Transient dynamics in motor control of patients with Parkinson’s diseaseAnne Beuter, Christiane Labrie, and Konstantinon Vasilakos Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science 1, 279 (1991); doi: 10.1063/1.165841 View online: http://dx.doi.org/10.1063/1.165841 View Table of Contents: http://scitation.aip.org/content/aip/journal/chaos/1/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Acoustic characteristics of Lombard speech in Parkinson’s disease patients. J. Acoust. Soc. Am. 124, 2558 (2008); 10.1121/1.4783044 Lip and tongue force control in patients with Parkinson’s disease J. Acoust. Soc. Am. 100, 2662 (1996); 10.1121/1.417468 Tremor: Is Parkinson’s disease a dynamical disease? Chaos 5, 35 (1995); 10.1063/1.166082 Aerodynamic and acoustic changes following intensive voice therapy for patients with Parkinson’s disease: Acase study J. Acoust. Soc. Am. 94, 1781 (1993); 10.1121/1.407980 The effect of learning due to voice assessment in acoustic analysis of vocal tremor in patients with Parkinson’sdisease J. Acoust. Soc. Am. 94, 1882 (1993); 10.1121/1.407580

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Transient dynamics in motor control of patients with Parkinson's disease Anne Beutera) Department of Kinanthropology, University of Quebec at Montreal, CP# 8888, SUCC A, Montreal, PQ H3C 3P8, Canada and Centre for Nonlinear Dynamics in Physiology and Medicine. McGill University, Montreal, PQ H3A 2T8, Canada

Christiane Labrie Department of Kinanthropology, University of Quebec at Montreal, CP# 8888, SUCC A, Montreal, PQ H3C 3P8, Canada

Konstantinon Vasilakos Centre for Nonlinear Dynamics in Physiology and Medicine, McGill UniverSity, Montreal, PQ H3A 2T8, Canada

(Received 17 June 1991; accepted for publication 17 July 1991)

Experimental observations of movement disorders including tremor and voluntary microdisplacements recorded in patients with Parkinson's 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 Parkinson'S disease, in terms of qualitative changes in oscillatory behaviors is emphasized. .

I. INTRODUCTION

In recent years there has been an extraordinary growth of scientific interest in the origin of complex dynamics in biological systems. One area that has been left relatively unexplored is the complex dynamics arising in distal limb movements following the degeneration of structures 10' cated in the central nervous system.

It is well known that regular and irregular rhythms may arise from the lesion of sUbcortical structures. These oscillatory behaviors have been described in detail clini­cally and inventories of these (a) rhythmical behaviors are now available (see, for example, Mackey and Milton l

).

However, we have no clear understanding yet of the mech­anisms by which these lesioned structures produce abnor­mal movements in the extremities. Myoclonus, for exam­ple, is a movement disorder associated with exceedingly abrupt shocklike contractions of muscles of irregular fre­quencies and amplitude. Myoclonus is often observed in association with certain types of epilepsy, encephalopathy, cerebellar disease, advanced Alzheimer'S disease, and some metabolic disorders. It is also observed in normal subjects since it includes the normal jerk of a limb as one falls asleep. Another example is clonus, which is associated with a rhythmic involuntary contraction at a frequency of 5 to 7 Hz in response to a sudden and steady stretch stimulus and is observed in pyramidal tract diseases. Again, clonus, which looks like a violent type of tremor, is a common phenomenon in the limb of the fatigued and stressed rock climber. As a result, the distinction between clonus and other movement disorders such as the cogwheel phenom­enon (Le., a rhythmically interrupted ratchetlike resistance

a)Requests for reprints should be sent to: Anne Beuter, Dept. of Kinan· thropology, University of Quebec at Montreal, CP 8888, Station A, Montreal, PQ H3C 3P8, Canada.

when an hypertonic muscle is passively stretched at a fre­quency between 6 and 9 Hz) observed in extrapyramidal tract diseases is unclear.

In both examples, the disorders are observed in healthy and diseased systems, they are common to a number of movement disorders, there is no standardized measure available, and no clear pathophysiological explanation is available.

Rather than focusing exclusively on the description of these (a) rhythmic patterns, one can characterize the qual­itative changes that affect movement output when relevant parameters are systematically varied. Mackey and Milton 1

have grouped qualitative changes in three categories. Os­cillatory behaviors may appear in a system that did not oscillate before, they may disappear in a system that oscil­lated before, or they may change in morphology (Le., am­plitude or frequency, or both) ..

In the central nervous system there are two main re­entrant subcortical loops that influence significantly the output of the cerebral cortex during movement and may induce qualitative changes in behavior (Fig. I and Ref. 2). One directly involves the basal ganglia and the other the cerebellum. In the present paper we examine the effect of basal ganglia lesions on inducing transient or sudden changes in limb tip dynamics. However, since we do not know exactly which motor tasks the basal ganglia normally subserve, it is difficult to give a simple coherent picture of the disorders of movement that occur when these struc­tures are lesioned.3

Parkinson's disease (PD) is generally considered as an acceptable model of basal ganglia disease even th,?ugh its pathology also involves other parts of the brain.3 The pri­mary neurochemical abnormality in PD appears to be a depletion of striatal dopamine which results from the loss of neurons from the substantia nigra containing dopamine

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280 Beuter, Labrie, and Vasilakds: Transient dynamics in motor control

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FIG. L Extremely simplified figure adapted from Nolte (Ref. 2, p. 285) illustrating how the cerebellum and the basal ganglia influence movement by modulating the output from the cerebral cortex (via nuclei of the thalamus, not represented) to the brain stem and spinal cord. The basal ganglia and the cerebellum act through different cortical areas and have output to the brain stem, especiaUy the cerebellum. In addition, the cer~ ebellurn receives large quantities of sensory information from noocortical sources.

and projecting to the basal ganglia. Classical features of PO, rigidity, akinesia (i.e., a difficulty to initiate move­ments) and postural abnormalities are often associated with some form of rest tremor sometimes maintained dur­ing posture, especially during the early stages of the dis­ease.

The disability caused by Parkinson's disease is usually described in terms of stages. Hoehn and Yahr,' for exam­ple, propose four stages. At stage I there is unilateral in­volvement with minimal or no disability. At stage II there is bilateral or midline involvement with minimal disability. At stage III righting reflexes are impaired (i.e., the patient is unsteady on his/her feet when turning or rising from a chair) and disability is mild to moderate. Finally at stage IV tremor, rigidity, and akinesia are present, standing and walking require assistance, and the disability is severe.

Some researchers claim that tremor at rest has an or­igin different from that of other sorts of tremor including action tremor (a tremor elicited by voluntary innervation), cogwheel phenomenon, and clonus,' while others believe

that action tremor is similar in its pathophysiology to tremor occurring at rest6 and may originate from an oscil­lation in an internal feedback loop between tbe motor cor­tex and the spinal cord. If this were the case, then how can we explain the difference in frequency between tremor at rest, which has a frequency between 4 and 5.5 Hz and action tremor, which has a frequency between 6 and 9 Hz?

It has been suggested that patients with PO cannot use preprogrammed fast movements and must instead rely heavily on slow movements controlled visually.' Visual cues, such as stripes on the floor can often assist patients with PD in the initiation and continuation of movement, countering the effects of akinesia.8

11. COMPLEX DYNAMICS IN MOTOR CONTROL OF PATIENTS WITH PO

A recent set of experiments has been aualyzing the effect of visual feedback on the maintenance of finger po. sition. Rather than using external stimuli (i.e., a target to track), the subject's own finger position was displayed on an oscilloscope. To elucidate the effect of the visual feed­back loop, a time delay was inserted in the system, display­ing the subject's finger position at a time up to 1400 ms in the past. One startling observation of these trials is that, as the time delay increased, slow intermittent oscillations of a period two to four times the delay appeared.'

Since it is believed that the visual feedback loop of patients with PO is intact, IO it would be expected that these patients would react analogously to control subjects under such conditions. Indeed, in half of the patients tested, sim­ilar complex oscillations but with larger amplitude were observed." But in the other half of the patients with PO, markedly different results occurred. Analysis of these pa­tients records may shed some light on other effects of PO on movement control and give clues as to the normal func­tions of the basal ganglia.

Ill. METHODS

The experimental procedures have been described elsewhere.' Briefly, a LVOT (linear variable displacement transformer) is attached to the index finger of the subject and measures flexion and extension at the metacarpal­phalangeal joint. The finger position monitored by the L VOT is passed through an analog delay line, introducing delays between 40 and 1400 ms, and then filtered by an eight-pole low-pass Bessel filter with a corner frequency of 30 Hz. The finger position is displayed on an oscilloscope along with a stable reference line directly in front of the subject. A finger displacement of I mm was displayed on the oscilloscope as a shift of 12 mm in the vertical axis.

Subjects sat upright 80 cm from the oscilloscope with their forearm in a trough and only their index finger pro­jecting beyond its end. The finger itself was hidden from the subject's view. Six tests were performed on each subject at 300, 600, 900, 1000, and 1400 ms delay. These tests were bracketed by two runs at 40 ms delay and each session ended with a run with the subject's eyes closed. No learn­ing occurred during the testing.'·l1 The data were con-

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Beuter, Labrie. and Vasilakos: Transient dynamics in motor control 281

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verted from analog to digital at a rate of 150 Hz, ensuring no aliasing occurred. Feur runs from each subject are used in the present paper (Le., at 40, 1000, and 1400 ms delay, and with eyes closed). All data analysis was completed on NEXUS (NEXUS was provided by Dr. R. Kearney, Depart­ment of Biomedical Engineering, McGill University).

In this paper we present data coilected on five patients with PD whose tremor amplitude was up to ten times larger than their matched control subjects. Complemen­tary analysis of the results for patients with PD whose tremor amplitude is only about twice that of control sub­jects can be found in Beuter et al. 11 Typically, patients were at stage III (Ref. 4), the more affected limb was tested, and they were all on medication. All patients except patient P2 had mild to moderate tremor and patient PI also exhibited a mild essential tremor. Except in the condition with eyes closed in which all patients and control snbjects tend to drift, the signal was stationary around the baseline. As expected, interindividual variability was larger in patients with PD than in the control subjects.

IV. EXPERIMENTAL RESULTS

Time series presented here contain oscillations con­trolled by two systems. The first system is under voluntary control and corresponds to corrections made by the subject to keep the finger controlled liue as close as possible to the stationary reference line. The frequency of these microdis­placements is generally below 3 or 4 Hz. The second sys­tem corresponds to physiological andlor pathological tremor and is not under voluntary control. These two sys­tems appear to be relatively independent so that tremor is superimposed upon voluntary corrections and is not af­fected by the introduction of a time delay.9

Figure 2 represents the time series of a control subject with delays of 40, 1000, and 1400 ms, and with eyes closed. With a 40-ms delay, tremor has an amplitude of about 0.25

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mm, while for the largest delay the amplitude of the oscil-lations is over 4- mm. The time series of patients with PD presented here do not contain intermittent oscillations when large delays were inserted. Figures 3 and 4 represent the same time series of two patients (PI and PS). Auto­correlations were used to identify the periodicities in the data at 1400 ms delay. As can be seen in Fig. 5, periodic­ities are evident in the time series of the typical control subject (PO) and they are either different (PI) or absent (P5, P7) in the patients examined.

As previously indicated, all patients examined in this paper have a tremor amplitude that is up to ten times larger than that of control subjects. No parameter other than tremor amplitude (e.g., tremor frequency, severity, or duration of illness, age, sex, etc.) could explain the differ­ence of behavior observed in patients without large-ampli· tude, low-frequency oscillations when a large delay is in­serted in the visual feedback loop (Figs. 3 and 4).

Transitions characterized by an abrupt change in am­plitude, frequency, duration, etc., are observed in several patients with PD (Figs. 6 and 7). Here, we present data from three of these patients (PI at 1400 ms time delay, P2 at zero delay, and P7 with eyes closed). In two cases the transition affects both the frequency and amplitude of the oscillations but differently (P1 and P7), while in the other case the transition corresponds to a change in amplitude only (P2).

P I is a stage III patient who has both a moderate rest tremor and an essential tremor. Subsequently, during test· ing the gain on the osciiioscope was reduced to heip the patient execute the task. The most striking feature of this patient's time series is the beating nature of tremor. It is evident from the multimodal nature of the FFT in the 5 Hz range (Fig. 7). The beat frequency (Le., the difference between the two frequencies) is about 0.5 Hz with eyes closed. Beating is more evident during the trials performed

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282 Seuter, Labrie, and VasiJakos: Transient dynamics in motor control

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later in the session such as with eyes closed and the second 40-ms delay (not shown) which may suggest a connection between beating and fatigue.

For this subject transitions appear to occur when am­plitude of the tremor drops to a minimum and the finger is going up (Fig. 7). During transitions, larger amplitude oscillations disappear. Intermittently, when the tremor in­creases especially during transitions, the shape of the os­cillations change. In particular the width of the oscillations increases and small secondary peaks ("hooks") appear (Fig. 7).

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60. FIG. 3. Time series for patient PI at 40 ms delay (upper left), 1000 ms delay (upper right), 1400 rus delay (lower left), and with eyes closed (lower right). Note the difference in scale between Figs, 1 and 2,

Patient P2 is a stage III patient who has no visible rest tremor. The most striking feature of his time series is a sudden decrease in tremor amplitude after about 18 s (Fig. S). The FFT contains more power before the transition than after but no peak frequency is apparent. However, the amplitude density histograms of a section of 12 s before and after the transition reveal completely different distri­butions (Fig. 8). The amplitude density histogram is platykurtic (i.e., wide and short) before the transition and becomes leptokurtic (i.e., tall and narrow) after. Although a clear transition is only observed for a delay of 40 ms, a

". 36. ". 60. FIG, 4, Time series for patient P5 at 40 time ms delay (upper left), 1000 ms delay

(upper right), 1400 ms delay (lower left), and with eyes closed (lower right). Note the difference in scale between Figs. 1 and 3.

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Seuter, Labrie, and Vasilakos: Transient dynamics in motor control 283

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similar pattern is present in most trials performed by this patient. We also observed a spiking pattern preceding the transition, whereas, after the transition, none was seen (Fig. 8).

Patient P7 is a stage II patient with a mild-moderate rest tremor. The most striking characteristic of the time series is the intermittent large-amplitude oscillatory behav­ior observed in a trial executed with eyes closed (Fig. 6). The patient went progressively into, and came suddenly out of a rhythm which had a frequency of about 6 Hz and an amplitude of about 25 mm (Fig. 9). This phenomenon

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was also observed, but with an amplitude 'almost ten times smaller in trials recorded toward the end of the session suggesting again the possibility of a link between this rhythm and fatigue (Fig. 9). In these later trials however, the pattern of onset and termination of the rhythms are reversed (Fig. 9).

V. DISCUSSION

The experiment performed here of a visually guided motor task is quite simple. Yet, the temporal data recorded

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CHAOS, Vol. 1, No.3, 1991

FIG. 6. Examples of transitions for P2 (top) at 40 ms delay and P7 (bottom) with eyes closed.

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show remarkably diverse dynamics within runs, between runs of different delays, and between different subjects. Siu­gle-Ioop negative feedback systems can be easily destabi­lized by increasing the gain or delay inherent to the system. The resulting oscillations are of a period two to four times the delay of the system. 12 As can be seen from the control subject time series, oscillations with this period occur, but they are intermittent and of varying amplitude. These rhythms have also been observed in patients with PD

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whose tremor is not too large suggesting that they are able to utilize information ill the same manner as healthy individualsp·ll

From the experimental results presented here, it is clear that records from patients with PD contain unusual patterns of oscillation. These microdisplacements involve both voluntary corrections and involuntary tremor and ap­pear in some cases to be exacerbated by fatigue. To gain some insight into the nature of the microdisplacements

I. FIG. 8. Blowup a section before (top left) and a section after (bottom left) of transition for P2 with corresponding am-plitude density histograms (right),

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Seuter, Labrie, and Vasilakos: Transient dynamics in motor control 285

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observed experimentally, we briefly examine these volun­tary and involuntary behaviors. There are two main theo­ries about the cause of physiological tremor. The first states that tremor is due to passive mechanical properties of the tissues coming, for example, from the asynchronous un­fused activity of motor units. 14 The second states that tremor is due to the intervention of neural circuits espe­cially the stretch reflex whose delays in the high gain feed­back loop cause oscillations between 8 and 12 Hz. Lakie et al. 14 conclude that "the most economical explanation for the physiological tremor is that the mechanical properties of the postural system produce an inbuilt instability which makes small oscillations inevitable ... there may however be synchronized activity of the nervous system when the mus­cles are fatigued or with pathological tremor" (p. 675). The real question to ask then is not about the origin of tremor but rather how it is modified in the presence of fatigue, or pathologies of the central nervous system. In this paper we have selected patients whose tremor ampli­tude was large and examined unusual patterns of interac­tions between different tremors.

With the delay, voluntary corrections normally used to compensate for displacements from the baseline lead to a series of over and undershooting causing the oscillations. These oscillations are not present in the patients examined. One possible explanation is that the large-amplitude tremor common to all these patients is hiding the real po­sition of the finger and preventing the subject from making appropriate corrections. This explanation is in agreement with recent claims from Sheridan and FlowerslS who sug­gest that PD may cause greater variability in the endpoints when patients attempt to make aiming movements with accuracy. In addition, the rate of positional corrections in humans when tracking a fast moving target is determined by the loop time in the visuomotor feedback circuit. 16 To compensate for this relatively slow tracking mechanism

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control subjects tend to alternate between a feedback con­trol strategy and a feedforward control one. Since patients with PD must rely more heavily on a vision strategy based on feedback control, they do not have the opportunity to make short-term predictions. Many mechanisms besides visual feedback are most likely involved in the generation of these delay-induced waveforms, including the interac­tions of proprioceptive feedback loops. The presence of proprioceptive dysfunctions during motor task in patients with PD claimed recently by different research groups in­cluding Viallet ei al. 17 may also add to the problem.

The transitions we have examined are important in that they reflect the effect of a lesion in the basal ganglia on movement output combined with the effect of the reorga­nization of the central nervous system to maintain its func­tional integrity. These transitions are not observed in con­trol subjects and in patients with cerebellar disease. Since the work of Gurfinkel and Osovetsl8 reporting the presence of abrupt transitions in the tremor of patients with PD only rew attempts have been made to explain theoretically and experimentally how complex dynamics occur in neural feedback mechanisms as certain parameters are varied.

In PI there are three discernable peaks in the FFT. One peak at about 5 Hz is similar in the trial at 1400 ms and with eyes closed. However, the first two peaks at 4.45 and 4.7 Hz are reversed in amplitude between the two runs suggesting that there. is a change in motor programs be­tween the two runs which affects the tremor. A similar pattern is also observed at 40 and 1000 ms. In a standard interpretation of the data, these three peaks could corre­spond to essential tremor and action tremors (postural and movement). One hypothesis is that at 1400 ms delay the subject is actively making corrections and with eyes closed he is merely maintaining a posture. However, we are deal­ing with an essentially nonlinear system and this classical approach is not necessarily appropriate.

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286 Beuter, Labrie. and Vasilakos: Transient dynamics in motor control

Visual inspection of blow ups of the data reveal qual­itative changes in the structure of the rhythms during tran­sitions. Apparently the shape of the oscillations is a prod­uct of multiple tremors. Perhaps the change in the structure corresponds to a change in one or more of the tremors during the transitions. EMG's of essential tremor show a high synchronicity of agonist and antagonist activ­ity, whereas the tremor in PD occurs in a clearly alternat­ing manner. 19 Thus the size of essential tremor would be smaller. The waveform of this tremor would subsequently be hidden by the other two until their amplitude decreased as is the case during the beats and the transitions.

In P2 a large-amplitude tremor suddenly decreases in amplitude without changing in frequency after about 18 s. The frequency estimated from visual inspection remains between 7 and 8 Hz before and after the transition. This transition, although less abrupt, was also noticed at the start of records for trials at 40 ms, 1000 ms, and with eyes closed. Given the stable frequency of this tremor, one pos­sible interpretation is that this patient is going from an enhanced physiological tremor to a ("regular") physiolog­ical tremor.

The series of rhythmic involuntary muscular contrac­tions of P7 have similarities with clonus which has usually a frequency around 6 Hz. In Parkinson's disease the typi­cal tremor when the hand is maintained in an extended posture has a peak around 6 Hz (Ref. 5). In normal sub­jects isometric co-contractions of hand muscles for several minutes also lead to a more regular appearance of tremor at 6 Hz (Ref. 5). Meanwhile, in clonus of spastic patients motor units recruited by segmented stretch reflexes become more synchronized under the influence of supraspinal input. 19 Perhaps in P7 a combination of two similar factors arises. In the lower traces, fatigue leads to an increase in tremor as in normal subjects. Meanwhile due to the pres­ence of PD, supraspinal influence would intermittently in­crease the gain of the segmental loops, destabilizing the system. Size of tremor would subsequently increase in the gradual manner displayed. With the removal of the central input, the gain would drop and the tremor would quickly return to its original form.

VI. CONCLUSION

In this study, the methods of analysis consisted of basic analytical tools in the temporal and spectral domains. This approach was selected with the intention of fully charac­terizing the time series involved. In particular, the nature of the transitions was investigated, with the purpose of delineating what parameters were altered during the tran­sitions. Unfortunately, due to the transient nature of these irregularities, and the subsequent short samples, the meth­ods used provided insufficient information on this area. Thus we resorted to the magnification of the time series, and qualitative visual analysis.

In the future, new methods of analysis should be con­sidered for such data. The innovative methods should clearly identify the transitions and characterize them in a unique fashion since they appear to be associated with the presence of pathologies. One possible avenue for future

analysis would be the modeling of such a system, perhaps through delay differential equations. By changing relevant parameters, or by adding external stimuli to simulate the pathologies involved, one can look for similar temporal records and transients. Through such modeling, or other techniques, new light may be shed on the pathways in­volved in motor control. It would become possible to de­termine whether a lesion has opened one of the control loops or one (or several) parameters are out of their nor­mal range.

ACKNOWLEDGMENTS

Support for this work was provided by NSERC and FCAR.

] M. C. Mackey and J. G. Milton, "Dynamical diseases. Perspectives in biological dynamics and theoretical medicine," Ann. NY Acad. Sci. 504, 16-32 (1987). .

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ical Neurophysiology in Parkinsonism, edited by P. J. Delwaide and A. Agnoli (Elsevier, Amsterdam, 1985), pp. 107-115.

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