Approximations of the Fisher information for the construction of efficient experimental designs in nonlinear mixed effects models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

Experimental design for mixed models with application to population pharmacokinetic studies

experimental design, mixed model, random coefficient regression model, population pharmacokinetics, approximate design

Modeling and simulation of population balances for particulate processes

This work focuses on the modeling and numerical approximations of population balance equations (PBEs) for the simulation of different phenomena occurring in process engineering. The population balance equation (PBE) is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models the one independent variable represents the time, the other(s) are property coordinate(s), e.g., the particle volume (size) in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes such as granulation, crystallization, polymerization, emulsion and cell dynamics. The semi-discrete high resolution schemes are proposed for solving PBEs modeling one and two-dimensional batch crystallization models. The schemes are discrete in property coordinates but continuous in time. The resulting ordinary differential equations can be solved by any standard ODE solver. To improve the numerical accuracy of the schemes a moving mesh technique is introduced in both one and two-dimensional cases ...

Development and Validation of Predictive Models of Cardiac Mortality and Transplantation in Resynchronization Therapy

AbstractBackground:30-40% of cardiac resynchronization therapy cases do not achieve favorable outcomes.Objective:This study aimed to develop predictive models for the combined endpoint of cardiac death and transplantation (Tx) at different stages of cardiac resynchronization therapy (CRT).Methods:Prospective observational study of 116 patients aged 64.8 ± 11.1 years, 68.1% of whom had functional class (FC) III and 31.9% had ambulatory class IV. Clinical, electrocardiographic and echocardiographic variables were assessed by using Cox regression and Kaplan-Meier curves.Results:The cardiac mortality/Tx rate was 16.3% during the follow-up period of 34.0 ± 17.9 months. Prior to implantation, right ventricular dysfunction (RVD), ejection fraction < 25% and use of high doses of diuretics (HDD) increased the risk of cardiac death and Tx by 3.9-, 4.8-, and 5.9-fold, respectively. In the first year after CRT, RVD, HDD and hospitalization due to congestive heart failure increased the risk of death at hazard ratios of 3.5, 5.3, and 12.5, respectively. In the second year after CRT, RVD and FC III/IV were significant risk factors of mortality in the multivariate Cox model. The accuracy rates of the models were 84.6% at preimplantation, 93% in the first year after CRT, and 90.5% in the second year after CRT. The models were validated by bootstrapping.Conclusion:We developed predictive models of cardiac death and Tx at different stages of CRT based on the analysis of simple and easily obtainable clinical and echocardiographic variables. The models showed good accuracy and adjustment, were validated internally, and are useful in the selection, monitoring and counseling of patients indicated for CRT.

Simulations for modelling of population balance equations of particulate processes using the discrete particle model (DPM)

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Numerical investigation of micro and macro mechanical behaviour of granular media via a discrete element approach

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Optimal designs for mixed effects poisson regression models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Simulation of interacting populations in inhomogeneous flows using reduced models

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2010

Conversive Hidden non-Markovian models

Magdeburg, Univ., Fak. für Informatik, Diss., 2012

Analysis and numerical investigation of dynamic models for liquid chromatography

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Optimal designs for multivariate linear models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Mathematical models of influenza A virus infection : from intracellular replication to virus growth in cell populations

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2015

Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Optimal designs for the prediction in hierarchical random coefficient regression models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

Analysis of animal models of neurodegenerative diseases with protein deposits

Otto-von-Guericke-Universität Magdeburg, Fakultät für Naturwissenschaften, Univ., Dissertation, 2016