Biomedical Engineering Reference
In-Depth Information
In this chapter I will discuss the requirements for biologically-detailed, realistic
network modelling. The requirements are divided into those for the neuron models,
the synaptic models, the pattern of connections between cells, the network inputs. I
will then discuss implementation of the model - choice of simulation environment
and numerical issues. Finally I will discuss putting-it-all-together - validation of the
network model as a whole. To illustrate these requirements I will use a model of the
granule cell layer in the cerebellum by Maex and De Schutter [23] and a model of
olfactory bulb developed by the author and collaborators [7, 8].
10.2
Cells
Most if not all biologically-realistic single neuron models are based on Hodgkin-
Huxley-like ion channel models [18] and the compartmental/cable modelling of
dendrites introduced by Rall [30]. Examples include models of cerebellar Purkinje
cells by De Schutter and Bower [11, 12], of olfactory bulb mitral cells by Bhalla and
Bower [3] and CA3 hippocampal pyramidal cells by Traub et al. [39]. For further
examples see the Senselab ModelDB website (http://senselab.med.yale.edu/SenseLab
/ModelDB).
These models are in general very complex and their simulation requires solution
of thousands of differential equations. The Bhalla and Bower mitral cell model, for
example, has almost 300 compartments with up to six ion channel types in each. The
De Schutter and Bower Purkinje cell model has 1600 compartments and nine ion
channels. Simulation of such models requires large amounts of computer power and
they are therefore in practice unsuitable for use in network models where hundreds
or thousands of cells must be simulated.
For network modelling we therefore require neuron models with a lower level
of complexity that nevertheless retain as much fidelity to the biology as possible.
A number of strategies have been used to construct such intermediate-complexity
single cell models. All take as their starting point a detailed compartmental neuron
model and attempt to simplify it while retaining the electrotonic properties and/or
input-output behaviour of the detailed model. One strategy is to concentrate on the
electrotonic properties and reduce the number of compartments in the cell while
conserving the membrane time constants and the cell input resistance [6, 37]. A
more drastic strategy is to attempt to abstract the key features of the cell into as
few compartments and channel types as possible, and constrain the simplified model
to have the same input-output properties as the detailed model, in terms of firing
rate response to synaptic or electrical stimulation [27]. Both strategies give shorter
simulation times than the fully-detailed models.
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