Cosinor Analysis of Biorhythm Data

This Demonstration models the 24-hour (circadian) variation of heart rate as a sinusoid with superimposed random noise. The methods of cosinor biorhythm analysis are used to estimate the magnitude, phase, and statistical significance of the modeled rhythm.

The cosinor method fits data to a cosine function,

F(t)=M+Acos(ωt+ϕ)

, where

M

and

A

are the mean and amplitude of the sinusoidal rhythm,

ω

is the period, and

ϕ

is the time of peak heart rate. In cosinor phraseology, the mean is called the mesor [1, 2, 3].

Plots are shown for the cosinor best-fit solution of

F(t)

and the bivariate error ellipse with amplitude and acrophase of 0.95 confidence intervals, which are dynamically computed and plotted on the polar graph.