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Strength–Duration Relationship for Intra- Versus Extracellular Stimulation with Microelectrodes

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Strength–Duration Relationship for Intra- Versus Extracellular Stimulation with Microelectrodes View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Neuroscience 214 (2012) 1–13 STRENGTH–DURATION RELATIONSHIP FOR INTRA- VERSUS EXTRACELLULAR STIMULATION WITH MICROELECTRODES F. RATTAY, a* L. P. PAREDES a AND R. N. LEAO b,c et al., 2009; Pezaris and Reid, 2009; Tehovnik et al., a Institute for Analysis and Scientific Computing, Vienna University 2009) while avoiding side effects like co-stimulation of of Technology, A-1040 Vienna, Austria bypassing axons arising from distant locations (Greenberg b Neurodynamics Laboratory, Department of Neuroscience, et al., 1999; Rattay and Resatz, 2004). Considering the Uppsala University, Uppsala, Sweden fact that neural substructures have different strength– c Brain Institute, Federal University of Rio Grande do Norte, duration characteristics may give an opportunity for more Natal-RN, Brazil selective stimulation. For example, in the treatment of chronic pain during spinal cord stimulation smaller dorsal column fibers can only be activated when pulse width is Abstract—Chronaxie, a historically introduced excitability sufficiently large (Holsheimer et al., 2011). time parameter for electrical stimulation, has been assumed Recently, the strength–duration relationship for extra- to be closely related to the time constant of the cell mem- cellular neural stimulation was analyzed under the brane. Therefore, it is perplexing that significantly larger chronaxies have been found for intracellular than for extra- assumption of a constant electrical field in flat, spherical cellular stimulation. Using compartmental model analysis, and cylindrical cells (Boinagrov et al., 2010). These inves- this controversy is explained on the basis that extracellular tigations provided a biophysical basis for the stimulation stimulation also generates hyperpolarized regions of the with large electrodes and also explained effects of stimu- cell membrane hindering a steady excitation as seen in the lation with ultrashort pulses (<5 ls). In accordance with intracellular case. The largest inside/outside chronaxie ratio retinal ganglion cell experiments (Jensen et al., 2005), for microelectrode stimulation is found in close vicinity of for pulse durations <2 ms, it was found that a 500 lm the cell. In the case of monophasic cathodic stimulation, diameter electrode placed above the soma caused excita- the length of the primarily excited zone which is situated tion with significantly lower thresholds compared to a between the hyperpolarized regions increases with elec- position above the axon. This result is unexpected given the trode–cell distance. For distant electrodes this results in an excitation process comparable to the temporal behavior assumption that the axon is the most excitable part of a of intracellular stimulation. Chronaxie also varies along the neuron externally stimulated (Nowak and Bullier, 1998; neural axis, being small for electrode positions at the nodes Rattay, 1999). Differences in experimental setups are of Ranvier and axon initial segment and larger at the soma the reason for the controversy about such observations. and dendrites. As spike initiation site can change for short Stimulation of the retina with large electrodes generates and long pulses, in some cases strength–duration curves a rather constant field and consequently transverse cur- have a bimodal shape, and thus, they deviate from a classi- rents depolarize the cell membrane at one side and cal monotonic curve as described by the formulas of Lapic- hyperpolarize the cell at the opposite side. On the other que or Weiss. hand, external excitation with small electrodes is mainly Ó 2012 IBRO. Published by Elsevier Ltd. Open access under based on stimulating effects resulting from extracellular CC BY-NC-ND license. potential variations along the neural structure (Rushton, Key words: chronaxie, strength–duration curve, electrical 1927; Ranck, 1975; Rattay, 1986, 1987, 1999). These stimulation, microelectrode, activating function. facts vary the expected excitation paradigm and should be carried in mind. Voltage sensitive ion channel types and densities are INTRODUCTION other important elements for neuron excitability. In rela- tion to retinal implant, electrode positions applied at a Selective neural stimulation is a great challenge in the dense two-dimensional grid around the soma region of development of neural prostheses. As an example, active rabbit ganglion cells showed the lowest thresholds along contacts of an electrode array implanted at the retina or a small section of the axon, about 40 lm from the soma. other structures along the visual pathway should stimulate At this axonal section, immunochemical staining revealed elements that elicit visual sensations corresponding to the a dense band of voltage-gated sodium channels (Fried place in the array (Brindley, 1955; Zrenner, 2002; et al., 2009). Similarly, high sodium channel densities at Dowling, 2005; Ferna´ndez et al., 2005; Fried et al., the axon initial segments (AIS) of cortical cells define sites 2006; Cohen, 2007; Sekirnjak et al., 2008; Horsager for action potential initiation under natural conditions (Stuart et al., 1997; Yu et al., 2008; Hu et al., 2009) as well *Corresponding author. Tel: +43-1-58801-10114. as spike initiation candidates for external stimulation with E-mail address: frank. rattay@tuwien. ac. at (F. Rattay). microelectrodes (Rattay and Wenger, 2010). Abbreviations: AIS, axon initial segments; VSD, voltage sensitive dye. 0306-4522 Ó 2012 IBRO. Published by Elsevier Ltd. Open access under CC BY-NC-ND license. http://dx.doi.org/10.1016/j.neuroscience.2012.04.004 1 2 F. Rattay et al. / Neuroscience 214 (2012) 1–13 A strength–duration curve describes electrode thresh- implants, significantly shorter chronaxies have been old current as function of stimulus pulse duration. Chron- described in long-term (compared to acute) deafened axie is defined as the time on such a strength–duration cochleae, indicating the loss of peripheral processes in curve for twice the minimum (rheobase) current needed many spiral ganglion cells (Shepherd et al., 2001). for very long pulses. Established by experimental find- Based on theoretical considerations, chronaxie has ings, this excitability parameter was assumed to be rather been suggested to be about 0.7 times the time constant independent from the distance between the current of the cell membrane (Blair, 1932; Ranck, 1975; Reilly, source and the excited cell (Weiss, 1901; Lapicque, 1992). Therefore, some authors assume chronaxie as 1907, 1929; Blair, 1932). independent of in- or outside stimulation of the cell As different neural structures have different chronax- (Nowak and Bullier, 1998). This hypothesis contrasts with ies, stimulus pulse duration is an important element for reports of considerably larger chronaxies for intracellular selective stimulation as well as for electrophysiological than for extracellular stimulation (Ranck, 1975). classification. For example, the shorter chronaxie of mye- Discrepancy among different works prompts specula- linated motorneurons compared to that of unmyelinated tions that experimental differences could be caused by fibers of the myocardium allows safe stimulation with artifacts like sampling errors or neuronal damage during short pulses during artificial respiration. Motoneurons recordings (Ranck, 1975). To address this controversy, then become activated with little disturbance of the we systematically reproduced experimental findings using myocardial function (Voorhees et al., 1992). In electro- computer simulations of a pyramidal cell and its simplified physiological studies, extracellular gray matter stimulation rectified version for electrode positions at the dendrite, the shows larger chronaxies for somas than for axons, soma, the lateral ending of the AIS and the myelinated supporting the idea that spike initiation occurs in the axon (Fig. 1). In all cases shown in Fig. 1B, the intracellu- axon (Nowak and Bullier, 1998). Additionally, in cochlear lar/extracellular chronaxie ratio is two or higher. It is A B dend SOMA apical soma dend is not excitable for shorter pulses dendrite DEND ais node AIS 100 NEURON 1 NEURON 2 NODE rectified CHRONAXIE neuron NODE electrode positions node AIS 50 µm main 10 dendrite DEND dend above dendrite dend ais d~4,7µm extracellular stimulation SOMA soma soma soma basal AIS axon hillock AIS dendrite naked 1 µA axon 0.01 0.1 1 10 ms N.R. PULSE DURATION N.R. naked (thin) axon SOMA myelin. N.R. node axon first dend N.R. N.R. internode DEND 0.1 N.R. N.R. soma unmyel. NODE N.R. = node of Ranvier axon N.R. N.R. N.R. 0.01 ais N.R. AIS N.R. internode intracellular stimulation 200µm N.R. node NODE N.R. N.R. 0.001 N.R. N.R. x N.R. 0.0001 Fig. 1. Strength–duration curves of the investigated pyramidal cell. (A) Neuron 1 (left) and Neuron 2 (right) with selected electrode positions. (B) Strength–duration curves with chronaxie values for electrode positions as marked in A. Lower and upper case letters are used for electrode positions for Neuron 1 and Neuron 2, respectively. Color coding of lines in B corresponds to electrode positions in A. For better discrimination some extracellular strength–duration curves are shown as broken lines. Colors of break point markers are without meaning. Anodic and cathodic square pulses for intra- and extracellular stimulation, respectively. F. Rattay et al. / Neuroscience 214 (2012) 1–13 3 important to note that these ratios depend on cell proper- equations of the different variables
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