ECE602%20BME%20I

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• ECE602 BME I
• Ordinary Differential Equations in Biomedical
  Engineering (Contd)

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BME Model Examples
Hodgkin Huxley Model

• An empirical model of an action potential in a
  squid giant axon

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BME Model Examples
Hodgkin Huxley Model

• Separation of charges across a membrane
• Negative ions along the inside of the cell
  membrane
• Positive ions along the outside of the cell
  membrane
• Elsewhere the negative and positive ions are
  approximately evenly distributed

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BME Model Examples
Hodgkin Huxley Model

• Channels allow ions to pass through the membrane
• Selective
• Either passive or active

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BME Model Examples
Hodgkin Huxley Model

• Passive Channels
• Always open
• Ion specific
• Responsible for resting potential (Nernst
  Equation)

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BME Model Examples
Hodgkin Huxley Model

• Active Channels
• Open or close
• Ion specific
• Responsible for action potential

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BME Model Examples
Hodgkin Huxley Model

• Action Potential (V)
• V Reaches threshold-gtNa channel open-gtinward
  flow of Na-gtfurther depolarization-gtincreases
  Na conductance-gtmore Na current-gtdriving V -gt
  concludes with the closure of the Na channel
• A similar, but slower change in K conductance
  drives V back to the resting potential.

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BME Model Examples
Hodgkin Huxley Model
V the internal minus the external potential
Electrical circuit model of the cell membrane
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BME Model Examples
Hodgkin Huxley Model

• The principle ionic currents
• The sodium current (INa)
• The potassium current (IK)
• The leakage current (IL)

gx the membrane conductance for X VX the
membrane resting potential for X
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BME Model Examples
Hodgkin Huxley Model

• The current flow through a population of
  channels

• s the proportion of open channels in a
  population
• c the I-V curve of a single channel

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BME Model Examples
Hodgkin Huxley Model
Closed
?(V)
Open
(1-s)
s
?(V)
(Steady state value)
(The time constant)
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BME Model Examples
Hodgkin Huxley Model

• The sodium conductance

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BME Model Examples
Hodgkin Huxley Model

• The potassium conductance

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BME Model Examples
Hodgkin Huxley Model

• The leakage conductance

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BME Model Examples
Hodgkin Huxley Model
The complete model
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BME Model Examples
Hodgkin Huxley Model
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BME Model Examples
Hodgkin Huxley Model
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BME Model Examples
Hodgkin Huxley Model
Reference J. Keener and J. Sneyd, Mathematical
Physiology, Springer 1998.