Load dependence of simulated central tremor

Previous studies have argued that tremors of central versus peripheral origin can be distinguished based on their load dependence: the frequency of peripheral tremor decreases when a weight is added to the tremulous limb, while the frequency of central tremors remains unchanged. The present study scrutinizes the latter statement. We simulated central tremor using a simple network of coupled neural oscillators, which receives proprioceptive feedback from the motor periphery. The network produced a self-sustained, stable oscillation. When the gain of proprioceptive feedback was high, oscillation frequency decreased in the presence of an inertial load. When the gain was low, the oscillation frequency was load independent. We conclude that load dependence is not an exclusive property of peripheral tremors but may be found in tremors of central origin as well. Therefore, the load test is not sufficient to reject a central tremor origin. Received: 1 October 1998 / Accepted in revised form: 28 January 1999     

Pathological tremors as diffusional processes

 Two types of pathological tremors, essential and Parkinsonian, are studied using dynamical systems theory. It is shown that pathological tremors can be characterized as diffusional processes. The time-scale range for the diffusional scaling law to be valid starts from about one to several tens of the mean oscillation period. This time-scale range contrasts sharply with the predictable time scale for deterministic chaos, which is usually only a small fraction of the mean oscillation period. The diffusions in pathological tremors are usually anomalous. A number of quantities are designed to characterize the diffusions in the tremor. Their relevance to potential clinical applications is discussed. It is argued that in order to discriminate between Parkinsonian and essential tremors, quantities not of purely dynamical origin may be more useful, since purely dynamical quantities emphasize more the dynamical similarities between the two types of tremors. Received: 30 May 2001 / Accepted in revised form: 6 November 2001     

Frequency and displacement amplitude relations for normal hand tremor.

Spectral analysis of hand tremor records obtained from normal subjects during continuous extension of the hand for 15-45 min revealed that the root-mean-square (rms) displacement amplitude of the tremor increased from control levels of about 30 mum to levels on the order of 100-1,000 times control. Associated with this increase in the displacement was a systematic decrease in the hand tremor frequency from control values of 8-9 Hz to values of 4-6 Hz. Spectral analysis of demodulated extensor EMG records indicated a consistent relation between EMG modulation amplitude at the tremor frequency and the tremor displacement amplitude for tremor records with rms displacement above about 100 mum. No consistent relation was found between these two variables for tremor records with displacements below 100 mum. Consideration of both mechanical and neural reflex effects indicated that a viscoelastic-mass mechanism primarily determined the small-amplitude (less than 100 mum) tremors, while the large displacement tremors may have involved both mechanical and neural feed back factors.     

Tremor disorders. Diagnosis and management.

Tremor is commonly encountered in medical practice, but can be difficult to diagnose and manage. It is an involuntary rhythmic oscillation of a body part produced by reciprocally innervated antagonist muscles. Tremors vary in frequency and amplitude and are influenced by physiologic and psychological factors and drugs. Categorization is based on position, posture, and the movement necessary to elicit the tremor. A resting tremor occurs when the body part is in repose. A postural tremor occurs with maintained posture and kinetic tremor with movement. Various pathologic conditions are associated with tremors. Essential tremor, which is the most common, is postural and kinetic, with a frequency between 4 and 8 Hz, and involves mainly the upper extremities and head. Essential tremor responds to treatment with primidone, beta-blockers, and benzodiazepines. Parkinson''s disease causes a 4- to 6-Hz resting tremor in the arms and legs that responds to the use of anticholinergics and a combination of carbidopa and levodopa. Tremor can also be a manifestation of Wilson''s disease, lesions of the cerebellum and midbrain, peripheral neuropathy, trauma, alcohol, and conversion disorders. Treatment should be directed to the underlying condition. Stereotactic thalamotomy of thalamic stimulation is a last resort.     

The frequency of plasmodesmata increases early in the whole shoot apical meristem of Sinapis alba L. during floral transition

 The frequency of plasmodesmata increases in the shoot apical meristem of plants of Sinapis alba L. induced to flower by exposure to a single long day. This increase is observed within all cell layers (L1, L2, L3) as well as at the interfaces between these layers, and it occurs in both the central and peripheral zones of the shoot apical meristem. The extra plasmodesmata are formed only transiently, from 28 to 48 h after the start of the long day, and acropetally since they are detectable in L3 4 h before they are seen in L1 and L2. These observations indicate that (i) in the Sinapis shoot apical meristem at floral transition, there is an unfolding of a single field with increased plasmodesmatal connectivity, and (ii) this event is an early effect of the arrival at this meristem of the floral stimulus of leaf origin. Since (i) the wave of increased frequency of plasmodesmata is 12 h later than the wave of increased mitotic frequency (A. Jacqmard et al. 1998, Plant cell proliferation and its regulation in growth and development, pp. 67–78; Wiley), and (ii) the increase in frequency of plasmodesmata is observed in all cell walls, including in walls not deriving from recent divisions (periclinal walls separating the cell layers), it is concluded that the extra plasmodesmata seen at floral transition do not arise in the forming cell plate during mitosis and are thus of secondary origin. Received: 4 October 1999 / Accepted: 23 December 1999     

Tremor and other oscillations in neuromuscular systems

A model has been analyzed which is based on recent experimental evidence concerning the properties of muscles and the sensory feedback pathways from muscles. Damped oscillations can arise in the absence of sensory feedback due to the interaction of a muscle with inertial loads. These mechanical oscillations can have a wide range of frequencies depending on the inertial and elastic loads that are attached to the muscle. Small amounts of sensory feedback will tend to reduce deviations from a steady muscle length, but larger amounts of feedback can produce oscillations. The frequency of these reflex oscillations is determined by the properties of the muscle and feedback pathway, and is rather independent of load. If the strength of the sensory feedback is sufficient, either the mechanical oscillations or the reflex oscillations or both can grow, rather than decay, with time. The growth of these oscillations is limited by saturation non-linearities in the muscle receptors and the muscle itself, so that the oscillations approach a steady amplitude and frequency. Using typical properties of muscles and spinal reflex pathways, the frequency of reflex oscillations will be within the range 8–12 Hz found for physiological tremor. With the longer latency found for supraspinal reflexes, oscillations will occur in the range 4–6 Hz which is characteristic of Parkinson's and cerebellar diseases. The role of longer latency reflexes in the generation of these tremors is discussed.     

Beta-Adrenergic Modulation of Tremor and Corticomuscular Coherence in Humans

Coherence between the bioelectric activity of sensorimotor cortex and contralateral muscles can be observed around 20 Hz. By contrast, physiological tremor has a dominant frequency around 10 Hz. Although tremor has multiple sources, it is partly central in origin, reflecting a component of motoneuron discharge at this frequency. The motoneuron response to ∼20 Hz descending input could be altered by non-linear interactions with ∼10 Hz motoneuron firing. We investigated this further in eight healthy human subjects by testing the effects of the beta-adrenergic agents propranolol (non-selective β-antagonist) and salbutamol (β₂-agonist), which are known to alter the size of physiological tremor. Corticomuscular coherence was assessed during an auxotonic precision grip task; tremor was quantified using accelerometry during index finger extension. Experiments with propranolol used a double-blind, placebo-controlled crossover design. A single oral dose of propranolol (40 mg) significantly increased beta band (15.3–32.2 Hz) corticomuscular coherence compared with placebo, but reduced tremor in the 6.2–11.9 Hz range. Salbutamol (2.5 mg) was administered by inhalation. Whilst salbutamol significantly increased tremor amplitude as expected, it did not change corticomuscular coherence. The opposite direction of the effects of propranolol on corticomuscular coherence and tremor, and the fact that salbutamol enhances tremor but does not affect coherence, implies that the magnitude of corticomuscular coherence is little influenced by non-linear interactions with 10 Hz oscillations in motoneurons or the periphery. Instead, we suggest that propranolol and salbutamol may affect both tremor and corticomuscular coherence partly via a central site of action.     

A method for the objective determination of tremors in the rat]

Two methods for determining tremors in the rat, acceleration pick-up and electromyogram, including electronic evaluation by impluse rate and frequency are described technically, and the results obtained with either method are compared. Both methods allow quantitative analysis of the drug induced (arecoline) tremor. Electromyographically, the tremor effect can be recorded already after lower doses compared with the electro-mechanical method. Besides, the EMG can be employed on immobilized animals.     

Suppression of Enhanced Physiological Tremor via Stochastic Noise: Initial Observations

Enhanced physiological tremor is a disabling condition that arises because of unstable interactions between central tremor generators and the biomechanics of the spinal stretch reflex. Previous work has shown that peripheral input may push the tremor-related spinal and cortical systems closer to anti-phase firing, potentially leading to a reduction in tremor through phase cancellation. The aim of the present study was to investigate whether peripherally applied mechanical stochastic noise can attenuate enhanced physiological tremor and improve motor performance. Eight subjects with enhanced physiological tremor performed a visuomotor task requiring the right index finger to compensate a static force generated by a manipulandum to which Gaussian noise (3–35 Hz) was applied. The finger position was displayed on-line on a monitor as a small white dot which the subjects had to maintain in the center of a larger green circle. Electromyogram (EMG) from the active hand muscles and finger position were recorded. Performance was measured by the mean absolute deviation of the white dot from the zero position. Tremor was identified by the acceleration in the frequency range 7–12 Hz. Two different conditions were compared: with and without superimposed noise at optimal amplitude (determined at the beginning of the experiment). The application of optimum noise reduced tremor (accelerometric amplitude and EMG activity) and improved the motor performance (reduced mean absolute deviation from zero). These data provide the first evidence of a significant reduction of enhanced physiological tremor in the human sensorimotor system due to application of external stochastic noise.     

A comparison of resonance tuning with positive versus negative sensory feedback

We used a computational model of rhythmic movement to analyze how the connectivity of sensory feedback affects the tuning of a closed-loop neuromechanical system to the mechanical resonant frequency (ω_r). Our model includes a Matsuoka half-center oscillator for a central pattern generator (CPG) and a linear, one-degree-of-freedom system for a mechanical component. Using both an open-loop frequency response analysis and closed-loop simulations, we compared resonance tuning with four different feedback configurations as the mechanical resonant frequency, feedback gain, and mechanical damping varied. The feedback configurations consisted of two negative and two positive feedback connectivity schemes. We found that with negative feedback, resonance tuning predominantly occurred when ω_r was higher than the CPG’s endogenous frequency (ω_CPG). In contrast, with the two positive feedback configurations, resonance tuning only occurred if ω_r was lower than ω_CPG. Moreover, the differences in resonance tuning between the two positive (negative) feedback configurations increased with increasing feedback gain and with decreasing mechanical damping. Our results indicate that resonance tuning can be achieved with positive feedback. Furthermore, we have shown that the feedback configuration affects the parameter space over which the endogenous frequency of the CPG or resonant frequency the mechanical dynamics dominates the frequency of a rhythmic movement.     

Corticomuscular Transmission of Tremor Signals by Propriospinal Neurons in Parkinson's Disease

Cortical oscillatory signals of single and double tremor frequencies act together to cause tremor in the peripheral limbs of patients with Parkinson''s disease (PD). But the corticospinal pathway that transmits the tremor signals has not been clarified, and how alternating bursts of antagonistic muscle activations are generated from the cortical oscillatory signals is not well understood. This paper investigates the plausible role of propriospinal neurons (PN) in C3–C4 in transmitting the cortical oscillatory signals to peripheral muscles. Kinematics data and surface electromyogram (EMG) of tremor in forearm were collected from PD patients. A PN network model was constructed based on known neurophysiological connections of PN. The cortical efferent signal of double tremor frequencies were integrated at the PN network, whose outputs drove the muscles of a virtual arm (VA) model to simulate tremor behaviors. The cortical efferent signal of single tremor frequency actuated muscle spindles. By comparing tremor data of PD patients and the results of model simulation, we examined two hypotheses regarding the corticospinal transmission of oscillatory signals in Parkinsonian tremor. Hypothesis I stated that the oscillatory cortical signals were transmitted via the mono-synaptic corticospinal pathways bypassing the PN network. The alternative hypothesis II stated that they were transmitted by way of PN multi-synaptic corticospinal pathway. Simulations indicated that without the PN network, the alternating burst patterns of antagonistic muscle EMGs could not be reliably generated, rejecting the first hypothesis. However, with the PN network, the alternating burst patterns of antagonist EMGs were naturally reproduced under all conditions of cortical oscillations. The results suggest that cortical commands of single and double tremor frequencies are further processed at PN to compute the alternating burst patterns in flexor and extensor muscles, and the neuromuscular dynamics demonstrated a frequency dependent damping on tremor, which may prevent tremor above 8 Hz to occur.     

Physiological model analysis of involuntary human-voice tremor

Frequency variations in the human voice result from voluntary and involuntary changes in the parameters of the vocal system. The present work deals with involuntary frequency perturbations from two theoretical aspects: 1) the influence of pitch period variations on frequency changes in the band-limited signal which results from the resonant characteristics of the vocal tract; 2) the physiological parameters of the vocal system which are potentially able to govern involuntary frequency changes. It is shown that the modulation function of the vocal-cord wave can theoretically be derived from its harmonics using FM demodulation techniques, and that higher distortion may appear at higher harmonics. It is also shown that involuntary geometrical changes of the vocal tract and its terminal impedance as well as tension and initialarea changes of the vocal cord—changes well within the physiological range—can influence frequency changes in the human voice. The present results are correlated with our reported experimental findings on involuntary voice tremor, used in psychological stress evaluation. The role of the central nervous system, and possible mechanisms for these phenomena, are discussed.     

Tremor modulation in patients with Parkinson’s disease compared to healthy counterparts during loaded postural holding

Through examining tremor dynamics, the study sought to investigate the effects of load characteristics upon control strategies in patients with Parkinson’s disease (PD) during postural holding. Eleven untreated patients and eleven healthy adults conducted a static pointing task with an outstretched arm, with a manipulated load of 100 g on the index finger. Oscillatory activities in the upper limb were contrasted between the unloaded and loaded conditions. The results showed that PD patients demonstrated abnormal modulation of tremor amplitude in the finger, hand, and upper arm in the opposing load condition. When the load was applied, the PD patients presented a nearly opposite pattern of tremor coupling between limb segments, contrary to the normal release and enhancement of tremor coupling in the finger–hand and hand–forearm complexes, respectively. Principal component analysis suggested that normal postural tremors could be explained by a load-dependent component that had high communality with tremors of the distal segments. In contrast, major principal components of PD tremor were invariant to load addition. Multi-segment tremors in PD were atypically organized during loaded postural holding, signifying that coordinative control of the upper limb in the patients was impaired in the absence of exploitation of a germane distal strategy against inertial perturbation.     

A note on the response characteristics of the extraocular muscle system

Using records of the response of the extraocular muscle system to a step input, the frequency response characteristics of the system have been calculated. They show a progressive reduction of gain for frequencies above 30–40 cps. The high frequency tremor of the eyes observed during “steady” fixation would thus be expected to be damped down and this is in fact borne out by frequency analyses of tremor records.     

Neurogenic contractile activity of the penis retractor muscle of Helix pomatia L.

Using convential mechanical and electromyographic recording methods 2 distinct types of neurogenically elicited activity can be observed in the penis retractor muslce (PRM) of Helix pomatia: (1) rhythmic, phasic contractions correlated with single or a few compound action potentials and (2) intervening, strong, prolonged contractions accompanied by sustained, high frequency electrical muscle activity. The 2 distinct types of muscle activity which seem to play a part in the normal behaviour of the PRM in the intact animal are mediated by both the central nervous system and peripheral neurons. While central neuronal structures are involved in causing the strong, prolonged contractions, the phasic activity is initiated by peripheral neuronal structures located at the proximal end of the PRM. There is evidence that the transmission of the excitation at the neuromuscular level of central and peripheral origin is mediated by ACh.     

A dynamical model for reflex activated head movements in the horizontal plane

 We present a controls systems model of horizontal-plane head movements during perturbations of the trunk, which for the first time interfaces a model of the human head with neural feedback controllers representing the vestibulocollic (VCR) and the cervicocollic (CCR) reflexes. This model is homeomorphic such that model structure and parameters are drawn directly from anthropomorphic, biomechanical and physiological studies. Using control theory we analyzed the system model in the time and frequency domains, simulating neck movement responses to input perturbations of the trunk. Without reflex control, the head and neck system produced a second-order underdamped response with a 5.2 dB resonant peak at 2.1 Hz. Adding the CCR component to the system dampened the response by approximately 7%. Adding the VCR component dampened head oscillations by 75%. The VCR also improved low-frequency compensation by increasing the gain and phase lag, creating a phase minimum at 0.1 Hz and a phase peak at 1.1 Hz. Combining all three components (mechanics, VCR and CCR) linearly in the head and neck system reduced the amplitude of the resonant peak to 1.1 dB and increased the resonant frequency to 2.9 Hz. The closed loop results closely fit human data, and explain quantitatively the characteristic phase peak often observed. Received: 15 April 1996 / Accepted in revised form: 1 July 1996     

The effects of extra-low-frequency atmospheric pressure oscillations on human mental activity

 Slight atmospheric pressure oscillations (APO) in the extra-low-frequency range below 0.1 Hz, which frequently occur naturally, can influence human mental activity. This phenomenon has been observed in experiments with a group of 12 healthy volunteers exposed to experimentally created APO with amplitudes 30–50 Pa in the frequency band 0.011–0.17 Hz. Exposure of the subjects to APO for 15–30 min caused significant changes in attention and short-term memory functions, performance rate, and mental processing flexibility. The character of the response depended on the APO frequency and coherence. Periodic APO promoted purposeful mental activity, accompanied by an increase in breath-holding duration and a slower heart rate. On the other hand, quasi-chaotic APO, similar to the natural perturbations of atmospheric pressure, disrupted mental activity. These observations suggest that APO could be partly responsible for meteorosensitivity in humans. Received: 22 August 1997/Revised: 3 December 1998/Accepted: 25 February 1999     

Characteristics of hand tremor time series

Tremor is classified into physiological, essential, and parkinsonian tremor by means of clinical criteria. The aim of our work was to extract quantitative features from the measurements of the acceleration of human postural hand tremor. Different mathematical methods were adopted and modified in order to separate these three types of tremor. Best discrimination between physiological and pathological tremors has been achieved by methods distinguishing nonlinear from linear behavior. On the other hand, methods separating different forms of nonlinear behavior have been found to be superior in discriminating parkinsonian and essential tremor. By these methods physiological and pathological tremors can be separated with an error rate below 20% and essential and parkinsonian tremor with an error rate below 10%. This may help to classify tremor time series by objective mathematical criteria and may increase the understanding of the pathophysiological differences underlying these kinds of tremor.     

Atypical task-invariant organization of multi-segment tremors in patients with Parkinson’s disease during manual tracking

The objective of the study was to investigate the interplay between involuntary tremulous activities and task performance under volitional control for patients with Parkinson’s disease (PD) during position tracking. A volunteer sample of nine untreated patients and nine age-matched healthy subjects participated in this study. They performed a sinusoidal tracking maneuver with a shoulder and a static pointing task; meanwhile, a position trace of the index and accelerometer data in the upper limb were recorded to characterize tracking performance and postural–kinetic tremors. In reference to postural tremor, the kinetic tremor of control subjects during tracking was considerably modulated, leading to a lower regularity and greater spectral deviation. In contrast, patients with PD demonstrated greater postural and kinetic tremors than control subjects, and tremulous movements of the patients were comparatively task-invariant. The prominent coherence peak, which occurred at 8–12 Hz in control subjects, was atypically presented at 5–8 Hz for PD patients with poorer tracking performance. Functionally, congruency of position tracking was related to amplitude of kinetic tremor after subtracting from amplitude of postural tremor. In conclusion, task-dependent organization of tremulous movements was impaired in patients with PD. The inferior tracking performance of the patients correlated implicitly with kinetic tremor, signifying some sharing of neural substrates for manual tracking and tremor generation.     

Leslie matrix models as “stroboscopic snapshots” of McKendrick PDE models

 High dimensional Leslie matrix models have long been viewed as discretizations of McKendrick PDE models. However, these two fundamental classes of models can be linked in a completely different way. For populations with periodic birth pulses, Leslie models of any dimension can be viewed as “stroboscopic snapshots” (in time) of an associated impulsive McKendrick model; that is, the solution of the discrete model matches the solution of the corresponding continuous model at every discrete time step. In application, McKendrick models of populations with birth pulses can be used to identify the state of the population between the discrete census times of the associated Leslie model. Furthermore, McKendrick models describing populations with near-synchronous birth pulses can be viewed as realistic perturbations of the associated Leslie model. Received: 7 August 1997 / Revised version: 15 January 1998