acrophases

Acrophase refers to the time in a rhythmic cycle when the measured variable reaches its maximum value. In circadian and chronobiology research, acrophase is a key descriptor of phase, alongside mesor (mean level), amplitude (extent of oscillation), and period (cycle length). The acrophase is often expressed as a clock time for a 24-hour cycle or as a phase angle.

In many analyses, rhythms are modeled with a cosine function: y(t) = M + A cos(ωt + φ), where M is the mesor, A the amplitude, ω = 2π/T is the angular frequency, T the period, and φ the phase parameter. The acrophase occurs at the peak of the cosine, i.e., when ωt + φ = 0 (mod 2π). Therefore the peak time is t_peak = (−φ/ω) mod T, and the corresponding acrophase angle is (−φ) mod 2π. For a 24-hour cycle, t_peak can be reported in hours and φ in radians.

Estimation of acrophase is usually done by fitting a cosinor model to time-series data or by nonparametric rhythm analyses; confidence intervals convey uncertainty. Rhythms with small amplitude or irregular sampling can yield ambiguous acrophases.

Applications include studying activity, body temperature, hormone levels, and gene expression. Acrophase shifts with aging, disease, or light exposure and is a key element in chronotherapy and in assessing circadian alignment in shift work and jet lag.