When analyzing pharmacokinetic data, one generally employs either model fitting using nonlinear regression analysis or non-compartmental analysis techniques (NCA). The method one actually employs depends on what is required from the analysis. If the primary requirement is to determine the degree of exposure following administration of a drug (such as AUC), and perhaps the drug's associated pharmacokinetic parameters, such as clearance, elimination half-life, T (max), C (max), etc., then NCA is generally the preferred methodology to use in that it requires fewer assumptions than model-based approaches. In this chapter we cover NCA methodologies, which utilize application of the trapezoidal rule for measurements of the area under the plasma concentration-time curve. This method, which generally applies to first-order (linear) models (although it is often used to assess if a drug's pharmacokinetics are nonlinear when several dose levels are administered), has few underlying assumptions and can readily be automated.In addition, because sparse data sampling methods are often utilized in toxicokinetic (TK) studies, NCA methodology appropriate for sparse data is also discussed.

Radiotherapy is one of the major therapy forms in oncology, and combination therapies involving radiation and chemical compounds can yield highly effective tumor eradication. In this paper, we develop a tumor growth inhibition model for combination therapy with radiation and radiosensitizing agents. Moreover, we extend previous analyses of drug combinations by introducing the tumor static exposure (TSE) curve. The TSE curve for radiation and radiosensitizer visualizes exposure combinations sufficient for tumor regression. The model and TSE analysis are then tested on xenograft data. The calibrated model indicates that the highest dose of combination therapy increases the time until tumor regrowth 10‐fold. The TSE curve shows that with an average radiosensitizer concentration of 1.0 normalμboldg/boldmboldL the radiation dose can be decreased from 2.2 boldGboldy to 0.7 boldGboldy. Finally, we successfully predict the effect of a clinically relevant treatment schedule, which contributes to validating both the model and the TSE concept.

Abstract.Combination therapies are widely accepted as a cornerstone for treatment of different cancer types. A tumor growth inhibition (TGI) model is developed for combinations of cetuximab and cisplatin obtained from xenograft mice. Unlike traditional TGI models, both natural cell growth and cell death are considered explicitly. The growth rate was estimated to 0.006 h −1 and the natural cell death to 0.0039 h −1 resulting in a tumor doubling time of 14 days. The tumor static concentrations (TSC) are predicted for each individual compound. When the compounds are given as single-agents, the required concentrations were computed to be 506 μg · mL −1 and 56 ng · mL −1 for cetuximab and cisplatin, respectively. A TSC curve is constructed for different combinations of the two drugs, which separates concentration combinations into regions of tumor shrinkage and tumor growth. The more concave the TSC curve is, the lower is the total exposure to test compounds necessary to achieve tumor regression. The TSC curve for cetuximab and cisplatin showed weak concavity. TSC values and TSC curves were estimated that predict tumor regression for 95% of the population by taking between-subject variability into account. The TSC concept is further discussed for different concentration-effect relationships and for combinations of three or more compounds.

The in vitro affinity of a compound for its target is an important feature in drug discovery, but what remains is how predictive in vitro properties are of in vivo therapeutic drug exposure. We assessed the relationship between in vitro potency and clinically efficacious concentrations for marketed small molecule drugs (n = 164) and how they may differ depending on therapeutic indication, mode of action, receptor type, target localization, and function. Approximately 70% of compounds had a therapeutic unbound plasma exposure lower than in vitro potency; the median ratio of exposure in relation to in vitro potency was 0.32, and 80% had ratios within the range of 0.007 to 8.7. We identified differences in the in vivo-to-in vitro potency ratio between indications, mode of action, target type, and matrix localization, and whether or not the drugs had active metabolites. The in vitro-assay variability contributions appeared to be the smallest; within the same drug target and mode of action the within-variability was slightly broader; but both were substantially less compared with the overall distribution of ratios. These data suggest that in vitro potency conditions, estimated in vivo potency, required level of receptor occupancy, and target turnover are key components for further understanding the link between clinical drug exposure and in vitro potency.

Purpose Radiation therapy, whether given alone or in combination with chemical agents, is one of the cornerstones of oncology. We develop a quantitative model that describes tumor growth during and after treatment with radiation and radiosensitizing agents. The model also describes long-term treatment effects including tumor regrowth and eradication. Methods We challenge the model with data from a xenograft study using a clinically relevant administration schedule and use a mixed-effects approach for model-fitting. We use the calibrated model to predict exposure combinations that result in tumor eradication using Tumor Static Exposure (TSE). Results The model is able to adequately describe data from all treatment groups, with the parameter estimates taking biologically reasonable values. Using TSE, we predict the total radiation dose necessary for tumor eradication to be 110 Gy, which is reduced to 80 or 30 Gy with co-administration of 25 or 100 mg kg −1 of a radiosensitizer. TSE is also explored via a heat map of different growth and shrinkage rates. Finally, we discuss the translational potential of the model and TSE concept to humans. Conclusions The new model is capable of describing different tumor dynamics including tumor eradication and tumor regrowth with different rates, and can be calibrated using data from standard xenograft experiments. TSE and related concepts can be used to predict tumor shrinkage and eradication, and have the potential to guide new experiments and support translations from animals to humans.

Abstract.In this paper, we derive explicit expressions for the concentrations of ligand L, target R and ligand-target complex RL at steady state for the classical model describing targetmediated drug disposition, in the presence of a constant-rate infusion of ligand. We demonstrate that graphing the steady-state values of ligand, target and ligand-target complex, we obtain striking and often singular patterns, which yield a great deal of insight and understanding about the underlying processes. Deriving explicit expressions for the dependence of L, R and RL on the infusion rate, and displaying graphs of the relations between L, R and RL, we give qualitative and quantitive information for the experimentalist about the processes involved. Understanding target turnover is pivotal for optimising these processes when target-mediated drug disposition (TMDD) prevails. By a combination of mathematical analysis and simulations, we also show that the evolution of the three concentration profiles towards their respective steady-states can be quite complex, especially for lower infusion rates. We also show how parameter estimates obtained from iv bolus studies can be used to derive steady-state concentrations of ligand, target and complex. The latter may serve as a template for future experimental designs.

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A mechanism-based biomarker model of TNF α -response, including different external provocations of LPS challenge and test compound intervention, was developed. The model contained system properties (such as k t , k out ), challenge characteristics (such as k s , k LPS , K m, LPS , S max , SC 50 ) and test-compound-related parameters ( I max , IC 50 ). The exposure to test compound was modelled by means of first-order input and Michaelis–Menten type of nonlinear elimination. Test compound potency was estimated to 20 nM with a 70% partial reduction in TNF α -response at the highest dose of 30 mg·kg −1 . Future selection of drug candidates may focus the estimation on potency and efficacy by applying the selected structure consisting of TNF α system and LPS challenge characteristics. A related aim was to demonstrate how an exploratory (graphical) analysis may guide us to a tentative model structure, which enables us to better understand target biology. The analysis demonstrated how to tackle a biomarker with a baseline below the limit of detection. Repeated LPS-challenges may also reveal how the rate and extent of replenishment of TNF α pools occur. Lack of LPS exposure-time courses was solved by including a biophase model, with the underlying assumption that TNF α -response time courses, as such, contain kinetic information. A transduction type of model with non-linear stimulation of TNF α release was finally selected. Typical features of a challenge experiment were shown by means of model simulations. Experimental shortcomings of present and published designs are identified and discussed. The final model coupled to suggested guidance rules may serve as a general basis for the collection and analysis of pharmacological challenge data of future studies. Electronic supplementary material The online version of this article (10.1007/s10928-019-09622-x) contains supplementary material, which is available to authorized users.