The relationship between local field potentials (LFPs) and the electromagnetic fields that give rise to them

Recently there has been a call (Reimann et al., 2013) for a re-evaluation of the genesis of local field potentials (LFPs), a measurement deeply correlated with normal and pathological excitable cell tissue operation (Einevoll et al., 2013;Friston et al., 2015). The lack of a full scientific account of LFP origins additionally means that brain augmentation hardware, a primary tool for which is the manipulation of LFPs, is in effect pulling unmarked levers. How can we knowledgeably control LFPs when LFP origin itself is a mystery? Here we investigate how the task of revisiting LFP origins might best be approached. LFPs originate in the two deeply interconnected fundamental physical fields of the brain: the vector electric field (E(r,t), V/m) and the vector magnetic field (B(r,t), V-s/m2). Each of these can be Helmholtz-decomposed into the gradient of a scalar potential (say Ф(r,t)) and the curl of a vector potential (say A(r,t)) (Groot and Suttorp, 1972;Landau et al., 1984;Malmivuo and Plonsey, 1995;Jackson, 1999). This means in practice that there are three ‘potential fields’ operating in the brain[1]. At present it is technologically impossible to directly measure the vector electric field or magnetic field at the resolution of tissue fine structure. Therefore neuroscientists rely on a technically straightforward measurement of voltage (call it LFP(r,t)) that imperfectly accesses the ‘potential fields’ and within which E and B are only indirectly represented. Empirical work over many decades has converged on transmembrane ionic current as the ultimate origin of the LFP (Buzsaki et al., 2012;Destexhe and Bedard, 2013). This means we must address the finest details of the formidably complex tissue ultra-structure typified by Figure 1(a) (Nicholson and Sykova, 1998;Briggman and Denk, 2006;Kinney et al., 2013)[2]. This is because the ionic currents originate in the membrane micro-environment indicated by the generic sources d1...d4 in Figure 1(a). Fundamental field theory tells us that E and B actually mediate LFP expression. This requires us to look at how membrane-related sources first cause E and B and through them, the LFP. We must treat transmembrane currents and their supporting systems of charge as electromagnetic (EM) field sources. LFP(r,t) measurement arose as a lab technique nearly seventy years ago (Brooks and Eccles, 1947) and still involves insertion of electrodes that are huge compared to the cyto-architectural scale of the tissue. These electrodes inevitably disrupt the structure around their insertion routes and the eventual measurement