Browsing by Subject "mathematical modeling"

Now showing 1 - 5 of 5
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    Application of quantitative analysis in treatment of osteoporosis and osteoarthritis
    (2013-11-08) Chen, Andy Bowei; Yokota, Hiroki, 1955-; Na, Sungsoo; Schild, John H.
    As our population ages, treating bone and joint ailments is becoming increasingly important. Both osteoporosis, a bone disease characterized by a decreased density of mineral in bone, and osteoarthritis, a joint disease characterized by the degeneration of cartilage on the ends of bones, are major causes of decreased movement ability and increased pain. To combat these diseases, many treatments are offered, including drugs and exercise, and much biomedical research is being conducted. However, how can we get the most out of the research we perform and the treatment we do have? One approach is through computational analysis and mathematical modeling. In this thesis, quantitative methods of analysis are applied in different ways to two systems: osteoporosis and osteoarthritis. A mouse model simulating osteoporosis is treated with salubrinal and knee loading. The bone and cell data is used to formulate a system of differential equations to model the response of bone to each treatment. Using Particle Swarm Optimization, optimal treatment regimens are found, including a consideration of budgetary constraints. Additionally, an in vitro model of osteoarthritis in chondrocytes receives RNA silencing of Lrp5. Microarray analysis of gene expression is used to further elucidate the mode of regulation of ADAMTS5, an aggrecanase associated with cartilage degradation, by Lrp5, including the development of a mathematical model. The math model of osteoporosis reveals a quick response to salubrinal and a delayed but substantial response to knee loading. Consideration of cost effectiveness showed that as budgetary constraints increased, treatment did not start until later. The quantitative analysis of ADAMTS5 regulation suggested the involvement of IL1B and p38 MAPK. This research demonstrates the application of quantitative methods to further the usefulness of biomedical and biomolecular research into treatment and signaling pathways. Further work using these techniques can help uncover a bigger picture of osteoarthritis's mode of action and ideal treatment regimens for osteoporosis.
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    Mechanisms of Left-Right Coordination in Mammalian Locomotor Pattern Generation Circuits: A Mathematical Modeling View
    (PLoS, 2015-05) Molkov, Yaroslav I.; Bacak, Bartholomew J.; Talpalar, Adolfo E.; Rybak, Ilya A.; Department of Mathematical Sciences, School of Science
    The locomotor gait in limbed animals is defined by the left-right leg coordination and locomotor speed. Coordination between left and right neural activities in the spinal cord controlling left and right legs is provided by commissural interneurons (CINs). Several CIN types have been genetically identified, including the excitatory V3 and excitatory and inhibitory V0 types. Recent studies demonstrated that genetic elimination of all V0 CINs caused switching from a normal left-right alternating activity to a left-right synchronized “hopping” pattern. Furthermore, ablation of only the inhibitory V0 CINs (V0D subtype) resulted in a lack of left-right alternation at low locomotor frequencies and retaining this alternation at high frequencies, whereas selective ablation of the excitatory V0 neurons (V0V subtype) maintained the left–right alternation at low frequencies and switched to a hopping pattern at high frequencies. To analyze these findings, we developed a simplified mathematical model of neural circuits consisting of four pacemaker neurons representing left and right, flexor and extensor rhythm-generating centers interacting via commissural pathways representing V3, V0D, and V0V CINs. The locomotor frequency was controlled by a parameter defining the excitation of neurons and commissural pathways mimicking the effects of N-methyl-D-aspartate on locomotor frequency in isolated rodent spinal cord preparations. The model demonstrated a typical left-right alternating pattern under control conditions, switching to a hopping activity at any frequency after removing both V0 connections, a synchronized pattern at low frequencies with alternation at high frequencies after removing only V0D connections, and an alternating pattern at low frequencies with hopping at high frequencies after removing only V0V connections. We used bifurcation theory and fast-slow decomposition methods to analyze network behavior in the above regimes and transitions between them. The model reproduced, and suggested explanation for, a series of experimental phenomena and generated predictions available for experimental testing.
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    Modeling of a Hydraulic Wind Power Transfer Utilizing a Proportional Valve
    (IEEE, 2015-03) Deldar, Majid; Izadian, Afshin; Vaezi, Masoud; Anwar, Sohel; Department of Mechanical Engineering, School of Engineering
    Hydraulic circuits can transfer remarkable amounts of energy in the desired direction without taking large space. To implement this technology for harvesting the energy of wind appropriately, models of the system are required. Hydraulic wind power technology has the benefits of eliminating expensive and bulky variable ratio gearbox and its costly maintenance, while enabling the integration of multiple wind turbines in a single generation unit. In this paper, the dynamics of different hydraulic elements are studied, nonlinearities are taken into account, pressure dynamics in different parts of the system are studied, and the motor load effects are considered. Based on these considerations, a novel nonlinear state-space representation of the system is introduced. Results of the mathematical model and the experimental data are compared to verify the proposed model. The comparison demonstrated that the mathematical model captures all major characteristics of the hydraulic circuit and can model the system behavior under different operating conditions.
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    Predicting Experimental Sepsis Survival with a Mathematical Model of Acute Inflammation
    (Frontiers, 2021-11) Barber, Jared; Carpenter, Amy; Torsey, Allison; Borgard, Tyler; Namas, Rami A.; Vodovotz, Yoram; Arciero, Julia; Mathematical Sciences, School of Science
    Sepsis is characterized by an overactive, dysregulated inflammatory response that drives organ dysfunction and often results in death. Mathematical modeling has emerged as an essential tool for understanding the underlying complex biological processes. A system of four ordinary differential equations (ODEs) was developed to simulate the dynamics of bacteria, the pro- and anti-inflammatory responses, and tissue damage (whose molecular correlate is damage-associated molecular pattern [DAMP] molecules and which integrates inputs from the other variables, feeds back to drive further inflammation, and serves as a proxy for whole-organism health status). The ODE model was calibrated to experimental data from E. coli infection in genetically identical rats and was validated with mortality data for these animals. The model demonstrated recovery, aseptic death, or septic death outcomes for a simulated infection while varying the initial inoculum, pathogen growth rate, strength of the local immune response, and activation of the pro-inflammatory response in the system. In general, more septic outcomes were encountered when the initial inoculum of bacteria was increased, the pathogen growth rate was increased, or the host immune response was decreased. The model demonstrated that small changes in parameter values, such as those governing the pathogen or the immune response, could explain the experimentally observed variability in mortality rates among septic rats. A local sensitivity analysis was conducted to understand the magnitude of such parameter effects on system dynamics. Despite successful predictions of mortality, simulated trajectories of bacteria, inflammatory responses, and damage were closely clustered during the initial stages of infection, suggesting that uncertainty in initial conditions could lead to difficulty in predicting outcomes of sepsis by using inflammation biomarker levels.
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    Using a Mathematical Model of Motivation, Volition, and Performance to Examine Students’ E-Text Learning Experiences
    (Springer, 2018-10) Novak, Elena; Daday, Jerry; McDaniel, Kerrie; Sociology, School of Liberal Arts
    This empirical study used Keller’s (Technol Instr Cogn Learn 16:79–104, 2008b) motivation, volition, and performance (MVP) theory to develop and statistically evaluate a mathematical MVP model that can serve as a research and policy tool for evaluating students’ learning experiences in digital environments. Specifically, it explored undergraduate biology students’ learning and attitudes toward e-texts using a MVP mathematical model in two different e-text environments. A data set (N = 1334) that included student motivation and e-text information processing, frustration with using e-texts, and student ability variables was used to evaluate e-text satisfaction. A regression analysis of these variables revealed a significant model that explained 77% of the variation in student e-text satisfaction in both e-text learning environments. Student motivation and intrinsic cognitive load were positive predictors of student satisfaction, while extraneous cognitive load and student prior knowledge and background variables were negative predictors. Practical implications for e-text learning and generalizability of a mathematical MVP model are discussed.