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1.2 Neuronal Modeling Methods

Currently it is impossible to simulate a biophysically accurate brain, though signif-
icant progress has been made toward this goal. The common approach to this problem
is to build networks of individual cells and then perform simulations to investigate
neural functions. The Blue Brain Project leads this area of research, having reached
a milestone of simulating a full cortical column (Markram, 2006). However, these
successes generally have come from advances in hardware rather than in modeling
methodologies. For example, the Blue Brain Project utilizes thousands of processors
running in parallel to achieve its goals, but progression to larger or more detailed
simulations will require waiting for Moore’s Law to yield corresponding increases in
processing power (Lansner, 2009). In contrast, a better model of individual cells will
work with existing hardware and, if it is more accurate or faster than current models,
will permit the next step in brain simulation to be achieved.

This type of “bottom-up” approach to brain modeling has as its foundation the
type of single-cell model that is used. Over a century of research has produced a
myriad of model neurons whose complexity has grown steadily. At the simplest level
are isopotential cells, which compress the entire neuronal morphology into a single
compartment. These can be extremely basic, such as the binary summing units of
McCulloch-Pitts models (McCulloch and Pitts, 1943), or they can be more complex
and include nonlinear biophysical mechanisms like ion channel kinetics, as in the
case of the Hodgkin-Huxley model (Hodgkin and Huxley, 1952). Between these

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