CN109447255A - A kind of simulated implementation simplifies the circuit of Hodgkin-Huxley neuron models - Google Patents

A kind of simulated implementation simplifies the circuit of Hodgkin-Huxley neuron models Download PDF

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CN109447255A
CN109447255A CN201811445919.6A CN201811445919A CN109447255A CN 109447255 A CN109447255 A CN 109447255A CN 201811445919 A CN201811445919 A CN 201811445919A CN 109447255 A CN109447255 A CN 109447255A
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CN109447255B (en
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胡晓宇
王大伟
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Northwestern Polytechnical University
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Abstract

The invention discloses the circuits that a kind of simulated implementation simplifies Hodgkin-Huxley neuron models, including the first exponential function circuit unit, the second exponential function circuit unit, third exponential function circuit unit, the 4th exponential function circuit unit, the 5th index functional circuit unit, the 6th exponential function circuit unit, the first proportional integral circuit unit, the second proportional integral circuit unit, third proportional integral circuit unit and the 4th proportional integral circuit unit.Compared with the existing technology, the present invention proposes that a kind of simulated implementation simplifies the circuit of Hodgkin-Huxley neuron models, mathematic(al) representation based on simplified Hodgkin-Huxley neuron models, using common analog electronics, cleverly design circuit, the nonlinear operation relationship in mathematic(al) representation can perfectly be presented, so that circuit output can accurately simulate the dynamic behavior of simplified Hodgkin-Huxley neuron models.

Description

A kind of simulated implementation simplifies the circuit of Hodgkin-Huxley neuron models
Technical field
The invention belongs to neuron circuit analogue technique field, in particular to a kind of simulated implementation simplifies Hodgkin- The circuit of Huxley neuron models.
Background technique
Neuron is the basic unit of nervous system, and neuronal quantity can reach tens of in mammal nervous system Hundred million.Neuron can be by providing electric signal, and electric signal is transmitted between different neurons, to realize to information Reception, transmission, processing etc., change proprioception external environment with this, or signal instruction that transmitting brain is sent, with Realize the interaction with external environment.For the working mechanism of in-depth study nervous system, related scholar establishes a variety of mathematics Model describes the discharge dynamics behavior of neuron, as Hodgkin-Huxley model, FitzHugh-Naguma model, Hindmarsh-Rose model, Morris-Lecar model etc..By studying neuron models power scholarship and moral conduct at different conditions For variation, can be effectively predicted Neural spike train activity, existing research shows that the diseases such as parkinsonism, epilepsy and nerve The paradoxical discharge of system has direct relation, therefore, to single neuron, coupled neural member and neuroid dynamic behavior Research can provide potential theories integration for the treatment of these diseases, have great importance.
It is most direct research mode to the reaction of different external environments that neuron is detected using biological experiment, however Actual biological experiment is often costly and experimental period is very long, therefore it is not a kind of optimal research nerve The dynamic (dynamical) mode of member；Neuron models are generally made of multiple differential equations, with the increase of neuronal quantity, to neuron The computation burden of system dynamics behavioural analysis will greatly increase, and the real-time of calculating cannot be protected, therefore, based on mind The dynamic behavior that neuron is studied through metamathematics model also receives certain limitation；In view of analog circuit has cost Cheaply, it is easily integrated, the advantages that real-time is good, neuron models, and the electric discharge row of imictron is such as realized by circuit For, will successfully overcome biological experiment it is costly, the period is long the disadvantages of, and can solve numerical value and calculate existing reality When property problem.Since the neuron models mathematical model that neuron models are based especially on conductance is complicated, such as Hodgkin- Huxley model, the function in model are difficult to be directly realized by with existing analog device, and therefore, it is necessary to further simplify mind Through meta-model, futuramic circuit topology accurately realizes complicated neuron models.These researchs can ensure further Exact reproduction neuron dynamic behavior, provide strong tool for research neuron and the working mechanism of nervous system, With important theory significance and actual application value.
Summary of the invention
In response to the problems existing in the prior art, the purpose of the present invention is to provide a kind of simulated implementations to simplify Hodgkin- The circuit of Huxley neuron models.
In order to achieve the above objectives, the present invention adopts the following technical scheme that realize:
A kind of simulated implementation simplifies the circuit of Hodgkin-Huxley neuron models, including the first exponential function circuit list Member, the second exponential function circuit unit, third exponential function circuit unit, the 4th exponential function circuit unit, the 5th index letter Number circuit units, the 6th exponential function circuit unit, the first proportional integral circuit unit, the second proportional integral circuit unit, the Three proportional integral circuit units and the 4th proportional integral circuit unit；Wherein,
The first exponential function circuit unit, third exponential function circuit unit and the 5th index functional circuit unit are equal It is made of reversed computing module, scale operation module and exponent arithmetic module；Wherein, the first exponential function circuit unit includes defeated Enter to hold E1I and output end E1O；Third exponential function circuit unit includes input terminal E3I and output end E3O；5th exponential function Circuit unit includes input terminal E5I and output end E5O；
The second exponential function circuit unit, the 4th exponential function circuit unit and the 6th exponential function circuit unit are equal It is made of scale operation module and exponent arithmetic module；Wherein, the second exponential function circuit unit includes input terminal E2I and output Hold E2O；4th exponential function circuit unit includes input terminal E4I and output end E4O；6th exponential function circuit unit includes defeated Enter to hold E6I and output end E6O；
The first proportional integral circuit unit, the second proportional integral circuit unit and third proportional integral circuit unit are equal It is made of two multiplying modules, reversed computing module and proportional integration module；Wherein, the first proportional integral circuit unit packet AI1 containing input terminal, AI2 and output terminals A O；Second proportional integral circuit unit includes input terminal BI1, BI2 and output end BO；The Three proportional integral circuit units include input terminal CI1, CI2 and output end CO；
The 4th proportional integral circuit unit is by seven multiplying modules, three subtraction modules, three gains Module, three voltage sources and a proportional integration module composition；It includes input terminal DI1, DI2, DI3, DI4, DI5, DI6 and defeated Outlet DO；
The input terminal AI1 of output end E1O connection the first proportional integral circuit unit of first exponential function circuit unit, the The input terminal AI2 of output end E2O connection the first proportional integral circuit unit of two exponential function circuit units, the first proportional integration The input terminal DI1 of the 4th proportional integral circuit unit of output terminals A O connection of circuit unit；Third exponential function circuit unit The input terminal BI1, the output end E4O of the 4th exponential function circuit unit of output end E3O connection the second proportional integral circuit unit The input terminal BI2 of the second proportional integral circuit unit is connected, the output end BO connection the 4th of the second proportional integral circuit unit is compared The input terminal DI2 of example integrating circuit unit；The output end E5O connection third proportional integral circuit of 5th index functional circuit unit The input terminal CI1 of unit, the input of the output end E6O connection third proportional integral circuit unit of the 6th exponential function circuit unit Hold CI2, the input terminal DI3 of the 4th proportional integral circuit unit of output end CO connection of third proportional integral circuit unit；4th The output end DO of proportional integral circuit unit is separately connected the first exponential function circuit unit input terminal E1I, the second exponential function Circuit unit input terminal E2I, third exponential function circuit unit input terminal E3I, the 4th exponential function circuit unit input terminal E4I, the 5th index functional circuit unit input terminal E5I, the 6th exponential function circuit unit input terminal E6I, the 4th proportional integration The input terminal DI4 of circuit unit, the input terminal DI5 of the 4th proportional integral circuit unit and the 4th proportional integral circuit unit it is defeated Enter to hold DI6.
A further improvement of the present invention lies in that reversed computing module is by resistance in the first exponential function circuit unit R1、R2With operational amplifier U1Composition；
Scale operation module is by resistance R3、R4With operational amplifier U2Composition；
Exponent arithmetic module is by bipolar transistor Q1、Q2, operational amplifier U3、U4, resistance R5、R6、R7With voltage source V1 Composition；
The input signal of first exponential function circuit unit E1 is by input terminal E1I through resistance R1It is connected to operational amplifier U1 Reverse input end, resistance R2Both ends be separately connected operational amplifier U1Reverse input end and output end, operational amplifier U1 Positive input ground connection；Operational amplifier U1Output end signal through resistance R3Connect operational amplifier U2Reverse input end, Resistance R4Both ends be respectively connected to operational amplifier U2Reverse input end and output end, operational amplifier U2Positive input End ground connection；Operational amplifier U2Output end connect bipolar transistor Q1Base stage, bipolar transistor Q1Collector connect fortune Calculate amplifier U3Reverse input end, bipolar transistor Q1Emitter through resistance R6Meet operational amplifier U3Output end；Electricity The anode of potential source V1 is through resistance R5Meet operational amplifier U3Reverse input end, voltage source V1 cathode ground connection；Operational amplifier U3 Positive input ground connection, operational amplifier U3Output end through resistance R6Connect bipolar junction transistor Q2Emitter；It is ambipolar Transistor Q2Base earth, bipolar transistor Q2Collector connect operational amplifier U4Reverse input end；Operation amplifier Device U4Positive input ground connection, resistance R7Both ends be separately connected operational amplifier U4Reverse input end and output end, operation Amplifier U4Output end signal be the first exponential function circuit unit output end E1O signal.
A further improvement of the present invention lies in that scale operation module is by resistance in the second exponential function circuit unit R8、R9With operational amplifier U5Composition；
Exponent arithmetic module is by bipolar transistor Q3、Q4, operational amplifier U6、U7, resistance R10、R11、R12And voltage source V2 composition；
The input signal of second exponential function circuit unit E2 is by input terminal E2I through resistance R8It is connected to operational amplifier U5 Reverse input end, resistance R9Both ends be separately connected operational amplifier U5Reverse input end and output end, operational amplifier U5 Positive input ground connection；Operational amplifier U5Output end connect bipolar transistor Q3Base stage, bipolar transistor Q3's Collector meets operational amplifier U6Reverse input end, bipolar transistor Q3Emitter through resistance R11Meet operational amplifier U6 Output end；The anode of voltage source V2 is through resistance R10Meet operational amplifier U6Reverse input end, voltage source V2 cathode ground connection； Operational amplifier U6Positive input ground connection, operational amplifier U6Output end through resistance R11Connect bipolar junction transistor Q4's Emitter；Bipolar junction transistor Q4Base earth, bipolar transistor Q4Collector connect operational amplifier U7It is reversed defeated Enter end；Operational amplifier U7Positive input ground connection, resistance R12Both ends be separately connected operational amplifier U7Reversed input End and output end, operational amplifier U7Output end signal be the first exponential function circuit unit output end E1O signal.
A further improvement of the present invention lies in that reversed computing module is by resistance in the third exponential function circuit unit R13、R14With operational amplifier U8Composition；
Scale operation module is by resistance R15、R16With operational amplifier U9Composition；
Exponent arithmetic module is by bipolar transistor Q5、Q6, operational amplifier U10、U11, resistance R17、R18、R19And voltage source V3 composition；
The input signal of third exponential function circuit unit E3 is by input terminal E3I through resistance R13It is connected to operational amplifier U8 Reverse input end, resistance R14Both ends be separately connected operational amplifier U8Reverse input end and output end, operational amplifier U8Positive input ground connection；Operational amplifier U8Output end signal through resistance R15Connect operational amplifier U9Reversed input End, resistance R16Both ends be respectively connected to operational amplifier U9Reverse input end and output end, operational amplifier U9Forward direction Input end grounding；Operational amplifier U9Output end connect bipolar transistor Q5Base stage, bipolar transistor Q5Collector Meet operational amplifier U10Reverse input end, bipolar transistor Q5Emitter through resistance R18Connect operational amplifier U10's Output end；The anode of voltage source V3 is through resistance R17Meet operational amplifier U10Reverse input end, voltage source V3 cathode ground connection； Operational amplifier U10Positive input ground connection, operational amplifier U10Output end through resistance R19Connect bipolar junction transistor Q6 Emitter；Bipolar junction transistor Q6Base earth, bipolar transistor Q6Collector connect operational amplifier U11It is anti- To input terminal；Operational amplifier U11Positive input ground connection, resistance R19Both ends be separately connected operational amplifier U11It is reversed Input terminal and output end, operational amplifier U11Output end signal be third exponential function circuit unit output end E3O letter Number.
A further improvement of the present invention lies in that scale operation module is by resistance in the 4th exponential function circuit unit R20、R21With operational amplifier U12Composition；
Exponent arithmetic module is by bipolar transistor Q7、Q8, operational amplifier U13、U14, resistance R22、R23、R24And voltage source V4 composition；
The input signal of 4th exponential function circuit unit E4 is by input terminal E4I through resistance R20It is connected to operational amplifier U12Reverse input end, resistance R21Both ends be separately connected operational amplifier U12Reverse input end and output end, operation amplifier Device U12Positive input ground connection；Operational amplifier U12Output end connect bipolar transistor Q7Base stage, bipolar transistor Pipe Q7Collector meet operational amplifier U13Reverse input end, bipolar transistor Q7Emitter through resistance R23Operation is connect to put Big device U13Output end；The anode of voltage source V4 is through resistance R22Meet operational amplifier U13Reverse input end, voltage source V4's is negative Pole ground connection；Operational amplifier U13Positive input ground connection, operational amplifier U13Output end through resistance R23Connect ambipolar crystalline substance Body pipe Q8Emitter；Bipolar junction transistor Q8Base earth, bipolar transistor Q8Collector connect operational amplifier U14 Reverse input end；Operational amplifier U14Positive input ground connection, resistance R24Both ends be separately connected operational amplifier U14's Reverse input end and output end, operational amplifier U14Output end signal be the 4th exponential function circuit unit output end E4O signal.
A further improvement of the present invention lies in that reversed computing module is by resistance in the 5th index functional circuit unit R25、R26With operational amplifier U15Composition；
Scale operation module is by resistance R27、R28With operational amplifier U16Composition；
Exponent arithmetic module is by bipolar transistor Q9、Q10, operational amplifier U17、U18, resistance R29、R30、R31And voltage Source V5 composition；
The input signal of 5th index functional circuit unit E5 is by input terminal E5I through resistance R25It is connected to operational amplifier U15Reverse input end, resistance R26Both ends be separately connected operational amplifier U15Reverse input end and output end, operation amplifier Device U15Positive input ground connection；Operational amplifier U15Output end signal through resistance R27Connect operational amplifier U16It is reversed Input terminal, resistance R28Both ends be respectively connected to operational amplifier U16Reverse input end and output end, operational amplifier U16's Positive input ground connection；Operational amplifier U16Output end connect bipolar transistor Q9Base stage, bipolar transistor Q9's Collector meets operational amplifier U17Reverse input end, bipolar transistor Q9Emitter through resistance R30Connect operational amplifier U17Output end；The anode of voltage source V5 is through resistance R29Meet operational amplifier U17Reverse input end, the cathode of voltage source V5 connects Ground；Operational amplifier U17Positive input ground connection, operational amplifier U17Output end through resistance R31Connect bipolar junction transistor Q10Emitter；Bipolar junction transistor Q10Base earth, bipolar transistor Q10Collector connect operational amplifier U18's Reverse input end；Operational amplifier U18Positive input ground connection, resistance R32Both ends be separately connected operational amplifier U18It is anti- To input terminal and output end, operational amplifier U18Output end signal be the 5th index functional circuit unit output end E5O Signal.
A further improvement of the present invention lies in that scale operation module is by resistance in the 6th exponential function circuit unit R32、R33With operational amplifier U19Composition；
Exponent arithmetic module is by bipolar transistor Q11、Q12, operational amplifier U20、U21, resistance R34、R35、R36And voltage Source V6 composition；
The input signal of 6th exponential function circuit unit E6 is by input terminal E6I through resistance R32It is connected to operational amplifier U19Reverse input end, resistance R33Both ends be separately connected operational amplifier U19Reverse input end and output end, operation amplifier Device U19Positive input ground connection；Operational amplifier U19Output end connect bipolar transistor Q11Base stage, bipolar transistor Pipe Q11Collector meet operational amplifier U20Reverse input end, bipolar transistor Q11Emitter through resistance R35Connect operation Amplifier U20Output end；The anode of voltage source V6 is through resistance R34Meet operational amplifier U20Reverse input end, voltage source V6's Cathode ground connection；Operational amplifier U20Positive input ground connection, operational amplifier U20Output end through resistance R35It connects ambipolar Transistor Q12Emitter；Bipolar junction transistor Q12Base earth, bipolar transistor Q12Collector connect operation amplifier Device U21Reverse input end；Operational amplifier U21Positive input ground connection, resistance R36Both ends be separately connected operational amplifier U21Reverse input end and output end, operational amplifier U21Output end signal be the defeated of the 6th exponential function circuit unit Outlet E6O signal.
A further improvement of the present invention lies in that in the first proportional integral circuit unit, two multiplying modules point It Wei not MA1 and MA2；
Reversed computing module is by resistance R37, R38With operational amplifier U22Composition；
Proportional integration module is by resistance R39, R40, R41, operational amplifier U23With capacitor C1Composition；
One of the input signal connection multiplying module MA1 of the input terminal AI1 of first proportional integral circuit unit A is defeated Enter end, another input terminal of multiplying module MA1 connects operational amplifier U23Output end, multiplicative operator module MA1 Output end through resistance R39Connect operational amplifier U22Reverse input end；The input terminal of first proportional integral circuit unit A The input signal of AI2 is through resistance R37It is connected to operational amplifier U22Reverse input end, resistance R38Both ends be separately connected operation Amplifier U22Reverse input end and output end, operational amplifier U22Positive input ground connection, operational amplifier U22Output End is through resistance R40Connect operational amplifier U23Reverse input end；The input terminal AI2's of first proportional integral circuit unit A is defeated Enter an input terminal of signal connection multiplying module MA2, another input terminal connection operation of multiplying module MA2 is put Big device U23Output end, the output end of multiplying module MA2 is through resistance R41Connect operational amplifier U23Reverse input end, Operational amplifier U23Positive input ground connection, capacitor C1Both ends be separately connected operational amplifier U23Reverse input end and defeated Outlet, operational amplifier U23Output end be the first proportional integral circuit unit output terminals A O.
A further improvement of the present invention lies in that in the second proportional integral circuit unit, two multiplying modules point It Wei not MB1 and MB2；
Reversed computing module is by resistance R42, R43With operational amplifier U24Composition；
Proportional integration module is by resistance R44, R45, R46, operational amplifier U25With capacitor C2Composition；
One of the input signal connection multiplying module MB1 of the input terminal BI1 of second proportional integral circuit unit B is defeated Enter end, another input terminal of multiplying module MB1 connects operational amplifier U25Output end, multiplicative operator module MB1 Output end through resistance R44Connect operational amplifier U24Reverse input end；The input terminal of second proportional integral circuit unit B The input signal of BI2 is through resistance R42It is connected to operational amplifier U24Reverse input end, resistance R43Both ends be separately connected operation Amplifier U24Reverse input end and output end, operational amplifier U24Positive input ground connection, operational amplifier U24Output End is through resistance R45Connect operational amplifier U25Reverse input end；The input terminal BI2's of second proportional integral circuit unit B is defeated Enter an input terminal of signal connection multiplying module MB2, another input terminal connection operation of multiplying module MB2 is put Big device U25Output end, the output end of multiplying module MB2 is through resistance R46Connect operational amplifier U25Reverse input end, Operational amplifier U25Positive input ground connection, capacitor C2Both ends be separately connected operational amplifier U25Reverse input end and defeated Outlet, operational amplifier U25Output end be the second proportional integral circuit unit output end BO；
In the third proportional integral circuit unit, two multiplying modules are respectively MC1 and MC2；
Reversed computing module is by resistance R47, R48With operational amplifier U26Composition；
Proportional integration module is by resistance R49, R50, R51, operational amplifier U27With capacitor C3Composition；
One of the input signal connection multiplying module MC1 of the input terminal CI1 of third proportional integral circuit unit C is defeated Enter end, another input terminal of multiplying module MC1 connects operational amplifier U27Output end, multiplicative operator module MC1 Output end through resistance R49Connect operational amplifier U26Reverse input end；The input terminal of third proportional integral circuit unit C The input signal of CI2 is through resistance R47It is connected to operational amplifier U26Reverse input end, resistance R48Both ends be separately connected operation Amplifier U26Reverse input end and output end, operational amplifier U26Positive input ground connection, operational amplifier U26Output End is through resistance R50Connect operational amplifier U27Reverse input end；The input terminal CI2's of third proportional integral circuit unit C is defeated Enter an input terminal of signal connection multiplying module MC2, another input terminal connection operation of multiplying module MC2 is put Big device U27Output end, the output end of multiplying module MC2 is through resistance R51Connect operational amplifier U27Reverse input end, Operational amplifier U27Positive input ground connection, capacitor C3Both ends be separately connected operational amplifier U27Reverse input end and defeated Outlet, operational amplifier U27Output end be third proportional integral circuit unit output end CO.
A further improvement of the present invention lies in that in the 4th proportional integral circuit unit, the 4th proportional integral circuit The output terminals A O of input terminal DI1 connection the first proportional integral circuit unit of unit, the input of the 4th proportional integral circuit unit The input signal of end DI1 is separately connected two input terminals of multiplying module MD5, the output end letter of multiplying module MD5 Two input terminals of multiplying module MD6 number are separately connected, the output end signal of multiplying module MD6 is connected to multiplication fortune An input terminal of module MD7 is calculated, the output end signal of multiplying module MD7 is connected to the input terminal of gain module G2, increases The output end signal of beneficial module G2 is through resistance R53It is connected to operational amplifier U28Reverse input end；4th proportional integral circuit The output end BO of input terminal DI2 connection the second proportional integral circuit unit of unit, the input of the 4th proportional integral circuit unit The input signal of end DI2 is respectively connected to two input terminals of multiplying module MD1, the output letter of multiplying module MD1 An input terminal of number connection multiplying module MD2, another input terminal of multiplying module MD2 connect the 4th ratio product The output end signal of the input signal of the input terminal DI2 of parallel circuit unit, multiplying module MD2 connects multiplying module An input terminal of MD3 a, input terminal of the output end signal connection multiplying module MD4 of multiplying module MD3, multiplies The input terminal of the output signal connection gain module G1 of method computing module MD4, the output end signal of gain module G1 is through resistance R54 It is connected to operational amplifier U28Reverse input end；The input terminal DI3 connection third ratio product of 4th proportional integral circuit unit The output end CO of parallel circuit unit, the input signal of the input terminal DI3 of the 4th proportional integral circuit unit are connected to multiplying Another input terminal of module MD3；The 4th proportional integral circuit unit of input terminal DI4 connection of 4th proportional integral circuit unit Output end DO, the input signal of the input terminal DI4 of the 4th proportional integral circuit unit is being connected to subtraction module S1 just Input terminal, the anode of the negative input end connection voltage source V7 of subtraction module S1, the cathode ground connection of voltage source V7, subtraction Another input terminal of the output end signal connection multiplying module MD4 of module S1；4th proportional integral circuit unit it is defeated Enter to hold the output end DO of the 4th proportional integral circuit unit of DI5 connection, the input terminal DI5's of the 4th proportional integral circuit unit is defeated Enter the positive input terminal that signal is connected to subtraction module S2, the negative input end connection voltage source V8 of subtraction module S2 is just Pole, the cathode ground connection of voltage source V8, another of the output end signal connection multiplying module MD7 of subtraction module S2 are defeated Enter end；The output end DO of the 4th proportional integral circuit unit of input terminal DI6 connection of 4th proportional integral circuit unit, the 4th ratio The input signal of the input terminal DI6 of example integrating circuit unit is connected to the positive input terminal of subtraction module S3, subtraction mould The anode of the negative input end connection voltage source V9 of block S3, the cathode ground connection of voltage source V9, the output end letter of subtraction module S3 Number connection gain module G3 input terminal；The output end signal of gain module G3 is through resistance R52It is connected to operational amplifier U28's Reverse input end；Impressed current stimulus signal I1 anode output signal is through resistance R55It is connected to operational amplifier U28It is reversed defeated Enter end, the cathode ground connection of impressed current stimulus signal I1；The both ends of capacitor C4 are separately connected operational amplifier U28Reversed input End and output end；Operational amplifier U28Output end signal be the 4th proportional integral circuit unit output end DO output letter Number.
The present invention has following beneficial technical effect:
Compared with the existing technology, the present invention proposes that a kind of simulated implementation simplifies the electricity of Hodgkin-Huxley neuron models Road, it is ingenious using common analog electronics based on the mathematic(al) representation of simplified Hodgkin-Huxley neuron models Design circuit, the nonlinear operation relationship in mathematic(al) representation can perfectly be presented, so that circuit output energy Enough accurate dynamic behaviors for simulating simplified Hodgkin-Huxley neuron models.
Due to using common analog electronics, low cost is easily integrated the realized circuit of the present invention；Since circuit is set Count ingenious, circuit structure is simple, and output effect is good.Designed circuit parameter dynamic regulation range is wide, and flexible adjustment is convenient, circuit Output is stablized, precision is high and strong antijamming capability.With the variation of circuit parameter, the circuit that the present invention is realized can simulate letter Change a variety of electric discharge shapes such as Hodgkin-Huxley neuron models tranquillization state, peak discharge (spiking), cluster electric discharge (bursting) Formula.To realize that real-time analysis, calculating and the application of coupled neural member and neuroid provide good support.
In conclusion a kind of simulated implementation proposed by the present invention simplifies the circuit of Hodgkin-Huxley neuron models, Ingenious in design, structure is simple, and low cost is easily integrated, and circuit is to the complete of simplified Hodgkin-Huxley neuron models It realizes, ensure that the various electric discharge behaviors of simplified Hodgkin-Huxley neuron models can be accurately presented in circuit, to realize Real-time analysis, calculating and the application of coupled neural member and neuroid provide good support.
Detailed description of the invention
Fig. 1 is the circuit diagram that simulated implementation simplifies Hodgkin-Huxley neuron models；
Fig. 2 is stimulated current I1Neuron tranquillization state waveform diagram when=5 μ A；
Fig. 3 is stimulated current I1Neuron peak discharge waveform diagram when=8 μ A；
Fig. 4 is stimulated current I1=15sin (2 π ft)) μ A, f=1Hz when Neural cluster discharge waveform figure.
Specific embodiment
For the technology contents, circuit structure, the purpose and effect realized that the present invention will be described in detail, below in conjunction with specific Embodiment simultaneously cooperates attached drawing to give to be described in detail.
Simplify Hodgkin-Huxley neuron models to be made of the equation group comprising four differential equations, this four-dimension is micro- Divide equation group as follows:
Wherein:
αn=0.0573e(0.0338V)
αm=0.369e(0.0328V)
αh=0.0775e(-0.0452V)
βn=0.1203e(-0.0258V)
βm=6e(-0.0769V)
βh=0.075e(0.0357V)
In formula: CMIt is cell membrane capacitance, V is film potential, gNa、gKAnd glIt is sodium-ion channel, potassium-channel and leakage respectively The electric conductivity value of ion channel, ENa、EKAnd ElIt is the equilibrium potential of sodium-ion channel, potassium-channel and leakage ion channel respectively, M, n and h is state variable, and value changes between 0 to 1 range, and controls the size of ion channel electric conductivity value.
Fig. 1 is the circuit diagram of the simplification Hodgkin-Huxley neuron models of the invention realized, wherein the region E1 is The first exponential function circuit unit, the region E2 are the second exponential function circuit unit, and the region E3 is described Third exponential function circuit unit, the region E4 are the 4th exponential function circuit unit, and the region E5 is the five fingers Number functional circuit unit, the region E6 are the 6th exponential function circuit unit, and a-quadrant is the first proportional integration electricity Road unit, B area are the second proportional integral circuit unit, and the region C is the third proportional integral circuit unit, D Region is the 4th proportional integral circuit unit.
A kind of simulated implementation provided by the invention simplifies the circuit of Hodgkin-Huxley neuron models, including first refers to Number functional circuit unit, the second exponential function circuit unit, third exponential function circuit unit, the 4th exponential function circuit list Member, the 5th index functional circuit unit, the 6th exponential function circuit unit, the first proportional integral circuit unit, the second ratio product Parallel circuit unit, third proportional integral circuit unit and the 4th proportional integral circuit unit.
Wherein, the first exponential function circuit unit, third exponential function circuit unit and the 5th index functional circuit Unit is made of reversed computing module, scale operation module and exponent arithmetic module；Wherein, the first exponential function circuit unit Include input terminal E1I and output end E1O；Third exponential function circuit unit includes input terminal E3I and output end E3O；The five fingers Number functional circuit unit includes input terminal E5I and output end E5O.
The second exponential function circuit unit, the 4th exponential function circuit unit and the 6th exponential function circuit unit are equal It is made of scale operation module and exponent arithmetic module；Wherein, the second exponential function circuit unit includes input terminal E2I and output Hold E2O；4th exponential function circuit unit includes input terminal E4I and output end E4O；6th exponential function circuit unit includes defeated Enter to hold E6I and output end E6O.
The first proportional integral circuit unit, the second proportional integral circuit unit and third proportional integral circuit unit are equal It is made of two multiplying modules, reversed computing module and proportional integration module；Wherein, the first proportional integral circuit unit packet AI1 containing input terminal, AI2 and output terminals A O；Second proportional integral circuit unit includes input terminal BI1, BI2 and output end BO；The Three proportional integral circuit units include input terminal CI1, CI2 and output end CO.
The 4th proportional integral circuit unit is by seven multiplying modules, three subtraction modules, three gains Module, three voltage sources and a proportional integration module composition；It includes input terminal DI1, DI2, DI3, DI4, DI5, DI6 and defeated Outlet DO.
Specific connection type is: output end E1O the first proportional integral circuit of connection of the first exponential function circuit unit The input terminal AI1 of unit, the input of output end E2O connection the first proportional integral circuit unit of the second exponential function circuit unit Hold AI2, the input terminal DI1 of the 4th proportional integral circuit unit of output terminals A O connection of the first proportional integral circuit unit；Third The input terminal BI1 of output end E3O connection the second proportional integral circuit unit of exponential function circuit unit, the 4th exponential function electricity The input terminal BI2 of output end E4O connection the second proportional integral circuit unit of road unit, the second proportional integral circuit unit it is defeated The input terminal DI2 of the 4th proportional integral circuit unit of outlet BO connection；The output end E5O connection of 5th index functional circuit unit The input terminal CI1 of third proportional integral circuit unit, the output end E6O connection third ratio product of the 6th exponential function circuit unit The input terminal CI2 of parallel circuit unit, the 4th proportional integral circuit unit of output end CO connection of third proportional integral circuit unit Input terminal DI3；The output end DO of 4th proportional integral circuit unit is separately connected the first exponential function circuit unit input terminal E1I, the second exponential function circuit unit input terminal E2I, third exponential function circuit unit input terminal E3I, the 4th exponential function Circuit unit input terminal E4I, the 5th index functional circuit unit input terminal E5I, the 6th exponential function circuit unit input terminal E6I, the input terminal DI4 of the 4th proportional integral circuit unit, the 4th proportional integral circuit unit input terminal DI5 and the 4th ratio The input terminal DI6 of integrating circuit unit.
In the first exponential function circuit unit, reversed computing module is by resistance R1、R2With operational amplifier U1Composition； Scale operation module is by resistance R3、R4With operational amplifier U2Composition；Exponent arithmetic module is by bipolar transistor Q1、Q2, operation Amplifier U3、U4, resistance R5、R6、R7It is formed with voltage source V1；The input signal of first exponential function circuit unit E1 is by input terminal E1I is through resistance R1It is connected to operational amplifier U1Reverse input end, resistance R2Both ends be separately connected operational amplifier U1It is anti- To input terminal and output end, operational amplifier U1Positive input ground connection；Operational amplifier U1Output end signal through resistance R3 Connect operational amplifier U2Reverse input end, resistance R4Both ends be respectively connected to operational amplifier U2Reverse input end and Output end, operational amplifier U2Positive input ground connection；Operational amplifier U2Output end connect bipolar transistor Q1Base Pole, bipolar transistor Q1Collector meet operational amplifier U3Reverse input end, bipolar transistor Q1Emitter through electricity Hinder R6Meet operational amplifier U3Output end；The anode of voltage source V1 is through resistance R5Meet operational amplifier U3Reverse input end, electricity The cathode of potential source V1 is grounded；Operational amplifier U3Positive input ground connection, operational amplifier U3Output end through resistance R6Connection Bipolar junction transistor Q2Emitter；Bipolar junction transistor Q2Base earth, bipolar transistor Q2Collector connect operation Amplifier U4Reverse input end；Operational amplifier U4Positive input ground connection, resistance R7Both ends be separately connected operation amplifier Device U4Reverse input end and output end, operational amplifier U4Output end signal be the defeated of the first exponential function circuit unit Outlet E1O signal.
Bipolar junction transistor Q1And Q2NPN transistor Q2N222, operational amplifier U can be selected1、U2、U3、U4Using model For OP-07, voltage source V1=120.3mV, resistance R1=R2=R3=1K Ω, R4=670.8 Ω, R5=R6=R7=1K Ω.
In the second exponential function circuit unit, scale operation module is by resistance R8、R9With operational amplifier U5Composition； Exponent arithmetic module is by bipolar transistor Q3、Q4, operational amplifier U6、U7, resistance R10、R11、R12It is formed with voltage source V2；The The input signal of two exponential function circuit unit E2 is by input terminal E2I through resistance R8It is connected to operational amplifier U5Reversed input End, resistance R9Both ends be separately connected operational amplifier U5Reverse input end and output end, operational amplifier U5Positive input End ground connection；Operational amplifier U5Output end connect bipolar transistor Q3Base stage, bipolar transistor Q3Collector connect fortune Calculate amplifier U6Reverse input end, bipolar transistor Q3Emitter through resistance R11Meet operational amplifier U6Output end；Electricity The anode of potential source V2 is through resistance R10Meet operational amplifier U6Reverse input end, voltage source V2 cathode ground connection；Operational amplifier U6Positive input ground connection, operational amplifier U6Output end through resistance R11Connect bipolar junction transistor Q4Emitter；It is bipolar Transistor npn npn Q4Base earth, bipolar transistor Q4Collector connect operational amplifier U7Reverse input end；Operation is put Big device U7Positive input ground connection, resistance R12Both ends be separately connected operational amplifier U7Reverse input end and output end, Operational amplifier U7Output end signal be the first exponential function circuit unit output end E1O signal.
Bipolar junction transistor Q3And Q4NPN transistor Q2N222, operational amplifier U can be selected5、U6、U7Using model OP-07, voltage source V2=57.3mV, resistance R8=R9=R10=1K Ω, R11=R12=1K Ω.
In the third exponential function circuit unit, reversed computing module is by resistance R13、R14With operational amplifier U8Composition； Scale operation module is by resistance R15、R16With operational amplifier U9Composition；Exponent arithmetic module is by bipolar transistor Q5、Q6, fortune Calculate amplifier U10、U11, resistance R17、R18、R19It is formed with voltage source V3；The input signal of third exponential function circuit unit E3 by Input terminal E3I is through resistance R13It is connected to operational amplifier U8Reverse input end, resistance R14Both ends be separately connected operation amplifier Device U8Reverse input end and output end, operational amplifier U8Positive input ground connection；Operational amplifier U8Output end signal Through resistance R15Connect operational amplifier U9Reverse input end, resistance R16Both ends be respectively connected to operational amplifier U9It is reversed Input terminal and output end, operational amplifier U9Positive input ground connection；Operational amplifier U9Output end connect bipolar transistor Pipe Q5Base stage, bipolar transistor Q5Collector meet operational amplifier U10Reverse input end, bipolar transistor Q5Hair Emitter-base bandgap grading is through resistance R18Connect operational amplifier U10Output end；The anode of voltage source V3 is through resistance R17Meet operational amplifier U10's Reverse input end, the cathode ground connection of voltage source V3；Operational amplifier U10Positive input ground connection, operational amplifier U10It is defeated Outlet is through resistance R19Connect bipolar junction transistor Q6Emitter；Bipolar junction transistor Q6Base earth, bipolar transistor Q6 Collector connect operational amplifier U11Reverse input end；Operational amplifier U11Positive input ground connection, resistance R19Two End is separately connected operational amplifier U11Reverse input end and output end, operational amplifier U11Output end signal be third The output end E3O signal of exponential function circuit unit.
Bipolar junction transistor Q5And Q6NPN transistor Q2N222, operational amplifier U can be selected8、U9、U10、U11Using type Number be OP-07, voltage source V3=6V, resistance R13=R14=R15=1K Ω, R16=878.8 Ω, R17=R18=R19=1K Ω.
In the 4th exponential function circuit unit, scale operation module is by resistance R20、R21With operational amplifier U12Group At；Exponent arithmetic module is by bipolar transistor Q7、Q8, operational amplifier U13、U14, resistance R22、R23、R24With voltage source V4 group At；The input signal of 4th exponential function circuit unit E4 is by input terminal E4I through resistance R20It is connected to operational amplifier U12It is anti- To input terminal, resistance R21Both ends be separately connected operational amplifier U12Reverse input end and output end, operational amplifier U12's Positive input ground connection；Operational amplifier U12Output end connect bipolar transistor Q7Base stage, bipolar transistor Q7's Collector meets operational amplifier U13Reverse input end, bipolar transistor Q7Emitter through resistance R23Connect operational amplifier U13Output end；The anode of voltage source V4 is through resistance R22Meet operational amplifier U13Reverse input end, the cathode of voltage source V4 connects Ground；Operational amplifier U13Positive input ground connection, operational amplifier U13Output end through resistance R23Connect bipolar junction transistor Q8Emitter；Bipolar junction transistor Q8Base earth, bipolar transistor Q8Collector connect operational amplifier U14It is anti- To input terminal；Operational amplifier U14Positive input ground connection, resistance R24Both ends be separately connected operational amplifier U14It is reversed Input terminal and output end, operational amplifier U14Output end signal be the 4th exponential function circuit unit output end E4O letter Number.
Bipolar junction transistor Q7And Q8NPN transistor Q2N222, operational amplifier U can be selected12、U13、U14Using model For OP-07, voltage source V4=369mV, resistance R20=R21=R22=1K Ω, R23=R24=1K Ω.
In the 5th index functional circuit unit, reversed computing module is by resistance R25、R26With operational amplifier U15Group At；Scale operation module is by resistance R27、R28With operational amplifier U16Composition；Exponent arithmetic module is by bipolar transistor Q9、 Q10, operational amplifier U17、U18, resistance R29、R30、R31It is formed with voltage source V5；The input of 5th index functional circuit unit E5 Signal is by input terminal E5I through resistance R25It is connected to operational amplifier U15Reverse input end, resistance R26Both ends be separately connected fortune Calculate amplifier U15Reverse input end and output end, operational amplifier U15Positive input ground connection；Operational amplifier U15It is defeated End signal is through resistance R out27Connect operational amplifier U16Reverse input end, resistance R28Both ends be respectively connected to operation amplifier Device U16Reverse input end and output end, operational amplifier U16Positive input ground connection；Operational amplifier U16Output end connect Meet bipolar transistor Q9Base stage, bipolar transistor Q9Collector meet operational amplifier U17Reverse input end, it is bipolar Property transistor Q9Emitter through resistance R30Meet operational amplifier U17Output end；The anode of voltage source V5 is through resistance R29Connect fortune Calculate amplifier U17Reverse input end, voltage source V5 cathode ground connection；Operational amplifier U17Positive input ground connection, operation Amplifier U17Output end through resistance R31Connect bipolar junction transistor Q10Emitter；Bipolar junction transistor Q10Base earth, Bipolar transistor Q10Collector connect operational amplifier U18Reverse input end；Operational amplifier U18Positive input Ground connection, resistance R32Both ends be separately connected operational amplifier U18Reverse input end and output end, operational amplifier U18Output End signal is the output end E5O signal of the 5th index functional circuit unit.
Bipolar junction transistor Q9And Q10NPN transistor Q2N222, operational amplifier U can be selected15、U16、U17、U18Using Model OP-07, voltage source V5=77.5mV, resistance R25=R26=R27=1K Ω, R28=1175.2 Ω, R29=R30=R31= 1KΩ。
In the 6th exponential function circuit unit, scale operation module is by resistance R32、R33With operational amplifier U19Group At；Exponent arithmetic module is by bipolar transistor Q11、Q12, operational amplifier U20、U21, resistance R34、R35、R36With voltage source V6 group At；The input signal of 6th exponential function circuit unit E6 is by input terminal E6I through resistance R32It is connected to operational amplifier U19It is anti- To input terminal, resistance R33Both ends be separately connected operational amplifier U19Reverse input end and output end, operational amplifier U19's Positive input ground connection；Operational amplifier U19Output end connect bipolar transistor Q11Base stage, bipolar transistor Q11's Collector meets operational amplifier U20Reverse input end, bipolar transistor Q11Emitter through resistance R35Connect operational amplifier U20Output end；The anode of voltage source V6 is through resistance R34Meet operational amplifier U20Reverse input end, the cathode of voltage source V6 connects Ground；Operational amplifier U20Positive input ground connection, operational amplifier U20Output end through resistance R35Connect bipolar junction transistor Q12Emitter；Bipolar junction transistor Q12Base earth, bipolar transistor Q12Collector connect operational amplifier U21's Reverse input end；Operational amplifier U21Positive input ground connection, resistance R36Both ends be separately connected operational amplifier U21It is anti- To input terminal and output end, operational amplifier U21Output end signal be the 6th exponential function circuit unit output end E6O Signal.
Bipolar junction transistor Q11And Q12NPN transistor Q2N222, operational amplifier U can be selected19、U20、U21Using type Number be OP-07, voltage source V6=75mV, resistance R32=R33=R34=1K Ω, R35=R36=1K Ω.
In the first proportional integral circuit unit, two multiplying modules are respectively MA1 and MA2；Reversed operation mould Block is by resistance R37, R38With operational amplifier U22Composition；Proportional integration module is by resistance R39, R40, R41, operational amplifier U23And electricity Hold C1Composition；One of the input signal connection multiplying module MA1 of the input terminal AI1 of first proportional integral circuit unit A Another input terminal of input terminal, multiplying module MA1 connects operational amplifier U23Output end, multiplicative operator module The output end of MA1 is through resistance R39Connect operational amplifier U22Reverse input end；The input of first proportional integral circuit unit A Hold the input signal of AI2 through resistance R37It is connected to operational amplifier U22Reverse input end, resistance R38Both ends be separately connected fortune Calculate amplifier U22Reverse input end and output end, operational amplifier U22Positive input ground connection, operational amplifier U22It is defeated Outlet is through resistance R40Connect operational amplifier U23Reverse input end；The input terminal AI2's of first proportional integral circuit unit A Input signal connects an input terminal of multiplying module MA2, and another input terminal of multiplying module MA2 connects operation Amplifier U23Output end, the output end of multiplying module MA2 is through resistance R41Connect operational amplifier U23Reversed input End, operational amplifier U23Positive input ground connection, capacitor C1Both ends be separately connected operational amplifier U23Reverse input end And output end, operational amplifier U23Output end be the first proportional integral circuit unit output terminals A O.
Operational amplifier U22、U23Using model OP-07, capacitor C1=0.001mF, resistance R37=R38=R39=R40= R41=1K Ω.
In the second proportional integral circuit unit, two multiplying modules are respectively MB1 and MB2；Reversed operation mould Block is by resistance R42, R43With operational amplifier U24Composition；Proportional integration module is by resistance R44, R45, R46, operational amplifier U25And electricity Hold C2Composition；One of the input signal connection multiplying module MB1 of the input terminal BI1 of second proportional integral circuit unit B Another input terminal of input terminal, multiplying module MB1 connects operational amplifier U25Output end, multiplicative operator module The output end of MB1 is through resistance R44Connect operational amplifier U24Reverse input end；The input of second proportional integral circuit unit B Hold the input signal of BI2 through resistance R42It is connected to operational amplifier U24Reverse input end, resistance R43Both ends be separately connected fortune Calculate amplifier U24Reverse input end and output end, operational amplifier U24Positive input ground connection, operational amplifier U24It is defeated Outlet is through resistance R45Connect operational amplifier U25Reverse input end；The input terminal BI2's of second proportional integral circuit unit B Input signal connects an input terminal of multiplying module MB2, and another input terminal of multiplying module MB2 connects operation Amplifier U25Output end, the output end of multiplying module MB2 is through resistance R46Connect operational amplifier U25Reversed input End, operational amplifier U25Positive input ground connection, capacitor C2Both ends be separately connected operational amplifier U25Reverse input end And output end, operational amplifier U25Output end be the second proportional integral circuit unit output end BO.
Operational amplifier U24、U25Using model OP-07, capacitor C2=0.001mF, resistance R42=R43=R44=R45= R46=1K Ω.
In the third proportional integral circuit unit, two multiplying modules are respectively MC1 and MC2；Reversed operation mould Block is by resistance R47, R48With operational amplifier U26Composition；Proportional integration module is by resistance R49, R50, R51, operational amplifier U27And electricity Hold C3Composition；One of the input signal connection multiplying module MC1 of the input terminal CI1 of third proportional integral circuit unit C Another input terminal of input terminal, multiplying module MC1 connects operational amplifier U27Output end, multiplicative operator module The output end of MC1 is through resistance R49Connect operational amplifier U26Reverse input end；The input of third proportional integral circuit unit C Hold the input signal of CI2 through resistance R47It is connected to operational amplifier U26Reverse input end, resistance R48Both ends be separately connected fortune Calculate amplifier U26Reverse input end and output end, operational amplifier U26Positive input ground connection, operational amplifier U26It is defeated Outlet is through resistance R50Connect operational amplifier U27Reverse input end；The input terminal CI2's of third proportional integral circuit unit C Input signal connects an input terminal of multiplying module MC2, and another input terminal of multiplying module MC2 connects operation Amplifier U27Output end, the output end of multiplying module MC2 is through resistance R51Connect operational amplifier U27Reversed input End, operational amplifier U27Positive input ground connection, capacitor C3Both ends be separately connected operational amplifier U27Reverse input end And output end, operational amplifier U27Output end be third proportional integral circuit unit output end CO.
Operational amplifier U26、U27Using model OP-07, capacitor C3=0.001mF, resistance R47=R48=R49=R50= R51=1K Ω.
In the 4th proportional integral circuit unit, the input terminal DI1 connection first of the 4th proportional integral circuit unit The output terminals A O of proportional integral circuit unit, the input signal of the input terminal DI1 of the 4th proportional integral circuit unit are separately connected Two input terminals of multiplying module MD5, the output end signal of multiplying module MD5 are separately connected multiplying module Two input terminals of MD6, the output end signal of multiplying module MD6 are connected to an input terminal of multiplying module MD7, The output end signal of multiplying module MD7 is connected to the input terminal of gain module G2, the output end signal warp of gain module G2 Resistance R53It is connected to operational amplifier U28Reverse input end；The input terminal DI2 connection second of 4th proportional integral circuit unit The output end BO of proportional integral circuit unit, the input signal of the input terminal DI2 of the 4th proportional integral circuit unit are separately connected To two input terminals of multiplying module MD1, the output signal of multiplying module MD1 connects multiplying module MD2's One input terminal, another input terminal of multiplying module MD2 connect the input terminal DI2's of the 4th proportional integral circuit unit Input signal, an input terminal of the output end signal connection multiplying module MD3 of multiplying module MD2, multiplying An input terminal of the output end signal connection multiplying module MD4 of module MD3, the output signal of multiplying module MD4 The input terminal of gain module G1 is connected, the output end signal of gain module G1 is through resistance R54It is connected to operational amplifier U28It is anti- To input terminal；The output end CO of the input terminal DI3 connection third proportional integral circuit unit of 4th proportional integral circuit unit, the The input signal of the input terminal DI3 of four proportional integral circuit units is connected to another input terminal of multiplying module MD3；The The output end DO of the 4th proportional integral circuit unit of input terminal DI4 connection of four proportional integral circuit units, the 4th proportional integration The input signal of the input terminal DI4 of circuit unit is connected to the positive input terminal of subtraction module S1, subtraction module S1's Negative input end connects the anode of voltage source V7, the cathode ground connection of voltage source V7, the output end signal connection of subtraction module S1 Another input terminal of multiplying module MD4；The 4th proportional integration of input terminal DI5 connection of 4th proportional integral circuit unit The output end DO of circuit unit, the input signal of the input terminal DI5 of the 4th proportional integral circuit unit are connected to subtraction mould The positive input terminal of block S2, the anode of the negative input end connection voltage source V8 of subtraction module S2, the cathode ground connection of voltage source V8, Another input terminal of the output end signal connection multiplying module MD7 of subtraction module S2；4th proportional integral circuit The output end DO of the 4th proportional integral circuit unit of input terminal DI6 connection of unit, the input of the 4th proportional integral circuit unit The input signal of end DI6 is connected to the positive input terminal of subtraction module S3, and the negative input end of subtraction module S3 connects electricity The anode of potential source V9, the cathode ground connection of voltage source V9, the output end signal connection gain module G3's of subtraction module S3 is defeated Enter end；The output end signal of gain module G3 is through resistance R52It is connected to operational amplifier U28Reverse input end；Impressed current thorn Energizing signal I1 anode output signal is through resistance R55It is connected to operational amplifier U28Reverse input end, impressed current stimulus signal The cathode of I1 is grounded；The both ends of capacitor C4 are separately connected operational amplifier U28Reverse input end and output end；Operational amplifier U28Output end signal be the 4th proportional integral circuit unit output end DO output signal.
Operational amplifier U28Using model OP-07, capacitor C4=0.001mF, resistance R52=R53=R54=R55=1K Ω, voltage source V7=115mV, V8=-12mV, V9=10.6mV.
A kind of simulated implementation provided by the invention simplifies the circuit of Hodgkin-Huxley neuron models, and analog circuit is It is fully achieved to Hodgkin-Huxley neuron models are simplified, ensure that simplified Hodgkin- can be accurately presented in circuit The various electric discharge behaviors of Huxley neuron models, to realize the real-time analysis of coupled neural member and neuroid, calculating And application provides good support.

Claims (10)

1. the circuit that a kind of simulated implementation simplifies Hodgkin-Huxley neuron models, which is characterized in that including the first index Functional circuit unit, the second exponential function circuit unit, third exponential function circuit unit, the 4th exponential function circuit unit, 5th index functional circuit unit, the 6th exponential function circuit unit, the first proportional integral circuit unit, the second proportional integration electricity Road unit, third proportional integral circuit unit and the 4th proportional integral circuit unit；Wherein,
The first exponential function circuit unit, third exponential function circuit unit and the 5th index functional circuit unit are by anti- It is formed to computing module, scale operation module and exponent arithmetic module；Wherein, the first exponential function circuit unit includes input terminal E1I and output end E1O；Third exponential function circuit unit includes input terminal E3I and output end E3O；5th index functional circuit Unit includes input terminal E5I and output end E5O；
The second exponential function circuit unit, the 4th exponential function circuit unit and the 6th exponential function circuit unit by than Example computing module and exponent arithmetic module composition；Wherein, the second exponential function circuit unit includes input terminal E2I and output end E2O；4th exponential function circuit unit includes input terminal E4I and output end E4O；6th exponential function circuit unit includes input Hold E6I and output end E6O；
The first proportional integral circuit unit, the second proportional integral circuit unit and third proportional integral circuit unit are by two A multiplying module, reversed computing module and proportional integration module composition；Wherein, the first proportional integral circuit unit includes defeated Enter to hold AI1, AI2 and output terminals A O；Second proportional integral circuit unit includes input terminal BI1, BI2 and output end BO；Third ratio Example integrating circuit unit includes input terminal CI1, CI2 and output end CO；
The 4th proportional integral circuit unit by seven multiplying modules, three subtraction modules, three gain modules, Three voltage sources and a proportional integration module composition；It includes input terminal DI1, DI2, DI3, DI4, DI5, DI6 and output ends DO；
The input terminal AI1 of output end E1O connection the first proportional integral circuit unit of first exponential function circuit unit, second refers to The input terminal AI2 of output end E2O connection the first proportional integral circuit unit of number functional circuit unit, the first proportional integral circuit The input terminal DI1 of the 4th proportional integral circuit unit of output terminals A O connection of unit；The output of third exponential function circuit unit Hold the input terminal BI1 of E3O connection the second proportional integral circuit unit, the output end E4O connection of the 4th exponential function circuit unit The input terminal BI2 of second proportional integral circuit unit, the 4th ratio of the output end BO connection product of the second proportional integral circuit unit The input terminal DI2 of parallel circuit unit；The output end E5O connection third proportional integral circuit unit of 5th index functional circuit unit Input terminal CI1, the input terminal of the output end E6O connection third proportional integral circuit unit of the 6th exponential function circuit unit CI2, the input terminal DI3 of the 4th proportional integral circuit unit of output end CO connection of third proportional integral circuit unit；4th ratio The output end DO of example integrating circuit unit is separately connected the first exponential function circuit unit input terminal E1I, the second exponential function electricity Road unit input terminal E2I, third exponential function circuit unit input terminal E3I, the 4th exponential function circuit unit input terminal E4I, 5th index functional circuit unit input terminal E5I, the 6th exponential function circuit unit input terminal E6I, the 4th proportional integral circuit Input terminal DI4, the input terminal DI5 of the 4th proportional integral circuit unit and the input terminal of the 4th proportional integral circuit unit of unit DI6。
2. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is that in the first exponential function circuit unit, reversed computing module is by resistance R1、R2With operational amplifier U1Composition；
Scale operation module is by resistance R3、R4With operational amplifier U2Composition；
Exponent arithmetic module is by bipolar transistor Q1、Q2, operational amplifier U3、U4, resistance R5、R6、R7It is formed with voltage source V1；
The input signal of first exponential function circuit unit E1 is by input terminal E1I through resistance R1It is connected to operational amplifier U1It is anti- To input terminal, resistance R2Both ends be separately connected operational amplifier U1Reverse input end and output end, operational amplifier U1Just To input end grounding；Operational amplifier U1Output end signal through resistance R3Connect operational amplifier U2Reverse input end, resistance R4Both ends be respectively connected to operational amplifier U2Reverse input end and output end, operational amplifier U2Positive input connect Ground；Operational amplifier U2Output end connect bipolar transistor Q1Base stage, bipolar transistor Q1Collector connect operation and put Big device U3Reverse input end, bipolar transistor Q1Emitter through resistance R6Meet operational amplifier U3Output end；Voltage source The anode of V1 is through resistance R5Meet operational amplifier U3Reverse input end, voltage source V1 cathode ground connection；Operational amplifier U3Just To input end grounding, operational amplifier U3Output end through resistance R6Connect bipolar junction transistor Q2Emitter；Bipolar transistor Pipe Q2Base earth, bipolar transistor Q2Collector connect operational amplifier U4Reverse input end；Operational amplifier U4 Positive input ground connection, resistance R7Both ends be separately connected operational amplifier U4Reverse input end and output end, operation amplifier Device U4Output end signal be the first exponential function circuit unit output end E1O signal.
3. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is that in the second exponential function circuit unit, scale operation module is by resistance R8、R9With operational amplifier U5Composition；
Exponent arithmetic module is by bipolar transistor Q3、Q4, operational amplifier U6、U7, resistance R10、R11、R12With voltage source V2 group At；
The input signal of second exponential function circuit unit E2 is by input terminal E2I through resistance R8It is connected to operational amplifier U5It is anti- To input terminal, resistance R9Both ends be separately connected operational amplifier U5Reverse input end and output end, operational amplifier U5Just To input end grounding；Operational amplifier U5Output end connect bipolar transistor Q3Base stage, bipolar transistor Q3Current collection Pole meets operational amplifier U6Reverse input end, bipolar transistor Q3Emitter through resistance R11Meet operational amplifier U6It is defeated Outlet；The anode of voltage source V2 is through resistance R10Meet operational amplifier U6Reverse input end, voltage source V2 cathode ground connection；Operation Amplifier U6Positive input ground connection, operational amplifier U6Output end through resistance R11Connect bipolar junction transistor Q4Transmitting Pole；Bipolar junction transistor Q4Base earth, bipolar transistor Q4Collector connect operational amplifier U7Reversed input End；Operational amplifier U7Positive input ground connection, resistance R12Both ends be separately connected operational amplifier U7Reverse input end And output end, operational amplifier U7Output end signal be the first exponential function circuit unit output end E1O signal.
4. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is that in the third exponential function circuit unit, reversed computing module is by resistance R13、R14With operational amplifier U8Composition；
Scale operation module is by resistance R15、R16With operational amplifier U9Composition；
Exponent arithmetic module is by bipolar transistor Q5、Q6, operational amplifier U10、U11, resistance R17、R18、R19With voltage source V3 group At；
The input signal of third exponential function circuit unit E3 is by input terminal E3I through resistance R13It is connected to operational amplifier U8It is anti- To input terminal, resistance R14Both ends be separately connected operational amplifier U8Reverse input end and output end, operational amplifier U8's Positive input ground connection；Operational amplifier U8Output end signal through resistance R15Connect operational amplifier U9Reverse input end, Resistance R16Both ends be respectively connected to operational amplifier U9Reverse input end and output end, operational amplifier U9Positive input End ground connection；Operational amplifier U9Output end connect bipolar transistor Q5Base stage, bipolar transistor Q5Collector connect fortune Calculate amplifier U10Reverse input end, bipolar transistor Q5Emitter through resistance R18Connect operational amplifier U10Output End；The anode of voltage source V3 is through resistance R17Meet operational amplifier U10Reverse input end, voltage source V3 cathode ground connection；Operation Amplifier U10Positive input ground connection, operational amplifier U10Output end through resistance R19Connect bipolar junction transistor Q6Hair Emitter-base bandgap grading；Bipolar junction transistor Q6Base earth, bipolar transistor Q6Collector connect operational amplifier U11It is reversed defeated Enter end；Operational amplifier U11Positive input ground connection, resistance R19Both ends be separately connected operational amplifier U11Reversed input End and output end, operational amplifier U11Output end signal be third exponential function circuit unit output end E3O signal.
5. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is that in the 4th exponential function circuit unit, scale operation module is by resistance R20、R21With operational amplifier U12Composition；
Exponent arithmetic module is by bipolar transistor Q7、Q8, operational amplifier U13、U14, resistance R22、R23、R24With voltage source V4 group At；
The input signal of 4th exponential function circuit unit E4 is by input terminal E4I through resistance R20It is connected to operational amplifier U12It is anti- To input terminal, resistance R21Both ends be separately connected operational amplifier U12Reverse input end and output end, operational amplifier U12's Positive input ground connection；Operational amplifier U12Output end connect bipolar transistor Q7Base stage, bipolar transistor Q7's Collector meets operational amplifier U13Reverse input end, bipolar transistor Q7Emitter through resistance R23Connect operational amplifier U13Output end；The anode of voltage source V4 is through resistance R22Meet operational amplifier U13Reverse input end, the cathode of voltage source V4 connects Ground；Operational amplifier U13Positive input ground connection, operational amplifier U13Output end through resistance R23Connect bipolar junction transistor Q8Emitter；Bipolar junction transistor Q8Base earth, bipolar transistor Q8Collector connect operational amplifier U14It is anti- To input terminal；Operational amplifier U14Positive input ground connection, resistance R24Both ends be separately connected operational amplifier U14It is reversed Input terminal and output end, operational amplifier U14Output end signal be the 4th exponential function circuit unit output end E4O letter Number.
6. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is that in the 5th index functional circuit unit, reversed computing module is by resistance R25、R26With operational amplifier U15Composition；
Scale operation module is by resistance R27、R28With operational amplifier U16Composition；
Exponent arithmetic module is by bipolar transistor Q9、Q10, operational amplifier U17、U18, resistance R29、R30、R31With voltage source V5 group At；
The input signal of 5th index functional circuit unit E5 is by input terminal E5I through resistance R25It is connected to operational amplifier U15It is anti- To input terminal, resistance R26Both ends be separately connected operational amplifier U15Reverse input end and output end, operational amplifier U15's Positive input ground connection；Operational amplifier U15Output end signal through resistance R27Connect operational amplifier U16Reverse input end, Resistance R28Both ends be respectively connected to operational amplifier U16Reverse input end and output end, operational amplifier U16Forward direction it is defeated Enter end ground connection；Operational amplifier U16Output end connect bipolar transistor Q9Base stage, bipolar transistor Q9Collector Meet operational amplifier U17Reverse input end, bipolar transistor Q9Emitter through resistance R30Meet operational amplifier U17It is defeated Outlet；The anode of voltage source V5 is through resistance R29Meet operational amplifier U17Reverse input end, voltage source V5 cathode ground connection；Fortune Calculate amplifier U17Positive input ground connection, operational amplifier U17Output end through resistance R31Connect bipolar junction transistor Q10's Emitter；Bipolar junction transistor Q10Base earth, bipolar transistor Q10Collector connect operational amplifier U18It is reversed Input terminal；Operational amplifier U18Positive input ground connection, resistance R32Both ends be separately connected operational amplifier U18It is reversed defeated Enter end and output end, operational amplifier U18Output end signal be the 5th index functional circuit unit output end E5O signal.
7. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is that in the 6th exponential function circuit unit, scale operation module is by resistance R32、R33With operational amplifier U19Composition；
Exponent arithmetic module is by bipolar transistor Q11、Q12, operational amplifier U20、U21, resistance R34、R35、R36With voltage source V6 Composition；
The input signal of 6th exponential function circuit unit E6 is by input terminal E6I through resistance R32It is connected to operational amplifier U19It is anti- To input terminal, resistance R33Both ends be separately connected operational amplifier U19Reverse input end and output end, operational amplifier U19's Positive input ground connection；Operational amplifier U19Output end connect bipolar transistor Q11Base stage, bipolar transistor Q11's Collector meets operational amplifier U20Reverse input end, bipolar transistor Q11Emitter through resistance R35Connect operational amplifier U20Output end；The anode of voltage source V6 is through resistance R34Meet operational amplifier U20Reverse input end, the cathode of voltage source V6 connects Ground；Operational amplifier U20Positive input ground connection, operational amplifier U20Output end through resistance R35Connect bipolar junction transistor Q12Emitter；Bipolar junction transistor Q12Base earth, bipolar transistor Q12Collector connect operational amplifier U21's Reverse input end；Operational amplifier U21Positive input ground connection, resistance R36Both ends be separately connected operational amplifier U21It is anti- To input terminal and output end, operational amplifier U21Output end signal be the 6th exponential function circuit unit output end E6O Signal.
8. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is, in the first proportional integral circuit unit, two multiplying modules are respectively MA1 and MA2；
Reversed computing module is by resistance R37, R38With operational amplifier U22Composition；
Proportional integration module is by resistance R39, R40, R41, operational amplifier U23With capacitor C1Composition；
An input of the input signal connection multiplying module MA1 of the input terminal AI1 of first proportional integral circuit unit A Another input terminal at end, multiplying module MA1 connects operational amplifier U23Output end, multiplicative operator module MA1's Output end is through resistance R39Connect operational amplifier U22Reverse input end；The input terminal AI2 of first proportional integral circuit unit A Input signal through resistance R37It is connected to operational amplifier U22Reverse input end, resistance R38Both ends be separately connected operation and put Big device U22Reverse input end and output end, operational amplifier U22Positive input ground connection, operational amplifier U22Output end Through resistance R40Connect operational amplifier U23Reverse input end；The input of the input terminal AI2 of first proportional integral circuit unit A Signal connects an input terminal of multiplying module MA2, and another input terminal of multiplying module MA2 connects operation amplifier Device U23Output end, the output end of multiplying module MA2 is through resistance R41Connect operational amplifier U23Reverse input end, fortune Calculate amplifier U23Positive input ground connection, capacitor C1Both ends be separately connected operational amplifier U23Reverse input end and output End, operational amplifier U23Output end be the first proportional integral circuit unit output terminals A O.
9. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is, in the second proportional integral circuit unit, two multiplying modules are respectively MB1 and MB2；
Reversed computing module is by resistance R42, R43With operational amplifier U24Composition；
Proportional integration module is by resistance R44, R45, R46, operational amplifier U25With capacitor C2Composition；
An input of the input signal connection multiplying module MB1 of the input terminal BI1 of second proportional integral circuit unit B Another input terminal at end, multiplying module MB1 connects operational amplifier U25Output end, multiplicative operator module MB1's Output end is through resistance R44Connect operational amplifier U24Reverse input end；The input terminal BI2 of second proportional integral circuit unit B Input signal through resistance R42It is connected to operational amplifier U24Reverse input end, resistance R43Both ends be separately connected operation and put Big device U24Reverse input end and output end, operational amplifier U24Positive input ground connection, operational amplifier U24Output end Through resistance R45Connect operational amplifier U25Reverse input end；The input of the input terminal BI2 of second proportional integral circuit unit B Signal connects an input terminal of multiplying module MB2, and another input terminal of multiplying module MB2 connects operation amplifier Device U25Output end, the output end of multiplying module MB2 is through resistance R46Connect operational amplifier U25Reverse input end, fortune Calculate amplifier U25Positive input ground connection, capacitor C2Both ends be separately connected operational amplifier U25Reverse input end and output End, operational amplifier U25Output end be the second proportional integral circuit unit output end BO；
In the third proportional integral circuit unit, two multiplying modules are respectively MC1 and MC2；
Reversed computing module is by resistance R47, R48With operational amplifier U26Composition；
Proportional integration module is by resistance R49, R50, R51, operational amplifier U27With capacitor C3Composition；
An input of the input signal connection multiplying module MC1 of the input terminal CI1 of third proportional integral circuit unit C Another input terminal at end, multiplying module MC1 connects operational amplifier U27Output end, multiplicative operator module MC1's Output end is through resistance R49Connect operational amplifier U26Reverse input end；The input terminal CI2 of third proportional integral circuit unit C Input signal through resistance R47It is connected to operational amplifier U26Reverse input end, resistance R48Both ends be separately connected operation and put Big device U26Reverse input end and output end, operational amplifier U26Positive input ground connection, operational amplifier U26Output end Through resistance R50Connect operational amplifier U27Reverse input end；The input of the input terminal CI2 of third proportional integral circuit unit C Signal connects an input terminal of multiplying module MC2, and another input terminal of multiplying module MC2 connects operation amplifier Device U27Output end, the output end of multiplying module MC2 is through resistance R51Connect operational amplifier U27Reverse input end, fortune Calculate amplifier U27Positive input ground connection, capacitor C3Both ends be separately connected operational amplifier U27Reverse input end and output End, operational amplifier U27Output end be third proportional integral circuit unit output end CO.
10. a kind of simulated implementation according to claim 1 simplifies the circuit of Hodgkin-Huxley neuron models, special Sign is, in the 4th proportional integral circuit unit, the input terminal DI1 connection first of the 4th proportional integral circuit unit is compared The output terminals A O of example integrating circuit unit, the input signal of the input terminal DI1 of the 4th proportional integral circuit unit, which is separately connected, to be multiplied Two input terminals of method computing module MD5, the output end signal of multiplying module MD5 are separately connected multiplying module MD6 Two input terminals, the output end signal of multiplying module MD6 is connected to an input terminal of multiplying module MD7, multiplies The output end signal of method computing module MD7 is connected to the input terminal of gain module G2, and the output end signal of gain module G2 is through electricity Hinder R53It is connected to operational amplifier U28Reverse input end；The input terminal DI2 connection second of 4th proportional integral circuit unit is compared The output end BO of example integrating circuit unit, the input signal of the input terminal DI2 of the 4th proportional integral circuit unit are respectively connected to Two input terminals of multiplying module MD1, the one of the output signal connection multiplying module MD2 of multiplying module MD1 A input terminal, another input terminal of multiplying module MD2 connect the defeated of the input terminal DI2 of the 4th proportional integral circuit unit Enter signal, an input terminal of the output end signal connection multiplying module MD3 of multiplying module MD2, multiplying mould An input terminal of the output end signal connection multiplying module MD4 of block MD3, the output signal of multiplying module MD4 connect The input terminal of gain module G1 is connect, the output end signal of gain module G1 is through resistance R54It is connected to operational amplifier U28It is reversed Input terminal；The output end CO of the input terminal DI3 connection third proportional integral circuit unit of 4th proportional integral circuit unit, the 4th The input signal of the input terminal DI3 of proportional integral circuit unit is connected to another input terminal of multiplying module MD3；4th The output end DO of the 4th proportional integral circuit unit of input terminal DI4 connection of proportional integral circuit unit, the 4th proportional integration electricity The input signal of the input terminal DI4 of road unit is connected to the positive input terminal of subtraction module S1, and subtraction module S1's is negative Input terminal connects the anode of voltage source V7, and the output end signal connection of the cathode ground connection of voltage source V7, subtraction module S1 multiplies Another input terminal of method computing module MD4；Input terminal DI5 connection the 4th proportional integration electricity of 4th proportional integral circuit unit The output end DO of road unit, the input signal of the input terminal DI5 of the 4th proportional integral circuit unit are connected to subtraction module The positive input terminal of S2, the anode of the negative input end connection voltage source V8 of subtraction module S2, the cathode ground connection of voltage source V8 subtract Another input terminal of the output end signal connection multiplying module MD7 of method computing module S2；4th proportional integral circuit list The output end DO of the 4th proportional integral circuit unit of input terminal DI6 connection of member, the input terminal of the 4th proportional integral circuit unit The input signal of DI6 is connected to the positive input terminal of subtraction module S3, and the negative input end of subtraction module S3 connects voltage The anode of source V9, the cathode ground connection of voltage source V9, the input of the output end signal connection gain module G3 of subtraction module S3 End；The output end signal of gain module G3 is through resistance R52It is connected to operational amplifier U28Reverse input end；Impressed current stimulation Signal I1 anode output signal is through resistance R55It is connected to operational amplifier U28Reverse input end, impressed current stimulus signal I1 Cathode ground connection；The both ends of capacitor C4 are separately connected operational amplifier U28Reverse input end and output end；Operational amplifier U28 Output end signal be the 4th proportional integral circuit unit output end DO output signal.
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