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 volume-conductor theory to compute the extracellular potential resulting from these membrane currents (step 2). In this chapter, we introduce ways to implement this scheme in computer simulations based on designated software such as LFPy, the NEURON simulator, or the Arbor simulator. We also introduce various methods for reducing the computational cost of simulating the extracellular potentials of large networks of neurons as well as introduce heuristic approximate signal prediction methods.

When a neuron fires an action potential, it causes a rapid fluctuation in the extracellular potential. This fluctuation is referred to as a spike and is normally “visible” only close to the neuron it originates from. Spikes are typically studied experimentally by high-pass filtering the extracellular potential. Here, we use computer simulations and approximate analytical formulas of spikes to explore how the amplitude and shape of spikes depend on various factors such as (i) the morphology of the neuron, (ii) the presence of active ion channels in the neuron’s dendrites, (iii) the part of the neuron (soma vs. dendrite) where the spike is recorded, (iv) the distance from the neuron the spike is recorded, and (v) the location in the neuron that the action potential is initiated. We also briefly discuss how the presence of the electrode can affect spike recordings as well as how to analyze data containing overlapping spikes from several neurons simultaneously.

The local field potential (LFP) is the low-pass filtered extracellular potential recorded inside brain tissue. Unlike spikes, which reflect neuronal action potentials and thus the output of neurons, the LFP is believed to predominantly reflect the synaptic inputs to neurons. Here, we use computer simulations and approximate analytical formulas of LFPs from single neurons and populations of neurons to give a comprehensive overview of the various factors that can contribute to shaping the LFP and its frequency content. We consider the effects of neural morphology, intrinsic dendritic filtering, synaptic distributions, synchrony in synaptic inputs, the position of the recording electrode, and possible contributions from action potentials, calcium spikes, NMDA spikes, and active subthreshold dendritic ion channels.

The electrocorticographic (ECoG) signal is the electric potential recorded above the cortical surface and reflects the combined activity of large populations of neurons. As ECoG recordings are closer to the neuronal sources than the EEG recordings and further away than LFP recordings, approximations used when modeling LFPs and EEG signals can not a priori be used to model ECoG signals. Here, we give a brief overview of the challenges involved when modeling the ECoG signal and give an overview of previous modeling studies.

The electroencephalographic (EEG) signal is the electric potential recorded on the scalp, and it is believed to originate from the combined activity of large populations of neurons. In forward models of EEG signals, one typically (i) represents neuronal sources in terms of effective current dipoles, (ii) defines a head model, which is a specification of the conductivity profile for the medium between the sources and the recording position (brain tissue, cerebrospinal fluid, skull, scalp), and (iii) uses volume-conductor theory to compute the resulting electric potential at the scalp. In this chapter, we introduce the key theory and computational frameworks for modeling EEG signals. We illustrate how biophysically detailed models of neurons can be reduced to approximate equivalent dipoles, and we discuss further ways to simplify neural simulations in order to reduce the computational cost. Using a combination of computational modeling and analytical approximations, we analyze how various factors are involved in shaping the EEG signal.

The magnetoencephalographic signal is the magnetic field recorded outside the scalp of the head. It is believed to originate from the combined activity of large populations of neurons. In forward models of MEG signals, the neural output is typically represented in terms of equivalent current dipoles. We here go through the mathematical equations for computing MEG signals from current dipoles, present computer simulations of MEG signals using simplified models of the head geometry, and show how the predicted MEG signals depend on the chosen head model and orientations of the dipoles. We also present a formalism for modeling the magnetic field inside brain tissue.