Entrainment Frequency Research Articles

Abnormalities of Neuronal Oscillations and Temporal Integration to Low- and High-Frequency Auditory Stimulation in Schizophrenia

Electroencephalography and magnetoencephalography studies indicate among schizophrenia patients (SZ) abnormal, often reduced, entrained steady-state (aSSR) and transient (N100/M100) neural responses to auditory stimuli. We complement this literature by focusing analyses on auditory cortices, assessing a wide range of stimulation frequencies with long driving periods and evaluating relationships between aSSR and M100 reductions in SZ. Seventeen SZ and 17 healthy subjects (H) participated. Stimuli were 1500 msec binaural broadband noise sequences modulated at 5, 20, 40, 80, or 160 Hz. Magnetoencephalography data were collected and co-registered with structural magnetic resonance images. The aSSRs and M100s projected into brain space were analyzed as a function of hemisphere, stimulus density, and time. For aSSR, SZ displayed weaker entrainment bilaterally at low (5-Hz) and high (80-Hz) modulation frequencies. To 40-Hz stimuli, SZ showed weaker entrainment only in right auditory cortex. For M100, while responses for H increased linearly with stimulus density, this effect was weaker or absent in SZ. A principal components analysis of SZ deficits identified low (5-Hz entrainment and M100) and high (40- to 80-Hz entrainment) frequency components. Discriminant analysis indicated that the low-frequency component uniquely differentiated SZ from H. The high-frequency component correlated with negative symptoms among SZ. The SZ auditory cortices were unable to 1) generate healthy levels of theta and high gamma band (80-Hz) entrainment (aSSR), and 2) augment transient responses (M100s) to rapidly presented auditory information (an index of temporal integration). Only the latter was most apparent in left hemisphere and may reflect a prominent neurophysiological deficit in schizophrenia.

Reentrant synchronization and pattern formation in pacemaker-entrained Kuramoto oscillators

We study phase entrainment of Kuramoto oscillators under different conditions on the interaction range and the natural frequencies. In the first part the oscillators are entrained by a pacemaker acting like an impurity or a defect. We analytically derive the entrainment frequency for arbitrary interaction range and the entrainment threshold for all-to-all couplings. For intermediate couplings our numerical results show a reentrance of the synchronization transition as a function of the coupling range. The origin of this reentrance can be traced back to the normalization of the coupling strength. In the second part we consider a system of oscillators with an initial gradient in their natural frequencies, extended over a one-dimensional chain or a two-dimensional lattice. Here it is the oscillator with the highest natural frequency that becomes the pacemaker of the ensemble, sending out circular waves in oscillator-phase space. No asymmetric coupling between the oscillators is needed for this dynamical induction of the pacemaker property nor need it be distinguished by a gap in the natural frequency.

Entrainment of Randomly Coupled Oscillator Networks by a Pacemaker

Entrainment by a pacemaker, representing an element with a higher frequency, is numerically investigated for several classes of random networks which consist of identical phase oscillators. We find that the entrainment frequency window of a network decreases exponentially with its depth, defined as the mean forward distance of the elements from the pacemaker. Effectively, only shallow networks can thus exhibit frequency locking to the pacemaker. The exponential dependence is also derived analytically as an approximation for large random asymmetric networks.

The effect of thermal stimulation on the heart-rate variability in neonates.

Thermoregulation in humans can be divided into three broad mechanisms of control, namely: shivering, sweating and vasomotor activity. Previous investigations suggested the presence of an autonomic rhythm, originating in the central nervous system, possibly related to thermal vasomotor control and directly affecting heart rate by reflex changes in cardiac sympathetic and parasympathetic activity. The objective of the present work was to study the maturation process of the thermoregulatory system in newborns. We used peripheral thermal entrainment and focused on the reflections of vasomotor control in the heart-rate (HR) power spectrum (PS). The study included three groups of neonates at three different ages: 10 premature infants, 6 full-terms and 7 older infants (4 to 6 months). Thermal stimulation was achieved by placing a hot and cold surface on the subject's right palm alternately at three different rates: replacing the touching surface every 4 s (0.25 Hz), 7 s (0.14 Hz) and 10 s (0.1 Hz). 'Double period' stimulation was defined as the total duration of each period of hot and cold stimulation at the three rates, namely 8 s (0.125 Hz), 14 s (0.07 Hz), 20 s (0.05 Hz). The ECG of every infant was measured and recorded during the various stages of the experiment. The HR power spectrum from 0.02 Hz up to 2.00 Hz was considered, focusing on narrow ranges around the thermal stimulation frequencies. We found that in most subjects, clear peaks arise in the HR PS at the thermal entrainment frequency and its corresponding half frequency ('double period'). In premature infants, the reaction is best in response to the longest (10 s) stimulus (9 out of 10 prematures reacted positively), in group B (full-term infants) the reaction responds best to the 7-s stimulus (6 out of 6 reacted) and in older infants the reaction is slightly better at the 4-s stimulus. Since sympathetic control is slower, this ability to entrain the control system at increasing frequencies, might be related to the gradual maturation of parasympathetic control after birth. The different reaction of the three groups may help to understand the maturation process of the thermoregulation system.

The components of fractional transport rate

Fractional transport rates are defined as the product of spatial grain entrainment, displacement length, and displacement frequency. Grain entrainment is defined relative to the population of grains on the bed surface at an initial time in order to account for partial transport, a condition in which only a portion of the exposed grains of a single size Di are mobilized over the duration of a transport event. A relation for grain displacement frequency is calculated from an assumed relation for displacement length and observed values of fractional transport rate, bed surface size distribution, and spatial entrainment in flume experiments. Fractional transport rates are independent of Di for fully mobilized fractions and decrease rapidly with Di for partially mobile fractions; the latter results from a decrease in both the displacement frequency and the mobilized proportion of each fraction. These two terms, which together determine the fractional entrainment rate, have different relations with flow strength and Di and should be independently included in a general fractional transport model. Grain‐size similarity in fractional transport rates does not hold for conditions of partial transport. Partial transport is a grain‐scale representation of incipient motion and can be directly related to the reference shear stress τri a surrogate for the critical shear stress for incipient motion based on transport rate rather than grain mobility. Fractional mobilization at different flows may be predicted from τri, and partial transport appears to be the general condition at the reference transport rate. Using τri as input, the transport component relations are used to predict the bed mobilization and fractional transport rates for a field case.

Entrainment of the locomotor rhythm by group Ib afferents from ankle extensor muscles in spinal cats

1. Previous studies have concluded that the timing of the locomotor rhythm can be strongly influenced by input from group Ib afferents from leg extensor muscles (Duysens and Pearson 1980; Conway et al. 1987). The main objective of the present study was to obtain additional evidence for this conclusion by examining the characteristics of entrainment of the locomotor rhythm by rhythmic stimulation of group I afferents and by rhythmic force pulses in the ankle extensor muscles. 2. A reduced, non-immobilized preparation was developed in spinal cats that allowed isometric contractions of ankle extensor muscles to be elicited by ventral root stimulation during the expression of locomotor activity. The same preparation was used to examine the influence of electrically stimulating group I afferents from the ankle extensors and the effect of rhythmically stretching these muscles. The locomotor rhythm was initiated by sustained mechanical stimulation of the perineum following the administration of Clonidine and, in some preparations, Naloxone. 3. The timing of the onset of flexor burst activity was examined during entrainment with saw-tooth and ramp-and-hold stretches of the ankle extensor muscles. Flexor bursts were initiated about 200 ms following the release from the stretch, and this latency was independent of the entrainment frequency. 4. The locomotor rhythm was readily entrained by rhythmic contractions of the ankle extensor muscles produced by ventral root stimulation provided the magnitude of the contractions was greater than about 10N. Repetitive stimulation of group I muscle afferents from the ankle extensors also entrained the locomotor rhythm, with the timing of motor activity being similar to that during entrainment with rhythmic muscle contractions. Burst activity in the ipsilateral extensors was coincident with the stimulus trains in both cases. This similarity argues for entrainment being produced mainly by input from group Ib afferents. 5. The functional implication of the results of this and previous studies is that input from group Ib afferents during the stance phase of walking acts to inhibit generation of flexor burst activity and to promote extensor activity. The proposal that a decline in Ib activity near the end of the stance phase is involved in regulating the stance to swing transition is discussed.

Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator

1. This paper reports the results of an investigation of the basic mechanisms underlying intersegmental coordination in lamprey locomotion, by the use of a combined mathematical and biological approach. 2. Mathematically, the lamprey central pattern generator (CPG) is described as a chain of coupled nonlinear oscillators; experimentally, entrainment of fictive locomotion by imposed movement has been investigated. Interpretation of the results in the context of the theory has allowed conclusions to be drawn about the nature of ascending and descending coupling in the lamprey spinal CPG. 3. Theory predicts and data show that 1) the greater the number of oscillators in the chain, the smaller is the entrainment frequency range and 2) it is possible to entrain both above and below the rest frequency at one end but only above or below at the other end. 4. In the context of the experimental results, the theory indicates the following: 1) ascending coupling sets the intersegmental phase lags, whereas descending coupling changes the frequency of the coupled oscillators; 2) there are differences in the ascending and descending coupling other than strength; and it also suggests that 3) coupling slows down the oscillators.

Analysis of entrainment of respiratory rhythm by somatic afferent stimulation in cats using phase response curves.

To elucidate how peripheral somatic afferents synchronize the respiratory rhythm to the exercise rhythm, the phrenic nerve activity in the vagotomized, paralyzed, and artificially ventilated cats anesthetized with chloralose-urethane was recorded during electrical stimulation of the superficial radial nerve afferents. At first, a single pulse train was given at various times of the respiratory cycle to obtain a phase-response curve (PRC). The stimulation given at mid to late expiration produced a phase advance, but the stimulation during inspiration produced no measurable phase shifts in most animals (8/10). The maximum phase advance changed depending on the stimulus intensity. The stronger the stimulus intensity, the greater became the maximum phase advance. Repetitive somatic afferent stimulation produced 1:1 entrainment of the respiratory frequency to the repetitive stimulation. Theoretical predictions on the stable entrainment phase and on the entrainment frequency range from the obtained PRC were close to the experimental results. The present study demonstrated the presence of a neuronal circuit synchronizing the respiratory rhythm to the periodic somatic afferents and the manner of how such entrainment occurs.

Entrainment of the locust central flight oscillator by wing stretch receptor stimulation

1. Experiments were designed to examine phase-dependent influences of the wing stretch receptor (SR) afferents on the central oscillator in the flight system of the locust. Reasons were also sought for the failure of earlier workers to find phase-dependent influences of SR activity on the flight oscillator. 2. In preparations with the hindwing sensory nerves left intact, electrical stimulation of the two forewing SRs caused an immediate increase in oscillator frequency reaching a maximum of 16–20 Hz as described by Pearson et al. (1983). After cutting the hindwing sensory nerves, the same stimulation increased the frequency from 6–8 Hz to 12–14 Hz. The absolute reduction in cycle period caused by the stimulation was reduced from 15–25 ms to 10–15 ms as a result of cutting the hindwing sensory nerves. 3. Stimulation of two forewing SRs in completely deafferented preparations in bursts occurring at a constant rate could entrain the flight oscillator. During entrainment, depressor spikes occurred close to the time of the stimulus. The flight oscillator could follow changes in the entrainment frequency, usually only up to 1 Hz (10% cycle period) compared to 4–6 Hz (40–50% cycle period) seen by Pearson et al. (1983). Entrainment could still be elicited when the chordotonal organ afferents were co-stimulated. 4. Bilateral stimulation of the hindwing SRs could also entrain the central flight oscillator over a similar range of frequencies as was observed for forewing SR stimulation. 5. Stimulation of a lateral pair of SRs (one forewing and the ipsilateral hindwing SR) was observed to produce 1∶1 entrainment in only one out of fifteen animals. However, a phase-dependent influence on the oscillator rhythm could be demonstrated by stimulation time-locked to the oscillator output (depressor EMG). SR stimulation close to the time of the depressor spike increased the oscillator frequency and prolonged the duration of rhythmic activity. Stimulation occurring approximately midway between depressor bursts had no obvious effect on the frequency or duration of the oscillator rhythm. 6. The only conditions under which a slow increase in oscillator frequency could be produced by stimulation of a lateral pair of SRs was when the SR stimulus frequency was set much higher than the central oscillator frequency. It is concluded that the failure of earlier workers to observe phase-dependent effects of SR stimulation on the oscillator frequency was due to stimulation of a lateral rather than segmental pair of SRs and the method they used in their attempt to demonstrate phase-dependence. Their observation of a slow phase-independent increase in flight frequency possibly resulted from the high SR stimulus frequencies employed.