Physiologically based modelling of the pharmacokinetics of three beta‐lactam antibiotics after intra‐mammary administration in dairy cows

Abstract

Understanding the pharmacokinetics of intra‐mammary antibiotics is important for the prediction of drug residues in milk and for the design of optimal dosage regimens. Unfortunately, compartmental pharmacokinetic models are not valid for this unique system. A minimal physiologically based pharmacokinetic model is presented incorporating the physiology of milk secretion, drug administration at the quarter level, drug absorption and dispersion, drug retention during the inter‐milking interval and episodic drug elimination at milking. The primary objective of the study was the development and exploration of a model for major factors controlling drug concentration in milk, rather than generation of rigorously predictive pharmaco‐statistical models for any particular drug. This model was implemented in a two‐stage approach, using published concentration data for penicillin, cefuroxime, cephapirin and desacetyl‐cephapirin in milk of healthy cows. Model simulations evaluated sensitivity and developed predictions of drug residues. The model successfully predicted both drug concentrations and drug residues in milk. The postmilking residual milk volume did not adequately explain antibiotic pharmacokinetics, requiring additional considerations for drug retention. Local sensitivity analysis indicated that increasing the number of quarters treated, the dosage, or the duration of the inter‐milking interval prolonged both the persistence of drug residues and the duration that antibiotic concentration exceeded typical minimum inhibitory concentrations. The model was flexible across different beta‐lactam drugs as a general description of intra‐mammary pharmacokinetics. This model is suitable for the design and analysis of dosage regimens, and could be applied for the prediction of withholding periods when these antibiotic preparations are used off‐label. The final model indicates that explicit consideration of the milking regimen is fundamental to the design and interpretation of pharmacokinetic studies of antibiotics in bovine milk.

Physiological parameter values for physiologically based pharmacokinetic models in food‐producing animals. Part III: Sheep and goat

“…( 2008 ). The milk productions in sheep and goats follow a linear regression (Castillo et al., 2008 ; Linzell, 1966 ; Salama et al., 2004 ) similar to the linear model used for milk production in cows from two recent studies (Woodward et al., 2020 ; Woodward & Whittem, 2019 ), which is different from the physiologically based milk secretion models using the Langmuir equation reported for dairy cows in earlier studies (Li et al., 2018 ; Whittem et al., 2012 ).…”

Population physiologically based modeling of pirlimycin milk concentrations in dairy cows

“…As in the prior work (Woodward and Whittem, 2019b), the structural model was implemented in MAT-LAB. To improve the speed of computation, ODE for the intermilking interval were solved using the backward differentiation formulas in SUNDIALS (Hindmarsh et al, 2005).…”

“…In the pharmacokinetic modeling, the volume of milk production from each milking was used directly in the model, instead of using a model-based prediction of milk volume as in earlier models (Whittem et al, 2012;Woodward and Whittem, 2019b). Where milk volume data points were missing from the data set, predictions for milk volume for these time points were generated, using conditional predictions from the general linear mixed model.…”

“…The pharmacokinetic model was adapted from a method developed for β-lactam antibiotics (Woodward and Whittem, 2019b), described in Figure 1. The final model comprises a systemic compartment that follows a standard 2-compartment model, having a central volume of distribution (V c ), drug elimination from the central compartment k 40 , and exchange with a second compartment with rate constants k 45 and k 54 .…”

“…Each quarter has a retention compartment with which drug is exchanged from milk, with rate constants k 23 and k 32 . The retention compartment represents a volume-independent mechanism for drug disposition during the intermilking interval, which is important for the total time course of drug concentration (Woodward and Whittem, 2019b). Doses are distributed throughout the quarters; where the data set included treatments of less than 4 quarters, treatments were assumed to have been administered to the rear quarters, as this detail was not available in the data set.…”