John G. Milton

The mind of expert motor performance is cool and focused

Extraordinary motor skills required for expert athletic or music performance require longstanding and intensive practice leading to two critical skills, a level of maximal performance that far exceeds that of non-experts and a degree of privileged focus on motor performance that excludes intrusions. This study of motor planning in expert golfers demonstrated their brain activation during their pre-shot routine to be radically different than in novices. The posterior cingulate, the amygdala-forebrain complex, and the basal ganglia were active only in novices, whereas experts had activation primarily in the superior parietal lobule, the dorsal lateral premotor area, and the occipital area. The fact that these differences are apparent before the golfer swings the club suggests that the disparity between the quality of the performance of novice and expert golfers lies at the level of the organization of neural networks during motor planning. In particular, we suggest that extensive practice over a long period of time leads experts to develop a focused and efficient organization of task-related neural networks, whereas novices have difficulty filtering out irrelevant information.

Complex oscillations in the human pupil light reflex with “mixed” and delayed feedback

Abstract Simple periodic as well as more complex behaviors are shown to occur in the human pupil light reflex with piecewise constant mixed and delayed feedback. The output of an infrared video pupillometer, an analog voltage proportional to pupil area, is processed by an electronic comparator which synthesizes the piecewise constant feedback. The system is described by a nonlinear delay differential equation which has been previously shown analytically to exhibit periodic and aperiodic behavior. After parameter estimation from the data, it is found that the observed simple periodic behaviors correlate well with the model behaviors. Although more complex behavior can be observed for parameter values which gave complicated dynamics in the model, there is not a one-to-one correspondence between the observed and predicted results. The effect of uncontrollable fluctuations in the parameters on the observability of complex dynamics in this system is discussed.

Dynamical disease: Identification, temporal aspects and treatment strategies of human illness.

Dynamical diseases are characterized by sudden changes in the qualitative dynamics of physiological processes, leading to abnormal dynamics and disease. Thus, there is a natural matching between the mathematical field of nonlinear dynamics and medicine. This paper summarizes advances in the study of dynamical disease with emphasis on a NATO Advanced Research Worshop held in Mont Tremblant, Quebec, Canada in February 1994. We describe the international effort currently underway to identify dynamical diseases and to study these diseases from a perspective of nonlinear dynamics. Linear and nonlinear time series analysis combined with analysis of bifurcations in dynamics are being used to help understand mechanisms of pathological rhythms and offer the promise for better diagnostic and therapeutic techniques. (c) 1995 American Institute of Physics.

Frequency analysis of the sleep EEG in depression

Eight patients with major depressive disorder (seven bipolar and one unipolar) and matched controls had sleep studies, on which frequency analysis of the electroencephalogram (EEG) was performed. Total sleep and sleep efficiency were decreased in the patients, but there was no significant difference in rapid eye movement (REM) latency between the two groups. Frequency analysis revealed no group differences in power in the delta band (0.23-2.5 Hz) or the whole EEG spectrum (0.23-25 Hz). These findings suggest that mean REM latencies are not always shorter in major depression. The results are discussed in light of a previous report of decreased delta energy in the sleep EEG of unipolar patients.

Human stick balancing: tuning Lèvy flights to improve balance control.

State-dependent, or parametric, noise is an essential component of the neural control mechanism for stick balancing at the fingertip. High-speed motion analysis in three dimensions demonstrates that the controlling movements made by the fingertip during stick balancing can be described by a Lèvy flight. The Lèvy index, alpha, is approximately 0.9; a value close to optimal for a random search. With increased skill, the index alpha does not change. However, the tails of the Lèvy distribution become broader. These observations suggest a Lèvy flight that is truncated by the properties of the nervous and musculoskeletal system; the truncation decreasing as skill level increases. Measurements of the cross-correlation between the position of the tip of the stick and the fingertip demonstrate that the role of closed-loop feedback changes with increased skill. Moreover, estimation of the neural latencies for stick balancing show that for a given stick length, the latency increases with skill level. It is suggested that the neural control for stick balancing involves a mechanism in which brief intervals of consciously generated, corrective movements alternate with longer intervals of prediction-free control. With learning the truncation of the Lèvy flight becomes better optimized for balance control and hence the time between successive conscious corrections increases. These observations provide the first evidence that changes in a Lèvy flight may have functional significance for the nervous system. This work has implications for the control of balancing problems ranging from falling in the elderly to the design of two-legged robots and earthquake proof buildings.

Limit Cycles, Tori, and Complex Dynamics in a Second-Order Differential Equation with Delayed Negative Feedback

We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The bifurcations occurring as the linear stability is lost are investigated by the construction of a center manifold: The nature of Hopf bifurcations and more degenerate, higher-codimension bifurcations are explicitly determined.

Timing of Seizure Recurrence in Adult Epileptic Patients: A Statistical Analysis

Summary: Seizure diaries were maintained prospectively in 24 epileptic patients (19 with partial complex, three with partial simple, and three with primary generalized seizures) who were selected consecutively, had stable seizure patterns, were reliable historians, and were known to be compliant with medications. Diaries were maintained for an average of 237 days (range, 61–365), and an average of 18 seizures were recorded per patient (range, 5–76). Seizure patterns were analyzed by using the methods appropriate for a time series of events (point process). Two patients had a decreasing trend in seizure frequency. For 12 patients, seizure occurrence was indistinguishable from that of a Poisson process. The remaining 10 patients had an exponential distribution of seizure intervals, but did not fit other criteria for a Poisson process; 3 of these showed evidence for seizure clustering; none showed evidence for a seizure cycle. It is concluded that the pattern of seizure occurrence in most epileptic people is random, but in approximately 50%, it is not occurring according to a Poisson process. These observations indicate that seizure cycling and/or clustering are not common in epileptic patients, but do not exclude the possibility that seizures have been precipitated by some randomly occurring event, such as sleep deprivation or increased stress.

On the road to automatic: Dynamic aspects in the development of expertise

One of the important steps on the road to becoming expert in a motor skill occurs when the individual can perform the movements in a seemingly effortless and automatic fashion. The authors review two lines of investigations, namely, fMRI and mathematically guided studies of the dynamics of skill acquisition, that suggest that this road to automatic involves two steps: (1) an increasing reliance on the self-regulatory aspects of the motor task, and (2) a minimization of the role of mechanisms based on intentionally directed corrective movements. The interplay between these two mechanisms implies that, at a given skill level, performance decreases whenever intention intervenes. The observation that psychological factors may be as important as mechanical repetition for the development of expertise has important implications for the design of neurorehabilitative strategies.

Balancing with positive feedback: the case for discontinuous control

Experimental observations indicate that positive feedback plays an important role for maintaining human balance in the upright position. This observation is used to motivate an investigation of a simple switch-like controller for postural sway in which corrective movements are made only when the vertical displacement angle exceeds a certain threshold. This mechanism is shown to be consistent with the experimentally observed variations in the two-point correlation for human postural sway. Analysis of first-passage times for this model suggests that this control strategy may slow escape by taking advantage of two intrinsic properties of a stochastic unstable first-order delay differential equation: (i) time delay and (ii) the possibility that the dynamics can be ‘temporarily confined’ near the origin.

Unstable dynamical systems: Delays, noise and control

Escape from an unstable fixed point in a time-delayed dynamical system in the presence of additive white noise depends on both the magnitude of the time delay, τ, and the initial function. In particular, the longer the delay the smaller the variance and hence the slower the rate of escape. Numerical simulations demonstrate that the distribution of first passage times is bimodal, the longest first passage times are associated with those initial functions that cause the greatest number of delayed zero crossings, i.e. instances where the deviations of the controlled variable from the fixed point at times t and t- τ have opposite signs. These observations support the utility of control strategies using pulsatile stimuli triggered only when variables exceed certain thresholds.