Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches

Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery

Input estimation for extended-release formulations exemplified with exenatide

Estimating the in vivo absorption profile of a drug is essential when developing extended-release medications. Such estimates can be obtained by measuring plasma concentrations over time and inferring the absorption from a model of the drug’s pharmacokinetics. Of particular interest is to predict the bioavailability—the fraction of the drug that is absorbed and enters the systemic circulation. This paper presents a framework for addressing this class of estimation problems and gives advice on the choice of method. In parametric methods, a model is constructed for the absorption process, which can be difficult when the absorption has a complicated profile. Here, we place emphasis on non-parametric methods that avoid making strong assumptions about the absorption. A modern estimation method that can address very general input-estimation problems has previously been presented. In this method, the absorption profile is modeled as a stochastic process, which is estimated using Markov chain Monte Carlo techniques. The applicability of this method for extended-release formulation development is evaluated by analyzing a dataset of Bydureon, an injectable extended-release suspension formulation of exenatide, a GLP-1 receptor agonist for treating diabetes. This drug is known to have non-linear pharmacokinetics. Its plasma concentration profile exhibits multiple peaks, something that can make parametric modeling challenging, but poses no major difficulties for non-parametric methods. The method is also validated on synthetic data, exploring the effects of sampling and noise on the accuracy of the estimates

In situ etching for total control over axial and radial nanowire growth

We report a method using in situ etching to decouple the axial from the radial nanowire growth pathway, independent of other growth parameters. Thereby a wide range of growth parameters can be explored to improve the nanowire properties without concern of tapering or excess structural defects formed during radial growth. We demonstrate the method using etching by HCl during InP nanowire growth. The improved crystal quality of etched nanowires is indicated by strongly enhanced photoluminescence as compared to reference nanowires obtained without etching

Input estimation in nonlinear dynamical systems for drug-discovery applications.

In mathematical modelling for drug discovery, nonparametric methods are an alternative to the more commonly used parametric methods, and have the advantage of requiring fewer modelling assumptions. This thesis considers nonparametric methods for performing input estimation (deconvolution) -- inferring the input to a dynamical system based on measurements of the system’s state. A typical application is to determine the absorption profile of an orally administered drug. Commonly used input-estimation methods are restricted to system models that are linear. This thesis aims to develop and evaluate methods which can be applied to nonlinear systems, and which are additionally able to provide uncertainty estimates. An input-estimation method is considered to be a particular choice of 1) prior, 2) function parameterisation, 3) desired statistical quantity, and 4) estimation algorithm. Two classes of methods have been selected and implemented: direct optimal-control methods and Markov chain Monte Carlo (MCMC) methods. These have been evaluated on two pharmacokinetic and two body-weight modelling applications, using simulated as well as real data. Evaluation was based on several criteria, including accuracy, computational speed, and usability. The results show that the methods can achieve good accuracy, provided that data are relatively densely sampled. Properly applied, optimal-control methods can achieve very high speed, approximately 0.1s for typical problems, at the expense of not providing uncertainty estimates. For MCMC methods, the performance is highly dependent on the method settings as well as on the problem. In many cases, MCMC running times can be significantly reduced by a suitable choice of function parameterisation and sampling method. In all cases, estimation is based on clearly stated, quantifiable assumptions

Lipomatous hypertrophy of the interatrial septum in a patient with carcinoma: a case report of the importanceof multi-modality imaging.

Introduction: Lipomatous hypertrophy of the interatrial cardiac septum is a benign disorder. In rare cases, the disorder can cause obstruction of atrial inflow, causing symptoms of heart failure, or cardiac arrhythmias resulting from the involvement of the atrial wall and atrioventricular conduction pathways. Case presentation: We present a case of a Caucasian 66-year-old man with urothelial carcinoma where transthoracic echocardiolography showed a mass in the basal part of the interatrial septum. After injection of echo contrast, it was suggested that the structure was vascularized, thus implying tumour. Transoesophageal echocardiography and cardiac magnetic resonance imaging gave the correct diagnosis of lipomatous hypertrophy. It was then discovered that the patient had been referred to a computed tomography (CT) earlier, but no mention of the mass was found in the report from the examination. Re-evaluation of the images showed a clearly visible mass indicative of fatty tissue. Conclusion: This case report highlights the importance of multi-modality imaging when the findings are not concordant. Moreover, this case report also highlights the importance of careful examination of the heart on routine CT scans, something that is often overlooked by the radiologists. In this case, the CT scan clearly indicated the diagnosis of lipomatous hypertrophy of the interatrial septum and thus could have prevented the subsequent imaging cascade

Naturally occurring radioactivity in some Swedish concretes and their constituents - Assessment by using I-index and dose-model

The reference level for effective dose due to gamma radiation from building materials and constructionproducts used for dwellings is set to 1 mSv per year (EC, 1996, 1999), (CE, 2014). Given the specificconditions presented by the EC in report 112 (1999) considering building and construction materials, anI-index of 1 may generate an effective dose of 1 mSv per year. This paper presents a comparison of theactivity concentrations of 40K, 226Ra and 232Th of aggregates and when these aggregates constitute a partof concrete. The activity concentration assessment tool for building and construction materials, the Iindex,introduced by the EC in 1996, is used in the comparison. A comparison of the I-indices values arealso made with a recently presented dose model by Hoffman (2014), where density variations of theconstruction material and thickness of the construction walls within the building are considered. Therewas a ~16e19% lower activity index in concretes than in the corresponding aggregates. The model byHoffman further implies that the differences between the I-indices of aggregates and the concretes' finaleffective doses are even larger. The difference is due, mainly to a dilution effect of the added cement withlow levels of natural radioisotopes, but also to a different and slightly higher subtracted backgroundvalue (terrestrial value) used in the modeled calculation of the revised I-index by Hoffman (2014). Onlyvery minimal contributions to the annual dose could be related to the water and additives used, due tot heir very low content of radionuclides reported.QC 20210428</p