On the Effect of High Stimulation Rates on Temporal Loudness Integration in Cochlear Implant Users.

Long stimuli have lower detection thresholds or are perceived louder than short stimuli with the same intensity, an effect known as temporal loudness integration (TLI). In electric hearing, TLI for pulse trains with a fixed rate but varying number of pulses, i.e. stimulus duration, has mainly been investigated at clinically used stimulation rates. To study the effect of an overall effective stimulation rate at 100% channel crosstalk, we investigated TLI with (a) a clinically used single-channel stimulation rate of 1,500 pps and (b) a high stimulation rate of 18,000 pps, both for an apical and a basal electrode. Thresholds (THR), a line of equal loudness (BAL), and maximum acceptable levels (MALs) were measured in 10 MED-EL cochlear implant users. Stimulus durations varied from a single pulse to 300 ms long pulse trains. At 18,000 pps, the dynamic range (DR) increased by 7.36±3.16 dB for the 300 ms pulse train. Amplitudes at THR, BAL, and MAL decreased monotonically with increasing stimulus duration. The decline was fitted with high accuracy with a power law function (R2=0.94±0.06). Threshold slopes were -1.05±0.36 and -1.66±0.30 dB per doubling of duration for the low and high rate, respectively, and were shallower than for acoustic hearing. The electrode location did not affect the amplitudes or slopes of the TLI curves. THR, BAL, and MAL were always lower for the higher rate and the DR was larger at the higher rate at all measured durations.

Clinical Feasibility and Familiarization Effects of Device Delay Mismatch Compensation in Bimodal CI/HA Users.

Subjects utilizing a cochlear implant (CI) in one ear and a hearing aid (HA) on the contralateral ear suffer from mismatches in stimulation timing due to different processing latencies of both devices. This device delay mismatch leads to a temporal mismatch in auditory nerve stimulation. Compensating for this auditory nerve stimulation mismatch by compensating for the device delay mismatch can significantly improve sound source localization accuracy. One CI manufacturer has already implemented the possibility of mismatch compensation in its current fitting software. This study investigated if this fitting parameter can be readily used in clinical settings and determined the effects of familiarization to a compensated device delay mismatch over a period of 3-4 weeks. Sound localization accuracy and speech understanding in noise were measured in eleven bimodal CI/HA users, with and without a compensation of the device delay mismatch. The results showed that sound localization bias improved to 0°, implying that the localization bias towards the CI was eliminated when the device delay mismatch was compensated. The RMS error was improved by 18% with this improvement not reaching statistical significance. The effects were acute and did not further improve after 3 weeks of familiarization. For the speech tests, spatial release from masking did not improve with a compensated mismatch. The results show that this fitting parameter can be readily used by clinicians to improve sound localization ability in bimodal users. Further, our findings suggest that subjects with poor sound localization ability benefit the most from the device delay mismatch compensation.

[Interaural stimulation timing mismatch in listeners provided with a cochlear implant and a hearing aid : A review focusing on quantification and compensation]. / Unterschiedliche Stimulationszeitpunkte bei bimodaler Versorgung mit Hörgerät und Cochleaimplantat : Übersichtsartikel zu Quantifizierung und Kompensation.

Bimodal provision of patients with asymmetric hearing loss with a hearing aid ipsilaterally and a cochlear implant (CI) contralaterally is probably the most complicated type of CI provision due to a variety of inherent variables. This review article presents all the systematic interaural mismatches between electric and acoustic stimulation that can occur in bimodal listeners. One of these mismatches is the interaural latency offset, i.e., the time difference of activation of the auditory nerve by acoustic and electric stimulation. Methods for quantifying this offset are presented by registering electrically and acoustically evoked potentials and measuring processing delays in the devices. Technical compensation of the interaural latency offset and its positive effect on sound localization ability in bimodal listeners is also described. Finally, most recent findings are discussed which may explain why compensation of the interaural latency offset does not improve speech understanding in noise in bimodal listeners.

Effect of a processing delay between direct and delayed sound in simulated open fit hearing aids on speech intelligibility in noise.

Introduction: Subjects with mild to moderate hearing loss today often receive hearing aids (HA) with open-fitting (OF). In OF, direct sound reaches the eardrums with minimal damping. Due to the required processing delay in digital HA, the amplified HA sound follows some milliseconds later. This process occurs in both ears symmetrically in bilateral HA provision and is likely to have no or minor detrimental effect on binaural hearing. However, the delayed and amplified sound are only present in one ear in cases of unilateral hearing loss provided with one HA. This processing alters interaural timing differences in the resulting ear signals. Methods: In the present study, an experiment with normal-hearing subjects to investigate speech intelligibility in noise with direct and delayed sound was performed to mimic unilateral and bilateral HA provision with OF. Results: The outcomes reveal that these delays affect speech reception thresholds (SRT) in the unilateral OF simulation when presenting speech and noise from different spatial directions. A significant decrease in the median SRT from -18.1 to -14.7 dB SNR is observed when typical HA processing delays are applied. On the other hand, SRT was independent of the delay between direct and delayed sound in the bilateral OF simulation. Discussion: The significant effect emphasizes the development of rapid processing algorithms for unilateral HA provision.

Effects of Degrees of Degeneration on the Electrical Excitation of Human Spiral Ganglion Neurons Based on a High-Resolution Computer Model.

After hearing loss retrograde degeneration of spiral ganglion neurons (SGNs) has been described. Studies modeling the effects of degeneration mostly omitted peripheral processes (dendrites). Recent experimental observations indicated that degenerating SGNs manifested also a reduced diameter of their dendrites. We simulated populations of 400 SGNs inside a high resolution cochlear model with a cochlear implant, based on µCT scans of a human temporal bone. Cochlear implant stimuli were delivered as biphasic pulses in a monopolar configuration. Three SGN situations were simulated, based on our previous measurements of human SGN dendrites: (A) SGNs with intact dendrites (before degeneration), (B) degenerating SGNs, dendrites with a smaller diameter but original length, (C) degenerating SGNs, dendrites omitted. SGN fibers were mapped to characteristic frequency, and place pitch was estimated from excitation profiles. Results from degenerating SGNs (B, C) were similar. Most action potentials were initiated in the somatic area for all cases (A, B, C), except for areas near stimulating electrodes in the apex with intact SGNs (A), where action potentials were initiated in the distal dendrite. In most cases, degenerating SGNs had lower thresholds than intact SGNs (A) (down to -2 dB). Excitation profiles showed increased ectopic activation, i.e., activation of unintended neuronal regions, as well as similar neuronal regions excited by different apical electrodes, for degenerating SGNs (B, C). The estimated pitch showed cases of pitch reversals in apical electrodes for intact SGNs (A), as well as mostly identical pitches evoked by the four most apical electrodes for degenerating SGNs (B, C). In conclusion, neuronal excitation profiles to electrical stimulation exhibited similar traits in both ways of modeling SGN degeneration. Models showed degeneration of dendrites caused increased ectopic activation, as well as similar excitation profiles and pitch evoked by different apical electrodes. Therefore, insertion of electrodes beyond approximately 450° may not provide any benefit if SGN dendrites are degenerated.

Coil Efficiency for Inductive Peripheral Nerve Stimulation.

Magnetic stimulation of peripheral nerves is evoked by electric field gradients caused by high-intensity, pulsed magnetic fields created from a coil. Currents required for stimulation are very high, therefore devices are large, expensive, and often too complex for many applications like rehabilitation therapy. For repetitive stimulation, coil heating due to power loss poses a further limitation. The geometry of the magnetic coil determines field depth and focality, making it the most important factor that determines the current required for neuronal excitation. However, the comparison between different coil geometries is difficult and depends on the specific application. Especially the distance between nerve and coil plays a crucial role. In this investigation, the electric field distribution of 14 different coil geometries was calculated for a typical peripheral nerve stimulation with a 27 mm distance between axon and coil. Coil parameters like field strength and focality were determined with electromagnetic field simulations. In a second analysis, the activating function along the axon was calculated, which quantifies the efficiency of neuronal stimulation. Moreover, coil designs were evaluated concerning power efficacy based on ohmic losses. Our results indicate that power efficacy of magnetic neurostimulation can be improved significantly by up to 40% with optimized coil designs.

Influence of Auditory Cues on the Neuronal Response to Naturalistic Visual Stimuli in a Virtual Reality Setting.

Virtual reality environments offer great opportunities to study the performance of brain-computer interfaces (BCIs) in real-world contexts. As real-world stimuli are typically multimodal, their neuronal integration elicits complex response patterns. To investigate the effect of additional auditory cues on the processing of visual information, we used virtual reality to mimic safety-related events in an industrial environment while we concomitantly recorded electroencephalography (EEG) signals. We simulated a box traveling on a conveyor belt system where two types of stimuli - an exploding and a burning box - interrupt regular operation. The recordings from 16 subjects were divided into two subsets, a visual-only and an audio-visual experiment. In the visual-only experiment, the response patterns for both stimuli elicited a similar pattern - a visual evoked potential (VEP) followed by an event-related potential (ERP) over the occipital-parietal lobe. Moreover, we found the perceived severity of the event to be reflected in the signal amplitude. Interestingly, the additional auditory cues had a twofold effect on the previous findings: The P1 component was significantly suppressed in the case of the exploding box stimulus, whereas the N2c showed an enhancement for the burning box stimulus. This result highlights the impact of multisensory integration on the performance of realistic BCI applications. Indeed, we observed alterations in the offline classification accuracy for a detection task based on a mixed feature extraction (variance, power spectral density, and discrete wavelet transform) and a support vector machine classifier. In the case of the explosion, the accuracy slightly decreased by -1.64% p. in an audio-visual experiment compared to the visual-only. Contrarily, the classification accuracy for the burning box increased by 5.58% p. when additional auditory cues were present. Hence, we conclude, that especially in challenging detection tasks, it is favorable to consider the potential of multisensory integration when BCIs are supposed to operate under (multimodal) real-world conditions.

Measuring and Modeling Cue Dependent Spatial Release from Masking in the Presence of Typical Delays in the Treatment of Hearing Loss.

In asymmetric treatment of hearing loss, processing latencies of the modalities typically differ. This often alters the reference interaural time difference (ITD) (i.e., the ITD at 0° azimuth) by several milliseconds. Such changes in reference ITD have shown to influence sound source localization in bimodal listeners provided with a hearing aid (HA) in one and a cochlear implant (CI) in the contralateral ear. In this study, the effect of changes in reference ITD on speech understanding, especially spatial release from masking (SRM) in normal-hearing subjects was explored. Speech reception thresholds (SRT) were measured in ten normal-hearing subjects for reference ITDs of 0, 1.75, 3.5, 5.25 and 7 ms with spatially collocated (S0N0) and spatially separated (S0N90) sound sources. Further, the cues for separation of target and masker were manipulated to measure the effect of a reference ITD on unmasking by A) ITDs and interaural level differences (ILDs), B) ITDs only and C) ILDs only. A blind equalization-cancellation (EC) model was applied to simulate all measured conditions. SRM decreased significantly in conditions A) and B) when the reference ITD was increased: In condition A) from 8.8 dB SNR on average at 0 ms reference ITD to 4.6 dB at 7 ms, in condition B) from 5.5 dB to 1.1 dB. In condition C) no significant effect was found. These results were accurately predicted by the applied EC-model. The outcomes show that interaural processing latency differences should be considered in asymmetric treatment of hearing loss.

eABR THR Estimation Using High-Rate Multi-Pulse Stimulation in Cochlear Implant Users.

We estimated the electrically-evoked auditory brainstem response thresholds (eABR THRs) in response to multi-pulses with high burst rate of 10,000 pulses-per-second (pps). Growth functions of wave eV amplitudes, root mean square (RMS) values, peak of phase-locking value (PLV), and the lowest valid data point (LVDP) were calculated in 1-, 2-, 4-, 8-, and 16-pulses conditions. The growth functions were then fitted and extrapolated with linear and exponential functions to find eABR THRs. The estimated THRs were compared to psychophysical THRs determined for multi-pulse conditions as well as to the clinical THRs measured behaviorally at the rate of 1,000 pps. The growth functions of features showed shallower growth slopes when the number of pulses increased. eABR THRs estimated in 4-, 8-, and 16-pulses conditions were closer to the clinical THRs, when compared to 1- and 2-pulses conditions. However, the smallest difference between estimated eABR THRs and clinical THRs was not always achieved from the same number of pulses. The smallest absolute difference of 30.3 µA was found for the linear fittings on growth functions of eABR RMS values in 4-pulses condition. Pearson's correlation coefficients (PCCs) between eABR THRs and psychophysical THRs were significant and relatively large in all but 16-pulses conditions. The PCCs between eABR THRs and clinical THRs, however, were smaller and in less cases significant. Results of this study showed that eABRs to multi-pulse stimulation could, to some extent, represent clinical stimulation paradigms, and thus in comparison to single pulses, could estimate clinical THRs with smaller errors.

Sound Localization Bias and Error in Bimodal Listeners Improve Instantaneously When the Device Delay Mismatch Is Reduced.

Users of a cochlear implant (CI) in one ear, who are provided with a hearing aid (HA) in the contralateral ear, so-called bimodal listeners, are typically affected by a constant and relatively large interaural time delay offset due to differences in signal processing and differences in stimulation. For HA stimulation, the cochlear travelling wave delay is added to the processing delay, while for CI stimulation, the auditory nerve fibers are stimulated directly. In case of MED-EL CI systems in combination with different HA types, the CI stimulation precedes the acoustic HA stimulation by 3 to 10 ms. A self-designed, battery-powered, portable, and programmable delay line was applied to the CI to reduce the device delay mismatch in nine bimodal listeners. We used an A-B-B-A test design and determined if sound source localization improves when the device delay mismatch is reduced by delaying the CI stimulation by the HA processing delay (τHA). Results revealed that every subject in our group of nine bimodal listeners benefited from the approach. The root-mean-square error of sound localization improved significantly from 52.6° to 37.9°. The signed bias also improved significantly from 25.2° to 10.5°, with positive values indicating a bias toward the CI. Furthermore, two other delay values (τHA -1 ms and τHA +1 ms) were applied, and with the latter value, the signed bias was further reduced in some test subjects. We conclude that sound source localization accuracy in bimodal listeners improves instantaneously and sustainably when the device delay mismatch is reduced.

Can Machine Learning Assist Locating the Excitation of Snore Sound? A Review.

In the past three decades, snoring (affecting more than 30 % adults of the UK population) has been increasingly studied in the transdisciplinary research community involving medicine and engineering. Early work demonstrated that, the snore sound can carry important information about the status of the upper airway, which facilitates the development of non-invasive acoustic based approaches for diagnosing and screening of obstructive sleep apnoea and other sleep disorders. Nonetheless, there are more demands from clinical practice on finding methods to localise the snore sound's excitation rather than only detecting sleep disorders. In order to further the relevant studies and attract more attention, we provide a comprehensive review on the state-of-the-art techniques from machine learning to automatically classify snore sounds. First, we introduce the background and definition of the problem. Second, we illustrate the current work in detail and explain potential applications. Finally, we discuss the limitations and challenges in the snore sound classification task. Overall, our review provides a comprehensive guidance for researchers to contribute to this area.

Electrical stimulation in the cochlea: Influence of modiolar microstructures on the activation of auditory nerve fibres.

Existing computational studies of cochlear implants have demonstrated that the structural detail of threedimensional (3D) cochlear models exerts influence on the current spread within the cochlea. Nevertheless, the significance of including the microstructures inside the modiolar bone in a cochlear model is still unclear in the literature. We employed two different multi-compartment neuron models to simulate auditory nerve fibres, and compared response characteristics of the fibre population between a detailed and a simplified 3D cochlear model. Results showed that although the prediction of firing is dependent on the details of the neuron model, the responses of the fibre population to the electrical stimulus, especially the location of the initiation of action potential, varied between the detailed and the simplified models. Therefore, the inclusion of the modiolar microstructures in a cochlear model may be necessary for fully understanding the firing of auditory nerve fibres.

Investigation of Electrically Evoked Auditory Brainstem Responses to Multi-Pulse Stimulation of High Frequency in Cochlear Implant Users.

We investigated the effects of electric multi-pulse stimulation on electrically evoked auditory brainstem responses (eABRs). Multi-pulses with a high burst rate of 10,000 pps were assembled from pulses of 45-µs phase duration. Conditions of 1, 2, 4, 8, and 16 pulses were investigated. Psychophysical thresholds (THRs) and most comfortable levels (MCLs) in multi-pulse conditions were measured. Psychophysical temporal integration functions (slopes of THRs/MCLs as a function of number of pulses) were -1.30 and -0.93 dB/doubling of the number of pulses, which correspond to the doubling of pulse duration. A total of 15 eABR conditions with different numbers of pulses and amplitudes were measured. The morphology of eABRs to multi-pulse stimuli did not differ from those to conventional single pulses. eABR wave eV amplitudes and latencies were analyzed extensively. At a fixed stimulation amplitude, an increasing number of pulses caused increasing wave eV amplitudes up to a certain, subject-dependent number of pulses. Then, amplitudes either saturated or even decreased. This contradicted the conventional amplitude growth functions and also contradicted psychophysical results. We showed that destructive interference could be a possible reason for such a finding, where peaks and troughs of responses to the first pulses were suppressed by those of successive pulses in the train. This study provides data on psychophysical THRs and MCLs and corresponding eABR responses for stimulation with single-pulse and multi-pulse stimuli with increasing duration. Therefore, it provides insights how pulse trains integrate at the level of the brainstem.

Comparison of Multi-Compartment Cable Models of Human Auditory Nerve Fibers.

Background: Multi-compartment cable models of auditory nerve fibers have been developed to assist in the improvement of cochlear implants. With the advancement of computational technology and the results obtained from in vivo and in vitro experiments, these models have evolved to incorporate a considerable degree of morphological and physiological details. They have also been combined with three-dimensional volume conduction models of the cochlea to simulate neural responses to electrical stimulation. However, no specific rules have been provided on choosing the appropriate cable model, and most models adopted in recent studies were chosen without a specific reason or by inheritance. Methods: Three of the most cited biophysical multi-compartment cable models of the human auditory nerve, i.e., Rattay et al. (2001b), Briaire and Frijns (2005), and Smit et al. (2010), were implemented in this study. Several properties of single fibers were compared among the three models, including threshold, conduction velocity, action potential shape, latency, refractory properties, as well as stochastic and temporal behaviors. Experimental results regarding these properties were also included as a reference for comparison. Results: For monophasic single-pulse stimulation, the ratio of anodic vs. cathodic thresholds in all models was within the experimental range despite a much larger ratio in the model by Briaire and Frijns. For biphasic pulse-train stimulation, thresholds as a function of both pulse rate and pulse duration differed between the models, but none matched the experimental observations even coarsely. Similarly, for all other properties including the conduction velocity, action potential shape, and latency, the models presented different outcomes and not all of them fell within the range observed in experiments. Conclusions: While all three models presented similar values in certain single fiber properties to those obtained in experiments, none matched all experimental observations satisfactorily. In particular, the adaptation and temporal integration behaviors were completely missing in all models. Further extensions and analyses are required to explain and simulate realistic auditory nerve fiber responses to electrical stimulation.

A Bag of Wavelet Features for Snore Sound Classification.

Snore sound (SnS) classification can support a targeted surgical approach to sleep related breathing disorders. Using machine listening methods, we aim to find the location of obstruction and vibration within a subject's upper airway. Wavelet features have been demonstrated to be efficient in the recognition of SnSs in previous studies. In this work, we use a bag-of-audio-words approach to enhance the low-level wavelet features extracted from SnS data. A Naïve Bayes model was selected as the classifier based on its superiority in initial experiments. We use SnS data collected from 219 independent subjects under drug-induced sleep endoscopy performed at three medical centres. The unweighted average recall achieved by our proposed method is 69.4%, which significantly ([Formula: see text] one-tailed z-test) outperforms the official baseline (58.5%), and beats the winner (64.2%) of the INTERSPEECH COMPARE Challenge 2017 Snoring sub-challenge. In addition, the conventionally used features like formants, mel-scale frequency cepstral coefficients, subband energy ratios, spectral frequency features, and the features extracted by the OPENSMILE toolkit are compared with our proposed feature set. The experimental results demonstrate the effectiveness of the proposed method in SnS classification.

Snoring - An Acoustic Definition.

Objective- The distinction of snoring and loud breathing is often subjective and lies in the ear of the beholder. The aim of this study is to identify and assess acoustic features with a high suitability to distinguish these two classes of sound, in order to facilitate an objective definition of snoring based on acoustic parameters. Methods- A corpus of snore and breath sounds from 23 subjects has been used that were classified by 25 human raters. Using the openSMILE feature extractor, 6 373 acoustic features have been evaluated for their selectivity comparing SVM classification, logistic regression, and the recall of each single feature. Results- Most selective single features were several statistical functionals of the first and second mel frequency spectrum-generated perceptual linear predictive (PLP) cepstral coefficient with an unweighted average recall (UAR) of up to 93.8%. The best performing feature sets were low level descriptors (LLDs), derivatives and statistical functionals based on fast Fourier transformation (FFT), with a UAR of 93.0%, and on the summed mel frequency spectrum-generated PLP cepstral coefficients, with a UAR of 92.2% using SVM classification. Compared to SVM classification, logistic regression did not show considerable differences in classification performance. Conclusion- It could be shown that snoring and loud breathing can be distinguished by robust acoustic features. The findings might serve as a guidance to find a consensus for an objective definition of snoring compared to loud breathing.

Electrical Stimulation in the Human Cochlea: A Computational Study Based on High-Resolution Micro-CT Scans.

Background: Many detailed features of the cochlear anatomy have not been included in existing 3D cochlear models, including the microstructures inside the modiolar bone, which in turn determines the path of auditory nerve fibers (ANFs). Method: We captured the intricate modiolar microstructures in a 3D human cochlea model reconstructed from µCT scans. A new algorithm was developed to reconstruct ANFs running through the microstructures within the model. Using the finite element method, we calculated the electrical potential as well as its first and second spatial derivatives along each ANF elicited by the cochlear implant electrodes. Simulation results of electrical potential was validated against intracochlear potential measurements. Comparison was then made with a simplified model without the microstructures within the cochlea. Results: When the stimulus was delivered from an electrode located deeper in the apex, the extent of the auditory nerve influenced by a higher electric potential grew larger; at the same time, the maximal potential value at the auditory nerve also became larger. The electric potential decayed at a faster rate toward the base of the cochlea than toward the apex. Compared to the cochlear model incorporating the modiolar microstructures, the simplified version resulted in relatively small differences in electric potential. However, in terms of the first and second derivatives of electric potential along the fibers, which are relevant for the initiation of action potentials, the two models exhibited large differences: maxima in both derivatives with the detailed model were larger by a factor of 1.5 (first derivative) and 2 (second derivative) in the exemplary fibers. More importantly, these maxima occurred at different locations, and opposite signs were found for the values of second derivatives between the two models at parts along the fibers. Hence, while one model predicts depolarization and spike initiation at a given location, the other may instead predict a hyperpolarization. Conclusions: Although a cochlear model with fewer details seems sufficient for analysing the current spread in the cochlear ducts, a detailed-segmented cochlear model is required for the reconstruction of ANF trajectories through the modiolus, as well as the prediction of firing thresholds and spike initiation sites.

Tractography Analysis for Electroconvulsive Therapy.

Computational human head models have been used in electrophysiological studies, and they have been able to provide useful information that is unable or difficult to acquire from experimental or imaging studies. However, most of these models are purely volume conductor models that overlooked the electric excitability of axons in the white matter of the brain. This study combined a finite element (FE) model of electroconvulsive therapy (ECT) with a whole-brain tractography analysis as well as the cable theory of neuronal excitation. We have reconstructed a whole-brain tractogram with 500 neural fibres from the diffusion-weighted magnetic resonance scans, and extracted the information on electrical potential from the FE ECT model of the same head. We then calculated the first and second spatial derivatives of the electrical potential, which describes the activating function for homogenous axons and investigated sensitive regions of white matter activation.

Influence of the Cochlear Implant Electrode Array Placement on the Current Spread in the Cochlea.

Three-dimensional (3D) computational models of the inner ear have been utilised to assist in investigating the factors that influence cochlear implant (CI) outcomes. A volume conductor cochlear model with an implanted electrode array was reconstructed from X-ray microtomography $(\mu$ CT) scans of a cadaveric human temporal bone. To mimic an in-vivo setting, the cochlea was embedded in a head model. The finite element (FE) method was used to analyse the electrical potential $\varphi$ in the cochlear nerve as a result of CI stimulation. In order to study the influence of electrode array placement on the current spread within the cochlea and the modiolus, computer simulations with six electrode array placements were conducted. $\varphi$ was evaluated at the tip of nerve fibres reconstructed within the cochlear nerve so as to predict the stimulation of a neuron population. It was found in most cases that a medial electrode array placement produced a narrower $\varphi$ peak at the fibre tip than a lateral one, although the differences were small.