Wave-shape oscillatory model for biomedical time series with applications
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The oscillations observed in physiological time series exhibit morphological variations over time. These morphological variations are caused by intrinsic or extrinsic changes to the state of the generating system, henceforth referred to as dynamics. To model such a time series, we provide a novel hierarchical model: the wave-shape oscillatory model. In this model, time-dependent variations in cycle morphology occur along a manifold called the wave-shape manifold. To estimate the wave-shape manifold associated with an oscillatory time series, study the dynamics, and visualize the time-dependent changes along it, we apply the well-established diffusion maps (DM) algorithm to the set of all observed oscillations. We provide a theoretical guarantee on the dynamical information recovered by the DM algorithm under the proposed model. Applying the proposed model to arterial blood pressure signals recorded during general anesthesia leads to the extraction of nociception information. Applying the wave-shape oscillatory model to cardiac cycles in the electrocardiogram (ECG) leads to a new ECG-derived respiratory signal.
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