SUMMARY

The main aim of this work is to study different waveforms for selective small fiber activation in order to minimize charge injection when using anodal blocking. In order to performe this study, computer simulations have been done.

STATE OF THE ART

Electrical nerve stimulation is used to restore control of different organs. However, electrical stimulation results in an inverse recruitment order of nerve fibers since large fibers are activated before smaller ones. As a consequence, fast onset of muscle fatigue and poor force gradation are some drawbacks. Moreover, some applications, such as electromicturition and electrodefecation, require activation of small fibers without activation of the larger ones /1/.

Different methods have been proposed to achieve a more natural recruitment order: selective anodal block /2,3/, slowly rising pulses /4/ and high frequency block /5/. We have focussed in this study on the anodal block technique. This technique takes advantage of the different excitation and blocking thresholds for small and large fibers. It is possible with this technique, using a combination of excitation and selective blocking, to activate primarily the small diameter nerve fibers.

In order to obtain anodal blocking, relative large pulse widths and high amplitudes are used compared with a traditional stimulation pattern. This induces a larger charge injection, which could be harmful not only to the tissue but also to the electrode /6/. In the present study new pulse shapes are developed so that injected charge could be reduced. Because the action potential needs time to travel from the cathode to the anode, strong hyperpolarization is not needed at the beginning of the pulse. Pulse shapes with two different amplitude levels (a smaller amplitude at the beginning of the pulse) and with an increasing slope, have been simulated in a computer model and the reduction in the amount of charge injected has been evaluated. In addition, the effect of the use of a hyperpolarizing prepulse on the excitation and blocking thresholds has been analysed. Parameters such as hyperpolarizing pulse amplitude, pulse width and delay have been optimised to obtain maximum charge reduction.

MATERIAL AND METHODS

The electrical potential field generated by a cuff electrode (2 mm inner diameter) with metal ring contacts, spaced 3 mm, has been calculated using a volume conductor model described by Rijkhoff et al./7/. A nerve bundle with a radius of 0.7 mm has been used.

A nerve fiber model used to analyze the responses of the membrane to the extracellular electrical potential field is described by McNeal /8/. The Frankenhaeuser-Huxley equations, adapted for a rabbit according to Chiu et al. /9/, have been used to describe the membrane kinetics. All temperature-dependent parameters were scaled to 37 ºC /10/. Two different fiber diameters have been analyzed to study the selectivity (12 mm and 4 mm). The 12 mm fiber has been placed on the axis of the bundle and the 4 mm has been placed at the border. The cathode was always situated right above the central node of Ranvier of the fiber.

Parametric simulations have been done in order to investigate the different effects. The pulse shape was optimized so that it would result in a minimum charge injection, allowing a faster recovery of charge (with the subsequent possibility of increasing the signal frequency) and a safer stimulation pattern, able to generate fiber diameter selectivity.

RESULTS

A study of the influence of the waveform on the charge per pulse needed to block a 12 mm fiber situated on the axis has been done. Two different waveform shapes have been used (see Fig. 1).

A rectangular pulse with an A₁ amplitude during t₁ followed by an amplitude A₂during the rest of the pulse has been applied.

Fig. 2 shows the relationship between the initial amplitude (A₁) and the maximum time (t₁), for two fixed amplitudes A₂,in order to block the action potential generated under the cathode, along with the charge injected. It is shown how an increase in the amplitude A₁ allows an increase in the time t₁since a bigger hyperpolarization is generated under the anode. If a rectangular pulse with the same total width (210 ms) is used, an amplitude of 336 mA is needed to block the 12 mm fiber situated on the axis. This pulse injects a charge of 70.5 nQ. By analyzing and comparing the charge injected between the pulses, it is shown how up to a 13% charge reduction can be achieved by using this new shape.

In order to increase the time t₁ and thus, decrease charge injection, a bigger hyperpolarization is needed. The first part of the waveform has been replaced with a linear increasing amplitude starting at A₁ which reaches amplitude A₂ after t₁ ms (see Fig. 1 right). The value A₂ is maintained during the rest of the pulse.

Figure 3 (a) shows the results of the performed simulations. Again, an increase in the initial amplitude allows to have a bigger time t₁. However, comparing the total amount of charge injected (Fig. 3 b), similar values to the ones achieved by means of the use of the previous waveform are found; additionally,
a reduction of charge, related to the rectangular pulse, is obtained.

The influence of a hyperpolarizing prepulse on the excitation and blocking threshold of a 12 um fiber situated on the axes of the bundle has been investigated. Fig. 4 (a) represents the effect of a square anodic pulse (pulsewidth: 210 ms) on the excitation threshold versus the delay between the anodic pulse and the excitation pulse, for different anodic pulse amplitudes. Threshold excitation amplitude without prepulse is 110 µA. It shows that an increase in amplitude of the hyperpolarizing pulse results in a decrease in the activation threshold. However, the amplitude of the anodic pulse is limited because during hyperpolarizing prepulses, the anodes become cathodes and, a large enough current excites the fiber. On the other hand, an increase in the delay will bring the threshold to the initial value (threshold without prepulse), indicating that the membrane has recovered to its initial state.

The effect of the hyperpolarizing prepulses on the blocking threshold of a 12 mm fiber is shown in fig. 4b. Two different anodic currents pulses, both with a pulse width of 210 us, have been analysed. In both cases, a decrease in the threshold, in relation to the waveform without prepulse (336 mA), has been observed. It is shown how an increase in the amplitude of the cathodic pulse decreases the threshold of blocking. However, an increase in the delay will lead the membrane to its original state, producing an increase in the blocking threshold.

From the results of the previous analysis, a hyperpolarizing prepulse can be used to reduce the excitation and blocking threshold. As a consequence, the prepulse reduces the charge injected during the cathodical pulse and the total amount of charge injected because of the charge extraction that is produced during the anodical pulse. This charge reduction will allow us to work with higher stimulation frequencies since less charge is needed to extract.

DISCUSSION

Based on this study we conclude that anodal blocking can be obtained with new waveforms, which allow for a reduced charge injection. In addition to this pulse modification, the influence of the hyperpolarizing prepulse in the activation and blocking thresholds has been studied. Besides the threshold modification, the hyperpolarizing prepulse generates a previous charge extraction just before the injection, reducing the charge that needs to be extracted after the stimulation. The use of these shapes will be safer in chronic applications of anodal blocking.

REFERENCES

/1/ N. J. M. Rijkhoff, H. Wijkstra, P. E. V. Van Kerrebroeck, F. M. J. Debruyne, Urinary bladder control by electrical stimulation. Review of electrical stimulation techniques in spinal cord injury, Neurourol. & Urodyn., vol. 16, pp. 39-53, 1996.

/2/ G. S. Brindley and M.D. Craggs, A technique for anodally blocking large nerve fibers through chronically implanted electrodes, J. of Neurol. Neurosurg. and Psychiatry, vol. 43, pp. 1083-1090, 1980

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/5/ Bruce R. Bowman, Donald R. McNeal, Response of single alpha motoneurons to high-frequency pulse trains. Firing behavior and conduction block phenomenon, Appl. Neurophysiol, 49, pp. 121-138, 1986.

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/8/ D. R. McNeal, Analysis of a model for excitation of myelinated nerve, IEEE Tran. BME, vol. BME-23, pp. 329-337, 1976.

/9/ S. Y. Chiu, J, M. Ritchie, R. B. Rogart and D. Stagg, A quantitative description of membrane currents in rabbit myelinated nerve, J. of Physiol., vol 292, pp. 149-166, 1979

/10/ J. J. Struijk, J. Holsheimer, G.G. van der Heide and H. B. K. Boom, Recruitment of dorsal column fibers in spinal cord stimulation: Influence of collateral branching, IEEE Tran. BME, vol. 39, n 9, pp. 903-912, 1992.

ACKNOWLEDGEMENTS

This work has been realized in the SMI center (Aalborg University, Denmark), supported in part by the CICYT (under project number TIC 2000-1398) and funded by a grant from the Comissionat per a Universitats i Recerca (Generalitat de Catalunya, Spain)

ANODAL BLOCK: A COMPUTER STUDY