Extracellular potential · Lobeworks/17

The extracellular potential is the voltage in the fluid around neurons, measured against a distant reference, and it is what every implanted electrode records: the trace the currents of nearby cells leave in the medium, tens to hundreds of microvolts for a spike close by.

Extracellular potential. The extracellular potential is the voltage in the fluid around neurons, measured against a distant reference, and it is what every implanted electrode records: the trace the currents of nearby cells leave in the medium, tens to hundreds of microvolts for a spike close by.

When a neuron fires, sodium flows in at one part of its membrane and current flows back out elsewhere, closing the loop through the fluid. The fluid conducts but resists, so that current sets up small voltage differences in it, Ohm's law spread through a volume. A point source of current III in a medium of conductivity σ\sigmaσ gives a potential that falls with distance rrr,

V(r)=I4πσrV(r) = \frac{I}{4\pi\sigma r}V(r)=4πσrI​

and since a neuron sends current in and out at nearby points, the two contributions largely cancel at a distance, so the potential of a cell falls faster than 1/r1/r1/r, roughly with the square of distance. The chain of a recording starts here: ions move, the field changes, the potential of the fluid changes, the electrode reads it.

Microvolts, never millivolts. Inside the cell a spike moves the membrane by about 100 mV; outside, tens of micrometres away, the same spike leaves 50 to a few hundred microvolts, about a thousand times less (100 µV is 0.0001 V).

The deflection is usually negative. Near the spot where sodium enters, positive charge leaves the fluid, so an electrode there sees a sharp downward spike.

Distance decides who is heard. Beyond about 100 µm one neuron is lost among the others and the noise, so a probe hears only the cells along its track, and spike sorting tells them apart by the shape of each cell's trace across neighbouring sites.

Slow currents make the local field potential. Synaptic currents of many cells summed together form the LFP, below a few hundred hertz; the spikes ride on top of it at higher frequencies, which is why recordings split the signal into two bands.

An electrode never catches a spike; it reads the voltage the spike leaves in the water.

Everything a probe knows about a neuron is a few microvolts of that voltage, seen from tens of micrometres away.

Questions: If electrodes only measure voltage, how does software know which neuron fired? By geometry: spike sorting. A neuron's extracellular potential falls fast with distance, so on a dense probe each spike appears on several neighbouring sites with different sizes, a footprint (template) that differs between cells tens of micrometres apart. Software such as Kilosort finds the spikes and groups them by footprint, one group per unit, the way several seismographs locate one earthquake. The electrode measures voltage; the neuron is found by geometry. How does the signal cross from the ions of the brain to the electrons of the chip? Through a field, by capacitive coupling. No ion enters the metal: at the boundary the ions of the fluid line up against the surface and the metal's electrons rearrange to face them, a few nanometres apart, forming the electrical double layer, which behaves as a capacitor (Q=CVQ = CVQ=CV). When a spike shifts the charge on the fluid side, the electrons on the metal side follow, and the voltage of the metal track moves with them. In one phrase: ions outside, electrons inside, a field in between. What is the signal-to-noise ratio of a spike recording, and where does its noise come from? The size of a spike compared with everything else on the trace: a 50 µV spike over about 6 µV of noise, as on Neuropixels, is a ratio near 8 and easy to detect, while the same spike under 50 µV would be lost. The noise comes from the thermal agitation of charges in the electrode and the amplifier, the transistors themselves, interference from mains and equipment, movement, and the spikes of all the other neurons. Amplification never improves the ratio, so it is set by the first stage, next to the electrode. What are the steps from a neuron firing to numbers in the computer? Ions move across the neuron's membrane, which changes the field and the potential of the fluid; the titanium nitride electrode on the shank picks that up by capacitive coupling; a CMOS switch on the shank connects it to a channel; in the base a low-noise amplifier and filters condition it and a 10-bit converter turns it into numbers 30,000 times a second; the numbers leave by the flex cable to the headstage and the computer, where spike sorting assigns them to neurons. In one line: ions, field, voltage, electrons, converter, numbers. What is aliasing, and what decides the bandwidth and the sampling rate of a recording? Aliasing is a fast signal sampled too slowly posing as a slow one, like the wheel of a filmed car turning backwards. To avoid it the sampling rate must exceed twice the bandwidth, fs>2Bf_s > 2Bfs​>2B, and an analog filter removes what lies above fs/2f_s/2fs​/2 before the converter. The bandwidth is decided by the physics of the signal (a spike of a millisecond reaches about 10 kHz) and enforced by the filter; the rate is then chosen above 2B2B2B and below what power, data and the link allow. What does each electrode on a probe actually measure? The extracellular potential: the voltage of the fluid at its surface, measured against a reference electrode. Nearby neurons push currents through the fluid when they fire, and because the fluid resists, those currents leave small voltage differences in it, tens to hundreds of microvolts close to a cell. The electrode does not detect a neuron or absorb a spike; it reads that voltage, and nothing else.