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 diffusion of ions in the extracellular space of the brain is normally assumed to have negligible effects on extracellular potentials. However, during periods of intense neural activity or in pathological conditions such as spreading depression, concentration gradients in brain tissue can become quite pronounced, and the effects of diffusion on electric potentials cannot be a priori neglected. We here present the theory for computing diffusion potentials, and we evaluate whether diffusion potentials can become “visible” within the frequency range considered in standard LFP recordings.

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.

Models of extracellular potentials are typically based on treating brain tissue as a continuous volume conductor. An important parameter, or sometimes variable, in volume-conductor theory is the conductivity. Here, we present both theoretical and experimental estimates of the conductivity of brain tissue. A common modeling approximation is to assume that the conductivity does not vary with position, is the same in all directions, and does not depend on the frequency of the electric signal. With references to both experimental and theoretical studies, we discuss whether these approximations are reasonable, and we introduce ways to relax these approximations in models.

We here round off a book on biophysical foundations and computational modeling of electric and magnetic signals in the brain. We summarize some key insights from such modeling, and we clear up some common misconceptions about extracellular potentials. We address the main limitations with the standard modeling framework used to compute extracellular potentials, discussing the uncertainty in model parameters and its neglect of ephaptic interactions between active neurons. We identify what we believe are key areas of future applications and give an outlook for future modeling challenges.

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). Here, we present the volume-conductor theory used in step 2. The neural output from step 1 can be represented in terms of (i) a set of point sources, (ii) a set of line sources, (iii) a current-source density, or (iv) one or several current dipoles. We derive equations for the extracellular potential under the approximations (i–iv), discuss the validity and applicability of the different approximations, and explain how they are related. We also discuss how to model the effects that the electrode itself can have on the measured extracellular potential.

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.