[Show abstract][Hide abstract] ABSTRACT: Chronic kidney disease causes a slow loss of kidney function over time and can eventually lead to end stage renal disease, where a patient must undergo dialysis to remove fluids and wastes from the body. These patients also suffer from a lack of the hormone erythropoietin (EPO), produced in the kidneys, that stimulates red blood cell (RBC) production. Without intervention, patients suffer from anemia. Patients are treated with both EPO and iron in order to stimulate RBC production. We develop a partial differential equation model for RBC dynamics using two structure variables, one for age and one for cellular iron endowment. We couple this with a set of ordinary differential equations modeling iron dynamics. We take into account the effects of both inflammation and neocytolysis, which are known to affect patients undergoing treatment.
International Journal of Pure and Applied Mathematics. 01/2012; 75(1).
[Show abstract][Hide abstract] ABSTRACT: In an effort to achieve higher power RF source performance, designers are utilizing distributed beam devices, such as sheet beams and multiple beams. A limitation is the amount of current that can be emitted by the cathode while still achieving long cathode lifetimes. The desire is to develop distributed beam devices that utilize fundamental mode cavities in the RF circuit. For multiple-beam devices, where the individual beams propagate at the same radius as the cathode, a limitation is reached, where the size of the cathode becomes limited by the space available. A solution is to place the cathodes at a larger radius and compress the beams toward the radius required for fundamental mode cavities. This paper describes the design of a multiple-beam gun where the ensemble of beams is compressed toward the device axis while still achieving parallel propagation through the RF circuit.
IEEE Transactions on Plasma Science 07/2010; · 0.87 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Benzene is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. After uptake into the body, benzene undergoes a series of metabolic transformations to multiple metabolites that exert toxic effects on the bone marrow. We developed a physiologically based pharmacokinetic model for the uptake and elimination of benzene in mice to relate the concentration of inhaled and orally administered benzene to the tissue doses of benzene and its key metabolites. This model takes into account the zonal distribution of enzymes and metabolism in the liver rather than treating the liver as one homogeneous compartment, and considers metabolism in tissues other than the liver. Analysis was done to examine the existence and uniqueness of solutions of the system. We then formulated an inverse problem to obtain estimates for the unknown parameters; data from multiple laboratories and experiments were used. Despite the sources of variability, the model simulations matched the data reasonably well in most cases. Our study shows that the multicompartment metabolism model does improve predictions over the previous model (Cole et al. in J. Toxicol. Environ. Health, 439-465, 2001) and that in vitro metabolic constants can be successfully extrapolated to predict in vivo data for benzene metabolism and dosimetry.
Bulletin of Mathematical Biology 04/2010; 72(3):507-40. · 2.02 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this paper three different filtering methods, the Extended Kalman Filter (EKF), the Gauss-Hermite Filter (GHF), and the Unscented Kalman Filter (UKF), are compared for state-only and coupled state and parameter estimation when used with log state variables of a model of the immunologic response to the human immunodeficiency virus (HIV) in individuals. The filters are implemented to estimate model states as well as model parameters from simulated noisy data, and are compared in terms of estimation accuracy and computational time. Numerical experiments reveal that the GHF is the most computationally expensive algorithm, while the EKF is the least expensive one. In addition, computational experiments suggest that there is little difference in the estimation accuracy between the UKF and GHF. When measurements are taken as frequently as every week to two weeks, the EKF is the superior filter. When measurements are further apart, the UKF is the best choice in the problem under investigation.
Mathematical Biosciences and Engineering 04/2010; 7(2):213-36. · 1.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In an effort to achieve higher power RF source performance, designers are utilizing distributed beam devices, such as sheet beams and multiple beams. The desire is to develop distributed beam devices that utilize fundamental mode cavities in the RF circuit. A limitation is the amount of current that can be emitted by the cathode while still achieving long cathode lifetimes. For multiple beam devices where the individual beams propagate at the same radius as the cathode, a limitation is reached when the size of the cathode becomes limited by the space available. A solution is to place the cathodes at a larger radius and compress the beams toward the radius required for fundamental mode cavities. This paper describes design of a multiple beam gun where the ensemble of beams is compressed toward the device axis while still achieving parallel propagation through the RF circuit.
[Show abstract][Hide abstract] ABSTRACT: The advent of high current density cathodes allows electron guns with low or zero compression beams. With little or no compression, it is easier to achieve high beam quality with reduced dependence on focusing structures. This is of particular interest for mm-wave tubes, where beam quality is critical and very tight tolerances are difficult to achieve.
[Show abstract][Hide abstract] ABSTRACT: This paper describes implementation of optimization routines in the 3-D trajectory code Beam Optics Analyzer (BOA). Specifically, techniques are being developed for designing confined flow electron guns for a variety of applications, including sheet beam and multiple beam guns. The current emphasis is on design of magnetic circuits to achieve a specified magnetic field profile for immersed flow. This includes specification of coil currents and polepiece geometries. The goal functions, optimization routines, and simulation results will be presented.
[Show abstract][Hide abstract] ABSTRACT: Creek Research, Inc. (CCR) is continuing development of optimization routines for design of both simple and complex electron beam devices. The principle computational tool is Beam Optics Analyzer (BOA), a 3-D finite element charged particle analysis program with electrostatic and magnetostatic solvers . CCR is teamed with scientists and students at North Carolina State University to integrate advanced optimization routines into BOA. Previous reserach developed routines for optimizing cathode anode spacing to achieve a specified beam current, magnetic field registration to achieve a specified beam size, electrode geometry to minimize field gradients, and cathode shape to reduce beam ripple [2, 3].
IEEE International Conference on Plasma Science 01/2010;
[Show abstract][Hide abstract] ABSTRACT: Three-dimensional design codes are allowing the development of more complex electron beam devices with significant performance improvements over axially symmetric devices. Distributed beam RF devices, including multiple-beam and sheet-beam designs, allow significant reduction in operating voltage with improved efficiency and bandwidth. The increased parameter space, however, makes the design process extremely complicated and costly. This paper describes optimization techniques to automate the most time-consuming tasks of the design, which is searching the available parameter space to optimize performance. Both sheet-beam and multiple-beam designs are considered.
IEEE Transactions on Electron Devices 06/2009; · 2.06 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An automated, GUI-accessible optimizer has been implemented into Beam Optics Analyzer; the optimizer uses iterative methods to model electron guns and surface electric fields.
[Show abstract][Hide abstract] ABSTRACT: Iterative computational design of asymmetrical electron beam devices, such as sheet beam and multiple beam klystrons, requires 3D analysis involving complex geometries. Manual, iterative design is extremely difficult and impractical for all but the simplest devices. Computer optimization tools and techniques are described that provide automated design of these devices using common personal computers with reasonable execution times.
[Show abstract][Hide abstract] ABSTRACT: This paper illustrates the methodology necessary to ultimately im-plement the feedback control of HIV infection. To that end we describe a model of the immunologic response of the human immunodeficiency virus (HIV) in in-dividuals. We illustrate how optimal control methodology can produce a drug dosing strategy and how this treatment strategy possesses features of struc-tured treatment interruptions (STI). We then perform a sensitivity analysis of the model, illustrating use of both classical sensitivity functions and general-ized sensitivity functions. We also investigate the use of stochastic estimation to develop filters and estimate states and parameters from noisy data. In the course of this analysis, we show that automatic differentiation (AD) can be a powerful tool in this type of analysis.
International Journal of Pure and Applied Mathematics ————————————————————————– Volume. 01/2009; 57:357-392.
[Show abstract][Hide abstract] ABSTRACT: An automated, GUI-accessible optimizer has been implemented into Beam Optics Analyzer; the optimizer uses iterative methods to model electron guns and surface electric fields. Beam Optics Analyzer (BOA) is an adaptive mesh, finite element, charged particle trajectory modeling tool for designing 3D electron devices. Previous research included the optimized design of Brillouin focused electron guns for traveling wave tubes and confined flow Pierce electron guns for high power devices. This research provided the foundation for the current work.
IEEE International Conference on Plasma Science 01/2009;
[Show abstract][Hide abstract] ABSTRACT: To improve RF source performance and operate at higher frequencies, designers are investigating distributed beam devices, including sheet beam and multiple beam sources. Non-axially symmetric geometries provide significant challenges for computational design. In addition to the increased computational resources required, the available parameter space makes manual design difficult or impractical. This is being addressed by developing techniques for computer optimized design of these devices. This presentation reports on progress to develop the necessary design tools.
[Show abstract][Hide abstract] ABSTRACT: Cerebral autoregulation is a homeostatic mechanism which maintains blood flow despite changes in blood pressure in order to meet local metabolic demands. Several mechanisms play a role in cerebral autoregulation in order to adjust vascular tone and caliber of the cerebral vessels, but the exact etiology of the dynamics of these mechanism is not well understood. In this study, we discuss two patient specific models predicting cerebral blood flow velocity during postural change from sitting to standing. One model characterises cerebral autoregulation, the other describes the beat-to-beat distribution of blood flow to the major regions of the brain. Both models have been validated against experimental data from a healthy young subject.
Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference 01/2009; 2009:5470-3.
[Show abstract][Hide abstract] ABSTRACT: Calabazas Creek Research, Inc. (CCR) and North Carolina State University (NCSU) are funded by the U.S. Department of Energy to develop optimization techniques for designing complex, 3D devices. Work is in progress to design a sheet beam electron device with a non-periodic magnetic field and a doubly convergent multiple beam electron gun. The sheet beam research is using optimization to develop iron structures to locally modify the magnetic field to prevent curling of the beam edges. The multiple beam gun research is using optimally shaped surfaces and directional beam launching to avoid beam spiraling and preserve the beam shape as it is compressed about its local axis and the axis of the device by electrostatic and magnetostatic fields. Results from this research are presented as well as a brief description of the optimization techniques.
IEEE International Conference on Plasma Science 01/2009;
[Show abstract][Hide abstract] ABSTRACT: Calabazas Creek Research, Inc. (CCR) and North Carolina State University are developing optimization techniques for advanced, 3D, electron guns. Our approach uses advanced solid modeling CAD programs capable of controlling geometrical parameters with design tables manipulated by an optimization control program. Geometrical and parametric changes are simulated using a 3D, finite element, adaptive meshing charged particle program. Results of the beam analysis are analyzed and an optimization routine modifies the parameters to obtain user-defined performance goals. These techniques are applied to a number of gun geometries, and the results are described.