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.

This review provides a tutorial for individuals interested in quantitative veterinary pharmacology and toxicology and offers a basis for establishing guidelines for physiologically based pharmacokinetic (PBPK) model development and application in veterinary medicine. This is important as the application of PBPK modeling in veterinary medicine has evolved over the past two decades. PBPK models can be used to predict drug tissue residues and withdrawal times in food-producing animals, to estimate chemical concentrations at the site of action and target organ toxicity to aid risk assessment of environmental contaminants and/or drugs in both domestic animals and wildlife, as well as to help design therapeutic regimens for veterinary drugs. This review provides a comprehensive summary of PBPK modeling principles, model development methodology, and the current applications in veterinary medicine, with a focus on predictions of drug tissue residues and withdrawal times in food-producing animals. The advantages and disadvantages of PBPK modeling compared to other pharmacokinetic modeling approaches (i.e., classical compartmental/noncompartmental modeling, nonlinear mixed-effects modeling, and interspecies allometric scaling) are further presented. The review finally discusses contemporary challenges and our perspectives on model documentation, evaluation criteria, quality improvement, and offers solutions to increase model acceptance and applications in veterinary pharmacology and toxicology.

Bottom-up Meets Top-down: Complementary Physiologically Based Pharmacokinetic and Population Pharmacokinetic Modeling for Regulatory Approval of a Dosing Algorithm of Valganciclovir in Very Young Children.

Population pharmacokinetic (PopPK) and physiologically based pharmacokinetic (PBPK) models are frequently used to support pediatric drug development. Both methods have strengths and limitations and we used them complementarily to support the regulatory approval of a dosing algorithm for valganciclovir (VGCV) in children <4 months old. An existing pediatric PBPK model was extended to neonates and showed that potential physiological differences compared with older children are minor. The PopPK model was used to simulate ganciclovir (GCV) exposures in children with population typical combinations of body size and renal function and to assess the effectiveness of an alternative dosing algorithm suggested by the US Food and Drug Administration. PBPK and PopPK confirmed that the proposed VGCV dosing algorithm achieves similar GCV exposures in children of all ages and that the alternative dosing algorithm leads to underexposure in a substantial fraction of patients. Our approach raised the confidence in the VGCV dosing algorithm for children <4 months old and supported the regulatory approval.

Developing Exposure/Response Models for Anticancer Drug Treatment: Special Considerations.

Anticancer agents often have a narrow therapeutic index (TI), requiring precise dosing to ensure sufficient exposure for clinical activity while minimizing toxicity. These agents frequently have complex pharmacology, and combination therapy may cause schedule-specific effects and interactions. We review anticancer drug development, showing how integration of modeling and simulation throughout development can inform anticancer dose selection, potentially improving the late-phase success rate. This article has a companion article in Clinical Pharmacology & Therapeutics with practical examples.

Qualitative and quantitative assessment of drug-drug interaction potential in man, based on Ki, IC50 and inhibitor concentration.

Strategies used to screen new drug entities as potential inhibitors of CYP450 enzymes are now widely used to select candidates in the drug discovery process. However, the information obtained based on IC50 values are usually more of qualitative nature. The aim of this study was to find out whether a more quantitative assessment of interaction potential could be achieved on the basis of the ratio I/Ki (I corresponds to inhibitor concentration). Ki values, in vivo data, namely plasma exposures under control condition vs in presence of inhibitors, were obtained from literature for 36 compounds. For a quantitative assessment, the following inhibitor concentrations were considered: I max and I in,max (respectively, maximum I in systemic circulation and in portal vein), I max,u and I in,max,u (respectively, maximum unbound I in systemic circulation and in portal vein). The predicted interaction was calculated as AUCinhibitor/AUCcontrol = 1 + I/Ki, where AUCcontrol and AUCinhibitor represent, respectively, the area under curve of the plasma concentration vs time profile under control conditions (ie without inhibitor) and with inhibitor. The use of I/Ki allowed a more quantitative estimation of the interaction potential. In this context, protein binding appeared to be a key parameter to be considered to avoid overestimation of DDI potential. Thus, 60% successful predictions could be achieved based on the ratio I max,u/Ki. Yet, some major deviations between in vivo DDI were obtained with this approach and the observations on the relevance of the inhibitor concentrations and the impact of binding need to be interpreted very cautiously in the absence of information on additional parameters such as fm and fh for example.

Revising axis V for DSM-IV: a review of measures of social functioning.

OBJECTIVE: Axis V, which uses the Global Assessment of Functioning Scale in the multiaxial system of DSM-III-R, is under review for DSM-IV. This article examines what is known about axis V and selectively reviews the literature on measures of social functioning to identify potential alternatives to the Global Assessment of Functioning Scale. METHOD: About 25 studies on the use, reliability, and validity of axis V in DSM-III and DSM-III-R are reviewed. In addition, nearly 30 measures of social functioning are reviewed and analyzed as potential substitutes for the Global Assessment of Functioning Scale. The analysis focuses on the strengths and weaknesses of each measure for assessing functioning on axis V. RESULTS: Axis V measures are modestly reliable and valid but not widely used. The authors identify and discuss two particular limitations of the Global Assessment of Functioning Scale: 1) the combination of measures of symptoms and measures of social functioning on a single axis and 2) the exclusion of physical impairments from the rating of functioning. CONCLUSIONS: None of the measures of social functioning reviewed is clearly superior to the Global Assessment of Functioning Scale for use on axis V. A modified version of the Global Assessment of Functioning Scale, separating the measures of social and occupational functioning from the measures of symptoms and psychological functioning, is proposed for field testing, along with a new set of instructions permitting the rating of limitations due to both physical and mental impairments.

Combining in vitro and in vivo pharmacokinetic data for prediction of hepatic drug clearance in humans by artificial neural networks and multivariate statistical techniques.

Several statistical regression models and artificial neural networks were used to predict the hepatic drug clearance in humans from in vitro (hepatocyte) and in vivo pharmacokinetic data and to identify the most predictive models for this purpose. Cross-validation was performed to assess prediction accuracy. It turned out that human hepatocyte data was the best predictor, followed by rat hepatocyte data. Dog hepatocyte data and dog and rat in vivo data appear to be uncorrelated with human in vivo clearance and did not significantly contribute to the prediction models. Considering the present evaluation, the most cost-effective and most accurate approach to achieve satisfactory predictions in human is a combination of in vitro clearances on human and rat hepatocytes. Such information is of considerable value to speed up drug discovery. This study also showed some of the limitations of the approach related to the size of the database used in the present evaluation.

Prediction of hepatic metabolic clearance based on interspecies allometric scaling techniques and in vitro-in vivo correlations.

This article reviews the methods available for predicting hepatic metabolic clearance in humans, and discusses their application to the processes of drug discovery and development. The application of these techniques has increased markedly during the past few years because of the improved availability of human liver samples, which has increased the opportunities to use in vitro studies to predict human clearance. The techniques available involve both empirical and physiologically based approaches. Allometric scaling using in vitro data from animals and humans combines certain aspects of both approaches. An evaluation of data retrieved from the literature indicates that, together with in vitro human data, allometric scaling based on a combination of in vitro and in vivo preclinical data can accurately predict clearance in humans. With this approach, 80% of the predictions were within a 2-fold factor of actual human clearance values, with an overall accuracy of 1.6-fold. The uncertainties and inaccuracies in predicting human clearance are related to: (i) the specific method that is used to make the prediction; (ii) the experimental design and the model used to determine the in vitro clearance; (iii) protein binding within the in vitro test system; and (iv) various in vivo factors such as the involvement of extrahepatic metabolism and active transport processes, interindividual variability and nonlinearity in pharmacokinetics. In contrast to purely empirical approaches, the physiological approach to predicting clearance gives an opportunity to integrate some of these complexities and, therefore, should provide more confidence in the prediction of clearance in humans.

Prediction of hepatic metabolic clearance: comparison and assessment of prediction models.

OBJECTIVE: To perform a comparative quantitative evaluation of the prediction accuracy for human hepatic metabolic clearance of 5 different mathematical models: allometric scaling (multiple species and rat only), physiologically based direct scaling, empirical in vitro-in vivo correlation, and supervised artificial neural networks. METHODS: The mathematical prediction models were implemented with a publicly available dataset of 22 extensively metabolised compounds and compared for their prediction accuracy using 3 quality indicators: prediction error sum of squares (PRESS), r2 and the fold-error. RESULTS: Approaches such as physiologically based direct scaling, empirical in vitro-in vivo correlation and artificial neural networks, which are based on in vitro data only, yielded an average fold-error ranging from 1.64 to 2.03 and r2 values greater than 0.77, as opposed to r2 values smaller than 0.44 when using allometric scaling combining in vivo and in vitro preclinical data. The percentage of successful predictions (less than 2-fold error) ranged from 55% (rat allometric scaling) to between 64 and 68% with the other approaches. CONCLUSIONS: On the basis of a diverse set of 22 metabolised drug molecules, these studies showed that the most cost-effective and accurate approaches, such as physiologically based direct scaling and empirical in vitro-in vivo correlation, are based on in vitro data alone. Inclusion of in vivo preclinical data did not significantly improve prediction accuracy; the prediction accuracy of the allometric approaches was at the lower end of all methods compared.

Activities of lipoprotein lipase and hepatic lipase on long- and medium-chain triglyceride emulsions used in parenteral nutrition.

Prolonged parenteral nutrition frequently includes lipid emulsions. This report investigates how emulsions containing triacylglycerols of different molecular weight affect the rate of clearance in vivo and the activity in vitro of the two enzymes responsible for this clearance: diaphragm lipoprotein lipase (LPL) and hepatic endothelial lipase (HL). Whatever their molecular weight, the triacylglycerols of the emulsions were hydrolyzed by LPL and HL. However, the reaction was faster with medium-chain triglycerides (MCT) than with long-chain triglycerides (LCT). To be active, LPL required the presence of serum (apolipoprotein CII); for maximum activity less serum was required for MCT than for LCT. In the case of HL, serum inhibited the effect on LCT but not on MCT. However, hydrolysis of emulsified triacylglycerols by LPL and HL required the presence of albumin as a transporter of the fatty acids released. Less albumin was needed for maximum activity with MCT than with LCT. In vivo, although MCT emulsions were eliminated more rapidly than LCT emulsions, the former resulted in a greater increase in plasma concentrations of triacylglycerols and free glycerol than did the latter. This is explained by the fact that MCT provides about 1.8 times more triacylglycerol molecules than the LCT. In vitro, LPL and HL hydrolyzed structured lipids (randomly esterified triacylglycerols of medium- and long-chain fatty acids) slightly less rapidly than they did control lipids, but there was no comparable difference in the blood lipid parameters examined in vivo. Because the MCT emulsions are cleared rapidly, their fatty acids are rapidly made available to the various tissues where they are oxidized.

A new extrapolation method from animals to man: application to a metabolized compound, mofarotene.

Allometric scaling (a technique which uses data obtained in laboratory animals to predict human pharmacokinetics) works well for drugs that are cleared intact, but is less successful with extensively metabolised compounds. This paper describes a new method to improve the accuracy of such projections, by integrating metabolic data obtained in vitro (e.g. with liver microsomes or hepatocytes) into these calculations. The approach was used prospectively, to predict the clearance of mofarotene (Ro 40-8757) in humans from in vivo kinetic data obtained in mouse, rat and dog. This compound was selected to illustrate this approach because it is exclusively eliminated through metabolism. Without the metabolic correction or using empirical correcting factors, the values predicted for man were 2.7 and 0.6 ml/min/kg. This fell outside the range subsequently obtained in healthy volunteers dosed orally with 300 mg of mofarotene (7.5 +/- 4.0 ml/min/kg, n = 12). However, inclusion of the microsomal or hepatocyte data gave values of 5.1 and 4.2 ml/min/kg, respectively, illustrating that the integration of in vitro metabolic data improves the accuracy of kinetic extrapolations. In contrast to the existing empirical techniques, this approach offers a rational basis to predict clearance of metabolized compounds in human.

Animal pharmacokinetics and interspecies scaling of Ro 25-6833 and related (lactamylvinyl)cephalosporins.

From a series of six (lactamylvinyl)cephalosporins, candidates for clinical evaluation were selected on the basis of their kinetic profile in animals and predicted pharmacokinetics in man. Exploratory pharmacokinetic studies with Ro 25-6833 and five related cephalosporins were performed following intravenous administration to rats, dogs, and cynomolgus monkeys. All compounds were characterized by a high protein binding in rat, monkey, and human plasma (unbound fraction < or = 5%), whereas in dog plasma, protein binding was markedly lower. Accordingly, for most compounds, clearance was highest in dogs, and lowest in monkeys. Comparison of the renal clearance of unbound drug with creatinine clearance suggests a renal elimination of Ro 25-6833 by glomerular filtration in both rats and dogs (urinary excretion in monkey was not determined due to drug instability in monkey urine). All other compounds showed different renal excretion mechanisms in rats and dogs, thus making the validity of allometric scaling questionable. Unbound clearances in man were predicted by allometric scaling (Ro 25-6833 only) and by a correlation analysis of cephalosporin pharmacokinetics in monkey and man. Limitations of both methods are discussed. When Ro 25-6833 was later studied in man, the predicted pharmacokinetic data in man from both approaches were found to be in good agreement with the observed values.

Integration of in vitro data into allometric scaling to predict hepatic metabolic clearance in man: application to 10 extensively metabolized drugs.

In this study, we investigated rational and reliable methods of using animal data to predict in humans the clearance of drugs which are mainly eliminated through hepatic metabolism. For 10 extensively metabolized compounds, adjusting the in vivo clearance in the different animal species for the relative rates of metabolism in vitro dramatically improved the predictions of human clearance compared to the approach in which clearance is directly extrapolated using body weight. Using hepatocyte data to normalize the in vivo clearances led to lower median deviations between the observed and predicted clearances in man compared to the approach normalizing data with brain weight (30-40% vs 60-80%, respectively). In addition, the approach integrating in vitro data appeared to be superior with respect to the range of deviations: approximately 2-fold underestimation, in the worst case, was observed by using in vitro data, whereas normalizing data by brain weight led to up to 10-fold underestimation of clearance in man. In addition, the integration of in vitro data provides a more rational basis to predict the metabolic clearance in man and may be applicable to compounds undergoing phase I and phase II metabolism as well.

Interspecies scaling of interferon disposition and comparison of allometric scaling with concentration-time transformations.

Interspecies scaling is used to extrapolate pharmacokinetic parameters from animals to humans, through the application of physiologically based models, by empirical allometric procedures, or using concentration-time transformations. The aim of this study was to compare the accuracies of the last two methods for predicting the pharmacokinetic parameters and concentration-time curves in humans. In the first part of this study, interspecies scaling techniques were applied to a hypothetical drug (extracellular distribution and elimination through glomerular filtration), to examine the influence of various laboratory animals (mouse, rat, cynomolgus monkey and dog) on the parameters predicted for man. The same techniques were also applied to interferon-alpha A, using the literature data for various animal species. The kinetic parameters predicted in man were then compared to the values published for man. Our theoretical example showed that, for allometric scaling, each species has a very different influence on the prediction in human. With the approach using concentration-time transformations, however, each animal species potentially makes a similar contribution to the prediction for man. Based on the pharmacokinetic data published for interferon-alpha A in laboratory animals, allometric equations underestimated the observed values of CL and Vdss in man by 2-3-fold, and the prediction of t1/2 was likely to be unreliable, due to a poor correlation. The use of equivalent time, kallynochron, and apolysichron transformations improved the pharmacokinetic predictions for all three parameters in man. In conclusion, concentration-time transformations make more adequate use of the data available in the different species of laboratory animals, to give better predictions of the pharmacokinetic parameters in man.

Animal pharmacokinetics and interspecies scaling from animals to man of lamifiban, a new platelet aggregation inhibitor.

Relating pharmacokinetic information obtained in animal species to man (interspecies scaling) can play an important role in enabling understanding of the differences and similarities between species, and helping to predict the kinetic profile of a new compound in man. Interspecies scaling techniques have been applied to lamifiban (Ro 44-9883), a new selective and potent nonpeptidic inhibitor of human glycoprotein IIb-IIIa intended for use in clinical treatment of, for example, acute coronary syndrome. The pharmacokinetic profile of lamifiban in man was predicted from animal data (in rats, dogs and cynomolgus monkeys) by using allometric scaling and concentration-time transformations. These extrapolations for lamifiban were performed prospectively, to help design the first pharmacokinetic studies in man. The approach based on equivalent time was preferred for our prospective predictions, in view of the high values found for the allometric exponents. Using allometric scaling, clearance (CL), half-life (t1/2) and volume of distribution (Vd) were overestimated by approximately two- to fourfold. Compared with allometric scaling, the transformation based on equivalent time improved the prediction for all human pharmacokinetic parameters. For t1/2 and CL, the observed values for man were within the range predicted from the various animal species. Of the individual animal species, the cynomolgus monkey gave the most reliable predictions of these two parameters, as well as accurately predicting the Vd value.

Interspecies pharmacokinetic comparisons and allometric scaling of napsagatran, a low molecular weight thrombin inhibitor.

The objective of this work was to assess the pharmacokinetics of napsagatran, a low molecular weight thrombin inhibitor, after intravenous administration in a variety of laboratory animals, and prospectively to help design the first pharmacokinetic studies in man. Napsagatran is actively excreted into the bile and urine of various species and pronounced species-differences in its pharmacokinetics are observed. It is, therefore, an interesting compound to use in tests of the limitations of presently available inter-species scaling methods. The present data suggest that allometric exponent values which are consistent with the values expected for physiological processes and small organic molecules are not necessarily associated with successful predictions in man when active transport processes are involved in the disposition of the compounds. For example, compared with the values observed in man, the clearance (CL), non-renal clearance (CL(nr)) and the volume of distribution at steady state (Vd(ss)) were over-predicted by 3-, 7- and 2-fold, respectively, by use of allometry. Of the species tested, the cynomolgus monkey seemed to be the most useful for predicting kinetics in man when the approach based on concentration-time transformations was used. Thus, for half-life (t(1/2)), CL and Vd(ss), the observed mean values of 1.7 h, 459 mL min(-1) and 24 L kg(-1) in man were very close to the values predicted from the cynomolgus monkey (1.7 h, 652 mL min(-1) and 22 L kg(-1), respectively). The results show that there are large inter-species differences for kidney and liver excretion of napsagatran. This is probably because of the involvement of active transport processes, which compromised the kinetic extrapolation from animal to man, although a more thorough investigation of the transporters involved in the disposition of napsagatran is necessary to enable better understanding of the species differences observed.

Piperidine renin inhibitors: from leads to drug candidates.

Non-peptidomimetic renin inhibitors of the piperidine type represent a novel structural class of compounds potentially free of the drawbacks seen with peptidomimetic compounds so far. Synthetic optimization in two structural series focusing on improvement of potency, as well as on physicochemical properties and metabolic stability, has led to the identification of two candidate compounds 14 and 23. Both display potent and long-lasting blood pressure lowering effects in conscious sodium-depleted marmoset monkeys and double transgenic rats harboring both the human angiotensinogen and the human renin genes. In addition, 14 normalizes albuminuria and kidney tissue damage in these rats when given over a period of 4 weeks. These data suggest that treatment of chronic renal failure patients with a renin inhibitor might result in a significant improvement of the disease status.

Challenges and opportunities with modelling and simulation in drug discovery and drug development.

The benefits of modelling and simulation at the pre-clinical stage of drug development can be realized through formal and realistic integration of data on physicochemical properties, pharmacokinetics, pharmacodynamics, formulation and safety. Such data integration and the powerful combination of physiologically based pharmacokinetic (PBPK) with pharmacokinetic-pharmacodynamic relationship (PK/PD) models provides the basis for quantitative outputs allowing comparisons across compounds and resulting in improved decision-making during the selection process. Such PBPK/PD evaluations provide crucial information on the potency and safety of drug candidates in vivo and the bridging of the PK/PD concept established during the pre-clinical phase to clinical studies. Modelling and simulation is required to address a number of key questions at the various stages of the drug-discovery and -development process. Such questions include the following. (1) What is the expected human PK profile for potential clinical candidate(s)? (2) Is this profile and its associated PD adequate for the given indication? (3) What is the optimal dosing schedule with respect to safety and efficacy? (4) Is a food effect expected? (5) How can formulation be improved and what is the potential benefit? (6) What is the expected variability and uncertainty in the predictions?

Comparison of clearance predictions using primary cultures and suspensions of human hepatocytes.

Various incubation conditions of human hepatocytes were compared for their accuracy in predicting the in vivo hepatic clearance (CL(H)) of model compounds. The test compounds were the highly cleared, low protein bound naloxone (in vivo CL(H) = 25 ml min(-1) kg(-1); free fraction = 0.6), the medium clearance, highly protein bound midazolam (CL(H) = 12 ml min(-1) kg(-1); free fraction = 0.04) and the low clearance, highly protein bound bosentan (CL(H) = 3.9 ml min(-1) kg(-1); free fraction = 0.02). Each compound was tested in three 'hepatocyte systems', using resections from three donors, in the presence and absence of human serum. Those hepatocyte systems were: conventional primary cultures, freshly isolated suspensions and cryopreserved suspended hepatocytes. Except for a twofold overestimated CL(H) for bosentan from conventional primary cultures, and despite variable cryopreservation recoveries, similar predictions of CL(H) were recorded with all hepatocyte systems. Moreover, the CL(H) values obtained with cryopreserved suspended hepatocytes were similar to those obtained with freshly isolated suspensions. For midazolam and bosentan, the predicted in vivo CL(H) was markedly higher in the presence of serum, whereas serum had little influence on the scaled-up CL(H) of naloxone. In vivo, CL(H) was properly approached for naloxone and bosentan (particularly from experiments in the presence of serum), but it was strongly underestimated for midazolam (particularly in the absence of serum). Additional compounds need to be investigated to confirm the above findings as well as to assess why the clearances of some highly protein-bound compounds are still considerably underestimated.

Public perception of the risks of floods: implications for communication.

Floods in the U.S. kill an average of 162 people each year and cause $3.4 billion in property damage. Flood control programs have been successful in lowering, but not eliminating, the risks to lives and property. Since the late 1960s, the federal government has emphasized flood insurance as a primary tool for improving location and flood-proofing decisions, as well as for reimbursing flood losses. Since only 12.7% of houses in flood plain areas are covered by flood insurance, the program has been ineffective. We interviewed people living in three communities that had recently been flooded. Most people had little knowledge of the cause of floods or what could be done to prevent damage. People who work and who are better educated know more and are more likely to have flood insurance. Current government publications about flood risks are not likely to be understood by those at risk. There is little effective communication about the nature and magnitude of the risks and what individuals can do to protect their lives and property and lower their financial risks. The risk management program should both emphasize communication and enforcement of the current law requiring people at risk who hold federally funded loans to be insured.