CN108596333A - A kind of cardiac Purkinje fibers memristor perturbation circuit design method based on Hodgkin-Huxley models - Google Patents
A kind of cardiac Purkinje fibers memristor perturbation circuit design method based on Hodgkin-Huxley models Download PDFInfo
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Abstract
A kind of cardiac Purkinje fibers memristor perturbation circuit design method based on Hodgkin Huxley models, as follows：(S1) the basic RC circuits of heart Hodgkin Huxley Purkinje fiber models are built；(S2) establish includes level-one memristor RK, two level memristor RNaMemristor circuit model；(S3) design potassium-channel is in equalization point QKThe equivalent LC memristor circuits of perturbation；(S4) design sodium-ion channel is in equalization point QNaThe equivalent LC memristor circuits of perturbation；(S5) perturbation equivalent memristor circuit design of the model intermediate ion channels heart Hodgkin Huxley in equalization point Q.The present invention analyzes the cardiac Purkinje fibers memristor characteristic of Hodgkin Huxley models, pass through the bionical memory function of circuit design neuron, it extends artificial neural network to apply in nonlinear kinetics field, the development for controlling Intelligent Information Processing and complex network has scientific meaning and application value.
Description
Technical field
The invention belongs to cell neural network fields, it mainly studies cardiac Purkinje fibers memristor characteristic, specifically carefully
Potassium ion, sodium ion memristor phenomenon existence in born of the same parents' synapses and related circuit design.
Background technology
In the 1950s, Britain physiologist Huo Qijin (Hodgkin) and Huxley (Huxley) are passed in biological neural
It leads aspect to have carried out deeply and fruitful experiment, they obtain huge cuttlefish synapses electro physiology using voltage clamp technology and live
Dynamic lot of experimental data, establishes the mathematical model of neuron film excitation, and gives the ionic current under different voltages
Quantitative formula, i.e., famous Hodgkin-Huxley models.The model successfully reproduces and predicts certain animal nerve fibers
Electrical activity, the pulse propagation in theory analysis and huge cuttlefish synapses coincide substantially.
In animal nerve tissue, cardiac muscle cell and the variation of resting potential and active electrical potential (also referred to as membrane potential) have
It closes.Research cardiac myocytes electro physiology is to further appreciating that the physiological property of cardiac muscle is of great significance.Containing rich in cardiac muscle cell
The working cardial cell of rich muscle fibril, it has contractile function, referred to as working cardial cell.It belongs to Non-Self-Governing cell, cannot generate work
Property, but there is excitability and conducting power, including atrial muscle cell and ventricular muscle cell.In addition also have in cardiac nerve and generate
The ability of rhythmical excitation is referred to as the cell of pacemaker, and Purkinje (Purkinje) cell, which just belongs to this, can generate the rhythm and pace of moving things
Contractile function, with the speed jitter of spontaneous discharge, the activity to controlling the rhythm of the heart plays an important role.Special cardiac muscle in human body
Conducting system includes sinoatrial node, atrioventricular node, atrioventircular bundle and Purkinje fiber, and Fig. 1 is human heart structure, wherein Purkinje fiber
It is distributed in ventricular endocardium end.
Invention content
The cardiac Purkinje fibers memristor perturbation based on Hodgkin-Huxley models that the purpose of the present invention is to propose to a kind of
Circuit design method, analysis of cardiac Purkinje fiber cell has similar memory function with cranial nerve, with heart Hodgkin-
Huxley models are research object, analyze the existence of weak memory characteristic in potassium-channel and sodium-ion channel, and respectively
Heart Hodgkin-Huxley models memristor circuit under the perturbation of small signal is devised in equalization point, theory deduction and meter are passed through
It calculates and completes relative electronic components parameter setting.
What the present invention was achieved by the following technical programs.
A kind of cardiac Purkinje fibers memristor perturbation circuit based on Hodgkin-Huxley models of the present invention is set
Meter method, as follows：
(S1)：Build the basic RC circuits of heart Hodgkin-Huxley Purkinje fiber models；
Heart Hodgkin-Huxley Purkinje fiber models are described as：
Wherein IKFor potassium current, INaFor sodium ion electric current, IAnFor Cl-currents, ImFor external stimulus electric current, CmFor
Cross-film capacitance, EmFor film potential, t is time variable；The analog circuit of the model is built with basic resistance and capacitance component.
(S2)：It includes level-one memristor R to establishK, two level memristor RNaMemristor circuit model：
It will be in Hodgkin-Huxley models RC circuits in (S1)WithPosition level-one memristor RKIt replaces, gNa
Position two level memristor RNaIt replaces, it includes level-one memristor R to establishK, two level memristor RNaMemristor Hodgkin-Huxley
Circuit model.
(S3)：Potassium-channel is designed in equalization point QKThe equivalent LC memristor circuits of perturbation；
Including an inductance L (K), a resistance R1(K), a resistance R2(K), wherein inductance L (K) and resistance R1(K)
After series connection again with resistance R2(K) in parallel.The level-one memristor R in its replacement step (S2) is used in combinationK, it is formed in equalization point QKIt is micro-
Disturb equivalent LC memristor circuits.
(S4)：Sodium-ion channel is designed in equalization point QNaThe equivalent LC memristor circuits of perturbation；
Including an inductance L1(Na), a resistance R1(Na), an inductance L2(Na), a resistance R3(Na), an electricity
Hinder R3(Na), wherein inductance L1(Na) with resistance R1(Na) series connection, inductance L2(Na) with resistance R2(Na) connect, then by the two with
Resistance R3(Na) in parallel.The two level memristor R in its replacement step (S2) is used in combinationNa, it is formed in equalization point QNaPerturbation it is equivalent
LC memristor circuits.
(S5)：Perturbation equivalent memristor circuit design of the model intermediate ion channels heart Hodgkin-Huxley in equalization point Q.
By the potassium-channel of (S3) in equalization point QKThe equivalent LC memristor circuits of perturbation replace (S2) level-one memristor
RK, the sodium-ion channel of (S4) is in equalization point QNaThe equivalent LC memristor circuits of perturbation replace (S2) two level memristor RNa, formed
Whole perturbation equivalent memristor circuit of the model intermediate ion channels heart Hodgkin-Huxley in equalization point Q.
The specific reasoning design procedure of the present invention is as follows：
In myocardium nerve cell, concentration of metal ions of the Purkinje cell film full of charge is very big, it is most of be sodium from
Sub (Na+), potassium ion (K+) and a small amount of chlorion (CL- or An-), the liquid of cell UF membrane contains various concentration, this
Sample generates potential difference and forms inside and outside transcellular movement.
1, the basic RC circuits of heart Hodgkin-Huxley Purkinje fiber models are built.
Cardiac Purkinje fibers film total current (Im) it is to be obtained by the sum of the electric current of ionic current and inflow film capacity
's.According to Ohm's law, Faraday's law and Kirchhoff's law, Hodgkin-Huxley model equations are as follows：
Wherein：
(1) formula and each variable in (2) formula are：
ImFor external stimulus electric current, INa、IK、IAnRespectively sodium ion electric current, potassium current and chloride electric current；EmFor film
Current potential, ENa、EK、EAnRespectively sodium ion equilibrium potential, potassium ion equilibrium potential, chloride counter current potential.CmFor cross-film capacitance,
gNa、gK1、gK2、gAnRespectively sodium-ion channel conductance, two potassium-channel conductances, chloride ion channel conductance, when t is
Between variable.
Cell membrane ion exchange can be completed by ion channel opening and closing operations, and heart Hodgkin-Huxley models can
Accurately to describe the film potential of cardiac Purkinje fibers.Fig. 2 shows heart Hodgkin-Huxley Purkinje fiber models
Basic RC (resistance and capacitance) circuit.
2, establish includes level-one memristor RK, two level memristor RNaMemristor circuit model.
(1) heart Hodgkin-Huxley Purkinje fibers model transmembrane voltage V and correlated variables description.
Due to there is negative resting potential E in Hodgkin-Huxley equationsr, so INa、IKBetween there is no coupling, when will
When V is defined as transmembrane voltage, vNa、vK、vAnThe respectively balance potential of sodium ion, potassium ion, chlorion, therefore voltage integrates equation
It is as follows：
We can obtain from formula (3)：
In addition, there is also leakage conductance, such as chlorion, but because Cl-currents amount is very small, therefore usual IAnIt is worth quilt
It is reduced to IAn=0.In conjunction with formula (1)-(4), we can obtain following result：
Wherein Cm=12 μ F/cm2, ENa=40mV, EK=-100mV, and
Variable m, h, n are respectively sodium ion activation variable, sodium ion inhibition variable and potassium ion activation variable.They are by one
Rank partial differential equation form, all mathematic(al) representation αm(V)、βm(V)、αh(V)、βh(V)、αn(V)、βn(V) all it is transmembrane voltage V
Nonnegative function, be defined as：
(2) R is determined by theory deduction and numerical simulationKIt is level-one memristor.
Potassium ion is can be seen that by two conductance (g from Fig. 2 circuitsK1And gK2) composition, according to electric current iKWith voltage vKPass
System, by vKAnd iKCharacter expression change is as follows：
iK=GK(x1)vK (8)
And
Upper (8)-(9) symbol is changed as follows：
From equation (9) and equation (6) is combined as can be seen that gK1The only exponential function of V, it is special that it does not have memory resistor
Property, and gK2It is the correlation function of variable n, electric current i can be passed throughKVariation is tested whether with memory characteristic.
Fig. 3 is shownIndividuallyCurve, wherein electric current select i=Asin (ω t).As can be seen from Figure 3It is zeroaxial closed annular " 8 " word curve, and as gradually envelope size reduces for the increase of frequencies omega, tool
There is the tight hysteresis characteristic of apparent memristor.
Fig. 4 be one withWithThe v drawn togetherK-iKCurve finds that only very weak tight hysteresis loop exists.This hair
Bright is synthesisWithMemory as research.
It according to the new symbol that above-mentioned formula (10) defines, defines, can be obtained in conjunction with formula (7) the variable differential equation：
Wherein EK=-100mV
Due to G in formula (9)KInclude only a variable x1, therefore the resistor R that potassium ion is formedKIt is referred to as level-one memristor
Device.
(3) R is determined by theory deduction and numerical simulationNaIt is two level memristor.
Equation (6) lists sodium ion gNaIt is made of the multinomial of two variables, according to electric current iNaWith voltage vNaPass
System, we are by vNaAnd iNaCharacter expression change is as follows：
iNa=GNa(x2,x3)vNa (12)
And
Upper (12)-(13) symbol is changed as follows：
Fig. 5 is a v drawn with different frequency ωNa-iNaCurve, wherein setting i=Asin (ω t), it can be with from Fig. 5
Find out vNa-iNaIt is zeroaxial closed annular " 8 " word curve, and as gradually envelope size reduces for the increase of frequencies omega,
With the tight hysteresis characteristic of apparent memristor.
It according to the new symbol that above-mentioned formula (14) defines, defines, can be obtained in conjunction with formula (7) the variable differential equation：
Wherein ENa=40mV
Due to the G in formula (13)NaIncluding x2And x3Two variables, therefore sodium ion formed resistor RNaIt is referred to as
Two level memristor.
(4) establish includes level-one memristor RK, two level memristor RNaMemristor circuit model.
It will be in Hodgkin-Huxley model RC circuits (such as Fig. 2)WithPosition level-one memristor RKIt replaces, gNa
Position two level memristor RNaIt replaces, it includes level-one memristor R to establishK, two level memristor RNaMemristor Hodgkin-Huxley
Circuit model (such as Fig. 7).
3, potassium-channel is in equalization point QKThe equivalent memristor circuit design of perturbation.
For a small signal disturbance, Hodgkin-Huxley models show nonlinear memory device on equalization point Q
Performance.
Assuming that voltage VK(QK) and electric current IK(QK) be potassium ion equalization point Q (K) value, small signal disturbance δ vKWith δ iKIt will change
Become equalization point voltage VK(QK) and electric current IK(QK), therefore, single order variableAlso there are δ i in equalization point Q (K)KOffset, it is assumed that
iK=IK(QK)+δiK=a00(QK)+a11(QK)δn+a12(QK)δvK+h.o.t (18)
Wherein
Indicate the first derivative of variable n.In equalization point QKUpper Taylor series expansion electric current IK(QK).It is disturbed small
Streaming current δ iKIt is introduced into the f in formula (11) with variable nn(n,vK) function definition, it can obtain：
Wherein
And h.o.t is a higher-order shear deformation, we can ignore it.Because in QKEqualization point
So (20) formula can be write as：
Consider variable iKIt is converted with the Laplace of each component of n：
For complex domainPlural s=σ+i ω, using Laplace transformation to each items of three Linearized state equations into
Row Laplace transform, obtains：
The last one non trivial solution,
If defining conductance YK(s；QK)：
Therefore
Formula (28) result is replaced with into LC (inductance capacitance) circuit formula, the solution of following (30) formula can be obtained：
Fig. 8 shows potassium-channel in equalization point QKThe equivalent memristor basic circuit structure of perturbation.
4, ion channel is received in equalization point QNaThe equivalent memristor circuit design of perturbation.
It is found that the performance of sodium ion memory is related with (m, h) two variables in formula (6), it is assumed that voltage VNa(QNa) and
Electric current INa(QNa) be sodium ion equalization point Q (Na) value, second order variableAlso there are δ iNaOffset, in QNaEqualization point point
It is as follows small-signal equivalent circuit has been analysed：
In equalization point QNaUpper Taylor series expansion electric current INa(QNa).By microvariations electric current δ iNaFormula is introduced with variable m
(15) f inm(m,vNa) function definition, it can obtain：
Wherein
δiNa=a11(QNa)δm+a12(QNa)δh+a13(QNa)δvNa (34)
Wherein：
Because in QNaEqualization pointTherefore h.o.t, which is a higher-order shear deformation, can ignore,
So (35) formula can be write as：
Variable h in small signal perturbation equation is converted, can be obtained by same method：
Wherein
For complex domainPlural s=σ+i ω, using Laplace transformation can obtain：
The last one solution of equations,
If defining conductance YNa(s；QNa)：
Therefore
If formula (45) is expressed as a transmission function, it can be write as
Wherein
Fig. 9 shows sodium-ion channel in equalization point QNaThe equivalent memristor basic circuit structure of perturbation.
5, perturbation equivalent memristor circuit design of the heart Hodgkin-Huxley models intermediate ion channel in equalization point Q
For small signal remember Hodgkin-Huxley models, integrate potassium ion in figure 8 with figure in sodium ion Fig. 9,
Intermediate ion channel of the present invention is shown in Figure 10 in the equivalent memristor circuit design result of perturbation of equalization point Q.
The present invention designs the Hodgkin-Huxley models potassium ion and sodium in equalization point by stringent mathematical reasoning
The small signal disturbance memristor circuit of ion has consistent conclusion with actual numerical value analogous diagram 4 and Fig. 5.
The present invention analyzes the cardiac Purkinje fibers memristor characteristic of Hodgkin-Huxley models, passes through circuit design nerve
The bionical memory function of member.The present invention extends artificial neural network and is applied in nonlinear kinetics field, to Intelligent Information Processing
And the development of complex network control has scientific meaning and application value.
Description of the drawings
Fig. 1 is human heart structure, and Purkinje (Purkinje) fiber is in ventricular endocardium end.
Fig. 2 is the Hodgkin-Huxley precircuits based on physics RC (resistance and capacitance).
Fig. 3 is the single potassium ion K of difference ω values of the invention2 Memristor characteristic curve.
Fig. 4 is the v of the potassium ion of difference ω values of the inventionK-iKWeak memristor characteristic curve.
Fig. 5 is the v of the sodium ion of difference ω values of the inventionNa-iNaMemristor characteristic curve.
Fig. 6 is the basic outside drawing of memristor of the present invention, wherein the conventional component that (a) is memristor indicates figure, it is (b) one
Grade potassium memristor RKComponent indicate figure, (c) be two level sodium ion memristor RNaComponent indicate figure.
Fig. 7 is that the present invention includes level-one memristor RKWith two level memristor RNaHodgkin-Huxley model circuit diagrams.
Fig. 8 is potassium-channel memory of the present invention in equalization point QK(VK,IK) on perturbation equivalent circuit.
Fig. 9 is sodium-ion channel memory of the present invention in equalization point QNa(VNa,INa) on perturbation equivalent circuit.
Figure 10 is perturbation equivalent electricity of the heart Hodgkin-Huxley molded passages memory of the present invention on equalization point Q
Road.
Figure 11 is potassium-channel memory of the present invention in VKPerturbation Equivalent Physical circuit when=100mV.
Figure 12 is sodium-ion channel memory of the present invention in VNaPerturbation Equivalent Physical circuit when=- 40mV.
Specific implementation mode
The present invention will be described further by following embodiment.
The memristor circuit physical design of potassium ion and sodium ion at equalization point, can specifically pass through following procedure in the present invention
It completes：
I) potassium-channel memory balancing circuitry：
The Y of formula (30)K(s；QK) it is balance QKUnder admittance function work as V using formula (19), formula (21)K=
When 100mV, L (K), R1(K) and R2(K) value be calculated by equation (30), wherein：
Specific component parameter is shown in Figure 11.
II) sodium-ion channel memory balancing circuitry：
The Y of formula (47)Na(s；QNa) it is balance QNaUnder admittance function, utilize formula (33), formula (36) and formula
(39), work as VNaWhen=- 40mV, inductance L1(Na),L2(Na), resistance R1(Na),R2(Na),R3(Na) value is by equation (47)
It is calculated, wherein：
Specific component parameter is shown in Figure 12.
Claims (1)
1. a kind of cardiac Purkinje fibers memristor perturbation circuit design method based on Hodgkin-Huxley models, it is characterized in that
As follows：
(S1)：Build the basic RC circuits of heart Hodgkin-Huxley Purkinje fiber models；
Heart Hodgkin-Huxley Purkinje fiber models are described as：
Wherein IKFor potassium current, INaFor sodium ion electric current, IAnFor Cl-currents, ImFor external stimulus electric current, CmFor cross-film electricity
Hold, EmFor film potential, t is time variable；The analog circuit of the model is built with basic resistance and capacitance component；
(S2)：It includes level-one memristor R to establishK, two level memristor RNaMemristor circuit model：
It will be in Hodgkin-Huxley models RC circuits in (S1)WithPosition level-one memristor RKIt replaces, gNaPosition
With two level memristor RNaIt replaces, it includes level-one memristor R to establishK, two level memristor RNaMemristor Hodgkin-Huxley circuits
Model；
(S3)：Potassium-channel is designed in equalization point QKThe equivalent LC memristor circuits of perturbation；
Including an inductance L (K), a resistance R1(K), a resistance R2(K), wherein inductance L (K) and resistance R1(K) it connects
Afterwards again with resistance R2(K) in parallel, the level-one memristor R in its replacement step (S2) is used in combinationK, it is formed in equalization point QKPerturbation etc.
The LC memristor circuits of effect；
(S4)：Sodium-ion channel is designed in equalization point QNaThe equivalent LC memristor circuits of perturbation；
Including an inductance L1(Na), a resistance R1(Na), an inductance L2(Na), a resistance R3(Na), a resistance R3
(Na), wherein inductance L1(Na) with resistance R1(Na) series connection, inductance L2(Na) with resistance R2(Na) it connects, then by the two and resistance
R3(Na) in parallel, the two level memristor R in its replacement step (S2) is used in combinationNa, it is formed in equalization point QNaThe equivalent LC of perturbation recall
Resistance circuit；
(S5)：Perturbation equivalent memristor circuit design of the model intermediate ion channels heart Hodgkin-Huxley in equalization point Q
By the potassium-channel of (S3) in equalization point QKThe equivalent LC memristor circuits of perturbation replace (S2) level-one memristor RK,
(S4) sodium-ion channel is in equalization point QNaThe equivalent LC memristor circuits of perturbation replace (S2) two level memristor RNa, form the heart
Whole perturbation equivalent memristor circuit of the dirty Hodgkin-Huxley models intermediate ion channel in equalization point Q.
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| CN109300547A (en) * | 2018-10-19 | 2019-02-01 | 江西理工大学 | A kind of research method of heart Hodgkin-Huxley Purkinje fiber model state transition |
| CN109447255A (en) * | 2018-11-29 | 2019-03-08 | 西北工业大学 | A kind of simulated implementation simplifies the circuit of Hodgkin-Huxley neuron models |
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| HODGKIN等: "A quantitative description of membrane current and its application to conduction and excitation in nerve", 《THE JOURNAL OF PHYSIOLOGY》 * |
| YINGXU等: "Synchronization between neurons coupled by memristor", 《CHAOS, SOLITONS & FRACTALS》 * |
| 吴政泽等: "Hodgkin-Huxley模型的心脏浦肯野纤维弱忆阻机理研究", 《江西理工大学学报》 * |
| 张小红等: "新型忆阻细胞神经网络的建模及电路仿真", 《系统仿真学报》 * |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109300547A (en) * | 2018-10-19 | 2019-02-01 | 江西理工大学 | A kind of research method of heart Hodgkin-Huxley Purkinje fiber model state transition |
| CN109300547B (en) * | 2018-10-19 | 2021-06-22 | 江西理工大学 | Method for researching state transition of heart Hodgkin-Huxley purkinje fiber model |
| CN109447255A (en) * | 2018-11-29 | 2019-03-08 | 西北工业大学 | A kind of simulated implementation simplifies the circuit of Hodgkin-Huxley neuron models |
| CN109447255B (en) * | 2018-11-29 | 2021-05-18 | 西北工业大学 | Circuit for simplifying Hodgkin-Huxley neuron model through simulation |
| CN109978159A (en) * | 2019-03-19 | 2019-07-05 | 常州大学 | A kind of easy Fitzhugh-Nagumo neuron circuit |
| CN109978159B (en) * | 2019-03-19 | 2023-03-24 | 常州大学 | Simple Fitzhugh-Nagumo neuron circuit |
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