Transcranial stimulability of phosphenes by long lightning electromagnetic pulses
aa r X i v : . [ phy s i c s . m e d - ph ] O c t Transcranial stimulability of phosphenesby long lightning electromagnetic pulses
J. Peer and A. Kendl ∗ Institut f¨ur Ionenphysik und Angewandte Physik, Universit¨at Innsbruck, Austria
Abstract
The electromagnetic pulses of rare long (order of seconds) repetitive lightning discharges nearstrike point (order of 100 m) are analyzed and compared to magnetic fields applied in standard clin-ical transcranial magnetic stimulation (TMS) practice. It is shown that the time-varying lightningmagnetic fields and locally induced potentials are in the same order of magnitude and frequencyas those established in TMS experiments to study stimulated perception phenomena, like mag-netophosphenes. Lightning electromagnetic pulse induced transcranial magnetic stimulation ofphosphenes in the visual cortex is concluded to be a plausible interpretation of a large class ofreports on luminous perceptions during thunderstorms.[Physics Letters A, Volume 374, Issue 29, 28 June 2010, Pages 2932-2935]
APPENDIX: Erratum and Addendum
The comparison of electric fields transcranially induced by lightning discharges and by TMSbrain stimulators via ~E = − ∂ t ~A is shown to be inappropriate. Corrected results with respect toevaluation of phosphene stimulability are presented. For average lightning parameters the correctinduced electric fields appear more than an order of magnitude smaller. For typical ranges ofstronger than average lightning currents, electric fields above the threshold for cortical phosphenestimulation 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 ofretinal phosphene perception has much lower threshold and appears most probable for lightningelectromagnetic fields.[Physics Letters A, Volume 374, Issue 47, 2010, Pages 4797-4799] PACS numbers: 52.80.Mg, 87.50.C-, 92.60.Pw ∗ Corresponding author: [email protected] ntroduction Transcranial magnetic stimulation (TMS) of neural activity in the human brain has de-veloped into an established method for neurophysical medical diagnosis and psychiatrictreatment [1, 2]. In particular, stimulation of the visual cortex by pulsed magnetic fieldsdirected at suitable positions towards the head has been reported to invoke phosphenes inprobands, which are perceived as luminous shapes within the visual field [3]. Here we showthat the near-field electromagnetic pulses of natural rare long (1-2 s) repetitive lightningstrokes can be expected to lead to neural induction currents above threshold values in thesame order of magnitude regarding frequency, duration and strength of stimulation as usedin medical TMS. For a small fraction of lightning flashes a near observer (ca. 20-200 m)should experience repetitive stimulation of perception activity similar to clinical TMS effects.We conclude evidence for a plausible interpretation of a large class of reports on luminousphenomena during thunderstorms as lightning electromagnetic pulse induced transcranialmagnetic stimulation of phosphenes in the human brain. An observer is likely to classifysuch an experience under the preconcepted collective term of ”ball lightning”.
Motivation: the phosphene interpretation of “ball lightning” reports
According to a comprehensive review by Stenhoff [4], “ball lightning” (BL) has beenreported in the open air, indoors, and within aircraft. Around one third of BL events maybe attributed to observations of stationary corona discharges in strong thunderstorm electricfields [4]. The majority of observations which have been analyzed in different surveys (cited ibidem ) reported BL to be directly succeeding a cloud-to-ground lightning flash. Somehypothetical scenarios for BL-like dust-gas fireballs appearing in very specific environmentalsituations after a stroke in sand or water have been suggested as a possible explanation [5–7].We here propose that a large class of reports (about the half) characterizing BL asluminous roundish objects arising in coincidence with lightning flashes and appearing tomove slowly at eye level of an observer for a few seconds (often accompanied by whitishnoises and smells) can be interpreted as magnetic phosphenes.The phosphene interpretation of “ball lightning” has been proposed earlier by J. Swith-enbank (reported in Ref. [4]) after personal BL observation, and was discussed (and firstbrought in context with TMS) in a skeptical review of BL theories [8]. Other authors havein Ref. [9] cursorily dismissed the phosphene hypothesis with an erroneous argument consid-2ring only magnetic field strengths (and not indeed their time derivative) and only the shortpulses of single stroke flashes. Recently, Cooray and Cooray [10] have presented a somewhatrelated hypothesis of BL-like visual perceptions to be possibly caused indrectly by epilepticseizures that may also be triggered by lightning electromagnetic pulses. A comprehensivereview of other (more or less plausible) BL theories is given in Ref. [4].In the following we show that the electric fields induced by nearby long repetitive lightningstrokes are indeed sufficient to evoke the perception of magnetophosphenes in the occipitalcortex.
Magnetophosphenes: visual perception by induction
The normal process of visual perception comprises the conversion of optical stimuli intoelectric signals by photoreceptors in the retina, and subsequent propagation of sensor poten-tials to the visual cortex in the occipital brain by neuron networks. Transmission of stimulioccurs in form of action potentials caused by processes opening and closing selective ionchannels in the cell membranes. Action potentials form irrevocably if the depolarization ofa cell membrane due to external stimuli exceeds a threshold value of U thr ∼
20 mV abovethe resting potential (-50 mV > U rest > -70 mV). The intensity of a stimulus is encoded bythe frequency of subsequent action potentials [11].Magnetic phosphenes are visual perceptions caused by time varying magnetic fields B ( x , t ), described by the vector potential A ( x , t ) from B = ∇ × A , that induce suffi-ciently strong electric fields E ind ( x , t ) = − ∂ t A ( x , t ) to cause a local potential (determindedvia E ind ( x , t ) = − ∇ U ind ( x , t )) on the membrane exceeding U ind > U thr . These changethe membrane potential and trigger an action potential either in the retina, in transmit-ting neurons, or directly in neurons of the visual cortex. The resulting visual perception istermed retinal phosphene or cortical phosphene, respectively, according to the location ofthe stimulus at the retina or in the cortex. Cortical phosphenes induced by transcranial magnetic stimulation
Transcranial magnetic stimulation (TMS) is a method for noninvasive selective magneticstimulation of local brain areas [1, 2]. Perceptible stimulation can be achieved by applicationof either single magnetic pulses or by repetitive pulses (rTMS) through stimulation coilsplaced on the outside of the head. Typical duration of a single neural TMS pulse is in the3rder of 250-450 µ s, and typical repetitive pulse frequencies are in the range of 1-50 Hz. Thetransient magnetic field induces a local electric field inside the brain which can form anaction potential in the stimulated area if U ind > U thr .Cortical phosphenes, which are perceived as luminous shapes within the visual field, arereported when the TM stimulus is applied to the area of the visual cortex and the localinduced field amplitude exceeds values in the range of 20-50 V/m, with varying thresholdsin different subjects [3]. Phosphenes are perceived in various shapes (ovals, bubbles, lines,patches) within the visual field, mostly appearing white, gray or in unsaturated colours [12].The duration of perception follows the duration of the single pulses or the whole repetitivecycle respectively. Phosphenes appear moving when the stimulation coil is shifted or thefixation site is changed. Impressions appear stronger and brighter with increasing stimulusstrength [13].Retinal phosphenes have even lower threshold values than their cortical counterparts [14,15]. Motivated by the availability of many well documented clinical TMS studies on corticalphosphenes, and by the established specifications of TMS induction coils, we restrict to thosein the following comparison with lightning electromagnetic pulses (LEMPs). Repetitive LEMPs and TMS
Phosphenes in clinical TMS are reported to occur only during the actual duration of stim-ulation (without significantly longer lasting after effects). A perception caused by LEMPscan therefore be duely expected for duration at least comparable to or longer than typicalTM stimulation experiment times of 250-450 µ s.Negative (CG-) downward discharges occur in 90% of cloud-to-ground lightning. TypicalCG- discharges begin with an electric stepped leader breakdown and a first return stroke,and are in most cases followed by multiple subsequent strokes, which are each initiated bya dart leader pulse through the pre-established channel. Single stroke CG- flashes have atypical duration of several hundred microseconds. Positive cloud-to-ground flashes (CG+)have rarer occurence and are usually limited to a single stroke, but may occur with highercontinuing currents for longer discharge times up to 0 . n =2 and 5, but more than 20 strokes per flash with atotal duration up to two seconds have been observed in detection networks [17]. Furthersubsequent strokes (possibly up to more than 40) with decreasing amplitudes often fail toenter the statistics by not exceeding the threshold of remotely distributed detectors.Although the electromagnetic pulses of the stepped leader and first return stroke couldlead to induced fields above the phosphene threshold, these are of minor importance for thelong term field evolution of high multiplicity flashes. The further discussion can be limitedto the effects of following dart leaders and subsequent return strokes. Repetitive stimulationby these multiple return strokes of n >
20 can occur with durations t > ·
50 ms in theorder of several seconds.
Calculation of lightning electromagnetic fields
Now we address the question if natural repetitive cloud-to-ground LEMPs generated bynearby strokes are able to transcranially induce electric fields comparable to those generatedby clinical TMS (of around 20-50 V/m), and thus sufficiently strong to stimulate similarsensory perceptions.For this purpose we have calculated the near electromagnetic fields of lightning dischargesfor various types and parameters of naturally occuring flashes. Previously published fieldcalculations have mostly been restricted either to far fields ( > km) relevant to lightning de-tection networks, or to direct impacts relevant to engineering problem of lighting protection.The model and numerical methods of our near field LEMP calculations, including theeffects of channel tortuosity and arbitrary observer location, are based on Refs. [16, 18–20].For details on the method and general results we refer to Ref. [21]: Maxwell’s equations areintegrated including retardation without scale approximations for given lightning channelbase currents to yield the electric field E ( x , t ) and electromagnetic vector potential A ( x , t )depending on time t and location x . Induced electric fields at location x o of a near observer(20-100 m horizontal distance from impact, level to perfectly conducting ground) are derivedfrom the time derivative of the vector potential A ( x o , t ) for various stroke types such as5eader, return strokes and M-components. For simplicty, cortical anisotropy and dielectricproperties have been neglected in this work. Results: stimulation induced by successive return strokes
We first consider straight vertical lightning channels using a leader model with a typi-cal value for the homogeneous charge distribution of q = 0 .
14 mC/m [16], and a currentgeneration type model for the return stroke [20].Our numerical calculations on subsequent mutiple CG- dart leaders and return strokesshow that in distances of the order of 20-100 m only the latter can induce above electricfields long enough to envoke perception: induced electric fields of dart leaders can in factreach E ind >
20 V/m above threshold, but the short dart leader pulse period of 2-3 µ s(compared to TMS pulses of several 100 µ s) may prohibit actual cognitive perception.Return strokes are characterized by a fast rising phase and a slower decline phase of thenearby local magnetic field strength. The calculated pulse shapes of transcranially inducedelectric fields begin with a strong field peak in the order of kilovolts per meter and durationof microseconds caused by the large time derivative of the magnetic field in the short risephase.The action of this initial peak is difficult to predict due to the lack of comparably sharpfield pulses in clinical brain stimulation. Assuming that the cell membrane of a single axoncan be modelled as an RC circuit (i.e. a capacitance with a parallel connected leakageresistance) characterised by the cortical time constant of 150 µ s [11, 22], we can roughlyestimate the resulting change in the membrane potential: The time dependent capacitorcharging voltage of an RC circuit is given by U ( t ) = U (1 − exp( − t/τ )) where U is theapplied voltage and τ is the time constant (i.e. the time taken by U ( t ) to increase to 63%of U ). Considering that a TMS induced electric field pulse of 20 V/m and 300 µ s is able totrigger an action potential, we can deduce from the above equation that the initial field peakof a lightning return stroke ( E ind ≈ t ≈ . µ s) leads to a membrane depolarisa-tion which is (cid:0) (cid:0) − exp( − . ) (cid:1)(cid:1) / (cid:0) (cid:0) − exp( − ) (cid:1)(cid:1) ≈ . µ s hasthe most relevance for stimulation: our calculations for average discharge parameters show6 IG. 1:
Electric field transcranially induced at various observation points (from bottom to top:20 - 100m distance from strike point) by the time derivative of the lightning magnetic field duringthe decline phase of one average negative cloud-to-ground subsequent return stroke within a longhigh-multiplicity flash. that in this phase LEMP induced potentials of the same order in amplitude and duration asrTMS pulses (larger than 20-50 V/m) occur in a distance less than around 100 m from thelightning channel. Results of the detailed simulations of this last phase of CG- return strokesare shown in Fig. 1 for various observer distances and otherwise standard parameters.High multiplicity lightning, which has similar pulse repetition frequency as rTMS, cantherefore be positively expected to stimulate cortical phosphenes for as long as several sec-onds. The observation of magnetophosphenes is actually not restricted to distances below100 m, but may be experienced up to 300 m from the impact point, as strokes can occurwith intensities (channel currents) up to 10 times larger than the average values used in ourcalculations.
Conclusion: likelihood to experience magnetophosphenes during a thunderstorm
In summary, we have calculated and analyzed the electric fields induced by all phasesof near multiple lightning electromagnetic pulses, and have shown a remarkable agreementwith fields induced by repetitive transcranial magnetic stimulation, which is known to cause7hosphene perception in observers when applied to the visual cortex.The chance for transcranial stimulability of LEMP induced phosphenes can be roughlyestimated. Occurence of a repetitive stroke near to an observer ( < O (200 m)) is essentialto achieve an above threshold induction potential. Noticeable perception of phosphenesvery likely occurs only when other sensory stimuli (or bodily injury of the observer) are notdominant. Direct observation of the blinding light and deafeningly loud thunder of lightningbolts may drown out phosphene perception. Magnetic fields of LEMPs are however able topenetrate walls and roofs, so that a direct line of sight to the bolt is not necessary toexperience phosphenes.Long perception in the order of seconds can be expected for the more rarely occuringrepetitive strokes with multiplicity higher than 20, which occur for 1-5% of CG- strokes,although published statistics of such events are scarce [16]. As a conservative estimate,roughly 1% of (otherwise unharmed) close lightning experiencers are likely to perceive tran-scranially induced above-threshold cortical stimuli. The activation by (time varying) weaklydamped penetrating magnetic fields allows observation within closed buildings or aircrafts.Broadband stimulation of other sensory activity (odours, sound) can also be expected, butvisual stimuli are usually dominantly perceived.An observer reporting this experience is likely to classify the event under the preconceptedterm of ”ball lightning”, which is used to subsume numerous reports on luminous perceptionsduring thunderstorm activity [4].Here we conclude evidence for interpretation of a large class of ”ball lightning” observa-tions as magnetic phosphenes transcranially stimulated by nearby long repetitive lightningstrokes. Acknowledgements
We thank Dr. Thomas Kammer (Head of the Laboratory for Transcranial Magnetic Stim-ulation), Department of Psychiatry, University of Ulm (Germany), for valuable discussions,advice and careful reading of the manuscript. The computational work has been funded bya junior research group grant (“Nachwuchsf¨orderung”) from the University of Innsbruck.8
1] M. Hallett, Nature , 147-150 (2000).[2] V. Walsh, and A. Cowey, Nature Reviews Neuroscience , 73-80 (2000).[3] E. Marg, Optometry and Visual Science , 427440 (1991)[4] M. Stenhoff, Ball Lightning: An Unsolved Problem in Atmospheric Physics. Kluwer Academic/ Plenum Publishers, New York, 1999.[5] J. Abrahamson, J. Dinniss, Nature , 519-521 (2000).[6] G.S. Paiva, et al. Phys. Rev. Lett. , 048501 (2007).[7] A. Versteegh, K. Behringer, U. Fantz, G. Fussmann, B. J¨uttner, S. Noack, Plasma SourcesScience and Technology , 1-8 (2008).[8] A. Kendl, Skeptiker , 65 (2001).[9] A.G. Keul, P. Sauseng, G. Diendorfer, Int. Journal of Meteorology , 89-95 (2008).[10] G. Cooray, V. Cooray, The Open Atmospheric Journal , 101 (2008).[11] T. Kammer, A. Thielscher, Nervenheilkunde , 168-176 (2003).[12] T. Kammer, K. Puls, M. Erb, W. Grodd, Experimental Brain Research , 129-140 (2005).[13] T. Kammer, Neuropsychologia , 191-198 (1999).[14] E. Litvak, K.R. Foster, and M.H. Repacholi, Bioelectromagn. , 68 (2002).[15] R. Kavet, W.H. Bailey, T. Dan Bracken, R.M. Patterson, Bioelectromagn. , 499 (2008).[16] V.A. Rakov, M.A. Uman, Lightning: Physics and Effects. Cambridge University Press, Cam-bridge, 2006.[17] V.A. Rakov, G.R. Huffines, Journal of Applied Meteorology , 1455-1462 (2003).[18] R. Thottappillil, V.A. Rakov, M.A. Uman, J. Geophys. Res. , 6987 (1997).[19] R. Thottappillil, M.A. Uman, J. Geophys. Res. , 22773 (1994).[20] V. Cooray, R. Montano, V.A. Rakov, J. Electrostat. , 97 (2004).[21] J. Peer, A. Kendl, On the effects of channel tortuosity on the close electromagnetic fields as-sociated with lightning return strokes.
Submitted to: Journal of Electrostatics (2009). Preprint:http://arxiv.org/abs/1004.3203[22] A.T. Barker, C. W. Garnham, I.L. Freeston, Electroenceph. Clin. Neurophysiol. , 227(1991). rratum and addendum J. Peer , V. Cooray , G. Cooray , A. Kendl
1) Institute for Ion Physics and Applied Physics, University of Innsbruck, Austria2) Division for Electricity, Department of Engineering Sciences, Uppsala University,Sweden3) Department of Neurophysiology, Karolinska Institute, Sweden
In Ref. [1] the electric fields ~E ind induced in the head of a nearby observer by naturallightning discharges (LD) were compared to laboratory transcranial magnetic brain stimu-lation (BS) fields and effects. In this respect an inappropriate assumption has been applied,that both ~E LDind and ~E BSind could be calculated by ~E = − ∂ t ~A, (1)which is valid if an electrostatic contribution −∇ φ to the right hand side due to space chargeaccumulation can be neglected. In the following we show that this assumption is normallyvalid for BS but not for LD.The vector potential ~A in the proximity of a straight vertical lightning channel is alsodirected vertically and its magnitude is decreasing with distance. In the case of a circularTMS field coil ~A is again oriented like the direction of the current flow, but here the currentand therefore also ~A form closed loops inside the head, which are approximately parallel tothe skull surface and do not necessarily cut through any surfaces. Hence there will be nocharge accumulation (and hence no buildup of an electrostatic potential φ ), if the cortex isassumed to be an isotropic conducting medium.Fig. 2 shows the direction of components of ~E = − d ~A/dt projected onto a ”quadraticloop” inside the head. For clinical brain stimulation, the components form a closed loop(”BS”, left figure part), while for a lightning magnetic field there is a net contribution fromone 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 thecortex or the skull), across which there are two media of different conductivity, there willbe charge accumulation on the surface. This will cause a non-zero scalar potential φ whichmust be included in calculating the total electric field. However, in the complex geometry ofthe different conducting media in the head an exact calculation is a highly nontrivial task.10ore generally, the electric field ~E ( t ) induced by a time varying magnetic ~B ( t ) field iscalculated from the Maxwell-Faraday equation ∇ × ~E = − ∂ t ~B so that U ind = I ~E · ~dl = − ∂ t Z ~B · ~dS = − ∂ t ψ (2)corresponds to the voltage induced in a loop surrounding an area S , enclosing the magneticflux ψ . The average electric field along the loop can be calculated by h E i = U ind /L = ∂ t ψ/L where L = R dl . FIG. 2:
Electric fields around a quadratic loop due to the vector potential of a brain stimulationcoil (left) and the vector potential of a lightning channel pointing in z -direction (right). In the literature concerning clinical BS (e.g. Ref. [2]), eq. (1) is used to compute E BSind . InRef. [1] we therefore used expression (1) as a reference quantity for the comparison of E LDind and E BSind . Eq. (1) indeed corresponds to E BSind when it is applied to brain stimulation coils. E LDind , however, is different from eq. (1) because of the different spatial variation of the vectorpotentials ~A LD and ~A BS in the area of integration, as is shown in the following.First consider E BSind , induced by the magnetic field of a brain stimulation coil with currentloops located close to the head. For simplicity a quadratic loop, shown in the left part ofFig. 2, with side length l is assumed. Thus, the vector potential ~A BS , and with it the electricfield ~E = − ∂ t ~A BS , forms closed loops. For the given loop this yields A BS x ( z ) = A BS x ( z + l ) = A BS z ( x ) = A BS z ( x + l ) = A BS , and the voltage induced in the loop can be expressed as U BSind = − R ~E · ~dl = ∂ t R ~A BS · ~dl = 4 l∂ t A BS . This results in E BSind = − U BSind / (4 l ) = − ∂ t A BS which corresponds to eq. (1). 11egarding the lightning case, a straight and vertical lightning channel pointing in z -direction and an observer on perfectly conducting ground may be assumed, so that thevector potential ~A LD has a vertical component only. Consider the quadratic loop shownin the right part of Fig. 2. Due to the small x -dependence of ~A LD we now have A LD z ( x ) = A LD z ( x + l ), and the voltage induced in the loop is given by U LDind = − R ~E · ~dl = ∂ t R ~A LD · ~dl = l∂ t (cid:2) A LD z ( x ) − A LD z ( x + l ) (cid:3) = − l ∂ t ∂ x A LD z resulting in E LDind = − U LDind / (4 l ) = ( l/ ∂ x ∂ t A LD z which is different from eq. (1).Consequently, E LDind can not be computed by eq. (1) but has to be calculated from eq. (2).For E BSind eqs. (1) and (2) yield the same result. Due to the incorrect use of eq. (1) the resultsfor lightning induced electric fields obtained in Ref. [1] for average lightning parameters aremore than an order of magnitude too large (depending on distance). Correct results for E LDind and their consequence on the probability of cortical and retinal phosphene stimulation usingeq. (2) are discussed in the following.We now do not focus on one specific (average) lightning channel base current and waveform like in Ref. [1], but rather explore a range of above average but still usual parameters. Itturns out that fields induced by the previously considered long current decline phase of returnstrokes (order of 100 µ s) are below known cortical phosphene thresholds for the range ofconsidered lightning parameters at relevant distances (i.e., more than several meters, whereother lightning effects and injury may not be expected to be dominant on an observer).We therefore now also reconsider the possibility of an effect of the return stroke current rise phase on cortical axon stimulation. Fig. 3 (top) shows the initial rise phase for differentchannel base current waveforms I ( t ) of return strokes, and Fig. 3 (bottom) shows the corre-sponding associated maximum values of the induced electric fields E LDind for different distancesfrom the lightning channel. E LDind is calculated from the time varying magnetic flux througha circular area with a cortex radius of 0 .
07 m. The figure shows that the maximum value of E LDind is mainly determined by ∂ t I . The cortical phosphene threshold of around 20 −
40 Vm − is exceeded in distances up to order of 50 m for return strokes that are characterised bya current rise of dIdt > ∼
100 kA µ s − . The duration of a single induced electric field pulse isdetermined by the current rise time (0 . − µ s) and repeated with the frequency of multiplestrokes.It is however not evident if these short pulses in the rise phase in the order of microsecondsactually allow stimulation of phosphenes, as no clinical experience with similar pulse forms12 −3 −2 −1 −2 −1 Time [ µ s] C hanne l ba s e c u rr en t [ k A ] Max(dI/dt) = 147 kA µ s −1
73 kA µ s −1
95 kA µ s −1
147 kA µ s −1
73 kA µ s −1
10 15 20 25 30 35 40020406080100120 Distance [m] I ndu c ed e l e c t r i c f i e l d [ V m − ] FIG. 3:
Logarithmic plot of the initial rise phase for a range of different channel base currentwaveforms I ( t ) (top), and associated maximum values of the induced electric fields E LDind for differentdistances from the lightning channel (bottom). For the two cases with max( dI/dt )=147 kA/µs ,waveforms with different maximum current amplitude and rise time are used. is available. In vitro experiments suggest that to fire axons may require longer exposure( > µ s) to electric fields of similar strength [4]. Stimulation of cortical phosphenes bymultiple lightning return strokes therefore appears improbable for relevant parameters anddistances above several ten meters.On the other hand, it had already been noted in Ref. [1] that retinal phosphenes have amuch lower threshold than their cortical counterparts [3], which is according to Refs. [5, 6] inthe range of 10 −
100 mV m − . The feasibility to stimulate retinal phosphenes with lightninginduced electric fields is therefore much higher than for cortical phosphenes. In Ref. [1] weexpressed the point of view that when lightning induced cortical phosphenes can be shownto possibly exist, then retinal phosphenes are an even more likely event under the samecircumstances. As lightning induced stimulation of cortical phosphenes has now been shownto be much less probable, we also re-evaluate the possibility of retinal phosphenes by meansof the corrected calculations: Indeed E LDind can reach above retinal phosphene threshold valuesat distances up to order of 50 m from the lightning channel also during the long return strokedecline phase of 100 − µ s pulse duration, and in even considerably longer distances (orderof 200 m) during the short rise phase. 13nfortunately no directly comparable specific retinal stimulation experiments could befound in the available literature. While the average frequency of return strokes in a multiplelightning discharge (20 Hz) coincides with the repetition frequencies usually used in retinalstimulation experiments, the pulse shapes of E LDind and E BSind considerably differ [5]: usually,the retina is stimulated by sinusoidal waveforms with a frequency of also 20 −
45 Hz byTMS, compared to return stroke pulse durations of several 100 µ s. Studies on direct currentelectrical excitation of the human retina however indeed show stimulability for short pulsedurations of 250 µs [7]. The possibility of stimulation of retinal phosphenes by lightningfields could of course in future be verified by physiological investigations using comparablemagnetic pulse forms.An experimental setup which covers both retinal and cortical stimulation regions mayindeed easily be devised with a pair of Helmholtz coils with radius and separation largerthan a human head, where currents are applied that directly generate nonfocal magneticfields with strengths and pulse shapes as calculated for realistic lightning conditions invarious distances. This suggested experimentum crucis is able to critically test the lightningelectromagnetic phosphene stimulation hypothesis.In spite of the previous overestimation of induced electric fields in Ref. [1], a stimulationof phosphenes induced by lightning electromagnetic pulses remains plausible. The mostprobable site of stimulation however appears to be the retina rather than the visual cortex. Acknowledgment:
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