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The standard two-step scheme for modeling extracellular signals is to first compute the neural membrane currents using multicompartment neuron models (step 1) and next use the volume-conductor theory to compute the extracellular potential resulting from these membrane currents (step 2). We here give a brief introduction to the multicompartment modeling of neurons in step 1. The formalism presented, which has become the gold standard within the field, combines a Hodgkin-Huxley-type description of membrane mechanisms with the cable theory description of the membrane potential in dendrites and axons.
It is common to study the electric activity of neurons by measuring the electric potential in the extracellular space of the brain. However, interpreting such measurements requires knowledge of the biophysics underlying the electric signals. Written by leading experts in the field, this volume presents the biophysical foundations of the signals as well as results from long-term research into biophysics-based forward-modeling of extracellular brain signals. This includes applications using the open-source simulation tool LFPy, developed and provided by the authors. Starting with the physical theory of electricity in the brain, this book explains how this theory is used to simulate neuronal activity and the resulting extracellular potentials. Example applications of the theory to model representations of real neural systems are included throughout, making this an invaluable resource for students and scientists who wish to understand the brain through analysis of electric brain signals, using biophysics-based modeling.
The membrane potential of a neuron varies widely across the spatial extent of a neuron. The membrane may have spatially distinct distributions of ion channels and synaptic inputs arrive at different dendritic locations and propagate to the cell body. The membrane potential varies along axons, as the action potential propagates. We therefore need neuron models that include spatial, as well as temporal, dimensions. The most common approach is compartmental modelling in which the spatial extent of a neuron is approximated by a series of small compartments, each assumed to be isopotential. In limited cases of simple neuron geometry, analytical solutions for the membrane potential at any point along a neuron can be obtained through the use of the cable theory. We describe both modelling approaches here. Two case studies demonstrate the power of compartmental modelling: (1) action potential propagation along axons; and (2) synaptic signal integration in pyramidal cell dendrites.
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