CN108596333B - Heart purkinje fiber memristor perturbation circuit design method based on Hodgkin-Huxley model - Google Patents

Heart purkinje fiber memristor perturbation circuit design method based on Hodgkin-Huxley model Download PDF

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CN108596333B
CN108596333B CN201810212736.3A CN201810212736A CN108596333B CN 108596333 B CN108596333 B CN 108596333B CN 201810212736 A CN201810212736 A CN 201810212736A CN 108596333 B CN108596333 B CN 108596333B
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吴政泽
张小红
钟小勇
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Jiangxi University of Science and Technology
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Abstract

A design method of a heart Purkinje fiber memristor perturbation circuit based on a Hodgkin-Huxley model comprises the following steps: (S1) constructing a basic RC circuit of the heart Hodgkin-Huxley purkinje fiber model; (S2) establishing a memristor R including a primary memristorKSecond-level memristor RNaThe memristive circuit model of (1); (S3) designing potassium channel at equilibrium point QKThe perturbation equivalent LC memristor circuit of (1); (S4) designing the sodium ion channel at equilibrium point QNaThe perturbation equivalent LC memristor circuit of (1); (S5) designing a perturbation equivalent memristor circuit of an ion channel at a balance point Q in a heart Hodgkin-Huxley model. The method analyzes the heart Purkinje fiber memristor characteristic of the Hodgkin-Huxley model, expands the application of the artificial neural network in the field of nonlinear dynamics by designing the bionic memory function of the neuron through the circuit, and has scientific significance and application value for the development of intelligent information processing and complex network control.

Description

Heart purkinje fiber memristor perturbation circuit design method based on Hodgkin-Huxley model
Technical Field
The invention belongs to the field of cellular neural networks, and mainly researches the memristive characteristics of Purkinje fibers of the heart, in particular to the existence of potassium ion and sodium ion memristive phenomena in cell touch and corresponding circuit design.
Background
In the 50 s of the 20 th century, England physiologists Hodgkin (Hodgkin) and Huxley (Huxley) performed intensive and fruitful experiments on biological nerve conduction, and they obtained a large amount of experimental data of giant cuttlefish touch-and-shoot electrophysiological activity by using a voltage clamp technology, established a mathematical model of neuron membrane excitation, and given an ionic current quantification formula under different voltages, namely a famous Hodgkin-Huxley model. The model successfully reproduces and predicts the electrical activity of certain animal nerve fibers, and theoretical analysis is basically consistent with pulse propagation in giant cuttlefish touch.
In animal neural tissue, cardiomyocytes are associated with changes in resting and activity potentials (also known as transmembrane potentials). The study of the electrophysiological properties of cardiac myocardium is of great significance for further understanding the physiological properties of cardiac myocardium. The cardiomyocytes contain working cells that are rich in myofibrils, which have a contractile function and are called working cells. It is a non-autonomous cell that is unable to produce activity, but has excitatory and conductive capabilities, including atrial and ventricular myocytes. In addition, the heart nerve has the capacity of generating rhythmic excitation, and is called a pacemaker, and Purkinje cells belong to the cells which can generate rhythmic contraction function, beat at the spontaneous discharge speed and play an important role in controlling the activity of the heart rhythm. The specific myocardial conduction system in the human body includes the sinoatrial node, the atrioventricular bundle and the purkinje fibers, fig. 1 shows the structure of the human heart, in which the purkinje fibers are distributed at the end of the endocardium.
Disclosure of Invention
The invention aims to provide a design method of a heart Purkinje fiber memristor perturbation circuit based on a Hodgkin-Huxley model, which is used for analyzing the memory function of heart Purkinje fiber cells similar to cranial nerves, takes the heart Hodgkin-Huxley model as a research object, analyzes the existence of weak memory characteristics in a potassium ion channel and a sodium ion channel, respectively designs the heart Hodgkin-Huxley model memristor circuit under perturbation of small signals at a balance point, and completes the parameter setting of related electronic components through theoretical derivation and calculation.
The invention is realized by the following technical scheme.
The invention relates to a design method of a heart Purkinje fiber memristor perturbation circuit based on a Hodgkin-Huxley model, which comprises the following steps:
(S1): constructing a basic RC circuit of a heart Hodgkin-Huxley Purkinje fiber model;
the heart Hodgkin-Huxley purkinje fiber model is described as:
Figure BDA0001597677290000011
wherein IKIs a potassium ion current, INaIs sodium ion current, IAnIs a current of chloride ions, ImAs an external stimulus current, CmIs a transmembrane capacitance, EmIs membrane potential, t is time variable; and constructing an analog circuit of the model by using basic resistance and capacitance components.
(S2): establishing a first-order memristor RKSecond-level memristor RNaMemristive circuit model of (1):
will (S1) be in the Hodgkin-Huxley model RC circuit
Figure BDA0001597677290000021
And
Figure BDA0001597677290000022
primary memristor R for positionKReplacement, gNaSecondary memristor R for positionNaInstead, the building block includes a first-order memristor RKSecond-level memristor RNaThe model of the memristor Hodgkin-Huxley circuit.
(S3): designing potassium ion channel at equilibrium point QKThe perturbation equivalent LC memristor circuit of (1);
comprises an inductor L (K), a resistor R1(K) A resistor R2(K) Wherein, the inductance L (K) and the resistance R1(K) Connected in series and then connected with a resistor R2(K) And (4) connecting in parallel. And replacing the primary memristor R in the step (S2) with the sameKFormed at equilibrium point QKPerturbation equivalent LC memristor circuits.
(S4): design of sodium ion channel at equilibrium point QNaThe perturbation equivalent LC memristor circuit of (1);
comprising an inductor L1(Na), a resistance R1(Na) an inductor L2(Na), a resistance R3(Na), a resistance R3(Na) in which the inductance L1(Na) and resistance R1(Na) series connection, inductance L2(Na) and resistance R2(Na) are connected in series, and then the two are connected with a resistor R3(Na) is connected in parallel. And replacing the secondary memristor R in the step (S2) with the sameNaFormed at equilibrium point QNaPerturbation equivalent LC memristor circuits.
(S5): and designing a perturbation equivalent memristor circuit of an ion channel in the heart Hodgkin-Huxley model at a balance point Q.
The potassium channel of (S3) is at equilibrium point QKThe perturbation equivalent LC memristor circuit replaces (S2) primary memristor RKThe sodium ion channel of (S4) is at equilibrium point QNaThe perturbation equivalent LC memristor circuit replaces (S2) a secondary memristor RNaAnd forming an integral perturbation equivalent memristor circuit of an ion channel in the heart Hodgkin-Huxley model at a balance point Q.
The specific reasoning design steps of the invention are as follows:
in the myocardial nerve cells, the Purkinje cell membrane is charged with a large concentration of metal ions, mostly sodium ions (Na +), potassium ions (K +) and a small amount of chloride ions (CL-or An-), and the separated liquid from the cell membrane contains different concentrations, thus creating a potential difference to create internal and external intercellular movement.
1. The basic RC circuit of the heart Hodgkin-Huxley Purkinje fiber model is constructed.
Purkinje fiber membrane total current (I) of heartm) Is derived from the sum of the ionic current and the current flowing into the membrane. According to ohm's law, faraday's law and kirchhoff's law, the Hodgkin-Huxley model equation is as follows:
Figure BDA0001597677290000023
wherein:
Figure BDA0001597677290000024
(1) the variables in formulas (1) and (2) are:
Imfor external stimulation of current, INa、IK、IAnSodium ion current, potassium ion current and chloride current respectively; emIs a membrane potential, ENa、EK、EAnRespectively, a sodium ion equilibrium potential, a potassium ion equilibrium potential and a chloride equilibrium potential. CmIs transmembrane capacitance, gNa、gK1、gK2、gAnRespectively sodium ion channel conductance, two potassium ion channel conductances and chloride ion channel conductance, and t is a time variable.
The ion exchange of the cell membrane can be completed by the opening and closing operation of an ion channel, and the heart Hodgkin-Huxley model can accurately describe the membrane potential of Purkinje fibers of the heart. Fig. 2 shows the basic RC (resistance and capacitance) circuit of the heart Hodgkin-Huxley purkinje fiber model.
2. Establishing a first-order memristor RKSecond-level memristor RNaThe memristive circuit model of (1).
(1) The heart Hodgkin-Huxley Purkinje fiber model transmembrane voltage V and related variables describe.
Due to the existence of negative resting potential E in Hodgkin-Huxley equationrTherefore I isNa、IKThere is no coupling between them, when V is defined as the transmembrane voltage, VNa、vK、vAnThe equilibrium potentials of sodium ion, potassium ion and chloride ion are respectively, so the voltage integration equation is as follows:
Figure BDA0001597677290000031
from equation (3) we can get:
Figure BDA0001597677290000032
in addition, there is also leakage conductance, such as chloride ions, but since the amount of chloride ion current is very small, generally IAnThe value is reduced to IAn0. In conjunction with formulas (1) - (4), we can obtain the following results:
Figure BDA0001597677290000033
wherein C ism＝12μF/cm2，ENa＝40mV，EKIs equal to-100 mV, and
Figure BDA0001597677290000034
variables m, h, n are respectively sodium ion activation variable, sodium ion inhibition variable and potassium ion activation variable. They consist of first order partial differential equations, all mathematical expressions alpham(V)、βm(V)、αh(V)、βh(V)、αn(V)、βn(V) is a non-negative function of the transmembrane voltage V, defined as:
Figure BDA0001597677290000041
(2) determination of R by theoretical derivation and numerical simulationKIs a first-order memristor.
As can be seen from the circuit of FIG. 2, the potassium ion has two conductances (g)K1And gK2) Composition according to current iKAnd voltage vKA relationship of vKAnd iKThe symbolic expression is modified as follows:
iK＝GK(x1)vK (8)
and is
Figure BDA0001597677290000042
The following changes are made to the upper (8) - (9) symbols:
Figure BDA0001597677290000043
as can be seen from equation (9) in combination with equation (6), gK1Only an exponential function of V, which has no memory resistance property, and gK2Is a function of the variable n, through which the current i passesKThe change test is for whether there is a memory characteristic.
FIG. 3 shows
Figure BDA0001597677290000044
Alone
Figure BDA0001597677290000045
Curve, where current is selected i ═ Asin (ω t). From FIG. 3, it can be seen that
Figure BDA0001597677290000046
The memristor hysteretic ring is a closed annular 8-shaped curve passing through a zero point, the envelope area is gradually reduced along with the increase of the frequency omega, and the memristor hysteretic ring has obvious characteristics.
FIG. 4 is a bar and
Figure BDA0001597677290000047
and
Figure BDA0001597677290000048
v drawn togetherK-iKIn the curve, only a very weak ring of hysteresis was found to exist. The invention is synthesized
Figure BDA0001597677290000049
And
Figure BDA00015976772900000410
as a memory for research.
From the new notation defined by equation (10) above, in combination with the variable differential equation definition of equation (7), we can obtain:
Figure BDA0001597677290000051
wherein EK＝-100mV
Due to G in the formula (9)KContaining only one variable x1Resistor R formed by potassium ionsKReferred to as primary memristors.
(3) Determination of R by theoretical derivation and numerical simulationNaIs a secondary memristor.
Equation (6) lists sodium ion gNaIs composed of a polynomial of two variables, dependent on the current iNaAnd voltage vNaIn relation to (v) we willNaAnd iNaThe symbolic expression is modified as follows:
iNa＝GNa(x2,x3)vNa (12)
and is
Figure BDA0001597677290000052
The following changes are made to the upper (12) - (13) symbols:
Figure BDA0001597677290000053
FIG. 5 is a graph of v plotted against different frequencies ωNa-iNaCurve, where i-Asin (ω t) is set, it can be seen from fig. 5 that v isNa-iNaThe memristor hysteretic ring is a closed annular 8-shaped curve passing through a zero point, the envelope area is gradually reduced along with the increase of the frequency omega, and the memristor hysteretic ring has obvious characteristics.
From the new notation defined by equation (14) above, in combination with the variable differential equation definition of equation (7), we can obtain:
Figure BDA0001597677290000054
Figure BDA0001597677290000061
wherein ENa＝40mV
Due to G in the formula (13)NaContaining x2And x3So that the sodium ions form a resistor RNaKnown as a secondary memristor.
(4) Establishing a first-order memristor RKSecond-level memristor RNaThe memristive circuit model of (1).
In a Hodgkin-Huxley model RC circuit (as shown in FIG. 2)
Figure BDA0001597677290000062
And
Figure BDA0001597677290000063
primary memristor R for positionKReplacement, gNaSecondary memristor R for positionNaInstead, the building block includes a first-order memristor RKSecond-level memristor RNaThe model of the memristive Hodgkin-Huxley circuit (as shown in fig. 7).
3. Potassium ion channel at equilibrium point QKThe perturbation equivalent memristor circuit design.
For a small signal disturbance, the Hodgkin-Huxley model shows the performance of the non-linear memory at the equilibrium point Q.
Assume voltage VK(QK) And current IK(QK) Is the value of the equilibrium point Q (K) of potassium ions, small signal perturbation δ vKAnd δ iKWill change the equilibrium point voltage VK(QK) And current IK(QK) Thus, a first order variable
Figure BDA0001597677290000064
At equilibrium point Q (K) also has δ iKIs assumed to be offset from
Figure BDA0001597677290000065
iK＝IK(QK)+δiK＝a00(QK)+a11(QK)δn+a12(QK)δvK+h.o.t (18)
Wherein
Figure BDA0001597677290000066
Figure BDA0001597677290000067
Representing the first derivative of the variable n. At equilibrium point QKExpanding the current I by Taylor seriesK(QK). Will small disturbance current delta iKAnd f introducing the variable n into the formula (11)n(n,vK) Function definition, one can get:
Figure BDA0001597677290000071
wherein
Figure BDA0001597677290000072
And h.o.t is a high order infinitesimal small, which we can ignore. Because at QKBalance point
Figure BDA0001597677290000073
Therefore, equation (20) can be written as:
Figure BDA0001597677290000074
taking into account the variable iKAnd Laplace transform of each component of n:
Figure BDA0001597677290000075
for complex domains
Figure BDA0001597677290000076
Applying Laplace transform to each term of the three linearized state equations to obtain:
Figure BDA0001597677290000077
Figure BDA0001597677290000078
the solution of the last equation is then determined,
Figure BDA0001597677290000079
if define conductance YK(s；QK)：
Figure BDA00015976772900000710
Thus, it is possible to provide
Figure BDA00015976772900000711
Figure BDA0001597677290000081
Replacing the result of equation (28) with an LC (inductor capacitor) circuit equation, a solution can be obtained for equation (30) below:
Figure BDA0001597677290000082
FIG. 8 shows potassium ion channels at equilibrium point QKThe perturbation equivalent memristor basic circuit structure is provided.
4. The nano ion channel is at the equilibrium point QNaThe perturbation equivalent memristor circuit design.
As shown in equation (6), the performance of the Na-ion memory is related to two variables (m, h), assuming that the voltage V isNa(QNa) And current INa(QNa) Is the value of the equilibrium point Q (Na) of the sodium ions, the second order variable
Figure BDA0001597677290000083
Also has delta iNaOffset at QNaThe equilibrium point analyzes the small signal equivalent circuit as follows:
Figure BDA0001597677290000084
at equilibrium point QNaExpanding the current I by Taylor seriesNa(QNa). Will small disturbance current delta iNaAnd f introducing the variable m into the formula (15)m(m,vNa) Function definition, one can get:
Figure BDA0001597677290000085
wherein
Figure BDA0001597677290000086
δiNa＝a11(QNa)δm+a12(QNa)δh+a13(QNa)δvNa (34)
Figure BDA0001597677290000091
Wherein:
Figure BDA0001597677290000092
because at QNaBalance point
Figure BDA0001597677290000093
h.o.t is a high order infinitesimal small and therefore negligible, so equation (35) can be written as:
Figure BDA0001597677290000094
in the same way, the variable h in the small signal perturbation equation is transformed, so that:
Figure BDA0001597677290000095
wherein
Figure BDA0001597677290000096
For complex domains
Figure BDA0001597677290000097
Is σ + i ω, applying Laplace transform results in:
Figure BDA0001597677290000098
Figure BDA0001597677290000099
Figure BDA00015976772900000910
the solution of the last system of equations,
Figure BDA00015976772900000911
if the conductance Y is definedNa(s；QNa)：
Figure BDA0001597677290000101
Thus, it is possible to provide
Figure BDA0001597677290000102
Let equation (45) be expressed as a transfer function, which can be written as
Figure BDA0001597677290000103
Wherein
Figure BDA0001597677290000104
FIG. 9 shows the sodium ion channel at equilibrium point QNaThe perturbation equivalent memristor basic circuit structure is provided.
5. Perturbation equivalent memristor circuit design of ion channel at balance point Q in heart Hodgkin-Huxley model
For the small-signal memory Hodgkin-Huxley model, potassium ions in the figure are integrated with sodium ions in the figure 8, and the sodium ions in the figure are integrated with the figure 9, and the design result of the perturbation equivalent memristor circuit of the ion channel at the balance point Q in the invention is shown in figure 10.
According to the invention, a small-signal disturbance memristor circuit of potassium ions and sodium ions of a Hodgkin-Huxley model at a balance point is designed through strict mathematical reasoning, and the conclusion is consistent with that of an actual numerical simulation figure 4 and an actual numerical simulation figure 5.
The heart Purkinje fiber memristor characteristic of the Hodgkin-Huxley model is analyzed, and the bionic memory function of the neuron is designed through a circuit. The invention expands the application of the artificial neural network in the field of nonlinear dynamics, and has scientific significance and application value for the development of intelligent information processing and complex network control.
Drawings
FIG. 1 shows a human heart structure with Purkinje (Purkinje) fibers at the end of the endocardial membrane.
Fig. 2 is a Hodgkin-Huxley model circuit based on physical RC (resistance and capacitance).
FIG. 3 shows a single K ion of different omega values according to the invention2Of an item
Figure BDA0001597677290000105
Memristive characteristics.
FIG. 4 shows the v values of potassium ions of different omega values according to the inventionK-iKWeak memristor characteristics.
FIG. 5 shows the v of sodium ions of different omega values according to the inventionNa-iNaMemristive characteristics.
FIG. 6 is a basic appearance diagram of a memristor according to the present invention, wherein (a) is a conventional component representation diagram of the memristor, and (b) is a first-order potassium memristor RKThe component (c) is a secondary sodium ion memristor RNaThe components of (a) represent diagrams.
FIG. 7 is a diagram of a primary memristor R-containing structure according to the present inventionKAnd two-stage memristor RNaThe Hodgkin-Huxley model circuit diagram.
FIG. 8 shows the equilibrium point Q of the potassium channel memory of the present inventionK(VK,IK) The perturbation equivalent circuit.
FIG. 9 shows the equilibrium point Q of the Na-channel memory of the present inventionNa(VNa,INa) The perturbation equivalent circuit.
FIG. 10 is a perturbation equivalent circuit of the channel memory of the heart Hodgkin-Huxley model at the balance point Q.
FIG. 11 shows a potassium channel memory of the present invention at VKPerturbation equivalent physical circuit at 100 mV.
FIG. 12 shows a sodium ion channel memory of the present invention at VNaPerturbation equivalent physical circuit at-40 mV.
Detailed Description
The invention will be further illustrated by the following examples.
The physical design of the memristor circuit of potassium ions and sodium ions at the balance point can be specifically completed through the following processes:
I) potassium channel memory balancing circuit:
y of the formula (30)K(s；QK) Is balance of QKThe admittance function of the following formula (19), formula (21), when VKAt 100mV, L (K), R1(K) And R2(K) Is calculated from equation (30), where:
Figure BDA0001597677290000111
the specific component parameters are shown in fig. 11.
II) a sodium channel memory balancing circuit:
y of the formula (47)Na(s；QNa) Is balance of QNaThe admittance function of when V is determined using formula (33), formula (36) and formula (39)NaInductance L at-40 mV1(Na),L2(Na) resistance R1(Na),R2(Na),R3The value of (Na) is calculated from equation (47), where:
Figure BDA0001597677290000112
the specific component parameters are shown in fig. 12.

Claims (1)

1. A heart Purkinje fiber memristor perturbation circuit design method based on a Hodgkin-Huxley model is characterized by comprising the following steps:
(S1): constructing a basic RC circuit of a heart Hodgkin-Huxley Purkinje fiber model;
the heart Hodgkin-Huxley purkinje fiber model is described as:
Figure FDA0003103724470000011
wherein IKIs a potassium ion current, INaIs sodium ion current, IAnIs a current of chloride ions, ImAs an external stimulus current, CmIs a transmembrane capacitance, EmIs membrane potential, t is time variable; constructing an analog circuit of the model by using basic resistor and capacitor components;
(S2): establishing a first-order memristor RKSecond-level memristor RNaMemristive circuit model of (1):
conductance of potassium ion channel in Hodgkin-Huxley model RC circuit in (S1)
Figure FDA0003103724470000012
And
Figure FDA0003103724470000013
with first-order memristors RKAlternative, sodium ion channel conductance gNaWith secondary memristor RNaInstead, the building block includes a first-order memristor RKSecond-level memristor RNaThe memristor Hodgkin-Huxley circuit model;
(S3): designing potassium ion channel at equilibrium point QKThe perturbation equivalent LC memristor circuit of (1);
comprises an inductor L (K), a resistor R1(K) A resistor R2(K) Wherein, the inductance L (K) and the resistance R1(K) Connected in series and then connected with a resistor R2(K) In parallel and replacing the primary memristor R in the step (S2) with the sameKFormed at equilibrium point QKThe perturbation equivalent LC memristor circuit of (1);
(S4): design of sodium ion channel at equilibrium point QNaThe perturbation equivalent LC memristor circuit of (1);
comprising an inductor L1(Na), a resistance R1(Na) an inductor L2(Na), a resistance R3(Na), a resistance R3(Na) in which the inductance L1(Na) and resistance R1(Na) series connection, inductance L2(Na) and resistance R2(Na) are connected in series, and then the two are connected with a resistor R3(Na) in parallel and substituted therewithSecondary memristor R in step (S2)NaFormed at equilibrium point QNaThe perturbation equivalent LC memristor circuit of (1);
(S5): perturbation equivalent memristor circuit design of ion channel at balance point Q in heart Hodgkin-Huxley model
The potassium channel of (S3) is at equilibrium point QKThe perturbation equivalent LC memristor circuit replaces (S2) primary memristor RKThe sodium ion channel of (S4) is at equilibrium point QNaThe perturbation equivalent LC memristor circuit replaces (S2) a secondary memristor RNaAnd forming an integral perturbation equivalent memristor circuit of an ion channel in the heart Hodgkin-Huxley model at a balance point Q.
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Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4994459A (en) * 1989-12-11 1991-02-19 American Home Products Corporation Aryloxypropane substituted piperazine derivatives with antiarrhythmic and antifibrillatory activity
JP2002150258A (en) * 2000-11-06 2002-05-24 Sony Corp Circuit using neuron model and information processing method
CN101630662A (en) * 2009-08-20 2010-01-20 黑龙江大学 Manufacturing method for protein structure quick switch memristor array
CN102361588A (en) * 2009-02-17 2012-02-22 神经芯片公司 System and method for cognitive rhythm generation
CN103097882A (en) * 2011-09-06 2013-05-08 瓦高希有限公司 Chemical sensor
CN103118591A (en) * 2010-09-23 2013-05-22 C·R·巴德股份有限公司 Apparatus and method for catheter navigation using indovascular energy mapping
KR101282884B1 (en) * 2012-03-20 2013-07-17 광운대학교 산학협력단 Complementary memristor driving circuits and control method of the complementary memristor
CN204797832U (en) * 2015-05-25 2015-11-25 赵存亮 Space cardiogram system device that array electrocardiosignal was realized
CN105264680A (en) * 2011-03-30 2016-01-20 阿姆巴托雷股份有限公司 Electrical, mechanical, computing, and/or other devices formed of extremely low resistance materials
CN106992249A (en) * 2017-02-22 2017-07-28 北京航空航天大学 A kind of ionic memristor with quantum conductance effect
CN107609338A (en) * 2017-10-24 2018-01-19 哈尔滨理工大学 A kind of Skeletal Muscle Contraction model based on metabolism physiology

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10191029B2 (en) * 2014-04-17 2019-01-29 Jacques Beaumont Method and system to extend the conditions of application of an inversion of the Hodgkin-Huxley gating model

Patent Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4994459A (en) * 1989-12-11 1991-02-19 American Home Products Corporation Aryloxypropane substituted piperazine derivatives with antiarrhythmic and antifibrillatory activity
JP2002150258A (en) * 2000-11-06 2002-05-24 Sony Corp Circuit using neuron model and information processing method
CN102361588A (en) * 2009-02-17 2012-02-22 神经芯片公司 System and method for cognitive rhythm generation
CN101630662A (en) * 2009-08-20 2010-01-20 黑龙江大学 Manufacturing method for protein structure quick switch memristor array
CN103118591A (en) * 2010-09-23 2013-05-22 C·R·巴德股份有限公司 Apparatus and method for catheter navigation using indovascular energy mapping
CN105264680A (en) * 2011-03-30 2016-01-20 阿姆巴托雷股份有限公司 Electrical, mechanical, computing, and/or other devices formed of extremely low resistance materials
CN103097882A (en) * 2011-09-06 2013-05-08 瓦高希有限公司 Chemical sensor
KR101282884B1 (en) * 2012-03-20 2013-07-17 광운대학교 산학협력단 Complementary memristor driving circuits and control method of the complementary memristor
CN204797832U (en) * 2015-05-25 2015-11-25 赵存亮 Space cardiogram system device that array electrocardiosignal was realized
CN106992249A (en) * 2017-02-22 2017-07-28 北京航空航天大学 A kind of ionic memristor with quantum conductance effect
CN107609338A (en) * 2017-10-24 2018-01-19 哈尔滨理工大学 A kind of Skeletal Muscle Contraction model based on metabolism physiology

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
A quantitative description of membrane current and its application to conduction and excitation in nerve;Hodgkin等;《The Journal of physiology》;19521231;第500-544页 *
Börgers C等.Three Simple Models of Neurons in Rodent Brains.《An Introduction to Modeling Neuronal Dynamics》.2017,第66卷第31-37页. *
Hodgkin-Huxley模型的心脏浦肯野纤维弱忆阻机理研究;吴政泽等;《江西理工大学学报》;20181031;第39卷(第5期);第85-89页 *
Synchronization between neurons coupled by memristor;YingXu等;《Chaos, Solitons & Fractals》;20171130;第104卷;第435-442页 *
弱信号在Hodgkin-Huxley神经元单向耦合系统中的传输特性;梁晓冰等;《物理学报》;20090731;第58卷(第7期);第5065-5069页 *
忆阻及其应用研究综述;王小平等;《自动化学报》;20131231;第39卷(第8期);第1170-1184页 *
新型忆阻细胞神经网络的建模及电路仿真;张小红等;《系统仿真学报》;20160831;第28卷(第08期);第1715-1724页 *

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