Cosinor Analysis Using Rotating Ellipse Tangents and Circle Collisions

Error Ellipse Parameters

semi-major axis

30

semi-minor axis

20

orientation angle

-0.5

Cosinor Parameters

amplitude (msec)

100

acrophase (0 to -2π)

-0.5

Cosinor analysis uses a least squares method to fit a cosine wave to biorhythm time series data. The method can be applied to nonuniformly sampled studies with missing data points. The fitted cosine function is given by

F(t)=Acos(t+ϕ)

, where

A

is the amplitude and

ϕ

is the acrophase of the time series [1], [2]. The acrophase is the time period in which the cycle peaks. The Demonstration plots the cosinor 95% bivariate error ellipse of the cosinor parameter estimates and dynamically computes associated confidence interval (CI) limits.

In the bookmarks, data is shown from cosinor analysis of 24-hour heart rate (HR) recordings in humans. HR is reported by its reciprocal parameter, RR interval, the time between consecutive heartbeats measured in milliseconds. Illnesses such as heart disease and depression disturb the amplitude and acrophase of 24-hour HR periodicity.