74
solve both systems we use ∆t = 0.1 ms. We vary the dimension of the reduced
system, using kv = kf, and run 20 simulations at each value (the same 20 input
patterns were used for each reduced system). The results, shown in Table 3.1, indicate
that reduced systems nearly 100-fold smaller than the original ones reproduce highly
accurate spiking patterns and are about 5 times faster.
It should be noted that throughout this thesis we use kv = kf, which is justified by
results of studies we performed on simple morphologies. For these studies we varied
kυ and kf independently and computed the performance metrics for each pair, but we
always found that kv = kf was the best choice. Hence we use this empirical heuristic
even for complex morphologies.
Table 3.1: Performance of reduced model (here kv = feʃ) of HH fiber, N = 1401, as
compared with the full model.__________________________
|
kv |
Speed-up |
% Matched |
% Mismatched |
Γ |
|
10 |
6.3× |
87.4 |
8.2 |
0.893 |
|
15 |
5.9× |
98.9 |
1.1 |
0.988 |
|
20 |
5.6× |
99.7 |
0 |
0.998 |
|
30 |
4.6× |
100 |
0.6 |
0.997 |
To assess the effects of different ion channel models on accuracy and speed, we
perform the same experiment, but with a channel model incorporating an A-type
K+ current (HHA model). Due to the decreased excitability of the distal part of the
fiber, we increase the number of stimuli to 500 and the range of amplitudes of the
step currents to 0-300 pA. As shown in Table 3.2, although the accuracy initially
decreases for very small kv values, it is rapidly regained so that nearly exact spike