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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 NSC 13663 No. of Pages 13, Model 5G 29 April 2012 Please cite this article in press as: Rattay F et al. Strength–duration relationship for intra- versus extracellular stimulation with microelectrodes. Neu- roscience (2012), http://dx.doi.org/10.1016/j.neuroscience.2012.04.004 1 Neuroscience xxx (2012) xxx–xxx 2 STRENGTH–DURATION RELATIONSHIP FOR INTRA- VERSUS 3 EXTRACELLULAR STIMULATION WITH MICROELECTRODES a a b,c 4 Q1 F. RATTAY, * L. P. PAREDES AND R. N. LEAO 2007; Sekirnjak et al., 2008; Horsager et al., 2009; Pezaris 21 5 a Institute for Analysis and Scientific Computing, Vienna University and Reid, 2009; Tehovnik et al., 2009) while avoiding side Q3 22 6 Q2 of Technology, A-1040 Vienna, Austria effects like co-stimulation of bypassing axons arising from 23 7 b Neurodynamics Laboratory, Department of Neuroscience, distant locations (Greenberg et al., 1999; Rattay and Re- 24 8 Uppsala University, Uppsala, Sweden satz, 2004). Considering the fact that neural substructures 25 9 c Brain Institute, Federal University of Rio Grande do Norte, Natal-RN, have different strength–duration characteristics may give 26 10 Brazil an opportunity for more selective stimulation. For example, 27 in the treatment of chronic pain during spinal cord stimula- 28 tion smaller dorsal column fibers can only be activated 29 11 Abstract—Chronaxie, a historically introduced excitability when pulse width is sufficiently large (Holsheimer et al., 30 time parameter for electrical stimulation, has been assumed to be closely related to the time constant of the cell mem- 2011). 31 brane. Therefore, it is perplexing that significantly larger Recently, the strength–duration relationship for extra- 32 chronaxies have been found for intracellular than for extra- cellular neural stimulation was analyzed under the 33 cellular stimulation. Using compartmental model analysis, assumption of a constant electrical field in flat, spherical 34 this controversy is explained on the basis that extracellular and cylindrical cells (Boinagrov et al., 2010). These inves- 35 stimulation also generates hyperpolarized regions of the tigations provided a biophysical basis for the stimulation 36 cell membrane hindering a steady excitation as seen in the with large electrodes and also explained effects of stimula- 37 intracellular case. The largest inside/outside chronaxie ratio tion with ultrashort pulses (<5 ls). In accordance with ret- 38 for microelectrode stimulation is found in close vicinity of inal ganglion cell experiments (Jensen et al., 2005), for 39 the cell. In the case of monophasic cathodic stimulation, pulse durations <2 ms, it was found that a 500 lm diam- 40 the length of the primarily excited zone which is situated between the hyperpolarized regions increases with eter electrode placed above the soma caused excitation 41 electrode–cell distance. For distant electrodes this results with significantly lower thresholds compared to a position 42 in an excitation process comparable to the temporal behav- above the axon. This result is unexpected given the 43 ior of intracellular stimulation. Chronaxie also varies along assumption that the axon is the most excitable part of a 44 the neural axis, being small for electrode positions at the neuron externally stimulated (Nowak and Bullier, 1998; 45 nodes of Ranvier and axon initial segment and larger at Rattay, 1999). Differences in experimental setups are the 46 the soma and dendrites. As spike initiation site can change reason for the controversy about such observations. Stim- 47 for short and long pulses, in some cases strength–duration ulation of the retina with large electrodes generates a 48 curves have a bimodal shape, and thus, they deviate from a rather constant field and consequently transverse currents 49 classical monotonic curve as described by the formulas of depolarize the cell membrane at one side and hyperpolar- 50 Lapicque or Weiss. Ó 2012 Published by Elsevier Ltd on behalf of IBRO. ize the cell at the opposite side. On the other hand, external 51 excitation with small electrodes is mainly based on stimu- 52 lating effects resulting from extracellular potential varia- 53 tions along the neural structure (Rushton, 1927; Ranck, 54 Key words: chronaxie, strength–duration curve, electrical 1975; Rattay, 1986, 1987, 1999). These facts vary the ex- 55 stimulation, microelectrode, activating function. pected excitation paradigm and should be carried in mind. 56 12 Voltage sensitive ion channel types and densities are 57 other important elements for neuron excitability. In rela- 58 13 INTRODUCTION tion to retinal implant, electrode positions applied at a 59 dense two-dimensional grid around the soma region of 60 14 Selective neural stimulation is a great challenge in the rabbit ganglion cells showed the lowest thresholds along 61 15 development of neural prostheses. As an example, active a small section of the axon, about 40 lm from the soma. 62 16 contacts of an electrode array implanted at the retina or At this axonal section, immunochemical staining revealed 63 17 other structures along the visual pathway should stimulate a dense band of voltage-gated sodium channels (Fried et 64 18 elements that elicit visual sensations corresponding to the al., 2009). Similarly, high sodium channel densities at the Q4 65 19 place in the array (Brindley, 1955; Zrenner, 2002; Dowling, axon initial segments (AIS) of cortical cells define sites for 66 20 ´ 2005; Fernandez et al., 2005; Fried et al., 2006; Cohen, action potential initiation under natural conditions (Stuart 67 et al., 1997; Yu et al., 2008; Hu et al., 2009) as well as 68 *Corresponding author. Tel: +43-1-58801-10114. spike initiation candidates for external stimulation with 69 E-mail address: [email protected] (F. Rattay). microelectrodes (Rattay and Wenger, 2010). 70 Abbreviations: AIS, axon initial segments; VSD, voltage sensitive dye. 0306-4522/12 $ - see front matter Ó 2012 Published by Elsevier Ltd on behalf of IBRO. http://dx.doi.org/10.1016/j.neuroscience.2012.04.004 1 NSC 13663 No. of Pages 13, Model 5G 29 April 2012 2 F. Rattay et al. / Neuroscience xxx (2012) xxx–xxx 71 A strength–duration curve describes electrode thresh- (Nowak and Bullier, 1998). Additionally, in cochlear im- 92 72 old current as function of stimulus pulse duration. Chron- plants, significantly shorter chronaxies have been de- 93 73 axie is defined as the time on such a strength–duration scribed in long-term (compared to acute) deafened 94 74 curve for twice the minimum (rheobase) current needed cochleae, indicating the loss of peripheral processes in 95 75 for very long pulses. Established by experimental find- many spiral ganglion cells (Shepherd et al., 2001). 96 76 ings, this excitability parameter was assumed to be rather Based on theoretical considerations, chronaxie has 97 77 independent from the distance between the current been suggested to be about 0.7 times the time constant 98 78 source and the excited cell (Weiss, 1901; Lapicque, of the cell membrane (Blair, 1932; Ranck, 1975; Reilly, 99 79 1907, 1929; Blair, 1932). 1992). Therefore, some authors assume chronaxie as 100 80 As different neural structures have different chronax- independent of in- or outside stimulation of the cell 101 81 ies, stimulus pulse duration is an important element for (Nowak and Bullier, 1998). This hypothesis contrasts with 102 82 selective stimulation as well as for electrophysiological reports of considerably larger chronaxies for intracellular 103 83 classification. For example, the shorter chronaxie of mye- than for extracellular stimulation (Ranck, 1975). 104 84 linated motorneurons compared to that of unmyelinated Discrepancy among different works prompts specula- 105 85 fibers of the myocardium allows safe stimulation with tions that experimental differences could be caused by 106 86 short pulses during artificial respiration. Motoneurons artifacts like sampling errors or neuronal damage during 107 87 then become activated with little disturbance of the recordings (Ranck, 1975). To address this controversy, 108 88 myocardial function (Voorhees et al., 1992). In electro- we systematically reproduced experimental findings using 109 89 physiological studies, extracellular gray matter stimulation computer simulations of a pyramidal cell and its simplified 110 90 shows larger chronaxies for somas than for axons, sup- rectified version for electrode positions at the dendrite, the 111 91 porting the idea that spike initiation occurs in the axon soma, the lateral ending of the AIS and the myelinated 112 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. Please cite this article in press as: Rattay F et al.
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