← All parts of this equation

Equation 2 · Part 10 · What a Neural Recording Actually Records

subscript

ϕ(r,t)=14πσ∑nIn(t)∥r−rn∥\phi(\mathbf{r},t) = \frac{1}{4\pi\sigma}\sum_{n}\frac{I_n(t)}{\lVert \mathbf{r}-\mathbf{r}_n \rVert}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Start with the most direct measurement available. A metal or silicon electrode placed in the extracellular space senses the potential produced by transmembrane currents in the surrounding tissue. Under the standard volume-conductor treatment, with the medium approximated as homogeneous, isotropic and purely resistive, and each current source treated as a point, the potential at position r\mathbf{r} is a superposition: ϕ(r,t)=14πσ∑nIn(t)∥r−rn∥\phi(\mathbf{r},t) = \frac{1}{4\pi\sigma}\sum_{n}\frac{I_n(t)}{\lVert \mathbf{r}-\mathbf{r}_n \rVert}. Three assumptions are visible in that expression, and all three are approximations rather than facts. The medium is not homogeneous. Conductivity may be frequency-dependent. And the sum runs over every current source in range, not over the neuron of…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.