Mathematical modeling and simulation in animal health – Part II : principles, methods, applications, and value of physiologically based pharmacokinetic modeling in veterinary medicine and food safety assessment

Expanding behavior pattern sensitivity analysis with model selection and survival analysis

Background

Sensitivity analysis is an essential step in mathematical modeling because it identifies parameters with a strong influence on model output, due to natural variation or uncertainty in the parameter values. Recently behavior pattern sensitivity analysis has been suggested as a method for sensitivity analyses on models with more than one mode of output behavior. The model output is classified by behavior mode and several behavior pattern measures, defined by the researcher, are calculated for each behavior mode. Significant associations between model inputs and outputs are identified by building linear regression models with the model parameters as independent variables and the behavior pattern measures as the dependent variables. We applied the behavior pattern sensitivity analysis to a mathematical model of tetracycline-resistant enteric bacteria in beef cattle administered chlortetracycline orally. The model included 29 parameters related to bacterial population dynamics, chlortetracycline pharmacokinetics and pharmacodynamics. The prevalence of enteric resistance during and after chlortetracycline administration was the model output. Cox proportional hazard models were used when linear regression assumptions were not met.

Results

We have expanded the behavior pattern sensitivity analysis procedure by incorporating model selection techniques to produce parsimonious linear regression models that efficiently prioritize input parameters. We also demonstrate how to address common violations of linear regression model assumptions. Finally, we explore the semi-parametric Cox proportional hazards model as an alternative to linear regression for situations with censored data. In the example mathematical model, the resistant bacteria exhibited three behaviors during the simulation period: (1) increasing, (2) decreasing, and (3) increasing during antimicrobial therapy and decreasing after therapy ceases. The behavior pattern sensitivity analysis identified bacterial population parameters as high importance in determining the trajectory of the resistant bacteria population.

Conclusions

Interventions aimed at the enteric bacterial population ecology, such as diet changes, may be effective at reducing the prevalence of tetracycline-resistant enteric bacteria in beef cattle. Behavior pattern sensitivity analysis is a useful and flexible tool for conducting a sensitivity analysis on models with varied output behavior, enabling prioritization of input parameters via regression model selection techniques. Cox proportional hazard models are an alternative to linear regression when behavior pattern measures are censored or linear regression assumptions cannot be met.

Application of TQSM polypharmacokinetics and its similarity approach to ascertain Q-marker by analyses of transitivity in vivo of five candidates in Buyanghuanwu injection

BACKGROUND

It is well-known that the public still have been facing on a severe issue about the inconsistency of quality and therapeutic efficacy of traditional medicines. Recently, Professor Chang-Xiao Liu has created a new promising concept for identifying relevant quality-markers (Q-marker) from herbs, their formulas and manufacturing products. Therefore, building up a new approach is necessary for us to bridge over quality to efficacy of pharmaceutical products.

STUDY DESIGN

In this paper, five candidate Q-markers, astragaloside IV, paeonflorin, amygdalin, tetramethylpyrazine, ferulic acid in Buyanghuanwu injection (BYHWI) had been designed to carry out in rat by using single and polypharmacokinetic models for total quanta to ascertain adequate Q-marker.

METHODS

The Q-marker transitivity in vivo was studied with polypharmacokinetic model and its similarity approach, which were modeled with TQSM principle. The Q-marker was ascertained with transitive similarity and bioavailability in polypharmacokinetics. Their concentrations in plasma sample of white rat were determined by RP-HPLC. Data analyses were used by the DAS software for singles and myself-written-program with EXCEL for multiples.

RESULTS

In BYHWI, five candidate Q-marker pharmacokinetic profiles were singly fixed to two compartmental models in rat using classical compartmental analysis, but there were tremendous differences among which the candidate parameters were fluctuated from nearly 3552 folds to equivalency. The theoretical value of TQSM polypharmacokinetic parameters such as AUC_T, MRT_T, VRT_T, CL_T, V_T over the mixure of five drugs were 110.8 ± 51.91 mg min ml^-1, 176.0 ± 36.5 min, 39,921 ± 4311 min², 0.3116 ± 0.02347 ml min^-1 kg^-1, 54.83 ± 7.683 ml kg^-1 respectively. The TQSM polypharmacokinetic parameters in astragaloside Ⅳ ordered by AUC_T, MRT_T, VRT_T, CL_T, V_T were 110.8 ± 51.91 mg min ml^-1, 176.0 ± 36.5 min, 39,921 ± 4311 min², 0.3116 ± 0.02347 ml min^-1 kg^-1, 54.83 ± 7.683 ml kg^-1, respectively, which were closed to the theoretical values. TQSM similarity versus astragaloside Ⅳ was 0.9661.

CONCLUSION

The results represented that the optimum Q-marker in BYHWI is astragaloside Ⅳ, whose transitivity in vivo similarity was close to the behavior of polypharmacokinetics with maximum bioavailability to the total quanta. It is feasible for Q-marker in CMMs to screen on the comparison of single pharmacokinetic behavior and bioavailability to the total quanta.

Population variability in animal health: Influence on dose-exposure-response relationships: Part II: Modelling and simulation

During the 2017 Biennial meeting, the American Academy of Veterinary Pharmacology and Therapeutics hosted a 1-day session on the influence of population variability on dose-exposure-response relationships. In Part I, we highlighted some of the sources of population variability. Part II provides a summary of discussions on modelling and simulation tools that utilize existing pharmacokinetic data, can integrate drug physicochemical characteristics with species physiological characteristics and dosing information or that combine observed with predicted and in vitro information to explore and describe sources of variability that may influence the safe and effective use of veterinary pharmaceuticals.

Mathematical modeling and simulation in animal health. Part III: Using nonlinear mixed-effects to characterize and quantify variability in drug pharmacokinetics

A common feature of human and veterinary pharmacokinetics is the importance of identifying and quantifying the key determinants of between-patient variability in drug disposition and effects. Some of these attributes are already well known to the field of human pharmacology such as bodyweight, age, or sex, while others are more specific to veterinary medicine, such as species, breed, and social behavior. Identification of these attributes has the potential to allow a better and more tailored use of therapeutic drugs both in companion and food-producing animals. Nonlinear mixed effects (NLME) have been purposely designed to characterize the sources of variability in drug disposition and response. The NLME approach can be used to explore the impact of population-associated variables on the relationship between drug administration, systemic exposure, and the levels of drug residues in tissues. The latter, while different from the method used by the US Food and Drug Administration for setting official withdrawal times (WT) can also be beneficial for estimating WT of approved animal drug products when used in an extralabel manner. Finally, NLME can also prove useful to optimize dosing schedules, or to analyze sparse data collected in situations where intensive blood collection is technically challenging, as in small animal species presenting limited blood volume such as poultry and fish.

A Population WB-PBPK Model of Colistin and its Prodrug CMS in Pigs: Focus on the Renal Distribution and Excretion

PURPOSE

The objective was the development of a whole-body physiologically-based pharmacokinetic (WB-PBPK) model for colistin, and its prodrug colistimethate sodium (CMS), in pigs to explore their tissue distribution, especially in kidneys.

METHODS

Plasma and tissue concentrations of CMS and colistin were measured after systemic administrations of different dosing regimens of CMS in pigs. The WB-PBPK model was developed based on these data according to a non-linear mixed effect approach and using NONMEM software. A detailed sub-model was implemented for kidneys to handle the complex disposition of CMS and colistin within this organ.

RESULTS

The WB-PBPK model well captured the kinetic profiles of CMS and colistin in plasma. In kidneys, an accumulation and slow elimination of colistin were observed and well described by the model. Kidneys seemed to have a major role in the elimination processes, through tubular secretion of CMS and intracellular degradation of colistin. Lastly, to illustrate the usefulness of the PBPK model, an estimation of the withdrawal periods after veterinary use of CMS in pigs was made.

CONCLUSIONS

The WB-PBPK model gives an insight into the renal distribution and elimination of CMS and colistin in pigs; it may be further developed to explore the colistin induced-nephrotoxicity in humans.

A Permeability-Limited Physiologically Based Pharmacokinetic (PBPK) Model for Perfluorooctanoic acid (PFOA) in Male Rats

Physiologically based pharmacokinetic (PBPK) modeling is a powerful in silico tool that can be used to simulate the toxicokinetics and tissue distribution of xenobiotic substances, such as perfluorooctanoic acid (PFOA), in organisms. However, most existing PBPK models have been based on the flow-limited assumption and largely rely on in vivo data for parametrization. In this study, we propose a permeability-limited PBPK model to estimate the toxicokinetics and tissue distribution of PFOA in male rats. Our model considers the cellular uptake and efflux of PFOA via both passive diffusion and transport facilitated by various membrane transporters, association with serum albumin in circulatory and extracellular spaces, and association with intracellular proteins in liver and kidney. Model performance is assessed using seven experimental data sets extracted from three different studies. Comparing model predictions with these experimental data, our model successfully predicts the toxicokinetics and tissue distribution of PFOA in rats following exposure via both IV and oral routes. More importantly, rather than requiring in vivo data fitting, all PFOA-related parameters were obtained from in vitro assays. Our model thus provides an effective framework to test in vitro-in vivo extrapolation and holds great promise for predicting toxicokinetics of per- and polyfluorinated alkyl substances in humans.

A physiologically based model for tramadol pharmacokinetics in horses

This work proposes an application of a minimal complexity physiologically based pharmacokinetic model to predict tramadol concentration vs time profiles in horses. Tramadol is an opioid analgesic also used for veterinary treatments. Researchers and medical doctors can profit from the application of mathematical models as supporting tools to optimize the pharmacological treatment of animal species. The proposed model is based on physiology but adopts the minimal compartmental architecture necessary to describe the experimental data. The model features a system of ordinary differential equations, where most of the model parameters are either assigned or individualized for a given horse, using literature data and correlations. Conversely, residual parameters, whose value is unknown, are regressed exploiting experimental data. The model proved capable of simulating pharmacokinetic profiles with accuracy. In addition, it provides further insights on un-observable tramadol data, as for instance tramadol concentration in the liver or hepatic metabolism and renal excretion extent.

Estimation of tulathromycin depletion in plasma and milk after subcutaneous injection in lactating goats using a nonlinear mixed-effects pharmacokinetic modeling approach

BACKGROUND

Extra-label use of tulathromycin in lactating goats is common and may cause violative residues in milk. The objective of this study was to develop a nonlinear mixed-effects pharmacokinetic (NLME-PK) model to estimate tulathromycin depletion in plasma and milk of lactating goats. Eight lactating goats received two subcutaneous injections of 2.5 mg/kg tulathromycin 7 days apart; blood and milk samples were analyzed for concentrations of tulathromycin and the common fragment of tulathromycin (i.e., the marker residue CP-60,300), respectively, using liquid chromatography mass spectrometry. Based on these new data and related literature data, a NLME-PK compartmental model with first-order absorption and elimination was used to model plasma concentrations and cumulative excreted amount in milk. Monte Carlo simulations with 100 replicates were performed to predict the time when the upper limit of the 95% confidence interval of milk concentrations was below the tolerance.

RESULTS

All animals were healthy throughout the study with normal appetite and milk production levels, and with mild-moderate injection-site reactions that diminished by the end of the study. The measured data showed that milk concentrations of the marker residue of tulathromycin were below the limit of detection (LOD = 1.8 ng/ml) 39 days after the second injection. A 2-compartment model with milk as an excretory compartment best described tulathromycin plasma and CP-60,300 milk pharmacokinetic data. The model-predicted data correlated with the measured data very well. The NLME-PK model estimated that tulathromycin plasma concentrations were below LOD (1.2 ng/ml) 43 days after a single injection, and 62 days after the second injection with a 95% confidence. These estimated times are much longer than the current meat withdrawal time recommendation of 18 days for tulathromycin in non-lactating cattle.

CONCLUSIONS

The results suggest that twice subcutaneous injections of 2.5 mg/kg tulathromycin are a clinically safe extra-label alternative approach for treating pulmonary infections in lactating goats, but a prolonged withdrawal time of at least 39 days after the second injection should be considered to prevent violative residues in milk and any dairy goat being used for meat should have an extended meat withdrawal time.

Biological and environmental surface interactions of nanomaterials: characterization, modeling, and prediction

The understanding of nano-bio interactions is deemed essential in the design, application, and safe handling of nanomaterials. Proper characterization of the intrinsic physicochemical properties, including their size, surface charge, shape, and functionalization, is needed to consider the fate or impact of nanomaterials in biological and environmental systems. The characterizations of their interactions with surrounding chemical species are often hindered by the complexity of biological or environmental systems, and the drastically different surface physicochemical properties among a large population of nanomaterials. The complexity of these interactions is also due to the diverse ligands of different chemical properties present in most biomacromolecules, and multiple conformations they can assume at different conditions to minimize their conformational free energy. Often these interactions are collectively determined by multiple physical or chemical forces, including electrostatic forces, hydrogen bonding, and hydrophobic forces, and calls for multidimensional characterization strategies, both experimentally and computationally. Through these characterizations, the understanding of the roles surface physicochemical properties of nanomaterials and their surface interactions with biomacromolecules can play in their applications in biomedical and environmental fields can be obtained. To quantitatively decipher these physicochemical surface interactions, computational methods, including physical, statistical, and pharmacokinetic models, can be used for either analyses of large amounts of experimental characterization data, or theoretical prediction of the interactions, and consequent biological behavior in the body after administration. These computational methods include molecular dynamics simulation, structure-activity relationship models such as biological surface adsorption index, and physiologically-based pharmacokinetic models. WIREs Nanomed Nanobiotechnol 2017, 9:e1440. doi: 10.1002/wnan.1440 For further resources related to this article, please visit the WIREs website.

Human Food Safety Implications of Variation in Food Animal Drug Metabolism

Violative drug residues in animal-derived foods are a global food safety concern. The use of a fixed main metabolite to parent drug (M/D) ratio determined in healthy animals to establish drug tolerances and withdrawal times in diseased animals results in frequent residue violations in food-producing animals. We created a general physiologically based pharmacokinetic model for representative drugs (ceftiofur, enrofloxacin, flunixin, and sulfamethazine) in cattle and swine based on extensive published literature. Simulation results showed that the M/D ratio was not a fixed value, but a time-dependent range. Disease changed M/D ratios substantially and extended withdrawal times; these effects exhibited drug- and species-specificity. These results challenge the interpretation of violative residues based on the use of the M/D ratio to establish tolerances for metabolized drugs.