A mechanistic modelling approach for the determination of the mechanisms of inhibition by cyclosporine on the uptake and metabolism of atorvastatin in rat hepatocytes using a high throughput uptake method

(1) Determine the inhibition mechanism through which cyclosporine inhibits the uptake and metabolism of atorvastatin in fresh rat hepatocytes using mechanistic models applied to data generated using a high throughput oil spin method. (2) Atorvastatin was incubated in fresh rat hepatocytes (0.05–150 nmol/ml) with or without 20 min pre-incubation with 10 nmol/ml cyclosporine and sampled over 0.25–60 min using a high throughput oil spin method. Micro-rate constant and macro-rate constant mechanistic models were ranked based on goodness of fit values. (3) The best fitting model to the data was a micro-rate constant mechanistic model including non-competitive inhibition of uptake and competitive inhibition of metabolism by cyclosporine (Model 2). The association rate constant for atorvastatin was 150-fold greater than the dissociation rate constant and 10-fold greater than the translocation into the cell. The association and dissociation rate constants for cyclosporine were 7-fold smaller and 10-fold greater, respectively, than atorvastatin. The simulated atorvastatin-transporter-cyclosporine complex derived using the micro-rate constant parameter estimates increased in line with the incubation concentration of atorvastatin. (4) The increased amount of data generated with the high throughput oil spin method, combined with a micro-rate constant mechanistic model helps to explain the inhibition of uptake by cyclosporine following pre-incubation

A mechanistic modelling approach for the determination of the mechanisms of inhibition by cyclosporine on the uptake and metabolism of atorvastatin in rat hepatocytes using a high throughput uptake method

Determine the inhibition mechanism through which cyclosporine inhibits the uptake and metabolism of atorvastatin in fresh rat hepatocytes using mechanistic models applied to data generated using a high throughput oil spin method. Atorvastatin was incubated in fresh rat hepatocytes (0.05–150 nmol/ml) with or without 20 min pre-incubation with 10 nmol/ml cyclosporine and sampled over 0.25–60 min using a high throughput oil spin method. Micro-rate constant and macro-rate constant mechanistic models were ranked based on goodness of fit values. The best fitting model to the data was a micro-rate constant mechanistic model including non-competitive inhibition of uptake and competitive inhibition of metabolism by cyclosporine (Model 2). The association rate constant for atorvastatin was 150-fold greater than the dissociation rate constant and 10-fold greater than the translocation into the cell. The association and dissociation rate constants for cyclosporine were 7-fold smaller and 10-fold greater, respectively, than atorvastatin. The simulated atorvastatin-transporter-cyclosporine complex derived using the micro-rate constant parameter estimates increased in line with the incubation concentration of atorvastatin. The increased amount of data generated with the high throughput oil spin method, combined with a micro-rate constant mechanistic model helps to explain the inhibition of uptake by cyclosporine following pre-incubation

System identification applied to a single area electric power system under frequency response

This research paper proposes a methodology to apply identification methods to find a simplified model of three different governors in a single area electric power system (SAEPS). A SAEPS with different governors-turbine is presented: a hydraulic turbine, a steam turbine and a steam reheat turbine. In this same investigation, an analytic reduction has been performed, a fifth order system was found analytically, thus a transfer function equivalent to the three different governor-turbine elements was obtained, this equivalent transfer function models the complete behavior of the three devices. Two systems identification (SI) algorithms have been proposed to apply them to this generic subspace state-space (N4SID) and generalized poisson moment functionals (GPMF) electrical system, these presented similar results. The results of the performance and simulation analysis exhibit that using the SI technique, fifth, fourth and third-order systems were obtained that graphically show a very small estimation error compared to the original signal, this fact could be check simulating the simplified models using the same input-output data. The results are presented in a table that shows a comparison of the model respond the fifth, fourth, third and second-order systems

Prediction of clinical transporter‐mediated drug–drug interactions via comeasurement of pitavastatin and eltrombopag in human hepatocyte Models

A structurally identifiable micro‐rate constant mechanistic model was used to describe the interaction between pitavastatin and eltrombopag, with improved goodness‐of‐fit values through comeasurement of pitavastatin and eltrombopag. Transporter association and dissociation rate constants and passive rates out of the cell were similar between pitavastatin and eltrombopag. Translocation into the cell through transporter‐mediated uptake was six times greater for pitavastatin, leading to pronounced inhibition of pitavastatin uptake by eltrombopag. The passive rate into the cell was 91 times smaller for pitavastatin compared with eltrombopag. A semimechanistic physiologically‐based pharmacokinetic (PBPK) model was developed to evaluate the potential for clinical drug–drug interactions (DDIs). The PBPK model predicted a twofold increase in the pitavastatin peak blood concentration and area under the concentration‐time curve in the presence of eltrombopag in simulated healthy volunteers. The use of structural identifiability supporting experimental design combined with robust micro‐rate constant parameter estimates and a semimechanistic PBPK model gave more informed predictions of transporter‐mediated DDIs

Mixed Effects Modeling of Deterministic and Stochastic Dynamical Systems - Methods and Applications in Drug Development

Mathematical models based on ordinary differential equations (ODEs) are commonly used for describing the evolution of a system over time. In drug development, pharmacokinetic (PK) and pharmacodynamic (PD) models are used to characterize the exposure and effect of drugs. When developing mathematical models, an important step is to infer model parameters from experimental data. This can be a challenging problem, and the methods used need to be efficient and robust for the modeling to be successful. This thesis presents the development of a set of novel methods for mathematical modeling of dynamical systems and their application to PK-PD modeling in drug development.A method for regularizing the parameter estimation problem for dynamical systems is presented. The method is based on an extension of ODEs to stochastic differential equations (SDEs), which allows for stochasticity in the system dynamics, and is shown to lead to a parameter estimation problem that is easier to solve.The combination of parameter variability and SDEs are investigated, allowing for an additional source of variability compared to the standard nonlinear mixed effects (NLME) model. For NLME models with dynamics described using either ODEs or SDEs, a novel parameter estimation algorithm is presented. The method is a gradient-based optimization method where the exact gradient of the likelihood function is calculated using sensitivity equations, which is shown to give a substantial improvement in computational speed compared to existing methods. The methods developed have been integrated into NLMEModeling, a freely available software package for mixed effects modeling in Wolfram Mathematica. The package allows for general model specifications and offers a user-friendly environment for NLME modeling of dynamical systems.The SDE-NLME framework is used in two applied modeling problems in drug development. First, a previously published PK model of nicotinic acid is extended to incorporate SDEs. By extending the ODE model to an SDE model, it is shown that an additional source of variability can be quantified. Second, the SDE-NLME framework is applied in a model-based analysis of peak expiratory flow (PEF) diary data from two Phase III studies in asthma. The established PEF model can describe several aspects of the PEF dynamics, including long-term fluctuations. The association to exacerbation risk is investigated using a repeated time-to-event model, and several characteristics of the PEF dynamics are shown to be associated with exacerbation risk.The research presented in this doctoral thesis demonstrates the development of a set of methods and applications of mathematical modeling of dynamical systems. In this work, the methods were primarily applied in the field of PK-PD modeling, but are also applicable in other scientific fields

Mathematical modelling of epidemic systems influenced by maternal antibodies and public health intervention

The general subject area of research considered in this thesis is population level epidemic modelling of infectious diseases, with specific application to the problems of model indeterminacy and systems that include processes associated with maternally acquired immunity. The work presents the derivation and analysis of a lumped systems model framework to study the influence of maternal antibodies on the population dynamics of infection among neonate and young infant age classes. The proposed models are defined by sets of ordinary and partial differential equations that describe the variation of distinct states in the natural history of infection with respect to time and/or age. The model framework is extended to explore the potential population level outcomes and consequences of mass maternal immunisation: an emerging targeted vaccine strategy that utilises the active transfer of neutralising antibodies during pregnancy in order to supplement neonatal immunity during the first few months of life. A qualitative analysis of these models has highlighted the importance of interaction with early childhood targeted vaccination campaigns, the potential to invoke transient epidemic behaviour and the prospective advantages of seasonal administration. The work considers the implications of structural identifiability, indistinguishability and formal sensitivity analyses on a number of fundamental model structures within the proposed framework. These methods are used to establish whether a postulated model structure, or the individual parameters within a known structure, are uniquely determinable from a given set of empirical observations. The main epidemiological measures available for the validation of epidemic models are inherently based on records of clinical disease or age serological surveys, which are not explicitly representative of infection and provide a very limited observation of the full system state. The analyses suggest that these issues give rise to problems of indeterminacy even in the most simple models, such that certain system characteristics cannot be uniquely estimated from available data.EThOS - Electronic Theses Online ServiceUniversity of Warwick. Dept. of EngineeringEngineering and Physical Sciences Research Council (EPSRC)GBUnited Kingdo

The input–output relationship approach to structural identifiability analysis

Analysis of the identifiability of a given model system is an essential prerequisite to the determination of model parameters from physical data. However, the tools available for the analysis of non-linear systems can be limited both in applicability and by computational intractability for any but the simplest of models. The input–output relation of a model summarises the input–output structure of the whole system and as such provides the potential for an alternative approach to this analysis. However for this approach to be valid it is necessary to determine whether the monomials of a differential polynomial are linearly independent. A simple test for this property is presented in this work. The derivation and analysis of this relation can be implemented symbolically within Maple. These techniques are applied to analyse classical models from biomedical systems modelling and those of enzyme catalysed reaction schemes

The input-output relationship approach to structural identifiability analysis

Analysis of the identifiability of a given model system is an essential prerequisite to the determination of model parameters from physical data. However, the tools available for the analysis of non-linear systems can be limited both in applicability and by computational intractability for any but the simplest of models. The input-output relation of a model summarises the input-output structure of the whole system and as such provides the potential for an alternative approach to this analysis. In order for this approach to be valid it is necessary to determine whether the monomials of a differential polynomial are linearly independent. A simple test for this property is presented in this work. The derivation and analysis of this relation can be implemented symbolically within Maple either using the built-in Rosenfeld_Groebner algorithm or via the observability normal form, an alternative representation of the model derived from observability criteria. These techniques are applied to analyse models of two reaction schemes. Such systems form the building blocks of metabolic pathway models which are increasingly used in drug discovery and development