H. T. Tran

North Carolina State University, Raleigh, NC, United States

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Publications (74)52.36 Total impact

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    John David, Hien Tran, H. T. Banks
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    ABSTRACT: This paper describes a model of the immunologic response of the human immunodeficiency virus (HIV) in individuals. It then illustrates how a Receding Horizon Control (RHC) methodology can be used to drive the system to a stable equilibrium in which a strong immune response controls the viral load in the absence of drug treatment. We also illustrate how this feedback methodology can overcome unplanned treatment interruptions, inaccurate or incomplete data and imperfect model specification. We consider how ideas from stochastic estimation can be used in conjunction with RHC to create a robust treatment methodology. We then consider the performance of this methodology over random simulations of the previously considered clinical conditions. Copyright © 2010 John Wiley & Sons, Ltd.
    Optimal Control Applications and Methods 10/2011; 32(6):681 - 699. · 1.06 Impact Factor
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    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
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    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
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    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.
    01/2010;
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    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.
    01/2010;
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    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 [1]. 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;
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    John David, Hien Tran, H T Banks
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    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.
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    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.
    01/2009;
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    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.
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    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;
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    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.
    01/2009;
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    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.
    01/2009;
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    Cardiovascular Engineering 04/2008; 8(1):1-4. · 0.81 Impact Factor
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    ABSTRACT: This paper considers the problem of designing electron guns using computer optimization techniques. Several different design parameters are manipulated while considering multiple design criteria, including beam and gun properties. The optimization routines are described. Examples of guns designed using these techniques are presented. Future research is also described.
    IEEE Transactions on Plasma Science 03/2008; · 0.87 Impact Factor
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    ABSTRACT: Inhaled gases can cause respiratory depression by irritating (stimulating) nerves in the nasal cavity. Respiratory depression, in turn, decreases the rate of delivery of those gases to the stimulated nerves, potentially leading to a complex feedback response. In order to better understand how the nervous system responds to such chemicals, a mathematical model is created to describe how the presence of irritants affects respiration in the rat. The ordinary differential equation model describes the dosimetry of these reactive gases in the respiratory tract, with particular focus on the physiology of the upper respiratory tract, and on the neurological control of respiration rate due to signaling from the irritant-responsive nerves in the nasal cavity. The ventilation equation is altered to account for an apparent change in dynamics between the initial ventilation decrease and the recovery to steady state as seen in formaldehyde exposure data. Further, the model is evaluated and improved through optimization of particular parameters to describe formaldehyde-induced respiratory response data and through sensitivity analysis. The model predicts the formaldehyde data well, and hence the model is thought to be a reasonable description of the physiological system of sensory irritation. The model is also expected to translate well to other irritants.
    Bulletin of Mathematical Biology 03/2008; 70(2):555-88. · 2.02 Impact Factor
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    ABSTRACT: The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523-1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.
    Cardiovascular Engineering 01/2008; 8(2):94-108. · 1.20 Impact Factor
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    ABSTRACT: In this study we describe a model predicting heart rate regulation during postural change from sitting to standing and during head-up tilt in five healthy elderly adults. The model uses blood pressure as an input to predict baroreflex firing-rate, which in turn is used to predict efferent parasympathetic and sympathetic outflows. The model also includes the combined effects of vestibular and central command stimulation of muscle sympathetic nerve activity, which is increased at the onset of postural change. Concentrations of acetylcholine and noradrenaline, predicted as functions of sympathetic and parasympathetic outflow, are then used to estimate the heart rate response. Dynamics of the heart rate and the baroreflex firing rate are modeled using a system of coupled ordinary delay differential equations with 17 parameters. We have derived sensitivity equations and ranked sensitivities of all parameters with respect to all state variables in our model. Using this model we show that during head-up tilt, the baseline firing-rate is larger than during sit-to-stand and that the combined effect of vestibular and central command stimulation of muscle sympathetic nerve activity is less pronounced during head-up tilt than during sit-to-stand.
    Cardiovascular Engineering 01/2008; 8(2):73-87. · 1.20 Impact Factor
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    ABSTRACT: In this paper we compare several approaches to identifying certain key respiratory control parameters relying on data normally available from non-invasive measurements. We consider a simple model of the respiratory control system and describe issues related to numerical estimates of key parameters involved in respiratory function such as central and peripheral control gains, transport delay, and lung compartment volumes. The combination of model-specific structure and limited data availability influences the parameter estimation process. Methods for studying how to improve the parameter estimation process are examined including classical and generalized sensitivity analysis, and eigenvalue grouping. These methods are applied and compared in the context of clinically available data. These methods are also compared in conjunction with specialized tests such as the minimally invasive single-breath CO2 test that can improve the estimation, and the enforced fixed breathing test, which opens the control loop in the system. The analysis shows that it is impossible to estimate central and peripheral gain simultaneously without usage of ventilation measurement and a controlled perturbation of the respiratory system, such as the CO2 test. The numerical results are certainly model dependent, but the illustrated methods, the nature of the comparisons, and protocols will carry over to other models and data configurations.
    Cardiovascular Engineering 01/2008; 8(2):120-34. · 1.20 Impact Factor
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    ABSTRACT: Computer optimization is applied to three dimensional design of electron guns. The resulting designs exhibit improved performance with significantly reduced design cost compared to manual design. Design tables update geometric parameters in a solid modeling program, including dimensions for points defining spline surfaces. Algorithms then modified the geometry and other parameters based on goal functions defining the desired performance. Optimal designs were achieved by automatic execution of the optimization loop. Results for confined flow Pierce guns, sheet beam guns, and multiple beam guns will be described.
    Infrared and Millimeter Waves, 2007 and the 2007 15th International Conference on Terahertz Electronics. IRMMW-THz. Joint 32nd International Conference on; 10/2007
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    H. T. Banks, B. M. Lewis, H. T. Tran
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    ABSTRACT: State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design and synthesis methods of nonlinear feedback controllers and estimators for a broad class of nonlinear regulator problems. In essence, the SDRE approach involves mimicking standard linear quadratic regulator (LQR) formulation for linear systems. In particular, the technique consists of using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficient matrices. Theoretical advances have been made regarding the nonlinear regulator problem and the asymptotic stability properties of the system with full state feedback. However, there have not been any attempts at the theory regarding the asymptotic convergence of the estimator and the compensated system. This paper addresses these two issues as well as discussing numerical methods for approximating the solution to the SDRE. The Taylor series numerical methods works only for a certain class of systems, namely with constant control coefficient matrices, and only in small regions. The interpolation numerical method can be applied globally to a much larger class of systems. Examples will be provided to illustrate the effectiveness and potential of the SDRE technique for the design of nonlinear compensator-based feedback controllers.
    Computational Optimization and Applications 05/2007; 37(2):177-218. · 1.28 Impact Factor

Publication Stats

821 Citations
52.36 Total Impact Points

Institutions

  • 1992–2011
    • North Carolina State University
      • • Center for Research in Scientific Computation
      • • Department of Mathematics
      Raleigh, NC, United States
  • 2010
    • Meredith College
      Raleigh, North Carolina, United States
  • 2008
    • Karl-Franzens-Universität Graz
      • Institute of Mathematics and Scientific Computing
      Graz, Styria, Austria
    • University of Oxford
      • Department of Physiology, Anatomy and Genetics
      Oxford, ENG, United Kingdom
  • 2006
    • Calabazas Creek Research, Inc.
      San Mateo, California, United States
  • 2005
    • CSU Mentor
      Long Beach, California, United States
    • Inha University
      • Department of Mathematics
      Seoul, Seoul, South Korea
  • 2004
    • University of Louisiana at Lafayette
      • Department of Mathematics
      Lafayette, LA, United States