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.

This chapter introduces the physical principles underlying the models of electrical activity of neurons. Starting with the neuronal cell membrane, we explore how its permeability to different ions and the maintenance by ionic pumps of concentration gradients across the membrane underpin the resting membrane potential. We show how these properties can be represented by an equivalent electrical circuit, which allows us to compute the response of the membrane potential over time to input current. We conclude by describing the integrate-and-fire neuron model, which is based on the equivalent electrical circuit.

The nervous system consists of not only neurons, but also of other cell types such as glial cells. They can be modelled using the same principles as for neurons. The extracellular space (ECS) contains ions and molecules that affect the activity of both neurons and glial cells, as does the transport of signalling molecules, oxygen and cell nutrients in the irregular ECS landscape. This chapter shows how to model such diffusive influences involving both diffusion and electrical drift. This formalism also explains the formation of dense nanometre-thick ion layers around membranes (Debye layers). When ion transport in the ECS stems from electrical drift only, this formalism reduces to the volume conductor theory, which is commonly used to model electrical potentials around cells in the ECS. Finally, the chapter outlines how to model ionic and molecular dynamics not only in the ECS, but also in the entire brain tissue comprising neurons, glial cells and blood vessels.