JSM 2005 - Toronto

Abstract #303589

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Activity Number: 74
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 8:00 PM to 9:50 PM
Sponsor: Biometrics Section
Abstract - #303589
Title: Sigmoidally-transformed Cosine Curves: Mathematical Model for Circadian Rhythms with Nonsinusoidal Shapes
Author(s): Matthew Marler*+ and Philip Gehrman and Jennifer Martin
Companies: University of California, San Diego and Pennsylvania Center for Sleep and Respiratory Physiology and University of California, Los Angeles
Address: 9500 Gilman Drive, La Jolla, CA, 92065, United States
Keywords: cosine ; circadian rhythms ; nonlinear Fourier analysis ; Hill function ; logistic function ; arctangent function
Abstract:

We introduce a family of nonlinear transformations of the traditional cosine curve used in the modeling of biological rhythms. The nonlinear transformation is the sigmoidal family, represented here by three family members: the Hill function, the logistic function, and the arctangent function. These transforms add two parameters that must be estimated in addition to the acrophase, MESOR, and amplitude (and period in some applications). However, the estimated curves have shapes requiring many more than two additional harmonics to achive the same fit when modeled by harmonic regression. Particular values of the additional parameters can yield rectangular waves, narrow pulses, wide pulses, and, for rectangular waves (representing alternating "on" and "off" states), the times of onset and offset. We illustrate the sigmoidally transformed cosine curves and compare them to harmonic regression modeling in a sample of eight activity recordings made on patients in a nursing home.

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