Lu.i experiment

Overview

To get accustomed to the concept of neuromorphic computation, you will work with Lu.i. Lu.i is an electronic neuron circuit mimicking and illustrating the basic dynamics of real, biological neurons. The printed circuit board (PCB) features a configurable, fully analog implementation of the leaky integrate-and-fire model and visualizes the internal state, the membrane potential, through a VU-meter-style chain of LEDs. The neuron emits a short pulse whenever the membrane potential crosses a predefined threshold voltage. Neurons communicate by exchanging these spikes because multiple boards can be connected via jumper wires to form networks.

../_images/lui-with-coin_lq_cropped.jpeg

You may find additional information including schematics in the main paper and on the project’s homepage, giantaxon.org.

Exercises

Getting familiar with Lu.i’s parameters

Before you begin, connect Lu.i’s membrane to the oscilloscope.

  • Familiarize yourself with the parameters of the neuron emulation. What happens if you increase the leak potential? Can you observe the membrane time constant? Note the impact of the individual potentiometers.

  • Connect two or multiple neurons to form a simple network and note how signals propagate across neurons, e.g., while playing with the synaptic weights and the synaptic time constant.

  • Pick a configuration where you can approximately measure \(\tau_\text{ref}\) and the threshold \(\vartheta\). Take notes of your results and your methods of determining the individual parameters.

Note

Keep the setting for the membrane time constant \(\tau_\text{mem}\) fixed for the following task.

Measuring of an f-I curve

Next, you will record your first f-I curve, i.e., the dependence of a neuron’s firing rate on its stimulating current. For this purpose, you will rely on a voltage-controlled current source.

../_images/lui_current_source.png

The output current of this circuit is governed by the following equation:

\[I(U) = \frac{V_\text{CC}-U}{R_\text{sense}}\]

In the present case, \(R_\text{sense}\) is 10 kΩ and the supply voltage of the voltage-controlled current source \(V_\text{CC}\) is 5V. Note that this supply voltage is different from that of the Lu.i. board, which is 3.3V, as indicated on its battery.

Make sure that Lu.i’s membrane is connected to both the oscilloscope and the current source. A second set of cables allows you to read out the voltage at the lower node of \(R_\text{sense}\) at the same time such that you can calculate the voltage drop across the resistor and thus the current.

  • Set the leak potential at its minimum. Now measure about 20 firing frequencies as a function of the input current to Lu.i.’s membrane. Make sure that the controlling voltage drop \(U\) measured on the oscilloscope is in a range of \(1.75V\) to \(5V\).

  • Plot your results.

  • Derive an equation for \(f_\text{theo}(I)\). Your function should depend on the chosen parametrization of the LIF equation, namely \(\vartheta\), \(C_m\), \(R\), and \(\tau_\text{ref}\). Here \(R\) is the membrane resistance of the Lu.i. board, the inverse of the membrane conductance, and \(C_m\) is the membrane capacitance. You might need to define your integration limits. (Hint 1: Consult equation (2) as a starting point; hint 2: You’ll find \(R\cdot I > \vartheta\) as a condition)

  • Fit the function to your measurements. You might find it helpful to extract the membrane capacitance value from the circuit diagram.