Hh model(me)
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The Hodgkin-Huxley model is a mathematical model that describes the generation and propagation of electrical signals in neurons. It consists of nonlinear differential equations that describe the voltage-dependent ionic currents that flow across the neuronal membrane. The model includes separate voltage-gated ion channels for sodium and potassium ions that allow the currents to change over time based on the membrane potential. The model can be used to simulate the membrane potential over time in response to an applied electric current stimulus.
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![Intracellular
extracellular
Na+
K+
Ve
Vi
)(])()[(])()[(
)()(
tIEtVtGEtVtG
R
tV
dt
tdV
C appKmKNamNa
m
mm
m
Rm
Cm
GK
ENa EK
GNa
Iapp
Hodgkin-Huxley membrane circuitMembrane and gate model
Lipid cell
membrane
(Hodgkin and Huxley, 1952)
Iapp
The Hodgkin-Huxley model](https://image.slidesharecdn.com/hhmodelme-200729064820/85/Hh-model-me-2-320.jpg)
![The Hodgkin-Huxley model
(+stochastic model)
)(])()[(])()[(
)()(
tIEtVtNEtVtN
R
tV
dt
tdV
C appKmKKNamNaNa
m
mm
m
Stochastic](https://image.slidesharecdn.com/hhmodelme-200729064820/85/Hh-model-me-8-320.jpg)
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Hh model(me)
- 1. HH MODEL 20185748 Nafiz Ishtiaque Ahmed
- 2. Intracellular extracellular Na+ K+ Ve Vi )(])()[(])()[( )()( tIEtVtGEtVtG R tV dt tdV C appKmKNamNa m mm m Rm Cm GK ENa EK GNa Iapp Hodgkin-Huxley membrane circuitMembrane and gate model Lipid cell membrane (Hodgkin and Huxley, 1952) Iapp The Hodgkin-Huxley model
- 3. 1. Set an electrical pulse 2. Set time increment △t (generally, set △t = 0.01ms) 3. Update m,h,n using Euler equation 4. Calculate each ion conductance, G 5. Update membrane potential, Vm, using Euler equation(or Runge-Kutta method) 6. Repeat steps from(3) Programming
- 4. 1. Set an electrical pulse & 2. Set time increment △t (set △t = 0.001ms) Current = 6.96nA
- 5. 3. Update m,h,n using Euler equation red = m , blue = h, black = n
- 6. 4. Calculate each ion conductance, G & 5. Update membrane potential, Vm, using Euler equation
- 7. The Hodgkin-Huxley model (+stochastic model) Stimulus level Spikefiring efficiency(%) 0 100 Stimulus level 0 100 dt st 50 Vi Rm Cm ENa EK Na K VeVe Rm Cm GK ENa EK GNa Vi … … StochasticDeterministic
- 8. The Hodgkin-Huxley model (+stochastic model) )(])()[(])()[( )()( tIEtVtNEtVtN R tV dt tdV C appKmKKNamNaNa m mm m Stochastic
- 10. latency mean & standard deviation