Neural modeling takes place on a variety of levels, depending on the purpose and resources available. More abstract models are easier to analyze and understand, and can be implemented most efficiently on conventional computers. More detailed models mirror biological reality more faithfully, but this complexity reduces our ability to rigorously analyze the system.

Four common levels of modeling, from abstract to detailed, are:

• Artificial Neural Networks

  ANNs are generally composed of elements which sum their inputs, apply an activation function, and generate an analog output. In "feed-forward" neural networks, this is only done once; activity driven by the input pattern is transformed into activity at the output pattern. Recurrent networks have reciprocal synapses, and so the update cycle may be repeated until the network reaches a stable state. Synaptic weights are often set by using a gradient-descent algorithm to minimize the output error over a training set. Elements in an ANN are only vaguely analogous to real neurons.

• Integrate-and-Fire Models

  In these models, the cells' output takes the form of discrete events ("action potentials" or "spikes"). One cell affects the others only when it spikes. At that point, the postsynaptic cells are updated (usually in a simple manner, e.g. adding a constant to the membrane potential), and their new firing times are calculated. Integrate-and-fire models can generate very realistic-looking spike trains, despite their very simple equations.

• Kernel-based Models

  A modeling paradigm which is receiving increased attention is based on kernels, which are simply arrays of numbers. Kernel 0 is a single number which represents the cell's average firing rate (or average membrane potential). Kernel 1 is a one-dimensional array, and determines the cell's response to past input. Kernel 2 is two-dimensional, and sets the cell response to combinations of inputs, and so on. Very realistic cell simulations can often be obtained with only the first three kernels. These simulations treat each neuron as a "black box" and can produce very complicated behavior, but it can be hard to relate the kernel numbers to any physiological values.

• Compartmental Models

  The most biologically detailed type of simulation is the compartmental model, described in more detail in the next section. This model actually implements the detailed morphology of a neuron. The neuron is divided into small compartments, and membrane potential at each compartment is determined by its neighbors, as well as active and passive ion channels. Compartmental models have the advantage that real physiological values (e.g., channel kinetics, cell morphology, etc.) can be directly implemented.

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