Electric fields, electric eels and how electricity travels through the scalp.

Hope that title confused you. Because this post is going to be on a topic that’s confusing to me. It started when I read this article Neurobiologists Find that Weak Electrical Fields in the Brain Help Neurons Fire Together .

Extracellular electric fields exist throughout the living brain. Their distant echoes can be measured outside the skull as EEG waves. These fields are particularly strong and robustly repetitive in specific brain regions such as the hippocampus, which is involved in memory formation, and the neocortex, the area where long-term memories are held. “The perpetual fluctuations of these extracellular fields are the hallmark of the living and behaving brain in all organisms, and their absence is a strong indicator of a deeply comatose, or even dead, brain,” Anastassiou explains.

Throughout the entire article they referred to electric fields. Electric fields? That’s a term I’m not familiar with, which I guess seems strange after having done more than a few electrical engineering subjects. Was an electrical field the same thing as voltage? A term I did understand, and If I substituted voltage for electric field the article made sense. But I decided to look into this further- meaning I decided to google it.

Thanks hyperphysics!

Thanks hyperphysics!

This was the first thing that came up. Disappointingly mathsy. But it showed that Electric fields and voltage were not the same thing. Rather an electric field is the change in voltage measured over a distance, with the unit of V/m or V/cm or mV/mm etc. etc.

Ok so why measure voltage over distance? In wired circuits, distance (despite circuit noise considerations)  based on what I’d studied, was never taken into account. Something was missing. And that something was made clear in this example I stumbled upon.

Question: Suppose an electric eel is 1 m long, and generates a voltage difference of 1000 volts between its head and tail. What is the electric field in the water around it?

Solution: We are only calculating the amount of field, not its direction, so we ignore positive and negative signs. Subject to the possibly inaccurate assumption of a constant field parallel to the eel’s body, we have 

Aha! So an electric field was something that was useful in describing electricity flowing through a substance like water, as opposed to electricity that flows through wires.

By the way, eels are awesome. Some eels like the Moray eel, have a double retractable jaw (like the creatures in Aliens). And the following info from Wikipedia

 The electric eel has an elongated, cylindrical body, typically growing to about 2 m (6 ft 7 in) in length, and 20 kg (44 lb) in weight. In the electric eel, some 5,000 to 6,000 stacked electroplaques are capable of producing a shock at up to 500 volts and 1 ampere of current (500 watts).  Such a shock could be deadly for an adult human. Juveniles produce smaller voltages (about 100 V).

They are capable of varying the intensity of the electrical discharge, using lower discharges for “hunting” and higher intensities for stunning prey, or defending themselves. When agitated, they are capable of producing these intermittent electrical shocks over a period of at least an hour without signs of tiring.

These fish have always been sought after by some animal collectors, but catching one is difficult, as the only option is usually to make the eels tire by continually discharging electricity. The fish’s electric organs will eventually become completely discharged, allowing the collector to wade into the water in comparative safety.

Keeping electric eels in captivity is difficult and mostly limited to zoos and aquariums, although a few hobbyists have kept them as pets. An electric eel requires an aquarium of at least 750 l (200 gal). It generally must be kept in the tank by itself, although adult electric eels generally tolerate one another. Young eels will often fight if placed in the same aquarium. Electric eels cannot be kept with any other fish, as they will attack them

After reading that I’m more determined than ever to one day have an electric eel as a pet.  Considering that your average bath tub is about 250 L, that should be large enough for a baby one. I’d train it to deliver electric shocks for food (simulating real life conditions!) and have some kind of circuitry so that it could charge my mobile phone. I’d call him/her Zappo and we’d be best of friends. Despite the fact I wouldn’t be able to pet them without the possibility of getting shocked. And when Zappo outgrew the bathtub,we’d travel back to South America, and I’d release him into a nice swamp/creek and it would be a very dramatic/tearful free Willy type of moment.

Alright, enough about eels, and back to electric fields, and how they are useful for describing electrical circuits that involve substances like water. So how does electricity travel through water?

The following image shows how electrical current flows between two probes submerged in water and connected to a battery.
Path of electrical current in water

Path of electrical current in water

With the top probe connected to the batteries’ positive terminal and the bottom probe connected to the negative one. The current radiates outwards from the source(the probes) in all directions, and current flow is represented by the solid black lines in the above picture. The voltage decreases  in value as the current moves away from the source, with measured voltage proportional to 1/distance squared. Thus if the inital voltage is measured to be 160 mV, 1 mm from the source, 10 mm away from the source the voltage measured will be 1.6 mV. The dashed lines in the picture represent  surfaces of equal voltages.

Water can be considered an isotropic homogenous volume conductor. Isotropic meaning that it conducts equally in all directions, homogeneous meaning that it has a uniform composition, and volume conductor refers to the fact that the electrical currents flow in three dimensions.

So that’s how electricity flows through water. Unlike water the human head cannot be considered isotropic or homogenous, as before any current can be picked up by electrodes placed on the scalp, it must travel through different mediums, from the brain, through celebral spinal fluid, bone and finally through the skin of the scalp- all of which have different resistivities.

Any current that can be measured, is due to millions of neurons (in parallel) firing in a synchronised fashion. From studies done by Cooper et al. 1965, and Ebersole 1997, it was shown that neurons in at least an area of 6 cm² of the cortex, had to be firing synchronously in order to produce a measurable EEG signal on the persons scalp.

Unlike the water/battery example above the electrical currents generated in the brain are AC rather than DC. However due to the low frequencies < 40 Hz, in building an electrical model of the brain they can generally be approximated as DC currents. In the same way that the brain itself can be modelled as an isotropic volume conductor, as the measured voltage drop off approximates the 1/(distance squared) rule mentioned above.

Reading anything academic on this subject, and you enter a world of complicated jargon where many different words are used to describe the exact same thing (to my understanding at least).

This all started when I didn’t understand what an electric field was, after further reading I came across the following

  • Dipole source
  • Dipole moment
  • Current flux
  • Current flux density
  • Action potential current source
  • Transcortical potential/ Scalp potential
  • Current source + membrane sink

First of all- anything potential = voltage. The author prefers to say that currents in the brain arise from current sources. Fine, but in real life all current sources are built from voltage sources, thus current source= voltage source.

A dipole = voltage, a more detailed explanation is that a dipole is an idealised point voltage source where “If one imagines an infinitely thin wire insulated over its extent except at its tip to be introducing a current into a uniform volume conductor of infinite extent, then we illustrate an idealized point source.” So it refers to a voltage that originates from an source, which is small enough to be approximated as a point. A dipole moment = voltage separated by distance… which sounds familiar…thus dipole moment = electric field.

The only words which need further looking into are current flux and current flux density. Current flux = current flow. Because we’re looking at a volume conductor, in the same way that electric field is better than voltage to describe electrical activity in a volume,  current flux density(J) is better than current, as it is current divided by area and has the units mA/mm² . It can be calculated by dividing an Electric field by the resistivity of the conductor.  J = E/ η

Resistivity(η) is not the same thing as resistance. Resistance is measured in ohms, and is dependant on resistivity( which is dependent on the conductor) as well as the cross sectional area, and length of the conductor.

Ω=η x length/ cross section area. Thus increasing the cross sectional area of a wire, lowers the resistance, thicker wires have less resistance than thinner ones, and are thus used in high voltage power lines to reduce power losses. Also from the formula, a wire 2x longer has 2x as much resistance.

Hope that makes everything clearer. When I was first trying to make sense of how an EEG worked, I didn’t understand what was happening with the electrode placement because I didn’t understand how voltage/currents flowed through a surface like the scalp. Next major post will be on electrode configuration/placement.


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