121
by a long branch, as shown in Figure 4.2. This neuron is the most highly-branched
one considered thus far, having 132 dendrites, and nearly half of these are contained
in the weak part, indicating the potential for a large reduction in dimension.
I discretize this cell with a desired compartment length of Ax = 2 μm, yielding
a model with 3996 compartments. The transition compartment is located ~ 94
pm from the distal end of dendrite 60 (see Figure 4.4), leading to strong and weak
dimensions of Ns = 1898 and Nw = 2097. The weak system is approximated using
kw = 15. Like the fork studies of the previous section, I run sets of 20 simulations
of 1000 ms each using the MIG and the MIG-P ion channel models. During each
simulation I apply 2000 step currents lasting 0-2 ms and having amplitudes of 0-
1500 pA to random dendritic locations. In order to reduce numerical instabilities in
the computed solutions, I use a time-step of At = 0.01.
The results of these simulations are shown in the histograms of Figure 4.3. Note
that the RSW model consistently performs better than the POD+DEIM model. The
RSW model is still significantly slower than the POD+DEIM one, but as mentioned
before this can be improved with optimized code. Furthermore, as shown in Figure
4.4, the RSW voltage traces more closely match those of the full system. This offers
evidence that the RSW model can improve accuracy for large cells using smaller
reduced system sizes than the POD÷DEIM model alone.
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