The Source of EEG

We have concluded our investigation into the sources of EEG, arriving at working hypothesis. We present our calculations and analysis in The Sources of EEG. The EEG signal is a potential in the extracellular fluid above the cortex. We can detect it well with a screw electrode 1 mm in diameter. Such an electrode cannot detect individual action potentials. The EEG signal results from tens of thousands of neurons acting coherently.

We believe there are two sources of the EEG signal. One is excitory post-synaptic currents flowing into the synapses of pyramidal neurons, down the apical dendrite, and out of the soma membrane capacitance. Current enters the extracellular fluid outside the soma and leaves it at the synapses, thus generating a current dipole in the extracellular fluid. When many, parallel pyramidal neurons act together, the effect of these circulating currents combines to produce a negative EEG voltage of order −1.5 mV for at least 10 ms.



The second source is a consequence of neuron activation. As activation starts in the soma and propagates down the apical dendrite of a pyramidal neuron, there is a fraction of a millisecond during which current is flowing along the apical dendrite prior to its activation. This current flows from the activated soma, along the apical dendrite, and out through the membrane capacitance of the dendrite endings. We call this the exctracellular activation current, because it flows from the dendrite endings, through the extracellular fluid, to the soma. We estimate it to be ten times the magnitude of the extracellular excitory current prior to activation, but its direction is opposite and its duration is only 1 ms.

With excitation of a layer of pyramidal neurons spread over 10 ms, we expect the activation to be spread out over a similar interval, so that the average activation current will be comparable to the excitory current, producing a +1.5 mV contribution to the EEG.

We believe that the baseline EEG signal, its usual frequency spectrum, hiss artifacts, spindle artifacts, and negative-going seizure spikes are all consistent with our hypothesis. But oscillations of greater than 150 Hz in the EEG are not.

Electric Fiber Heating Element

We would like to taper the end of the optical fiber which penetrates the brain. The fiber diameter will decrease from 300 to 25 microns over the span of 1-2mm. This profile will facilitate insertion and minimize damage to brain tissue. We also hope that the taper will maximize the volume of tissue which receives optical intensity above the threshold required to activate the target proteins.

Our current taper machine was designed to produce long tapers (20mm) out of 500 micron fiber. It burns propane, fed through a small torch nozzle, to heat the fiber. This torch tends to heat more than one millimeter of the fiber at a time, making it challenging to create very short tapers. Additionally, the flow of burning propane and associated air turbulence perturbs the fiber, often making the taper slightly asymmetric.

An ideal heat source for our project would be able to heat a very small section of fiber (<1mm) to the temperature at which it becomes malleable (~1800K) without inducing air currents that perturb the fiber. Some fiber heaters use electricity to generate heat, though few or none are designed to heat very small sections of fiber. We decided to try building a simple electric heater.

Most wire heating elements are made from resistance wire alloys such as nickel-chrome. We didn't have any resistance wire on hand in the lab, so we wound a coil out of 0.02" diameter, 7 strand, stainless steel wire. We attached a power supply and began increasing the current through the coil. The coil began to glow visibly red. We gradually increased the current and the coil glowed brighter and became yellow-orange. 

We laid a 300 micron silica optic fiber through the center of the coil. We bent the fiber twenty degrees while still touching the coil, and it kept its bent shape after returning to room temperature. The coil burned out in this process, but not before it had transferred enough heat to the fiber to soften it and, in principle, make a taper.


Unfortunately, it is impractical for our fiber to touch the coil directly while making tapers. Can this simple heater soften glass with radiation only, or did the glass heat principally due to to conduction?


Our stainless steel coil can be maintained at a yellow glow without failure, which correlates to approximately 1270K. We model the heated wire as a black body and use Wien's displacement law to calculate the peak emission wavelength to be ~2.3 microns. Unfortunately, at this wavelength, a 300 micron thick section of our fiber absorbs far under 1% of radiation (as inferred from the datasheet). However, absorption of radiation increases rapidly with wavelength (silica glass absorbs nearly 100% of radiation over λ=5 micron). By roughly integrating Planck's law we see that up to 40% of radiation from the coil may be absorbed by the fiber. Of course, only a fraction of radiation will strike the fiber to begin with, most will radiate into the surrounding area or into other parts of the coil.

We positioned the coil in place of the torch in the fiber-stretching machine. We inserted a fiber through its axis, ensuring that it did not touch the coil. We applied 10V to the coil and gradually increased the current flowing through the fiber until it reached 1 amp, glowing yellow hot. After one minute, tension was applied to the fiber by the machine. The fiber failed to stretch, and instead, was simply pulled through the coil at a rate of 4mm/minute. The polyimide coating cleanly burned away, but the glass did not reach a temperature sufficient for tapering.

Above: 300 micron fiber in position to be tapered, inside of a stainless steel heating element. The element's temperature gradient is apparent by the color transition from red (~960K) near the alligator clips to yellow (~1270K) near the coil center.

We increased the current to 1.1A, which was still insufficient to soften the fiber. This corresponds to 11W of power. If we assume that 10% of radiated power intersects the fiber, and 40% is absorbed, the fiber receives energy at a rate of about 0.4W. This is insufficient to heat the fiber, but we can estimate the amount of power that would be necessary. We assume that the majority of heat leaves the hot zone via conduction along the fiber, and use Fourier's law to calculate the rate at which heat is dissipated. For the fiber to exist in thermal equilibrium at 1800K, we calculate that heat is dissipated at a rate of 1.5W per side of the hotzone. We must transfer 3W into the fiber to soften it.

We increased the current further, and by 1.2A, the coil failed by a combination of oxidation and melting.

Above: Coil after failure. Melted area apparent near right side. Note the polyimmide coating (left of coil) and bare silica (right of coil) where the fiber had moved through the coil. 

Stainless steel is not an ideal material for the job since it oxidizes quickly and can't be maintained at a temperature much over 1270K. Alloys such as Kanthal A-1 are designed for use at temperatures up to 1670K. Since total power radiated goes as T^4 (Stefan-Boltzmann), this increase in temperature represents a three time increase in power radiated over stainless steel. Materials such as MoSi2 can radiate 7 times as much power as our steel coil. We can investigate these materials to see whether they're capable of softening glass. It may turn out that because the overall efficiency is so poor that it is impossible to use a conventional heating element to heat a small section of fiber to the softening point by radiation alone. In that case, we'll proceed with our original plan of upgrading to a thin-flamed oxy-hydrogen torch.

Additional Pages: Silica glass properties

Introduction

In this blog we will record the development of the Implantable Sensor with Lamp (ISL) at Open Source Instruments Inc (OSI). We introduce the ISL development program in our Technical Proposal and present it in detail in our Conceptual Design.

The blog is registered under the OSI Google account (opensourceinstruments@gmail.com). I, Kevan Hashemi, will administer the blog. To make posts of your own, you need a Google account, and I must add you to the list of users entitled to make posts. Anyone with a Google account can leave comments.

One you are set up as post author, you can look at the lists of existing posts, create new posts, and edit posts. You can configure the text editor to interpret your typing as HTML, or to perform the HTML encoding for you. You will have to experiment with the preview button to learn how what you type and what you see are related.

You can store image files on our OSI ftp site, and display them in your posts with hot links, or you can upload the images directly to the blog. If you prefer to store your images on the OSI site, you can obtain the user name and password for upload to the OSI site from me. Put your images in the ISL directory and display them with a hot link in your post. Here is an example. Look at the source code for this post to see how to add hot links. Click on the image for a larger version.




Working on the ISL development at OSI are: Michael Collins (the glass fiber taper), Michael Bradshaw (the LED mounting and gluing to the taper), Jim Bensinger (mechanical design of head fixture), and Kevan Hashemi (electronic circuits).