An exploited single-species population model with a density dependent reproductive function is constructed, in which recruitment to the adult breeding population may occur in one of several possible age classes. The parent is assumed capable of giving birth only once. It is also assumed that all density dependence is concentrated in the first year of life. A linearized stability analysis of the multiply-delayed difference equation model is carried out and a sufficient condition for stability is derived for the general case, while necessary and sufficient conditions are found in specific examples. Some indication of the complicated bifurcation structure of the model is given by a series of computer simulation plots. Finally, the method of Lagrange multipliers is used to find the optimal equilibrium escapement level for the original exploited population model. / Science, Faculty of / Mathematics, Department of / Graduate

A semi-stochastic model was developed to simulate tree growth and stand yield information required for managing aspen (Populas tremuloides (Michx.)). The model is based upon new approaches for evaluating inter-tree competition effects, representing actual tree spatial arrangement, defining interactions between increments of height and d.b.h. and competition measures, and representing random components of variation in tree growth and mortality. In building the model, components of tree growth and mortality were identified and described mathematically or represented directly in the computer. Inter-tree competition, the most important component in the model, was extensively studied. The maximum zone of influence of a tree was derived from estimates of fully open grown crown width. A new hypothesis was advanced and mathematically expressed to describe competition effects on tree growth by exponential terms of ratios based on relative tree size. The model simulates height increments as if each tree was dominant or open-growing. The rate of height growth is a function of site quality. Simulated "potential" height increment is reduced, according to the tree's competitive status, to obtain height increment. D.b.h. increment is based on data from open grown aspen then reduced in proportion to tree competition. Reductions from the maximum rate of growth are based on tree growth and mortality expected in normal aspen stands. In the model mortality is directly related to the tree's competitive status and inversely to its current increment, including random variation, in relation to a specified threshold value. The model was calibrated with data from a normal stand growing on an above average aspen site in Saskatchewan. Input data were from a suitable permanent sample plot having fairly uniform clonal structure. After a few calibration runs and model refinements, simulated stand growth statistics showed satisfactory correspondence with actual growth on the permanent sample plot, and with comparable yield table statistics. Simulations were made also for normal stands growing on poor sites and on the best sites in the same region. The model was generally satisfactory and could replace normal yield tables. After certain extensions, the revised model also simulated growth and development of initially open stands reasonably well. The model also was used to simulate aspen stand growth and productivity in terms of tree component dry matter weights for normal stands on average sites with weight regressions determined in an associated study. For maximum production of wood fibre, the optimum rotation was 33 years for either volume or weight. Although tested only for pure aspen stands, the model can be modified for use with other species. With further refinement, it may be possible also to simulate the growth of mixed stands and uneven-aged stands. / Forestry, Faculty of / Graduate

No description available.

Thesis (M.S.)--Ohio University, August, 2009. / Title from PDF t.p. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 103-113).

Thesis (Ph. D.) -- University of Maryland, College Park, 2005. / Thesis research directed by: Marine-Estuarine-Environmental Sciences. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

Osteoarthritis (OA) is a debilitating degenerative joint disease affecting 27 million Americans over the age of 25. Whereas OA is a disease of the entire joint organ, the contribution of the synovium, a specialized lining that envelops the knee joint, to cartilage degeneration and disease progression has been underappreciated. Synovial inflammation often precedes the development of cartilage damage and is observed in early and late stage OA. The onset of synovitis is driven by both elevated concentrations of pro-inflammatory cytokines and tissue debris in the joint space. Accordingly, surgeons have observed cartilaginous debris embedded within the synovium of OA patients presenting with severe synovial hyperplasia. It has been hypothesized that the fibrotic shortening of the synovial capsule results in OA pain and joint stiffness and contributes to further joint destruction through the release of degradative enzymes. Current strategies to treat synovial inflammation and joint pain, such as intra-articular injections and synovectomy, have had limited and variable success. To this end, cell and tissue engineering culture models provide a versatile platform to study the tissues and cells involved in OA. Our lab has typically employed mechanical overload or cytokine insult of chondrocytes and cartilage explants to study cartilage degradation. Similarly, to isolate the role of synovium in OA, synovial explants or fibroblast-like synoviocytes (FLS) can be exposed to chemical or physical OA stimuli. Although often overlooked as an instigator of OA, cartilage wear particles have been reported to induce synovial inflammation and OA-like joint changes in various animal models. As opposed to non-biologic (metal or plastic) wear particles, small (sub-10um) cartilage wear particles are comprised of extracellular matrix constituents that are degradable and may interact with cells beyond phagocytosis. Using cells derived from the pathologic joint provides the opportunity to study inherent changes to OA cells (both FLS and chondrocytes) within their own de novo extracellular matrix. The work presented in this dissertation aims to combine knowledge from basic science and pre-clinical culture models of OA to develop a clinically relevant disease model using cells derived from clinical samples.

Computer models are used extensively to investigate biological systems. Many of these systems can be described in terms of fields???spatially- and temporally- varying scalar, vector and tensor properties defined over domains. For example, the spatial variation of muscle fibers is a vector field, the spatial and temporal variation in temperature of an organ is a scalar field, and the distribution of stress across muscle tissue is a tensor field. In this thesis I present my research on how to represent fields in a format that allows researchers to store and distribute them independently of models and to investigate and manipulate them intuitively. I also demonstrate how the work can be applied to solving and analysing biomedical models. To represent fields I created a two-layer system. One layer, called the Field Representation Language (FRL), represents fields by storing numeric, analytic and meta data for storage and distribution. The focus of this layer is efficiency rather than usability. The second layer, called the Abstract Field Layer (AFL), provides an abstraction of fields so that they are easier for researchers to work with. This layer also provides common operations for manipulating fields as well as transparent conversion to and from FRL representations. The applications that I used to demonstrate the use of AFL and FRL are (a) a fields visualisation toolkit, (b) integration of models from different scales and solvers, and (c) a solver that uses AFL internally. The layered architecture facilitated the development of tools that use fields. A similar architecture may also prove useful for representations of other modelled entities.

The large-scale production of monoclonal antibodies (MAb) by mammalian cells in batch and fed-batch culture systems is limited by the unwanted decline in cell viability and reduced productivity that may result from changes in culture conditions. Therefore, it becomes imperative to gain an in-depth knowledge of the factors affecting cell growth and cell viability that in turn determine the antibody production. An attempt has been made to obtain an overall model that predicts the behaviour of both batch and fed-batch systems as a function of the extra-cellular nutrient/metabolite concentrations. Such model formulation will aid in identifying and eventually controlling the dominant factors in play to optimize monoclonal antibody (MAb) production in the future. Murine hybridoma 130-8F producing anti-F-glycoprotein monoclonal antibody was grown in D-MEM medium (Gibco 12100) with 2% FBS. A systematic approach based on Metabolic Flux Analysis (MFA) was applied for the calculation of intracellular fluxes for metabolites from available extracellular concentration values. Based on the set of identified significant fluxes (from MFA), the original metabolic network was reduced to a set of significant reactions. The reactions in the reduced metabolic network were then combined to yield a set of macro-reactions obeying Monod kinetics. Half saturation constants were fixed empirically to avoid computational difficulties that parameter estimation for an over-parameterized system of equations would cause. Using Quadratic Programming, the proposed Dynamic Model was calibrated and model prediction was carried out individually for batch and fed-batch runs. Flux distribution for batch and fedbatch modes were compared to determine whether the same model structure could be applied to both the feeding profiles. Correlation analysis was performed to formulate a Biomass Model for predicting cell concentration and viability as a function of the extracellular metabolite concentrations in batch and fed-batch experiments. Quadratic Programming was applied once again for estimation of growth and death coefficients in the equations for viable and dead cell predictions. The prediction accuracy of these model equations was tested by using experimental data from additional runs. Further, the Dynamic Model was integrated with the Biomass Model to get an Integrated Model capable of predicting concentration values for substrates, extracellular metabolites, and viable and dead cell concentration by utilizing only starting concentrations as input. It was found that even though the set of significant fluxes was the same for batch and fedbatch operations, the order of these fluxes was different between the two systems. There was a gradual metabolic shift in the fed-batch system with time indicating that under conditions of nutrient limitation, the available energy is channeled towards maintenance rather than growth. Also, available literature with regard to cell kinetics during fed-batch operation suggests that under nutrient limited conditions, the cells move from a viable, non-apoptotic state to a viable apoptotic state. This is believed to lead to variations in antibody production rates and might explain inaccurate predictions for MAb obtained from the model proposed in the current work. As a result more detailed analysis of the system and in particular, the switch from non-apoptotic to apoptotic state is required. As a continuation of efforts to study the system in-depth, fluorescence imaging is currently being applied as a tool to capture the changes in cell morphology along the course of experimental batch and fed-batch runs. These experiments maybe able to elucidate the transition from non-apoptotic to apoptotic cells and this information maybe used in the future to improve the accuracy of the existing mathematical model.

The large-scale production of monoclonal antibodies (MAb) by mammalian cells in batch and fed-batch culture systems is limited by the unwanted decline in cell viability and reduced productivity that may result from changes in culture conditions. Therefore, it becomes imperative to gain an in-depth knowledge of the factors affecting cell growth and cell viability that in turn determine the antibody production. An attempt has been made to obtain an overall model that predicts the behaviour of both batch and fed-batch systems as a function of the extra-cellular nutrient/metabolite concentrations. Such model formulation will aid in identifying and eventually controlling the dominant factors in play to optimize monoclonal antibody (MAb) production in the future. Murine hybridoma 130-8F producing anti-F-glycoprotein monoclonal antibody was grown in D-MEM medium (Gibco 12100) with 2% FBS. A systematic approach based on Metabolic Flux Analysis (MFA) was applied for the calculation of intracellular fluxes for metabolites from available extracellular concentration values. Based on the set of identified significant fluxes (from MFA), the original metabolic network was reduced to a set of significant reactions. The reactions in the reduced metabolic network were then combined to yield a set of macro-reactions obeying Monod kinetics. Half saturation constants were fixed empirically to avoid computational difficulties that parameter estimation for an over-parameterized system of equations would cause. Using Quadratic Programming, the proposed Dynamic Model was calibrated and model prediction was carried out individually for batch and fed-batch runs. Flux distribution for batch and fedbatch modes were compared to determine whether the same model structure could be applied to both the feeding profiles. Correlation analysis was performed to formulate a Biomass Model for predicting cell concentration and viability as a function of the extracellular metabolite concentrations in batch and fed-batch experiments. Quadratic Programming was applied once again for estimation of growth and death coefficients in the equations for viable and dead cell predictions. The prediction accuracy of these model equations was tested by using experimental data from additional runs. Further, the Dynamic Model was integrated with the Biomass Model to get an Integrated Model capable of predicting concentration values for substrates, extracellular metabolites, and viable and dead cell concentration by utilizing only starting concentrations as input. It was found that even though the set of significant fluxes was the same for batch and fedbatch operations, the order of these fluxes was different between the two systems. There was a gradual metabolic shift in the fed-batch system with time indicating that under conditions of nutrient limitation, the available energy is channeled towards maintenance rather than growth. Also, available literature with regard to cell kinetics during fed-batch operation suggests that under nutrient limited conditions, the cells move from a viable, non-apoptotic state to a viable apoptotic state. This is believed to lead to variations in antibody production rates and might explain inaccurate predictions for MAb obtained from the model proposed in the current work. As a result more detailed analysis of the system and in particular, the switch from non-apoptotic to apoptotic state is required. As a continuation of efforts to study the system in-depth, fluorescence imaging is currently being applied as a tool to capture the changes in cell morphology along the course of experimental batch and fed-batch runs. These experiments maybe able to elucidate the transition from non-apoptotic to apoptotic cells and this information maybe used in the future to improve the accuracy of the existing mathematical model.