Lactation related milk volume changes: implementation in a PBPK cow model for oxytetracycline
Ilse R Dubbelboer (1,2), Ronette Gehring (1)
(1) Department Population Health Sciences, Faculty of Veterinary Medicine, Utrecht University, the Netherlands (2) Dept. of Pharmaceutical Biosciences, Uppsala University, Sweden
Objectives: Lactation is a complex physiological process that is influenced by various factors, including maternal physiology, lactation stage, and milk flow rate. Physiologically based kinetic (PBK) models can be used to better understand drug distribution and accumulation in milk, and help to improve the safety and efficacy of drugs used during lactation. These models have been used since the 1980’s and mathematically can describe lactational excretion of toxicological (PBTK) and pharmacological (PBPK) compounds. The aim of these models is often risk assessment, in human lactation but also in food-producing animals. As such, they are key in ensuring clean dairy products, and thus have a place in both human and veterinary medicine. However, these models seldomly include milk composition or the changes in milk volume due to milk production and subsequent milking or lactation. Compound excretion to and accumulation in milk can be greatly affected by these two factors, and are key for species translations. The objective of this study was to establish an optimized description of the milk variability over time and between milkings in the cow udder and implement this module in an already established PBPK lactation model for oxytetracycline.
Methods: The PBPK cow model by Tardiveau et al. [1] describes the pharmacokinetics of the test compound oxytetracycline. This PBPK model was translated from Monolix into R language. The mrgsolve package was used as an ODE solver. A milk volume module, consisting of 2 compartments with variable volume, described the alveolar and cisternal milk spaces. The milk volume inside the udder (alveoli and cistern) was adapted to be variable over time in agreement with lactation curves and milkings. Cisternal milk volume was dependent on the alveolar milk volume. Milk production and elimination parameters were estimated in R by calibrating the milk volume module to historically observed milked volumes from cows. The R packages FME and minpack.lm were used for parameter estimations. The milk module was thereafter implemented into the Tardiveau PBPK cow model.
Results: The PBPK cow model by Tardiveau et al. was successfully translated to R, using mrgsolve. Historical data on milk volumes in cow udders were well described with the newly established milk volume module. The module could describe the changing alveolar, cisternal, and total milk volumes between milkings, with both short (4 to 6h) and longer (up to 24h) milking intervals. The slow initial increase in cisternal volume was captured by the module. The module described milk volumes in cow udder during early lactation (0-120 days postpartum), mid lactation (120-240 days postpartum) and late lactation (240-360 days postpartum). This milk volume module was implemented into the established PBPK cow model by Tardiveau. Elimination of the test compound oxytetracycline was described by the same elimination parameters as for the milk volume.
Conclusions: The milk volume model was successfully established and implemented into a generic and translational PBPK cow model for oxytetracycline. Milk volumes were well described. A more detailed description of the milk volumes in the udder increases the opportunity for species translations of lactational PBK models. Future works will focus on description of milk volumes in the mammary glands of other milk-producing species and the prediction of lactational excretion of xenobiotics.
References:
[1] Tardiveau et al. FCT (2022); 161, 112848