Measurements and models of electric fields in the in vivo human brain during transcranial electric stimulation
Yu Huang, Anli A Liu, Belen Lafon, Daniel Friedman, Michael Dayan, Xiuyuan Wang, Marom Bikson, Werner K Doyle, Orrin Devinsky, Lucas C Parra, Yu Huang, Anli A Liu, Belen Lafon, Daniel Friedman, Michael Dayan, Xiuyuan Wang, Marom Bikson, Werner K Doyle, Orrin Devinsky, Lucas C Parra
Abstract
Transcranial electric stimulation aims to stimulate the brain by applying weak electrical currents at the scalp. However, the magnitude and spatial distribution of electric fields in the human brain are unknown. We measured electric potentials intracranially in ten epilepsy patients and estimated electric fields across the entire brain by leveraging calibrated current-flow models. When stimulating at 2 mA, cortical electric fields reach 0.8 V/m, the lower limit of effectiveness in animal studies. When individual whole-head anatomy is considered, the predicted electric field magnitudes correlate with the recorded values in cortical (r = 0.86) and depth (r = 0.88) electrodes. Accurate models require adjustment of tissue conductivity values reported in the literature, but accuracy is not improved when incorporating white matter anisotropy or different skull compartments. This is the first study to validate and calibrate current-flow models with in vivo intracranial recordings in humans, providing a solid foundation to target stimulation and interpret clinical trials.
Keywords: computational current-flow model; human; intracranial recordings; neuroscience; transcranial electric stimulation.
Conflict of interest statement
MB: Has significant interest in Soterix Medical Inc. which commercializes hardware and software for TES. He is listed as inventors on patents (U.S. Patent application No.13/264,142) related to TES.
LCP: Has significant interest in Soterix Medical Inc. which commercializes hardware and software for TES. He is listed as inventors on patents (U.S. Patent application No.13/264,142) related to TES.
The other authors declare that no competing interests exist.
Figures
References
- Acar ZA, Makeig S. Neuroelectromagnetic forward head modeling toolbox. Journal of Neuroscience Methods. 2010;190:258–270. doi: 10.1016/j.jneumeth.2010.04.031.
- Akhtari M, Bryant HC, Mamelak AN, Flynn ER, Heller L, Shih JJ, Mandelkern M, Matlachov A, Ranken DM, Best ED, DiMauro MA, Lee RR, Sutherling WW. Conductivities of three-layer live human skull. Brain Topography. 2002;14:151–167. doi: 10.1023/A:1014590923185.
- Alam M, Truong DQ, Khadka N, Bikson M. Spatial and polarity precision of concentric high-definition transcranial direct current stimulation (HD-tDCS) Physics in Medicine and Biology. 2016;61:4506–4521. doi: 10.1088/0031-9155/61/12/4506.
- Alekseichuk I, Diers K, Paulus W, Antal A. Transcranial electrical stimulation of the occipital cortex during visual perception modifies the magnitude of BOLD activity: a combined tES-fMRI approach. NeuroImage. 2016;140 doi: 10.1016/j.neuroimage.2015.11.034.
- Ali MM, Sellers KK, Fröhlich F. Transcranial alternating current stimulation modulates large-scale cortical network activity by network resonance. Journal of Neuroscience. 2013;33:11262–11275. doi: 10.1523/JNEUROSCI.5867-12.2013.
- Andersson JL, Skare S, Ashburner J. How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage. 2003;20:870–888. doi: 10.1016/S1053-8119(03)00336-7.
- Andersson JL, Sotiropoulos SN. An integrated approach to correction for off-resonance effects and subject movement in diffusion MR imaging. NeuroImage. 2016;125:1063–1078. doi: 10.1016/j.neuroimage.2015.10.019.
- Ashburner J, Friston KJ. Unified segmentation. NeuroImage. 2005;26:839–851. doi: 10.1016/j.neuroimage.2005.02.018.
- Audet C, Dennis JE. Analysis of generalized pattern searches. SIAM Journal on Optimization. 2002;13:889–903. doi: 10.1137/S1052623400378742.
- Auvichayapat N, Rotenberg A, Gersner R, Ngodklang S, Tiamkao S, Tassaneeyakul W, Auvichayapat P. Transcranial direct current stimulation for treatment of refractory childhood focal epilepsy. Brain Stimulation. 2013;6:696–700. doi: 10.1016/j.brs.2013.01.009.
- Baker JM, Rorden C, Fridriksson J. Using transcranial direct-current stimulation to treat stroke patients with aphasia. Stroke. 2010;41:1229–1236. doi: 10.1161/STROKEAHA.109.576785.
- Bangera NB, Schomer DL, Dehghani N, Ulbert I, Cash S, Papavasiliou S, Eisenberg SR, Dale AM, Halgren E. Experimental validation of the influence of white matter anisotropy on the intracranial EEG forward solution. Journal of Computational Neuroscience. 2010;29:371–387. doi: 10.1007/s10827-009-0205-z.
- Baumann SB, Wozny DR, Kelly SK, Meno FM. The electrical conductivity of human cerebrospinal fluid at body temperature. IEEE Transactions on Biomedical Engineering. 1997;44:220–223. doi: 10.1109/10.554770.
- Bikson M, Bulow P, Stiller JW, Datta A, Battaglia F, Karnup SV, Postolache TT. Transcranial direct current stimulation for major depression: a general system for quantifying transcranial electrotherapy dosage. Current Treatment Options in Neurology. 2008;10:377–385. doi: 10.1007/s11940-008-0040-y.
- Bikson M, Datta A, Rahman A, Scaturro J. Electrode montages for tDCS and weak transcranial electrical stimulation: role of "return" electrode's position and size. Clinical Neurophysiology. 2010;121:1976–1978. doi: 10.1016/j.clinph.2010.05.020.
- Burger HC, MILAAN JB. Measurements of the specific resistance of the human body to direct current. Acta Medica Scandinavica. 1943;114:584–607. doi: 10.1111/j.0954-6820.1943.tb11253.x.
- Collignon A, Maes F, Delaere D, Vandermeulen D, Suetens P, Marchal G. Automated Multi-Modality Image Registration Based on Information Theory. Bizais; 1995.
- Cook PA, Bai Y, Nedjati-Gilani S, Seunarine KK, Hall MG, Parker GJ, Alexander DC. 14thScientific Meeting of the International Society for Magnetic Resonance in Medicine. 2006. Camino: open-source diffusion-MRI reconstruction and processing; p. 2759.
- Cramér H. Mathematical Methods of Statistics. Princeton: Princeton University Press; 1999.
- Crille GW, Hosmer HR, Rowland AF. The electrical conductivity of animal tissues under normal and pathological conditions. American Journal of Physiology. 1922;60:59–106.
- Dannhauer M, Lanfer B, Wolters CH, Knösche TR. Modeling of the human skull in EEG source analysis. Human Brain Mapping. 2011;32:1383–1399. doi: 10.1002/hbm.21114.
- Dannhauer M, Brooks D, Tucker D, MacLeod R. A pipeline for the simulation of transcranial direct current stimulation for realistic human head models using SCIRun/BioMesh3D. 2012 Annual International Conference of the IEEE. 2012:5486–5489. doi: 10.1109/embc.2012.6347236.
- Datta A, Elwassif M, Battaglia F, Bikson M. Transcranial current stimulation focality using disc and ring electrode configurations: fem analysis. Journal of Neural Engineering. 2008;5:163–174. doi: 10.1088/1741-2560/5/2/007.
- Datta A, Bansal V, Diaz J, Patel J, Reato D, Bikson M. Gyri-precise head model of transcranial direct current stimulation: improved spatial focality using a ring electrode versus conventional rectangular pad. Brain Stimulation. 2009;2:201–207. doi: 10.1016/j.brs.2009.03.005.
- Datta A, Bikson M, Fregni F. Transcranial direct current stimulation in patients with skull defects and skull plates: high-resolution computational FEM study of factors altering cortical current flow. NeuroImage. 2010;52:1268–1278. doi: 10.1016/j.neuroimage.2010.04.252.
- Datta A, Baker JM, Bikson M, Fridriksson J. Individualized model predicts brain current flow during transcranial direct-current stimulation treatment in responsive stroke patient. Brain Stimulation. 2011;4:169–174. doi: 10.1016/j.brs.2010.11.001.
- Datta A, Truong D, Minhas P, Parra LC, Bikson M. Inter-Individual variation during transcranial direct current stimulation and normalization of dose using MRI-Derived computational models. Frontiers in Psychiatry. 2012;3:91. doi: 10.3389/fpsyt.2012.00091.
- Datta A, Zhou X, Su Y, Parra LC, Bikson M. Validation of finite element model of transcranial electrical stimulation using scalp potentials: implications for clinical dose. Journal of Neural Engineering. 2013;10:036018. doi: 10.1088/1741-2560/10/3/036018.
- De Mercato G, Garcia Sanchez FJ. Correlation between low-frequency electric conductivity and permittivity in the diaphysis of bovine femoral bone. IEEE Transactions on Biomedical Engineering. 1992;39:523–526. doi: 10.1109/10.135546.
- Dmochowski JP, Datta A, Bikson M, Su Y, Parra LC. Optimized multi-electrode stimulation increases focality and intensity at target. Journal of Neural Engineering. 2011;8:046011. doi: 10.1088/1741-2560/8/4/046011.
- Dmochowski JP, Bikson M, Parra LC. The point spread function of the human head and its implications for transcranial current stimulation. Physics in Medicine and Biology. 2012;57:6459–6477. doi: 10.1088/0031-9155/57/20/6459.
- Dmochowski JP, Datta A, Huang Y, Richardson JD, Bikson M, Fridriksson J, Parra LC. Targeted transcranial direct current stimulation for rehabilitation after stroke. NeuroImage. 2013;75:12–19. doi: 10.1016/j.neuroimage.2013.02.049.
- Dockery CA, Hueckel-Weng R, Birbaumer N, Plewnia C. Enhancement of planning ability by transcranial direct current stimulation. Journal of Neuroscience. 2009;29:7271–7277. doi: 10.1523/JNEUROSCI.0065-09.2009.
- Edwards D, Cortes M, Datta A, Minhas P, Wassermann EM, Bikson M. Physiological and modeling evidence for focal transcranial electrical brain stimulation in humans: a basis for high-definition tDCS. NeuroImage. 2013;74:266–275. doi: 10.1016/j.neuroimage.2013.01.042.
- Ferdjallah M, Bostick FX, Barr RE. Potential and current density distributions of cranial electrotherapy stimulation (CES) in a four-concentric-spheres model. IEEE Transactions on Biomedical Engineering. 1996;43:939–943. doi: 10.1109/10.532128.
- Frank E, Schecklmann M, Landgrebe M, Burger J, Kreuzer P, Poeppl TB, Kleinjung T, Hajak G, Langguth B. Treatment of chronic tinnitus with repeated sessions of prefrontal transcranial direct current stimulation: outcomes from an open-label pilot study. Journal of Neurology. 2012;259:327–333. doi: 10.1007/s00415-011-6189-4.
- Fregni F, Boggio PS, Nitsche M, Bermpohl F, Antal A, Feredoes E, Marcolin MA, Rigonatti SP, Silva MT, Paulus W, Pascual-Leone A. Anodal transcranial direct current stimulation of prefrontal cortex enhances working memory. Experimental Brain Research. 2005;166:23–30. doi: 10.1007/s00221-005-2334-6.
- Fregni F, Boggio PS, Lima MC, Ferreira MJ, Wagner T, Rigonatti SP, Castro AW, Souza DR, Riberto M, Freedman SD, Nitsche MA, Pascual-Leone A. A sham-controlled, phase II trial of transcranial direct current stimulation for the treatment of central pain in traumatic spinal cord injury. Pain. 2006a;122:197–209. doi: 10.1016/j.pain.2006.02.023.
- Fregni F, Boggio PS, Santos MC, Lima M, Vieira AL, Rigonatti SP, Silva MT, Barbosa ER, Nitsche MA, Pascual-Leone A. Noninvasive cortical stimulation with transcranial direct current stimulation in Parkinson's disease. Movement Disorders. 2006b;21:1693–1702. doi: 10.1002/mds.21012.
- Fregni F, Gimenes R, Valle AC, Ferreira MJ, Rocha RR, Natalle L, Bravo R, Rigonatti SP, Freedman SD, Nitsche MA, Pascual-Leone A, Boggio PS. A randomized, sham-controlled, proof of principle study of transcranial direct current stimulation for the treatment of pain in Fibromyalgia. Arthritis & Rheumatism. 2006c;54:3988–3998. doi: 10.1002/art.22195.
- Fregni F, Thome-Souza S, Nitsche MA, Freedman SD, Valente KD, Pascual-Leone A. A controlled clinical trial of cathodal DC polarization in patients with refractory epilepsy. Epilepsia. 2006d;47:335–342. doi: 10.1111/j.1528-1167.2006.00426.x.
- Fregni F, Freedman S, Pascual-Leone A. Recent advances in the treatment of chronic pain with non-invasive brain stimulation techniques. The Lancet Neurology. 2007;6:188–191. doi: 10.1016/S1474-4422(07)70032-7.
- Freygang WH, Landau WM. Some relations between resistivity and electrical activity in the cerebral cortex of the cat. Journal of Cellular and Comparative Physiology. 1955;45:377–392. doi: 10.1002/jcp.1030450305.
- Friston KJ, Ashburner J, Frith CD, Poline J-B, Heather JD, Frackowiak RSJ. Spatial registration and normalization of images. Human Brain Mapping. 1995;3:165–189. doi: 10.1002/hbm.460030303.
- Fröhlich F, McCormick DA. Endogenous electric fields may guide neocortical network activity. Neuron. 2010;67:129–143. doi: 10.1016/j.neuron.2010.06.005.
- Gabriel C. Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies. Brooks Air Force Base, Texas: Ocuptational and Environmental Health Directorate; 1996.
- Gabriel C, Gabriel S, Corthout E. The dielectric properties of biological tissues: I. literature survey. Physics in Medicine and Biology. 1996;41:2231–2249. doi: 10.1088/0031-9155/41/11/001.
- Geddes LA. Optimal stimulus duration for extracranial cortical stimulation. Neurosurgery. 1987;20:94–99. doi: 10.1097/00006123-198701000-00023.
- Griffiths DJ. Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice Hall; 1999.
- Guler S, Dannhauer M, Erem B, Macleod R, Tucker D, Turovets S, Luu P, Erdogmus D, Brooks DH. Optimization of focality and direction in dense electrode array transcranial direct current stimulation (tDCS) Journal of Neural Engineering. 2016;13:036020. doi: 10.1088/1741-2560/13/3/036020.
- Güllmar D, Haueisen J, Reichenbach JR. Influence of anisotropic electrical conductivity in white matter tissue on the EEG/MEG forward and inverse solution. A high-resolution whole head simulation study. NeuroImage. 2010;51:145–163. doi: 10.1016/j.neuroimage.2010.02.014.
- Hallez H, Vanrumste B, Hese PV, Delputte S, Lemahieu I. Dipole estimation errors due to differences in modeling anisotropic conductivities in realistic head models for EEG source analysis. Physics in Medicine and Biology. 2008;53:1877–1894. doi: 10.1088/0031-9155/53/7/005.
- Hasted JB. Aqueous Dielectrics. Studies in Chemical Physics. London: Chapman and Hall; 1973.
- Hayes KJ. The current path in electric convulsion shock. Archives of Neurology and Psychiatry. 1950;63:102–109. doi: 10.1001/archneurpsyc.1950.02310190108008.
- Herrmann CS, Rach S, Neuling T, Strüber D. Transcranial alternating current stimulation: a review of the underlying mechanisms and modulation of cognitive processes. Frontiers in Human Neuroscience. 2013;7:279. doi: 10.3389/fnhum.2013.00279.
- Hoekema R, Wieneke GH, Leijten FSS, van Veelen CWM, van Rijen PC, Huiskamp GJM, Ansems J, van Huffelen AC. Measurement of the conductivity of skull, temporarily removed during epilepsy surgery. Brain Topography. 2003;16:29–38. doi: 10.1023/A:1025606415858.
- Huang Y, Dmochowski JP, Su Y, Datta A, Rorden C, Parra LC. Automated MRI segmentation for individualized modeling of current flow in the human head. Journal of Neural Engineering. 2013;10:066004. doi: 10.1088/1741-2560/10/6/066004.
- Huang Y, Parra LC. Fully automated whole-head segmentation with improved smoothness and continuity, with theory reviewed. Plos One. 2015;10:e0125477. doi: 10.1371/journal.pone.0125477.
- Im CH, Jung HH, Choi JD, Lee SY, Jung KY. Determination of optimal electrode positions for transcranial direct current stimulation (tDCS) Physics in Medicine and Biology. 2008;53:N219–N225. doi: 10.1088/0031-9155/53/11/N03.
- Jones DK, Basser PJ. "Squashing peanuts and smashing pumpkins": how noise distorts diffusion-weighted MR data. Magnetic Resonance in Medicine. 2004;52:979–993. doi: 10.1002/mrm.20283.
- Jung YJ, Kim JH, Im CH. COMETS: a MATLAB toolbox for simulating local electric fields generated by transcranial direct current stimulation (tDCS) Biomedical Engineering Letters. 2013;3:39–46. doi: 10.1007/s13534-013-0087-x.
- Kar K, Krekelberg B. Testing the assumptions underlying fMRI adaptation using intracortical recordings in area MT. Cortex. 2016;80:21–34. doi: 10.1016/j.cortex.2015.12.011.
- Koessler L, Colnat-Coulbois S, Cecchin T, Hofmanis J, Dmochowski JP, Norcia AM, Maillard LG. In-vivo measurements of human brain tissue conductivity using focal electrical current injection through intracerebral multicontact electrodes. Human Brain Mapping. 2017;38:974–986. doi: 10.1002/hbm.23431.
- Kronberg G, Bridi M, Abel T, Bikson M, Parra LC. Direct current stimulation modulates LTP and LTD: activity dependence and dendritic effects. Brain Stimulation. 2017;10:51–58. doi: 10.1016/j.brs.2016.10.001.
- Lee WH, Lisanby SH, Laine AF, Peterchev AV. Electric field model of transcranial electric stimulation in nonhuman primates: correspondence to individual motor threshold. IEEE Transactions on Biomedical Engineering. 2015;62:2095–2105. doi: 10.1109/TBME.2015.2425406.
- Logan DL. A First Course in the Finite Element Method. Toronto: Nelson; 2007.
- Logothetis NK, Kayser C, Oeltermann A. In vivo measurement of cortical impedance spectrum in monkeys: implications for signal propagation. Neuron. 2007;55:809–823. doi: 10.1016/j.neuron.2007.07.027.
- Lustenberger C, Boyle MR, Alagapan S, Mellin JM, Vaughn BV, Fröhlich F. Feedback-Controlled transcranial alternating current stimulation reveals a functional role of sleep spindles in motor memory consolidation. Current Biology. 2016;26:2127–2136. doi: 10.1016/j.cub.2016.06.044.
- Luu P, Essaki Arumugam EM, Anderson E, Gunn A, Rech D, Turovets S, Tucker DM. Slow-Frequency pulsed transcranial electrical stimulation for modulation of cortical plasticity based on reciprocity targeting with precision electrical head modeling. Frontiers in Human Neuroscience. 2016;10:377. doi: 10.3389/fnhum.2016.00377.
- Marshall L, Mölle M, Hallschmid M, Born J. Transcranial direct current stimulation during sleep improves declarative memory. Journal of Neuroscience. 2004;24:9985–9992. doi: 10.1523/JNEUROSCI.2725-04.2004.
- Mekonnen A, Salvador R, Ruffini G, Miranda PC. The relationship between transcranial current stimulation electrode montages and the effect of the skull orbital openings. Conference Proceedings : Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference. 2012;2012:831–834. doi: 10.1109/EMBC.2012.6346060.
- Minhas P, Bikson M, Woods AJ, Rosen AR, Kessler SK. Transcranial direct current stimulation in pediatric brain: a computational modeling study. Conference Proceedings : Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. 2012;2012:859–862.
- Miranda PC, Pajevic S, Pierpaoli C, Hallett M, Basser PJ. The distribution of currents induced in the brain by magnetic stimulation: a finite element analysis incorporating DT-MRI-derived conductivity data. Proceedings of the International Society for Magnetic Resonance in Medicine. 2001;9
- Miranda PC, Lomarev M, Hallett M. Modeling the current distribution during transcranial direct current stimulation. Clinical Neurophysiology. 2006;117:1623–1629. doi: 10.1016/j.clinph.2006.04.009.
- Nitsche MA, Paulus W. Excitability changes induced in the human motor cortex by weak transcranial direct current stimulation. The Journal of Physiology. 2000;527:633–639. doi: 10.1111/j.1469-7793.2000.t01-1-00633.x.
- Nitsche MA, Paulus W. Sustained excitability elevations induced by transcranial DC motor cortex stimulation in humans. Neurology. 2001;57:1899–1901. doi: 10.1212/WNL.57.10.1899.
- Nitsche MA, Nitsche MS, Klein CC, Tergau F, Rothwell JC, Paulus W. Level of action of cathodal DC polarisation induced inhibition of the human motor cortex. Clinical Neurophysiology. 2003;114:600–604. doi: 10.1016/S1388-2457(02)00412-1.
- Noury N, Hipp JF, Siegel M. Physiological processes non-linearly affect electrophysiological recordings during transcranial electric stimulation. NeuroImage. 2016;140:99–109. doi: 10.1016/j.neuroimage.2016.03.065.
- Oostendorp TF, Delbeke J, Stegeman DF. The conductivity of the human skull: results of in vivo and in vitro measurements. IEEE Transactions on Biomedical Engineering. 2000;47:1487–1492. doi: 10.1109/TBME.2000.880100.
- Opitz A, Legon W, Rowlands A, Bickel WK, Paulus W, Tyler WJ. Physiological observations validate finite element models for estimating subject-specific electric field distributions induced by transcranial magnetic stimulation of the human motor cortex. NeuroImage. 2013;81:253–264. doi: 10.1016/j.neuroimage.2013.04.067.
- Opitz A, Paulus W, Will S, Antunes A, Thielscher A. Determinants of the electric field during transcranial direct current stimulation. NeuroImage. 2015;109:140–150. doi: 10.1016/j.neuroimage.2015.01.033.
- Opitz A, Falchier A, Yan CG, Yeagle EM, Linn GS, Megevand P, Thielscher A, Deborah A R, Milham MP, Mehta AD, Schroeder CE. Spatiotemporal structure of intracranial electric fields induced by transcranial electric stimulation in humans and nonhuman primates. Scientific Reports. 2016;6:31236. doi: 10.1038/srep31236.
- Parazzini M, Fiocchi S, Rossi E, Paglialonga A, Ravazzani P. Transcranial direct current stimulation: estimation of the electric field and of the current density in an anatomical human head model. IEEE Transactions on Bio-Medical Engineering. 2011;58:1773–1780. doi: 10.1109/TBME.2011.2116019.
- Park JH, Hong SB, Kim DW, Suh M, Im CH. A novel array-type transcranial direct current stimulation (tDCS) system for accurate focusing on targeted brain areas. IEEE Transactions on Magnetics. 2011;47:882–885. doi: 10.1109/tmag.2010.2072987.
- Pereira JB, Junqué C, Bartrés-Faz D, Martí MJ, Sala-Llonch R, Compta Y, Falcón C, Vendrell P, Pascual-Leone A, Valls-Solé J, Tolosa E. Modulation of verbal fluency networks by transcranial direct current stimulation (tDCS) in Parkinson's disease. Brain Stimulation. 2013;6:16–24. doi: 10.1016/j.brs.2012.01.006.
- Peters J, Stinstra G, Hendriks MM. Estimation of the electrical conductivity of human tissue. Electromagnetics. 2001;21:545–557.
- Radhakrishna Rao C. Information and the accuracy attainable in the estimation of statistical parameters. Bulletin of the Calcutta Mathematical Society. 1945;37:81–91.
- Radman T, Ramos RL, Brumberg JC, Bikson M. Role of cortical cell type and morphology in subthreshold and suprathreshold uniform electric field stimulation in vitro. Brain Stimulation. 2009;2:215–228. doi: 10.1016/j.brs.2009.03.007.
- Rampersad S, Stegeman D, Oostendorp T. OP 11. optimized tDCS electrode configurations for five targets determined via an inverse FE modeling approach. Clinical Neurophysiology. 2013;124:e61–e62. doi: 10.1016/j.clinph.2013.04.078.
- Ranck JB. Specific impedance of rabbit cerebral cortex. Experimental Neurology. 1963;7:144–152. doi: 10.1016/S0014-4886(63)80005-9.
- Ranieri F, Podda MV, Riccardi E, Frisullo G, Dileone M, Profice P, Pilato F, Di Lazzaro V, Grassi C. Modulation of LTP at rat hippocampal CA3-CA1 synapses by direct current stimulation. Journal of Neurophysiology. 2012;107:1868–1880. doi: 10.1152/jn.00319.2011.
- Reato D, Rahman A, Bikson M, Parra LC. Low-intensity electrical stimulation affects network dynamics by modulating population rate and spike timing. Journal of Neuroscience. 2010;30:15067–15079. doi: 10.1523/JNEUROSCI.2059-10.2010.
- Reato D, Rahman A, Bikson M, Parra LC. Effects of weak transcranial alternating current stimulation on brain activity-a review of known mechanisms from animal studies. Frontiers in Human Neuroscience. 2013;7:687. doi: 10.3389/fnhum.2013.00687.
- Reis J, Fritsch B. Modulation of motor performance and motor learning by transcranial direct current stimulation. Current Opinion in Neurology. 2011;24:590–596. doi: 10.1097/WCO.0b013e32834c3db0.
- Rice JK, Rorden C, Little JS, Parra LC. Subject position affects EEG magnitudes. NeuroImage. 2013;64:476–484. doi: 10.1016/j.neuroimage.2012.09.041.
- Ruffini G, Wendling F, Merlet I, Molaee-Ardekani B, Mekonnen A, Salvador R, Soria-Frisch A, Grau C, Dunne S, Miranda PC. Transcranial current brain stimulation (tCS): models and technologies. IEEE Transactions on Neural Systems and Rehabilitation Engineering. 2013;21:333–345. doi: 10.1109/TNSRE.2012.2200046.
- Ruffini G, Fox MD, Ripolles O, Miranda PC, Pascual-Leone A. Optimization of multifocal transcranial current stimulation for weighted cortical pattern targeting from realistic modeling of electric fields. NeuroImage. 2014;89:216–225. doi: 10.1016/j.neuroimage.2013.12.002.
- Rullmann M, Anwander A, Dannhauer M, Warfield SK, Duffy FH, Wolters CH. EEG source analysis of epileptiform activity using a 1 mm anisotropic hexahedra finite element head model. NeuroImage. 2009;44:399–410. doi: 10.1016/j.neuroimage.2008.09.009.
- Rush S, Driscoll DA. Current distribution in the brain from surface electrodes. Anesthesia & Analgesia. 1968;47:717–723. doi: 10.1213/00000539-196811000-00016.
- Rush S, Driscoll DA. EEG electrode sensitivity–an application of reciprocity. IEEE Transactions on Bio-Medical Engineering. 1969;16:15–22.
- Sadleir RJ, Argibay A. Modeling skull electrical properties. Annals of Biomedical Engineering. 2007;35:1699–1712. doi: 10.1007/s10439-007-9343-5.
- Sadleir RJ, Vannorsdall TD, Schretlen DJ, Gordon B. Transcranial direct current stimulation (tDCS) in a realistic head model. NeuroImage. 2010;51:1310–1318. doi: 10.1016/j.neuroimage.2010.03.052.
- Schlaug G, Renga V, Nair D. Transcranial direct current stimulation in stroke recovery. Archives of Neurology. 2008;65:1571–1576. doi: 10.1001/archneur.65.12.1571.
- Senço NM, Huang Y, D'Urso G, Parra LC, Bikson M, Mantovani A, Shavitt RG, Hoexter MQ, Miguel EC, Brunoni AR. Transcranial direct current stimulation in obsessive-compulsive disorder: emerging clinical evidence and considerations for optimal montage of electrodes. Expert Review of Medical Devices. 2015;12:381–391. doi: 10.1586/17434440.2015.1037832.
- Shahid S, Wen P, Ahfock T. Numerical investigation of white matter anisotropic conductivity in defining current distribution under tDCS. Computer Methods and Programs in Biomedicine. 2013;109:48–64. doi: 10.1016/j.cmpb.2012.09.001.
- Smith SM. Fast robust automated brain extraction. Human Brain Mapping. 2002;17:143–155. doi: 10.1002/hbm.10062.
- Smith SM, Jenkinson M, Woolrich MW, Beckmann CF, Behrens TE, Johansen-Berg H, Bannister PR, De Luca M, Drobnjak I, Flitney DE, Niazy RK, Saunders J, Vickers J, Zhang Y, De Stefano N, Brady JM, Matthews PM. Advances in functional and structural MR image analysis and implementation as FSL. NeuroImage. 2004;23 Suppl 1:S208–S219. doi: 10.1016/j.neuroimage.2004.07.051.
- Stecker MM. Transcranial electric stimulation of motor pathways: a theoretical analysis. Computers in Biology and Medicine. 2005;35:133–155. doi: 10.1016/j.compbiomed.2003.12.005.
- Suh HS, Lee WH, Kim TS. Influence of anisotropic conductivity in the skull and white matter on transcranial direct current stimulation via an anatomically realistic finite element head model. Physics in Medicine and Biology. 2012;57:6961–6980. doi: 10.1088/0031-9155/57/21/6961.
- Thielscher A, Antunes A, Saturnino GB. Field modeling for transcranial magnetic stimulation: a useful tool to understand the physiological effects of TMS?. Engineering in Medicine and Biology Society (EMBC), 2015 37th Annual International Conference of the IEEE; IEEE; 2015. pp. 222–225.
- Truong DQ, Magerowski G, Blackburn GL, Bikson M, Alonso-Alonso M. Computational modeling of transcranial direct current stimulation (tDCS) in obesity: impact of head fat and dose guidelines. NeuroImage: Clinical. 2013;2:759–766. doi: 10.1016/j.nicl.2013.05.011.
- Tuch DS, Wedeen VJ, Dale AM, George JS, Belliveau JW. Conductivity tensor mapping of the human brain using diffusion tensor MRI. PNAS. 2001;98:11697–11701. doi: 10.1073/pnas.171473898.
- Vorwerk J, Cho JH, Rampp S, Hamer H, Knösche TR, Wolters CH. A guideline for head volume conductor modeling in EEG and MEG. NeuroImage. 2014;100:590–607. doi: 10.1016/j.neuroimage.2014.06.040.
- Wagner TA, Zahn M, Grodzinsky AJ, Pascual-Leone A. Three-dimensional head model simulation of transcranial magnetic stimulation. IEEE Transactions on Biomedical Engineering. 2004;51:1586–1598. doi: 10.1109/TBME.2004.827925.
- Wagner T, Fregni F, Fecteau S, Grodzinsky A, Zahn M, Pascual-Leone A. Transcranial direct current stimulation: a computer-based human model study. NeuroImage. 2007;35:1113–1124. doi: 10.1016/j.neuroimage.2007.01.027.
- Wagner S, Rampersad SM, Aydin Ü, Vorwerk J, Oostendorp TF, Neuling T, Herrmann CS, Stegeman DF, Wolters CH. Investigation of tDCS volume conduction effects in a highly realistic head model. Journal of Neural Engineering. 2014;11:016002. doi: 10.1088/1741-2560/11/1/016002.
- Windhoff M, Opitz A, Thielscher A. Electric field calculations in brain stimulation based on finite elements: an optimized processing pipeline for the generation and usage of accurate individual head models. Human Brain Mapping. 2013;34:923–935. doi: 10.1002/hbm.21479.
- Wolters CH, Anwander A, Tricoche X, Weinstein D, Koch MA, MacLeod RS. Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: a simulation and visualization study using high-resolution finite element modeling. NeuroImage. 2006;30:813–826. doi: 10.1016/j.neuroimage.2005.10.014.
- Yang AI, Wang X, Doyle WK, Halgren E, Carlson C, Belcher TL, Cash SS, Devinsky O, Thesen T. Localization of dense intracranial electrode arrays using magnetic resonance imaging. NeuroImage. 2012;63:157–165. doi: 10.1016/j.neuroimage.2012.06.039.
Source: PubMed