Gives a brief review of systems biology and synthetic biology with populations of bacteria.

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.

Readers who do not have strong schooling in physics can consult this book chapter for an introduction to key concepts such as ion fluxes, electric fields, electric potentials, and electric currents as well as for definitions of the ohmic, electrodiffusive, and capacitive currents that govern the electrodynamics of brain tissue. Building on the biophysical principles and approximations introduced here, we explain how the electric potential surrounding neurons can be computed based on the principles of current conservation and electroneutrality, and wegive a brief overview of modeling schemes designed to perform such computations on computers. Towards the end of the chapter, we show how the standard theory for computing extracellular potentials relates to Maxwell’s equations and list the approximations that we typically make when we apply these equations in a complex medium like brain tissue.

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 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.