Strength-duration relationship for extracellular neural stimulation

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POSTER PRESENTATION Open Access
Strength-duration relationship for extracellular
neural stimulation
David Boinagrov1,2*, Jim Loudin1,3, Daniel Palanker1,4
From Nineteenth Annual Computational Neuroscience Meeting: CNS*2010
San Antonio, TX, USA. 24-30 July 2010
Understanding the mechanisms and dynamics of extra-
cellular neural stimulation is very important for the
development of electro-neural interfaces in general, and
for the design of stimulation waveforms and electrode
configurations for neural prosthetic implants, in particu-
lar. The most common type of neural stimulation is
extracellular, and yet its mechanisms and dynamics have
scarcely been explored and described. Its strength-dura-
tion relationship is often assumed to be similar to the
classical intracellular dependence, with a slope asympto-
tically approaching 1/τ at pulse durations τ shorter than
chronaxy. The current study explores the basic mechan-
isms of extracellular stimulation and derives its
strength-duration curve in a wide range of stimulus
durations for various waveforms and cell shapes.
We used two different models of active membrane
properties: the Hodgkin-Huxley model of the squid
giant axon [1], and a six-channel salamander retinal
ganglion cell model [2]. Three cell geometries were ana-
lyzed: an idealized planar cell with two uniformly polar-
ized flat surfaces, and more realistic spherical and
cylindrical shapes corresponding to the soma and
unmyelinated axon or axon hillock.
The strength-duration relationship was found to differ
significantly from classical intracellular models. For the
Hodgkin-Huxley model at pulse durations between 4 μs
and 5 ms stimulation is dominated by sodium channels,
and has a slope of approximately –0.72 in log-log coor-
dinates. At shorter durations it is dominated by the
potassium channels, and has a much lower slope of
about –0.13. With pulses shorter than cell polarization
time (typically about 0.1-1 μs), it is dominated by polari-
zation dynamics, and asymptotically approaches the
classical –1 slope. For retinal ganglion cells we
demonstrate that extracellular stimulation can have not
only lower but also upper thresholds, and may be
impossible below certain pulse durations. For both cell
models we have found that in some stimulation regimes
the stimulus can hyperpolarize cells, suppressing rather
than stimulating spiking behavior. Thresholds for burst
stimuli can be either higher or lower than that of a sin-
gle pulse, depending on pulse duration. The modeled
thresholds were found to be comparable to published
experimental data obtained with rabbit retinal ganglion
cells. These results provide a biophysical basis for
understanding stimulation dynamics, and guidance for
optimizing the efficacy and safety of extracellular neural
stimulation.
Author details
1Hansen Experimental Physics Laboratory, Stanford University, Stanford,
CA 94305, USA.2Department of Physics, Stanford University, Stanford, CA
94305, USA.3Department of Applied Physics, Stanford University, Stanford,
CA 94305, USA.4Department of Ophthalmology, Stanford University,
Stanford, CA 94305, USA.
Published: 20 July 2010
References
1.Hodgkin AL, Huxley AF: A quantitative description of membrane current
and its application to conduction and excitation in nerve. Journal of
Physiology 1952, 117:500-554.
2.Fohlmeister JE, Miller RF: Impulse Encoding Mechanisms of Ganglion Cells
in the Tiger Salamander Retina. Journal of Neurophysiology 1997,
78:1935-1947.
doi:10.1186/1471-2202-11-S1-P144
Cite this article as: Boinagrov et al.: Strength-duration relationship for
extracellular neural stimulation. BMC Neuroscience 2010 11(Suppl 1):P144.
* Correspondence: boinagrov@gmail.com
1Hansen Experimental Physics Laboratory, Stanford University, Stanford,
CA 94305, USA
Boinagrov et al. BMC Neuroscience 2010, 11(Suppl 1):P144
http://www.biomedcentral.com/1471-2202/11/S1/P144
© 2010 Boinagrov et al; licensee BioMed Central Ltd.