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Noise and selectivity of velocity-selective multi-electrode nerve cuffs

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Abstract

Using a multi-electrode nerve-signal recording cuff and a method of signal processing described previously, activity in axons with different propagation velocities can be distinguished, and the relative amplitude of the small-fibre signals increased. This paper is, largely, an analysis of the selectivity and noise of this system though impedance measurements from an actual cuff are included. The signal processor includes narrow band-pass filters. It is shown that the selectivity and noise both increase with the centre frequencies of these filters. A convenient approach is to make the filter frequencies inversely related to the artificial time delays so that the filter ‘Q’s are approximately constant and the noise densities are equal for all velocity filters. Numerical calculations, using formulae for this system and for the conventional tripole, based on a fixed cuff size and tissue resistivity, find the number of action potentials per second that must pass through the cuff so that the signal power equals the noise power. For slow fibres (20 m/s), the rate is 14 times lower for the multi-electrode cuff than the tripole, a significant advantage for recording from these fibres.

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Fig. 1
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Fig. 3
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Fig. 5
Fig. 6

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Abbreviations

A, B, C :

constants of TMAP function (Eq. 2)

DSP:

digital signal processor

v :

velocity of action potentials (AP)

V AO :

voltage spectrum at the adder output (AO)

V m :

voltage spectrum of the trans-membrane action potential (TMAP)

H 0 :

transfer function of the tripole

G :

transfer function of the delay-&-add

d :

electrode pitch

R s :

spreading resistance of one electrode

R e :

axial resistance through the cuff between the end electrodes

L e :

axial distance through the cuff between the end electrodes

N :

number of tripoles in the multi-electrode cuff (MEC)

τ :

artificial time delay (Fig. 1)

v0, v+, v−:

centre, higher −3 dB, and lower −3 dB velocities of the velocity-selective filter

Q v :

Q-factor for filter where \( Q_{v} = \frac{{v_{0} }}{{v_{ + } - v_{ - } }} \)

α, β, γ :

fractions of noise added after delays (Eq. 14)

P :

power spectral density (PSD)

E :

energy spectral density (ESD)

TAO:

tripolar amplifier output

k :

Boltzmann’s constant (1.38 × 10−23 J/K)

T :

absolute temperature

G 1, G 2 :

gains of first- and second-rank amplifiers A1 and A2 (Fig. 5)

n :

index for elements in Fig. 5

Ψ :

function of cuff defined by Eq. 21 and used in Eq. 22

SNR:

signal-to noise ratio after the bandpass filters (BPF)

SPU:

signal processing unit (see Fig. 1)

BPF:

bandpass filter (always narrow in this paper)

f :

frequency equivalent to ω/(2π)

r :

average action potential rate (AP/s), from all fibres in appropriate range of velocity

f1, f2:

band edges of wide-band tripole amplifier (500 and 5,000 Hz here)

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Acknowledgments

We thank the UK EPSRC (Grant GR/S93790/01) and the CEU (IMANE STREP 026602) for supporting this work; and also the German Academic Exchange Service (DAAD) for M. Schuettler’s fellowship.

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Authors and Affiliations

  1. Implanted Devices Group, University College London, London, UK

    N. Donaldson

  2. Department of Electronic Engineering, National Sun Yat Sen University, Kaohsiung, Taiwan, ROC

    R. Rieger

  3. IMTEK, Albert-Ludwigs University of Freiburg, Freiburg, Germany

    M. Schuettler

  4. Department of Electronic Engineering, University of Bath, Bath, UK

    J. Taylor

  5. Department of Medical Physics and Bioengineering, University College, Gower Street, London, WC1E 6BT, UK

    N. Donaldson

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  1. N. Donaldson
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  2. R. Rieger
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  4. J. Taylor
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Correspondence to N. Donaldson.

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Donaldson, N., Rieger, R., Schuettler, M. et al. Noise and selectivity of velocity-selective multi-electrode nerve cuffs. Med Biol Eng Comput 46, 1005–1018 (2008). https://doi.org/10.1007/s11517-008-0365-4

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  • DOI: https://doi.org/10.1007/s11517-008-0365-4

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