A compartmental model describing changes in progesterone concentrations during the oestrous cycle

Abstract

The objective of this study was to develop a mathematical model that accurately describes the rise and decline in plasma progesterone concentrations, and is able to define parameters describing progesterone appearance and disappearance during the bovine oestrous cycle. Daily plasma progesterone data from 27 cows were used to develop a compartmental model consisting of an appearance function and an appearance modulating function. Model outputs included an apparent appearance or secretion duration, appearance rate and an average disappearance rate (expressed as arbitrary units per day; units/d). Shape-based clustering identified three common shape-based groups (or clusters) of progesterone profiles defined as either 'peaked' profile, with the profile reaching a distinguishable peak, 'structured', with the profile exhibiting a wave-like pattern, or 'flat top', with the profile reaching a plateau. Differences in the model parameters for the three different shapes of progesterone profiles were examined: peaked (n=13), flat top (n=7) and structured (n=7). The mean duration of apparent appearance was 11.49 (SD 0.17 d) for all 27 profiles. The model estimates for total appearance of progesterone (area under the curve; ng/ml per cycle), mean appearance rate and maximum appearance rate were 69.04 ng/ml per cycle (SD 15.2 ng/ml per cycle), 3.19 ng/ml per cycle (sd 0.7 ng/ml per d) and 6.70 ng/ml (SD 1.31 ng/ml), respectively. The average disappearance rate was 1.0 units/d (SD 0.04 units/d). The apparent appearance duration was greatest (P<0.01) in the flat top profiles (12.54, SD 0.41 d) followed by the structured (11.77, SD 0.66 d) and the peaked (10.80, SD 0.30 d) profiles. Total and mean progesterone appearance, maximum progesterone appearance rate, and the progesterone disappearance rates were not different between the profiles. The model successfully simulated all components of the progesterone profile and was able to define specific parameters of different shaped progesterone profiles. A simple model able to estimate parameters describing progesterone appearance and disappearance can be used to explore the relationships between profile shapes and reproductive outcomes.