Biomedical Engineering Reference
In-Depth Information
grams have been described (63-67). These programs generally provide a net-
work definition phase, in which the user specifies the numbers and types of cells
required and the rules for generating connections between them. These connec-
tions can be entirely prespecified, perhaps by input matrices, or can be generated
at random according to specified statistical rules. The program builds appropri-
ate data structures in memory according to these specifications. Also provided
are suitable constructs to define the dynamical properties of the cells in the net-
work. The details of this process vary according to the type of cell being mod-
eled (rate-coded, integrate-and-fire, multicompartment, etc.) and the method of
treating synaptic inputs. Full-featured general-purpose simulators will also pro-
vide methods for stimulating the network and for recording cell responses and
relevant statistics such as mean firing rates.
Greater operating speed, at the cost of significantly longer development
time and the need for specialized engineering knowledge, can be obtained by the
construction of special purpose simulation hardware, otherwise known as "neu-
romorphic" devices (see Part IV, chapter 6 [by Northmore, Moses, and Elias],
this volume).
The detailed method of updating in network models needs to be considered
carefully. The time step must be small enough to provide reasonable accuracy,
but as large as possible to minimize computing time. More complex integration
schemes, such as Runge-Kutta methods, may allow the time step to be increased
relative to straightforward Euler integration but at the cost of greater computa-
tional complexity (68). More aggressively, the step size can be adapted to cellu-
lar activity, small when rapid changes in membrane potential are occurring,
large at other times (69). Taken to an extreme, this idea leads to event-driven
modeling (70), in which the equations for
V
m
are solved analytically in the ab-
sence of synaptic input. Detailed simulation is then only necessary when input
disturbs the analytical solution. However, in network models, events of interest
occur at different times in different cells, making the bookkeeping for such
models very difficult.
An additional consideration is the method of updating cell activity levels as
seen by other cells. If cell firings are propagated to postsynaptic cells as soon as
they are computed, then cells earlier in the update cycle will have an artificial
advantage in competitive networks. On the other hand, if cell firings are propa-
gated simultaneously at the end of each update cycle, then artifactual oscillations
may be observed in the overall network. These problems can be mitigated by
randomly changing the update order in each cycle, but then special care must be
taken to allow simulation runs to be replicated, and replication will be particu-
larly difficult or lead to unacceptable serialization in a parallel computing envi-
ronment.
In summary, a great variety of simulation techniques and software packages
for neuronal and neuronal network simulation is available. When contemplating
a new modeling project, the prospective modeler should carefully consider the
