Physics Letters A 374 (2010) 4797–4799 Contents lists available at ScienceDirect Physics Letters A www.elsevier.com/locate/pla Erratum Erratum and addendum to “Transcranial stimulability of phosphenes by long lightning electromagnetic pulses” [Phys. Lett. A 374 (2010) 2932] J. Peer a , V. Cooray b , G. Cooray c , A. Kendl a,∗ a Institute for Ion Physics and Applied Physics, University of Innsbruck, Austria b Division for Electricity, Department of Engineering Sciences, Uppsala University, Sweden c Department of Neurophysiology, Karolinska Institute, Sweden article info abstract Article history: Received 15 June 2010 Received in revised form 24 August 2010 Accepted 12 September 2010 Available online 8 October 2010 Communicated by C.R. Doering The comparison of electric fields transcranially induced by lightning discharges and by TMS brain stimulators via  E =−∂ t  A is shown to be inappropriate. Corrected results with respect to evaluation of phosphene stimulability are presented. For average lightning parameters the correct induced electric fields appear more than an order of magnitude smaller. For typical ranges of stronger than average lightning currents, electric fields above the threshold for cortical phosphene stimulation can be induced only for short distances (order of meters), or in medium distances (order of 50 m) only for pulses shorter than established axon excitation periods. Stimulation of retinal phosphene perception has much lower threshold and appears most probable for lightning electromagnetic fields.  2010 Elsevier B.V. All rights reserved. In Ref. [1] the electric fields  E ind induced in the head of a nearby observer by natural lightning discharges (LD) were com- pared to laboratory transcranial magnetic brain stimulation (BS) fields and effects. In this respect an inappropriate assumption has been applied, that both  E LD ind and  E BS ind could be calculated by  E =−∂ t  A, (1) which is valid if an electrostatic contribution −∇φ to the right- hand side due to space charge accumulation can be neglected. In the following we show that this assumption is normally valid for BS but not for LD. The vector potential  A in the proximity of a straight vertical lightning channel is also directed vertically and its magnitude is decreasing with distance. In the case of a circular TMS field coil  A is again oriented like the direction of the current flow, but here the current and therefore also  A form closed loops inside the head, which are approximately parallel to the skull surface and do not necessarily cut through any surfaces. Hence there will be no charge accumulation (and hence no buildup of an electrostatic po- tential φ), if the cortex is assumed to be an isotropic conducting medium. Fig. 1 shows the direction of components of  E =−d  A/dt pro- jected onto a “quadratic loop” inside the head. For clinical brain DOI of original article: 10.1016/j.physleta.2010.05.023. * Corresponding author. E-mail address: alexander.kendl@uibk.ac.at (A. Kendl). stimulation, the components form a closed loop (“BS”, left figure part), while for a lightning magnetic field there is a net contri- bution from one corner to its opposite on the loop (“LD”, right part). If, as it is the case for lightning fields, the vector potential does cut a surface (of the cortex or the skull), across which there are two media of different conductivity, there will be charge accumu- lation on the surface. This will cause a non-zero scalar potential φ which must be included in calculating the total electric field. How- ever, in the complex geometry of the different conducting media in the head an exact calculation is a highly nontrivial task. More generally, the electric field  E (t ) induced by a time varying magnetic  B (t ) field is calculated from the Maxwell–Faraday equa- tion ∇×  E =−∂ t  B so that U ind =   E ·  dl =−∂ t   B ·  dS =−∂ t ψ (2) corresponds to the voltage induced in a loop surrounding an area S , enclosing the magnetic flux ψ . The average electric field along the loop can be calculated by 〈 E 〉= U ind /L = ∂ t ψ/L where L =  dl . In the literature concerning clinical BS (e.g. Ref. [2]), Eq. (1) is used to compute E BS ind . In Ref. [1] we therefore used expression (1) as a reference quantity for the comparison of E LD ind and E BS ind . Eq. (1) indeed corresponds to E BS ind when it is applied to brain stimulation coils. E LD ind , however, is different from Eq. (1) because of the differ- ent spatial variation of the vector potentials  A LD and  A BS in the area of integration, as is shown in the following. 0375-9601/$ – see front matter  2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2010.09.071