On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy

summary:A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence of that parameter on the solution of the model's system of ordinary differential equations is given and it is pointed out that some ingredients of the analysis might be useful for more general pharmacodynamic models. Numerical experiments are presented to illustrate the performance of related parameter estimation procedures based on least-squares minimization

Improving Triangular Preconditioner Updates for Nonsymmetric Linear Systems

Abstract. We present an extension of an update technique for preconditioners for sequences of non-symmetric linear systems that was proposed in [5]. In addition, we describe an idea to improve the implementation of the update technique. We demonstrate the superiority of the new approaches in numerical experiments with a model problem.

Modern methods for solving linear systems.

In the thesis we show that we can accelerate the convergence speed of restarted GMRES processes with the help of rank-one updated matrices of the form A - byT, where A is the system matrix, b is the right-hand side and y is a free parameter vector. Although some attempts to improve projection methods with rank-one updates of a different form have been undertaken, our approach, based on the Sherman-Morrison formula, is new. It allows to solve a parameter dependent auxiliary problems with the same right-hand side but a different system matrix. Regardless of the properties of A we can force any convergence speed of the second system when the initial guess is zero. Moreover, reasonable convergence speed of the second system is able to overcome stagnation of the original problem. This has been tested on different kinds of problems from practice.Available from STL Prague, CZ / NTK - National Technical LibrarySIGLECZCzech Republi

Krylov methods for nonsymmetric linear systems: from theory to computations

This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing.The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations