Here I demonstrate how to use a single microcontroller pin to generate action-potential-like waveforms. The output is similar my fully analog action potential generator circuit, but the waveform here is created in an entirely different way. A microcontroller is at the core of this project and determines when to fire action potentials. Taking advantage of the pseudo-random number generator (rand() in AVR-GCC’s stdlib.h), I am able to easily produce unevenly-spaced action potentials which more accurately reflect those observed in nature. This circuit has a potentiometer to adjust the action potential frequency (probability) and another to adjust the amount of overshoot (afterhyperpolarization, AHP). I created this project because I wanted to practice designing various types of action potential measurement circuits, so creating an action potential generating circuit was an obvious perquisite.
The core of this circuit is a capacitor which is charged and discharged by toggling a microcontroller pin between high, low, and high-Z states. In the high state (pin configured as output, clamped at 5V) the capacitor charges through a series resistor as the pin sources current. In the low state (pin configured as output, clamped at 0V) the capacitor discharges through a series resistor as the pin sinks current. In the high-Z / high impedance state (pin configured as an input and little current flows through it), the capacitor rests. By spending most of the time in high-Z then rapidly cycling through high/low states, triangular waveforms can be created with rapid rise/fall times. Amplifying this transient and applying a low-pass filter using a single operational amplifier stage of an LM-358 shapes this transient into something which resembles an action potential. Wikipedia has a section describing how to use an op-amp to design an active low-pass filter like the one used here.
The code to generate the digital waveform is very straightforward. I’m using PB4 to charge/discharge the capacitor, so the code which actually fires an action potential is as follows:
// rising part = charging the capacitor
DDRB|=(1<<PB4); // make output (low Z)
PORTB|=(1<<PB4); // make high (5v, source current)
_delay_ms(2); // 2ms rise time
// falling part
DDRB|=(1<<PB4); // make output (low Z)
PORTB&=~(1<<PB4); // make low (0V, sink current)
_delay_ms(2); // 2ms fall time
_delay_us(150); // extra fall time for AHP
// return to rest state
DDRB&=~(1<<PB4); // make input (high Z)
Programming the microcontroller was accomplished after it was soldered into the device using test clips attached to my ICSP (USBtinyISP). I only recently started using test clips, and for one-off projects like this it’s so much easier than adding header sockets or even wiring up header pins.
I am very pleased with how well this project turned out! I now have an easy way to make irregularly-spaced action potentials, and have a great starting point for future projects aimed at measuring action potential features using analog circuitry.
Action potential half-width (relating to the speed of the action potential) could be adjusted in software by reducing the time to charge and discharge the capacitor. A user control was not built in to the circuit shown here, however it would be very easy to allow a user to switch between regular and fast-spiking action potential waveforms.
I am happy that using the 1n4148 diode on the positive input of the op-amp works, but using two 100k resistors (forming a voltage divider floating around 2.5V) at the input and reducing the gain of this stage may have produced a more reliable result.
Action potential frequency (probability) is currently detected by sensing the analog voltage output by a rail-to-rail potentiometer. However, if you sensed a noisy line (simulating random excitatory and inhibitory synaptic input), you could easily make an integrate-and-fire model neuron which fires in response to excitatory input.
Discussion related to the nature of this “model neuron” with respect to other models (i.e., Hodgkin–Huxley) are on the previous post.
Something like this would make an interesting science fair project
Few biological cells are as interesting to the electrical engineer as the neuron. Neurons are essentially capacitors (with a dielectric cell membrane separating conductive fluid on each side) with parallel charge pumps, leak currents, and nonlinear voltage-dependent currents. When massively parallelized, these individual functional electrical units yield complex behavior and underlie consciousness. The study of the electrical properties of neurons (neurophysiologically, a subset of electrophysiology) often involves the development and use of sensitive electrical equipment aimed at studying these small potentials produced by neurons and currents which travel through channels embedded in their membranes. It seems neurophysiology has gained an emerging interest from the hacker community, as evidenced by the success of Back Yard Brains, projects like the OpenEEG, and Hack-A-Day’s recent feature The Neuron – a Hacker’s Perspective.
In pondering designs for complex action potential detection and analysis circuitry, I realized that it would be beneficial to be able to generate action-potential-like waveforms on my workbench. The circuit I came up with to do this is a fully analog (technically mixed signal) action potential generator which produces lifelike action potentials.
Cellular Neurophysiology for Electrical Engineers (in 2 sentences): Neuronaction potentials (self-propagating voltage-triggered depolarizations) in individual neurons are measured in scientific environments using single cell recording tools such as sharp microelectrodes and patch-clamp pipettes. Neurons typically rest around -70mV and when depolarized (typically by external excitatory input) above a threshold they engage in a self-propagating depolarization until they reach approximately +40mV, at which time a self-propagating repolarization occurs (often over-shooting the initial rest potential by several mV), then the cell slowly returns to the rest voltage so after about 50ms the neuron is prepared to fire another action potential. Impassioned budding electrophysiologists may enjoy further reading Active Behavior of the Cell Membraneand Introduction to Computational Neuroscience.
The circuit I describe here produces waveforms which visually mimic action potentials rather than serve to replicate the exact conductances real neurons employ to exhibit their complex behavior. It is worth noting that numerous scientists and engineers have designed more physiological electrical representations of neuronal circuitry using discrete components. In fact, the Hodgkin-Huxley model of the initiation and propagation of action potentials earned Alan Hodgkin and Andrew Huxley the Nobel Prize in Physiology and Medicine in 1936. Some resources on the internet describe how to design lifelike action potential generating circuits by mimicking the endogenous ionic conductances which underlie them, notably Analog and Digital Hardware Neural Models, Active Cell Model, and Neuromorphic Silicon Neuron Circuits. My goal for this project is to create waveforms which resemble action potentials, rather than waveforms which truly model them. I suspect it is highly unlikely I will earn a Nobel Prize for the work presented here.
The analog action potential simulator circuit I came up with creates a continuous series action potentials. This is achieved using a 555 timer (specifically the NE555) in an astable configuration to provide continuous square waves (about 6 Hz at about 50% duty). The rising edge of each square wave is isolated with a diode and used to charge a capacitor*. While the charge on the capacitor is above a certain voltage, an NPN transistor (the 2N3904) allows current to flow, amplifying this transient input current. The capacitor* discharges predictably (as an RC circuit) through a leak resistor. A large value leak resistor slows the discharge and allows that signal’s transistor to flow current for a longer duration. By having two signals (fast and slow) using RC circuits with different resistances (smaller and larger), the transistors are on for different durations (shorter and longer). By making the short pulse positive (using the NPN in common collector configuration) and the longer pulse negative (using the NPN in common emitter configuration), a resistor voltage divider can be designed to scale and combine these signals into an output waveform a few hundred mV in size with a 5V power supply. Pictured below is the output of this circuit realized on a breadboard. The blue trace is the output of the 555 timer.
*Between the capacitance of the rectification diode, input capacitance of the transistor, and stray parasitic capacitance from the physical construction of my wires and the rails on my breadboard, there is sufficient capacitance to accumulate charge which can be modified by changing the value of the leak resistor.
This circuit produces similar output when simulated. I’m using LTspice (free) to simulate this circuit. The circuit shown is identical to the one hand-drawn and built on the breadboard, with the exception that an additional 0.1 µF capacitor to ground is used on the output to smooth the signal. On the breadboard this capacitance-based low-pass filtering already exists due to the capacitive nature of the components, wires, and rails.
A few improvements naturally come to mind when considering this completed, functional circuit:
Action potential frequency: The resistor/capacitor network on the 555 timer determines the rate of square pulses which trigger action potentials. Changing these values will cause a different rate of action potential firing, but I haven’t attempted to push it too fast and suspect the result would not be stable is the capacitors are not given time to fully discharge before re-initiating subsequent action potentials.
Microcontroller-triggered action potentials: Since action potentials are triggered by any 5V rising edge signal, it is trivially easy to create action potentials from microcontrollers! You could create some very complex firing patterns, or even “reactive” firing patterns which respond to inputs. For example, add a TSL2561 I2C digital light sensor and you can have a light-to-frequency action potential generator!
Adjusting size and shape of action potentials: Since the waveform is the combination of two waveforms, you can really only adjust the duration (width) or amplitude (height) of each individual waveform, as well as the relative proportion of each used in creating the summation. Widths are adjusted by changing the leak resistor on the base of each transistor, or by adding additional capacitance. Amplitude and the ratio of each signal may be adjusted by changing the ratio of resistors on the output resistor divider.
Producing -70 mV (physiological) output: The current output is electirically decoupled (through a series capacitor) so it can float at whatever voltage you bias it to. Therefore, it is easy to “pull” in either direction. Adding a 10k potentiometer to bias the output is an easy way to let you set the voltage. A second potentiometer gating the magnitude of the output signal will let you adjust the height of the output waveform as desired.
The 555 could be replaced by an inverted ramp (sawtooth):An inverted ramp / sawtooth pattern which produces rapid 5V rising edges would drive this circuit equally well. A fully analog ramp generator circuit can be realized with 3 transistors: essentially a constant current capacitor charger with a threshold-detecting PNP/NPN discharge component.
This action potential is not all-or-nothing: In real life, small excitatory inputs which fail to reach the action potential threshold do not produce an action potential voltage waveform. This circuit uses 5V rising edges to produce action potential waveforms. However, feeding a 1V rising edge would produce an action potential 1/5 the size. This is not a physiological effect. However, it is unlikely (if not impossible) for many digital signal sources (i.e., common microcontrollers) to output anything other than sharp rising edge square waves of fixed voltages, so this is not a concern for my application.
Random action potentials:When pondering how to create randomly timed action potentials, the issue of how to generate random numbers arises. This is surprisingly difficult, especially in embedded devices. If a microcontroller is already being used, consider Make’s write-up on the subject, and I think personally I would go with a transistor-based avalanche nosie generator to create the randomness.
A major limitation is that irregularly spaced action potentials have slightly different amplitudes. I found this out the next day when I created a hardware random number generator (yes, that happened) to cause it to fire regularly, missing approximately half of the action potentials. When this happens, breaks in time result in a larger subsequent action potential. There are several ways to get around this, but it’s worth noting that the circuit shown here is best operated around 6 Hz with only continuous regularly-spaced action potentials.
In the video I also demonstrate how to record the output of this circuit using a high-speed (44.1 kHz) 16-bit analog-to-digital converter you already have (the microphone input of your sound card). I won’t go into all the details here, but below is the code to read data from a WAV file and plot it as if it were a real neuron. The graph below is an actual recording of the circuit described here using the microphone jack of my sound card.
Let’s make some noise! Just to see what it would look like, I created a circuit to generate slowly drifting random noise. I found this was a non-trivial task to achieve in hardware. Most noise generation circuits create random signals on the RF scale (white noise) which when low-pass filtered rapidly approach zero. I wanted something which would slowly drift up and down on a time scale of seconds. I achieved this by creating 4-bit pseudo-random numbers with a shift register (74HC595) clocked at a relatively slow speed (about 200 Hz) having essentially random values on its input. I used a 74HC14 inverting buffer (with Schmidt trigger inputs) to create the low frequency clock signal (about 200 Hz) and an extremely fast and intentionally unstable square wave (about 30 MHz) which was sampled by the shift register to generate the “random” data. The schematic illustrates these points, but note that I accidentally labeled the 74HC14 as a 74HC240. While also an inverting buffer the 74HC240 will not serve as a good RC oscillator buffer because it does not have Schmidt trigger inputs.
The addition of noise was a success, from an electrical and technical sense. It isn’t particularly physiological. Neurons would fire differently based on their resting membrane potential, and the peaks of action potential should all be about the same height regardless of the resting potential. However if one were performing an electrical recording through a patch-clamp pipette in perforated patch configuration (with high resistance between the electrode and the internal of the cell), a sharp microelectrode (with high resistance due to the small size of the tip opening), or were using electrical equipment or physical equipment with amplifier limitations, one could imagine that capacitance in the recording system would overcome the rapid swings in cellular potential and result in “noisy” recordings similar to those pictured above. They’re not physiological, but perhaps they’re a good electrical model of what it’s like trying to measure a physiological voltage in a messy and difficult to control experimental environment.
This project was an interesting exercise in analog land, and is completed sufficiently to allow me to move toward my initial goal: creating advanced action potential detection and measurement circuitry. There are many tweaks which may improve this circuit, but as it is good enough for my needs I am happy to leave it right where it is. If you decide to build a similar circuit (or a vastly different circuit to serve a similar purpose), send me an email! I’d love to see what you came up with.
So I was reviewing my website statistics generated by a Python script I wrote when I noticed a peculiarity so bizarre that it made me questin the very purpose of my life. Okay maybe it wasn’t that bizarre, but it was interesting. The python script (which is automatically run every hour) downloads my latest access.log and saves it to its own folder. It then analyzes the data, creates some charts and graphs, and dumps out a bare-bones results file displaying some of the information I found useful. Of note is the number of times each page is hit.
This is where things get funny. Outperforming my home page by nearly double was indexOld.php (now indexOld22.php) – a simple webpage I tossed of for about a year before I put my big blog back online! Why were people still going to this page? Further investigation (from the referring sites section of my stats page) revealed a lot of hits from Google image-searches. I started looking at the actual requests and realized that many of these hits were people searching for the term Dwarf Gouramis “a type of freshwater aquarium fish) which was mentioned on that old webpage. The ironic part about it is what happens when you google image search for dwarf gouramis there is a picture of an extremely rare zebra pleco which is actually a link to my website! However the link APPEARS to be to wallpaperfishtalk.com because on my page I just linked to their image.
My conclusion: People are Google image-searching for ‘dwarf gouramis’, and an amazing picture of a zebra pleco is coming up which links to my site (due to the fact that months ago I talked about dwarf gouramis but posted a photo of a zebra pleco) and people (in their awe at this amazing fish) are clicking on it. So what did I do? I pulled a bait-and-switch! You bet I did. Now when you go to indexOld2.php it just forwards you to my current website – mua ha ha ha ha
PS: I’m appending to this entry at 2:17pm to note that I made a wonderful breakthrough in the lab today. Due to intellectual property protection blah blah and the fact that I don’t want anyone else to beat me to my research goal I will not describe what this is, I’ll just say that it took months of preparation and today – presto! It worked beautifully =oD