Browsing by Subject "Mathematical Modeling"
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Item Experimental and computational investigations of therapeutic drug release from biodegradable poly(lactide-co-glycolide) (plg) microspheres(2009-05-15) Berchane, Nader SamirThe need to tailor release-rate profiles from polymeric microspheres remains one of the leading challenges in controlled drug delivery. Microsphere size, which has a significant effect on drug release rate, can potentially be varied to design a controlled drug delivery system with desired release profile. In addition, drug release rate from polymeric microspheres is dependent on material properties such as polymer molecular weight. Mathematical modeling provides insight into the fundamental processes that govern the release, and once validated with experimental results, it can be used to tailor a desired controlled drug delivery system. To these ends, PLG microspheres were fabricated using the oil-in-water emulsion technique. A quantitative study that describes the size distribution of poly(lactide-coglycolide) (PLG) microspheres is presented. A fluid mechanics-based correlation that predicts the mean microsphere diameter is formulated based on the theory of emulsification in turbulent flow. The effects of microspheres? mean diameter, polydispersity, and polymer molecular weight on therapeutic drug release rate from poly(lactide-co-glycolide) (PLG) microspheres were investigated experimentally. Based on the experimental results, a suitable mathematical theory has been developed that incorporates the effect of microsphere size distribution and polymer degradation on drug release. In addition, a numerical optimization technique, based on the least squares method, was developed to achieve desired therapeutic drug release profiles by combining individual microsphere populations. The fluid mechanics-based mathematical correlation that predicts microsphere mean diameter provided a close fit to the experimental results. We show from in vitro release experiments that microsphere size has a significant effect on drug release rate. The initial release rate decreased with an increase in microsphere size. In addition, the release profile changed from first order to concave-upward (sigmoidal) as the microsphere size was increased. The mathematical model gave a good fit to the experimental release data. Using the numerical optimization technique, it was possible to achieve desired release profiles, in particular zero-order and pulsatile release, by combining individual microsphere populations at the appropriate proportions. Overall, this work shows that engineering polymeric microsphere populations having predetermined characteristics is an effective means to obtain desired therapeutic drug release patterns, relevant for controlled drug delivery.Item Quantitative Modeling and Estimation in Systems Biology using Fluorescent Reporter Systems(2013-12-10) Bansal, LoveleenaBuilding quantitative models of biological systems is a challenging task as these models can consist of a very large number of components with complex interactions between them and the experimental data available for model validation is often sparse and noisy. The focus in this work is on modeling and parameter estimation of biological systems that are monitored using fluorescent reporter systems. Fluorescent reporter systems are widely used for various applications such as monitoring gene expression, protein localization and protein-protein interactions. This dissertation presents various techniques to facilitate modeling of biological systems containing fluorescent reporters with special attention given to challenges arising due to limited experimental data, simultaneous monitoring of multiple events and variability in the observed response due to phenotypic differences. First, an inverse problem is formulated to estimate the dynamics of transcription factors, a crucial molecule that initiates the transcription process, using data of fluorescence intensity profiles obtained from a fluorescent reporter system. The resulting inverse problem is ill-conditioned and it is solved with the aid of regularization techniques. The main contribution is that, with the presented technique, any complex dynamics of transcription factors can be estimated using limited data of fluorescence measurements. The technique has been evaluated using simulated data as well as experimental data of a GFP reporter system of STAT3. Second, an experimental design formulation is developed to facilitate the use of multiple fluorescent reporters, with overlapping emission spectra, in the same experiment. This work develops a criterion to select the fluorescent proteins for simultaneous use such that the accuracy in the estimated contributions of individual proteins to the overall observed intensity is maximized. This technique has been validated using mixtures of different E. coli strains which express different fluorescent proteins. Finally, a population balance model of a cell population containing a fluorescence reporter system is developed to describe the variability in the observed fluorescence in cells. Factors such as rate of fluorescent protein formation as well as partitioning of the fluorescent protein on cell division have been taken into account to describe the dynamics of fluorescence intensity distributions in the cell populations. The model has been used to obtain preliminary hypotheses to explain the difference in response of HeLa cells containing the Tet-on expression system on stimulation by different levels doxycycline. Thus, this work describes techniques for building robust predictive models of biological systems such as regularization for solving ill-posed estimation problems, experimental design techniques as well as using population balance modeling to model complex multi-scale dynamics. Moreover, while the examples discussed here are motivated for fluorescent reporter systems, the developed techniques can be used for different kinds of linear or non-linear dynamic biological systems.