Hien Tran

North Carolina State University, Raleigh, North Carolina, United States

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Publications (102)82.49 Total impact

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    ABSTRACT: In nonlinear mixed effect (NLME) modeling, the intra-individual variability is a collection of errors due to assay sensitivity, dosing, sampling, as well as model misspecification. Utilizing stochastic differential equations (SDE) within the NLME framework allows the decoupling of the measurement errors from the model misspecification. This leads the SDE approach to be a novel tool for model refinement. Using Metformin clinical pharmacokinetic (PK) data, the process of model development through the use of SDEs in population PK modeling was done to study the dynamics of absorption rate. A base model was constructed and then refined by using the system noise terms of the SDEs to track model parameters and model misspecification. This provides the unique advantage of making no underlying assumptions about the structural model for the absorption process while quantifying insufficiencies in the current model. This article focuses on implementing the extended Kalman filter and unscented Kalman filter in an NLME framework for parameter estimation and model development, comparing the methodologies, and illustrating their challenges and utility. The Kalman filter algorithms were successfully implemented in NLME models using MATLAB with run time differences between the ODE and SDE methods comparable to the differences found by Kakhi [10] for their stochastic deconvolution.
    No preview · Article · Nov 2015 · Journal of Pharmacokinetics and Pharmacodynamics
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    ABSTRACT: The cardiovascular control system is continuously engaged to maintain homeostasis, but it is known to fail in a large cohort of patients suffering from orthostatic intolerance. Numerous clinical studies have been put forward to understand how the system fails, yet non-invasive clinical data are sparse, typical studies only include measurements of heart rate and blood pressure, as a result it is difficult to determine what mechanisms that are impaired. It is known, that blood pressure regulation is mediated by changes in heart rate, vascular resistance, cardiac contractility and a number of other factors. Given that numerous factors contribute to changing these quantities it is difficult to devise a physiological model describing how they change in time. One way is to build a model that allows these controlled quantities to change and to compare dynamics between subject groups. To do so, requires more knowledge of how these quantities change for healthy subjects. This study compares two methods predicting time-varying changes in cardiac contractility and vascular resistance during headup tilt. Similar to the study by Williams et al. [57], the first method uses piecewise linear splines, while the second uses the ensemble transform Kalman filter (ETKF) [1], [12], [13], [35]. In addition, we show that the delayed rejection adaptive Metropolis (DRAM) algorithm can be used for predicting parameter uncertainties within the spline methodology, which is compared with the variability obtained with the ETKF. While the spline method is easier to set up, this study shows that the ETKF has a significantly shorter computational time. Moreover, while uncertainty of predictions can be augmented to spline predictions using DRAM, these are readily available with the ETKF.
    No preview · Article · Mar 2015 · IEEE transactions on bio-medical engineering
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    ABSTRACT: A method is presented for optimizing the design of klystron circuits. This automates the selection of cavity positions, resonant frequencies, quality factors, R/Q and other circuit parameters to maximize the efficiency with required gain. The method is based on deterministic sampling methods. In this paper, we describe the procedure and give several examples for both narrow-band and wideband klystrons, using the klystron codes AJDISK and TESLA.
    No preview · Article · Mar 2015 · IEEE Transactions on Electron Devices
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    ABSTRACT: Filtering is a methodology used to combine a set of observations with a model to obtain the optimal state. This technique can be extended to estimate the state of the system as well as the unknown model parameters. Estimating the model parameters given a set of data is often referred to as the inverse problem. Filtering provides many benefits to the inverse problem by providing estimates in real time and allowing model errors to be taken into account. Assuming a linear model and Gaussian noises, the optimal filter is the Kalman filter. However, these assumptions rarely hold for many problems of interest, so a number of extensions have been proposed in the literature to deal with nonlinear dynamics. In this chapter, we illustrate the application of one approach to deal with nonlinear model dynamics, the so-called unscented Kalman filter. In addition, we will also show how some of the tools for model validation discussed in other chapters of this volume can be used to improve the estimation process.
    No preview · Article · Jan 2013 · Lecture Notes in Mathematics -Springer-verlag-
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    ABSTRACT: Filtering is a methodology used to combine a set of observations with a model to obtain the optimal state. This technique can be extended to estimate the state of the system as well as the unknown model parameters. Estimating the model parameters given a set of data is often referred to as the inverse problem. Filtering provides many benefits to the inverse problem by providing estimates in real time and allowing model errors to be taken into account. Assuming a linear model and Gaussian noises, the optimal filter is the Kalman filter. However, these assumptions rarely hold for many problems of interest, so a number of extensions have been proposed in the literature to deal with nonlinear dynamics. In this chapter, we illustrate the application of one approach to deal with nonlinear model dynamics, the so-called unscented Kalman filter. In addition, we will also show how some of the tools for model validation discussed in other chapters of this volume can be used to improve the estimation process.
    No preview · Chapter · Jan 2013
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    H.T. Banks · Karen M. Bliss · Hien Tran
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    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.
    Full-text · Article · Jan 2012 · International Journal of Pure and Applied Mathematics

  • No preview · Chapter · Jan 2012
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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.
    Full-text · Article · Nov 2011 · Optimal Control Applications and Methods
  • Brian M. Lewis · Hien T. Tran
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    ABSTRACT: In this paper, we consider the real-time synthesis of reduced order model based control methodologies for the attenuation of vibrations of a cantilever beam caused by either a transient spike disturbance or a narrow-band exogenous force in a smart structure paradigm. By a narrow-band exogenous force we mean a periodic force over a narrow frequency band or a particular harmonic. The control methods under consideration are based on the minimization of two specific quadratic cost functionals. One of these cost functionals is a typical time domain cost functional constrained by an affine plant. The other is a cost functional that is frequency dependent. These control methods have been used successfully in various applications but this investigation differs from other works in that it emphasizes the development of real-time control methodologies based on reduced order models derived from physical first principles. In particular, we consider two reduced order model based control approaches: reduce the order of the model followed by control formulation and formulate a control based on the full order model followed by control reduction.
    No preview · Article · Jan 2011
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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. 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.
    No preview · Article · Jul 2010 · IEEE Transactions on Plasma Science
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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.
    No preview · Article · May 2010
  • Michael Read · Lawrence Ives · Thuc Bui · Hien Tran
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    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.
    No preview · Article · May 2010
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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.
    Full-text · Article · Apr 2010 · Bulletin of Mathematical Biology
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    H Thomas Banks · Shuhua Hu · Zackary R Kenz · Hien T Tran
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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.
    Full-text · Article · Apr 2010 · Mathematical Biosciences and Engineering
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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.
    No preview · Article · Jan 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].
    No preview · Article · Jan 2010 · IEEE International Conference on Plasma Science
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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.
    Full-text · Article · Sep 2009 · Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference
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    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.
    No preview · Article · Jun 2009 · IEEE Transactions on Electron Devices
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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.
    Full-text · Article · Jan 2009 · International Journal of Pure and Applied Mathematics
  • R. L. Ives · T. Bui · M. Read · W. Tallis · A. Attarian · H. T. Tran
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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.
    No preview · Article · Jan 2009 · IEEE International Conference on Plasma Science

Publication Stats

2k Citations
82.49 Total Impact Points

Institutions

  • 1992-2015
    • North Carolina State University
      • • Department of Mathematics
      • • Center for Research in Scientific Computation
      Raleigh, North Carolina, United States
  • 2002-2006
    • Calabazas Creek Research, Inc.
      San Mateo, California, United States
  • 2005
    • Inha University
      • Department of Mathematics
      Seoul, Seoul, South Korea
  • 2004
    • Meredith College
      Raleigh, North Carolina, United States