@article{banks_holm_wanner_cintron-arias_kepler_wetherington_2009, title={A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system}, volume={50}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2009.02.007}, abstractNote={We present a preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart. We use a compartmental mass balance approach to develop a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection. We discuss sensitivity analysis as well as methodology for minimizing mass in the heart while maximizing mass delivered to the lungs on a first circulatory pass.}, number={7-8}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Holm, Kathleen and Wanner, Nathan C. and Cintron-Arias, Ariel and Kepler, Grace M. and Wetherington, Jeffrey D.}, year={2009}, month={Oct}, pages={959–974} }
 @article{kepler_banksa_davidian_rosenberg_2009, title={A model for HCMV infection in immunosuppressed patients}, volume={49}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2008.06.003}, abstractNote={We propose a model for HCMV infection in healthy and immunosuppressed patients. First, we present the biological model and formulate a system of ordinary differential equations to describe the pathogenesis of primary HCMV infection in immunocompetent and immunosuppressed individuals. We then investigate how clinical data can be applied to this model. Approximate parameter values for the model are derived from data available in the literature and from mathematical and physiological considerations. Simulations with the approximated parameter values demonstrates that the model is capable of describing primary, latent, and secondary (reactivated) HCMV infection. Reactivation simulations with this model provide a window into the dynamics of HCMV infection in (D-R+) transplant situations, where latently-infected recipients (R+) receive transplant tissue from HCMV-naive donors (D-).}, number={7-8}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Kepler, G. M. and Banksa, H. T. and Davidian, M. and Rosenberg, E. S.}, year={2009}, month={Apr}, pages={1653–1663} }
 @article{segal_kepler_kimbell_2008, title={Effects of differences in nasal anatomy on airflow distribution: A comparison of four individuals at rest}, volume={36}, ISSN={["1573-9686"]}, DOI={10.1007/s10439-008-9556-2}, abstractNote={Differences in nasal anatomy among human subjects may cause significant differences in respiratory airflow patterns and subsequent dosimetry of inhaled gases and particles in the respiratory tract. This study used computational fluid dynamics (CFD) to study inter-individual differences in nasal airflow among four healthy individuals. Magnetic resonance imaging (MRI) scans were digitized and nasal-surface-area-to-volume ratios (SAVR) were calculated for 15 adults. Two males and two females, representative of the range of SAVR values, were selected for flow analysis. Nasal CFD models were constructed for each subject by a semi-automated process that provided input to a commercial mesh generator to generate structured hexahedral meshes (Gambit, Fluent, Inc., Lebanon, NH, USA). Steady-state inspiratory laminar airflow at 15 L/min was calculated using commercial CFD software (FIDAP, Fluent, Inc., Lebanon, NH, USA). Streamline patterns, velocities, and helicity values were compared. In all subjects, the majority of flow passed through the middle and ventral regions of the nasal passages; however, the amount and location of swirling flow differed among individuals. Cross-sectional flow allocation analysis also indicated inter-individual differences. Laboratory water-dye experiments confirmed streamlines and velocity magnitudes predicted by the computational model. These results suggest that significant inter-individual differences exist in bulk airflow patterns in the nose.}, number={11}, journal={ANNALS OF BIOMEDICAL ENGINEERING}, author={Segal, Rebecca A. and Kepler, Grace M. and Kimbell, Julia S.}, year={2008}, month={Nov}, pages={1870–1882} }
 @article{kepler_nguyen_webster-cyriaque_banks_2007, title={A dynamic model for induced reactivation of latent virus}, volume={244}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2006.08.020}, abstractNote={We develop a deterministic mathematical model to describe reactivation of latent virus by chemical inducers. This model is applied to the reactivation of latent KSHV in BCBL-1 cell cultures with butyrate as the inducing agent. Parameters for the model are first estimated from known properties of the exponentially growing, uninduced cell cultures. Additional parameters that are necessary to describe induction are determined from fits to experimental data from the literature. Our initial model provides good agreement with two independent sets of experimental data, but also points to the need for a new class of experiments which are required for further understanding of the underlying mechanisms.}, number={3}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Kepler, G. M. and Nguyen, H. K. and Webster-Cyriaque, J. and Banks, H. T.}, year={2007}, month={Feb}, pages={451–462} }
 @article{banks_ito_kepler_toivanen_2006, title={Material surface design to counter electromagnetic interrogation of targets}, volume={66}, ISSN={["1095-712X"]}, DOI={10.1137/040621430}, abstractNote={Utilization of controllable ferromagnetic layers coating a conducting object to provide an attenuation capability against electromagnetic interrogation is discussed. The problem is formulated as a differential game and/or a robust optimization. The scattered field due to interrogation can be attenuated with the assumption of an uncertainty in the interrogation wave numbers. The controllable layer composed of ferromagnetic materials [H. How and C. Vittoria, Implementation of Microwave Active Nulling, private communication; H. How and C. Vittoria, IEEE Trans. Microwave Theory Tech., 52 (2004), pp. 2177-2182] is incorporated in a mathematical formulation based on the time-harmonic Maxwell equation. Fresnel's law for the reflectance index is extended to the electromagnetic propagation in anisotropic composite layers of ferromagnetic and electronic devices and is used to demonstrate feasibility of control of reflections. Our methodology is also tested for a nonplanar geometry of the conducting object (an NACA ...}, number={3}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Banks, HT and Ito, K and Kepler, GM and Toivanen, JA}, year={2006}, pages={1027–1049} }
 @article{banks_beeler_kepler_tran_2002, title={Reduced order modeling and control of thin film growth in an HPCVD reactor}, volume={62}, ISSN={["1095-712X"]}, DOI={10.1137/S0036139901383280}, abstractNote={This paper describes the development of a reduced order model-based feedback control methodology for regulation of the growth of thin films in a high-pressure chemical vapor deposition (HPCVD) reactor. Precise control of the film thickness and composition is highly desirable, making real-time control of the deposition process very important. The source vapor species transport is modeled by the standard gas dynamics partial differential equations, with species decomposition reactions, reduced down to a small number of ordinary differential equations through use of the proper orthogonal decomposition technique. This system is coupled with a reduced order model of the surface reactions involved in the source vapor decomposition and film growth on the substrate. Also modeled is the real-time observation technique used to obtain a partial measurement of the deposition process.The utilization of reduced order models greatly simplifies the mathematical formulation of the physical process so that it can be solved...}, number={4}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Banks, HT and Beeler, SC and Kepler, GM and Tran, HT}, year={2002}, month={Apr}, pages={1251–1280} }
 @article{kepler_tran_banks_2001, title={Compensator control for chemical vapor deposition film growth using reduced-order design models}, volume={14}, ISSN={["1558-2345"]}, DOI={10.1109/66.939820}, abstractNote={We present a summary of investigations on the use of proper orthogonal decomposition techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapor deposition (HPCVD) reactor. These investigations incorporate multiple species and controls, gas phase reactions, and time dependent tracking signals that are consistent with pulsed vapor reactant inputs. Numerical implementation of the model-based feedback control uses a reduced-order state estimator, based on partial state observations of the fluxes of reactants at the substrate center, which can be achieved with current sensing technology. We demonstrate that the reduced-order state estimator or compensator system is capable of substantial control authority when applied to the full system.}, number={3}, journal={IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING}, author={Kepler, GM and Tran, HT and Banks, HT}, year={2001}, month={Aug}, pages={231–241} }
 @article{kepler_oprea_2001, title={Improved inference of mutation rates: I. An integral representation for the Luria-Delbruck distribution}, volume={59}, ISSN={["0040-5809"]}, DOI={10.1006/tpbi.2000.1498}, abstractNote={The estimation of mutation rates is ordinarily performed using results based on the Luria-Delbrück distribution. There are certain difficulties associated with the use of this distribution in practice, some of which we address in this paper (others in the companion paper, Oprea and Kepler, Theor. Popul. Biol., 2001). The distribution is difficult to compute exactly, especially for large values of the random variable. To overcome this problem, we derive an integral representation of the Luria-Delbrück distribution that can be computed easily for large culture sizes. In addition, we introduce the usual assumption of very small probability of having a large proportion of mutants only after the generating function has been computed. Thus, we obtain information on the moments for the more general case. We examine the asymptotic behavior of this system. We find a scaling or "standardization" technique that reduces the family of distributions parameterized by three parameters (mutation rate, initial cell number, and final cell number) to a single distribution with no parameters, valid so long as the product of the mutation rate and the final culture is sufficiently large. We provide a pair of techniques for computing confidence intervals for the mutation rate. In the second paper of this series, we use the distribution derived here to find approximate distributions for the case where the cell cycle time is not well-described as an exponential random variable as is implicitly assumed by Luria-Delbrück distribution.}, number={1}, journal={THEORETICAL POPULATION BIOLOGY}, author={Kepler, TB and Oprea, M}, year={2001}, month={Feb}, pages={41–48} }
 @article{kepler_tran_banks_2000, title={Reduced order model compensator control of species transport in a CVD reactor}, volume={21}, ISSN={["0143-2087"]}, DOI={10.1002/1099-1514(200007/08)21:4<143::AID-OCA671>3.0.CO;2-Y}, abstractNote={We propose the use of proper orthogonal decomposition (POD) techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapour deposition (HPCVD) reactor. In this paper, we present a proof-of-concept computational implementation of this method with a simplified growth example for III–V layers in which we implement Dirichlet boundary control of a dilute Group III reactant transported by convection and diffusion to an absorbing substrate with no reactions. We implement the model-based feedback control using a reduced order state estimator based on observations of the flux of reactant at the substrate centre. This is precisely the type of measurements available with current sensing technology. We demonstrate that the reduced order state estimator or compensator system is capable of substantial control authority when applied to a high-order system. In principle, these ideas can be extended to more general HPCVD control situations by including multiple species with gas-phase reactions and surface reactions. Copyright © 2000 John Wiley & Sons, Ltd.}, number={4}, journal={OPTIMAL CONTROL APPLICATIONS & METHODS}, author={Kepler, GM and Tran, HT and Banks, HT}, year={2000}, pages={143–160} }
 @article{bachmann_banks_hopfner_kepler_lesure_mccall_scroggs_1999, title={Optimal design of a high pressure organometallic chemical vapor deposition reactor}, volume={29}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(99)00071-0}, abstractNote={A team composed of material scientists, physicists, and applied mathematicians have used computer simulations as a fundamental design tool in developing a new prototype High Pressure Organometallic Chemical Vapor Deposition (HPOMCVD) reactor for use in thin film crystal growth. Early design of the HPOMCVD reactor dramatically evolved long before any physical reactor was built. This effort offers a strong endorsement of such multidisciplinary, computationally based modeling teams in the design of new products in areas of emerging technologies where heretofore extensive and costly experimental design was the central paradigm.}, number={8}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Bachmann, KJ and Banks, HT and Hopfner, C and Kepler, GM and LeSure, S and McCall, SD and Scroggs, JS}, year={1999}, month={Apr}, pages={65–80} }
 @article{kepler_richardson_morgan_kimbell_1998, title={Computer simulation of inspiratory nasal airflow and inhaled gas uptake in a rhesus monkey}, volume={150}, ISSN={["0041-008X"]}, DOI={10.1006/taap.1997.8350}, abstractNote={There is increasing evidence that inspiratory airflow patterns play a major role in determining the location of nasal lesions induced in rats by reactive, water-soluble gases such as formaldehyde and chlorine. Characteristic lesion patterns have also been seen in inhalation toxicity studies conducted in rhesus monkeys, the nasal anatomy of which resembles that of humans. To examine the hypothesis that regions of high airflow-dependent uptake and lesions occur in similar nasal locations in the primate, airflow and gas uptake patterns were simulated in an anatomically accurate computer model of the right nasal airway of a rhesus monkey. The results of finite-element simulations of steady-state inspiratory nasal airflow for the full range of resting physiological flow rates are reported. Simulated airflow patterns agreed well with experimental observations, exhibiting secondary flows in the anterior nose and streamlined flow posteriorly. Simulated airflow results were used to predict gas transport to the nasal passage walls using formaldehyde as an example compound. Results from the uptake simulations were compared with published observations of formaldehyde-induced nasal lesions in rhesus monkeys and indicated a strong correspondence between airflow-dependent transport patterns and local lesion sites. This rhesus computer model will provide a means for confirming the extrapolation of toxicity data between species by extrapolating rat simulation results to monkeys and comparing these predictions with primate lesion data.}, number={1}, journal={TOXICOLOGY AND APPLIED PHARMACOLOGY}, author={Kepler, GM and Richardson, RB and Morgan, KT and Kimbell, JS}, year={1998}, month={May}, pages={1–11} }
 @article{kepler_hopfner_scroggs_bachmann_1998, title={Simulation of a vertical reactor for high pressure organometallic chemical vapor deposition}, volume={57}, ISSN={["0921-5107"]}, DOI={10.1016/s0921-5107(98)00256-6}, abstractNote={The suitability of a vertical cylindrical reactor with highly constrained radial flow from a central gas injection port past a set of heated substrate wafers that are embedded in the top channel wall has been evaluated in the context of organometallic chemical vapor deposition (OMCVD) at elevated pressure. Numerical simulations showed that, in addition to the limitation on the channel height necessary for preventing buoyancy driven recirculation, negotiating the ninety-degree bend at the inlet is problematic and also constrains the channel height below a critical value, at which the radial flow area after the inlet bend is equal to the cross-sectional area of the central gas injection port. Restricting the channel height poses the danger of heating of the channel wall opposite to the substrate wafers causing potential problems with deposition of decomposition products and competitive polycrystalline film growth at this location. These problems can be avoided by actively cooling the channel wall opposite to the substrate and by keeping the retention time of the source vapor molecules and fragments thereof in the wafer location below a critical value.}, number={1}, journal={MATERIALS SCIENCE AND ENGINEERING B-SOLID STATE MATERIALS FOR ADVANCED TECHNOLOGY}, author={Kepler, GM and Hopfner, C and Scroggs, JS and Bachmann, KJ}, year={1998}, month={Dec}, pages={9–17} }
 @article{backmann_kepler_1997, title={Heteroepitaxial processes at low and elevated pressures}, volume={3123}, ISBN={["0-8194-2545-1"]}, DOI={10.1117/12.277707}, abstractNote={Based on design criteria established in preceding work for conditions of moderately elevated pressure (less than or equal to 8 bar) we have designed and evaluated a reactor for chemical vapor deposition (CVD) at high pressure (less than or equal to 100 bar). While at moderate pressure non-turbulent unidirectional forced channel flow past a heated substrate wafer can be realized, at high pressure, the flow is expected to become turbulent. Due to phase front distortions and variations in angle of incidence associated with density fluctuations and density gradients in the high pressure vapor phase in the vicinity of the hot substrate -- the precision of methods of real-time optical process monitoring that employ polarized light, such as, p-polarized reflectance spectroscopy (PRS), is degraded. Above a critical pressure, features in the optical signals related to chemical kinetics and to the kinetics of heteroepitaxy, thus are no longer resolved. Therefore, experimentation at reduced gravity, which extends the pressure range of non-turbulent flow, and alternative robust methods of real-time optical process monitoring are considered. At very high pressures, where real-time process monitoring is severely curtailed, CVD processing must rely on predictions of numerical models -- validated by experimentation at lower pressure/low gravity. Experimentation at high pressure is needed to access materials, properties and/or structures that otherwise cannot be realized.}, journal={MATERIALS RESEARCH IN LOW GRAVITY}, author={Backmann, KJ and Kepler, GM}, year={1997}, pages={64–74} }