Browsing by Subject "Mathematical model"

Now showing 1 - 10 of 10
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    Design and Evaluate the Factors for Flipped Classrooms for Data Management Courses
    (Institute of Electrical and Electronics Engineers, 2020-10) Mithun, Shamima; Luo, Xiao; Engineering Technology, School of Engineering and Technology
    This Research to Practice Full Paper presents a framework to evaluate and design flipped classroom activities for data science and management courses. Variants of flipped classrooms have been employed in STEM fields with great success in students' learning outcomes. Research shows that flipped classrooms would improve students' learning if it is implemented following rigorous procedures of an efficient instructional design. As a result, one of the critical focus of current flipped classroom research is what factors educators need to consider when designing a flipped learning environment. Currently, educators incorporate various factors such as "pre-recorded video lecture", "group activity" as a trial and error basis and adjust these factors based on their own experience and students' feedback. On the other hand, the emergence of big data expects a new graduate to demonstrate mastery of concepts and skills for data acquisition, management, and analysis of inference from data when they enter the workforce. Currently, there is no systematic approach available to design a flipped classroom that is for the data science and management courses. In this research, we develop a framework first to investigate and evaluate the flipped classroom factors mentioned in the literature and identify a few that are most relevant to the two data management courses at our institute. Then, we classify each course topics into broader categories. So that the flipped classroom model can be developed for each category. For the flipped classroom for each category, we identify the pre-class and in-class activities to meet a certain learning objective for that topic category for each course. To evaluate the effectiveness of different factors as well as our flipped classroom models, students' performance data, interviews, and surveys are conducted. This process is transformative and can be employed by other STEM disciplines to find the most influential factors to design effective flipped learning classrooms.
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    An Integrative multi-lineage model of variation in leukopoiesis and acute myelogenous leukemia
    (BMC, 2017-08-25) Sarker, Joyatee M.; Pearce, Serena M.; Nelson, Robert P.; Kinzer-Ursem, Tamara L.; Umulis, David M.; Rundell, Ann E.; Medicine, School of Medicine
    Background Acute myelogenous leukemia (AML) progresses uniquely in each patient. However, patients are typically treated with the same types of chemotherapy, despite biological differences that lead to differential responses to treatment. Results Here we present a multi-lineage multi-compartment model of the hematopoietic system that captures patient-to-patient variation in both the concentration and rates of change of hematopoietic cell populations. By constraining the model against clinical hematopoietic cell recovery data derived from patients who have received induction chemotherapy, we identified trends for parameters that must be met by the model; for example, the mitosis rates and the probability of self-renewal of progenitor cells are inversely related. Within the data-consistent models, we found 22,796 parameter sets that meet chemotherapy response criteria. Simulations of these parameter sets display diverse dynamics in the cell populations. To identify large trends in these model outputs, we clustered the simulated cell population dynamics using k-means clustering and identified thirteen ‘representative patient’ dynamics. In each of these patient clusters, we simulated AML and found that clusters with the greatest mitotic capacity experience clinical cancer outcomes more likely to lead to shorter survival times. Conversely, other parameters, including lower death rates or mobilization rates, did not correlate with survival times. Conclusions Using the multi-lineage model of hematopoiesis, we have identified several key features that determine leukocyte homeostasis, including self-renewal probabilities and mitosis rates, but not mobilization rates. Other influential parameters that regulate AML model behavior are responses to cytokines/growth factors produced in peripheral blood that target the probability of self-renewal of neutrophil progenitors. Finally, our model predicts that the mitosis rate of cancer is the most predictive parameter for survival time, followed closely by parameters that affect the self-renewal of cancer stem cells; most current therapies target mitosis rate, but based on our results, we propose that additional therapeutic targeting of self-renewal of cancer stem cells will lead to even higher survival rates. Electronic supplementary material The online version of this article (doi:10.1186/s12918-017-0469-2) contains supplementary material, which is available to authorized users.
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    Introducing a Concise Formulation of the Jacobian Matrix for Newton-Raphson Power Flow Solution in the Engineering Curriculum
    (IEEE Xplore, 2021-04) Conlin, Elijah; Dahal, Niraj; Rovnyak, Steven M.; Rovnyak, James L.; Electrical and Computer Engineering, School of Engineering and Technology
    The power flow computer program is fundamentally important for power system analysis and design. Many textbooks teach the Newton-Raphson method of power flow solution. The typical formulation of the Jacobian matrix in the NR method is cumbersome, inelegant, and laborious to program. Recent papers have introduced a method for calculating the Jacobian matrix that is concise, elegant, and simple to program. The concise formulation of the Jacobian matrix makes writing a power flow program more accessible to students. However, its derivation in the research literature involves advanced manipulations using higher dimensional derivatives, which are challenging for dual level students. This paper presents alternative derivations of the concise formulation that are suitable for undergraduate students, where some cases can be presented in lecture while other cases are assigned as exercises. These derivations have been successfully taught in a dual level course on computational methods for power systems for about ten years.
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    Mathematical Model and Experimental Design of Nanocomposite Proximity Sensors
    (IEEE, 2020-08) Moheimani, Reza; Pasharavesh, Abdolreza; Agarwal, Mangilal; Dalir, Hamid; Engineering Technology, School of Engineering and Technology
    A mathematical model of fringe capacitance for a nano-based proximity sensor, which takes the presence of different resistivities into account, is developed. An analytical solution obtained for a rectangular-shape sensor with applying of Gauss, Conversation of Charge and Ohm laws into Laplace's equation ∇2V (x, y, z, t) = 0 gives the electric potential distribution by which the fringe capacitance in a 2D domain area can be calculated. The calculated capacitance evidently decreases drastically due to the fringe phenomena while object moves toward the polymeric sensor. The model also asserts that the change of capacitance is under a noticeable influence of sensor resistivity, particularly in the range of 103-105Ω.m, the initial capacitance varies from 0.045pF to 0.024 pF. The fabricated flexible nanocomposite sensors, Thermoplastic Polyurethane (TPU) reinforced by 1wt.% Carbon Nanotubes (CNTs) having resistivity 105Ω.m, are capable of detecting presence of an external object in a wide range of distance and indicating remarkable correlation with the mathematical solution. Our proximity sensor fabrication is straightforward and relatively simple. An unprecedented detection range of measurement reveals promising ability of this proximity sensor in applications of motion analysis and healthcare systems.
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    Metabolic blood flow regulation in a hybrid model of the human retinal microcirculation
    (Elsevier, 2023) Albright, Amanda; Fry, Brendan C.; Verticchio, Alice; Siesky, Brent; Harris, Alon; Arciero, Julia; Mathematical Sciences, School of Science
    The retinal vascular network supplies perfusion to vital visual structures, including retinal ganglion cells responsible for vision. Impairments in retinal blood flow and oxygenation are involved in the progression of many ocular diseases, including glaucoma. In this study, an established theoretical hybrid model of a retinal microvascular network is extended to include the effects of local blood flow regulation on oxygenation. A heterogeneous representation of the arterioles based on confocal microscopy images is combined with a compartmental description of the downstream capillaries and venules. A Green’s function method is used to simulate oxygen transport in the arterioles, and a Krogh cylinder model is applied to the capillary and venular compartments. Acute blood flow regulation is simulated in response to changes in pressure, shear stress, and metabolism. Model results predict that both increased intraocular pressure and impairment of blood flow regulation can cause decreased tissue oxygenation, indicating that both mechanisms represent factors that could lead to impaired oxygenation characteristic of ocular disease. Results also indicate that the metabolic response mechanism reduces the fraction of poorly oxygenated tissue but that the pressure- and shear stress-dependent response mechanisms may hinder the vascular response to changes in oxygenation. Importantly, the heterogeneity of the vascular network demonstrates that traditionally reported average values of tissue oxygen levels hide significant localized defects in tissue oxygenation that may be involved in disease processes, including glaucoma. Ultimately, the model framework presented in this study will facilitate future comparisons to sectorial-specific clinical data to better assess the role of impaired blood flow regulation in ocular disease.
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    Metabolic Signaling in a Theoretical Model of the Human Retinal Microcirculation
    (MDPI, 2021) Arciero, Julia; Fry, Brendan; Albright, Amanda; Mattingly, Grace; Scanlon, Hannah; Abernathy, Mandy; Siesky, Brent; Verticchio Vercellin, Alice; Harris, Alon; Mathematical Sciences, School of Science
    Impaired blood flow and oxygenation contribute to many ocular pathologies, including glaucoma. Here, a mathematical model is presented that combines an image-based heterogeneous representation of retinal arterioles with a compartmental description of capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. Every terminal arteriole is connected in series to compartments for capillaries and venules, yielding a hybrid model for predicting blood flow and oxygenation throughout the retinal microcirculation. A metabolic wall signal is calculated in each vessel according to blood and tissue oxygen levels. As expected, a higher average metabolic signal is generated in pathways with a lower average oxygen level. The model also predicts a wide range of metabolic signals dependent on oxygen levels and specific network location. For example, for high oxygen demand, a threefold range in metabolic signal is predicted despite nearly identical PO2 levels. This whole-network approach, including a spatially nonuniform structure, is needed to describe the metabolic status of the retina. This model provides the geometric and hemodynamic framework necessary to predict ocular blood flow regulation and will ultimately facilitate early detection and treatment of ischemic and metabolic disorders of the eye.
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    Modeling cerebrovascular responses to assess the impact of the collateral circulation following middle cerebral artery occlusion
    (Wiley, 2024) Zhao, Erin; Barber, Jared; Mathew-Steiner, Shomita S.; Khanna, Savita; Sen, Chandan K.; Arciero, Julia; Mathematical Sciences, School of Science
    Objective: An improved understanding of the role of the leptomeningeal collateral circulation in blood flow compensation following middle cerebral artery (MCA) occlusion can contribute to more effective treatment development for ischemic stroke. The present study introduces a model of the cerebral circulation to predict cerebral blood flow and tissue oxygenation following MCA occlusion. Methods: The model incorporates flow regulation mechanisms based on changes in pressure, shear stress, and metabolic demand. Oxygen saturation in cerebral vessels and tissue is calculated using a Krogh cylinder model. The model is used to assess the effects of changes in oxygen demand and arterial pressure on cerebral blood flow and oxygenation after MCA occlusion. Results: An increase from five to 11 leptomeningeal collateral vessels was shown to increase the oxygen saturation in the region distal to the occlusion by nearly 100%. Post-occlusion, the model also predicted a loss of autoregulation and a decrease in flow to the ischemic territory as oxygen demand was increased; these results were consistent with data from experiments that induced cerebral ischemia. Conclusions: This study highlights the importance of leptomeningeal collaterals following MCA occlusion and reinforces the idea that lower oxygen demand and higher arterial pressure improve conditions of flow and oxygenation.
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    Modeling the Potential of Treg-Based Therapies for Transplant Rejection: Effect of Dose, Timing, and Accumulation Site
    (Frontiers Media, 2022-04-11) Lapp, Maya M.; Lin, Guang; Komin, Alexander; Andrews, Leah; Knudson, Mei; Mossman, Lauren; Raimondi, Giorgio; Arciero, Julia C.; Mathematical Sciences, School of Science
    Introduction: The adoptive transfer of regulatory T cells (Tregs) has emerged as a method to promote graft tolerance. Clinical trials have demonstrated the safety of adoptive transfer and are now assessing their therapeutic efficacy. Strategies that generate large numbers of antigen specific Tregs are even more efficacious. However, the combinations of factors that influence the outcome of adoptive transfer are too numerous to be tested experimentally. Here, mathematical modeling is used to predict the most impactful treatment scenarios. Methods: We adapted our mathematical model of murine heart transplant rejection to simulate Treg adoptive transfer and to correlate therapeutic efficacy with Treg dose and timing, frequency of administration, and distribution of injected cells. Results: The model predicts that Tregs directly accumulating to the graft are more protective than Tregs localizing to draining lymph nodes. Inhibiting antigen-presenting cell maturation and effector functions at the graft site was more effective at modulating rejection than inhibition of T cell activation in lymphoid tissues. These complex dynamics define non-intuitive relationships between graft survival and timing and frequency of adoptive transfer. Conclusion: This work provides the framework for better understanding the impact of Treg adoptive transfer and will guide experimental design to improve interventions.
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    Performance Estimates for a Fuel-Free Stationary Platform in the Stratosphere
    (Institute of Electrical and Electronics Engineers, 2022) Schubert, Peter J.; van Wynsberghe, Erinn; Finnell, Abigail J. Kragt; Salgueiro, Cristian; Suri, Ramaa Saket; Electrical and Computer Engineering, School of Engineering and Technology
    High-altitude pseudo-satellites (HAPS) may be kept aloft indefinitely with station-keeping provided by plasma air thrusters (PAT) using wireless power transfer (WPT) from a terrestrial phased array antenna (PAA). One example is the patented “Sitallite” superpressure balloon with a rectifying antenna (rectenna) covering its underside, with thrusters around the periphery. Such a stationary platform can provide continuous observation and communications capabilities covering vast areas for a fraction of the cost required for an orbiting satellite. This work builds upon the design and safety study published elsewhere to provide performance estimates for a long-duration, persistent HAPS powered by electronically-steerable microwave beams. Newly-derived efficiency equations are used to provide accurate estimates of free-space WPT transfer efficiency based on the dimensions of the ground-based PAA and the rectenna. Calculations of air drag for a spheroidal bouyant shape are used to derive PAT power requirements, and these, together with power conversion circuitry, are used to size the overall system. Accurate estimates of cost are derived. These performance estimates can be used to help make economic and logistic decisions, as a fuel-free HAPS with PAT and powered by WPT can be lofted in less time, and with lower risk, than an orbital satellite of comparable capabilities.
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    Vehicle sensor-based pedestrian position identification in V2V environment
    (2016-12-03) Huang, Zhi; Chien, Stanley; Chen, Yaobin; Christopher, Lauren
    This thesis presents a method to accurately determine the location and amount of pedestrians detected by different vehicles equipped with a Pedestrian Autonomous Emergency Braking (PAEB) system, taking into consideration the inherent inaccuracy of the pedestrian sensing from these vehicles. In the thesis, a mathematical model of the pedestrian information generated by the PAEB system in the V2V network is developed. The Greedy-Medoids clustering algorithm and constrained hierarchical clustering are applied to recognize and reconstruct actual pedestrians, which enables a subject vehicle to approximate the number of the pedestrians and their estimated locations from a larger number of pedestrian alert messages received from many nearby vehicles through the V2V network and the subject vehicle itself. The proposed methods determines the possible number of actual pedestrians by grouping the nearby pedestrians information broadcasted by different vehicles and considers them as one pedestrian. Computer simulations illustrate the effectiveness and applicability of the proposed methods. The results are more integrated and accurate information for vehicle Autonomous Emergency Braking (AEB) systems to make better decisions earlier to avoid crashing into pedestrians.