TY - JOUR

T1 - Detecting scaling in the period dynamics of multimodal signals

T2 - application to Parkinsonian tremor

AU - Sapir, Nir

AU - Karasik, Roman

AU - Havlin, Shlomo

AU - Simon, Ely

AU - Hausdorff, Jeffrey M

PY - 2003/3

Y1 - 2003/3

N2 - Patients with Parkinson's disease exhibit tremor, involuntary movement of the limbs. The frequency spectrum of tremor typically has broad peaks at "harmonic" frequencies, much like that seen in other physical processes. In general, this type of harmonic structure in the frequency domain may be due to two possible mechanisms: a nonlinear oscillation or a superposition of (multiple) independent modes of oscillation. A broad peak spectrum generally indicates that a signal is semiperiodic with a fluctuating period. These fluctuations may posses intrinsic order that can be quantified using scaling analysis. We propose a method to extract the correlation (scaling) properties in the period dynamics of multimodal oscillations, in order to distinguish between a nonlinear oscillation and a superposition of individual modes of oscillation. The method is based on our finding that the information content of the temporal correlations in a fluctuating period of a single oscillator is contained in a finite frequency band in the power spectrum, allowing for decomposition of modes by bandpass filtering. Our simulations for a nonlinear oscillation show that harmonic modes possess the same scaling properties. In contrast, when the method is applied to tremor records from patients with Parkinson's disease, the first two modes of oscillations yield different scaling patterns, suggesting that these modes may not be simple harmonics, as might be initially assumed.

AB - Patients with Parkinson's disease exhibit tremor, involuntary movement of the limbs. The frequency spectrum of tremor typically has broad peaks at "harmonic" frequencies, much like that seen in other physical processes. In general, this type of harmonic structure in the frequency domain may be due to two possible mechanisms: a nonlinear oscillation or a superposition of (multiple) independent modes of oscillation. A broad peak spectrum generally indicates that a signal is semiperiodic with a fluctuating period. These fluctuations may posses intrinsic order that can be quantified using scaling analysis. We propose a method to extract the correlation (scaling) properties in the period dynamics of multimodal oscillations, in order to distinguish between a nonlinear oscillation and a superposition of individual modes of oscillation. The method is based on our finding that the information content of the temporal correlations in a fluctuating period of a single oscillator is contained in a finite frequency band in the power spectrum, allowing for decomposition of modes by bandpass filtering. Our simulations for a nonlinear oscillation show that harmonic modes possess the same scaling properties. In contrast, when the method is applied to tremor records from patients with Parkinson's disease, the first two modes of oscillations yield different scaling patterns, suggesting that these modes may not be simple harmonics, as might be initially assumed.

KW - Humans

KW - Models, Statistical

KW - Normal Distribution

KW - Oscillometry

KW - Parkinson Disease/pathology

KW - Time Factors

U2 - 10.1103/PhysRevE.67.031903

DO - 10.1103/PhysRevE.67.031903

M3 - Article

C2 - 12689097

SN - 1539-3755

VL - 67

SP - 031903

JO - Physical review. E, Statistical, nonlinear, and soft matter physics

JF - Physical review. E, Statistical, nonlinear, and soft matter physics

IS - 3 Pt 1

ER -