PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Ray Meddis: A model scientist
Christian J. Sumner1
1

Department of Psychology, Nottingham Trent University, Nottingham, UK

ABSTRACT
Ray was a scientist in the classical sense: a creative intellect who sought the truth. He was also someone who
had a profound impact on the career of many hearing scientists. Ray believed that to understand hearing it
was necessary to replicate its behavior in a computer model. His first major contribution in hearing was the“Meddis Haircell”, and a series of papers exploring the adaptation of firing rate in auditory nerve fibers.
These were accompanied by models of stream segregation, of pitch, of the segregation of concurrent vowels,
numerous models of the processing of sound by neurons in the auditory brainstem, and a non-linear model ofthe basilar membrane. In later years, Ray became increasingly interested in hearing loss, and the role of theolivocochlear system. Technology also deserves a special mention: Ray’s models were implemented insilicon, evaluated using automatic speech recognition, and even inspired a smart-phone based hearing aid.
Ray lives on in his work, but also his colleagues: those of us that learnt from him, worked with him, disagreed
with (yes!), were influenced by his work, and shared his passion for models of the auditory system.
Keywords: Ray Meddis, computational models, hearing

1. INTRODUCTION
Roll back to the 1980s (for me, at least): Live Aid, Dungeons and Dragons, and theBBC-microcomputer (32K, of course). But, though I didn’t know it yet, another 80’s classic, theMeddis Haircell (5), was going to be just as iconic and influential in my life.
Ray was the first hearing researcher I met. In the 1990s he was unique in the UK: a full time
auditory modeler (not one of those experimentalists who dabbled with models). I visited his labs, firstat the University of Loughborough and then the University of Essex. Like anyone else who showed apassion for hearing, and especially models of hearing, he welcomed me warmly from the first day. And
like for many others, meeting Ray Meddis was a pivotal event in my career.
Ray’s own career in research did not begin with hearing. His PhD was on the psychometrics ofmood, in which he studied the factor structure and correlations between different ratings of mood .
Following this he published several articles about rank methods in statistics, before beginning a
program of research into sleep, including publishing a book on his theories (7).
Eventually, Ray discovered his calling: developing computer models of how we hear. For over 35
years, Ray developed computer models of the auditory system, ranging from cochlear filtering toauditory scene analysis. In this article, I will attempt to provide a review of some of his (early) work,and the work that has had the greatest influence on my own. It is not possible to discuss all his work,and I apologize for that which has been omitted. Neither is it possible to provide the complete context
of related work by other authors of the time (more apologies). However, I will attempt to mention someof the developments that followed Ray’s contributions, to indicate his influence.
Overall, I wish to convey his creativity. He was a scientist who generated many ideas, about anaspect of the world that fascinated him. His ideas were not always right, but they were always of great
intellectual value and utility, and served to push forward our understanding of the auditory system.

2. THE PERIPHERY
Ray’s work in hearing began with the auditory periphery, and this is the area of hearing in which hepublished the most papers (32 articles) and arguably had the most impact on the field (>2500 citations at
the time of writing, according to Google Scholar).
1

christian.sumner@ntu.ac.uk

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2.1 The “Meddis Haircell”
The first publication in the field was a model of the inner haircell (IHC), and the adaptation of firing
rate observed on the auditory nerve (5). The model simulated the sound driven release, and recyclingof neurotransmitter at the IHC-auditory nerve synapse (Stage 5 in Figure 1). This model was
remarkably successful in reproducing the firing properties of the auditory nerve.
Previous models (reviewed in 4) had introduced increasingly complex arrangements ofneurotransmitter reservoirs, in order to account for observed adaptation characteristics. His model
proposed a process consistent with physiological evidence at other synapses: the recycling of
neurotransmitter. The limited supply rate of new transmitter, and the limited rates of reuptake andrecycling, all contributed to the adaptation and saturation characteristics of firing rate at the synapse.
It also had acceptable input-output non-linearity, rectification and phase-locking properties. This is agood example of Ray’s modeling philosophy: that a model’s properties should emerge naturally fromfaithful modelling of the mechanism, rather than by engineering-in each property explicitly.
Numerous modelling studies in the 1990s, including Ray’s, employed an initial bandpass filter tomodel the outer/middle ear transfer function, a linear Gammatone filterbank to model the mechanicalfiltering of the basilar membrane, and a haircell model. Often this was an array of “Meddis haircells”,
or a subsequent model proposed by Westerman and Smith which performed quite similarly but was
analytically tractable (8, 9). Either way, the result was a computationally efficient, and remarkably
functional “auditory frontend” which could be used as the input to models of subsequent processing.
These models were not without limitations. They did not capture the compressive nature of thecochlear filtering (due to the linear modelling of basilar membrane filtering). Nor could they accountfor the variation in firing rate as a function of level seen in different types of auditory nerve fibers. The
Meddis haircell also phase-locked to higher frequencies that that of mammals. In 2002, Ray, myself,
Lowel O’Mard and Enrique Lopez-Poveda published a revised IHC model (2) (Figure 1A). The
incorporation of a biophysical model of the filtering by the haircell membrane (10) provided thefurther low-pass filtering to correctly model the phase locking seen both in the haircell itself and theauditory nerve.

A.

Model schematic (2002)

Figure 1. Models of the auditory periphery. A. A
single channel of the DRNL and IHC model,
reproduced from (2). B. Diagram showing the
responses of the DNRL output (top) and the auditory
nerve model output (bottom), to individual pure tones
played at the CF of the DRNL filter: the contributionof the linear (L; grey) and non-linear (NL; black)pathways, and the effect of increasing the maximum
calcium conductance at the synapse. C. The
corresponding responses to pure tones of fixed levelthat vary in frequency. The upper panel in C shows
the responses of the linear and non-linear path
separately

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The 2002 model also proposed that Calcium channels at each synapse might determine the auditory
nerve fiber type. It is well established that, in all synapses, depolarization of the cell membrane(neuron or haircell) leads to the influx of Calcium, which in turn leads to the release of
neurotransmitter (Figure 1A, stage 4). Scaling the overall amount of Calcium (the number of ionchannels) at a synapse could act as a “gain” mechanism to determine the spontaneous rate.
Simultaneously, this determined the window of dynamic range over which the synapse operated,
determining the threshold of the nerve fiber and the shape of the rate-level function (Figure 1B).
Ray was passionate that wherever possible, the models should reflect mechanisms faithfully; that
this would lead to more elegant models with more predictive power. At the time there was noexperimental evidence to support the Calcium hypothesis for fiber type. Yet, recent data lend some
support to this idea (11). This model also proposed that he number of vesicles of neurotransmitter
ready for release at any one time was proposed to be small (~10), and this influenced the statistics ofauditory nerve action potentials. Recent work has greatly expanded the range of spiking statistics thatcan be accounted for by models with as few as 4 quanta (12, 13).
2.2 Basilar membrane filtering
The Dual-Resonance Non-Linear (DRNL) filter, developed with Enrique Lopez-Poveda and Lowel
O’Mard (14) to address the limitations of a linear filterbank, was a “non-linear bandpass” model (15).
It proposed that the basilar membrane could be modeled as two parallel filter pathways (Figure 1A,
Stage 2). The compressive pathway had a higher gain, and so determined the responses at low soundlevels, producing the sensitive ‘tip’ of the tuning curve. The linear pathway was of lower gain, but
because of the compression in the non-linear pathway, the output of the linear pathway dominated theoverall output at high sound levels (Figure 1B). The linear-pathway produced the low-frequency tailsof tuning curves, and led to a shift in center frequency with increasing sound levels (Figure 1C).
The DRNL was straightforward to fit to basilar membrane laser interferometry data (16); it
produced suppression effects and distortion products (14). It could also account for masking data inhuman subjects (17). In keeping with Ray’s modelling philosophy, several observed aspects ofcochlear non-linearity, such as two-tone suppression and phase reversal, were emergent properties ofthe model. Furthermore, by changing a single parameter in the DRNL, one could control the gain of the“cochlear amplifier”. Thus it could stimulate outer haircell damage, or the efferent control by the
medial oliviocochlear system, which synapses on to outer haircells, and modulate the energy that they
can impart to BM motion (18, 19).
The work of Ray, colleagues and others (20, 21) brought us the modern phenomenological cochlear
model: capable of reproducing a great many of the known properties of the auditory periphery. In someinstances such models can replace recordings from the auditory nerve, e.g.(22).
Recent data has consolidated the view that human auditory filters are narrower than in typicalexperimental mammals (23). The controversy surrounding this arose in part because different
psychophysical methods of estimating auditory filter widths give different estimates of cochlear
tuning (24). To my knowledge, no model of the auditory periphery has yet successfully accounted forboth ways of estimating cochlear tuning. Human models are necessarily are less constrained than thoseof animals; we do not know what human auditory nerve tuning curves look like. A well constrainedmodel of the human periphery, which can account quantitatively for this difference, and for other datasuch as two-tone suppression, would surely be a valuable step in fully understanding how cochlear
filtering influences human perception and communication.

3. PITCH
3.1 The autocorrelation model of pitch
In 1991, Michael Hewitt and Ray produced the definitive computational model of pitch processing(25) and his most cited work (>600 citations at the time of writin g). Based on the original
autocorrelation model proposed by Licklider (26), this model encapsulated the development of thisand contemporary theories at the time (27) concerning the importance of temporal coding of
periodicity in the auditory system for determining our perception of pitch.
The first stage of the model (Figure 2A) is a filterbank model of the auditory periphery similar tothat already described. The autocorrelation stage then reveals the periodic variation in firing rate ineach channel (Figure 2B, upper plot). These functions are pooled (i.e. averaged) across the filterbank

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channels and a subsequent algorithm identifies the pitch from this pooled -autocorrelation function(Figure 2B, lower plot), often by finding the delay at which the highest p eak occurs in the function.
Several similar models were produced since from Ray and others, e.g. (28). Although addressing
various limitations, a wide range of studies support that autocorrelation is a good model of pitch.
In the intervening years, there has been no evidence of autocorrelation being performed in any partof the auditory pathway. Numerous alternative mechanisms have been proposed e.g. (29), but the
puzzle of pitch remains.
Figure 2. The
autocorrelation modelof pitch. A. Model
schematic adaptedfrom (1). B. Example
autocorrelation output,
based on the modelfrom Smith et al. (4).
C. Pooled ACF
function.

4. BRAINSTEM AND MIDBRAIN NEURAL MODELS
Facilitated by their work on peripheral models, Ray and colleagues were well placed to study how
the representation produced by the cochlea might be transformed by the brainstem and midbrain.
4.1 Cochlear nucleus cells
The cochlear nucleus (CN) is the first site of auditory processing in the central nervous s ystem. To
a crude approximation, the CN can be considered as a set of parallel processing pathways operating on
the input from the auditory nerve. Knowledge of the connections, and understanding of the role ofthese connections within CN continues to grow. However, the responses of some CN neurons can beunderstood from the way that they integrate information across multiple auditory nerve fibers, andtheir intrinsic membrane properties. Stellate cells receive innervation from a number of auditory nerve
fibers with similar CFs. Below threshold they act as comparatively linear leaky-integrators of their
inputs. In response to a pure tone stimulus they exhibit particular precision in the timing of the first 2-3
action potentials. In a histogram of the timing of these spikes as a function of the time within thestimulus (a peri-stimulus time histogram; PSTH), this is visible as two or three distinct peaks at the
beginning of the response (Figure 3B). Due to these peaks, these neurons are classified as ‘choppers’.

Figure 3. Stellate cell model. A. Model
Schematic (adapted from 3). B. Example
of a sustained chopper (ChS) response
from (adapted from 3). C. Coefficient ofvariation (CV) of the response in B and of
a less regular transient chopper model
adapted from (3). D. Phase-locking in asustained chopper model to the frequency
of a sinusoidally amplitude modulatedtone, expressed as gain relative to themodulation in the stimulus waveform
adapted from (6).

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Chopper neurons vary in the degree to which the regularity of this spiking continues throughout the
response to a pure tone. Evidence suggested that inhibition played a key role in determining this (30).
Hewitt and Meddis (3) demonstrated further, that a single ‘integrate-and-fire’ type model neuron(Figure 3A) with no inhibition could reproduce this behavior, and regularity was dependent on thenumber of auditory nerve fibers innervating the neuron, the threshold and the current magnitude of theindividual inputs.
A further interesting property of this cell type was the way that it encoded the acoustic envelope.
The mean firing rate of neurons in CN is generally insensitive to frequency of amplitude modulation(AM). Rather, information about any modulation is encoded in the timing of spikes. This is notdissimilar to the way that auditory nerve fibers ‘phase-lock’ to low frequency carriers and AM.
However, unlike the auditory nerve, phase-locking in individual chopper neurons is ‘tuned’ to specificmodulation frequencies (31). Thus a logical hypothesis was that these neurons formed the first stage inan envelope extraction process in the brain, with different neurons being tuned to different modulation
frequencies. Meddis and Hewitt (32) demonstrated that their simple stellate neuron model
demonstrated similar phase-locking to the envelope as that observed in vivo.
Computer models have continued to contribute to our understanding of processing in the CN. For
example, models have shown how auditory nerve innervation contributes to the responses of onset andprimary-like neurons (33, 34), and have been instrumental in synthesizing how different membranecurrents contribute to response properties (35-37). Models of stellate-cells also successfully predicted
the existence of mode-locked (more complex patterns of synchronization to envelopes) spike trains inthese neurons (38). Such models are now informing our understanding about the consequences ofsynaptopathy (39).
4.2 Comodulation masking release
Although many properties of cochlear nucleus cells appear to arise from their int rinsic membrane
properties and their innervation via the auditory nerve, the importance of network processing in the
CN is becoming increasingly clear (40). One of the best established sources of local connections in the
VCN are the inhibitory connections provided by the D-stellates which are associated with‘onset-chopper’ responses. Ray and colleagues proposed that this wideband inhibitory circuit could
enhance signals in noise, by providing inhibition which was time locked to wide-band envelope
fluctuations, suppressing the response to the masker in conditions where a masker’s spectral energy
was co-modulated across a wide frequency range. This lead to an effect similar to the psychophysicalphenomenon known as co-modulation masking release (41, 42). This work highlighted how models of
the VCN could yield meaningful predictions about circuit processing , as has been more frequently
demonstrated in the dorsal region of CN, e.g. (43). Evidence continues to accumulate of circuitry in
VCN, e.g. (44). Perhaps the next frontier is to bring these models together at a large scale, e.g.(40).
With ever more computational power, simulating the entire cochlear nucleus may be sight.
4.3 Coincidence detection in the midbrain
One of the most controversial debates in the encoding of modulation has been the topographical (orperiodotopic) arrangement of neurons in the inferior colliculus (IC) which, unlike in the CN, show
rate-tuning to modulation frequency (45). The contribution of Hewitt and Meddis (32) was to show apossible way in which this firing rate sensitivity might arise from temporal modulation tuning ofcochlear nucleus stellate cells, which project to the IC. In this model, the firing rate-tuning isdetermined by the temporal tuning of a number of CN neurons converging onto one IC neuron. The
converging CN neurons have similar temporal tuning. Their locking to the envelope is most coincident
when stimulated with modulation frequencies close to the peak in the tMTFs of the CN model neurons.
Thus, the firing rate of the IC neuron increases close to the tMTF peaks in the CN stellate cells
projecting to it. The model was effective at reproducing the rate-sensitivity of IC neurons, and theeffects of sound level on those functions (45). It is clear, e.g. (46, 47) that several other factors can also
influence modulation tuning in the IC. Nevertheless this model demonstrated that it was relatively
simple to transform the temporal coding in the brainstem into a rate code in the midbrain.
4.4 A chopper neuron based pitch model
The possible role of cochlear nucleus stellate cells and coincidence detection in the IC for pitch
processing was subsequently investigated by Weigrebe and Meddis (48) and Meddis and O’Mard (49).
Their model was proposed as a physiologically plausible equivalent of the previous autocorrelation
model, with a similar overall architecture, but with different individual components. In place of an659

autocorrelation operation, for each frequency channel of the coch lear filterbank there was an array ofcochlear nucleus stellate cells. This was followed by a layer of inferior colliculus coincidence
detectors, individually tuned to the range of pitch periods required. Duplicated across the frequency
range of the cochlea, this created a two-dimensional ‘correlogram-like’ map of the periodicities
present in each frequency range. A subsequent set of across-frequency integrators for each delay
tuning, also presumed to be in the IC, formed the equivalent of the pooled -autocorrelation function
from which pitch judgements were to be made. This stellate cell model and the subsequent stages in the
IC demonstrated sensitivity to variations in stimuli consistent with pitch, such as the ability to extract
the pitch from a harmonic complex with a missing fundamenta l or sensitivity to linearly shifted (i.e.
inharmonic) components. This study stands as a valuable addendum to autocorrelation models ofpitch: the brain does have the computational facility to process the cues for pitch. The potential ofcoincidence detection for processing pitch has now been demonstrated several times, e.g. (50-52).

5. FINAL REMARKSThis short article has focused on a subset of Ray’s work. It omits many other contributions by him,
his colleagues, and does a poor service to many other scientists who shared his passion and inspired
him. Ray had a tremendous influence on not only the research but the lives of individuals. He careddeeply not only about the topic but also the people he worked with, mentored, and his colleagues in thewider community. One last point: Ray began his work in hearing, creating models of the auditory
system was a relative rarity. Today, complex numerical methods and computational models areindispensable and standard tools. This means there are more opportunities for the next generation ofauditory modelers to follow in the footsteps of Ray. I’m pretty sure he would be happy about that.

ACKNOWLEDGEMENTS
I would like to thank Sam Smith for providing the model outputs used in Figure 2, and to Sam andan anonymous reviewer for helpful comments on this manuscript.

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