The theory of velocity selective neural recording: a study based on simulation.
ABSTRACT This paper describes the improvements to the theory of velocity selective recording and some simulation results. In this method, activity in different groups of axons is discriminated by their propagation velocity. A multi-electrode cuff and an array of amplifiers produce multiple neural signals; if artificial delays are inserted and the signals are added, the activity in axons of the matched velocity are emphasized. We call this intrinsic velocity selective recording. However, simulation shows that interpreting the time signals is then not straight-forward and the selectivity Q(v) is low. New theory shows that bandpass filters improve the selectivity and explains why this is true in the time domain. A simulation study investigates the limits on the available velocity selectivity both with and without additive noise and with reasonable sampling rates and analogue-to-digital conversion parameters. Bandpass filters can improve the selectivity by factors up to 7 but this depends on the speed of the action potential and the signal-to-noise ratio.
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ABSTRACT: In this paper, we describe the design and testing of a system for recording electroneurographic signals (ENG) from a multielectrode nerve cuff (MEC). This device, which is an extension of the conventional nerve signal recording cuff, enables ENG to be classified by action potential velocity. In addition to electrical measurements, we provide preliminary in vitro data obtained from frogs that demonstrate the validity of the technique for the first time. Since typical ENG signals are extremely small, on the order of 1 1 microV, very low-noise, high-gain amplifiers are required. The ten-channel system we describe was realized in a 0.8 microm CMOS technology and detailed measured results are presented. The overall gain is 10 000 and the total input-referred root mean square (rms) noise in a bandwidth 1 Hz-5 kHZ is 291 nV. The active area is 12 mm(2) and the power consumption is 24 mW from +/-2.5 V power supplies.IEEE Transactions on Neural Systems and Rehabilitation Engineering 01/2007; 14(4):427-37. · 3.26 Impact Factor
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ABSTRACT: A model is presented for the calculation of single myelinated fiber action potentials in an unbounded homogeneous medium and in nerve cuff electrodes. The model consists of a fiber model, used to calculate the action currents at the nodes of Ranvier, and a cylindrically symmetrical volume conductor model in which the fiber's nodes are represented as point current sources. The extracellular action potentials were shown to remain unchanged if the fiber diameter and the volume conductor geometry are scaled by the same factor (principle of corresponding states), both in an unbounded homogeneous medium and in an inhomogeneous volume conductor. The influence of several cuff electrode parameters, among others, cuff length and cuff diameter, were studied, and the results were compared, where possible, with theoretical and experimental results as reported in the literature.Biophysical Journal 07/1997; 72(6):2457-69. · 3.67 Impact Factor
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ABSTRACT: In the paper, a method using multiple-electrode nerve cuffs is presented that enables electroneurographic signals (ENG) to be recorded selectively by action potential velocity. The theory uses a one-dimensional model of the electrodes in the cuff. Using this model, the transfer function for a single tripole is derived, and it is shown that more than one tripole signal can be recorded from within a cuff. When many tripole signals are available and are temporally aligned by artificial delays and summed, there is a significant increase in the amplitude of the recorded action potential, depending on the cuff length and the action potential velocity, with the greatest gain occurring for low velocities. For example, a cuff was considered that was constrained by surgical considerations to 30 mm between the end electrodes. For action potentials with a velocity of 120 m s(-1), it was shown that, as the number of tripoles increased from one, the peak energy spectral density of the recorded output increased by a factor of about 1.6 with three tripoles, whereas, for 20 m s(-1), the increase was about 19, with ten tripoles. The time delays and summation act as a velocity-selective filter. With consideration of the energy spectral densities at frequencies where these are maximum (to give the best signal-to-noise ratio), the tuning curves are presented for these velocity-selective filters and show that useful velocity resolution is possible using this method. For a 30 mm cuff with nine tripoles, it is demonstrated that it is possible to resolve at least five distinct velocity bands in the range 20-120m s(-1).Medical & Biological Engineering & Computing 10/2004; 42(5):634-43. · 1.79 Impact Factor
Taylor, J., Clarke, C., Schuettler, M. and Donaldson, N. (2012)
The theory of velocity selective neural recording: a study based
on simulation. Medical and Biological Engineering and
Computing, 50 (3). pp. 309-318. ISSN 0140-0118
Link to official URL (if available): http://dx.doi.org/10.1007/s11517-
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The Theory of Velocity Selective Neural Recording: A
Study Based on Simulation
John Taylor1, Martin Schuettler2, Chris Clarke1 and Nick Donaldson3
1. Department of Electronic and Electrical Engineering, University of Bath, Bath UK
2. Laboratory for Biomedical Microtechnology, Department of Microsystems Engineering –
IMTEK, University of Freiburg, 79110 Freiburg, Germany.
3. Department Medical Physics and Bioengineering, University College London, London WC1 UK.
Corresponding author: John Taylor. Tel +44 (0)1225 38 3910; email firstname.lastname@example.org
Abstract- This paper describes improvements to the theory of velocity selective recording and some
simulation results. In this method, activity is different groups of axons is discriminated by their
propagation velocity. A multi-electrode cuff and an array of amplifiers produce multiple neural signals;
if artificial delays are inserted and the signals are added, the activity in axons of the matched velocity are
emphasized. We call this intrinsic velocity selective recording. However, simulation shows that
interpreting the time signals is then not straight-forward and the selectivity Qv is low. New theory shows
that bandpass filters improve the selectivity and explains why this is true in the time domain. A
simulation study investigates the limits on the available velocity selectivity both with and without
additive noise and with reasonable sampling rates and analogue-to-digital conversion (ADC) parameters.
Bandpass filters can improve the selectivity by factors up to 7 but this depends on the speed of the action
potential and the signal-to-noise ratio.
Keywords: Electroneurogram recording, Simulation, Multielectrode cuffs, Velocity selective recording
Total text words: 5848
Words in the abstract: 159
Number of figures: 6
Number of Tables: 2
Velocity selective recording (VSR) is a technique which should allow more information to be extracted
from an intact nerve with a recording set-up that does not allow action potentials from single fibres to be
seen at spikes [9, 1]. The method is in essence very simple and relies on taking measurements of a
propagating action potential (AP) at two or more points. The distance between the sample points divided
by the delay between two appearance of the AP provides a measure of the propagation velocity.
Conversely, artificially delaying one or more signals before adding them gives a maximum response at
the matched velocity. This simple idea is not new and various researchers have investigated practical
adaptations of it in the past-e.g. [6, 11, 2, 3].
However, at present the idea has not been demonstrated with naturally-occurring nerve traffic though
experimenters have used multi-electrode cuffs (MECs) to observe appropriate outputs from compound
action potentials [5, 6, 11]. Two papers about the theory of VSR have been published by the same
authors [9, 1]. The first presented a spectral analysis of a single axon in an MEC with a tripolar (double-
differential) amplifier system and the signal processing arrangement shown in Figure 1. The bandpass
filter (BPF) that follows the adder was shown to improve selectivity in the velocity domain, however the
filters were ideal and of infinitesimal bandwidth. We envisage that a useful VSR system might actually
have several signal processing units (Figure 1), each matched to one of the propagation velocities of
functional significance .
The second theory paper  considered the thermal noise generated by the detection system and
compared its amplitude to that of the signal resulting from the summation of multiple single fibre action
potentials (SFAPs) which were assumed to occur at random times. This allowed the firing rates required
from various sizes of nerve fibre in a given MEC to provide a signal that could be detected above the
background noise to be calculated.
The current paper presents material which supplements and expands our earlier work [9, 1]. In essence it
is a study (by simulation) of improvements in velocity selectivity obtainable by the use of BPFs,
investigating in particular the limitations of the method with and without noise. The intended outcome of
this work is to achieve a significant improvement in the performance of VSR systems so that they can be
employed to discriminate between populations of naturally-occurring APs. As already noted, the
relatively poor velocity selectivity of the VSR systems tested to date has limited their application to
Deterministic models of nerve signals (i.e. SFAPs) are used exclusively in the study, the effects of
random signal generation being reserved for presentation in a subsequent paper.
2.1 Basic principles
The response of an MEC to a propagating SFAP has been discussed in detail elsewhere and is only very
briefly summarised here [9, 1]. The input to the MEC is a trans-membrane action potential function
(TMAP), Vm(t), with the corresponding spectrum Vm(f). The resulting SFAP is a propagating wave with
the time dependence of the underlying TMAP function, the relationship between the two being explained
in . For the purpose of simulation, we represent the TMAP function and its spectrum by the Fourier
transform pair :
Vm(t) = Atne-Bt
where A, B and n are constants and f is frequency (the symbology has been preserved from ). This
function has been proposed as a suitable basis for the simulation of mammalian ENG [8, 7, 10]. The
output Y(f, v), which is a function of both frequency and velocity, is obtained by treating the MEC as a
linear time-invariant system with transfer function H(f, v):
This equation describes the output of a cuff with N tripoles, electrode pitch d and propagation velocity v.
Ra, the intra-axonal resistance per unit length, has been assumed to be large compared to Re, the extra-
axonal resistances per unit length inside the cuff. The artificial time delays are multiples of (see  for
a full explanation). Equation 2 is the product of the spectrum of the TMAP (Vm(f)), the transfer function
of one tripole (Ho(f,v)), and the transfer function of the delay-and-add block (G(f,v)). At matched
velocities (i.e. where τ = d/v and v = vo in eqn (2)), eqn (2) reduces to:
The output of the system Y(f,v) is a function of two variables and it was pointed out in  that if f is
fixed by passing the output through a bandpass filter (so that f = f0), Y becomes a function of propagation
velocity v only, enabling the velocity selectivity profile (see the tuning curves in ) to be calculated.
We define a velocity quality factor, Qv, by analogy with linear systems in the frequency domain :
where v0 is the matched (i.e. peak) velocity and v3+ and v3- are the velocities at which the output has
fallen to 1/√2 (-3 dB) of the peak value. Close to the matched velocities, the velocity selectivity is
dominated by the function G(f,v) and an approximate formula for Qv was derived in :
Qv and its approximation (eqn (5)) will be used to characterise velocity profiles in this paper.
2.2 The intrinsic velocity spectrum (IVS)
If bandpass filtering is not applied, as noted above, the output will depend on v and on frequency
dependent elements in the system including the spectral properties of the input signal (i.e. the TMAP
function) and the characteristics of the channel. For these reasons, unlike the bandpass filtered version,
the resulting time domain function is difficult to interpret. Simulating in the time domain, Fig 2 is the
time-domain output of the adder in Fig 1 when the system is stimulated with a TMAP resulting in an
SFAP propagating at a velocity of 30 m/s. Two TMAP functions are considered, based on equation (1),
with the parameters given in Figs 2(b) and 2(c) (the scaling parameter A has been adjusted in both cases
so that the peak amplitudes of the functions are normalised to unity). The matched velocity vo is treated
as a parameter leading to the family of curves shown in Fig 2(a). The peak value is reached when the