vii
3.2.2 Reduction of the Nonlinear Term via the Discrete Empirical
Interpolation Method....................... 65
3.2.3 Numerical Solution of the Reduced System........... 69
3.3 Results on Simplified Morphologies................... 71
3.3.1 Straight Fiber........................... 71
3.3.2 Challenges of Branched Cells .................. 75
3.3.3 Forked Neuron Results...................... 83
3.3.4 Branched Cell Obeying Rall’s 3/2 Power Law......... 85
3.4 Results on Realistic Morphologies.................... 87
3.4.1 Results on Neuron AR-l-20-04-A................ 87
3.4.2 Results on Other Morphologies ................. 88
3.4.3 Cells With Weakly Excitable Dendrites............. 91
3.5 Synaptic Conductances vs. Current Injection.............. 94
3.6 Discussion................................. 96
4 The Reduced Strong-Weak Model 99
4.1 Constructing the Strong-Weak Model.................. 100
4.1.1 Model Reduction of the Weak Part............... 106
4.1.2 Model Reduction of the Strong Part............... 107
4.1.3 Results for the Reduced Strong-Weak Fiber.......... 109
4.2 Generalizing the Strong-Weak Model to Arbitrary Morphologies ... Ill
4.3 Results on Branched Cells........................ 118
4.3.1 Forked Neuron Results...................... 118
4.3.2 Neuron pl8 Results........................ 120
4.4 Discussion................................. 122
5 Future Work 127
5.1 Modeling Synaptic Inputs via Receptors................ 127
5.1.1 Reduction of the NMDA Magnesium Block Term....... 129
5.2 Augmenting the POD and DEIM Snapshot Sets............ 131
5.3 Network Simulations of Reduced Cells ................. 132
6 Conclusion 134
A Constructing the Hines Matrix 136
A.l Current Implementation......................... 136
A.2 Second-order Approximations of Boundary Conditions ........ 141
B Ion Channel Kinetics 142
Bibliography 145
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