IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY Phys. Med. Biol. 52 (2007) 5603–5617 doi:10.1088/0031-9155/52/18/009 Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fields P C Miranda 1 , L Correia 1 , R Salvador 1 and P J Basser 2 1 Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, 1749-016 Lisbon, Portugal 2 Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, MD 20892-1428, USA E-mail: pcmiranda@fc.ul.pt Received 16 April 2007, in final form 27 June 2007 Published 3 September 2007 Online at stacks.iop.org/PMB/52/5603 Abstract We investigate the heterogeneity of electrical conductivity as a new mechanism to stimulate excitable tissues via applied electric fields. In particular, we show that stimulation of axons crossing internal boundaries can occur at boundaries where the electric conductivity of the volume conductor changes abruptly. The effectiveness of this and other stimulation mechanisms was compared by means of models and computer simulations in the context of transcranial magnetic stimulation. While, for a given stimulation intensity, the largest membrane depolarization occurred where an axon terminates or bends sharply in a high electric field region, a slightly smaller membrane depolarization, still sufficient to generate action potentials, also occurred at an internal boundary where the conductivity jumped from 0.143 S m −1 to 0.333 S m −1 , simulating a white- matter-grey-matter interface. Tissue heterogeneity can also give rise to local electric field gradients that are considerably stronger and more focal than those impressed by the stimulation coil and that can affect the membrane potential, albeit to a lesser extent than the two mechanisms mentioned above. Tissue heterogeneity may play an important role in electric and magnetic ‘far-field’ stimulation. 1. Introduction Neural stimulation using low frequency electric fields may be achieved through a variety of mechanisms. For long, straight, uniform unmyelinated fibres, the passive response of the axon to an applied electric field,  E, can be modelled in terms of the cable equation (Basser and Roth 1991, Roth and Basser 1990) λ 2 ∂ 2 V ′ ∂ 2 x − τ ∂V ′ ∂t − V ′ = λ 2 ∂E x ∂x , (1) 0031-9155/07/185603+15$30.00 © 2007 IOP Publishing Ltd Printed in the UK 5603