Browsing by Subject "Mathematical modeling"
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Item Open Access A Multi-Disciplinary Systems Approach for Modeling and Predicting Physiological Responses and Biomechanical Movement Patterns(2017) Mazzoleni, MichaelIt is currently an exciting time to be doing research at the intersection of sports and engineering. Advances in wearable sensor technology now enable large quantities of physiological and biomechanical data to be collected from athletes with minimal obstruction and cost. These technological advances, combined with an increased public awareness of the relationship between exercise, fitness, and health, has created an environment where engineering principles can be integrated with biomechanics, exercise physiology, and sports science to dramatically improve methods for physiological assessment, injury prevention, and athletic performance.
The first part of this dissertation develops a new method for analyzing heart rate (HR) and oxygen uptake (VO2) dynamics. A dynamical system model was derived based on the equilibria and stability of the HR and VO2 responses. The model accounts for nonlinear phenomena and person-specific physiological characteristics. A heuristic parameter estimation algorithm was developed to determine model parameters from experimental data. An artificial neural network (ANN) was developed to predict VO2 from HR and exercise intensity data. A series of experiments was performed to validate: 1) the ability of the dynamical system model to make accurate time series predictions for HR and VO2; 2) the ability of the dynamical system model to make accurate submaximal predictions for maximum heart rate (HRmax) and maximal oxygen uptake (VO2max); 3) the ability of the ANN to predict VO2 from HR and exercise intensity data; and 4) the ability of a system comprising an ANN, dynamical system model, and heuristic parameter estimation algorithm to make submaximal predictions for VO2max without requiring VO2 data collection. The dynamical system model was successfully validated through comparisons with experimental data. The model produced accurate time series predictions for HR and VO2 and, more importantly, the model was able to accurately predict HRmax and VO2max using data collected during submaximal exercise. The ANN was successfully able to predict VO2 responses using HR and exercise intensity as system inputs. The system comprising an ANN, dynamical system model, and heuristic parameter estimation algorithm was able to make accurate submaximal predictions for VO2max without requiring VO2 data collection.
The second part of this dissertation applies a support vector machine (SVM) to classify lower extremity movement patterns that are associated with increased lower extremity injury risk. Participants for this study each performed a jump-landing task, and experimental data was collected using two video cameras, two force plates and a chest-mounted single-axis accelerometer. The video data was evaluated to classify the lower extremity movement patterns of the participants as either excellent or poor using the Landing Error Scoring System (LESS) assessment method. Two separate linear SVM classifiers were trained using the accelerometer data and the force plate data, respectively, with the LESS assessment providing the classification labels during training and evaluation. The same participants from this study also performed several bouts of treadmill running, and an additional set of linear SVM classifiers were trained using accelerometer data and gyroscope data to classify movement patterns, with the LESS assessment again providing the classification labels during training and evaluation. Both sets of SVM's performed with a high level of accuracy, and the objective and autonomous nature of the SVM screening methodology eliminates the subjective limitations associated with many current clinical assessment tools.
Item Open Access An Experimental and Quantitative Analysis of E. coli Stress Response: Metabolic and Antibiotic Stressors(2014) Jalli, Inderpreet SinghA series of experiments and mathematical models explore the response of the bacteria E. coli to stressors. Experimentally, the effect of L-homocysteine, a non-protein amino acid, is explored, and via math models, the effect of trimethoprim, a common antibiotic, is also explored. Previous work on L-homocysteine labels it a stressor, and this assertion is refined via the presented work. A mathematical model that improves on a previous work published by Kwon et al. (2008) explores the response of E. coli to various supplementations of amino acids when exposed to trimethoprim. New methods of developing antibiotics and therapeutic drug treatments are also explored.
Item Open Access Analysis of the Stability and Response of Deep-Seated Landslides by Monitoring their Basal Temperature(2020) Seguí, CarolinaDeep-seated landslides are known as large slides involving millions of cubic meters that move as a rigid block on top of a deep (below the roots of the trees and the groundwater level) basal layer of heavily deformed minerals. This kind of landslides geometrically shears as translational/rotational (depending on the stratigraphy of the area), with very low velocities (cm/year) during long periods (years to tens of years). However, their collapse is usually very sudden, happening within minutes and without previous warning, reaching high velocities up to 120m/s (as the 1963 Vaiont landslide in Italy, \cite{Muller1964}). The catastrophic and fast collapse of this kind of landslides makes the evacuation of the area that is going to be affected almost impossible, thereby possibly causing fatalities and infrastructure damages. Moreover, the lack of understanding of the physical processes behind the mechanisms of failure of this kind of landslides makes the development of reliable early warning systems (or tools/protocols to stop the acceleration of the landslide) challenging, therefore potentially causing significant damages to civil infrastructures. The landslide-prone areas are widespread around the world, having a detrimental fatality rate of tens of thousands. Hence, landslides are a globally threatening natural hazard with disproportional consequences.
This thesis focuses on the understanding of the mechanism of the fast collapse of large deep-seated landslides and provides the first-stage tool for the early warning system. First, is described the Vardoulakis Forecasting Model (VFM), which is a heat energy-based mathematical model that considers that the temperature of the shear band material is critical in the behavior and stability of the landslide. The model contemplates the external and internal factors of this kind of landslide. The external factors of a landslide are considered as the loading conditions, such as groundwater level. And the internal factors of the landslide are focused on the thin shear band, such as the reduction of the friction coefficient of the material, hence, the loss of resistance of the basal material due to continuous friction and cycles of loading-unloading of external forces such as the groundwater. Moreover, the constitutive law used in the VFM theoretically implies that the material of the shear band (usually clay or clay-like material) is rate (velocity) hardening and thermal softening \cite{Vardoulakis2002}, but this assumption has never been tested experimentally. This model has been applied previously by \cite{Veveakis2007} for the case of the famous Vaiont landslide, which collapsed catastrophically in 1963 causing over 2000 fatalities. However, the study did not consider a time-dependence of the loading conditions, and the parameters of the basal material were taken from the literature. This thesis thus presents an extension of the work that the late Professor Vardoulakis and Professor Veveakis started from 2002 until 2007, by implementing the VFM to other case studies with time-dependent loading conditions. Moreover, the present thesis proves the theory that the temperature plays a critical role in the behavior of deep-seated landslides by instrumenting an active deep-seated landslide for the first time, called El Forn landslide (Andorra), with a thermometer in the shear band. The log-samples of this landslide have been studied in the laboratory in different ways, firstly in the triaxial machine to test the theoretical constitutive law of Vardoulakis that the clay material inside the shear band is rate hardening and thermal softening. The tests performed in the triaxial machine have validated for the first time that, indeed, the basal material (as a clay-like material) behaves as Vardoulakis postulated. Furthermore, micro-scale tests, such as X-Ray diffraction, SEM-EDS, MicroCT, and Plasticity Index have been performed to understand the effect of this behavior. Hence, mineralogical, textural, porosity, and plasticity results have been obtained for the samples, and, indeed exists a correlation of why the basal material is velocity and thermal sensitive.
Field data of the El Forn landslide has been obtained, such as the shear band's temperature, groundwater pressure, and displacement of the landslide. The data has demonstrated that, indeed, the temperature of the material of the shear band varies when the pressure changes, and then the landslide accelerates. The field data has shown that for this case study, the material is thermal sensitive when the water pressure varies, not when the landslide accelerates and, due to friction, the material heats.
The VFM model has been applied to four different cases, Vaiont (Italy), Shuping (Three Gorges Dam, China), Mud Creek (California, USA), and the El Forn (Andorra) landslides. The first three landslides have been implemented in the model by using literature data, and the model has reproduced with accuracy the behavior of the three landslides. Finally, the El Forn landslide has been applied to the VFM by implementing field and experimental data, thus reducing the uncertainty of the mathematical model, which accurately reproduces its behavior as well.
The VFM allows to forecast and control deep-seated landslides by using the heat-energy based mathematical model, and the constitutive law. This model works in a dimensionless form of the parameters, to avoid complications in the model by working with so many parameters. Furthermore, this unique model allows accounting in it the external loading and several parameters of the material of the shear band. By taking the heat-diffusion equation in dimensionless form, allows working with only a single dimensionless parameter, that includes the material parameters and the external loading. The single dimensionless parameter is then plotted against the temperature of the shear band (calculated by the model) and is, thus, mapped in the phase space. The phase-space is a curve calculated by the heat equation in the dimensionless form at a steady-state. It is a generic curve for all materials and allows to map the behavior of the landslide with the single dimensionless parameter against the temperature. This mapping allows to locate the creeping stage of the landslide and see if the landslide is close to collapse. Hence, the VFM can become a very useful tool to control and forecast the behavior of a deep-seated landslide and take remediation measures in time.
Item Open Access Development of a High Performance, Biological Trickling Filter to Upgrade Raw Biogas to Renewable Natural Gas Standards(2019) Dupnock, Trisha LeeUpgrading raw biogas (~60% CH4, 40% CO2, 1000-5000 ppmv H2S) to renewable natural gas (RNG) (> 97% CH4, < 2% CO2, < 4 ppmv H2S) for injection into the grid is a desirable endeavor. RNG would allow for a clean alternative to natural gas derived from fossil origin, and it also have a versatile use as a transportation fuel and source of heating energy. Current physical-chemical technologies, such as pressure swing absorption and organic chemical scrubbing, can successfully upgrade raw biogas to meet RNG standards (1,2). However, they are energy intensive, costly, and can remove fractions of methane gas along with the impurities. Recently, biological biogas upgrading technologies have emerged as a promising solution for converting raw biogas to RNG. The method relies on hydrogenotrophic methanogens to reduce the CO2 fraction of raw biogas to CH4 using H2 as the electron donor. This method is advantageous compared to traditional biogas upgrading methods because is sequesters carbon emissions while increasing the volumetric production of methane. While early studies on biological biogas upgrading in continuously stirred tank reactors were conceptually validating, hydrogen mass transfer resistance from the gas-to-liquid phase prevented fast upgrading capacities from being realized. Slow biogas upgrading rates hinder the economic feasibility of the process. Furthermore, these studies only focused on CO2 removal when in reality, other impurities, such as corrosive H2S, must also be removed before RNG injection into the natural gas pipeline.
The overall objective of this thesis research is to develop a biological trickling filter reactor that can upgrade biogas to RNG standards at fast upgrading capacities while biologically co-removing H2S. A biological trickling filter was chosen for this investigation because they are characterized by a high specific surface area for biofilm growth, high biomass density, and are known for their high overall mass transfer coefficients; all factors that contribute to high conversion rates. A proof-of-concept study validated that this approach could achieve upgrading rates that were 5 – 30 times faster than other bioreactor configurations. This finding supported further studies that aimed to investigate hydrogen mass transfer resistance specifically in a biological trickling filter reactor. This was accomplished using a highly sensitive dissolved hydrogen sensor, which collected concentrations in real-time. Using this sensor, experiments were conducted to assess mass transfer resistance in the gas and liquid films. It was discovered that there was no external resistance in the gas-film. Furthermore, the liquid phase was a main barrier for mass transfer and reducing the liquid film thickness can significantly improve biogas upgrading capacities by 20%.
In addition to laboratory experiments, a robust and conceptually correct mathematical model was developed for a biogas upgrading biological trickling filter. The model was used to provide deeper insight into process fundamental and identify biological versus mass transfer limitations in the bioreactor. The model successfully replicated complex experimental findings and confirmed that liquid transport through the bioreactor bed was faster than the rates of mass transfer and biological conversion. A sensitivity analysis revealed that the model was most sensitive to the empty bed contact time and the maximum rate of reaction. Interestingly, the mass transfer coefficient for the liquid film (kLa) did not significantly improve the biogas upgrading rate for the bioreactor. This is because the model predicts that the bulk of hydrogen mass transfer occurs from the gas to non-wetted biofilm phase.
Concluding mass transfer resistance testing and process optimization, it was demonstrated that the engineered bioreactor could successfully upgrade various biogas compositions to RNG standards. The rates achieved for these experiments (10 – 20 m3CH4 m-3 d-1) were 1.5 – 25 times faster than other comparable research studies. To determine the economic feasibility of this technology, a paper scale-up cost analysis was conducted to estimate the investment and operation costs of a biological trickling filter upgrading raw biogas (60% CH4, 40% CO2) to RNG (> 97% CH4 < 2% CO2). This was accomplished by using experimental findings to scale the dimensions and determine heating and cooling requirements based on seasonal temperatures. Cost estimates for parts were acquired through vendor quotes. The cost analysis showed that the bioreactor is economically feasible however, the H2 acquisition cost was ~ 650% of the bioreactor investment cost. This is because H2 was acquired from the electrolysis of excess wind and solar energy and the cost of the hydrolyzer was ~ $1,000,000. Despite this significant cost, the total amortized cost of the biological biogas upgrading system was comparable to current physical-chemical upgrading technologies.
The final study of this thesis investigated the potential to biologically co-treat CO2 and H2S using nitrate as the terminal electron donor. Since the addition of nitrate favored undesired oxidation-reduction reaction pathways with hydrogen, a method was developed to map electron transfers. The effect of nitrate on methanogensis was tested with and without sulfur oxidizing bacteria. Under both conditions, nitrate had a negative impact on methanogenesis and ultimately, prevented co-treatment from being achieved. While attempting to co-treat H2S and CO2, it was discovered that dissimilatory nitrate reduction to ammonium was favored over denitrification. The electron balance confirmed that a competition for electrons from hydrogen did exist. This competition required N:S feeding ratios upwards of 16:1, which far exceeded the theoretical ratios of (4:1) for denitrifying bacteria. While the high nitrate loading rates allowed for high H2S removal efficiencies (98%), they inhibited methanogenesis so that carbon dioxide removal efficiencies did not meet RNG standards. Thus, future work should focus on alternative electron donors for sulfur oxidation and quantifying methanogenesis inhibition caused by sulfur-oxidation/denitrification pathways.
Item Open Access Drivers of Dengue Within-Host Dynamics and Virulence Evolution(2016) BenShachar, RotemDengue is an important vector-borne virus that infects on the order of 400 million individuals per year. Infection with one of the virus's four serotypes (denoted DENV-1 to 4) may be silent, result in symptomatic dengue 'breakbone' fever, or develop into the more severe dengue hemorrhagic fever/dengue shock syndrome (DHF/DSS). Extensive research has therefore focused on identifying factors that influence dengue infection outcomes. It has been well-documented through epidemiological studies that DHF is most likely to result from a secondary heterologous infection, and that individuals experiencing a DENV-2 or DENV-3 infection typically are more likely to present with more severe dengue disease than those individuals experiencing a DENV-1 or DENV-4 infection. However, a mechanistic understanding of how these risk factors affect disease outcomes, and further, how the virus's ability to evolve these mechanisms will affect disease severity patterns over time, is lacking. In the second chapter of my dissertation, I formulate mechanistic mathematical models of primary and secondary dengue infections that describe how the dengue virus interacts with the immune response and the results of this interaction on the risk of developing severe dengue disease. I show that only the innate immune response is needed to reproduce characteristic features of a primary infection whereas the adaptive immune response is needed to reproduce characteristic features of a secondary dengue infection. I then add to these models a quantitative measure of disease severity that assumes immunopathology, and analyze the effectiveness of virological indicators of disease severity. In the third chapter of my dissertation, I then statistically fit these mathematical models to viral load data of dengue patients to understand the mechanisms that drive variation in viral load. I specifically consider the roles that immune status, clinical disease manifestation, and serotype may play in explaining viral load variation observed across the patients. With this analysis, I show that there is statistical support for the theory of antibody dependent enhancement in the development of severe disease in secondary dengue infections and that there is statistical support for serotype-specific differences in viral infectivity rates, with infectivity rates of DENV-2 and DENV-3 exceeding those of DENV-1. In the fourth chapter of my dissertation, I integrate these within-host models with a vector-borne epidemiological model to understand the potential for virulence evolution in dengue. Critically, I show that dengue is expected to evolve towards intermediate virulence, and that the optimal virulence of the virus depends strongly on the number of serotypes that co-circulate. Together, these dissertation chapters show that dengue viral load dynamics provide insight into the within-host mechanisms driving differences in dengue disease patterns and that these mechanisms have important implications for dengue virulence evolution.
Item Open Access Modeling the Folate Pathway in Escherichia coli(2013-05-06) Lopez, CarmenFolates are a class of metabolites that are essential to living cells across all life. Because these molecules are especially important in aiding cell division, folates are targets for antibiotics, such as trimethoprim. I aim to model the pathways of folate production and interconversion in Escherichia coli. I began my work by assessing a previously published mathematical model of the E. coli folate pathways, published by Kwon and Rabinowitz, which explored the effects of trimethoprim on the system. I explored the model in depth and found avenues for improvement. My model produced enhancements in accuracy and laid the foundation for future work. In the future, this model can be expanded further and be used to model a variety of other experimental conditions under the effect of trimethoprim.Item Open Access Quantitative analysis of cellular networks: cell cycle entry(2010) Lee, Tae J.Cellular dynamics arise from intricate interactions among diverse components, such as metabolites, RNAs, and proteins. An in-depth understanding of these interactions requires an integrated approach to the investigation of biological systems. This task can benefit from a combination of mathematical modeling and experimental validations, which is becoming increasingly indispensable for basic and applied biological research.
Utilizing a combination of modeling and experimentation, we investigate mammalian cell cycle entry. We begin our investigation by making predictions with a mathematical model, which is constructed based on the current knowledge of biology. To test these predictions, we develop experimental platforms for validations, which in turn can be used to further refine the model. Such iteration of model predictions and experimental validations has allowed us to gain an in-depth understanding of the cell cycle entry dynamics.
In this dissertation, we have focused on the Myc-Rb-E2F signaling pathway and its associated pathways, dysregulation of which is associated with virtually all cancers. Our analyses of these signaling pathways provide insights into three questions in biology: 1) regulation of the restriction point (R-point) in cell cycle entry, 2) regulation of the temporal dynamics in cell cycle entry, and 3) post-translational regulation of Myc by its upstream signaling pathways. The well-studied pathways can serve as a foundation for perturbations and tight control of cell cycle entry dynamics, which may be useful in developing cancer therapeutics.
We conclude by demonstrating how a combination of mathematical modeling and experimental validations provide mechanistic insights into the regulatory networks in cell cycle entry.
Item Open Access Reduction of HIV-virion Transport for Prevention of HIV Transmission(2010) Lai, Bonnie E.This dissertation explores strategies for reducing HIV-virion transport to mucosal surfaces to prevent HIV infection. Infection requires contact between HIV and an infectable cell, so any means of inhibiting this step could contribute to HIV prevention. Our goals were to quantify the effects of strategies that reduce transport of HIV virions and to evaluate them in the context of HIV prevention. We used fundamental transport theory to design two basic strategies: (1) modifying the effective radius of virions; and (2) modifying the native medium through which virions diffuse. We proposed to implement these strategies using (1) anti-HIV antibodies that would bind and aggregate virions and (2) topically-applied semi-solid gels that coat vaginal epithelial surfaces.
We measured diffusion coefficients of HIV virions and HIV-like particles in the presence of antibodies and within semi-solid gels. In experiments with antibodies, we did not observe reductions in the diffusion coefficients. In experiments using particle tracking to measure the diffusion coefficients of virions in vaginal gels, we found that the diffusion coefficients in gels were approximately 10,000 times lower than those in water.
We proceeded to evaluate the potential for semi-solid gels to prevent HIV transmission at mucosal surfaces. From previous experiments in our lab that characterized the topical deployment of vaginal gels in vivo, we know that vaginal gels form an uneven coating on the epithelium with gel layer thicknesses of the order of hundreds of microns. Thus, we determined whether semi-solid gels could function as physical barriers to HIV when deployed as thin, incomplete layers on the epithelium.
We developed an experimental system to test the barrier functioning of thin gel layers. We applied thin gel layers to the porous membrane of a Transwell system, and added a solution of HIV to the top compartment. After incubation, samples were assayed for levels of HIV. We found that thin gel layers reduced levels of HIV in the bottom compartment compared to controls where no gel had been applied: There was a log reduction in levels of HIV in conditions where gel layers of approximately 150 μm thickness had been applied to the membrane after 0-, 4-, and 8-hour incubation. Thus, it appears possible for gel layers of thicknesses found in vivo to function as physical barriers to HIV over biologically-relevant time scales.
We studied how nonuniform deployment of semi-solid gels affects accumulation of virions in tissue using a mathematical model. We used transport theory to develop a model of HIV diffusing from semen, through gel layers where present, to tissue. Our findings suggest that comprehensive coating of over 80% of the tissue surface area and gel layer thicknesses over 100 μm are crucial to the barrier functioning of topical gels. Under these conditions, the level of viral restriction makes a significant contribution to increasing the time required for virions to reach tissue.
Overall, the work presented here applies transport theory in the context of HIV transmission and prevention. Results contribute to theoretical and experimental frameworks that can help understand events in HIV transmission and to design and evaluate new technologies for HIV prevention.
Item Open Access Transport Phenomena in Anti-HIV Microbicide Delivery Vehicles(2008-04-21) Geonnotti, III, Anthony RobertThere were 2.5 million people newly infected with HIV in 2007, clearly motivating the need for additional novel prevention methods. In response, topical vaginal antimicrobials, or microbicides, are being developed. These products aim to stop HIV transmission through local, vaginal delivery of antiviral compounds. To succeed, microbicides require a potent active compound within a well-engineered delivery vehicle.
A well-engineered delivery vehicle provides an antiviral compound with the greatest opportunity to interact with HIV and/or infected cells, thereby increasing overall microbicide effectiveness. The theoretical and experimental investigations within this dissertation are concerned with the study of HIV and active compound transport within microbicide delivery vehicles and with the mechanisms by which these transport processes can be affected to maximize viral neutralization. To initially investigate the factors contributing to microbicide effectiveness, a combined pharmacokinetic and pharmacodynamic model of HIV transport and neutralization within a microbicide product was created. Model results suggested that thin (~100µm) layers of microbicide product may protect against HIV infection. Model results also indicated that a specific and engineerable property of delivery vehicles - the ability to restrict viral transport - may increase the overall effectiveness of a microbicide. Two new experimental assays were developed to test the hypothesis that delivery vehicles can slow viral transport. First, a novel methodology was created to measure particle diffusion over length scales relevant to microbicide delivery (50-500µm). Results showed that current vehicles significantly restrict the transport of small molecules and proteins. The second assay was designed to test HIV transport in a biologically relevant, layered (fluid-microbicide-tissue) configuration of a microbicide product in vivo; infectious HIV was placed above a thin layer of a microbicide delivery vehicle. Assay results showed that HIV transport is significantly slowed by two different placebo gels. This experimental confirmation of viral restriction in hydrogels, combined with the theoretical finding that viral restriction increased microbicide effectiveness, strongly motivates the future development of new delivery vehicles that intentionally slow viral transport. These new experimental methodologies can also be used to screen and compare future delivery vehicles to produce optimal microbicide products.
Finally, a two-dimensional, computational finite-element vaginal model was created to evaluate the transport of drugs from an intravaginal ring. This model determined that while IVRs may be effective in the delivery of antiviral compound, their performance is influenced by the flow of vaginal fluid. The analysis also warns about the potential for local toxicity.
Well-engineered delivery vehicles are an essential component to microbicide performance because they maximize the opportunities for active compounds to interact with and neutralize HIV. The studies in this dissertation demonstrate that delivery vehicles have a significant effect on active compound and HIV transport. To create an effective microbicide, vehicle effects on transport processes must be well understood, purposefully engineered, and carefully optimized to ensure maximal interactions between antiviral compounds and virus. Directed engineering of delivery vehicles contribute to the foundation for microbicide success.