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We also developed a new turnover model that describes the adaptation seen in plasma FFA concentrations in lean Sprague-Dawley and obese Zucker rats following acute and chronic NiAc exposure. The data were analyzed using a nonlinear mixed-effects framework. We conducted a meta-analysis on a rich pre-clinical data set of the NiAc-FFA interaction to establish the acute and chronic exposure-response relations from a macro perspective. Sustained NiAc exposure is associated with tolerance development (drug resistance) and complete adaptation (FFA returning to pretreatment levels).
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Acute administration results in a rapid reduction of plasma free fatty acid (FFA) concentrations. Nicotinic acid (NiAc) is a potent inhibitor of adipose tissue lipolysis. Finally, we successfully predict the effect of a clinically relevant treatment schedule, which contributes to validating both the model and the TSE concept. The TSE curve shows that with an average radiosensitizer concentration of 1.0 μg/mL the radiation dose can be decreased from 2.2 Gy to 0.7 Gy. The calibrated model indicates that the highest dose of combination therapy increases the time until tumor regrowth tenfold. The model and TSE analysis are then tested on xenograft data. The TSE curve for radiation and radiosensitizer visualizes exposure combinations sufficient for tumor regression. Moreover, we extend previous analyses of drug combinations by introducing the Tumor Static Exposure (TSE) curve. In this paper, we develop a tumor growth inhibition model for combination therapy with radiation and radiosensitizing agents. Radiation therapy is one of the major therapy form in oncology, and combination therapies involving radiation and chemical compounds can yield highly effective tumor eradication. We conclude that parameter estimation using FOCE with exact gradients can successfully be applied to SDE-NLME models. Additionally, gradient precision/accuracy was significantly better in the exact gradient case. When finite difference gradients were replaced by exact gradients at both FOCE levels, relative runtimes improved between 6- and 32-fold, depending on model complexity. The exact gradient FOCE method was implemented in Mathematica 11 and evaluated on SDE versions of three common PK/PD models. Following previous work, the uncertainty of the state variables was accounted for using the extended Kalman filter (EKF). A simulation-estimation study was set up whereby finite difference approximations of the gradients of each level were interchanged with the exact gradients.
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The aims of this work were to develop an exact gradient version of the first-order conditional estimation (FOCE) method for SDE-NLME models and to investigate whether it enabled faster estimation and better gradient precision/accuracy compared to the use of gradients approximated by finite differences. This article presents a summary of the main contributions to SDE-NLME models found in the literature. SDE-NLME models go beyond the realm of standard population modeling as they consider stochastic dynamics, thereby introducing a probabilistic perspective on the state variables. Nonlinear mixed effects (NLME) modeling based on stochastic differential equations (SDEs) have evolved into a promising approach for analysis of PK/PD data. 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. 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. Finally, we discuss the translational potential of the model and TSE concept to humans. TSE is also explored via a heat map of different growth and shrinkage rates. 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. The model is able to adequately describe data from all treatment groups, with the parameter estimates taking biologically reasonable values. We use the calibrated model to predict exposure combinations that result in tumor eradication using Tumor Static Exposure (TSE). 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. The model also describes long-term treatment effects including tumor regrowth and eradication.
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We develop a quantitative model that describes tumor growth during and after treatment with radiation and radiosensitizing agents. Radiation therapy, whether given alone or in combination with chemical agents, is one of the cornerstones of oncology.
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