multiple initial electrical stimulation signals corresponding to the exit from the Alzheimer's state includes: Acquire the frequency and amplitude of all initial electrical stimulation signals that cause the equivalent linear closed-loop system to be in an Alzheimer's state; Obtain the maximum frequency and maximum amplitude within the range of electrical stimulation parameters; The initial electrical stimulation signal is selected based on the frequency, amplitude, maximum frequency, and maximum amplitude. The initial electrical stimulation signal with the smallest selection reference value is selected as the candidate electrical stimulation signal.

[0013] According to the technical solution provided by the present invention, the calculation method of the screening reference value is as follows:

[0014] Where X represents the filter reference value, This represents the frequency of the i-th candidate electrical stimulation signal. Maximum frequency, This represents the amplitude of the i-th candidate electrical stimulation signal. This indicates the maximum amplitude.

[0015] The beneficial effects of this invention are as follows: To address the technical problem of determining effective electrical stimulation signal parameters that can help the brain overcome Alzheimer's disease in existing technologies, this invention employs a method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions. First, a virtual cortical network containing various virtual neurons is constructed to simulate the Alzheimer's state of the patient's brain. Then, the virtual cortical network model is linearized using the describing function method to obtain an equivalent linear closed-loop system. Multiple initial electrical stimulation signals are generated based on the patient's tolerable range of electrical stimulation parameters and input into the equivalent linear closed-loop system. By analyzing the system's response state under the influence of each initial electrical stimulation signal, candidate electrical stimulation signals capable of helping the system overcome Alzheimer's disease are selected. This approach solves the problem that existing linear system theoretical models cannot intuitively represent the dynamic regulation of biological neural networks by electrical stimulation; it can efficiently screen effective electrical stimulation signals within the patient's tolerable range of electrical stimulation parameters, avoiding the drawbacks of blindly trying electrical signals of different frequencies and amplitudes. Attached Figure Description

[0016] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart illustrating a method for screening oscillatory electrical stimulation signals in Alzheimer's disease based on describing functions. Figure 2 This is a schematic diagram showing that the curve of the negative reciprocal function and the Nyquist curve do not intersect. Figure 3 This is a schematic diagram showing the intersection of the negative reciprocal function curve and the Nyquist curve; Among them, 1. Nyquist curve; 2. Negative reciprocal function curve. Detailed Implementation

[0017] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] refer to Figure 1 This invention provides a method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions, comprising: S1: Construct a virtual cortical network containing multiple virtual neurons; the synaptic coupling strength between the virtual neurons is consistent with the synaptic coupling strength between the patient's neurons, in order to simulate the Alzheimer's state of the patient's brain. Specifically, virtual neurons include: virtual pyramidal neurons, virtual fast inhibitory interneurons, virtual excitatory interneurons, and virtual slow inhibitory interneurons.

[0020] Among them, at least the following condition must be met: the synaptic coupling strength of the virtual fast inhibitory interneuron to the virtual pyramidal neuron is consistent with the synaptic coupling strength of the patient's fast inhibitory interneuron to the pyramidal neuron, so as to simulate the Alzheimer's state of the patient's brain nerves.

[0021] A virtual neuron consists of two parts: a nonlinear function and a second-order transfer function. The nonlinear function is used to simulate the input and output of electrical signals in the virtual neuron; the second-order transfer function is used to simulate the dynamic characteristics of the virtual neuron under electrical stimulation.

[0022] The nonlinear function S(v) is expressed as:

[0023] Where e0 represents the maximum firing rate of the virtual neuron (consistent with the maximum firing rate of brain neurons), e is the natural exponent, r represents the slope of the nonlinear function S(v), and v is the postsynaptic membrane potential.

[0024] When used as a nonlinear function for different types of virtual neurons, e0 is substituted with the maximum firing rate of the corresponding type of virtual neuron; v is substituted with the postsynaptic membrane potential of the corresponding type of virtual neuron.

[0025] Second-order transfer function of virtual pyramidal neurons Represented as:

[0026] Second-order transfer function of virtual excitatory interneurons Represented as:

[0027] Second-order transfer function of virtual slow inhibitory interneurons Represented as:

[0028] Second-order transfer function of virtual fast inhibitory interneurons Represented as:

[0029] in, tRepresents time, greater than or equal to 0; A is the excitatory synaptic gain, B is the slow inhibitory synaptic gain, and G is the fast inhibitory synaptic gain; a is the excitatory synaptic time constant, b is the slow inhibitory synaptic time constant, and g is the fast inhibitory synaptic time constant.

[0030] The dynamic characteristics of virtual cortical networks should be mathematically described by the following set of differential equations:

[0031]

[0032]

[0033]

[0034] in, This represents the Sigmoid function. p Indicates the average pulse density; This represents the membrane potential state of a virtual pyramidal neuron. This represents the first-order differential of the membrane potential state of a virtual pyramidal neuron after the Laplace transform. The second derivative of the membrane potential state of a virtual pyramidal neuron after Laplace transform; This represents the membrane potential state of a virtual excitatory interneuron. This represents the first-order differential of the membrane potential state of a virtual excitatory interneuron after the Laplace transform. The second derivative of the membrane potential state of a virtual excitatory interneuron after Laplace transform; This represents the membrane potential state of a virtual slow inhibitory interneuron. This represents the first-order differential of the membrane potential state of a virtual slow-inhibitory interneuron after the Laplace transform. The second derivative of the membrane potential state of a virtual slow inhibitory interneuron after Laplace transform; This represents the membrane potential state of a virtual fast inhibitory interneuron. This represents the first-order differential of the membrane potential state of a virtual fast inhibitory interneuron after the Laplace transform. The second derivative of the membrane potential state of a virtual fast inhibitory interneuron after Laplace transform; This indicates the synaptic coupling strength between the virtual excitatory interneuron and the virtual pyramidal neuron; This indicates the synaptic coupling strength between the virtual slow inhibitory interneuron and the virtual pyramidal neuron; This indicates the synaptic coupling strength between the virtual fast inhibitory interneuron and the virtual pyramidal neuron; This indicates the synaptic coupling strength between the virtual pyramidal neuron and the virtual excitatory interneuron; This indicates the synaptic coupling strength between the virtual pyramidal neuron and the virtual fast inhibitory interneuron; This indicates the synaptic coupling strength between the virtual slow inhibitory interneuron and the virtual fast inhibitory interneuron.

[0035] To ensure that the virtual cortical network can generate both normal and Alzheimer's states at inhibitory synapses, the following requirements must be met: When simulating pathological conditions, parameter settings (including all parameters in the system of differential equations) ensure that the model can... When changes occur, both the normal state and the Alzheimer's state are simultaneously present: when When maintained at physiological levels, the virtual cortical network exhibits normal oscillatory characteristics; when When the value drops to the pathological threshold, the virtual cortical network exhibits atypical oscillations in the theta band characteristic of Alzheimer's disease.

[0036] The virtual cortical network constructed in step S1 can accurately reproduce the abnormal enhancement of the theta band caused by the weakening of synaptic inhibition of pyramidal neurons by fast inhibitory interneurons in Alzheimer's disease by simulating the synaptic coupling strength between neurons in patients, thus providing an accurate analytical model for the subsequent screening of electrical stimulation signals.

[0037] S2: The virtual cortical network model is linearized using the describing function method to obtain an equivalent linear closed-loop system; the equivalent linear closed-loop system is used to equivalently characterize the Alzheimer's pathological oscillation state of the virtual cortical network model, including: S2-1: Obtain multiple nonlinear functions of various virtual neurons, as well as multiple second-order transfer functions; S2-2: Obtain the describing function; the describing function is the ratio of the output fundamental frequency of the nonlinear function to the complex value of the electrical stimulation signal input to the nonlinear function; Furthermore, obtain the describing function, including: An electrical stimulation signal is provided to represent the input nonlinear function; the electrical stimulation signal is a sinusoidal signal and contains unknown frequency and amplitude. The electrical stimulation signal is input into a nonlinear function, and the output periodic signal of the nonlinear function is expanded into a Fourier series to obtain the Fourier series output signal. The output fundamental frequency is obtained by calculating the Fourier series signal using Fourier integration; The Fourier series output signal is shown below:

[0038] Where A0 represents the DC component, Let A be the kth harmonic component. k B k These are the Fourier coefficients.

[0039] The description function is obtained by calculating the complex value ratio of the electrical stimulation signal to the output fundamental wave.

[0040] By applying the describing function method, the original nonlinear S(v) can be mathematically combined with the electrical stimulation signal to obtain the equivalent nonlinear characteristics, which facilitates the analysis and judgment of the effect of the electrical stimulation signal on the virtual cortical network.

[0041] Assuming the output signal of the virtual cortical network remains constant within period T, we can investigate the response characteristics of the virtual cortical network under electrical stimulation, i.e., determine the effect of electrical stimulation on the pathological oscillation state of the cortical network. In this case, S(v) can be re-expressed as:

[0042] In this context, the period T of the output signal is set to 1 millisecond, τ represents the duration of a single electrical stimulation cycle, and m represents the corresponding amplitude. .

[0043] The describing function N(Y) of a nonlinear function with an input electrical stimulation signal Y can be expressed as:

[0044] Since S(v) is an odd-symmetric function, its DC component A0 is zero, and the Fourier coefficients A for all k values ​​are... K All are zero. Considering the low-pass characteristic of the virtual cortical network, higher harmonics (k>1) will be attenuated through the virtual cortical network; therefore, i.e. .

[0045] The output fundamental frequency B1 can be obtained through Fourier integration:

[0046] The calculation yielded the following results:

[0047] Then, the describing function can be obtained by calculating the complex value ratio of the output fundamental wave B1 to the electrical stimulation signal Y.

[0048]

[0049] Step S2-2 decomposes the output of the nonlinear function into fundamental and higher harmonics through harmonic analysis, and uses the low-pass filtering characteristics of the system to ignore the higher harmonics, retaining only the fundamental component. This process transforms the complex nonlinear response of neurons into an analytical descriptive function, laying the mathematical foundation for subsequent linearization analysis and selection of electrical stimulation parameters, and significantly reducing the computational complexity of the model.

[0050] S2-3: Replace the nonlinear function in the corresponding virtual neuron with the described function, and calculate the equivalent transfer function of the virtual neuron after replacement. Specifically, it means:

[0051] in, This is the frequency domain representation of the second-order transfer function of a virtual excitatory interneuron. This is the frequency domain representation of the second-order transfer function of a virtual slow-inhibitory interneuron. The frequency domain representation of the second-order transfer function of a virtual fast inhibitory interneuron; This indicates the synaptic coupling strength between the virtual pyramidal neuron and the virtual slow inhibitory interneuron; The equivalent gain for virtual slow inhibitory interneurons, The equivalent gain for virtual fast inhibitory interneurons, This represents the equivalent gain of a virtual excitatory interneuron.

[0052] The virtual cortical network S(v) is also described by the description function N(Y), which can be further expressed as the equivalent gain:

[0053]

[0054]

[0055] Where Y0 is the membrane potential of the virtual pyramidal neuron ( y 0 (t) The amplitude of ), Y1 is the total input membrane potential acting on the fast inhibitory interneuron ( The amplitude of ).

[0056] S2-4: Recombine multiple description functions, multiple equivalent transfer functions and corresponding second-order transfer functions into multiple virtual neurons to obtain the equivalent linear closed-loop system.

[0057] Furthermore, the nonlinear function comprises a linear part and a nonlinear part; The describing function replaces the nonlinear part of the nonlinear function; the equivalent transfer function replaces the linear part of the nonlinear function.

[0058] By using the above method, the nonlinear part of the nonlinear function is replaced with a describing function, thereby completing the linearization process of the virtual cortical network model. This allows the virtual neurons contained in the virtual cortical network model to be processed by the linearized function to complete the calculation, so as to complete the screening of electrical stimulation signals.

[0059] The methods for determining the linear and nonlinear components include: Based on the mathematical form of the nonlinear function S(v), it is decomposed into a part that can be approximated as linear and a part of nonlinear characteristics that must be retained.

[0060] Specifically, by performing small-signal analysis on S(v), its gain characteristics within the linear operating region are identified as the linear component. Simultaneously, a Fourier series expansion of the input signal is performed to extract the fundamental component of the output for use in the describing function calculation, while higher harmonics are considered as manifestations of the nonlinear component. Furthermore, considering the system's low-pass filtering characteristics, the fundamental component in the output of the nonlinear function, which shares the same frequency as the input, is separated and used as the equivalent response of the linear component. The remaining higher harmonic components are classified as part of the nonlinear component and are equivalently linearized by the describing function. Through this method, the linear and nonlinear components of the nonlinear function can be clearly distinguished, laying the foundation for subsequently replacing the linear component with an equivalent transfer function and the nonlinear component with a describing function.

[0061] S3: Generate multiple initial electrical stimulation signals based on the range of electrical stimulation parameters; the range of electrical stimulation parameters is the range of electrical stimulation signals that the patient can tolerate. Furthermore, the range of electrical stimulation parameters includes: frequency range and amplitude range; In this embodiment, the frequency range is 0 to 250 Hz; the amplitude range is 0 to 10 microamps.

[0062] Multiple initial electrical stimulation signals are generated based on the range of electrical stimulation parameters, including: By iterating through all the values ​​within the specified frequency range, multiple reference frequency values ​​are obtained; By iterating through all the values ​​within the range of amplitude, multiple reference amplitudes are obtained; Multiple reference frequency values ​​and multiple reference amplitude values ​​are combined to obtain multiple parameter sets; Multiple initial electrical stimulation signals are generated based on multiple sets of parameters.

[0063] Specifically, the reference frequency and reference amplitude values ​​can be set according to the adjustment accuracy of the equipment.

[0064] Step S3 generates multiple initial electrical stimulation signals by iterating through all frequency and amplitude combinations based on the patient's tolerable range of electrical stimulation parameters. This method ensures that all candidate signals are within a safe range, avoiding harm to the patient due to inappropriate parameters, while providing a comprehensive and systematic set of input signals for subsequent screening, thus improving the coverage and reliability of the screening.

[0065] S4: Input the multiple initial electrical stimulation signals into the equivalent linear closed-loop system respectively to obtain the response state of the equivalent linear closed-loop system when affected by each initial electrical stimulation signal; the response state includes: being in the Alzheimer's state and being out of the Alzheimer's state; Step S4 specifically includes: Calculate the Nyquist curve of the equivalent linear closed-loop system; the input process still uses the nonlinear part as the input description function and the linear part as the input equivalent transfer function.

[0066] Multiple initial electrical stimulation signals are respectively input into the equivalent linear closed-loop system, and the negative reciprocal function curves of the descriptive functions in various virtual neurons of the equivalent linear closed-loop system under the action of the initial electrical stimulation signals are calculated. If the Nyquist curve intersects the negative reciprocal function curve, the equivalent linear closed-loop system is determined to be in the Alzheimer's state; otherwise, the equivalent linear closed-loop system is determined to be out of the Alzheimer's state.

[0067] Specifically, the negative reciprocal function curve is actually the curve obtained by taking the negative reciprocal of the expression describing the function.

[0068] After S2 linearization, the virtual cortical network is equivalent to a classic nonlinear closed-loop system, whose nonlinear part is characterized by the describing function N(Y), and whose linear part is characterized by the equivalent transfer function G. teq (s) characterization, the characteristic equation of the system is 1+N(Y)G teq (jω)=0.

[0069] To analyze the inhibitory effect of electrical stimulation on pathological oscillations, the negative reciprocal function curve -1 / N(Y) of the nonlinear part and the Nyquist curve G of the linear part were compared. teq(jω) are plotted in the same complex plane. According to nonlinear control theory, the relative position of the two curves directly determines the oscillation state of the system: if the two curves intersect, the system has periodic oscillations, and the frequency and amplitude corresponding to the intersection point are the frequency and amplitude of the pathological oscillations; if the two curves do not intersect, the system is in a stable state and no oscillations are generated.

[0070] In the pathological state of Alzheimer's disease, the synaptic inhibition of pyramidal neurons by fast inhibitory interneurons weakens, leading to an expansion of the Nyquist curve range and its intersection with the negative reciprocal function curve, generating pathological oscillations in the theta band (4 to 8 Hz). When a candidate electrical stimulation signal is applied, the describing function N(Y) changes, causing the position of the negative reciprocal function curve -1 / N(Y) to shift. If the electrical stimulation parameters are appropriate, the negative reciprocal function curve will shift to the left or deform, causing it to no longer intersect with the Nyquist curve, thus determining that the system has emerged from the Alzheimer's state. This method transforms the complex nonlinear system dynamics into an intuitive frequency domain graphical analysis, enabling rapid evaluation of the inhibitory effect of electrical stimulation of different frequencies and amplitudes on pathological oscillations.

[0071] For details, please refer to the following: Figure 2 The negative reciprocal function curve 2 and the Nyquist curve 1 do not intersect, indicating that the body is in a state of escaping Alzheimer's disease; see reference. Figure 3 The negative reciprocal function curve intersects with the Nyquist curve, indicating an Alzheimer's state.

[0072] Step S4 employs the Nyquist criterion, quantifying the inhibitory effect of each initial electrical stimulation signal on pathological oscillations by determining whether the Nyquist curve of the equivalent linear closed-loop system intersects with the curve of the negative reciprocal of the describing function. This method transforms the complex nonlinear system response into an intuitive frequency domain graphical judgment, enabling rapid identification of effective stimulation parameters that lift the system out of Alzheimer's state, thus avoiding extensive time-consuming time-domain simulation calculations.

[0073] S5: Select candidate electrical stimulation signals from multiple initial electrical stimulation signals corresponding to the exit from Alzheimer's state, including: Acquire the frequency and amplitude of all initial electrical stimulation signals that cause the equivalent linear closed-loop system to be in an Alzheimer's state; Obtain the maximum frequency and maximum amplitude within the range of electrical stimulation parameters; The initial electrical stimulation signal is selected based on the frequency, amplitude, maximum frequency, and maximum amplitude. The initial electrical stimulation signal with the smallest selection reference value is selected as the candidate electrical stimulation signal.

[0074] Furthermore, the calculation method for the screening reference value is as follows:

[0075] Where X represents the filter reference value, This represents the frequency of the i-th candidate electrical stimulation signal. Maximum frequency, This represents the amplitude of the i-th candidate electrical stimulation signal. This indicates the maximum amplitude.

[0076] The candidate electrical stimulation signal obtained at this point is actually the optimal electrical stimulation signal to be applied to Alzheimer's patients. Subsequently, theoretical research or treatment of Alzheimer's disease can be conducted based on this signal. Using the initial electrical stimulation signal with the smallest selection reference value as the candidate electrical stimulation signal can minimize the impact on the patient's brain and reduce the likelihood of trauma during subsequent Alzheimer's treatment.

[0077] This invention constructs a cortical network model comprising pyramidal cells, excitatory interneurons, and slow and fast inhibitory interneurons to explore the pathophysiological mechanisms of early Alzheimer's disease. The research framework can reveal how synaptic dysfunction pushes the cortical network into a pathological state, and how virtual cortical stimulation pulls the virtual cortical network back from this pathological state.

[0078] This invention uses the describing function method to decompose the nonlinear function in the virtual cortical network into two parts: nonlinear and linear.

[0079] The results show that as the inhibition of pyramidal neuron synapses by rapidly inhibitory interneurons weakens, the coverage of the Nyquist curve gradually expands, while the starting point of the negative reciprocal function curve remains unchanged. The intersection of the two curves indicates that the virtual cortical network is pushed into a pathological state due to weakened synaptic inhibition. The intersection information determines the amplitude and frequency of oscillations in the nonlinear cortical network; these parameters can be used to analyze the oscillatory characteristics of the virtual cortical network. This method can quickly and accurately determine suitable electrical stimulation signals.

[0080] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention is not limited to the specific combination of the above-described technical features, but also includes other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in this invention.

Claims

1. A method for screening oscillatory electrical stimulation signals in Alzheimer's disease based on describing functions, characterized in that, include: S1: Construct a virtual cortical network containing multiple virtual neurons; the synaptic coupling strength between the virtual neurons is consistent with the synaptic coupling strength between the patient's neurons, in order to simulate the Alzheimer's state of the patient's brain. S2: The virtual cortical network model is linearized using the describing function method to obtain an equivalent linear closed-loop system; the equivalent linear closed-loop system is used to equivalently characterize the Alzheimer's pathological oscillation state of the virtual cortical network model. S3: Generate multiple initial electrical stimulation signals based on the range of electrical stimulation parameters; the range of electrical stimulation parameters is the range of electrical stimulation signals that the patient can tolerate. S4: Input the multiple initial electrical stimulation signals into the equivalent linear closed-loop system respectively to obtain the response state of the equivalent linear closed-loop system when affected by each initial electrical stimulation signal; the response state includes: being in the Alzheimer's state and being out of the Alzheimer's state; S5: Select candidate electrical stimulation signals from multiple initial electrical stimulation signals corresponding to the exit from Alzheimer's state.

2. The method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions according to claim 1, characterized in that, The virtual cortical network model is linearized using the describing function method to obtain an equivalent linear closed-loop system, including: S2-1: Obtain multiple nonlinear functions and multiple second-order transfer functions of various virtual neurons; the nonlinear functions are used to simulate the input and output of electrical signals of virtual neurons; the second-order transfer functions are used to simulate the dynamic characteristics of virtual neurons under electrical stimulation. S2-2: Obtain the describing function; the describing function is the ratio of the output fundamental frequency of the nonlinear function to the complex value of the electrical stimulation signal input to the nonlinear function; S2-3: Replace the nonlinear function in the corresponding virtual neuron with the described function, and calculate the equivalent transfer function of the virtual neuron after replacement; S2-4: Recombine multiple description functions, multiple equivalent transfer functions and corresponding second-order transfer functions into multiple virtual neurons to obtain the equivalent linear closed-loop system.

3. The method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions according to claim 2, characterized in that, Obtain the description function, including: An electrical stimulation signal is provided to represent the input nonlinear function; the electrical stimulation signal is a sinusoidal signal and contains unknown frequency and amplitude. The electrical stimulation signal is input into a nonlinear function, and the output periodic signal of the nonlinear function is expanded into a Fourier series to obtain the Fourier series output signal. The output fundamental frequency is obtained by calculating the Fourier series signal using Fourier integration; The description function is obtained by calculating the complex value ratio of the electrical stimulation signal to the output fundamental wave.

4. The method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions according to claim 2, characterized in that, The nonlinear function comprises a linear part and a nonlinear part; The describing function replaces the nonlinear part of the nonlinear function; The equivalent transfer function replaces the linear portion of the nonlinear function.

5. The method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions according to claim 2, characterized in that, Multiple initial electrical stimulation signals are respectively input into the equivalent linear closed-loop system to obtain the response state of the equivalent linear closed-loop system under the influence of each initial electrical stimulation signal, including: Calculate the Nyquist curve of the equivalent linear closed-loop system; Multiple initial electrical stimulation signals are respectively input into the equivalent linear closed-loop system, and the negative reciprocal function curves of the descriptive functions in various virtual neurons of the equivalent linear closed-loop system under the action of the initial electrical stimulation signals are calculated. If the Nyquist curve intersects the negative reciprocal function curve, the equivalent linear closed-loop system is determined to be in the Alzheimer's state; otherwise, the equivalent linear closed-loop system is determined to be out of the Alzheimer's state.

6. The method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions according to claim 1, characterized in that, The range of electrical stimulation parameters includes: frequency range and amplitude range; The generation of multiple initial electrical stimulation signals based on the range of electrical stimulation parameters includes: By iterating through all the values ​​within the specified frequency range, multiple reference frequency values ​​are obtained; By iterating through all the values ​​within the range of amplitude, multiple reference amplitudes are obtained; Multiple reference frequency values ​​and multiple reference amplitude values ​​are combined to obtain multiple parameter sets; Multiple initial electrical stimulation signals are generated based on multiple sets of parameters.

7. The method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions according to claim 1, characterized in that, Candidate electrical stimulation signals are selected from multiple initial electrical stimulation signals corresponding to the exit from Alzheimer's state, including: Acquire the frequency and amplitude of all initial electrical stimulation signals that cause the equivalent linear closed-loop system to be in an Alzheimer's state; Obtain the maximum frequency and maximum amplitude within the range of electrical stimulation parameters; The initial electrical stimulation signal is selected based on the frequency, amplitude, maximum frequency, and maximum amplitude. The initial electrical stimulation signal with the smallest selection reference value is selected as the candidate electrical stimulation signal.

8. The method for screening Alzheimer's pathological oscillatory electrical stimulation signals based on describing functions according to claim 7, characterized in that, The calculation method for the screening reference value is as follows: Where X represents the filter reference value, This represents the frequency of the i-th candidate electrical stimulation signal. Maximum frequency, This represents the amplitude of the i-th candidate electrical stimulation signal. This indicates the maximum amplitude.

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