Vocal responses to perturbations in voice auditory feedback in individuals with Parkinson's disease

Background

One of the most common symptoms of speech deficits in individuals with Parkinson''s disease (PD) is significantly reduced vocal loudness and pitch range. The present study investigated whether abnormal vocalizations in individuals with PD are related to sensory processing of voice auditory feedback. Perturbations in loudness or pitch of voice auditory feedback are known to elicit short latency, compensatory responses in voice amplitude or fundamental frequency.

Methodology/Principal Findings

Twelve individuals with Parkinson''s disease and 13 age- and sex- matched healthy control subjects sustained a vowel sound (/α/) and received unexpected, brief (200 ms) perturbations in voice loudness (±3 or 6 dB) or pitch (±100 cents) auditory feedback. Results showed that, while all subjects produced compensatory responses in their voice amplitude or fundamental frequency, individuals with PD exhibited larger response magnitudes than the control subjects. Furthermore, for loudness-shifted feedback, upward stimuli resulted in shorter response latencies than downward stimuli in the control subjects but not in individuals with PD.

Conclusions/Significance

The larger response magnitudes in individuals with PD compared with the control subjects suggest that processing of voice auditory feedback is abnormal in PD. Although the precise mechanisms of the voice feedback processing are unknown, results of this study suggest that abnormal voice control in individuals with PD may be related to dysfunctional mechanisms of error detection or correction in sensory feedback processing.     

The Dynamic Range Paradox: A Central Auditory Model of Intensity Change Detection

In this paper we use empirical loudness modeling to explore a perceptual sub-category of the dynamic range problem of auditory neuroscience. Humans are able to reliably report perceived intensity (loudness), and discriminate fine intensity differences, over a very large dynamic range. It is usually assumed that loudness and intensity change detection operate upon the same neural signal, and that intensity change detection may be predicted from loudness data and vice versa. However, while loudness grows as intensity is increased, improvement in intensity discrimination performance does not follow the same trend and so dynamic range estimations of the underlying neural signal from loudness data contradict estimations based on intensity just-noticeable difference (JND) data. In order to account for this apparent paradox we draw on recent advances in auditory neuroscience. We test the hypothesis that a central model, featuring central adaptation to the mean loudness level and operating on the detection of maximum central-loudness rate of change, can account for the paradoxical data. We use numerical optimization to find adaptation parameters that fit data for continuous-pedestal intensity change detection over a wide dynamic range. The optimized model is tested on a selection of equivalent pseudo-continuous intensity change detection data. We also report a supplementary experiment which confirms the modeling assumption that the detection process may be modeled as rate-of-change. Data are obtained from a listening test (N = 10) using linearly ramped increment-decrement envelopes applied to pseudo-continuous noise with an overall level of 33 dB SPL. Increments with half-ramp durations between 5 and 50,000 ms are used. The intensity JND is shown to increase towards long duration ramps (p<10⁻⁶). From the modeling, the following central adaptation parameters are derived; central dynamic range of 0.215 sones, 95% central normalization, and a central loudness JND constant of 5.5×10⁻⁵ sones per ms. Through our findings, we argue that loudness reflects peripheral neural coding, and the intensity JND reflects central neural coding.     

Perceived Loudness of Self-Generated Sounds Is Differentially Modified by Expected Sound Intensity

Performing actions with sensory consequences modifies physiological and behavioral responses relative to otherwise identical sensory input perceived in a passive manner. It is assumed that such modifications occur through an efference copy sent from motor cortex to sensory regions during performance of voluntary actions. In the auditory domain most behavioral studies report attenuated perceived loudness of self-generated auditory action-consequences. However, several recent behavioral and physiological studies report enhanced responses to such consequences. Here we manipulated the intensity of self-generated and externally-generated sounds and examined the type of perceptual modification (enhancement vs. attenuation) reported by healthy human subjects. We found that when the intensity of self-generated sounds was low, perceived loudness is enhanced. Conversely, when the intensity of self-generated sounds was high, perceived loudness is attenuated. These results might reconcile some of the apparent discrepancies in the reported literature and suggest that efference copies can adapt perception according to the differential sensory context of voluntary actions.     

Dissociation of Detection and Discrimination of Pure Tones following Bilateral Lesions of Auditory Cortex

It is well known that damage to the peripheral auditory system causes deficits in tone detection as well as pitch and loudness perception across a wide range of frequencies. However, the extent to which to which the auditory cortex plays a critical role in these basic aspects of spectral processing, especially with regard to speech, music, and environmental sound perception, remains unclear. Recent experiments indicate that primary auditory cortex is necessary for the normally-high perceptual acuity exhibited by humans in pure-tone frequency discrimination. The present study assessed whether the auditory cortex plays a similar role in the intensity domain and contrasted its contribution to sensory versus discriminative aspects of intensity processing. We measured intensity thresholds for pure-tone detection and pure-tone loudness discrimination in a population of healthy adults and a middle-aged man with complete or near-complete lesions of the auditory cortex bilaterally. Detection thresholds in his left and right ears were 16 and 7 dB HL, respectively, within clinically-defined normal limits. In contrast, the intensity threshold for monaural loudness discrimination at 1 kHz was 6.5±2.1 dB in the left ear and 6.5±1.9 dB in the right ear at 40 dB sensation level, well above the means of the control population (left ear: 1.6±0.22 dB; right ear: 1.7±0.19 dB). The results indicate that auditory cortex lowers just-noticeable differences for loudness discrimination by approximately 5 dB but is not necessary for tone detection in quiet. Previous human and Old-world monkey experiments employing lesion-effect, neurophysiology, and neuroimaging methods to investigate the role of auditory cortex in intensity processing are reviewed.     

A ratio code for vibrotactile pitch

Subjective impressions of pitch for 80 different sinusoidal vibrotactile stimuli delivered to the index finger were measured by free magnitude estimation in four subjects. In three of the subjects, pitch at a given frequency decreased as stimulus amplitude increased. The data of these subjects were well described by a model of pitch based on the relative levels of activation of the three major tactile channels. The main element in this model was a ratio of P channel activity to the sum of the activity levels of the P, NPI, and NPIII channels. Activity levels of the channels were estimated on the basis of the psychophysical literature, including a study of vibrotactile loudness using the same subjects and stimuli as those employed here. A fourth subject, whose pattern of loudness judgments had previously been shown to differ from those of the other subjects, did not conform to this pitch model: her data revealed significant increases in pitch with increases in amplitude, and appear to reflect an inability to combine signals across vibrotactile channels. Pitch changes resulting from vibrotactile adaptation were directionally consistent with our ratio model: pitch was slightly increased by adaptation to a 25 Hz stimulus, and slightly decreased by 200 Hz adaptation.     

Variations in the loudness of a brief sound compared to another brief sound as a function of the duration of both sounds]

Loudness equalizations between two short 2500 Hz tones (15 to 120 ms, about 50 dB SPL) were made. One tone, either the first or the second one, was twice as long as the other. The intensity level differences between tones of the same loudness were calculated. Results show that the relations between duration and loudness of the tones differ for different subjects. Nevertheless the calculated differences diminished with subject experience. Subject evaluations in accordance with the intensity levels of tones, i.e. independently of the duration, were quite often obtained even for the pairs 15 ms-30 ms.     

Magnitude-matching: the measurement of taste and smell

In the method of magnitude-matching, subjects try to judge intensitiesof sensations from two or more modalities on a single, commonscale. Using responses to one modality as a standard makes itpossible to compare subjects' suprathreshold perceptions onthe other, test modality. A series of ten experiments revealedthe following: (i) magnitude-matching ‘works’: withboth loudness of tones and lightness of grays as standards,tasters versus nontasters of 6-n-prophylthiouracil (PROP) (asdefined by a threshold criterion) show much greater responceto suprathreshold PROP and slightly greater response to surcose;(ii) though superior to rating-scale judgements of sensory intensitymade without reference to a second modality, magnitude-matchingis not, however, flawless: the cross-modality matching relationproduced by a set of magnitude-matches depends systematicallyon the contextual sets of stimulus levels presented for judgement;(iii) with taste as the standard, old versus young subjectsshowed only a 25% decrement in responce to the odor intensityof butanol when both groups recieved the same physical (concentration)levels, but a >50% decrement in responce when both groupsrecieved about the same perceptual levels; (iv) magnitude-matchesare much the same whether subjets make their judgements on abounded rating-scale or an open-ended magnitude-estimation scale:and (v) loudness, lightness and odor intensity serve about equallyin magnitude-matching with taste intensity.     

Transient reduction of tinnitus intensity is marked by concomitant reductions of delta band power

Background

Tinnitus is an auditory phantom phenomenon characterized by the sensation of sounds without objectively identifiable sound sources. To date, its causes are not well understood. Previous research found altered patterns of spontaneous brain activity in chronic tinnitus sufferers compared to healthy controls, yet it is unknown whether these abnormal oscillatory patterns are causally related to the tinnitus sensation. Partial support for this notion comes from a neurofeedback approach developed by our group, in which significant reductions in tinnitus loudness could be achieved in patients who successfully normalized their patterns of spontaneous brain activity. The current work attempts to complement these studies by scrutinizing how modulations of tinnitus intensity alter ongoing oscillatory activity.

Results

In the present study the relation between tinnitus sensation and spontaneous brain activity was investigated using residual inhibition (RI) to reduce tinnitus intensity and source-space projected magnetencephalographic (MEG) data to index brain activity. RI is the sustained reduction (criteria: 50% for at least 30 s) in tinnitus loudness after cessation of a tonal tinnitus masker. A pilot study (n = 38) identified 10 patients who showed RI. A significant reduction of power in the delta (1.3–4.0 Hz) frequency band was observed in temporal regions during RI (p ≤ 0.001).

Conclusion

The current results suggest that changes of tinnitus intensity induced by RI are mediated by alterations in the pathological patterns of spontaneous brain activity, specifically a reduction of delta activity. Delta activity is a characteristic oscillatory activity generated by deafferented/deprived neuronal networks. This implies that RI effects might reflect the transient reestablishment of balance between excitatory and inhibitory neuronal assemblies, via reafferentation, that have been perturbed (in most tinnitus individuals) by hearing damage. As enhancements have been reported in the delta frequency band for tinnitus at rest, this result conforms to our assumption that a normalization of oscillatory properties of cortical networks is a prerequisite for attenuating the tinnitus sensation. For RI to have therapeutic significance however, this normalization would have to be stabilized.     

Effects of unexpected chords and of performer's expression on brain responses and electrodermal activity

Background

There is lack of neuroscientific studies investigating music processing with naturalistic stimuli, and brain responses to real music are, thus, largely unknown.

Methodology/Principal Findings

This study investigates event-related brain potentials (ERPs), skin conductance responses (SCRs) and heart rate (HR) elicited by unexpected chords of piano sonatas as they were originally arranged by composers, and as they were played by professional pianists. From the musical excerpts played by the pianists (with emotional expression), we also created versions without variations in tempo and loudness (without musical expression) to investigate effects of musical expression on ERPs and SCRs. Compared to expected chords, unexpected chords elicited an early right anterior negativity (ERAN, reflecting music-syntactic processing) and an N5 (reflecting processing of meaning information) in the ERPs, as well as clear changes in the SCRs (reflecting that unexpected chords also elicited emotional responses). The ERAN was not influenced by emotional expression, whereas N5 potentials elicited by chords in general (regardless of their chord function) differed between the expressive and the non-expressive condition.

Conclusions/Significance

These results show that the neural mechanisms of music-syntactic processing operate independently of the emotional qualities of a stimulus, justifying the use of stimuli without emotional expression to investigate the cognitive processing of musical structure. Moreover, the data indicate that musical expression affects the neural mechanisms underlying the processing of musical meaning. Our data are the first to reveal influences of musical performance on ERPs and SCRs, and to show physiological responses to unexpected chords in naturalistic music.     

Tinnitus: distinguishing between subjectively perceived loudness and tinnitus-related distress

Objectives

Overall success of current tinnitus therapies is low, which may be due to the heterogeneity of tinnitus patients. Therefore, subclassification of tinnitus patients is expected to improve therapeutic allocation, which, in turn, is hoped to improve therapeutic success for the individual patient. The present study aims to define factors that differentially influence subjectively perceived tinnitus loudness and tinnitus-related distress.

Methods

In a questionnaire-based cross-sectional survey, the data of 4705 individuals with tinnitus were analyzed. The self-report questionnaire contained items about subjective tinnitus loudness, type of onset, awareness and localization of the tinnitus, hearing impairment, chronic comorbidities, sleep quality, and psychometrically validated questionnaires addressing tinnitus-related distress, depressivity, anxiety, and somatic symptom severity. In a binary step-wise logistic regression model, we tested the predictive power of these variables on subjective tinnitus loudness and tinnitus-related distress.

Results

The present data contribute to the distinction between subjective tinnitus loudness and tinnitus-related distress. Whereas subjective loudness was associated with permanent awareness and binaural localization of the tinnitus, tinnitus-related distress was associated with depressivity, anxiety, and somatic symptom severity.

Conclusions

Subjective tinnitus loudness and the potential presence of severe depressivity, anxiety, and somatic symptom severity should be assessed separately from tinnitus-related distress. If loud tinnitus is the major complaint together with mild or moderate tinnitus-related distress, therapies should focus on auditory perception. If levels of depressivity, anxiety or somatic symptom severity are severe, therapies and further diagnosis should focus on these symptoms at first.     

Time course of perceptual discrimination and single neuron reliability

The reliability of identification of a visual target increases with time available for inspection of the stimulus. We suggest that the neural basis of this improvement is the existence of a mechanism for integrating a noisy firing rate over some period, leading to a reduction in mean firing rate variance with available processing time. We have determined the experimental time course of the improvement in reliability in a parallel search task where the available inspection time is limited by the presentation of a mask at various times after a brief stimulus. We compare the resulting psychometric functions with the predictions of a model based on Signal Detection Theory. The model is based on the assumption that the reliability of the observer's response is limited by the variability of the responses of individual neurons. The reliability of the discrimination between two stimuli at the neuronal level is then directly related to the ratio of the difference between their integrated mean responses (over many trials) to the response standard deviation. This reliability increases with inspection time. To demonstrate application of the model to electrophysiological data, neurometric functions are derived from the firing rates of a monkeyV1 cortical neuron. The data were obtained while the animal was active in a discrimination task. The results correspond qualitatively to our observed human psychometric functions.     

Distinct Features of Auditory Steady-State Responses as Compared to Transient Event-Related Potentials

Transient event-related potentials (ERPs) and steady-state responses (SSRs) have been popularly employed to investigate the function of the human brain, but their relationship still remains a matter of debate. Some researchers believed that SSRs could be explained by the linear summation of successive transient ERPs (superposition hypothesis), while others believed that SSRs were the result of the entrainment of a neural rhythm driven by the periodic repetition of a sensory stimulus (oscillatory entrainment hypothesis). In the present study, taking auditory modality as an example, we aimed to clarify the distinct features of SSRs, evoked by the 40-Hz and 60-Hz periodic auditory stimulation, as compared to transient ERPs, evoked by a single click. We observed that (1) SSRs were mainly generated by phase synchronization, while late latency responses (LLRs) in transient ERPs were mainly generated by power enhancement; (2) scalp topographies of LLRs in transient ERPs were markedly different from those of SSRs; (3) the powers of both 40-Hz and 60-Hz SSRs were significantly correlated, while they were not significantly correlated with the N1 power in transient ERPs; (4) whereas SSRs were dominantly modulated by stimulus intensity, middle latency responses (MLRs) were not significantly modulated by both stimulus intensity and subjective loudness judgment, and LLRs were significantly modulated by subjective loudness judgment even within the same stimulus intensity. All these findings indicated that high-frequency SSRs were different from both MLRs and LLRs in transient ERPs, thus supporting the possibility of oscillatory entrainment hypothesis to the generation of SSRs. Therefore, SSRs could be used to explore distinct neural responses as compared to transient ERPs, and help us reveal novel and reliable neural mechanisms of the human brain.     

Introducing the Event Related Fixed Interval Area (ERFIA) Multilevel Technique: a Method to Analyze the Complete Epoch of Event-Related Potentials at Single Trial Level

In analyzing time-locked event-related potentials (ERPs), many studies have focused on specific peaks and their differences between experimental conditions. In theory, each latency point after a stimulus contains potentially meaningful information, regardless of whether it is peak-related. Based on this assumption, we introduce a new concept which allows for flexible investigation of the whole epoch and does not primarily focus on peaks and their corresponding latencies. For each trial, the entire epoch is partitioned into event-related fixed-interval areas under the curve (ERFIAs). These ERFIAs, obtained at single trial level, act as dependent variables in a multilevel random regression analysis. The ERFIA multilevel method was tested in an existing ERP dataset of 85 healthy subjects, who underwent a rating paradigm of 150 painful and non-painful somatosensory electrical stimuli. We modeled the variability of each consecutive ERFIA with a set of predictor variables among which were stimulus intensity and stimulus number. Furthermore, we corrected for latency variations of the P2 (260 ms). With respect to known relationships between stimulus intensity, habituation, and pain-related somatosensory ERP, the ERFIA method generated highly comparable results to those of commonly used methods. Notably, effects on stimulus intensity and habituation were also observed in non-peak-related latency ranges. Further, cortical processing of actual stimulus intensity depended on the intensity of the previous stimulus, which may reflect pain-memory processing. In conclusion, the ERFIA multilevel method is a promising tool that can be used to study event-related cortical processing.     

Changes to respiratory mechanisms during speech as a result of different cues to increase loudness.

The purpose of the present study was to determine whether different cues to increase loudness in speech result in different internal targets (or goals) for respiratory movement and whether the neural control of the respiratory system is sensitive to changes in the speaker's internal loudness target. This study examined respiratory mechanisms during speech in 30 young adults at comfortable level and increased loudness levels. Increased loudness was elicited using three methods: asking subjects to target a specific sound pressure level, asking subjects to speak twice as loud as comfortable, and asking subjects to speak in noise. All three loud conditions resulted in similar increases in sound pressure level . However, the respiratory mechanisms used to support the increase in loudness differed significantly depending on how the louder speech was elicited. When asked to target at a particular sound pressure level, subjects used a mechanism of increasing the lung volume at which speech was initiated to take advantage of higher recoil pressures. When asked to speak twice as loud as comfortable, subjects increased expiratory muscle tension, for the most part, to increase the pressure for speech. However, in the most natural of the elicitation methods, speaking in noise, the subjects used a combined respiratory approach, using both increased recoil pressures and increased expiratory muscle tension. In noise, an additional target, possibly improving intelligibility of speech, was reflected in the slowing of speech rate and in larger volume excursions even though the speakers were producing the same number of syllables.     

Otoacoustic emissions at different click intensities: invariant and subject-dependent features.

A study of click-evoked otoacoustic emissions (CEOAEs) elicited at stimulation intensities from 35 to >80 dB was carried out by recurrence quantification analysis on signals from both normal and hearing-impaired subjects. In normal subjects, a clear scaling of determinism with increasing stimulation intensity was observed in the click intensity range from 41 to 59 dB. Outside that range and, in particular, above its upper end, subject-dependent features appeared in the form of different maximal levels of determinism. A comparative analysis of responses from hearing-impaired subjects with conductive hearing losses and sensorineural hearing losses suggested that the principal contributor to this behavior is the middle ear and allowed us to discriminate the two pathologies solely on the basis of CEOAEs. These observations are consistent with a simple phenomenological model of the auditory periphery in which different functional modules are sequentially recruited at increasing stimulus intensities, with a consequent rise in CEOAE coherence.     

Dynamic integration of reward and stimulus information in perceptual decision-making

In perceptual decision-making, ideal decision-makers should bias their choices toward alternatives associated with larger rewards, and the extent of the bias should decrease as stimulus sensitivity increases. When responses must be made at different times after stimulus onset, stimulus sensitivity grows with time from zero to a final asymptotic level. Are decision makers able to produce responses that are more biased if they are made soon after stimulus onset, but less biased if they are made after more evidence has been accumulated? If so, how close to optimal can they come in doing this, and how might their performance be achieved mechanistically? We report an experiment in which the payoff for each alternative is indicated before stimulus onset. Processing time is controlled by a “go” cue occurring at different times post stimulus onset, requiring a response within msec. Reward bias does start high when processing time is short and decreases as sensitivity increases, leveling off at a non-zero value. However, the degree of bias is sub-optimal for shorter processing times. We present a mechanistic account of participants'' performance within the framework of the leaky competing accumulator model [1], in which accumulators for each alternative accumulate noisy information subject to leakage and mutual inhibition. The leveling off of accuracy is attributed to mutual inhibition between the accumulators, allowing the accumulator that gathers the most evidence early in a trial to suppress the alternative. Three ways reward might affect decision making in this framework are considered. One of the three, in which reward affects the starting point of the evidence accumulation process, is consistent with the qualitative pattern of the observed reward bias effect, while the other two are not. Incorporating this assumption into the leaky competing accumulator model, we are able to provide close quantitative fits to individual participant data.     

Auditory Frequency and Intensity Discrimination Explained Using a Cortical Population Rate Code

The nature of the neural codes for pitch and loudness, two basic auditory attributes, has been a key question in neuroscience for over century. A currently widespread view is that sound intensity (subjectively, loudness) is encoded in spike rates, whereas sound frequency (subjectively, pitch) is encoded in precise spike timing. Here, using information-theoretic analyses, we show that the spike rates of a population of virtual neural units with frequency-tuning and spike-count correlation characteristics similar to those measured in the primary auditory cortex of primates, contain sufficient statistical information to account for the smallest frequency-discrimination thresholds measured in human listeners. The same population, and the same spike-rate code, can also account for the intensity-discrimination thresholds of humans. These results demonstrate the viability of a unified rate-based cortical population code for both sound frequency (pitch) and sound intensity (loudness), and thus suggest a resolution to a long-standing puzzle in auditory neuroscience.     

Individualized and clinically derived stimuli activate limbic structures in depression: an fMRI study

Objectives

In the search for neurobiological correlates of depression, a major finding is hyperactivity in limbic-paralimbic regions. However, results so far have been inconsistent, and the stimuli used are often unspecific to depression. This study explored hemodynamic responses of the brain in patients with depression while processing individualized and clinically derived stimuli.

Methods

Eighteen unmedicated patients with recurrent major depressive disorder and 17 never-depressed control subjects took part in standardized clinical interviews from which individualized formulations of core interpersonal dysfunction were derived. In the patient group such formulations reflected core themes relating to the onset and maintenance of depression. In controls, formulations reflected a major source of distress. This material was thereafter presented to subjects during functional magnetic resonance imaging (fMRI) assessment.

Results

Increased hemodynamic responses in the anterior cingulate cortex, medial frontal gyrus, fusiform gyrus and occipital lobe were observed in both patients and controls when viewing individualized stimuli. Relative to control subjects, patients with depression showed increased hemodynamic responses in limbic-paralimbic and subcortical regions (e.g. amygdala and basal ganglia) but no signal decrease in prefrontal regions.

Conclusions

This study provides the first evidence that individualized stimuli derived from standardized clinical interviewing can lead to hemodynamic responses in regions associated with self-referential and emotional processing in both groups and limbic-paralimbic and subcortical structures in individuals with depression. Although the regions with increased responses in patients have been previously reported, this study enhances the ecological value of fMRI findings by applying stimuli that are of personal relevance to each individual''s depression.     

Psychoneural models of the auditory masking process.

Two mathematical models are presented which describe perception of the loudness of a tone masked by noise. The designation “psychoneural” indicates that the models are consistent with accepted findings in the fields of neuroanatomy, neurophysiology, and psychophysics. Each of the models consists of two channels, one which responds only to noise and another which responds to a weighted sum of tone and noise. Each channel is functionally equivalent to the model proposed by MacKay to explain intensity perception. In the first of the two masking models, it is assumed that the noise decreases the perceived loudness of the tone by lateral inhibition at a central location. In the second model, it is assumed that the noise decreases the loudness of the tone by efferent inhibition which acts at the periphery. The quantitative predictions of both models are identical and, with the appropriate adjustment of certain parameters, can be brought into close agreement with psychophysical masking data. The relative merits and handicaps of the models are discussed in the context of a more complex representation of the masking process in which a separate channel is assigned to each critical frequency band.     

An analog VLSI implementation of a visual interneuron: enhanced sensory processing through biophysical modeling

Flies are capable of rapid, coordinated flight through unstructured environments. This flight is guided by visual motion information that is extracted from photoreceptors in a robust manner. One feature of the fly's visual processing that adds to this robustness is the saturation of wide-field motion-sensitive neuron responses with increasing pattern size. This makes the cell's responses less dependent on the sparseness of the optical flow field while retaining motion information. By implementing a compartmental neuronal model in silicon, we add this "gain control" to an existing analog VLSI model of fly vision. This results in enhanced performance in a compact, low-power CMOS motion sensor. Our silicon system also demonstrates that modern, biophysically-detailed models of neural sensory processing systems can be instantiated in VLSI hardware.