On-line identification of sensory systems using pseudorandom binary noise perturbations

Models of vestibular semicircular canal afferent neuron firing activity

Semicircular canal afferent neurons transmit information about head rotation to the brain. Mathematical models of how they do this have coevolved with concepts of how brains perceive the world. A 19th-century "camera" metaphor, in which sensory neurons project an image of the world captured by sense organs into the brain, gave way to a 20th-century view of sensory nerves as communication channels providing inputs to dynamical control systems. Now, in the 21st century, brains are being modeled as Bayesian observers who infer what is happening in the world given noisy, incomplete, and distorted sense data. The semicircular canals of the vestibular apparatus provide an experimentally accessible, low-dimensional system for developing and testing dynamical Bayesian generative models of sense data. In this review, we summarize advances in mathematical modeling of information transmission by semicircular canal afferent sensory neurons since the first such model was proposed nearly a century ago. Models of information transmission by vestibular afferent neurons may provide a foundation for developing realistic models of how brains perceive the world by inferring the causes of sense data.

Efficiency turns the table on neural encoding, decoding and noise

Sensory neurons are usually described with an encoding model, for example, a function that predicts their response from the sensory stimulus using a receptive field (RF) or a tuning curve. However, central to theories of sensory processing is the notion of 'efficient coding'. We argue here that efficient coding implies a completely different neural coding strategy. Instead of a fixed encoding model, neural populations would be described by a fixed decoding model (i.e. a model reconstructing the stimulus from the neural responses). Because the population solves a global optimization problem, individual neurons are variable, but not noisy, and have no truly invariant tuning curve or receptive field. We review recent experimental evidence and implications for neural noise correlations, robustness and adaptation.

A framework for identification of brain network dynamics using a novel binary noise modulated electrical stimulation pattern

Modeling and identification of brain network dynamics is of great importance both for understanding brain function and for closed-loop control of brain states. In this work, we present a multi-input-multi-output (MIMO) linear state-space model (LSSM) to describe the brain network dynamics in response to electrical stimulation. The LSSM maps the parameters of electrical stimulation, such as frequency, amplitude and pulse-width to recorded brain signals such as electrocorticography (ECoG) and electroencephalography (EEG). Effective identification of the LSSM in open-loop stimulation experiments, however, is strongly dependent on the open-loop input stimulation design. We propose a novel input design to accurately identify the LSSM by integrating the concept of binary noise (BN) with practical constraints on stimulation waveforms. The designed input pattern is a pulse train modulated by stochastic BN parameters. We show that this input pattern both satisfies the necessary spectral condition for accurate system identification and can incorporate any desired pulse shape. Using numerical experiments, we show that the quality of identification depends heavily on the input signal pattern and the proposed binary noise modulated pattern achieves satisfactory identification results, reducing the relative estimation error more than 300 times compared with step sequence modulated, single-sinusoid modulated and multi-sinusoids modulated input patterns.

Estimation of hypoxic ventilatory dynamics using pseudorandom inputs

Using experimental and simulation studies, we assessed the applicability of pseudorandom binary hypoxic stimulation (PRBS) for estimating the dynamic respiratory response to a single breath of hypoxia. In experimental studies on rats we tested whether the transient ventilatory response to hypoxia based on the PRBS technique converges to the measured response to a true single breath of hypoxia. Plethysmographic volume recordings were obtained from 7 urethane anesthetized, bilaterally vagotomized rats while the inspired O2 level was switched pseudorandomly between 21% and 12%. The psuedorandom estimates were comparable to the ensemble averaged responses to 15-40 trials of a single-breath inspiration of 12% O2. Ventilation peaked in 2-3 breaths and the response lasted for 15-20 breaths and was primarily due to a decrease in breath duration. Changes in CO2 concentration in the blood cause an underestimate of the purely hypoxic transient response. In simulation studies we also demonstrated the applicability of this technique to human subjects using a mathematical model of human respiratory control. We conclude that the pseudorandom technique will provide a very good estimate of the ventilatory dynamics to inhalation of a single breath of hypoxic gas in rats and humans.

The simple frequency response of human stretch reflexes in which either short- or long-latency components predominate

1. The stretch reflexes of the human abductor digiti minimi (ADM) and biceps brachii muscles were compared using small-amplitude sinusoidal stretching at 10-50 Hz and recording the surface EMG. The stimulus was applied either to the relevant proximal phalanx or to the biceps tendon while the muscle studied was contracting; the same amplitude was used for all frequencies (range 0.5-2 mm for ADM, 0.1-1 mm for biceps). 2. As the frequency increased, the response of ADM decreased while that of biceps increased. Neither muscle showed a minimum at 20-25 Hz, as previously found for wrist muscles and attributed to an interaction between short- and long-latency components of the reflex. 3. For both muscles, the phase of the response lagged behind the stimulus by an amount which increased approximately linearly with frequency, without the gross inflexion found for wrist muscles. Such linearity would be found for a system dominated by a fixed time delay; its value sets the slope. The slope for biceps was half that for ADM. The values of reflex delay calculated from the slope of the phase plots agreed reasonably with the absolute latencies of the responses evoked by tap or ramp stimulation. Part of the difference between the muscles was due to differences in peripheral conduction time, since ADM lies more distally. Most of it, however, was due to different reflexes being involved, with biceps being predominantly controlled by short-latency pathways and ADM by long-latency pathways. 4. For both muscles, the phase lag at any given frequency was less than that expected from the reflex latency, determined from the slope of the phase plot. Thus, sensory transduction and central transmission had produced a phase advance in the reflex. The 'neural phase advance' of biceps was appreciably larger than that of ADM, and more than would be expected from the behaviour of its spindle afferents. The excess is suggested to be due to the action of Renshaw inhibition, which ADM may lack. 5. The results were substantiated by recording from single motor units in biceps. Stretching at the present amplitudes had rather little effect on the overall rhythmic behaviour, as shown by interspike interval histograms. However, cycle histograms showed that the discharge was modulated reasonably sinusoidally by the stretching, whatever its frequency (i.e. the probability of the occurrence of a spike varied over the cycle). Cyclic changes were also found in autocorrelograms and amplitude spectra of the spike trains.(ABSTRACT TRUNCATED AT 400 WORDS)

Modeling human diaphragmatic electromyogram and airflow responses to imperceptible mechanical loads

We used an esophageal electrode to measure the amplitude and timing responses of diaphragmatic electrical activity and airflow in response to flow resistive and elastic loads at or below the threshold for conscious detection, applied pseudorandomly to the oral airway of eight normal human subjects. The mechanical and neural parameter responses to mechanical loading were cross-correlated with the pseudorandom loading sequence to obtain estimates of the impulse responses. We convolved the resultant impulse response estimates with the loading sequence to obtain the responses predicted from the linear component of the generalized Wiener kernel model. Highly significant correlations and close correspondence were found between the model-predicted and ensemble-averaged experimental responses for nearly all neural and mechanical parameters in all subjects. For nearly every aspect of the pattern, with few exceptions, the response to these small load perturbations in all eight subjects was adequately explained by an impulse response, leaving negligible nonlinearity to require higher-order cross-correlations. These results indicate that the estimated impulse responses accurately model the dynamics of the neural and mechanical responses in human subjects for the types and magnitudes of loads applied. This study supports use of the pseudorandom loading technique to determine the neural and mechanical responses to imperceptible mechanical loads in conscious humans.

Pseudorandom binary sequence stimulation applied to the visual evoked response. Normative data and a comparative study with pattern and flash stimulation

The investigation of patients who are unable to fixate the pattern visual stimulus generally requires the use of diffuse flash stimulation to elicit the visual evoked response. However, by comparison with pattern, flash stimulation has proved relatively insensitive in identifying lesions of the visual pathway. We investigated a more complex method of flash stimulation. A pseudorandom binary sequence has been used to generate the diffuse visual evoked response stimulus. The pseudorandom binary sequence, rather than producing a single flash, switches in a pseudorandom fashion between two levels of illumination. The result is a diffuse visual stimulus approximating band-limited white noise. The series is periodic, enabling signal averaging to be performed. By applying the methods of random signal analysis, the impulse or transient response of the visual pathway can be determined. Our normal pseudo-random binary sequence visual evoked response impulse function, derived from 29 normal subjects, had the morphologic characteristics of the conventional flash visual evoked response and a major positive component (P100), whose latency mean and standard deviation closely matched that of our normative pattern visual evoked response. However, the P100 amplitude standard deviation was significantly greater than that produced by conventional pattern and flash stimulation. We investigated 140 patients by means of pattern, flash and pseudorandom binary sequence stimulation. The pseudorandom binary sequence visual evoked response proved to be almost 12 times more effective than flash visual evoked response in detecting lesions of the visual system.

Use of pseudorandom noise in studies of auditory evoked potentials

The extent to which sensorineural systems such as the auditory system are nonlinear depends on the type of stimulus that is used, and the part of the system from which recordings are made. An estimate of the first-order Wiener kernel of the evoked response from the inferior colliculus to amplitude-modulated tones and noise was obtained by cross-correlating the response with the same pseudorandom noise as was used to amplitude modulate the sounds that were used as stimuli, in order to characterize the linear portion of the system. The shape of these cross-correlograms resembled the potentials evoked to short bursts of the unmodulated tones and noise. The degree of nonlinearity in the response to amplitude-modulated tones and noise was determined, and information about the type of nonlinearity was obtained using the inverse-repeat feature of the pseudorandom noise. Recordings both from the surface and from deep in the nucleus of the inferior colliculus revealed nonlinearities that were predominantly of an even order, but the magnitude of the nonlinearities depended on what stimulus was used, the stimulus intensity, and from which neural structure the recording was made.

Responses of mono- and bi-articular muscles to load perturbations of the human arm

We studied the behavior of muscles acting synergistically in elbow flexion in response to load perturbations. The perturbations were applied either proximally or distally to the elbow joint and consisted of single pulses or steps of torque and of pseudo-random sequences of torque pulses. They produced changes in angular position and torque at both the shoulder and elbow joints. The electromyographic (EMG) responses evoked in biceps, brachio-radialis and brachialis muscles were different when elbow and shoulder motion was in the same direction and when the two angular motions were oppositely directed. For example, elbow extension resulted both when a downward force perturbation was applied to the forearm as well as when a posteriorly directed force applied to the upper arm was released. Elbow flexors were activated at a short latency only in the former case and not in the latter. The modulation of EMG activity in elbow flexors evoked by the perturbations was related to the global motion of the limb, including the angular motions at both the shoulder and elbow joints. The time course of the EMG responses in biceps, which acts on both joints, differed from that of brachio-radialis and brachialis muscles, which act only at the elbow. The results are discussed in the context of the possible mechanisms responsible for the muscle responses to the perturbations.

EMG responses to load perturbations of the upper limb: effect of dynamic coupling between shoulder and elbow motion

Load perturbations were applied to the arm of human subjects under conditions where both limb segments (upper arm and forearm) were free to move. The perturbations consisted of pulses of torque 50 ms in duration and of pseudo-random sequences of such pulses. They were applied to either the forearm or the upper arm. Under all conditions, the perturbations resulted in angular motion at the shoulder and elbow joints and evoked consistent responses in muscles acting about these joints (biceps, triceps, anterior and posterior deltoid). Activity in biceps and triceps was not related simply to angular motion at the elbow joint. For example, activation of biceps could be evoked during elbow flexion (by applying a torque perturbation at the shoulder) as well as during elbow extension (by applying a torque perturbation at the elbow). The effect of varying degrees of dynamic coupling between upper arm and forearm on EMG responses was investigated by applying torque perturbations to the upper arm over a wide range of elbow angles. When the forearm is extended, such a perturbation induces a greater amount of elbow flexion than when the forearm is in a flexed position. The results of these experiments showed that the larger was the amount of flexion of the forearm induced by the perturbation, the larger was the activation of biceps. The results are incompatible with the notion of a negative feedback of total muscle length as being responsible for the EMG activity following the load perturbations. It is suggested that the EMG responses can best be interpreted functionally in terms of parameters more global than muscle length. Among such global parameters, changes in net torque at a joint resulting from the perturbation gave the best correlation with the pattern of EMG activities observed.

Dynamic properties of the responses of single neurons in the inferior colliculus of the rat

The responses of single cells in the central nucleus of the inferior colliculus of the rat were studied with characteristic frequency tones amplitude modulated by pseudorandom noise or sinusoidal waveforms, in order to investigate the degree to which these responses can be described by a linear model. When pseudorandom noise was used as the modulating waveform, period histograms of the response locked to the periodicity of the noise were cross-correlated with a single period of the noise. The response of a model, having this cross-correlogram as its impulse response and the pseudorandom noise sequence as the input waveform, differed in appearance from the corresponding period histogram of the neural discharges, indicating that the latter contained a non-negligible, nonlinear component. Further manipulation of the data showed that the most significant nonlinearities were of even order, which indicates that the changes in neural discharge rate to increments and decrements in stimulus intensity are asymmetrical. In some units, particularly at low mean stimulus intensities, this was clearly evident as a halfwave rectification of the period histogram. The magnitude of the modulation of the period histograms increased as a function of the sound intensity for some units, while in others it decreased; in still other units the magnitude of the modulation of the neural discharges was relatively constant over a large range of stimulus intensities. When the modulation transfer functions were estimated from the responses to noise-modulated sounds they were found to be very similar to those obtained using sinusoidally modulated sound, despite large degrees of nonlinearity being present in the responses to both types of sound.

A new photographic method for mapping spatio-temporal receptive field using television snow stimulation

A means was devised to measure simultaneously spatial as well as temporal characteristics of visual receptive fields by stimulating the retina with the noise obtained on an unused television channel. The input, television snow, and the output, neural response, were recorded on a video tape. The tape was played back to obtain the (linear) spatio-temporal Wiener kernel by cross-correlating the input with the output. This method can be applied to extract the linear part of the visual responses in time and space.

Postural stability and rotational tests: their effectiveness for screening dizzy patients

Results of independently interpreted computerized stationary platform posturography and white noise rotational tests were compared with diagnoses for 110 patients. Using the criterion that an abnormal result from either test classified the subject as abnormal, the sensitivity estimate for the pair of tests was 78% for persons with diagnoses known to result in vestibular dysfunction. The specificity estimate was 90%. Both a vestibulo-ocular and a vestibulo-spinal test were required for effective screening. Consecutive tests performed over five days showed the rotation test to be much less variable than posturography. Rotation testing is therefore preferred for following the performance of patients having disorders thought to cause fluctuating vestibular systems. Interobserver reliability rates were 83% for posturography and 93% for rotation tests.

Use of pseudorandom noise in studies of frequency selectivity: the periphery of the auditory system

Frequency selectivity of single auditory nerve fibers in the rat was studied using pseudorandom noise based on ternary m-sequences as the stimulus, and the results were compared to those of earlier studies in which noise based on binary m-sequences was used. Pseudorandom noise based on ternary m-sequences has fewer anomalies than noise based on binary m-sequences. Detailed tests using linear and nonlinear filters showed that the present method provides accurate measures of bandwidth and center frequency. Period histograms of the response, locked to the periodicity of the noise, were cross-correlated with one period of the noise to obtain estimates of the impulse response function of the peripheral auditory system. Fourier transforms of these cross-correlograms were used as estimates of the filter function of single auditory nerve fibers. The results obtained using ternary noise were not different from previous results showing a downward shift in center frequency and increase in bandwidth with increasing stimulus intensity for fibers with center frequencies between 1000 and 5000 Hz. The difference between spectral selectivity based on phase-locked responses and that based on discharge rate is discussed.

Slow changes and Wiener analysis of nonlinear summation in contractions in cat muscles

With regular trains of stimuli at a high frequency, the contribution of each stimulus to the force generated over time declines from the second to about the tenth stimulus, but then begins to increase again. This late increase is referred to as tetanic potentiation in analogy with the post-tetanic potentiation of the twitch after such a period of stimulation. With regular trains of stimuli at a low frequency, a progressive decrease in the essentially unfused twitches (negative staircase) is observed in the slow soleus muscle of the cat, while a progressive increase (positive staircase) is observed for the fast plantaris muscle. The time constant for the approximately exponential changes observed is on the order of 10 s. Random trains of stimuli were applied at intermediate frequencies and analyzed in terms of general methods of analysis for nonlinear systems. Systematic decreases in the magnitude and increases in the time course of the average tension per stimulus were observed with increasing mean rates of stimulation. Similar changes were observed for short intervals between stimuli within a given random train at a constant mean rate. These changes can be described in terms of an early depression and a later facilitation described in the previous papers in this series.

The mechanical behavior of the human forearm in response to transient perturbations

Static and dynamic components of mechanical impedance of human forearm were evaluated by applying two kinds of perturbations: 1) large viscoelastic loads, and 2) small pseudo-random perturbations. When the task involved the active resistance of the perturbations, both stiffness and viscosity increased relatively to their values in the passive task, the increment in stiffness being larger than that in viscosity. The time course of such changes was investigated during the transition between the two operating points defined by the instructions "do not resist" and "resist" the applied perturbations. The changes in stiffness and viscosity were relatively slow, those in the latter lagging behind those in the former.

Neural delay in the ascending auditory pathway

Evoked responses from the cochlea and cochlear nucleus in the rat were studied using two types of stimuli: (1) bursts of tones or noise, and (2) continuous tones or noise that were amplitude modulated with pseudorandom noise. While the responses to the first type of stimuli were averaged only in the conventional way, the responses to the continuous and amplitude modulated sounds were averaged over one period of the pseudorandom noise. This average was then cross correlated with one period of the noise. The morphology of these cross correlation functions was in many ways similar to the response to transient sounds. Recordings from the round window of the cochlea and the cochlear nucleus showed that the latencies of these peaks in the responses to tone bursts and those of the cross correlation functions obtained from the continuous tones modulated with pseudorandom noise were similar. However, the latencies of the peaks in the cross correlation functions were slightly shorter and showed less dependency on the stimulus intensity than did the peaks in the responses to tone bursts. When the responses to noise bursts and the responses to noise that was amplitude modulated were compared, it was found that the latencies of the peaks in the cross correlation functions were nearly independent of the stimulus intensity. However, the peaks in the averaged responses to noise bursts showed a decrease in latency with increasing sound intensity.

Spatio-temporal cross-correlation analysis of catfish retinal neurons

1. The receptive field properties of visual neurons in the retina of the catfish are studied by a white noise spatio-temporal stimulus. The spatial and temporal inputs of the stimulus are independent and lead to complete linear characterizations and local nonlinear characterizations of the neural response. 2. Horizontal cells, bipolar cells, and sustained or Type N amacrine cells all yield spatially coherent linear correlations. The horizontal cells have the shortest latency by these methods and exhibit a late depolarizing component that is wider in spatial extent than the initial hyperpolarizing component. Depolarizing Type N neurons have center-hyperpolarizing local nonlinearity. 3. Transient or Type C amacrine cells do not correlate well with the intensity of the stimulus, even though the Fast variety responds vigorously to the stimulus. 4. Ganglion cells are classified into Excitatory, Inhibitory and biphasic classes based upon their linear correlations. Some ganglions exhibit responses dependent upon the orientation of stimulus. Although linear correlation of the Excitatory class is similar to that of the depolarizing Type N cell, the locally nonlinear character of these cell types is distinct. The receptive field of the inhibitory ganglion cells has strong locally excitatory nonlinearity.

Physiological and anatomical characteristics of primary vestibular afferent neurons in the bullfrog

Intracellular recordings were made in the VIIIth nerve of the bullfrog (Rana catesbiana) to measure the membrane characteristics and obtain records of spontaneous and evoked spike activity of primary semicircular canal afferents. Physiological stimulation of the canals was achieved by rotating the preparation on a servomotor driven turntable with the animals' head centered in the rotational axis. The responses of each neuron to sinusoidal rotations at frequencies of 0.05Hz, 0.5Hz and for impulsive accelerations of 400 deg/sec2 were obtained. Membrane characteristics measured included the cell resting and action potential amplitude, and spike-activation threshold for applied currents. Physiologically characterized neurons were injected with horseradish peroxidase by applying pneumatic pressure and/or iontophoretic currents to the micropipettes containing 5% HRP in 1 M KCI. Following survival times of 12--48 h, the VIIIth nerve and attached vestibular end organ was removed for histochemical processing using a diaminobenzidine procedure to visualize the HRP reaction product. Light microscopy was used to discern the anatomical features of the neurons and to trace their peripheral dendritic trajectories from the ganglion to their termination(s) in the crista. Our studies have revealed that the bullfrog's primary vestibular afferents are characterized by a broad range of soma and axon diameters which correspond to an equally broad range of spontaneous and evoked activity characteristics. The largest neurons had more irregular spontaneous firing rates and consistently exhibited the greatest gain and smallest phase shifts with respect to head acceleration. These neurons consistently terminated at or near the central region of the crista. On the other hand, the smallest neurons were characterized by having the most regular spontaneous discharge patterns, the lowest gains, and greatest phase shifts with respect to head acceleration. Our findings are thus consistent with the view that the anatomical features of the primary vestibular neurons are important in determining the neuron's physiological characteristics. In terms of response dynamics our observations indicate that the receptors in the frog's crista ampullaris are heterogeneous and differentially sensitive to a wide range of stimulus frequencies.

The power spectra of visually evoked potentials to pseudorandom contrast reversals of gratings

Visually evoked potentials (VEPs) were recorded in response to the temporal pseudorandom contrast reversal of spatially sinusoidal gratings with different spatial frequencies. The stimulus mimicked bandwidth limited white noise in the temporal domain except for an inherent periodicity which permitted signal averaging. The power spectra of the resulting VEPs were calculated. For high spatial frequency gratings (7.5-15 c/degree) VEP power was localized to the temporal frequency range from 3 to 7 Hz. For medium spatial frequency gratings (0.75-3 c/degree) VEP power was distributed in a roughly bimodal way with peaks near 6 and 18 Hz. The VEP power spectra due to high frequency gratings were similar in 2 subjects studied in detail, but the power spectra to medium frequency gratings differed substantially.

A distributed computer system for hierarchical control of a clinical vestibular laboratory

A vestibular testing laboratory with five test stations was implemented as a clinical research and testing facility, automating and adapting tests for patients with inner-ear balance disorders. These were designed to quantitate postural control, and eye movement response to rotational, caloric, and visual (optokinetic) stimuli. Microprocessors were used as satellite processors in a star network under hierarchical control of a host minicomputer. All disk storage was controlled by the host, with data transfer from satellites via parallel interfaces. Network software was designed and implemented to be under control of the host in a foreground-background structure. The practical operation of this laboratory required that technicians at each satellite test station initiate, perform, and complete an individual test in dependently of other tests. Examples from two test stations are presented. A 2-year data base of test results provides important multitest correlations for use in diagnostic evaluations.

Clinical use of pseudorandom binary sequence white noise in assessment of the human vestibulo-ocular system

White noise rotational stimulation has been used to evaluate the human vestibulo-ocular response for 30 normal subjects over the frequency range from 0.02 to 1.6 Hz and is being extended to characterize response of patients having documented abnormalities. For clinical use, the white noise stimulus has the advantages of shortening the test time by presenting all stimulus frequencies simultaneously, and being well-tolerated by both normal subjects and patients alike. Cross spectral calculations which compare the computer reconstructed slow phase eye velocity response to the pseudorandom acceleration stimulus yield a set of linear and nonlinear estimates of the vestibulo-ocular response. Pilot data indicate that a classification of the disease state can be made using this set of estimates. This classification will be presented and discussed.