Regulation of the body-substrat-distance in the stick insect: Responses to sinusoidal stimulation

The stick insect Carausius morosus maintains the distance between the substrate and its body. The underlying feed-back servo mechanism has been analyzed in intact animals under open loop conditions by changing the body-substrate distance in a sinusoidal fashion. The center position z _c has been varied as parameter and the force the animal elicits along its high axis has been measured. The response amplitude A is a nonlinear function of z _c. This nonlinear relationship between A and z _c is most probably caused by the relationship between the torque excerted at the joints and the measured force. The responses to sinusoidal stimulation reveal band-pass character of the feed-back loop. Due to the nonlinearity of the system the average value of the response to sinusoidal disturbances depends upon the frequency of modulation. The change of the average value with the frequency of modulation is partially due to cocontraction of the extensor and flexor muscles.     

A simple model for phase locking of biological oscillators

Summary A mathematical model is presented for phase locking of a biological oscillator to a sinusoidal stimulus. Analytical, numerical and topological considerations are used to discuss the patterns of phase locking as a function of the amplitude of the sinusoidal stimulus and the relative frequencies of the oscillator and the sinusoidal stimulus. The sorts of experimental data which are needed to make comparisons between theory and experiment are discussed.     

Stimulus-response properties of cricket cereal filiform receptors

The dynamic ranges and stimulus-response properties of a large sample of cereal filiform receptors in Acheta domesticus were investigated electrophysiologically. The relation between receptor response and stimulus velocity was a sigmoid function, the log-linear portion of which spanned 1–1.5 log units of peak air-current velocity. Different receptors responded over different but overlapping velocity ranges, such that the system velocity sensitivity range spanned at least 2.5 log units. Plots of receptor response amplitude vs. stimulus direction were sinusoidal, with a period of 360°. Long-hair receptors responded in phase with air-current velocity, and intermediate-hair receptors responded in phase with air-current acceleration. These results extend those of Shimozawa and Kanou (1984a) and Kämper and Kleindienst (1990), in which the dynamics of receptor responses were shown to depend on hair length. When individual hairs were directly mechanically deflected, their receptors responded in phase with the first derivative of hair deflection. The signal transform between the air-current stimulus and the receptor response is comprised of two processes, one biomechanical/aerodynamic and one membrane biophysical. The results of this study suggest that the parametric sensitivities of receptors are primarily determined by hair biomechanical/aerodynamic properties.Abbreviation IR infrared     

Contrast transfer function of the visual system]

Visually evoked potentials were used to determine the spatial contrast response function of the visual system and the visual acuity of the pigeon. The spatial contrast response describes the relationship between the contrast in a pattern of vertical stripes, whose luminance is a function of position, and the amplitude of the visually evoked response at various spatial frequencies for a given temporal frequency (pattern reversal frequency); it indicates how particular spatial frequencies are attenuated in the visual system. The visually evoked responses were recorded using monopolar stainless steel electrodes inserted into the stratum griseum superficiale of the optic tectum; the depth of penetration was determined on the basis of a stereotactic atlas. The stimulus patterns were generated on a video monitor placed 75 cm in front of the animal's eye perpendicular to the optic axis. The spatial contrast response function measured at 10% contrast and 0.5 Hz reversal frequency shows a peak at a spatial frequency of 0.5 c/deg, corresponding to 1 degree of visual angle, and decreases progressively at higher spatial frequencies. The high-frequency limit (cut-off frequency) for resolution of sinusoidal gratings, estimated from the contrast response function, is 15.5 c/deg, corresponding to a visual acuity of 1.9 min of arc.     

Methods for the identification of evoked response components in the frequency and combined time/frequency domains

Two prominent frequency components designated f1 and f2 have been identified in the visual evoked response to the transient presentation of sinusoidal luminance gratings in the range of 0.5–8 c/deg. The components occur at temporal frequencies below the alpha band, with the f1 frequency roughly half that of the f2 frequency. The f1 component is largest at low spatial frequencies with f2 becoming progressively dominant as spatial frequency is increased.The frequency and amplitude of f1 and f2 change substantially over the time course of the response. This has been studied by calculating the temporal frequency spectrum of the transient evoked potential over successive short-time epochs running through the response. Using this technique, the response is shown to consist of narrow- and frequency peaks or ‘formants’ emerging at different times after stimulus onset. These formants occur at frequencies other than those of the spontaneous EEG and undergo changes in frequency and amplitude over the time course of the response.Two spectrum analysis techniques were employed: the Discrete Fourier Transform and Linear Predictive Coding. Frequency components were successfully identified in single-trial responses using the LPC technique.     

Functional significance of the statistical properties of the retinal discharge

Summary In this paper the effect of the statistical properties of the ganglion cell discharge on the transfer characteristics of the cat's retinal sensory system is studied. On the basis of results reported by the literature, a mathematical model of the system is defined. The model is then studied by digital computer, to obtain the amplitude of its response to sinusoidal stimulation as a function of frequency. The results show that, as the discharge is not Poisson-like, a positive resonance exists between stimulus and discharge at stimulus frequencies whose period is of the same order as, or smaller than the mean interval of the discharge. The amplitude of the resonance is a function of the statistical parameters of the discharge. These results fit well experiments recently carried out.     

Normal variability of the amplitude and phase of steady-state VEPs

The present study quantifies the amplitude and phase variability of steady-state VEPs (S-VEPs) and compares this variability between subjects and between individual runs. The S-VEPs were recorded repeatedly in 14 normal subjects with varying spatial and temporal frequencies of sinusoidal gratings; 6 spatial frequencies (range 0.5–8.0 c/deg) with 3 temporal frequencies (4, 6 and 8 Hz) were used. A total of 75 responses were averaged and analyzed by the Fourier method. Four recordings were obtained in each spatio-temporal combination.In general, the phase data showed small inter- and intrasubject variability. As anticipated, the amplitude data showed a large degree of intersubject variability, although the intrasubject variability was very small. In addition, in some stimulus conditions the inter- and intrasubject variability increased, which thus suggested the existence of an optimal spatio-temporal combination. Therefore, these stimulus parameters should be taken into consideration when S-VEPs are applied in clinical practice.     

Sinusoidal voltage clamp of the Hodgkin-Huxley model.

A voltage clamp consisting of a sinusoidal voltage of amplitude V1 and frequency f, superimposed on a steady voltage level V0, is applied to the Hodgkin-Huxley model of the squid giant axon membrane. The steady-state response is a current composed of sinusoidal components of frequencies O, f, 2f, 3f,... The frequencies greater than f arise from the nonlinearity of the membrane. The total current is described by a power series in V1; each coefficient of this series is composed of current components for one or more frequencies. For different frequencies one can derive higher-order generalized admittances characterizing the nonlinear as well as the linear properties of the membrane. Formulas for the generalized admittances are derived from the Hodgkin-Huxley equations for frequencies up to 3f, using a perturbation technique. Some of the resulting theoretical curves are compared with experimental results, with good qualitative agreement.     

Electromotility of outer hair cells from the cochlea of the echolocating bat,Carollia perspicillata

Isolated outer hair cells (OHCs) and explants ot the organ of Corti were obtained from the cochlea of the echolocating bat, Carollia perspicillata, whose hearing range extends up to about 100 kHz. The OHCs were about 10–30 m long and produced resting potentials between-30 to -69 mV. During stimulation with a sinusoidal extracellular voltage field (voltage gradient of 2 mV/m) cyclic length changes were observed in isolated OHCs. The displacements were most prominent at the level of the cell nucleus and the cuticular plate. In the organ of Corti explants, the extracellular electric field induced a radial movement of the cuticular plate which was observed using video subtraction and photodiode techniques. Maximum displacements of about 0.3–0.8 m were elicited by stimulus frequencies below 100 Hz. The displacement amplitude decreased towards the noise level of about 10–30 nm for stimulus frequencies between 100–500 Hz, both in apical and basal explants. This compares well with data from the guinea pig, where OHC motility induced by extracellular electrical stimulation exhibits a low pass characteristic with a corner frequency below 1 kHz. The data indicate that fast OHC movements presumably are quite small at ultrasonic frequencies and it remains to be solved how they participate in amplifying and sharpening cochlear responses in vivo.Abbreviations BM basilar membrane - FFT fast Fourier Transfer - IHC inner hair cell - OHC outer hair cell     

Fluid waves in renal tubules.

Autoregulation of renal blood flow is ineffective when arterial pressure perturbations occur at frequencies above 0.05 Hz. To determine whether wave propagation velocity to the macula densa is rate limiting, we estimated compliances of the proximal tubule and the loop of Henle, and used these values in a model of pressure and flow as functions of time and distance in the nephron. Compliances were estimated from measurements of pressures and flows in early proximal, late proximal, and early distal tubules in rats under normal and Ringer-loaded conditions. A model of steady pressure and flow in a compliant, reabsorbing tubule was fitted to these results. The transient model was a set of nonlinear, hyperbolic partial differential equations with split, nonlinear boundary conditions, and was solved with finite difference methods. The loop of Henle compliance was larger than the proximal tubule compliance, and impulses in glomerular filtration rate were attenuated in magnitude and delayed in time in the loop of Henle. Simulated step forcings revealed a similar pattern. Periodic variations of GFR were attenuated at frequencies greater than 0.05 Hz, and there was a delay of 5 s between variations in GFR and macula densa flow rate. The high compliance of the loop slows wave propagation to the macular densa and reduces the amplitude of high frequency waves originating in the glomerulus, but other parts of the signal chain also contribute to the slow response of macula densa feedback.     

Model of the cone-horizontal cell circuit in the catfish retina

A model of the cone-L-type horizontal cell circuit of the catfish contains 3 stages. The outer segment consists of a compression factor producing the Naka-Rushton relationship between amplitude of response and intensity and 7 low-pass filters in tandem that produces an absolute delay of about 15 ms. The cone pedicle consists of an internal negative feedback circuit in series with a low-pass filter. The L-type horizontal cell acts as a linear low-pass filter and forms the external negative feedback circuit with the cone pedicle. The system shows peicewise linearity with the feedback gain of the external negative feedback circuit directly proportional to the dc level of the horizontal cell. Thus, at any given mean illuminance the impulse response of the cone and L-HC adequately defines the dynamics of the responses. The conversion of a slow monophasic to a faster biphasic impulse response due to either an increase in mean illuminace or use of a steady annulus results from the change in the characteristic equation as the effective value of the feedback gain changes. By proper adjustement of gains and time constants, the cone-L-HC circuit of the catfish retina simulates the experimental data.     

Basilar membrane nonlinearity]

The nonlinear correction of the cochlear partitions movement equation becomes the main part in the resonant section. In the neighbourhood of this section the periodic solution, having the drawing force frequency omega, gets the region of the non-stability in the interval (see abstract), where a is the vibration amplitude and h is the basilar membrane thickness. The amplitude jump in the unstable region may be a stimulus exciting the hair cells and also the cause of cochlear eddies phenomenon.     

Performance of a model for a local neuron population

A model of a local neuron population is considered that contains three subsets of neurons, one main excitatory subset, an auxiliary excitatory subset and an inhibitory subset. They are connected in one positive and one negative feedback loop, each containing linear dynamic and nonlinear static elements. The network also allows for a positive linear feedback loop. The behaviour of this network is studied for sinusoidal and white noise inputs. First steady state conditions are investigated and with this as starting point the linearized network is defined and conditions for stability is discovered. With white noise as input the stable network produces rhythmic activity whose spectral properties are investigated for various input levels. With a mean input of a certain level the network becomes unstable and the characteristics of these limit cycles are investigated in terms of occurence and amplitude. An electronic model has been built to study more closely the waveforms under both stable and unstable conditions. It is shown to produce signals that resemble EEG background activity and certain types of paroxysmal activity, in particular spikes.     

Sensory cues for the gradual frequency fall responses of the gymnotiform electric fish, Rhamphichthys rostratus

The sensory cues for a less known form of frequency shifting behavior, gradual frequency falls, of electric organ discharges (EODs) in a pulse-type gymnotiform electric fish, Rhamphichthys rostratus, were identified. We found that the gradual frequency fall occurs independently of more commonly observed momentary phase shifting behavior, and is due to perturbation of sensory feedback of the fish's own EODs by EODs of neighboring fish. The following components were identified as essential features in the signal mixture of the fish's own and the neighbor's EOD pulses: (1) the neighbor's pulses must be placed within a few millisecond of the fish's own pulses, (2) the neighbor's pulses, presented singly at low frequencies (0.2–4 Hz), were sufficient, (3) the frequency of individual pulse presentation must be below 4 Hz, (4) amplitude modulation of the sensory feedback of the fish's own pulses induced by such insertions of the neighbor's pulses must contain a high frequency component: sinusoidal amplitude modulation of the fish's own EOD feedback at these low frequencies does not induce gradual frequency falls. Differential stimulation across body surfaces, which is required for the jamming avoidance response (JAR) of wave-type gymnotiform electric fish, was not necessary for this behavior. We propose a cascade of high-pass and low-pass frequency filters within the amplitude processing pathway in the central nervous system as the mechanism of the gradual frequency fall response.Abbreviations EOD electric organ discharge - f frequency of EOD or pacemaker command signal - JAR jamming avoidance response - S ₁ stimulus mimicking fish's own EOD - f ₁ frequency of S₁ - S ₂ stimulus mimicking neighbor's EOD - f ₂ frequency of S₂     

Filter characteristics of cercal afferents in the cockroach

Summary The response dynamics of cercal afferents in the cockroach, Periplaneta americana, were determined by means of a cross-correlation technique using a Gaussian white noise modulation of wind as a stimulus. The white noise stimulus could evoke sustained firing activity in most of the afferents examined (Fig. 1). The spike discharges were unitized and then cross-correlated with the stimulus to compute 1st- and 2nd-order Weiner kernels. The Ist-order kernels from a total of 28 afferents were biphasic and closely matched the time differential of a pulse (Figs. 1, 3 and 4). The amplitude and waveform of the kernels depended on the stimulus angle in such a way that the kernels were the mirror image of those on the polar opposite side (Figs. 2 and 3). The 2nd-order kernels were also differential. They had 2 diagonal peaks and 2 off-diagonal valleys in a 2-dimensional plot with 2 time axes (Figs. 1, 5 and 6). This 4-eye configuration was basically invariant irrespective of the stimulus angle, although the kernels varied in amplitude when the stimulus angle was changed. The time between the peak and a following trough of the 1st-order kernel was constant and had a mean of 4.6±0.1 ms, whereas the time between 2 diagonal peaks of the 2nd-order kernels was 4.7±0.1 ms (Figs. 4 and 6), suggesting that wind receptors (filiform sensilla) on cerci act as a band-pass filter with a peak frequency of about 106 Hz. The peak time, however, varies from 2.3 to 6.9 ms in both kernels, which may reflect the spatial distribution of the corresponding hairs on the cercus. The summation of the 1st- (linear) and 2nd-order (nonlinear) models precisely predicted the timing of the spike firing (Fig. 8). Thus, these 2 lower-order kernels can totally characterize the response dynamics of the wind receptors. The nonlinear response explains the directional sensitivity of the sensory neurons, while the differentiating 1st-order kernel explains the velocity sensitivity of the neurons. The nonlinearity is a signal compression in which one of the diagonal peaks of the 2nd-order kernel always offsets the downward phase of the 1st-order kernel (Fig. 7) and obviously represents a half-wave rectification property of the wind receptors that are excited by hair movement in only one direction and inhibited by hair movement in the polar opposite direction.     

Experimental and finite element comparison of various fixation designs in combined loads

The short- and long-term successes of tibial cementless implants depend on the initial fixation stability often provided by posts and screws. In this work, a metallic plate was fixed to a polyurethane block with either two bone screws, two smooth-surfaced posts, or two novel smooth-surfaced posts with adjustable inclinations. For this last case, inclinations of 0, 1.5, and 3 deg were considered following insertion. A load of 1031 N was eccentrically applied on the plate at an angle of approximately 14 deg, which resulted in a 1000 N axial compressive force and a 250 N shear force. The response was measured under static and repetitive loading up to 4000 cycles at 1 Hz. The measured results demonstrate subsidence under load, lift-off on the unloaded side, and horizontal translation of the plate specially at the loaded side. Fatigue loading increased the displacements, primarily during the first 100 cycles. Comparison of various fixation systems indicated that the plate with screw fixation was the stiffest with the least subsidence and liftoff. The increase in post inclination from 0 to 3 deg stiffened the plate by diminishing the liftoff. All fixation systems demonstrated deterioration under repetitive loads. In general, the finite element predictions of the experimental fixation systems were in agreement with measurements. The finite element analyses showed that porous coated posts (modeled with nonlinear interface friction with and without coupling) generated slightly less resistance to liftoff than smooth-surfaced posts. In the presence of porous coated posts, Coulomb friction greatly overestimated the rigidity by reducing the liftoff and subsidence to levels even smaller than those predicted for the design with screw fixation. The sequence of combined load application also influenced the predicted response. Finally, the finite element model incorporating measured interface friction and pull-out responses can be used for the analysis of cementless total joint replacement systems during the post-operation period.     

Excitation properties of the squid axon membrane and model systems with current stimulation. Statistical evaluation and comparison.

The space-clamped squid axon membrane and two versions of the Hodgkin-Huxley model (the original, and a strongly adapting version) are subjected to a first order dynamic analysis. Stable, repetitive firing is induced by phase-locking nerve impulses to sinusoidal currents. The entrained impulses are then pulse position modulated by additional, small amplitude perturbation sinusoidal currents with respect to which the frequencies response of impulse density functions are measured. (Impulse density is defined as the number of impulses per unit time of an ensemble of membranes with each membrane subject to the same stimulus). Two categories of dynamic response are observed: one shows clear indications of a corner frequency, the other has the corner frequency obscured by dynamics associated with first order conductance perturbations in the interspike interval. The axon membrane responds with first order perturbations whereas the unmodified Hodgkin-Huxley model does not. Quantitative dynamic signatures suggest that the relaxation times of axonal recovery excitation variables are twice as long as those of the corresponding model variables. A number of other quantitative differences between axon and models, including the values of threshold stimuli are also observed.