A general Richards family growth curve fit in European livestock for use in physiologically-based toxicokinetic modelling.

backgroundPhysiologically-based toxicokinetic models in livestock need to account for growth during long-term exposure studies due to increase in tissue volume and subsequent dilution of concentration. Growth of an average individual of a livestock species was modelled through the Richards family of sigmoidal growth curve models. Average weight gain data of multiple breeds stemming from beef and dairy cattle, laying hens, broiler chickens, and sheep were obtained from scientific literature and industry. Growth curves including the four-parameter Richards curve possessing a flexible inflection point and the three-parameter West, Von Bertalanffy, Monomolecular, and Gompertz curves were fitted to pooled and breed-specific species data. Regression weights were applied to counteract heteroscedasticity, and correlation between residuals was modelled. Fits were compared with the Akaike and Bayesian information criteria, the root mean squared error, and likelihood-ratio tests. Physiological plausibility of curve estimates was also considered. Averages of breed weight gain were used, thus random effects pertaining to individuals were not modelled.

resultsFor the pooled fits in beef and dairy cattle, best results were attained by the Von Bertalanffy followed by the West and Richards curves. In laying hen, best fits were attained by the Gompertz curve, followed by the West curve. In male broiler chickens, the Richards curve alone performed best, while in female broiler chickens, the West curve performed similarly well to the Richards curve. For sheep, the Monomolecular curve fitted best. In the breed-specific fits, the Richards curve outperformed the other curve models in all species except laying hens. No statistical difference was found in estimating a breed-specific or a common inflection point of the Richards curve in beef and dairy cattle, provided all other curve parameters were breed-specific. A size-scaled comparison using all animal data showed that the Von Bertalanffy curve returned smallest root mean squared error.

conclusionIn the pooled fits, parsimonious curve models such as the West and Von Bertalanffy curves performed similarly to the more flexible Richards curve. The parameter estimates in this study can be used for risk assessment to integrate growth of an individual in a generic physiologically-based toxicokinetic model.