In this dissertation, I consider the problem of model reduction in both oscillatory and networked systems. Previously, the Manifold Boundary Approximation Method (MBAM) has been demonstrated as a data-driven tool for reducing the parametric complexity of so-called sloppy models. To be effective, MBAM requires the model manifold to have low curvature. I show that oscillatory models are characterized by model manifolds with high curvature in one or more directions. I propose methods for transforming the model manifolds of these models into ones with low curvature and demonstrate on a couple of test systems. I demonstrate MBAM as a tool for data-driven network reduction on a small model from power systems. I derive multiple effective networks for the model, each tailored to a specific choice of system observations. I find several important types of parameter reductions, including network reductions, which can be used in large power systems models. Finally, I consider the problem of piecemeal reduction of large systems. When a large system is split into pieces that are to be reduced separately using MBAM, there is no guarantee that the reduced pieces will be compatible for reassembly. I propose a strategy for reducing a system piecemeal while guaranteeing that the reduced pieces will be compatible. I demonstrate the reduction strategy on a small resistor network.

OBJECTIVE: Type 2 diabetes (T2D), the most common type of diabetes characterized by high blood glucose and insulin resistance, results from both genetic and environmental factors. Our lab has proposed that chronic excess nutrients induce insulin hypersecretion from the pancreatic ß-cell, contributing to hyperinsulinemia, a prequel to T2D. Normal glucose-stimulated insulin secretion (GSIS) is oscillatory, a feature that is lost in patients with T2D. In this thesis we examine the oscillatory secretion profiles of clonal pancreatic ß-cells cultured in normal and excess nutrients that mimic conditions of T2D. We also begin to examine oscillations in protein phosphorylation that may contribute to normal ß-cell metabolism and GSIS, but if altered might potentially lead to impaired insulin secretion. METHODS: Nutrient regulation of oscillatory insulin release was studied in clonal pancreatic β-cells (INS-1) cultured in multiwell plates in both low (4 mM) and high (11 mM) glucose. Insulin secretion was stimulated in cells from multiwell plates one well at a time at 30 sec intervals and sampled simultaneously at the end of the timecourse. Insulin secretion and insulin content were measured using a homogenous time-resolved fluorescence (HTRF) insulin kit (Cisbio). Protein was extracted from these same cells for analysis of time-dependent phosphorylation by western blot using specific antibodies. Protein phosphorylation was detected using SuperSignal West Femto chemiluminescence reagent (ThermoFisher) and imaged on an iBright Imaging System (Invitrogen). RESULTS: Insulin secretion from INS-1 cells grown in separate plates and in 4 mM glucose oscillated with a period of 8.2  0.5 min compared to 5.0  0.5 min in cells cultured at 11 mM glucose. The amplitude of oscillations was 40.4  11.5 and 14.6  1.5 for cells cultured in 4 and 11 mM glucose respectively. Oscillations in secretion from cells cultured in 4 and 11 mM glucose in the same plate were not different in period but different in amplitude due in part to reduced insulin content. Oscillation in the phosphorylation patterns of acetyl-CoA carboxylase (ACC) and myristoylated alanine rich C kinase substrate (MARCKS) were measured in cells cultured in 4 mM glucose and both exhibited a peak in phosphorylation that occurred at the nadir of the insulin oscillation between peaks of insulin release. CONCLUSION: Insulin secretion from pancreatic ß-cells is affected by nutrient status as excess nutrients decrease the amplitude of oscillations in insulin release. The period of oscillations can also be affected. Oscillations in protein phosphorylation are consistent with both ACC and MARCKS contributing to normal GSIS. These initial studies provide evidence of the suitability of this model system to correlate oscillations in protein activity to exocytosis. Future studies focused on the effects of low and high glucose will potentially reveal new important therapeutic targets that may help prevent/reverse/ameliorate insulin hypersecretion leading to insulin resistance and T2D.

No description available.

<p> The inter/intramolecular interactions and associations between constituents determine the microstructure of food and its response to mechanical deformation and flow. The characterization of food rheology enables the design of efficient processing equipment, production of high-quality, stable end products, prediction of textural and sensorial attributes, and assurance of consumer acceptability. Foods are subjected to rapid and large deformations during processing operations and consumption. Dynamic oscillatory shear tests are carried out by subjecting food to a sinusoidal deformation (or stress) and probing the mechanical stress (or strain) and recording the response as a function of time. In the SAOS region, the mechanical response is in the form of a perfect sinusoidal curve and interpretation is straightforward as expected from a linear model. On the other hand, LAOS response requires complex mathematical relations to extract meaningful rheological parameters. In this dissertation, Fourier Transform-Chebyshev Decomposition (FTC) and Sequence of Physical Processes (SPP) methods were utilized to quantify the LAOS response of selected food materials. The objective of this study is to gain new insights into the nonlinear rheology and structural architecture of food materials. To offer insights into the microstructure–rheology relations, rheological measurements were accompanied by various techniques probing chemical interactions (FTIR), imaging (Cryo-SEM, SEM), quantitative network analysis, and molecular size (SDS-PAGE). This dissertation showed that LAOS rheology is highly correlated with the network structure of food shown by the quantitative network analysis utilizing SEM images. It is a powerful tool to detect the effect of small molecules on the nonlinear rheology of food (HMW-LMW glutenin ratio, gliadin for dough, fat content in yogurt, and amylopectin/amylose ratio of starch in a suspension). Nonlinear parameters were sensitive to structural changes occurring in dough structure during processing conditions including aging at room and elevated temperatures. Lastly, the SPP method enabling time-resolved interpretation of nonlinear rheology provided detailed transient microstructural interpretations whereas the FTC method gave static measures at specific strains in an oscillation cycle. Thus, nonlinear rheology of doughs with various gluten subfractions in MAOS and LAOS regions as well as shear thickening characteristic of starch suspensions with changing amylopectin/amylose ratio interpreted by the SPP method gave more sensitive results than the FTC method. The application of fundamental knowledge from this work can be a guide to evaluating the architecture and nonlinear rheology of food for the assurance of consumer acceptancy and the fabrication of efficient machinery by building more accurate mechanical models of complex food systems. </p>

This project addresses characterization of the material properties of aortic tissue. Understanding of these properties is important for a variety of studies including tissue engineering, effects of aging and diseases, stents engineering, and traumatic aorta rupture. The goal of the presented research was to characterize the stress-strain relationship of aorta in dynamic oscillatory biaxial loading. A setup was developed that supplied pressure loading from the physiological to sub-failure levels (between 7 and 76 kPa) to porcine aorta at frequencies ranging from 0.50Hz to 5.00Hz. Samples tested were constrained at both ends while the deformation and the pressure were recorded. Volumetric strain versus pressure was used to characterize the structural behavior of the material which showed frequency dependency and hysteresis indicating viscoelastic response. An offset method was developed to account for drifting behavior exhibited by some of the samples. The structural behavior of aorta was modeled using a quasi-linear viscoelastic (QLV) creep theory. The QLV model included a logarithmic steady state elastic function v = 0.663 +/- 0.040 + 0.241 +/- 0.011 ln(P) for pressure in kPa, and a Prony series creep function ( J0 = 0.472 +/- 0.021, J2 = 0.109 +/- 0.060, J3 = 0.419 +/- 0.056). Modeling results were then used to determine the relationships between the circumferential and longitudinal stresses and strains of the material. The results exhibited that the stress in the transverse direction was about 1.5 times larger than in the axial direction. However, in the axial direction material was stiffer and the deformation was 30% less. The relaxation function of the material was determined by linearizing the non-linear component of the QLV model and applying to it the linear viscoelastic theory. Furthermore, literature comparison revealed that aorta's creep function, as well as its elastic modulus, is within the range of what has been reported in the literature. In conclusion, an experimental model was developed that can be used to predict the behavior of porcine aorta under physiological and sub-failure conditions at quasi-static and dynamic loading. / Mechanical Engineering

Oscillatory states in the Electroencephalogram (EEG) reflect the rhythmic synchronous activation in large networks of neurons. Time-frequency methods quantify the spectral content of the EEG as a function of time. As such, they are well suited as tools for the study of spontaneous and induced changes in oscillatory states. We have used time-frequency techniques to analyze the flow of activity patterns between two strongly connected brain structures: the entorhinal cortex and the hippocampus, which are believed to be involved in information storage. EEG was recorded simultaneously from the entorhinal cortex and the hippocampus of behaving rats. During the recording, low-intensity trains of electrical pulses at frequencies between 1 and 40 Hz were applied to the olfactory (piriform) cortex. The piriform cortex projects to the entorhinal cortex, which then passes the signal on to the hippocampus. Several time-frequency methods, including the short-time Fourier transform (STFT), Wigner-Ville distribution (WVD) and multiple window (MW) time-frequency analysis (TFA), were used to analyse EEG signals. To monitor the signal transmission between the entorhinal cortex and hippocampus, the time-frequency coherence functions were used. The analysed results showed that stimulation-related power in both sites peaked near 15 Hz, but the coherence between the EEG signals recorded from these two sites increased monotonically with stimulation frequency. Among the time-frequency methods used, the STFT provided time-frequency distributions not only without cross-terms which were present in the WVD, but also with higher resolutions in both time and frequency than the MW-TFA. The STFT seems to be the most suitable time-frequency method to study the stimulation-induced signals presented in this thesis. The MW-TFA, which gives low bias and low variance estimations of the time-frequency distribution when only one realization of data is given, is suitable for stochastic and nonstationary signals such as spontaneous EEG. We also compared the performance of the MW-TFA using two different window functions: Slepian sequences and Hermite functions. By carefully matching the two window functions, we found no noticeable difference in time-frequency plane between them. / Thesis / Master of Engineering (ME)

Heart valve tissue engineering (HVTE) stands as a potential intervention that could reduce the prevalence of congenital heart valve disease in juvenile patients. Prior studies in our laboratory have utilized mechanobiological testing to quantify the forces involved in the development of heart valve tissue, utilizing a Flow-Stretch-Flexure (FSF) bioreactor to condition bone marrow stem cells (BMSCs)-derived valve tissue. Simulations have demonstrated that certain sets of flow conditions can introduce specific levels of oscillatory shear stress (OSS)-induced stimuli, augmenting the growth of engineered valves as well as influencing collagen formation, extracellular matrix (ECM) composition and gene expression. The computational findings discussed in this thesis outline the methods in which flow conditions, when physiologically relevant, induce specific oscillatory shear stresses which could not only lead to an optimized valve tissue phenotype (at 0.18≤ OSI≤ 0.23), but could identify native valve tissue remodeling indicative of aortic valve disease.

No description available.

The performance evaluation and parametric studies of an Inertance Tube Pulse Tube Refrigerator (IPTR) are performed for different length-to-diameter ratios, with the Computational Fluid Dynamics (CFD) package FLUENT. The integrated model consists of individual models of the components, namely, the compressor, compressor cooler, regenerator, cold heat exchanger, pulse tube, warm heat exchanger, inertance tube and the reservoir. The formulation consists of the governing equations expressing the conservation of mass, momentum and energy with axi-symmetry assumption and relations for the variable thermophysical properties of the working medium and the regenerator matrix, and friction factor and heat transfer coefficients in oscillatory flows. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of heat exchangers and the regenerator which are treated as porous zones. In addition, the wall thickness of the components is also accounted for. Dynamic meshing is used to model the compressor zone. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the overall performance. The thermal non-equilibrium results in a higher cold heat exchanger temperature due to inefficiencies. The dynamic characteristics of pulse tube are analyzed by introducing a time constant. The study is extended to other types of PTRs, namely, the Orifice type Pulse Tube Refrigerator (OPTR), Double Inlet type Pulse Tube Refrigerator (DIPTR) and a PTR with parallel combination of inertance tube and orifice (OIPTR). The focus of the second phase of analysis is the pulse tube region. The oscillatory flow and temperature fields in an open-ended pipe driven by a time-wise sinusoidally varying pressure at one end and subjected to an ambient-to-cryogenic temperature difference across the ends, is numerically studied both with and without the inclusion of buoyancy effects. Conjugate effects arising out of the interaction of oscillatory flow with heat conduction in the pipe wall are taken into account by considering a finite thickness wall with an insulated exterior surface. Parametric studies are conducted with frequencies in the range 5-15 Hz for an end-to-end temperature difference of 200 K. As the pressure amplitude increases, the temperature difference between the wall and the fluid decreases due to mixing at the cold end. The pressure amplitude and the frequency have negligible effect on the time averaged Nusselt number. The effect of buoyancy is studied for hot side up and cold side up configurations. It is found that the time averaged Nusselt number does not change significantly with orientation or Rayleigh number. Sharp changes in Nusselt number and velocity profiles and an increase in energy transfer through solid and gas were observed when natural convection comes into play with hot end placed down. Cooldown experiments are conducted on a preliminary experimental setup. Comparison of the numerical and experimental cooldown curves disclosed a number of areas where improvement is required, primarily the leakage past the piston and the design of the heat exchangers. The setup is being improved to bring out a second and improved version for attaining the lower cold heat exchanger temperature.

Utilizando uma faixa de temperatura entre 5° a 45°C, observou-se duas regiões de diferentes tendências para com o aumento da temperatura durante as oscilações (eletro-oxidação galvanostática, mesma corrente normalizada aplicada) no sistema ácido fórmico sobre platina policristalina em meio ácido. Até 25°C, o comportamento cinético operou de modo convencional, do tipo Arrhenius, sendo que acima desse ponto crítico observou-se o fenômeno de (sobre)compensação de temperatura. O sistema foi caracterizado fazendo uso de técnicas eletroquímicas clássicas e espectroscopia de impedância eletroquímica tendo ficado evidente um ponto de inflexão a 25°C que marca uma quebra na tendência em todas as frequências do sistema (f, Hopf,Sosc) e taxa de envenenamento. Os resultados foram discutidos em termos do papel-chave das espécies de PtO, que acoplam quimicamente as dinâmicas rápidas/lentas. Fomos capazes de: (i) identificar a competição entre duas etapas de reação como responsáveis pelos dois domínios de temperatura; (ii) comparar as energias de ativação relativas dessas duas etapas; E ademais (iii) especulamos sobre o papel de uma determinada etapa de reação no conjunto de reações responsáveis pelo aumento do período oscilatório. Com ajuda de métodos deconvolutivos, reforçamos a hipótese de que as etapas por trás do drift possuem menor energia de ativação que as etapas LH durante tais dinâmicas. Também estão aqui discutidos experimentos de monitoramento de temperatura local durante as dinâmicas oscilatórias. Duas estratégias experimentais foram empregadas: uma utilizando eletrodos-termômetros a base de termistores e outra utilizando um micro calorímetro onde sensores piroelétricos monitoraram as oscilações na temperatura do eletrodo de trabalho, altamente em fase com as oscilações de potencial. Destacamos que ambas configurações foram capazes de acompanhar as diferenças de temperatura durante as dinâmicas oscilatórias (na faixa de 0,1&#126;0,5mK por ciclo). Os resultados obtidos para a reconstrução dos fluxos de calor (&#248;) corroboram com o atual modelo mecanístico da eletro-oxidação oscilante de ácido fórmico em Pt em meio ácido. Observamos que as etapas de envenenamento do eletrodo são acompanhadas pelo aumento no &#248; enquanto a reativação do eletrodo é acompanhada pela diminuição no &#248;. / The oscillating electro-oxidation of formic acid on polycrystalline platinum in acidic media, as a model system, was employed to investigate the temperature effects on the coupling of fast and slow dynamics processes belonging to its oscillatory dynamics, i.e. the core oscillator (fast dynamics) and the slow term deactivation of surface caused by the oxygen place-exchange process. Using a temperature range from 5 to 45°C, we observed two disparate regions of tendencies upon temperature increment on the galvanostatic oxidation. The system exhibits conventional Arrhenius behavior for T up to 25°C and, on the other hand, T &gt; 25° revealed the occurrence of temperature (over)compensation. The system was characterized by means of conventional electrochemical techniques and electrochemical impedance spectroscopy. Clearly, we observed an inflexion point at 25°C marked by a break on the tendency of oscillatory frequency ( f, hopf, Sosc) and poisoning rates. Results were discussed in terms of the key role of PtO species, which chemically couple slow and fast dynamics. In summary we were able to: (i) identify the competition between two reaction steps as responsible for the two temperature domains; (ii) compare the relative activation energies of these two steps; and (iii) suggest the role of a given reaction step on the period-increasing set of reactions involved in the oscillatory dynamics. In addition, we performed experiments to monitor the local temperature of the interface during oscillatory dynamics. Two experimental strategies were applied: low cost thermometers-electrodes and a more sophisticated experimental set up based on pyroelectric detection. It should be noted that both configurations were able to monitor temperature differences during oscillatory dynamics (in the range of 0.1 &#126; 0.5mK per cycle). The results obtained for the reconstruction of the heat fluxes (&#248;) corroborate with the current mechanistic model of the oscillating electro-oxidation of formic acid in Pt in acidic medium. We observed that the poisoning stages of the electrode are accompanied by the increase in &#248; while the reactivation of the electrode is accompanied by the decrease in &#248;.