3D Printing Neuron Equivalent Circuits: An Undergraduate Laboratory Exercise

Abstract

The electrical equivalent circuit for a neuron is composed of common electrical components in a configuration that replicates the passive electrical properties and behaviors of the neural membrane. It is a powerful tool used to derive such fundamental neurophysiological equations as the Hodgkin-Huxley equations, and it is also the basis for well-known exercises that help students to model the passive (Ohmic) properties of the neuronal membrane. Unfortunately, as these exercises require basic knowledge of electronics, they are generally not physically conducted in biomedical courses, but remain merely conceptual exercises in a book or simulations on a computer. In such manifestations, they lack the "hands-on" appeal for students and teachers afforded by laboratory experimentations. Here, we propose a new approach to these experiments in which a desktop 3D printer and conductive paint are used to build the circuit and the popular programmable microcontroller, the Arduino UNO, is used as a graphical oscilloscope when connected to a standard computer. This set-up has the advantage of being very easy to build and less clumsy than a circuit in a prototyping board or connected with alligator clips, with the added benefit of being conveniently portable for classroom demonstrations. Most importantly, this method allows the monitoring of real-time changes in the current flowing through the circuit by means of a graphical display (by way of the Arduino) at a fraction of the cost of commercially available oscilloscopes.

Keywords: 3D printing; Arduino UNO; DIY; electrical equivalent circuit; neuron electrical model; oscilloscope.

Figure 1

The 3D printed components. The main board is divided into a smaller section (left) which holds the Arduino microcontroller and a larger working space (right) in which resistors (R1 and R2) and capacitors (C) can be attached and detached easily. There are also three deep square wells in which wires will be attached that can plug into the pin connectors on the Arduino. These wells are labeled in the diagram according to the pin connector on the Arduino that they connect to: analog input pin A5, digital output pin 13 and any of the three ground (GND) pins. The second, much smaller printed piece (far right) is printed (at least) in quadruplicate, and contains two holes through which a resistor or a capacitor can be attached. Attaching resistors and capacitors is thus as simple as plugging the smaller printed part holder into the appropriate spot on the working space, where it fits snug in a complementary fashion, not unlike Lego building blocks.

Figure 2

Circuit diagram of the printed project shown in the Figure 1. Note that the capacitance is in series with the resistance in this circuit, not parallel as is envisioned in the cell membrane. This provides electrical isolation between the input and output pins of the Arduino. The time constant is the product of resistance and capacitance whether or not they are in parallel or in series. According to Thévenin’s Theorem, the parallel RC configuration of the membrane is a linear circuit that can be reduced to a single voltage source and a single resistance in series with a load, which is in this case the capacitor across which the voltage is read by the Arduino.

Figure 3

Effect of “ion channels” on membrane voltage rise time. In the upper panel, the circuit consists of a 100 MΩ resistor at R1, a 100 nF capacitor at C and R2 is open. In the lower trace, there is also a 100 MΩ resistor at R2. This simulates a doubling of the number of open ion channels in the membrane, and it is evident from the charging curves that the time constant is approximately twice as long. Note that there is stray resistance from the electroconductive paint throughout the circuit that may make the measured time constants significantly longer than would be predicted from the resistor and capacitor alone. These exercises are meant to visually relate the time constant to resistance and capacitance, as a supplement to simulations and calculations traditionally done in neurobiology classes.

Figure 4

Effect of membrane capacitance on the charging time of the membrane. Upper trace: In this configuration, there is a 100 MΩ resistor at position R1 but both positions R2 and C are open. With the capacitor removed, it is clear that the voltage measured at A5 changes instantaneously with the voltage change at pin 13. Lower trace: The configuration has a 100 MΩ resistor at position R1, position R2 is open, and there is a 1μF capacitor at the C position. Compare these traces to the upper panel of Figure 2, which also has a total resistance of 100 MΩ.

Figure 5

A demonstration of temporal summation using the project. The settings include a pulse duration of 50 ms, a duty cycle of 0.75 and 5 pulses per train.