# Talk:Local field potential

## Contents |

## A quick comment

Apologies for commenting on an article that is still in progress, but I'd like to note that the draft so far is missing something very important -- this is something I learned a long time ago from theoretical papers by Charles Nicholson, especially the paper on CSD analysis by Nicholson and Freeman. Nicholson pointed out that it is impossible for charge to accumulate at any point in a conductive medium, and consequently the current source density across the entire membrane of a neuron must always sum to zero. The consequence is that every LFP can be decomposed into a sum of dipoles -- there is no monopole component. That means that the only way to get a large field is for the dipoles to align, which usually only happens when cells are arranged in layers. It also means that there is always going to be a polarity reversal between fields recorded from above and below a layer of generating cells (which is very useful to know for an experimenter trying to figure out the source of an LFP). William E. Skaggs 01:55, 1 August 2013 (UTC)

## Response:

This is indeed a very interesting issue, and you are right in a metal conductor, but it may not be true in biological media where the mobility of charge carriers (ions) is several orders of magnitude lower than electrons in a metal - there is a possibility for charge accumulation, and also for electric monopoles. Moreover, biological media are highly non-uniform (contrary to a uniform conductor in your reasoning), and so there will be accumulation of charges depending on the scale considered, in particular at "microscopic" scales (order of microns). At "macroscopic" scales (larger than the inhomogeneities), electroneutrality is respected and there is no monopoles at such scales. So it all depends on the scale the electrode sees...

Whether monopoles occur in neurons, and at which scales, should be investigated by appropriate experiments (see the discussion of these aspects in the article)

Alain Destexhe and Claude Bedard

- Thanks for the explanation. I can't say that I am totally convinced, but it makes sense. Best regards, William E. Skaggs 15:51, 15 August 2013 (UTC)

## Review of the article:

The article is very interesting, well written and gives much insight into the current understanding of LFP, especially for the non-specialist. Nevertheless the authors are asked to consider the following comments:

Introduction:

- since EcoG is mentioned in Fig.1, it is necessary to explain/mention it briefly in the Introduction since readers may take a look at Fig.1 and its caption when starting to read the article.

Example of LFPs generated by a simple model:

- it is suggested to replace the two sentences by a single one : " In this model, the spike-and-wave patterns were generated using a simple LFP model identical to the one explained above. The LFP was calculated using the standard model (see above), using a linear " --> " In this model, the spike-and-wave patterns were generated using the standard model (see above), considering a linear"

Frequency filtering properties of LFPs :

- The first paragraph is very similar if not identical to the last paragraph in the Introduction. One fully understands the motivation of re-calling the frequency properties of action potentials and post-synaptic potentials, but the authors should find another solution; maybe shortening dramatically the paragraph in the Introduction may be a solution.

Model of LFP in inhomogeneous extracellular space:

- To clarify what the authors mean by 'Fourier space' and for pedagogical reasons, it is suggested to replace "(written in Fourier space)" by "(written in frequency Fourier space)". In addition replace "gives the evolution " by "gives the spatial evolution" to clarify that there is no temporal evolution.

- paragraph starting with "This model of non-homogeneous…": it is necessary to explain that a single neuron is supposed to be located in the coordinate system origin and thus a decaying function \sigma(x) means an increasing distance from the (probably point-like) neuron. Or, equivalently, the authors should explain what they mean by 'distance' when stating "but in general when \sigma is high at short distances and decays with larger distances, a low-pass filter is observed. "

Example of a model of frequency-filtering LFPs:

- what do the authors mean by 'immediately' in "membrane is immediately surrounded " ? The extra-cellular fluid seems to always surround the neuron membrane and is not time-dependent.

- in addition, it seems to be more reasonable to include this section into the previous section "Model of LFP in inhomogeneous extracellular space" since it gives a nice example of the theory presented in the previous section.

- the expression "the initial conductivity" appears to be misleading and it is suggested to replace it by "the conductivity at the neuron".

Mean-field model of LFPs:

- there seem to be a typo in the parameter for the volume "V ol".

- please add that the volume Vol is assumed to be located at position \bar{x}.

- "This frequency dependence arises from the renormalization process, and is necessary for the macroscopic equations to be consistent.": please add further short explanations or add a reference.

Modeling the 1/f scaling of LFPs:

- typo in "…filter scaling as 1/sqrt(\Omega) (which will …."

Controversies about the sources of the LFP:

- typos in -- "suggesting the existence of monololar sources" -- "that in ome cases,"

- comment on "because charges will take a significant time to start moving, and an inward current will not be instantaneously balanced by an outward current." : in this context one also may note that the theory of ionic currents strongly assumes a fixed relation between ionic concentrations and voltage, for instance in the definition of the Nernst-potential as the basis of the definition of the reversal potential. However this definition assumes the thermodynamic equilibrium, which may hold for large times only and not in each instance. This argument seems to fit to the line of argumentation given by the authors.

Conclusions:

- replace "this model is complex" by "this model is too complex" ?

On references:
- the reference Nunez and Srinivasan (2005) should be moved from 'Further reading' to 'References' since it is cited regularly in the text.

- the book of Landau and Lifshitz is given as reference both in 'References' and in 'Further reading' and should be removed in the latter.

## Response:

Many thanks for the very useful review and for spotting the typos, we have corrected all the points as suggested. For the renormalisation, we added a footnote to explain it intuitively. We also changed Fig 6 to make it more clear how the LFP model of spike-and-wave fits experimental data.

Alain Destexhe and Claude Bedard