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Neuroprosthetics
Week 4
Neuron Modelling
Implants excite neurons
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Retina – ganglion or bipolar cells
Cochlea/Ear – spiral ganglion cells
Motor prostheses – nerve-muscle junction
In each example – interface between
electrode and neuronal membrane
Passive properties of neuronal
membrane
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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
Passive limitations
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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
Passive response
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Voltage profile for a constant current on
peripheral nerve of KW
Active Membranes
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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
Ion channels
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“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
Gating
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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
Permeation
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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
Permeation
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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
Nerve Tissue
Membrane voltage
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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
Threshold
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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
Axon models
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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
Temperature effects
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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!
Compartment models
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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!
Model variability
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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)
Problems
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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