96
system, as Table 3.10 illustrates. Compared to Table 3.6 the accuracy and speed-
ups in Table 3.11 are less, due to the fact that synaptic input is more complex than
current injection, but the reduced system is still very successful at capturing the cell’s
behavior.
Table 3.10: Alpha synapse shutoff mechanism (ε = 10 4) accelerates the reduced system
of neuron AR-l-20-04-A.
|
Type |
Dimension |
Sim. Time (sec) |
With shutoff |
|
Full |
N = 2233 |
115 |
115 |
|
Reduced |
kv = kf = 60 |
41 |
15 |
|
Reduced |
kv == kf = 90 |
73 |
32 |
Table 3.11: AR-l-20-04-A, N = 2233 (here kv = feʃ), 500 alpha synapses, HHA model.
|
kv |
Speed-up |
% Matched |
% Mismatched |
Γ |
|
60 |
8.4× |
86.6 |
22.8 |
0.807 |
|
75 |
5.9× |
92.8 |
12.8 |
0.894 |
|
90 |
4.7× |
93.9 |
15.1 |
0.886 |
|
105 |
3.6× |
98.6 |
6.8 |
0.955 |
|
120 |
2.9× |
98.6 |
5.9 |
0.961 |
3.6 Discussion
We have applied nonlinear model reduction techniques to morphologically realistic
cells in a way that preserves the input-output relationships while accurately reproduc-
ing the complete voltage dynamics. We approximate the voltage using a POD basis,
which reduces the number of state variables. Using the DEIM we build a set of spa-
tial interpolation points and basis vectors to reduce the complexity of the nonlinear