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ECE602 BME I Ordinary Differential Equations in Biomedical Engineering (Cont’d)

ECE602 BME I Ordinary Differential Equations in Biomedical Engineering (Cont’d). BME Model Examples. Hodgkin – Huxley Model. An empirical model of an action potential in a squid giant axon. BME Model Examples. Hodgkin – Huxley Model. Separation of charges across a membrane

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ECE602 BME I Ordinary Differential Equations in Biomedical Engineering (Cont’d)

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  1. ECE602 BME I Ordinary Differential Equations in Biomedical Engineering (Cont’d)

  2. BME Model Examples Hodgkin – Huxley Model • An empirical model of an action potential in a squid giant axon

  3. 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

  4. BME Model Examples Hodgkin – Huxley Model • Channels allow ions to pass through the membrane • Selective • Either passive or active

  5. BME Model Examples Hodgkin – Huxley Model • Passive Channels • Always open • Ion specific • Responsible for resting potential (Nernst Equation)

  6. BME Model Examples Hodgkin – Huxley Model • Active Channels • Open or close • Ion specific • Responsible for action potential

  7. BME Model Examples Hodgkin – Huxley Model • Action Potential (V) • V Reaches threshold->Na+ channel open->inward flow of Na+->further depolarization->increases Na+ conductance->more Na+ current->driving V -> concludes with the closure of the Na+ channel • A similar, but slower change in K+ conductance drives V back to the resting potential.

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

  9. 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

  10. 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

  11. BME Model Examples Hodgkin – Huxley Model Closed (V) Open (1-s) s (V) (Steady state value) (The time constant)

  12. BME Model Examples Hodgkin – Huxley Model • The sodium conductance

  13. BME Model Examples Hodgkin – Huxley Model • The potassium conductance

  14. BME Model Examples Hodgkin – Huxley Model • The leakage conductance

  15. BME Model Examples Hodgkin – Huxley Model The complete model:

  16. BME Model Examples Hodgkin – Huxley Model

  17. BME Model Examples Hodgkin – Huxley Model

  18. BME Model Examples Hodgkin – Huxley Model Reference: J. Keener and J. Sneyd, “Mathematical Physiology”, Springer: 1998.

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