Neuroprosthetics

Neuroprosthetics Week 4 Neuron Modelling

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

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

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

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

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

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

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

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

Nerve Tissue

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

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

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

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!

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!

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)

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

Neuroprosthetics