Showing papers in "Biological Cybernetics in 1983"

Physical principles for economies of skilled movements

Abstract: This paper presents some elementary principles regarding constraints on movements, which may be useful in modeling and interpreting motor control strategies for skilled movements. Movements which are optimum with respect to various objectives, or "costs", are analyzed and compared. The specific costs considered are related to movement time, distance, peak velocity, energy, peak acceleration, and rate of change of acceleration (jerk). The velocity patterns for the various minimum cost movements are compared with each other and with some skilled movement patterns. The concept of performance trade-offs between competing objectives is used to interpret the distance-time relationships observed in skilled movements. Examples of arm movements during violin bowing and jaw movements during speech are used to show how skilled movements are influenced by considerations of physical economy, or "ease", of movement. Minimum-cost solutions for the various costs, which include the effect of frictional forces, are given in Appendices.

Figure-ground discrimination by relative movement in the visual system of the fly: Part II: Towards the neural circuitry

Abstract: A moving object can be separated from its surround on the basis of motion information alone. It has been known for some time that various species and especially the housefly can discriminate relative motion of an object and its background, even when the two have an identical texture. An earlier paper (Reichardt and Poggio, 1979) has analyzed on the basis of behavioural experiments the main features of the algorithm used by the fly to separate figure from ground. This paper (a) proposes the basic structure of a neuronal circuitry possibly underlying the detection of discontinuities in the optical flow by the visual system of the houseflyMusca; (b) compares detailed predictions of the model circuitry with old and new behavioural experiments onMusca (measuring its attempts to fixate an object), and (c) studies the neuronal realization of the model circuitry in terms of electrophysiological recordings from the lobula plate horizontal cells of the blowflyCalliphora.

A proposed neural network for the integrator of the oculomotor system

Abstract: Single-unit recordings, stimulation studies, and eye movement measurements all indicate that the firing patterns of many oculomotor neurons in the brain stem encode eye-velocity commands in premotor circuits while the firing patterns of extraocular motoneurons contain both eye-velocity and eye-position components. It is necessary to propose that the eye-position component is generated from the eye-velocity signal by a leaky hold element or temporal integrator. Prior models of this integrator suffer from two important problems. Since cells appear to have a steady, background signal when eye position and velocity are zero, how does the integrator avoid integrating this background rate? Most models employ some form of lumped, oositive feedback the gain of which must be kept within totally unreasonable limits for proper operation. We propose a lateral inhibitory network of homogeneous neurons as a model for the neural integrator that solves both problems. Parameter sensitivity studies and lesion simulations are presented to demonstrate robustness of the model with respect to both the choice of parameter values and the consequences of pathological changes in a portion of the neural integrator pool.

Lotka-Volterra equation and replicator dynamics: A two-dimensional classification

Abstract: The replicator equation arises if one equips a certain game theoretical model for the evolution of behaviour in animal conflicts with dynamics. It serves to model many biological processes not only in sociobiology but also in population genetics, mathematical ecology and even in prebiotic evolution. After a short survey of these applications, a complete classification of the two-dimensional phase flows is presented. The methods are also used to obtain a classification of phase portraits of the well-known generalized Lotka-Volterra equation in the plane.

Spatial cross-correlation

Abstract: We propose in this paper a new class of model processes for the extraction of spectral information from the neural representation of acoustic signals in mammals. We are concerned particularly with mechanisms for detecting the phase-locked activity of auditory neurons in response to frequencies and intensities of sound associated with speech perception. Recent psychophysical tests on deaf human subjects implanted with intracochlear stimulating electrodes as an auditory prosthesis have produced results which are in conflict with the predictions of the classical place-pitch and periodicity-pitch theories. In our model, the detection of synchronicity between two phase-locked signals derived from sources spaced a finite distance apart on the basilar membrane can be used to extract spectral information from the spatiotemporal pattern of basilar membrane motion. Computer simulations of this process suggest an optimal spacing of about 0.3---0.4 of the wavelength of the frequency to be detected. This interval is consistent with a number of psychophysical, neurophysiological, and anatomical observations, including the results of high resolution frequency-mapping of the anteroventral cochlear nucleus which are presented here. One particular version of this model, invoking the binaurally sensitive cells of the medial superior olive as the critical detecting elements, has properties which are useful in accounting for certain complex binaural psychophysical observations.

Three dimensional arm trajectories

Abstract: Planar arm trajectories are characterized by a segmentation of the hand velocity profile and by a coupling between shape and speed. The question addressed in this paper is whether such coupling, observed in two dimensions, still holds in three dimensions. This matter was investigated experimentally by recording three dimensional "aimless" movements of the arm, particularly three dimensional scribbles, and the answer suggested by the experimental data is that only the "bending" of the trajectory is coupled with speed, whereas the "twisting" is independent of speed. The same behaviour was also found to characterize a computational model of trajectory formation which is based on the spatial composition of chains of planar strokes, overlapped in time.

Slant-tilt: The visual encoding of surface orientation

Abstract: A specific form for the internal representation of local surface orientation is proposed, which is similar to Gibson's (1950) "amount and direction of slant". Slant amount is usually quantifed by the angle ? between the surface normal and the line of sight (0°???90°). Slant direction corresponds to the direction of the gradient of distance from the viewer to the surface, and may be defined by the image direction ? to which the surface normal would project (0°???360°). Since the direction of slant is specified by the tilt of the projected surface normal, it is referred to as surface tilt (Stevens, 1979; Marr, 1982). The two degrees of freedom of orientation are therefore quantified by slant, an angle measured perpendicular to the image plane, and tilt, an angle measured in the image plane. The slanttilt form provides several computational advantages relative to some other proposals and is consistent with various psychological phenomena. Slant might be encoded by various means, e.g. by the cosine of the angle, by the tangent, or linearly by the angle itself. Experimental results are reported that suggest that slant is encoded by an internal parameter that varies linearly with slant angle, with resolution of roughly one part in 100. Thus we propose that surface orientation is encoded in human vision by two quantities, one varying linearly with slant angle, the other varying linearly with tilt angle.

Effects of muscle model parameter dispersion and multi-loop segmental interaction on the neuromuscular system performance

Abstract: The effects of parameter dispersion among motor units on the neuromuscular system performance as well as interaction between muscle segments and spinal cord mechanisms are investigated. Elementary components of the system are modeled to simulate with simple models their input-output characteristics. A leaky SS-IPFM encoder with a time-dependent threshold simulates the motor-neuron encoding characteristics. An amplitude and time dependent non-linear model represent the motor unit mechanical output to neuronal input relationship. The dispersion of parameters in the components of the whole muscle control model is investigated in the open loop mode. It is shown that the dispersion of parameters in the multi-efferent channels converging on a common tendon provides a spatial filtration generating a smoother muscle force in addition to extending the linear dynamic range compared to a similar system having identical motor units. Muscle segmental interaction is investigated in this distributed model by closing the loop through a coupling matrix, representing afferent-motorneuron interaction on the spinal cord level. A diagonal matrix represents no segmental interaction and a uniform matrix represents a uniform interaction between segments through the muscle spindles and Golgi tendon feedback elements. The close loop simulation studied shows that (a). The type of segmental interaction has little effect on the overall system performance, i.e., range of linerity and stability, which is the result of having a muscle system with a large number of motor units. (b) There are only minor differences in results between the uniform and normal parameter distributions tested. (c) A loop gain of 4÷8 in the distributed model can provide linearity through the full physiological force range. (d) Type of segmental interaction has significant effects on the individual segment. A uniform matrix provides a more stable segment due to the spatial filtration resulting from the segmental interaction, while the diagonal noninteracting matrix shows instabilities on the local segmental level despite global stability. The more realistic exponentially decaying spatial interaction matrix yields both global neuromuscular and local segmental stability with the same linear dynamic range generated with the uniform or diagonal matrices.

Peripheral vision and perceived visual direction

Abstract: Experiments are described in which the subjects had to localize brief light stimuli presented up to 10° from the fixation center. The localization was performed relative to a continuously illuminated scale with numbered or lettered divisions. Systematic errors were obtained, the stimuli being mislocated nearer the fixation point than they were actually presented. The angular size of errors increased with the increase of stimulus eccentricity. It appeared to be a characteristic of the stimulated retinal locus, independent of the viewing distance and the scale element corresponding to this locus. It is concluded that despite the presence of a visible background frame of reference, subjects prefer to base their reports on the perceived egocentric direction of the stimulus which does not coincide with the physical direction of the stimulus. A parallel is drawn between this study and the studies on serial position function for letter identification.

Model emulates human smooth pursuit system producing zero-latency target tracking

Abstract: Humans can overcome the 150 ms time delay of the smooth pursuit eye movement system and track smoothly moving visual targets with zero-latency. Our target-selective adaptive control model can also overcome an inherent time delay and produce zero-latency tracking. No other model or man-made system can do this. Our model is physically realizable and physiologically realistic. The technique used in our model should be useful for analyzing other time-delay systems, such as man-machine systems and robots.

Textural segmentation, second-order statistics, and textural elements

Abstract: Beck (1972, 1973) hypothesized that textural segmentation occurs strongly on the basis of simple properties such as brightness, color, size, and the slopes of contours and lines of the elemental descriptors of a texture or textural elements. The experiment reported supports the hypothesis that specific stimulus features, rather than second-order statistics, account for textural segmentation. The results agree with Julesz (1981a, b) who has reported evidence disproving his original conjecture of the importance of second-order statistics. Julesz (1981a, b) now hypothesizes textural segmentation to be a function of local features which he called textons. Textons are features that give textural segmentation when textures have identical second-order statistics. The two hypotheses are to date in complete agreement on the stimulus features producing textural segmentation, and the experiment reported is consistent with both.

A neural theory of circadian rhythms: The gated pacemaker

Abstract: This article describes a behaviorally, physiologically, and anatomically predictive model of how circadian rhythms are generated by each suprachiasmatic nucleus (SCN) of the mammalian hypothalamus. This gated pacemaker model is defined in terms of competing on-cell off-cell populations whose positive feedback signals are gated by slowly accumulating chemical transmitter substances. These components have also been used to model other hypothalamic circuits, notably the eating circuit. A parametric analysis of the types of oscillations supported by the model is presented. The complementary reactions to light of diurnal and nocturnal mammals as well as their similar phase response curves are obtained. The "dead zone" of the phase response curve during the subjective day of a noctural rodent is also explained. Oscillations are suppressed by high intensities of steady light. Operations that alter the parameters of the model transmitters can phase shift or otherwise change its circadian oscillation. Effects of ablation and hormones on model oscillations are summarized. Observed oscillations include regular periodic solutions, periodic plateau solutions, rippled plateau solutions, period doubling solutions, slow modulation of oscillations over a period of months, and repeating sequences of oscillation clusters. The model period increases inversely with the transmitter accumulation rate but is insensitive to other parameter choices except near the breakdown of oscillations. The model's clocklike nature is thus a mathematical property rather than a formal postulate. A singular perturbation approach to the model's analysis is described.

Stimulus dependent neural correlations in the auditory midbrain of the grassfrog (Rana temporaria L.)

Abstract: Few-unit recordings were obtained using metal microelectrodes. Separation into single-unit spike trains was based on differences in spike amplitude and spike waveform. For that purpose a hardware microprocessor based spike waveform analyser was designed and built. Spikes are filtered by four matched filters and filter outputs at the moments of spike occurrence are read by a computer and used for off-line separation and spike waveform reconstruction. Thirthy-one double unit recordings were obtained and correlation between the separated spike trains was determined. After stimulus correction correlation remained in only 8 of the double unit records. It appeared that in most cases this neural correlation was stimulus dependent. Continuous noise stimulation resulted in the strongest neural correlation remaining after correction for stimulus coupling, stimulation with 48 ms duration tonepips presented once per second generally did not result in a significant neural correlation after the correction procedure for stimulus lock. The usefulness of the additive model for neural correlation and the correction procedure based thereupon is discussed.

The control of walking movements in the leg of the rock lobster

Abstract: 1. Experiments with rock lobsters walking on a treadmill were undertaken to obtain information upon the system controlling the movement of the legs. Results show that the position of the leg is an important parameter affecting the cyclic movement of the walking leg. Stepping can be interrupted when the geometrical conditions for terminating either a return stroke or a power stroke are not fullfilled. 2. The mean value of anterior and posterior extreme positions (AEP and PEP respectively) of the walking legs do not depend on the walking speed (Fig. 1). 3. When one leg is isolated from the other walking legs by placing it on a platform the AEPs and PEPs of the other legs show a broader distribution compared to controls (Figs. 2 and 3). 4. Force measurements (Fig. 4) are in agreement with the hypothesis that the movement of the leg is controlled by a position servomechanism. 5. When one leg stands on a stationary force transducer this leg develops forces which oscillate with the step rhythm of the other legs (Fig. 5). 6. A posteriorly directed influence is found, by which the return stroke of a leg can be started when the anterior leg performs a backward directed movement. 7. Results are compared with those obtained from stick insects. The systems controlling the movement of the individual leg are similar in both, lobster and stick insect but the influences between the legs seem to be considerably different.

Selective stabilization of muscle innervation during development: A mathematical model

Abstract: The biochemical model presented concerns a critical step of the development of skeletal muscle innervation. After invasion of the muscle by exploratory motor axons, several nerve terminals converge from different motoneurons onto each muscle fibre at a single endplate. During the folloing weeks the redundant innervation disappears: a single nerve ending per muscle fibre becomes stabilized. The model is based on the assumption that the numbers of motoneurons and of muscle fibres remain constant during this evolution and that the selective stabilization of the adult connectivity results from the competition of the active nerve terminals for a postsynaptic retrograde factor μ. At the peak of the multiple innervation, the synthesis of μ by the muscle fiber stops, possibly as a consequence of muscle electrical and/or mechanical activity. The stock of μ becomes limited; a retrograde trans-synaptic diffusion of μ from the muscle to the nerve endings takes place. Within each nerve ending, μ enters into a chemical autocatalytic reaction which results in the production of a presynaptic stabilization factor s. The nerve impulses reaching the nerve terminal initiate this reaction. Any given nerve terminal become stabilized when the concentration of s reaches a threshold value. The mathematical analysis of the model shows that there exists a unique solution which is physically acceptable. Its application and computer simulation predict that only one nerve terminal becomes stabilized per muscle fibre. The model accounts for the experimental observations that the reduction in size of the motor units is not necessarily accompanied by a reduction in the variability of their size. The model also accounts for the acceleration or delay in regression which follows modifications of the chronic activity of the nerve endings and for the variability of the pattern of innervation observed in isogenic organisms. Plausible biochemical hypotheses concerning the factors engaged in the "selective stabilization" of the nerve-endings are discussed.

Influence of loading parallel to the body axis on the walking coordination of an insect

Abstract: It is often reported in the early literature that insects walk with the legs protacting in diagonal pairs rather than the triplet of three legs associated with the tripod step pattern. The diagonal pattern implies that legs of the same segment have a phase relationship significantly different from 0.5. Such a pattern of leg recovery has been demonstrated quantitatively for the stick insect (Graham, 1972). Such patterns occur in several insects and systematic asymmetry can even be detected in the earliest quantitative study on cockroaches (Hughes, 1957) when the animals are walking slowly. More recently Spirito and Mushrush (1979) have reported systematic deviations from a phase of 0.5 similar to those observed in stick insects. Asymmetry has also been quantitatively demonstrated in Katydids (Graham, 1978) and has recently been observed in Mantid walking (Thomson, personal communication). This phenomenon seems to be a general characteristic of slow walking coordination in insects. In stick insects asymmetry only becomes obvious in gait II at slow speeds although there can be systematic differences in ipsilateral coordination on right and left sides even at the highest speeds in this gait (Graham, 1972).

A new method for the simulation of electric fields, generated by electric fish, and their distorsions by objects

Abstract: Among the many species of fishes endowed with electric organs Mormyriformes and Gymnotoidei are known to emit and receive electric signals for the purposes of intraspecific communication and recognition of objects. Models which have been proposed for this electro-sensory system generally assume steady-state conditions. On the other hand, the very character of the signals itself and the idea that the cerebellum might be working as a clock point to the importance of the signal dynamics. Therefore a new approach to the simulation of electric fields is described in the paper. The basic idea is to superpose the fields of point charges in a way that the sum is in accordance with the fish's electric field. The same technique could be used to simulate the influence of objects on the electric field. Following a suggestion of Dr. E. Kasper I used a simpler but equal effective approach for object simulation consisting in the use of a dipole instead of point charges. The model described is easily applied to diverse situations and allows one to estimate the influence of various parameters (size, shape, and position) on the "electric image" of an object. Furthermore, the well-known behaviour of tailbending and its consequences in object recognition can be simulated. The results underline the importance of signal dynamics for species with pulse-type discharges.

Dynamic behaviour of α motoneurone sub-pools subjected to inhomogeneous Renshaw cell inhibition

Abstract: The spinal ?-motoneurone-Renshaw cell system was simulated by a meshed system of three principal negative feedback loops interconnected via "cross"-feedback pathways. Three types of ?-motoneurone (MN): S-type, FR-type, and FF-type MNs, and their differing connections to and from Renshaw cells (RCs) were taken into account. The dynamic behaviour of RCs was taken from data provided by Cleveland and Ross (1977) and assumed to be given by a transfer function with one zero and two poles whose time constants ?i depended on the overall amount of excitatory input to RCs. Also, the static gain of recurrent inhibition was taken to decrease with increasing excitatory input from ?-MN axon collaterals (Cleveland et al., 1981) and to be depressed by spinally descending motor command signals. S-type MNs as well as F-type MNs were assumed to have high-pass characteristics though with slightly different cut-off frequencies. The closed-loop frequency responses of each sub-pool of MNs, S, FR, and FF, at three different levels of recruitment of these sub-pools, were calculated and shown to change significantly with recruitment level. These changes were essentially due to two reasons: firstly, to the general reduction of static gains within the recurrent inhibitory pathways with increasing motor output (recruitment), and secondly, to the increasing complexity of the whole network by recruitment of each new MN type. The particularly strong effect of the latter factor could easily be demonstrated by a comparison of the frequency responses of the MN types when these were, firstly, integrated into the network at their particular level of recruitment, and when they were, secondly, hypothetically assumed "isolated" from the remaining network, i.e., when subjected only to "self-inhibition", the cross-inhibitory links to other MN types being cut. These results illustrate that the dynamic behaviour of ?-MNs submitted to an inhomogeneously distributed recurrent and variable inhibition are not invariant, but depend upon the variable characteristics of a complex MN-RC network. This suggests that an important physiological function of recurrent inhibition via Renshaw cells, particularly of its inhomogeneous distribution, may be to adjust the dynamic MN sensitivity to the particular requirements prevailing at different motor output levels.

Generation of random sequences with jointly specified probability density and autocorrelation functions

Abstract: A new method is presented for the generation of stochastic (random) sequences with an arbitrarily specified first-order probability distribution function (PDF) and an arbitrarily specified first-roder auto-correlation function (ACF). A set of numbers with the desired PDF are first generated. These are then given a white (independent) ACF by double stochastic interchange. The desired ACF is then obtained by stochastically shuffling the series to minimize a sum of squares criterion between desired and actual ACFs. The technique is particularily useful for generating experimental stimuli for system identification, sequences for numerical simulation, and test series for evaluating signal processing algorithms when colored (non-white) non-Gaussian data are required.

A Boolean complete neural model of adaptive behavior

Abstract: A multi-layered neural assembly is developed which has the capability of learning arbitrary Boolean functions. Though the model neuron is more powerful than those previously considered, assemblies of neurons are needed to detect non-linearly separable patterns. Algorithms for learning at the neuron and assembly level are described. The model permits multiple output systems to share a common memory. Learned evaluation allows sequences of actions to be organized. Computer simulations demonstrate the capabilities of the model.

The information transmitted at final position in visually triggered forearm movements

Abstract: Visually triggered forearm movements were analyzed by an Information Theory approach. Human subjects made smooth movements which were characterized by moderate speeds, ranging about 100 degrees per second, by continuity in the position and velocity traces, and attainment of final average EMG levels before completion of the movement. We calculated the information transmitted by final position, biceps EMG, triceps EMG, and the ratio of the EMGs. The results were: (1) The information transmitted by final joint angle increased with number of targets but gradually levelled off. The maximum value was slightly over 3 bits, corresponding to an equivalent number of less than nine independent arm positions for a single movement. (2) The information transmitted by the ratio of the EMGs exceeds that transmitted by the biceps or triceps alone. (3) A previous theoretical prediction based on a spring model (Sakitt, 1980a) gives a moderately good fit to the experimental EMG ratio as a function of final position over a large range of angles. Our results lend consistency to two ideas about the nature of visually triggered forearm movements. First, our finding about the EMG ratio suggests that the basic motor program for final position is probably in terms of relative allocation of innervations, rather than looking up individual values. Second, single movements of this kind transmit surprisingly little information. If this is the case, it suggests that very fine accuracy is not achieved by a single program but requires feedback in order to program and execute additional movement.

Two spatio-temporal filters in human vision

Abstract: 1. We have studied visual detection of a circular target moving across a spatially and/or temporally modulated background. Illumination, I t , for threshold detection of the target has been measured as a function of background modulation frequency and changes in I t associated with background modulation provide a means of determining the frequency response characteristics of visual channels. 2. Temporal frequency responses obtained with temporally modulated, spatially uniform backgrounds have pass-band characteristics and the temporal frequency for peak response increases with increase in mean background illumination. These temporal frequency responses resemble those of the de Lange (1954) filter, but the latter incorporates the incremental thresholds for steady backgrounds. 3. The amplitude of this temporal response saturates at low (~40%) background modulation, decreases to zero as the target velocity falls to zero, and is maximum for a circular target of diameter 2°. 4. The spatial characteristics of this temporal filter were measured with a background field consisting of alternate steady and flickering bars. The resulting spatial frequency curve peaks at 1 cycle deg-1 for all background illuminations and is independent of the background grating orientation. This spatial response differs significantly from the IMG spatial functions observed with a background grating (Barbur and Ruddock, 1980). 5. The spatial and temporal responses reviewed above exhibit similar parametric variations and we therefore associate them with a single spatiotemporal filter, ST2. 6. A second temporal response, with low-pass frequency characteristics, was observed with a background field consisting of two matched gratings, presented in spatial and temporal antiphase. This response has parametric properties similar to those of the IMG spatial response described previously by Barbur and Ruddock (1980), thus we associated the two sets of data with a single spatio-temporal filter, ST1. 7. We show that the ST2 responses can be obtained by combining ST1 responses, and we present a network incorporating the two filters. 8. We review other psychophysical studies which imply the activity of two spatio-temporal filters with properties of the kind revealed in our studies. We argue that filter ST1 has properties equivalent to those of X-type and filter ST2 has properties equivalent to those of Y-type electrophysiological mechanisms.

Random currents through nerve membranes

Abstract: The linear cable equation with uniform Poisson or white noise input current is employed as a model for the voltage across the membrane of a onedimensional nerve cylinder, which may sometimes represent the dendritic tree of a nerve cell. From the Green's function representation of the solutions, the mean, variance and covariance of the voltage are found. At large times, the voltage becomes asymptotically wide-sense stationary and we find the spectral density functions for various cable lengths and boundary conditions. For large frequencies the voltage exhibits "1/f 3/2 noise". Using the Fourier series representation of the voltage we study the moments of the firing times for the diffusion model with numerical techniques, employing a simplified threshold criterion. We also simulate the solution of the stochastic cable equation by two different methods in order to estimate the moments and density of the firing time.

The influence of load and leg amputation upon coordination in walking crustaceans: A model calculation

Abstract: The following results were obtained by earlier authors when investigating the leg coordination of walking crustaceans (Decepoda): 1) After a leg is amputated, its stump moves in anti-phase with the next posterior intact leg. This corresponds to the coordination of intact animals. The stump, however, moves in-phase with the next anterior intact leg which contrasts with the coordination of intact animals (Clarac and Chasserat, 1979; Clarac, 1981). 2) Different results have been reported for the relation between the return stroke duration and step period: some authors found a significant dependency (e.g. MacMillan, 1975), others found none (e.g. Ayers and Davis, 1977). The calculation presented here shows, that these results can be described by a model incorporating the following assumptions: A) The forces developed by both, return stroke and power stroke muscles depend upon the load under which the leg walks. B) The influences which produce the coordinating effects found by Clarac and Chasserat for amputees also exist in intact animals and their strength depends upon the intensity of the motor output of the controlling leg. Within the model the selection of protraction or retraction is made at a "central unit" which calculates a value corresponding to the sum of graded inputs from several sources. The resulting fluctuation in this value might be considered analogous to graded oscillations recorded from central non-spiking interneurons. Qualitatively the model describes similar results obtained from insects.

Behavior of a single neuron in a recurrent excitatory loop

Abstract: A recurrent excitation loop was constructed by enabling each impulse from the slowly adapting stretch receptor organ SAO (crayfish) to trigger through an electronic circuit a brief stretch, or "tug," of the receptor. When applied independently, each tug influenced the discharge as would an EPSP. Recurrent excitation led to characteristic discharge timings; hence, even an isolated neuron can have intrinsic mechanisms that prevent positive feedback from freezing it in an extreme non-operational state. Such timings depended critically on the "phase", i.e., on the time elapsed between an SAO impulse and the tug. When the control discharge was stationary (because the SAO length remained invariant), phases of a few ms simply changed the pattern to one of doublets, and affected little the average rate. As the phase increased, bursts appeared, bursts and interburst intervals became more prolonged, and average rates increased. With the largest phases examined (40 ms), the discharge consisted of a slow alternation of high rate bursts, separated by long intervals. When the discharge was modulated (by 0.2/s sinusoidal length variation) with recurrent excitation, the peak-to-peak rate swing, i.e., the sensitivity, and the proportion of the cycle without afferent discharges increased, and the rate vs. length display was distorted even though remaining "loop-plus-extension." Changes were phase-dependent: for example, loops could have a sharp high peak at one phase and be flat-topped at another. When the interspike interval variability was exaggerated (by a length jitter superimposed upon either invariant or sinusoidally varying lengths), recurrent excitation exerted fewer, weaker and somewhat different effects: e.g., it reduced the overall intensity of the invariant cases and the peak-to-peak swing in the modulated one. The precise mechanisms of these results can only be conjectured at but are likely to involve an electrogenic pump, electromechanical interactions, topographical issues, as well as their interplays. The functional implications involve, for instance, the modulation of the intensity, duration and occurrence of the bursting patterns in oscillating functions (e.g., breathing, chewing, etc.).

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

Abstract: 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 acurate 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.

Pervasive locking, saturation, asymmetric rate sensitivity and double-valuedness in crayfish stretch receptors

Abstract: The correspondence between afferent discharges and sinusoidal length modulations (0.2---10 cps, under 10% of the natural length variations) was studied in isolated fast-adapting stretch receptor organs (FAO) of crayfish, largely using average displays of rate vs. length (or derivatives) along the cycle. Rate modulations were greatest during early cycles and then stabilized, an initial adjustment remindful of mechanical preconditioning. Responses to stimulation in the FAO, as in the slowly-adapting organs (SAO) and possibly other receptors, exhibit the following features, all striking because of their magnitude and ubiquity. i) A zig-zag overall afferent rate vs. stimulus frequency graph with positively and negatively sloped segments. This precludes the straighforward use of Bode plots. ii) Marked non-linearities as an obvious stimulus-response locking in the positively sloped segments, a double-valuedness with one rate while stretching and another while shortening, a lower-limit saturation with the receptor silent for more than half a cycle, and an asymmetric rate sensitivity. iii) Clear-cut discharge leads relative to the stimulus at low frequencies and lags at high ones. The FAO responds worse than the SAO to low frequencies, and better to high ones; it is locked 1-to-1 in a much broader range (e.g., 3---100 vs. 1---3 cps). All features were strongly frequency-dependent. With higher frequencies: i) the number of impulses per cycle fell from several to just one and finally to one every several cycles at higher values; ii) the two values of each length approached one another usually but not always; iii) the silent proportion of the cycle increased; and iv) the rate sensitivity changed. Each feature can arise in principle at any of the transduction stages from length to discharge: the mechanical transduction from length to dendritic deformation, and the encoder one from generator potentials to discharges are particularly likely candidates.

A systems model for the pupil size effect

Abstract: The human pupillary control system is a paradigm for linearized biological control systems. It also exhibits a series of interesting nonlinear behaviors, particularly asymmetry, "pupillary escape", and "pupillary capture." We present a nonlinear model in which a signal dependent upon pupil size is fed back internally to cause a change in system parameters related to gains and rates of light adaptation. The model was simulated on a digital computer, a variety of experimental data was well matched, and improvements over previous pupil models demonstrated. A candidate physiological mechanism for adaptive components of the model might have the form of an inverse "Henneman coded" neuronal pool.

Evaluation of neuronal coupling dynamics

Abstract: Temporary correlated activity of neuron assemblies is believed to play a substantial role for the brain's pattern recognition ability. To study the underlying principles of such mechanisms, a method is proposed for the characterization of the interneuronal and stimulus-response coupling changes of two periodically driven and simultaneously recorded units. The coupling measure is derived from the cross correlation function by calculating the actual correlation contributions without performing the subsequent time-average (which would give the cross correlation function). Examples are given for simultaneously recorded spike trains from visual cortical units, but the method can be applied equally well to evoked potentials or intracellular recordings.