Figure 1. The Neuron Circuit.
This page is about my spiking neuron circuit, which I plan to use as a building block in my electronic auditory pathway. On this page, I'll compare the measured output of the chip with the Post Stimulus Time Histograms (PSTHs) of the different Ventral Cochlear Nucleus (VCN) neurons. I'm able to create other types of neurons too with this chip, but I chose to start with the VCN neurons, since their PSTHs are well known, and do not need inhibition as some Dorsal Cochlear Nucleus (DCN) neurons do. I should be able to create this inhibition to with my chip, but I haven't got to testing it yet.
The proposed neuron model is shown in figure 1. The membrane of a biological neuron is modeled by a capacitance, Cmem, and the membrane leakage current is controlled by the gate voltage, Vleak, of an NMOS transistor. In the absence of any input (Iex=0), the membrane voltage will be drawn to its resting potential (controlled by Vrest), by this leakage current. Excitatory inputs simply add charge to the membrane capacitance, whereas inhibitory inputs are simply modeled by a negative Iex. If an excitatory current larger than the leakage current of the membrane is injected, the membrane potential will increase from its resting potential. This membrane potential, Vmem, is compared with a controllable threshold voltage Vthres, using a basic transconductance amplifier driving a high impedance load. If Vmem exceeds Vthres, an action potential will be generated.
The generation of the action potential happens in a similar way as in the biological neuron, where an increased sodium conductance creates the upswing of the spike, and a delayed increase of the potassium conductance creates the downswing. In the circuit this is modelled as follows. If Vmem rises above Vthres, the output voltage of the comparator will rise to the positive power supply. The output of the following inverter will thus go low, thereby allowing the "sodium current" INa to pull up the membrane potential. At the same time however, a second inverter will allow the capacitance CK to be charged at a speed which can be controlled by the current IKup. As soon as the voltage on CK is high enough to allow conduction of the NMOS to which it is connected, the "potassium current" IK will be able to discharge the membrane capacitance.
Two different potassium channel time constants govern the opening and closing of the potassium channels. The current IKup which charges CK will control the spike width, since the delay between the opening of the sodium channels and the opening of the potassium channels is inversely proportional to IKup. If Vmem now drops below Vthres, the output of the first inverter will become high, cutting off the current INa. Furthermore, the second inverter will then allow CK to be discharged by the current IKdown. If IKdown is small, the voltage on CK will decrease only slowly, and, as long as this voltage stays high enough to allow IK to discharge the membrane, it will be impossible to stimulate the neuron if Iex is smaller than IK. Therefore IKdown can be said to control the "refractory period" of the neuron. 32 neurons as shown in figure 1 have been realised, together with some circuitry to facilitate communication of signals on- and off-chip on a 1mmx2.5mm die, using the ECPD10 (1mm) technology of ES2. All transistors are 10mm/10mm except for the switches and inverters, which are 2mm/10mm, and CK and Cmem are 10pF.
The PSTHs of the 6 major types of neurons in the VCN are shown below, together with the measured output of my chip using different settings to model the different neurons.
The way I obtained these graphs is the following. I presented a 5kHz sinusoid (100mV peak-peak amplitude) of 40ms duration seperated by pauses of about the same length to the IHC circuit. The output of the IHC is a current which is proportional to the positive half of the input waveform only, and which has some temporal adaptation, giving it a higher output amplitude at the onset of the sinusoid.
The 32 neurons on the all have the same setting (bias voltages and currents) and in this case also have the same input current coming from the IHC. Whenever a neuron generates an action potential, it injects a fixed height, fixed duration current pulse onto the common output line. If all 32 neurons are synchronised, the current on the output line will be a single pulse 32 times as high as the unit current and only 1 unit duration long. (Off course, the unit current and unit duration are externally controllable parameters.) Since the pulse duration is relatively short, the timing would need to be exactly right for the currents to add up. This would not be possible considering the mismatch between the 32 neurons. However, I'm not measuring the output current with the oscilloscope, but the voltage difference created by this current over a 20 kOhm resistor. Since the chip's output pin, the board and the oscilloscope's probe all add a certain capacitance to this node, the output voltage will be a low-pass filtered representation of the output current, thereby summing current pulses arriving within a certain delay.
The final graphs are the result of the summed (arithmetically) responses of 20 repeated presentations of the input signal, normalised to the voltage created over the resistance by 1 unit current (to convert the voltage into a number of spikes).
The different graphs are obtained by playing mainly with the bias voltages that control the 'membrane leakage', the 'action potential threshold voltage' and the 'refractory period'.
N.B. All cells receive the same input. They generate different output due to the mismatches between the neurons. The threshold comparators have offsets; 15mV between adjacent comparators is a typical variation. The membrane leakage current will vary somewhere between 5 and 10 percent from cell to cell for a given setting, and the main influence is coming from the current controlling the refractory period, since this is a small current. The smaller the current, the smaller the relative precision. So for longer refractory periods, you'll get even more variation between the cells. A good example is to set the cell as a chopper which chops every 10ms; I get very nice big bumbs due to the 'Gaussian' spread of the refractory periods. (I'm not sure if the spread is actually Gaussian, but it should be something like it).
I presented a paper on this, entitled "An Analogue Electronic Model of Ventral Cochlear Nucleus Neurons," at MicroNeuro'96 which was held here at the EPFL, February 12-14, 1996. You can find a postscript version of the paper here. Off course you can always contact me by email.