neuroprosthetics - 4

8/7/2019 Neuroprosthetics - 4

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NeuroprostheticsNeuroprosthetics

Week 4Week 4

Neuron ModellingNeuron Modelling


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Implants excite neuronsImplants excite neurons

RetinaRetina ganglion or bipolar cellsganglion or bipolar cells

Cochlea/EarCochlea/Ear spiral ganglion cellsspiral ganglion cells

Motor prosthesesMotor prostheses nervenerve--muscle junctionmuscle junction

In each exampleIn each example interface betweeninterface betweenelectrode and neuronal membraneelectrode and neuronal membrane


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Passive properties of neuronalPassive properties of neuronal

membranemembrane

Resistance from intra and extra cellular fluidsResistance from intra and extra cellular fluids

Capacitance of membrane (like a cable)Capacitance of membrane (like a cable) Combination means spatial and temporalCombination means spatial and temporal

filtering of voltage signalsfiltering of voltage signals

Typical low pass RC circuitTypical low pass RC circuit losses/fidelitylosses/fidelity

Spinal motor neurons or axons from retinaSpinal motor neurons or axons from retinaganglion to thalamus in brain must reliably carryganglion to thalamus in brain must reliably carrysignals with a frequency up to 4KHz/1KHz for upsignals with a frequency up to 4KHz/1KHz for upto 1 metreto 1 metre


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Passive limitationsPassive limitations

Rise and fall of signals given by:Rise and fall of signals given by:

V(t) = V(0)exp(V(t) = V(0)exp(--t/T) where T = RCt/T) where T = RC Typical RC = 1 to 100msecTypical RC = 1 to 100msec so voltage changesso voltage changes

are slowedare slowed

Same equation for distance that a signal can beSame equation for distance that a signal can bedetected:detected:

V(x) = V(0)exp(V(x) = V(0)exp(--x/X) where X = length constantx/X) where X = length constant

Typical X is a few hundred micrometersTypical X is a few hundred micrometers


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Passive responsePassive response

Voltage profile for a constant current onVoltage profile for a constant current onperipheral nerve of KWperipheral nerve of KW


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Active MembranesActive Membranes

Active membranes overcome temporal andActive membranes overcome temporal andspatial degradationsspatial degradations

Ionic gradients exist between the inside andIonic gradients exist between the inside andoutside of cellsoutside of cells

Exchanges between sodium, calcium andExchanges between sodium, calcium andpotassiumpotassium ions driven in and out of cellsions driven in and out of cells

Action potential

Action potential brief, transient, regeneratingbrief, transient, regeneratingdepolarizationdepolarization

Resting potential typicallyResting potential typically --70mV. External70mV. Externalstimulus brings membrane to threshold. Cellstimulus brings membrane to threshold. Cellfires or not, peak amplitude may reach +40mVfires or not, peak amplitude may reach +40mV


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Ion channelsIon channels

Whole cell currents represent the ensembleWhole cell currents represent the ensemble

of thousands of individual channelsof thousands of individual channels Thousands of individual ion channels areThousands of individual ion channels are

responsible for membrane conductanceresponsible for membrane conductance

changeschanges Channels are selective for different types ofChannels are selective for different types of

ionsions


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GatingGating

Time dependence of the opening andTime dependence of the opening and

closing of a channelclosing of a channel Probability of finding a channel in an openProbability of finding a channel in an open

or closed stateor closed state as a function of:as a function of:

membrane potentialmembrane potential the presence of a drug orthe presence of a drug or

neurotransmitterneurotransmitter


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PermeationPermeation

Conductive properties of a channel inConductive properties of a channel in

terms of its selectivity for specific ionsterms of its selectivity for specific ions The rate at which ions can pass throughThe rate at which ions can pass through

the channel (hence max current)the channel (hence max current)

Effects of blocking drugsEffects of blocking drugs


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PermeationPermeation

Conductive properties of a channel inConductive properties of a channel in

terms of its selectivity for specific ionsterms of its selectivity for specific ions The rate at which ions can pass throughThe rate at which ions can pass through

the channel (hence max current)the channel (hence max current)

Effects of blocking drugsEffects of blocking drugs


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Nerve TissueNerve Tissue


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Membrane voltageMembrane voltage

The main equation for stimulation of the Soma isThe main equation for stimulation of the Soma isalways:always:

I(st) = I(io) + C dV/dtI(st) = I(io) + C dV/dt One part of the current loads the cell membraneOne part of the current loads the cell membrane

capacity and the other part passes through the ioncapacity and the other part passes through the ionchannelschannels

Alternatively: dV/dt = [ I(st)Alternatively: dV/dt = [ I(st) I(io) ]/CI(io) ]/C Apositive stimulating current causes V to increaseApositive stimulating current causes V to increase

To generate a spike this current must cause V toTo generate a spike this current must cause V toreach its threshold valuereach its threshold value


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ThresholdThreshold

Once the threshold voltage is reached many of theOnce the threshold voltage is reached many of the(sodium) ion channels open(sodium) ion channels open

The voltage increases to an action potential withoutThe voltage increases to an action potential withoutthe need for further stimulationthe need for further stimulation

Once the threshold is reached the stimulus can beOnce the threshold is reached the stimulus can beswitched offswitched off

Alternatively, once the threshold is reachedAlternatively, once the threshold is reachedincreasing the stimulating current further hasincreasing the stimulating current further haslittle/no effectlittle/no effect

But different cells have different threshold valuesBut different cells have different threshold values

depends on size of axons and somasdepends on size of axons and somas


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Temperature effectsTemperature effects

Usually membrane model data is gathered at lowUsually membrane model data is gathered at lowtemperaturestemperatures

Raising the temperature generally causes aRaising the temperature generally causes ashortening of the action potential and an increaseshortening of the action potential and an increasein spike propagation velocityin spike propagation velocity

For temperatures higher than 31 to 33 degC actionFor temperatures higher than 31 to 33 degC actionpotentials no longer propagate in squid axonspotentials no longer propagate in squid axons

In warm blooded animals spike durations shortenIn warm blooded animals spike durations shortenconsiderablyconsiderably but no heat blockbut no heat block

Threshold levels changeThreshold levels change warmer means easier towarmer means easier to

excite!excite!


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Compartment modelsCompartment models

Pieces of neuron can be treated as elementsPieces of neuron can be treated as elements

Awhole neuron is represented by an electricalAwhole neuron is represented by an electrical

networknetwork Currents injected then can be treated with KirchoffsCurrents injected then can be treated with Kirchoffs

lawlaw

Resistances become internal resistances ofResistances become internal resistances ofneighbouring compartmentsneighbouring compartments

Modeller must decide about degree of complexityModeller must decide about degree of complexity

Much research in this area!Much research in this area!


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ProblemsProblems

Selective stimulation of neural tissue is anSelective stimulation of neural tissue is anenormous challengeenormous challenge

Example: in bladder controlExample: in bladder control activation of theactivation of the

detrusor muscle without activation of the urethaldetrusor muscle without activation of the urethalsphinctersphincter

Every type of neuron exhibits different operatingEvery type of neuron exhibits different operatingcharacteristicscharacteristics big problem inbig problem inmodelling/simulationmodelling/simulation

Neural geometry is complex, leading to complexNeural geometry is complex, leading to complexmodels which require a high computational effortmodels which require a high computational efforteven for simple studieseven for simple studies

External stimulation/monitoring very limitedExternal stimulation/monitoring very limited


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neuroprosthetics - 4

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