Optimal Pulse Widths for Effective Use of the Electrode Surface Area

Mesut Sahin, IEEE Senior Member Department of Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ, USA

Abstract—The strength-duration curve defines the relation between pulse amplitude and pulse width for threshold pulses in neural stimulation. Both Blair’s and Lapicque’s equations predict the minimum charge to occur at the shortest pulse widths. On the other hand, the maximum injectable charge through a practical neural electrode increases with the pulse width, as suggested by some reports. Therefore, it is conceivable that there may be an optimum pulse width where the goal function of charge injection capacity of the electrode / the activation threshold for neural stimulation is maximized. In this paper, the strength-duration relation for mammalian nerves was simulated using a local nerve model and the charge injection capacity of titanium nitride electrodes was measured experimentally. The goal function was maximum for the smallest pulse width tested with the rectangular pulses. However, the optimal point occurred at larger pulse widths for the linearly decreasing pulse waveforms. These optimized pulse parameters may be preferable in applications where current requirements are demanding in order to keep the electrode contact areas small. Keywords--- Local nerve models, charge injection capacity, titanium nitride electrodes

I. INTRODUCTION

Electrical stimulation currently offers a method to improve the disrupted function in a number of neurological disorders and many new applications are on the horizon [1-3]. Historically the rectangular waveform has been the choice for the current or voltage pulses employed in neural stimulators. Current pulses are preferred over voltage pulses to eliminate variations in the stimulation threshold as a result of the changes in the electrode-tissue impedance. For rectangular stimuli, the amplitude and duration together determine the stimulus strength and therefore the volume of activation in neural tissue. The relation between the amplitude and pulse duration was named strength-duration curve and it was formulated by Lapicque [4],[5] first who showed that the strength-duration curves for all excitable tissues had a similar form with different chronaxie times. Later Blair [6],[7] assumed that tissue can be modeled by an RC network and proposed an exponential function for the strength-duration curve. These two formula have been found mostly sufficient to explain experimental data for

interacellular and extracellular stimulation of neurons. Some reports recently criticized their ability to fit experimental data [8],[9].

The chronaxie time (C) and rheobase current (Ir) are the two parameters that define the strength-duration curve. Some recent reports suggest that the chronaxie time for neural stimulation is a function of the stimulus waveform. Wessale et al. quantitatively compared the threshold stimulus currents of rectangular and exponentially decaying waveforms, and found that the chronaxie time of the latter was about twice as long as that of the former [10]. To our knowledge, there have been no other reports of how the strength-duration curve is affected by the stimulus waveform.

On the other hand, electrodes of micro scale are needed to localize the volume of activation in many neural prosthetic applications, particularly in the central nervous system. Small electrode sizes demand larger charge densities than traditional noble metal and capacitor electrodes can provide, such as platinum and tantalum oxide electrodes. Novel materials with higher charge injection capacities have been searched to reduce the size of stimulation electrodes [11]-[13].

The large interface capacitance of the electrode-electrolyte interface measured with slow cyclic voltammetry is not available at fast rates of current injection [11],[13]. This led to the proposal of electrode-electrolyte interface models similar to that of a transmission line to explain the differential behavior of the interface for short and long pulses [12].

It leads from the above discussion that non-rectangular pulse shapes may exist that can move the chronaxie time to longer pulse durations where the electrodes can handle more charges per unit surface area of the electrode. The optimal stimulus waveform should maximize the injectable charge through the electrode interface while keeping the activation threshold at a minimum.

In this report, the threshold charge for neural stimulation was investigated for rectangular and linearly decreasing waveforms using a local mammalian nerve model [14]. The charge injection capacity of titanium nitride electrodes were also measured for the same waveforms experimentally. Considering these simulated and experimental data, the waveforms that minimize the threshold charge for activation and maximize the injectable charge were determined. Titanium nitride was chosen because of its popularity as an electrode materials since it readily lends itself to reactive sputtering method and provides significant charge injection rates.

Proceedings of the 3rd InternationalIEEE EMBS Conference on Neural EngineeringKohala Coast, Hawaii, USA, May 2-5, 2007

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II. METHODS

A. Computer Simulations

Several models have been developed to study the basic

mechanisms underlying the generation and propagation of action potentials [15]-[19]. In this study, simulation of the membrane dynamics was based on the CRRSS model of Chiu et al. [18] with modification of Sweeney et al. [14] to adjust the temperature of the model to 37ºC. All simulations were conducted in Matlab®. Model variables were generated recursively using a time resolution of 0.1µs.

The pulse width was varied from 0.001 to 0.5ms both for rectangular (Rect) and linearly decreasing ramps (LinDec). The computer algorithm searched for the activation threshold at each pulse width by increasing the stimulus strength ( K ) in small steps. Activation was decided when the action potential peak crossed the zero line. The stimulus charge and energy were computed for this threshold stimulus. The threshold charge ( thQ ) was calculated as the integral of the stimulus waveform (Equ.1) and the threshold energy ( thE ) as the integral of the stimulus waveform squared (Equ. 2). Definitions of rheobase current ( rI ) and chronaxie time ( C ) were adopted from the Lapicque’s expression for strength-duration curve (Equ. 3 [7],[8]):

∫=τ

τ0

)()( dttIQ thth (Equ.1)

∫∝τ

τ0

2)()( dttIE thth (Equ.2)

)1()(τ

τ CIK rth += (Equ.3)

where τ is the pulse duration, and thI (t) is the current pulse waveform at threshold strength (Kth). The stimulus strength (Kth) is a scalar for the stimulus waveform. The electrode impedance is omitted from the energy equation (Equ. 2). B. Charge Injection Capacity (CIC) Measurements

The electrodes of this study were provided by the CNCT at University of Michigan. Three titanium nitride (TiN) contacts with areas of 177µm2 were studied. The electrodes were placed in a phosphate buffered normal saline (pH=7.4) at room temperature and the bias voltage was set to zero with respect to a large Ag/AgCl reference electrode. For measurements of CIC, cathodic current pulses were applied at a slow repetition rate (2.5Hz) to allow recovery between pulses. The pulse duration was set to 20, 40, 60, 80, 100, 200, 300, and 500µs. The selected stimulus waveform was generated in LabVIEW and outputted through PCI6071 data acquisition board (both from National Inst.). The computer generated voltage waveform was

converted into a current pulse using a custom designed circuit to ensure a fast rise time (<0.5µs) and thereby allowing an accurate measurement of the access voltage with a step function. The access voltage was subtracted from the applied voltage to find the electrode back voltage. The back voltage and the electrode current were sampled into the computer at 1MHz. Spike triggered averaging method was employed to reduce the noise in the current signal. The injected current amplitude was increased slowly with the help of a potentiometer in the voltage/current converter circuitry until the electrode back voltage reached a peak of -1.2V. This value was reported as the negative limit of the water window for TiN electrodes [13]. This procedure was repeated at each pulse width and the maximum current amplitudes were recorded. The CIC was calculated as the area under the current waveform and plotted against the pulse width. The ratio of the measured charge injection capacity of the electrodes over the simulated threshold charge from the nerve model was defined as the goal function that was to be maximized.

III. RESULTS

A. Chronaxie Times

Using Lapicque’s expression for the strength-duration curve (Equ. 3), the chronaxie time could be determined as the point where the energy was minimum (Equ. 2, Fig. 2). The chronaxie times were 59 and 90µs for Rect and LinDec pulses respectively.

B. Threshold Charge as a Function of Pulse Width

Threshold charges are plotted in Fig. 1 as a function of the pulse width. At short pulse widths, the charge for activation converges approximately to 85pC/cm2 in this local model for both waveforms. Although Rect requires more charge than LinDec at all pulse widths, it has a lower

Figure 1. Threshold charge versus pulse width for rectangular (solid line) and linearly decreasing pulse shapes.

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0

200

400

600

800

1000

0 0.1 0.2 0.3 0.4 0.5

pulse width (ms)

inje

cted

cha

rge

(pC

)

RectLinDec

Figure 3. Charge injection capacity of the titanium nitride microelectrodes tested for the rectangular and linearly decreasing pulse waveforms. Surface area of the electrodes was 177µm2. The voltage was limited at -1.2V and the bias was zero. The mean CIC at 0.5ms was 950±100 and 1057±93 (n=3 for all) for Rect and LinDec waveforms respectively.

charge threshold when each waveform is evaluated at its own chronaxie time (126 vs. 136 pC/cm2).

C. Charge Injection Capacity of TiN Electrodes

Charge injection capacity (CIC) of the TiN microelectrodes was measured experimentally as a function of pulse width (Fig. 3). The CIC increased several fold from

0.02ms to 0.5ms for both waveforms. The LinDec allowed the maximum charge injection for all pulse durations. D. The Goal Function

The CIC divided by the activation threshold was used as a measure to compare the stimulus waveforms quantitatively. Because each parameter was obtained in different platforms the ratio could only be used for comparison as a unitless variable. This measure is plotted in Fig. 4 at the pulse width values where the CIC was measured with the TiN electrodes. For the Rect waveform, the maximum did not occur within the pulse width range studied. The LinDec had a maximum that was larger than that of the Rect stimulus at 0.2ms. Thus, the LinDec waveforms proved to be more efficient for delivery of the stimulus current through TiN electrodes. This implies that the stimulation effect would be stronger for the maximum charge that can be delivered through an electrode with a given surface area. This in turn should result in more effective use of the electrode area and allow smaller electrode designs.

IV. CONCLUSIONS Computer simulations of our local nerve membrane

model show that the strength-duration relation and hence the chronaxie time varies as a function of the stimulus waveform. The CIC of titanium nitride microelectrodes is also stimulus waveform dependent. Linearly decreasing ramp provided the best charge injection for the pulse width range of 0.02 to 0.5ms. The linearly decreasing pulse waveform also generated a more efficient neural stimulation than the rectangular pulses at optimal pulse widths. Maximization of the stimulation effect implies more efficient use of the available electrode surface area and

Figure 2. Threshold energy versus pulse width for rectangular (solid line) and linearly increasing (dash) waveforms. Energy was calculated using Equ. 2 and the current pulse density that it takes to stimulate the local model.

Figure 4. The goal function for the rectangular(solid line) and linearly decreasing (dash line) waveforms. The CIC values measured in Fig. 3 were divided by the threshold charges simulated in Fig. 1 for each waveform. The vertical scale is in arbitrary units.

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hence allowing smaller electrode designs in demanding applications for the electrode size.

ACKNOWLEDGMENT Titanium nitride electrodes of this study were kindly provided by the Center of Neural Communication Technology, University of Michigan.

REFERENCES [1] T. Hillman, A.N. Badi, R.A. Normann, T. Kertesz, and C. Shelton,

“Cochlear nerve stimulation with a 3-dimensional penetrating electrode array,” Otol Neurotol. vol. 24(5), pp. 764-768, 2003.

[2] K.J. Otto, P.J. Rousche, and D.R. Kipke, “Microstimulation in auditory cortex provides a substrate for detailed behaviors,” Hear Res. vol. 210(1-2), pp. 112-117, 2005.

[3] P.J. Rousche and R.A. Normann, “Chronic intracortical microstimulation (ICMS) of cat sensory cortex using the Utah Intracortical Electrode Array,” IEEE Trans Rehab. Eng. vol. 7(1), pp. 56-68, March, 1999.

[4] H.A. Blair, “On the intensity-time relations for stimulation by electric currents. I.” J. Gen. Physiol., vol. 15, pp. 709-729, 1932.

[5] H.A. Blair, “On the intensity-time relations for stimulation by electric currents. II.” J. Gen. Physiol. vol. 15, pp. 731-755, 1932.

[6] L. Lapicque, “Definition experimentale de l’excitabilite,” Comptes Rendus Acad. Sci., vol. 67(2), pp. 280-283, 1909.

[7] L. Lapicque, “L’excitabilite en function du temps,” Paris: Presses Universitaries de France, 1926.

[8] G.M. Ayers, S.W. Aronson, L.A. Geddes, “Comparison of the ability of the Lapicque and exponential strength-duration curves to fit experimentally obtained perception threshold data,” Australasian Phys. & Eng. Sci. Med., vol. 9: pp. 111-116, 1986.

[9] G. Mouchawar, L.A. Geddes, J.D. Bourland, J.A. Pearce, “Ability of the Lapicque and Blair strength-duration curves to fit experimentally obtained data from the dog heart.” IEEE Trans. Biomed. Eng., vol. 36(9): pp. 971-974, 1989.

[10] J.L. Wessale, L.A. Geddes, G.M. Ayers, and K.S. Foster, “Comparison of rectangular and exponential current pulses for evoking sensation,” Ann Biomed Eng., vol. 20, pp. 237-244, 1992.

[11] S. Cogan, P.R. Troyk, J. Ehrlich, T.D. Plante, and D.E. Detlefsen, “Potential-biased, asymmetric waveforms for charge-injection with activated iridium oxide (AIROF) neural stimulation electrodes,” IEEE Tran. on BME., vol. 53, pp. 327-337, 2006.

[12] A. Norlin, J. Pan, and C. Leygraf, “Investigation of Electrochemical behavior of stimulating/sensing materials for pacemaker electrode applications. I. Pt, Ti, and TiN coated electrodes,” J. of Electroche mical Soc., vol. 152(2), pp. J7-J15, 2005.

[13] D.M. Zhou, R.J Greenberg, “ Electrochemical Characterization of Titanium Nitride Microelectrode Arrays for Charge-Injection Applications,’ IEEE Eng. in Med. and Biol. Conf., pp. 1964-1967, 2003.

[14] J.D. Sweeney, J.T. Mortimer, and D. Durand, “Modeling of mammalian myelinated nerve for functional neuromuscular electrostimulation,” IEEE 9th Ann. Conf. Eng. Med Biol. Soc., Boston, MA, pp. 1577-1578, 1987.

[15] A.L. Hodgkin and A.F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J.Physiol., vol.117, pp. 500-544, 1952.

[16] B. Frankenhaeuser and A.F. Huxley, “The action potential in the myelinated nerve fibre of Xenopus Laevis as computed on the basis of voltage clamp data,” J.Physiol., vol. 171, pp. 302-315, 1964.

[17] M. Horackova, W. Nonner, and R. Stampfli, “Action potentials and voltage clamp currents of single rat Ranvier nodes,” Pro. Int. Union Physiol. Sci., vol. 7, pp. 198, 1968.

[18] S.Y. Chiu, J.M. Ritchie, R.B. Rogart, and D. Stagg, “A quantitative description of membrane currents in rabbit myelinated nerve,” J. Physiol., vol. 292, pp.149-166, 1979.

[19] J.R. Schwarz and G. Eikhof, “Na currents and action potentials in rat myelinated nerve fibers at 20 and 37oC,” Pflugers Arch., vol. 409, pp. 569-577, 1987.

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