Multiscale computer modeling of brain excitability: applications to spreading depression and neuronal impedance

Abstract

Multiscale modeling of biological systems integrates disparate experimental results into unified theoretical frameworks. We used multiscale modeling to investigate excitability in neural systems at the scales of dendrites, single neurons, and tissue-scale activation patterns. We employed impedance analysis to study subthreshold excitability in morphologically and biophysically detailed models of neocortical layer 5b pyramidal neurons, which predicted that the interaction of hyperpolarization-activated cyclic nucleotide-gated (HCN) and Twik-associated acid-sensitive K+ (TASK) channels are integral to producing their observed impedance profiles. Impedance analysis is properly limited to studying neuronal responses to small, subthreshold stimuli, but this excludes a great deal of neuronal function. To overcome the limitations of impedance analysis, we developed an analog to impedance phase to characterize high amplitude signals, both sub- and suprathreshold. For high amplitude stimuli, we found different phase shifts during hyperpolarizing and depolarizing half-cycles. We also found two nonstationary phase relationships between spiking and stimulus: phase retreat, where action potentials occurred progressively later in cycles of the input stimulus resulting from adaptation, and phase advance, where action potentials occurred progressively earlier. In a separate study, we developed a computer model of spreading depolarization (SD) in brain slices using the NEURON simulator: 36,000+ neurons in the extracellular space (ECS) of a slice with ion and oxygen (O2) diffusion and equilibration with a surrounding bath. Simulations reproduced key features of SD, including its speed moving across the tissue and firing properties of individual neurons, and led to a number of experimentally-testable predictions. We have also developed a model of neocortex in vivo with realistic distributions of O2 sources based on histology from human subjects. This model can be used to investigate the role of connectivity in SD propagation and how ischemic insults lead to SD initiation.