Neuroprosthetics

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Neuroprosthetics

• Week 4
• Neuron Modelling

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Implants excite neurons

• Retina ganglion or bipolar cells
• Cochlea/Ear spiral ganglion cells
• Motor prostheses nerve-muscle junction
• In each example interface between electrode and
  neuronal membrane

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Passive properties of neuronal membrane

• Resistance from intra and extra cellular fluids
• Capacitance of membrane (like a cable)
• Combination means spatial and temporal filtering
  of voltage signals
• Typical low pass RC circuit losses/fidelity
• Spinal motor neurons or axons from retina
  ganglion to thalamus in brain must reliably carry
  signals with a frequency up to 4KHz/1KHz for up
  to 1 metre

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Passive limitations

• Rise and fall of signals given by
• V(t) V(0)exp(-t/T) where T RC
• Typical RC 1 to 100msec so voltage changes
  are slowed
• Same equation for distance that a signal can be
  detected
• V(x) V(0)exp(-x/X) where X length constant
• Typical X is a few hundred micrometers

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Passive response

• Voltage profile for a constant current on
  peripheral nerve of KW

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Active Membranes

• Active membranes overcome temporal and spatial
  degradations
• Ionic gradients exist between the inside and
  outside of cells
• Exchanges between sodium, calcium and potassium
  ions driven in and out of cells
• Action potential brief, transient, regenerating
  depolarization
• Resting potential typically -70mV. External
  stimulus brings membrane to threshold. Cell fires
  or not, peak amplitude may reach 40mV

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Ion channels

• Whole cell currents represent the ensemble of
  thousands of individual channels
• Thousands of individual ion channels are
  responsible for membrane conductance changes
• Channels are selective for different types of
  ions

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Gating

• Time dependence of the opening and closing of a
  channel
• Probability of finding a channel in an open or
  closed state as a function of
• membrane potential
• the presence of a drug or neurotransmitter

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Permeation

• Conductive properties of a channel in terms of
  its selectivity for specific ions
• The rate at which ions can pass through the
  channel (hence max current)
• Effects of blocking drugs

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Permeation

• Conductive properties of a channel in terms of
  its selectivity for specific ions
• The rate at which ions can pass through the
  channel (hence max current)
• Effects of blocking drugs

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Nerve Tissue
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Membrane voltage

• The main equation for stimulation of the Soma is
  always
• I(st) I(io) C dV/dt
• One part of the current loads the cell membrane
  capacity and the other part passes through the
  ion channels
• Alternatively dV/dt I(st) I(io) /C
• A positive stimulating current causes V to
  increase
• To generate a spike this current must cause V to
  reach its threshold value

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Threshold

• Once the threshold voltage is reached many of the
  (sodium) ion channels open
• The voltage increases to an action potential
  without the need for further stimulation
• Once the threshold is reached the stimulus can be
  switched off
• Alternatively, once the threshold is reached
  increasing the stimulating current further has
  little/no effect
• But different cells have different threshold
  values depends on size of axons and somas

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Axon models

• Operation of axons have been modelled extensively
  for e.g. squid, frogs, rabbits and rats
• An expression for human nerve fibres is given by
• dV/dt -I(Na)-I(K)-I(L)I(st) /C
• Where I(L) is a leakage current
• Each current is then defined by means of a
  complex minimum (first) order equation

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Temperature effects

• Usually membrane model data is gathered at low
  temperatures
• Raising the temperature generally causes a
  shortening of the action potential and an
  increase in spike propagation velocity
• For temperatures higher than 31 to 33 degC action
  potentials no longer propagate in squid axons
• In warm blooded animals spike durations shorten
  considerably but no heat block
• Threshold levels change warmer means easier to
  excite!

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Compartment models

• Pieces of neuron can be treated as elements
• A whole neuron is represented by an electrical
  network
• Currents injected then can be treated with
  Kirchoffs law
• Resistances become internal resistances of
  neighbouring compartments
• Modeller must decide about degree of complexity
• Much research in this area!

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Model variability

• Large variability in neuron models due partly to
  the large variability in neurons
• Example absolute threshold current at the soma
  for a point source stimulation was
• Passive model 32.9
  microA
• Hodgkin-Huxley model 43
  microA
• FCM(5 ion channels) model 71 microA
• Compare with our studies (human)80 to 100 microA
• Passive (based on RC) HH (based on squids)

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Problems

• Selective stimulation of neural tissue is an
  enormous challenge
• Example in bladder control activation of the
  detrusor muscle without activation of the urethal
  sphincter
• Every type of neuron exhibits different operating
  characteristics big problem in
  modelling/simulation
• Neural geometry is complex, leading to complex
  models which require a high computational effort
  even for simple studies
• External stimulation/monitoring very limited

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