Anne Beuter

Nonlinear Dynamics in Physiology and Medicine

This book deals with the application of mathematics in modeling and understanding physiological systems, especially those involving rhythms. It is divided roughly into two sections. In the first part of the book, the authors introduce ideas and techniques from nonlinear dynamics that are relevant to the analysis of biological rhythms. The second part consists of five in-depth case studies in which the authors use the theoretical tools developed earlier to investigate a number of physiological processes: the dynamics of excitable nerve and cardiac tissue, resetting and entrainment of biological oscillators, the effects of noise and time delay on the pupil light reflex, pathologies associated with blood cell replication, and Parkinsonian tremor. One novel feature of the book is the inclusion of classroom-tested computer exercises throughout, designed to form a bridge between the mathematical theory and physiological experiments. This book will be of interest to students and researchers in the natural and physical sciences wanting to learn about the complexities and subtleties of physiological systems from a mathematical perspective. The authors are members of the Centre for Nonlinear Dynamics in Physiology and Medicine. The material in this book was developed for use in courses and was presented in three Summer Schools run by the authors in Montreal.

Time delays, oscillations, and chaos in physiological control systems

Many physiological systems operate by feedback mechanisms in which there are time delays from the sensing of some disturbance to the mounting of an appropriate physiological response. Theoretical studies show that using either “mixed” feedback or multiple negative feedback loops with different delays, it is possible to generate complex periodic and aperiodic, chaotic rhythms. In an experimental study of finger tracking using visual feedback, a variable time delay can be added to the feedback circuit. As this delay is varied, complex rhythms of finger displacement are observed. We suggest that the complex dynamics observed in diverse physiological systems in normal individuals may be associated with chaotic dynamics arising from the interaction of multiple feedback loops.

Lack of efficacy of a nicotine transdermal treatment on motor and cognitive deficits in Parkinson's disease

UNLABELLED Studies assessing the efficacy of nicotine in Parkinsons disease (PD) have generated contradictory results. The controversy seems to stem from uncontrolled factors including the lack of objective measures, the practice effect in a test-retest design, and the absence of plasmatic dosage. This study aimed at further controlling these factors using transdermal nicotine in PD. METHODS Twenty-two nonsmoking PD patients received a transdermal nicotine treatment over 25 days in increasing titrated doses. Motor and cognitive assessments were carried out on days 11 and 25 (low-dose and high-dose assessments, respectively) and after a 14-day washout period. RESULTS Patients tolerated nicotine poorly. Thirteen (59%) withdrew, mostly because of acute side effects. In the remaining nine patients, nicotine neither improved nor worsened motor or cognitive functioning in comparison with 10 age, gender and education matched controls. CONCLUSIONS Transdermal nicotine is not effective in treating motor and cognitive deficits in PD. The results obtained with our objective measures confirm a recent double-blind, placebo-controlled study that used clinical measures. It is possible that nicotine lacks specificity in targeting critical nicotinic receptors that might be involved in PD pathophysiology. The low tolerability may be related to such a lack of specificity of nicotine, which would directly stimulate the autonomic nervous system.

The measurement of tremor using a velocity transducer: comparison to simultaneous recordings using transducers of displacement, acceleration and muscle activity

Precise kinematic measurements of tremor have historically been obtained using accelerometers. However, current technology permits precise measurements in velocity and displacement. The primary advantage of velocity recording is that only one step of integration or differentiation is required for either displacement or acceleration. A method is presented of measuring finger tremor using a laser system that transduces velocity precisely. Measurements of postural finger tremor thus obtained were compared to those simultaneously obtained from a laser system that transduces displacement, from an accelerometer and from surface electromyography (EMG) of the extensor digitorum communis. A range of amplitude and frequency content was obtained by testing control subjects and subjects with Parkinsons disease. The velocity transducer showed excellent correspondence of amplitude and frequency measurement with the displacement transducer. Measures of absolute and relative amplitude correlated well (r > or = 0.96 in amplitude measures in displacement, velocity and acceleration), and high coherence was found throughout the frequency range of interest. Measurements by the accelerometer generally showed poorer correspondence with those of the other instruments. EMG measurements showed good correspondence in some trials but poorer correspondence in others, attributed to the low level of muscle activity required in the task. Precise kinematic measurements appear to be highly sensitive to neuromotor impairment.

Dynamics of Parkinsonian tremor during deep brain stimulation

The mechanism by which chronic, high frequency, electrical deep brain stimulation (HF-DBS) suppresses tremor in Parkinsons disease is unknown. Rest tremor in subjects with Parkinsons disease receiving HF-DBS was recorded continuously throughout switching the deep brain stimulator on (at an effective frequency) and off. These data suggest that the stimulation induces a qualitative change in the dynamics, called a Hopf bifurcation, so that the stable oscillations are destabilized. We hypothesize that the periodic stimulation modifies a parameter affecting the oscillation in a time dependent way and thereby induces a Hopf bifurcation. We explore this hypothesis using a schematic network model of an oscillator interacting with periodic stimulation. The mechanism of time-dependent change of a control parameter in the model captures two aspects of the dynamics observed in the data: (1) a gradual increase in tremor amplitude when the stimulation is switched off and a gradual decrease in tremor amplitude when the stimulation is switched on and (2) a time delay in the onset and offset of the oscillations. This mechanism is consistent with these rest tremor transition data and with the idea that HF-DBS acts via the gradual change of a network property. (c) 2001 American Institute of Physics.

Using frequency domain characteristics to discriminate physiologic and parkinsonian tremors.

The manner in which characteristics of time series in the frequency domain can enhance discrimination between physiologic and parkinsonian tremor when tremor amplitude is low was examined. Rest tremor and postural tremor with and without visual feedback were recorded twice in the two hands of a group of patients with Parkinsons disease (PD) (n = 21) and a group of healthy control subjects (n = 30) using displacement laser systems. Recordings were analyzed quantitatively using amplitude and seven frequency domain characteristics. Postural tremor with no visual feedback allowed the most efficient discrimination between the two groups of subjects especially in velocity and acceleration (derived from displacement) and allowed identification of more patients with PD as separate from the range observed in the control group. Moreover, the frequency domain characteristics that were investigated identified the majority of the patients even when amplitude did not. After eliminating redundant (correlated) characteristics, it was found that the frequency composition of tremor in PD can be described adequately with four characteristics, which are the most reliable, independent, and discriminative elements for detecting early or subtle modifications in tremor. Also, a series of finger flexions was found to enhance physiologic tremor but not tremor in PD. Discrimination of low-amplitude tremor in PD from normal physiologic tremor is enhanced by examining the median frequency of oscillations, the concentration of power in the power spectrum, and the distribution of power in particular ranges. Tremor measurement should not be limited to acceleration data as some information is more visible in velocity time series.

Complex dynamics and bifurcations in neurology.

The neurologist is often faced with patients who exhibit a bewildering array of abnormal oscillations and complex rhythms that pose therapeutic problems. These problems take many forms (Mackey & Milton, 1987; Glass & Mackey, 1988). Most commonly there is an appearance of an oscillation in a neurological control system not normally characterized by a rhythmic process. Examples include ankle clonus in patients with corticospinal tract disease (Dimitrijevic et al., 1978), various movement disorders (e.g. essential and Parkinsons tremors, Marsden, 1984a, b), and the abnormal paroxysmal oscillations in the discharges of neurons which are associated with seizures (Ayala et aL, 1973). There can be a qualitative change in the oscillations produced by an already rhythmic process, for example, gait abnormalities (Beuter & Garfinkel, 1985), Cheyne-Stokes respiration (Cherniack & Longobardo, 1973), altered sleep-wake cycles (Wehr et al., 1982) and rapid cycling manic-depressive illness (Wehr & Goodwin, 1983). In addition, there can be the disappearance of a rhythmic process as occurs in patients with depression in whom there is the disappearance of the diurnal rhythm in cortisol secretion (Hollister et aL, 1980). Finally, some clinical events recur in a seemingly random fashion, for example, seizures in adult epileptics (Milton et al., 1987). The traditional explanation given by the neurologist is to relate the appearance of abnormal dynamical behaviors to pathological processes which destroy or modify neural control mechanisms. The abnormal breathing patterns (Plum & Posner, 1980) and rhythmic movements of the palate (Lapresle & Hamida, 1970) which can occur

Transient dynamics in motor control of patients with Parkinson’s disease

Experimental observations of movement disorders including tremor and voluntary microdisplacements recorded in patients with Parkinsons disease (PD) during a simple visuomotor tracking task are analyzed. The performance of patients with PD having a very large amplitude tremor is characterized either by the intermittent appearance of transient dynamics or by the presence of sudden transitions in the amplitude or frequency of the signal. The need to develop new tools to characterize changes in dynamics (i.e., transitions) and to redefine neurological degeneration, such as Parkinsons disease, in terms of qualitative changes in oscillatory behaviors is emphasized.

The measurement of tremor using simple laser systems

Quantification of movement pathologies is an important challenge of the clinical and research laboratories today. Basically, two problems must be addressed. The first one is to find the appropriate technology; the second is to develop adequate measures from the raw data which will best discriminate between health and pathology. In this paper, we propose a simple method to record and analyse tremor and other microdisplacements of the upper extremities based on the recording of position by laser analog sensors. Any microcomputer equipped to perform analog-digital conversion is compatible for use with this system. The performance of the laser system is examined and compared with the performance of accelerometers. Finally, data recorded with a laser analog sensor from a patient with Parkinsons disease and a control subject are presented. This new laser-based quantitative method may prove to be an important tool in early and differential diagnosis of neurodegenerative diseases of the central nervous system.

Postural sway and effect of levodopa in early Parkinson's disease

OBJECTIVE To characterize postural stability control and levodopa responsiveness in early Parkinsons disease (PD). METHODS Postural sway was studied during quiet stance in ten patients within six years of PD onset, both before (OFF) and after (ON) regular oral levodopa dosing. Postural sway was recorded using a force platform during 30 sec with eyes open, and six dependent variables were examined. RESULTS Mild baseline subclinical changes in postural sway were recorded in our patients. Clear benefit was observed in five out of six characteristics (mean sway, transversal sway, sagittal sway, sway intensity, and sway area) in the ON condition. CONCLUSION Postural control mechanisms are affected early in PD and modulated by dopamine.