Model construction method for recruitment of lumbar motor neuron pool in white noise state

Abstract

The invention discloses a model construction method for recruitment of a lumbar motor neuron pool in a white noise state, and relates to the field of physiological simulation. According to the method, through the technical means of mathematical modeling and analogue simulation, a white noise and oscillation factor model is introduced, and a motor neuron pool collection model in a white noise state is constructed. The collection effect of ion channel oscillation on the motor neuron pool in the white noise state can be researched, the working mechanism of the motor neuron can be deeply known, a research direction is provided for related physiological experiments, and a theoretical basis is provided for neurological disease research.

Description

Technical Field

[0001] The invention relates to the field of physiological simulation, and in particular to a method for constructing a model of lumbar motor neuron pool recruitment under white noise conditions. Background Art

[0002] Locomotion is the most basic form of movement in vertebrates, involving almost all behaviors of animals throughout their life, such as eating, walking, running, etc. Its main feature is that the limbs repeat simple movements, resulting in displacement of the body. Locomotion is inseparable from motor neurons and muscle contraction. It is guided and controlled by the Mesencephalic Locomotor Region located in the midbrain, and executed and operated by the Central Pattern Generator distributed in the spinal cord. Finally, skeletal muscles are stimulated to contract, thereby generating locomotion. In this process, the process in which motor neurons generate action potentials to trigger skeletal muscle contraction is called the recruitment of motor neurons. The number of activated motor units and the frequency of action potentials generated by motor units are important factors in determining the magnitude of the force generated by skeletal muscle contraction. Impairment of the recruitment process of motor neurons will affect the locomotion of vertebrates and lead to typical motor neuron diseases, such as amyotrophic lateral sclerosis, or "Lou Gehrig's disease". The recruitment of motor neuron pools is an orderly process of stimulating motor neurons from small to large and from weak to strong. This principle is called the "size principle". According to size and electrical properties, lumbar motor neurons can be divided into slow fatigue-resistant type (S type), fast fatigue-resistant type (FR type) and fast fatigable type (FF type). Under normal physiological conditions, the recruitment of motor neurons generally follows the order from S type to FR type and then to FF type. The recruitment of motor neurons is essentially based on the electrical properties of the cell membrane (passive membrane properties) and can be regulated by the ionic properties of the motor neurons (active membrane properties). Studies have shown that cell membrane oscillations play an important role in regulating the excitability of spinal motor neurons and ion channel regulation. Injecting white noise current signals into a single neuron can simulate similar cell membrane oscillations, thereby regulating the excitability of neurons. However, it is not clear how ion channel regulation affects the recruitment of the motor neuron pool during membrane potential oscillations. The following are the main problems:

[0003] 1. The complexity of the nervous system and the uncertainty of physiological experiments. The human central nervous system has about 10 12 There are huge differences in the morphology and size of neurons, and the cell membrane characteristics and action mechanisms of motor neurons are also very different. At the same time, physiological experiments consume a lot of time and manpower costs, and the results are volatile and unstable, with poor repeatability.

[0004] 2. The basic framework of modern neuronal electrophysiological models is derived from the model created by Hodgkin and Huxley. Currently, neuronal modeling and simulation focuses on the modeling of single neurons, mainly observing the voltage threshold, current threshold, input-output relationship, etc. of single neurons to explore the impact of experiments on the excitability of single neurons.

[0005] Therefore, technicians in this field are committed to developing a model construction method for the recruitment of lumbar motor neuron pools under white noise conditions. The present invention introduces white noise and oscillation factor models through mathematical modeling and simulation techniques to construct a model for the recruitment of motor neuron pools under white noise conditions. The recruitment effect of ion channel oscillations on motor neuron pools under white noise conditions can be studied, the working mechanism of motor neurons can be deeply understood, and research directions can be provided for related physiological experiments, providing a theoretical basis for the study of neurological diseases. Summary of the invention

[0006] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is to understand the working mechanism of motor neurons and provide a theoretical basis for the study of neurological diseases.

[0007] To achieve the above object, the present invention provides a method for constructing a model of lumbar motor neuron pool recruitment under white noise conditions, comprising the following steps:

[0008] Step 1: construct a single lumbar motor neuron model;

[0009] Step 2, constructing a lumbar motor neuron pool model;

[0010] Step 3: Introduce the white noise model and the oscillation factor model into the motor neuron pool model.

[0011] Furthermore, in step 1, a single lumbar motor neuron model is constructed in combination with the cell membrane characteristic data of lumbar motor neurons from physiological experiments.

[0012] Furthermore, in step 2, the excitatory synaptic and inhibitory synaptic inputs whose weights obey normal distribution are used to integrate the single motor neuron model into a lumbar motor neuron pool model.

[0013] Furthermore, in step 3, a white noise model is added to the motor neuron pool model to simulate physiological cell membrane oscillations.

[0014] Furthermore, in step 3, an oscillator factor model is introduced into the ion channel of the motor neuron to simulate the ion channel oscillation.

[0015] Furthermore, in step 3, an oscillatory factor is introduced into the ion channel of a single motor neuron to modify the standard Hodgkin-Huxley ion channel kinetic equation.

[0016] Furthermore, the model outputs excitability indicators such as the number of motor neurons recruited into the motor neuron pool and the input-output relationship.

[0017] Furthermore, the step 1 comprises the following steps:

[0018] Step 1.1, establish a cabin model based on cable theory according to the cell morphology of neurons;

[0019] Step 1.2: According to the excitability characteristics of neurons, insert ion channels based on the Hodgkin-Huxley model into the compartment model;

[0020] Step 1.3: calibrate and debug the cell membrane properties of the lumbar motor neuron model.

[0021] Furthermore, in step 2, the 100 motor neuron models are integrated into a motor neuron pool model.

[0022] Furthermore, the oscillation factor model is simplified to a sine wave, which is added to the ion channel conductance to simulate the ion channel oscillation.

[0023] The existing model construction method is mainly used to construct a single motor neuron model, study the influence of the cell membrane characteristics of neurons on neuronal excitability, and the input-output relationship obtained is somewhat different from the physiological experiment. At the same time, for the recruitment mechanism of the motor neuron pool, the relevant model simulation technology is not perfect, and the recruitment effect of cell membrane oscillation and ion channel oscillation on the motor neuron pool is not considered. The present invention combines the cell membrane characteristic data of lumbar motor neurons in physiological experiments, and integrates the single motor neuron model into the lumbar motor neuron pool model through the descending neuron synaptic input whose weight obeys the normal distribution on the basis of the single motor neuron model. A white noise model is added to the motor neuron pool model to simulate physiological cell membrane oscillations. At the same time, an oscillation factor model is introduced into the ion channel of the motor neuron to correct the error between the model simulation and the physiological experiment results, and explore the ion channel mechanism of the motor neuron pool. This model finally outputs the excitability indicators such as the number of motor neurons recruited by the motor neuron pool and the input-output relationship, solves the model construction problem of the motor neuron pool and considers the ion channel mechanism of recruitment. The present invention integrates the motor neuron model into the motor neuron pool model by using excitatory synapses and inhibitory synaptic inputs that conform to the normal distribution. Using the same synaptic input can reduce the impact of noise, provide redundancy, and ensure the stability of group responses, which is in line with the physiological connection and functional modular design of the actual nervous system. Membrane potential oscillation is one of the main regulatory mechanisms of neuronal excitability. White noise can induce cell membrane potential oscillation. Introducing oscillation factors into the ion channels of single motor neurons to modify the standard Hodgkin-Huxley ion channel kinetic equations confirms that white noise-induced ion channel oscillations are the key mechanism for the generation of membrane potential oscillations. Therefore, introducing the white noise model and the oscillation factor model into the motor neuron pool is in line with the principles of neuronal modeling and is more in line with neurophysiological data.

[0024] like Figure 4 As shown, the action potential and input-output relationship of a single motor neuron in the motor neuron pool model are consistent with neurophysiological experimental data.

[0025] like Figure 6 As shown, the recruitment numbers output by the model for motor neuron pool recruitment are consistent with the model input expectations.

[0026] like Figure 8 As shown, by introducing the white noise model and the oscillation factor model, the recruitment output of the motor neuron pool model has a certain gain compared with the original model.

[0027] The innovation of the present invention is the introduction of white noise and oscillation factor models, which helps to explore the recruitment mechanism of the motor neuron pool and provide a research direction for motor neuron diseases.

[0028] Compared with the prior art, the present invention has the following obvious substantial features and significant advantages:

[0029] The present invention introduces white noise and oscillation factor models through mathematical modeling and simulation techniques to construct a model of motor neuron pool recruitment under white noise conditions. It can study the recruitment effect of ion channel oscillations on motor neuron pools under white noise conditions, gain a deeper understanding of the working mechanism of motor neurons, provide research directions for related physiological experiments, and provide a theoretical basis for neurological disease research.

[0030] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a cell membrane equivalent circuit diagram of a preferred embodiment of the present invention;

[0032] Figure 2 It is a cell membrane equivalent circuit diagram of the Hodgkin-Huxley model of a preferred embodiment of the present invention;

[0033] Figure 3 A motor neuron model comprising two compartments is a preferred embodiment of the present invention;

[0034] Figure 4 is an action potential generated by a single FR motor neuron of a preferred embodiment of the present invention;

[0035] Figure 5 It is a motor neuron pool model stimulated by synaptic input of a preferred embodiment of the present invention;

[0036] Figure 6 is the output result of the motor neuron pool model of a preferred embodiment of the present invention;

[0037] Figure 7 is a white noise model of a preferred embodiment of the present invention;

[0038] Figure 8 It is the output of the motor neuron pool model including the white noise model and the oscillation factor model of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0039] The following describes several preferred embodiments of the present invention with reference to the drawings in the specification, so that the technical content is clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0040] In the drawings, components with the same structure are indicated by the same numerical reference numerals, and components with similar structures or functions are indicated by similar numerical reference numerals. The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. In order to make the illustration clearer, the thickness of the components is appropriately exaggerated in some places in the drawings.

[0041] 1. Construction of a single lumbar motor neuron model

[0042] Neuron Modeling

[0043] 1. Establish a cabin model based on cable theory according to the cell morphology of neurons

[0044] Cable theory provides a mathematical method to model the passive characteristics of neurons. The basic assumptions of cable theory are: (1) The cell membrane is passive, that is, it is independent of voltage and is homogeneous. (2) The axial conductor of the dendrite has a constant cross-section and the resistance of the intracellular fluid can be expressed in ohms. (3) The extracellular resistivity is negligible, that is, the outside of the cell is uniformly equipotential. (4) The current input to the dendrite is the linear integration of the currents at different nodes in the dendrite. The cable equation is obtained:

[0045]

[0046] Among them, λ is the space constant, τ m time constant, x the dendrite axial distance, v the cell membrane voltage.

[0047] Due to the complex morphology of neurons, the compartment model is used to discretize the physical structure of the neuron morphology. The compartment model decomposes the complex morphology of neurons into a series of compartments or segments, each of which can represent a part of a neuron, such as a dendrite or axon. The voltage in the same segment is equal, and the segments are connected to each other through coupling resistors. The different segments have different cable lengths and different cable diameters, but each segment can be described by a parallel RC circuit, such as Figure 1 shown.

[0048] Considering the complexity of the motor neuron pool model, the present invention simplifies a single lumbar motor neuron into a two-compartment model, including a cell body and a dendrite. For different types of motor neurons, their passive model characteristics are different. For FR type motor neurons, the present invention sets:

[0049] The cell body length is 150-200um, the diameter is 18-20um, and the membrane resistance is 5000Ω·cm 2 , axial resistance is 20Ω·cm, membrane capacitance is 1uF / cm 2 .

[0050] Dendrite length is 450-500um, diameter is 10-15um, membrane resistance is 5000Ω·cm 2 , axial resistance is 60Ω·cm, membrane capacitance is 1uF / cm 2 .

[0051] 2. According to the excitability characteristics of neurons, insert ion channels based on the Hodgkin-Huxley model into the compartment model

[0052] Generating action potentials is an important ability of neurons to encode and decode information transmission. The compartment modeling of neurons is only a physiological description of the passive behavior of neurons. Adding ion channels to the model can make the model have the most important function of neurons - excitability.

[0053] like Figure 2 As shown, according to the Hodgkin-Huxley model, the present invention inserts ion channels into the motor neuron compartment model, wherein the cell body is distributed with transient sodium ion channels (NaT), persistent sodium channels (NaP), delayed rectifier potassium ion channels (K(DR)), calcium-activated potassium channels (K(AHP)) and H channels; and the dendrites are distributed with voltage-activated L-type calcium ion channels (CaL). The membrane potential equations of each compartment of the model are:

[0054]

[0055] Among them, C m Cell membrane capacitance (F / cm) V m is the membrane potential, I ion is the ion current, I ext is the external current.

[0056] Different types of motor neurons have different conductance densities of their individual ion channels. For FR motor neurons, the instantaneous sodium ion channel conductance density is 80 to 300 mS / cm 2 , the conductivity density of the continuous sodium channel is 0.2~0.5mS / cm 2 , the conductance density of delayed rectifier potassium ion channels is 80-200 mS / cm 2 , the conductivity density of calcium-activated potassium channels is 100-200 mS / cm 2 , the H channel conductivity density is 1mS / cm 2 , the conductance density of voltage-activated L-type calcium channels is 3 mS / cm 2 , the leakage channel conductivity density on the cell body is 0.1mS / cm 2 , the leakage channel conductance density on the dendrite is 25mS / cm 2 .

[0057] Figure 3is a motor neuron model with two compartments. The conductance expression of each ion channel is:

[0058]

[0059] I H =g H ·m H ·(V m -E H )

[0060] I L_CaL =g L_CaL ·m L_CaL ·(V m -E Ca )

[0061] I H_CaL =g H_CaL ·m H_CaL ·(V m -E Ca )

[0062]

[0063] The left side is the ion current, and the right side is g H , g L_CaL , g H_CaL , are the conductances of transient sodium, sustained sodium, delayed rectifier potassium, AHP potassium, H-current, L-type calcium, high voltage activated L-type calcium, and leak potassium channels, respectively; m, n, q, etc. represent state variables (with or without subscripts) defined by the Hodgkin-Huxley equation; E Na 、E K 、E Ca 、E H and E Leak Na + , K + , Ca 2+ The equilibrium potentials of the H, Leak and V currents were set to 55mV, -75mV, 80mV, -55mV and -70mV, respectively; m --The resting membrane potential of the model cell is set to -70mV.

[0064] 3. Based on known experimental data, calibrate and debug the cell membrane characteristics of the lumbar motor neuron model

[0065] Modify and debug the parameters in the model within a reasonable range to make the output data of the neuron model as close or consistent as possible with the data collected from the physiological experiment. The final FR motor neuron model parameters and the mean values ​​of the data collected from the physiological experiment are:

[0066]

[0067]

[0068] The parameters in the table show that the FR motor neuron constructed by the present invention can be used for simulation research of spinal motor neurons within a limited physiological range. A single FR motor neuron model can generate action potentials, such as Figure 4 shown.

[0069] 2. Construction of Lumbar Motor Neuron Pool Model

[0070] First, considering the diversity and complexity of motor neurons, FR motor neurons were further divided into 9 different subtypes based on their input resistance.

[0071]

[0072] Secondly, in order to make the motor neuron pool model constructed by the present invention simulate physiological phenomena and have lower computational complexity, 100 FR motor neuron models are planned to be integrated into a motor neuron pool model. Almost any network, such as computer networks, transportation networks, and power networks, has its topological structure, and different network connection methods will have completely different effects on the operation of the entire network. In a neural network, there are two types of connections between neurons, one is synaptic connection and the other is gap connection. The present invention mainly uses synaptic input to simultaneously regulate 100 FR motor neurons, making them a group that can characterize the recruitment effect of the motor neuron pool.

[0073] The excitatory and inhibitory synaptic inputs to descending neurons are characterized by:

[0074]

[0075] The maximum conductance g ex represents the excitatory synaptic current (I ex ), g in represents the inhibitory synaptic current (I in ). ex 、E in is the equilibrium potential of excitatory synapses and inhibitory synapses, set to 0mV and -80mV respectively. w represents the weight of synaptic input, which obeys normal distribution. τ 1 and τ 2is the time constant of synaptic current, which is 3ms and 2ms respectively. Motor neurons are excited with the increase of excitatory synaptic current and inhibit discharge with the increase of inhibitory synaptic current. In the present invention, the total time process of alternation of excitatory and inhibitory (step cycle) is about 0.4Hz. Therefore, the external current of the compartment membrane potential in the first part is the synaptic current, and the equation is transformed into:

[0076]

[0077] Inserting excitatory and inhibitory synaptic inputs into the cell bodies and dendrites in the compartment model, integrated into a motor neuron pool model, e.g. Figure 5 shown.

[0078] like Figure 6 As shown, the output of the motor neuron pool model is the number of motor neurons recruited during synaptic input, the action potential of a single motor neuron, the input-output relationship, etc., which well characterizes the recruitment process of the motor neuron pool.

[0079] 3. Introducing white noise model and oscillation factor model into the motor neuron pool model

[0080] Membrane potential oscillation is one of the main regulatory mechanisms of neuronal excitability. Studies have shown that white noise can induce membrane oscillation, and it has been confirmed that white noise-induced ion channel oscillation is the key mechanism for the generation of membrane potential oscillation. However, the role of white noise and its induced ion channel oscillation in the recruitment of motor neuron pools is still unclear. Therefore, the present invention introduces a white noise model and an oscillation factor model into the motor neuron pool model. The white noise model equation and output results are as follows: Figure 7 As shown:

[0081] I WN =g e (t)(V m -V e )+g i (t)(V m -V i )

[0082] Among them, V e 、V i are the reversal potentials of excitatory and inhibitory synapses, 0mV and -75mV respectively. e (t) represents the conductance of the excitatory current, g i (t) represents the conductance of the inhibitory current.

[0083] The same oscillation factor model is added to the ion channel of each FR motor neuron model to simulate the recruitment effect of the ion channel oscillation of the motor neuron pool. The oscillation factor model is simplified to a sine wave, which is added to the ion channel conductance to simulate the ion channel oscillation. The period and amplitude of the oscillation factor are related to the ion channel type and have a limited range. The present invention mainly includes four types of ion channel oscillations to correct the excitability of the motor neuron pool, and its specific expression is:

[0084]

[0085] like Figure 8 As shown, after adding the white noise model and the oscillation factor model, the recruitment output of the motor neuron pool model has a certain gain. By adjusting the relevant parameters of the white noise and the oscillation factor, the performance of the motor neuron pool model can be affected, indicating that the motor neuron pool model construction method of the present invention can be used to explore the ion channel mechanism of motor neuron pool recruitment, and provide a research plan and theoretical basis for motor neuron diseases.

[0086] The preferred specific embodiments of the present invention are described in detail above. It should be understood that ordinary technicians in the field can make many modifications and changes based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by technicians in the technical field based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for constructing a model of lumbar motor neuron pool recruitment under white noise conditions, characterized in that: The following steps are involved: Step 1: construct a single lumbar motor neuron model; Step 2, constructing a lumbar motor neuron pool model; Step 3: Introduce the white noise model and the oscillation factor model into the motor neuron pool model.

2. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: The step 1 is to construct a single lumbar motor neuron model in combination with the cell membrane characteristic data of lumbar motor neurons from physiological experiments.

3. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: In the step 2, the excitatory synapses and inhibitory synaptic inputs of descending neurons whose weights obey normal distribution are used to integrate the single lumbar motor neuron model into a lumbar motor neuron pool model.

4. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: In the step 3, a white noise model is added to the motor neuron pool model to simulate physiological cell membrane oscillations.

5. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: The step 3 is to introduce an oscillator factor model into the ion channel of the motor neuron to simulate the ion channel oscillation.

6. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: In step 3, an oscillatory factor is introduced into the ion channel of a single motor neuron to modify the standard Hodgkin-Huxley ion channel kinetic equation.

7. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: The model outputs the number of motor neurons recruited into the motor neuron pool and the neuronal input-output relationship.

8. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: The step 1 comprises the following steps: Step 1.1, establish a cabin model based on cable theory according to the cell morphology of neurons; Step 1.2: According to the excitability characteristics of neurons, insert ion channels based on the Hodgkin-Huxley model into the compartment model; Step 1.3: calibrate and debug the cell membrane properties of the lumbar motor neuron model.

9. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: In the step 2, 100 motor neuron models are integrated into a motor neuron pool model.

10. The method for constructing a model for recruiting lumbar motor neuron pools under white noise conditions as claimed in claim 1, characterized in that: The oscillation factor model is simplified to a sine wave, which is added to the ion channel conductance to simulate the ion channel oscillation.

Images