MESOR

Mesor, short for midline estimating statistic of rhythm, is a parameter used in cosinor analysis to describe rhythmic biological data. It represents the midline or baseline level around which a rhythmic variable oscillates. In a simple cosinor model, y(t) = M + A cos(ωt + φ) + ε(t), where M is the mesor, A is the amplitude, ω is the angular frequency (often ω = 2π/T with T the period), and φ is the phase. The mesor is the mean value of the fitted sinusoid over time and can be interpreted as the rhythm-adjusted average level of the variable.

Estimation: M, A, and φ are estimated from observed data by least-squares (or maximum likelihood) fitting of the cosine model. The chosen period T (or frequency ω) is either specified from prior knowledge (e.g., T ≈ 24 hours for circadian data) or estimated from the data.

Interpretation and use: The mesor reflects the baseline or average state of the system across the cycle. Changes in mesor between conditions or over time indicate a shift in the overall level of the measured variable, independent of the rhythmic fluctuation. The amplitude describes the extent of oscillation, and the phase indicates timing of peaks within the cycle.

Limitations: The mesor assumes a primarily sinusoidal rhythm with a known or fixed period; real data may require multiple harmonics or non-sinusoidal models. The estimated mesor can be sensitive to sampling, outliers, and the chosen period.

See also: cosinor analysis, rhythm analysis, circadian biology.