Biomedical Engineering Reference
In-Depth Information
Threshold
FIgURE 2.4:
Threshold and fire or integrate and fire model.
(passive leak) resistance, and absolute refractory period. It is a good approximation over the normal
operating range of most neurons, and it introduces the important nonlinearity (threshold) of real
neurons (i.e., the neural spike). The threshold-fire neuron also has a few limitations, which include
the lack of spatial extent (they are “point” neurons) and the electrochemical properties of dendrites
are neglected. Membrane ionic currents tend to be nonlinear functions of both membrane potential
and time. The linear summation of dendritic inputs is also inconsistent with the highly irregular
firing statistics found in most cortical neurons.
∂
u t
t
( )
=− +
u t
( )
RI t
( )
∂
(2.1)
This figure represents what has been called a generalized linear model, which is much more
complex because of the feedback. Although the threshold-fire provides a computational approach
to simulating the occurrences of spiking neurons, in practice in the electrophysiology laboratory,
neuroscientists have dealt with the complexities of the raw extracellular potentials by developing a
discrete representation for neuronal activity. The nature of the “all-or-nothing” firing of the action
potential event has lead to the common treatment of action potentials as point processes where the
continuous voltage waveform is converted into a series of timestamps indicating the instance when
the spike occurred. Using the timestamps, a series of pulses or spikes (zeros or ones) can be used
to visualize the activity of each neuron; this time-series (Figure
2.3
c) is referred to as a
spike train
.
Here, a group of electrodes are capable of capturing a subsampling of the local population (white
dots) of neuronal activity indicated by the black dots.
2.5 SToChaSTIC ModElINg
Single-neuron recording of this type and the analysis of spike trains reveal that most often neural
responses are enormously irregular under constant stimulus. The spike trains of neural populations
have several properties including sparsity and nonstationarity. This is a very different result from
the threshold-fire model activity discussed previously. How do we quantify and describe the neural
