fraction

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 $\mathbf{r}$ is a superposition: $\phi(\mathbf{r},t) = \frac{1}{4\pi\sigma}\sum_{n}\frac{I_n(t)}{\lVert \mathbf{r}-\mathbf{r}_n \rVert}$. 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…

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