Complex dynamics and bifurcations in neurology.
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Algorithms↗
Biomedical subjects
A Longtin
Publications and source records attributed to A Longtin.
Insight into the transfer function, gain, and oscillation onset for the pupil light reflex using nonlinear delay-differential equations.
Analogies are drawn between a physiologically relevant nonlinear delay-differential equation (DDE) model for the pupil light reflex and servo control analytic approaches. This DDE is shown to be consistent with the measured open loop transfer function and hence physiological insight can be obtained into the gain of the reflex and its properties. A Hopf bifurcation analysis of the DDE shows that a limit cycle oscillation in pupil area occurs when the first mode of the characteristic equation becomes unstable. Its period agrees well with experimental measurements. Beyond the point of instability onset, more modes become unstable corresponding to multiple encirclings of (-1, 0) on the Nyquist plot. These modes primarily influence the shape of the oscillation. Techniques from dynamical systems theory, e.g. bifurcation analysis, can augment servo control analytic methods for the study of oscillations produced by nonlinear neural feedback mechanisms.
Blinking↗
Modelling autonomous oscillations in the human pupil light reflex using non-linear delay-differential equations.
Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g. edge-light pupil cycling.
Feedback↗
Irregular pupil cycling as a characteristic abnormality in patients with demyelinative optic neuropathy.
We used an infrared videopupillometer combined with an electronic circuit that regulated the retinal light level as a function of pupil area to assess the regularity of pupil cycling in normal subjects and in patients with known abnormalities in the pupil light reflex pathways. The light stimulus was turned on whenever pupil area exceeded a preset value. Two types of abnormalities were observed for patients with demyelinative optic neuropathy: a failure of the pupil to cycle despite a preserved pupillary response to a single light pulse; and, for those patients in whom cycling was possible, a characteristic intermittent irregularity in the amplitude of pupil cycling. These abnormalities were not seen in normal subjects or in patients with ischemic optic neuropathy, surgical lesions involving the optic chiasm, Adie's syndrome, or Horner's syndrome.
Adolescent↗
A new model of the acoustic reflex.
A system-type model of the acoustic reflex in man is proposed with the intention of sheding light on certain of its nonlinear behaviors. This model is the first to incorporate into the multipath structure of the reflex arc the adaptation and recovery processes. Parameter distribution in the parallel pathways is based on the current knowledge on the stapedius muscle and on motoneuron pool organization. A piecewise linear system is used in modeling adaptation at onset and recovery at offset. The model is calibrated at 2000 Hz, a frequency for which all the important parameters are available. Two nonlinear behaviors of the adaptation rate are explained: the frequency and intensity dependence, related respectively to the frequency dependence of the feedback gain and to the sigmoidal shape of the closed-loop stimulus-response curve. Underlying physiological mechanisms are discussed, along with other plausible nonlinear models, and extensions of the model to other stimuli are suggested.
Acoustic Stimulation↗
Multicompartment model of lung dynamics.
A mathematical model was developed to simulate the function of the lungs. The lungs are represented by 24 compartments each corresponding to a generation of the Weibel model A. In the model it is assumed that gases are transported in the lungs by convection and diffusion from one compartment to the other. Furthermore, the clearance of gases from the lungs by the blood perfusion is taken into account. The driving force of the inhalation and exhalation processes is the filling and emptying of the alveolar volume which follows a sinusoidal pattern. Mathematically the model is represented by two sets (one for inhalation, the other for exhalation) of 24 first-order coupled ordinary differential equations which were numerically integrated by means of a computer. The model predicts quite well the buildup of gases in the lungs and the washout of gases from the lungs.
Computers↗
Use of a diet supplement in Laënnec's cirrhosis.
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Alcoholism↗