@article{banks_hu_rosenberg_2017, title={A dynamical modeling approach for analysis of longitudinal clinical trials in the presence of missing endpoints}, volume={63}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2016.07.002}, abstractNote={Randomized longitudinal clinical trials are the gold standard to evaluate the effectiveness of interventions among different patient treatment groups. However, analysis of such clinical trials becomes difficult in the presence of missing data, especially in the case where the study endpoints become difficult to measure because of subject dropout rates or/and the time to discontinue the assigned interventions are different among the patient groups. Here we report on using a validated mathematical model combined with an inverse problem approach to predict the values for the missing endpoints. A small randomized HIV clinical trial where endpoints for most of patients are missing is used to demonstrate this approach.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Hu, Shuhua and Rosenberg, Eric}, year={2017}, month={Jan}, pages={109–117} }
 @article{banks_hu_link_rosenberg_mitsuma_rosario_2016, title={Modelling immune response to BK virus infection and donor kidney in renal transplant recipients}, volume={24}, ISSN={["1741-5985"]}, DOI={10.1080/17415977.2015.1017484}, abstractNote={In this paper, we develop and validate with bootstrapping techniques a mechanistic mathematical model of immune response to both BK virus infection and a donor kidney based on known and hypothesized mechanisms in the literature. The model presented does not capture all the details of the immune response but possesses key features that describe a very complex immunological process. We then estimate model parameters using a least squares approach with a typical set of available clinical data. Sensitivity analysis combined with asymptotic theory is used to determine the number of parameters that can be reliably estimated given the limited number of observations.}, number={1}, journal={INVERSE PROBLEMS IN SCIENCE AND ENGINEERING}, author={Banks, H. T. and Hu, Shuhua and Link, Kathryn and Rosenberg, Eric S. and Mitsuma, Sheila and Rosario, Lauren}, year={2016}, month={Jan}, pages={127–152} }
 @article{banks_catenacci_hu_2016, title={Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems}, volume={24}, number={4}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Catenacci, J. and Hu, S. H.}, year={2016}, pages={413–433} }
 @article{brewin_birch_mehta_reeves_shaw_kruse_whiteman_hu_kenz_banks_et al._2015, title={Characterisation of Elastic and Acoustic Properties of an Agar-Based Tissue Mimicking Material}, volume={43}, ISSN={["1573-9686"]}, DOI={10.1007/s10439-015-1294-7}, abstractNote={As a first step towards an acoustic localisation device for coronary stenosis to provide a non-invasive means of diagnosing arterial disease, measurements are reported for an agar-based tissue mimicking material (TMM) of the shear wave propagation velocity, attenuation and viscoelastic constants, together with one dimensional quasi-static elastic moduli and Poisson’s ratio. Phase velocity and attenuation coefficients, determined by generating and detecting shear waves piezo-electrically in the range 300 Hz–2 kHz, were 3.2–7.5 ms−1 and 320 dBm−1. Quasi-static Young’s modulus, shear modulus and Poisson’s ratio, obtained by compressive or shear loading of cylindrical specimens were 150–160 kPa; 54–56 kPa and 0.37–0.44. The dynamic Young’s and shear moduli, derived from fitting viscoelastic internal variables by an iterative statistical inverse solver to freely oscillating specimens were 230 and 33 kPa and the corresponding relaxation times, 0.046 and 0.036 s. The results were self-consistent, repeatable and provide baseline data required for the computational modelling of wave propagation in a phantom.}, number={10}, journal={ANNALS OF BIOMEDICAL ENGINEERING}, author={Brewin, M. P. and Birch, M. J. and Mehta, D. J. and Reeves, J. W. and Shaw, S. and Kruse, C. and Whiteman, J. R. and Hu, S. and Kenz, Z. R. and Banks, H. T. and et al.}, year={2015}, month={Oct}, pages={2587–2596} }
 @article{banks_catenacci_hu_2015, title={Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance}, volume={23}, number={5}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Catenacci, J. and Hu, S. H.}, year={2015}, pages={491–509} }
 @inproceedings{criner_cherry_cooney_katter_banks_hu_catenacci_2015, title={Identification of thermal degradation using probabilistic models in reflectance spectroscopy}, volume={1650}, booktitle={41st annual review of progress in quantitative nondestructive evaluation, vol 34}, author={Criner, A. K. and Cherry, A. J. and Cooney, A. T. and Katter, T. D. and Banks, H. T. and Hu, S. H. and Catenacci, J.}, year={2015}, pages={1898–1906} }
 @article{banks_flores_hu_rosenberg_buzon_yu_lichterfeld_2015, title={Immuno-modulatory strategies for reduction of HIV reservoir cells}, volume={372}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2015.02.006}, abstractNote={Antiretroviral therapy is able to suppress the viral load to below the detection limit, but it is not able to eradicate HIV reservoirs. Thus, there is a critical need for a novel treatment to eradicate (or reduce) the reservoir in order to eliminate the need for a lifelong adherence to antiretroviral therapy, which is expensive and potentially toxic. In this paper, we investigate the possible pharmacological strategies or combinations of strategies that may be beneficial to reduce or possibly eradicate the latent reservoir. We do this via studies with a validated mathematical model, where the parameter values are obtained with newly acquired clinical data for HIV patients. Our findings indicate that the strategy of reactivating the reservoir combined with enhancement of the killing rate of HIV-specific CD8+ T cells is able to eradicate the reservoir. In addition, our analysis shows that a targeted suppression of the immune system is also a possible strategy to eradicate the reservoir.}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Banks, H. T. and Flores, Kevin B. and Hu, Shuhua and Rosenberg, Eric and Buzon, Maria and Yu, Xu and Lichterfeld, Matthias}, year={2015}, month={May}, pages={146–158} }
 @inproceedings{banks_catenacci_hu_kenz_2014, title={Decomposition of permittivity contributions from reflectance using mechanism models}, booktitle={2014 american control conference (acc)}, author={Banks, H. T. and Catenacci, J. and Hu, S. H. and Kenz, Z. R.}, year={2014}, pages={367–372} }
 @article{banks_birch_brewin_greenwald_hu_kenz_kruse_maischak_shaw_whiteman_2014, title={High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling}, volume={98}, ISSN={["1097-0207"]}, DOI={10.1002/nme.4631}, abstractNote={SUMMARY}, number={2}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING}, author={Banks, H. T. and Birch, Malcolm J. and Brewin, Mark P. and Greenwald, Stephen E. and Hu, Shuhua and Kenz, Zackary R. and Kruse, Carola and Maischak, Matthias and Shaw, Simon and Whiteman, John R.}, year={2014}, month={Apr}, pages={131–156} }
 @article{banks_hu_kenz_kruse_shaw_whiteman_brewin_greenwald_birch_2014, title={MODEL VALIDATION FOR A NONINVASIVE ARTERIAL STENOSIS DETECTION PROBLEM}, volume={11}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2014.11.427}, abstractNote={A current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use one-dimensional shear wave experimental data from novel acoustic phantoms to validate a corresponding viscoelastic mathematical model. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.}, number={3}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. Thomas and Hu, Shuhua and Kenz, Zackary R. and Kruse, Carola and Shaw, Simon and Whiteman, John and Brewin, Mark P. and Greenwald, Stephen E. and Birch, Malcolm J.}, year={2014}, month={Jun}, pages={427–448} }
 @article{banks_hu_kenz_kruse_shaw_whiteman_brewin_greenwald_birch_2013, title={Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology}, volume={21}, number={1}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Hu, S. H. and Kenz, Z. R. and Kruse, C. and Shaw, S. and Whiteman, J. R. and Brewin, M. P. and Greenwald, S. E. and Birch, M. J.}, year={2013}, pages={25–57} }
 @article{banks_hu_joyner_broido_canter_gayvert_link_2012, title={A COMPARISON OF COMPUTATIONAL EFFICIENCIES OF STOCHASTIC ALGORITHMS IN TERMS OF TWO INFECTION MODELS}, volume={9}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2012.9.487}, abstractNote={In this paper, we investigate three particular algorithms: a stochastic simulation algorithm (SSA), and explicit and implicit tau-leaping algorithms. To compare these methods, we used them to analyze two infection models: a Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunodeficiency Virus (HIV) within host infection model. While the first has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative efficiency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational efficiency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred.}, number={3}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. Thomas and Hu, Shuhua and Joyner, Michele and Broido, Anna and Canter, Brandi and Gayvert, Kaitlyn and Link, Kathryn}, year={2012}, month={Jul}, pages={487–526} }
 @article{banks_hu_2012, title={A zero-sum electromagnetic evader-interrogator differential game with uncertainty}, volume={91}, ISSN={["1563-504X"]}, DOI={10.1080/00036811.2012.667081}, abstractNote={We consider dynamic electromagnetic evasion-interrogation games in which the evader can use ferroelectric material coatings to attempt to avoid detection while the interrogator can manipulate the interrogating frequencies to enhance detection. The resulting problem is formulated as a two-player zero-sum dynamic differential game in which the cost functional is based on the expected value of the intensity of the reflected signal. We show that there exists a saddle point for the relaxed form of this dynamic differential game in which the relaxed controls appear bilinearly in the dynamics governed by a partial differential equation. We also present a computational framework for construction of approximate saddle point strategies in feedback form for a special case of this relaxed differential game with strategies and payoff in the sense of Berkovitz.}, number={4}, journal={APPLICABLE ANALYSIS}, author={Banks, H. T. and Hu, Shuhua}, year={2012}, pages={645–674} }
 @article{banks_hu_jang_kwon_2012, title={Modelling and optimal control of immune response of renal transplant recipients}, volume={6}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2012.655328}, abstractNote={We consider the increasingly important and highly complex immunological control problem: control of the dynamics of immunosuppression for organ transplant recipients. The goal in this problem is to maintain the delicate balance between over-suppression (where opportunistic latent viruses threaten the patient) and under-suppression (where rejection of the transplanted organ is probable). First, a mathematical model is formulated to describe the immune response to both viral infection and introduction of a donor kidney in a renal transplant recipient. Some numerical results are given to qualitatively validate and demonstrate that this initial model exhibits appropriate characteristics of primary infection and reactivation for immunosuppressed transplant recipients. In addition, we develop a computational framework for designing adaptive optimal treatment regimes with partial observations and low-frequency sampling, where the state estimates are obtained by solving a second deterministic optimal tracking problem. Numerical results are given to illustrate the feasibility of this method in obtaining optimal treatment regimes with a balance between under-suppression and over-suppression of the immune system.}, number={2}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Hu, Shuhua and Jang, Taesoo and Kwon, Hee-Dae}, year={2012}, pages={539–567} }
 @misc{banks_hu_kenz_2011, title={A Brief Review of Elasticity and Viscoelasticity for Solids}, volume={3}, ISSN={["2075-1354"]}, DOI={10.4208/aamm.10-m1030}, abstractNote={Abstract}, number={1}, journal={ADVANCES IN APPLIED MATHEMATICS AND MECHANICS}, author={Banks, Harvey Thomas and Hu, Shuhua and Kenz, Zackary R.}, year={2011}, month={Feb}, pages={1–51} }
 @article{banks_hu_ito_muccio_2011, title={Dynamic evasion-interrogation games with uncertainty in the context of electromagetics}, volume={4}, number={3}, journal={Numerical Mathematics: Theory, Methods and Applications}, author={Banks, H. T. and Hu, S. H. and Ito, K. and Muccio, S. G.}, year={2011}, pages={359–378} }
 @article{wendelsdorf_dean_hu_nordone_banks_2011, title={Host immune responses that promote initial HIV spread}, volume={289}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2011.08.012}, abstractNote={The host inflammatory response to HIV invasion is a necessary component of the innate antiviral activity that vaccines and early interventions seek to exploit/enhance. However, the response is dependent on CD4+ T-helper cell 1 (Th1) recruitment and activation. It is this very recruitment of HIV-susceptible target cells that is associated with the initial viral proliferation. Hence, global enhancement of the inflammatory response by T-cells and dendritic cells will likely feed viral propagation. Mucosal entry sites contain inherent pathways, in the form of natural regulatory T-cells (nTreg), that globally dampen the inflammatory response. We created a model of this inflammatory response to virus as well as inherent nTreg-mediated regulation of Th1 recruitment and activation. With simulations using this model we sought to address the net effect of nTreg activation and its specific functions as well as identify mechanisms of the natural inflammatory response that are best targeted to inhibit viral spread without compromising initial antiviral activity. Simulation results provide multiple insights that are relevant to developing intervention strategies that seek to exploit natural immune processes: (i) induction of the regulatory response through nTreg activation expedites viral proliferation due to viral production by nTreg itself and not to reduced Natural Killer (NK) cell activity; (ii) at the same time, induction of the inflammation response through either DC activation or Th1 activation expedites viral proliferation; (iii) within the inflammatory pathway, the NK response is an effective controller of viral proliferation while DC-mediated stimulation of T-cells is a significant driver of viral proliferation; and (iv) nTreg-mediated DC deactivation plays a significant role in slowing viral proliferation by inhibiting T-cell stimulation, making this function an aide to the antiviral immune response.}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Wendelsdorf, K. and Dean, G. and Hu, Shuhua and Nordone, S. and Banks, H. T.}, year={2011}, month={Nov}, pages={17–35} }
 @article{banks_davis_ernstberger_hu_artimovich_dhar_2009, title={Experimental design and estimation of growth rate distributions in size-structured shrimp populations}, volume={25}, number={9}, journal={Inverse Problems}, author={Banks, H. T. and Davis, J. L. and Ernstberger, S. L. and Hu, S. H. and Artimovich, E. and Dhar, A. K.}, year={2009} }
 @article{ackleh_hu_2007, title={Comparison between stochastic and deterministic selection-mutation models}, volume={4}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2007.4.133}, abstractNote={We present a deterministic selection-mutation model with a discrete trait variable. We show that for an irreducible selection-mutation matrix in the birth term the deterministic model has a unique interior equilibrium which is globally stable. Thus all subpopulations coexist. In the pure selection case, the outcome is known to be that of competitive exclusion, where the subpopulation with the largest growth-to-mortality ratio will survive and the remaining subpopulations will go extinct. We show that if the selection mutation matrix is reducible, then competitive exclusion or coexistence are possible outcomes. We then develop a stochastic population model based on the deterministic one. We show numerically that the mean behavior of the stochastic model in general agrees with the deterministic one. However, un like the deterministic one, if the differences in the growth-to-mortality ratios are small in the pure selection case, it cannot be determined a priori which subpopulation will have the highest probability of surviving and winning the competition.}, number={2}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Ackleh, Azmy S. and Hu, Shuhua}, year={2007}, month={Apr}, pages={133–157} }
 @article{banks_bokil_hu_2007, title={Monotone approximation for a nonlinear size and class age structured epidemic model}, volume={8}, ISSN={["1468-1218"]}, DOI={10.1016/j.nonrwa.2006.03.008}, abstractNote={In this paper, we study a nonautonomous size and class age structured epidemic model with nonlinear and nonlocal boundary conditions. We establish a comparison principle and construct convergent monotone sequences to prove the existence of solutions. Uniqueness of solutions is also established.}, number={3}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, H. T. and Bokil, V. A. and Hu, Shuhua}, year={2007}, month={Jul}, pages={834–852} }
 @article{ackleh_deng_hu_2007, title={On a nonlinear size-structured phytoplankton-zooplankton aggregation model}, volume={14}, number={2}, journal={Dynamics of Continuous, Discrete & Impulsive Systems. Series A, Mathematical Analysis}, author={Ackleh, A. S. and Deng, K. and Hu, S. H.}, year={2007}, pages={265–285} }
 @article{banks_grove_hu_ma_2005, title={A hierarchical Bayesian approach for parameter estimation in HIV models}, volume={21}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/21/6/001}, abstractNote={A hierarchical Bayesian approach is developed to estimate parameters at both the individual and the population levels in a HIV model, with the implementation carried out by Markov Chain Monte Carlo (MCMC) techniques. Sample numerical simulations and statistical results are provided to demonstrate the feasibility of this approach.}, number={6}, journal={INVERSE PROBLEMS}, author={Banks, HT and Grove, S and Hu, S and Ma, YY}, year={2005}, month={Dec}, pages={1803–1822} }