Biomedical Engineering Reference
In-Depth Information
1.
NEURONAL SYSTEMS DYNAMICS
The nervous system is a complex object, and so the modeling of neuronal
systems dynamics is necessarily a complex subject. Space here permits only the
most superficial survey of some of the more common techniques. References are
given to textbooks and original literature where more details can be found. Dif-
ferent approaches are available depending on one's general philosophy about the
goals of modeling. Some believe, for example, that models should be used only
to test very explicit hypotheses, while others are happy to use models in a looser
mode simply to explore the consequences of a particular network architecture or
synaptic-efficacy modification rule. In evaluating published models, one should
always ask oneself to what extent the assumptions were chosen to give inevita-
bly the desired results (that is, whether the results were "built into" the model
from the start) or whether the assumptions were justified for principled reasons
other than their success at predicting the desired results. To avoid this potential
pitfall, some authors prefer a so-called "bottom-up" approach, in which model
features are derived as much as possible from experimental data. Others prefer a
"top-down" approach, in which a particular theoretical point of view, for exam-
ple, one based on a computational metaphor, is used to guide the choice of as-
sumptions. The former class of models is often referred to as "neurally realistic,"
whereas the latter may be only "neurally inspired." On the other hand, it can be
argued that simply putting all the known facts into a model may produce a good
emulation of some brain function, but may do little to indicate which particular
features of the nervous system make that function possible. In the end, these
decisions become a matter for expert debate. For our purposes, we would like to
understand better how the brain operates, of course, because this is one of the
remaining great questions in modern biology, but more specifically so we can
relate the basic principles of brain operation to the disruptions that occur in
pathological conditions, particularly tumor growth, a subject treated in Part III,
ยง6 (this volume). This would suggest that a rather detailed "bottom-up" ap-
proach would be most appropriate, keeping in mind always that computational
limits to our simulations are likely for some time to remain tighter than those
imposed by biology on the brain. Therefore, we must be careful to distinguish
these two sources of constraint when interpreting brain models.
1.1. Single-Neuron Models
We begin by asking how detailed a model of a single neuron must be in
order to make it useful for modeling complex neural systems (1). The basic
charge-balance equation that must be satisfied for any volume enclosed by an
active membrane is
