Michele L. Joyner

Nondestructive evaluation using a reduced order computational methodology

This paper uses eddy current based techniques and reduced order modeling to explore the feasibility of detecting a subsurface damage in structures such as air foils and pipelines. To identify the geometry of a damage, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. Therefore, our computational methods are based on the reduced order Karhunen-Loeve or Proper Orthogonal Decomposition (POD) techniques. For proof-of-concept, we implement the methodology on a 2-D problem and find the methods to be efficient and robust even with data containing 10 Furthermore, the methods are fast; our findings suggest we can reduce the computational time on average by a factor of 3000.

Modeling the effects of introducing a new antibiotic in a hospital setting: A case study.

The increase in antibiotic resistance continues to pose a public health risk as very few new antibiotics are being produced, and bacteria resistant to currently prescribed antibiotics is growing. Within a typical hospital setting, one may find patients colonized with bacteria resistant to a single antibiotic, or, of a more emergent threat, patients may be colonized with bacteria resistant to multiple antibiotics. Precautions have been implemented to try to prevent the growth and spread of antimicrobial resistance such as a reduction in the distribution of antibiotics and increased hand washing and barrier preventions; however, the rise of this resistance is still evident. As a result, there is a new movement to try to re-examine the need for the development of new antibiotics. In this paper, we use mathematical models to study the possible benefits of implementing a new antibiotic in this setting; through these models, we examine the use of a new antibiotic that is distributed in various ways and how this could reduce total resistance in the hospital. We compare several different models in which patients colonized with both single and dual-resistant bacteria are present, including a model with no additional treatment protocols for the population colonized with dual-resistant bacteria as well as models including isolation and/or treatment with a new antibiotic. We examine the benefits and limitations of each scenario in the simulations presented.

A numerical study of the POD method in NDE

Abstract In a previous paper [H.T. Banks, M.L. Joyner, B. Wincheski, W.P. Winfree, Real-time computational algorithms for eddy current-based damage detection, Inverse Problems 18 (2002) 795–823], we demonstrated the viability of using the proper orthogonal decomposition (POD) (also called principal component analysis) method in conjunction with eddy current nondestructive evaluation techniques when using either simulated or experimental data. In this paper we explore which factors impact the effectiveness of the POD method in the NDE damage detection problem. We examine whether or not the number of snapshots used to form the POD basis affects the accuracy of the estimation of the damage parameter. We also consider whether or not it is necessary to vary the damage parameters in the set of snapshots incrementally or whether it is possible to utilize random damage parameters and result in the same order of accuracy in the damage estimation. In addition, we examine how much relative error in the POD approximation we can sustain and still obtain fairly precise results in the inverse problem. We also consider whether or not the answers to the above questions are the same for different damage parameters or if the parameter we wish to approximate has an impact on the answers to these questions.

AIC under the framework of least squares estimation

Abstract In this note we explain the use of the Akiake Information Criterion and its related model comparison indices (usually derived for maximum likelihood estimator inverse problem formulations) in the context of least squares (ordinary, weighted, iterative weighted or “generalized”, etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in biology.

Comparison of two techniques for implementing the proper orthogonal decomposition method in damage detection problems

The viability of using the reduced-order proper orthogonal decomposition (POD) (alsocalled principal component analysis) methods to reduce the total computational time to detect damages using eddy current nondestructive evaluation techniques was demonstrated in a previous paper [1]. In this paper, we concentrate on various alternatives used to form the reduced-order solution to the forward problem, still in the context of eddy current damage detection. In particular, we focus on two different algorithms, a POD/Galerkin technique and a POD/interpolation technique. The POD/Galerkin method is a popular choice in the implementation of the POD method; however, in this paper, we will point out some of the problems in the traditional implementation of the reduced-order POD/Galerkin method when used in conjunction with eddy current damage detection. We will also compare the POD/Galerkin method to the POD/interpolation method and argue that in certain circumstances, the POD/interpolation method may be a better choice.

An aggregate stochastic model incorporating individual dynamics for predation movements of Anelosimus studiosus.

In this paper, we discuss methods for developing a stochastic model which incorporates behavior differences in the predation movements of Anelosimus studiosus (a subsocial spider). Stochastic models for animal movement and, in particular, spider predation movement have been developed previously; however, this paper focuses on the development and implementation of the necessary mathematical and statistical methods required to expand such a model in order to capture a variety of distinct behaviors. A least squares optimization algorithm is used for parameter estimation to fit a single stochastic model to an individual spider during predation resulting in unique parameter values for each spider. Similarities and variations between parameter values across the spiders are analyzed and used to estimate probability distributions for the variable parameter values. An aggregate stochastic model is then created which incorporates the individual dynamics. The comparison between the optimal individual models to the aggregate model indicate the methodology and algorithm developed in this paper are appropriate for simulating a range of individualistic behaviors.

MODELING THE DIFFERENCES IN THE DEVELOPMENT OF A NEW ANTIBIOTIC CLASS VERSUS THE DEVELOPMENT OF A NEXT GENERATION ANTIBIOTIC ON THE TOTAL RESISTANCE IN A HOSPITAL SETTING

The increase in antibiotic resistance continues to pose a major public health risk leading to a more intense focus on ways to limit and even reduce this threat. One such effort is the push for twenty new classes of antibiotics by the year 2020. Most of the current antibiotics used today are derivations of antibiotics first introduced forty to fifty years ago. In this paper, we develop mathematical models to simulate the difference between implementing a next generation antibiotic versus a new class antibiotic within a hospital setting. Using these models, we simulate the short term and long term effects of using the new antibiotic to combat existing levels of antimicrobial resistance. In addition to analyzing the difference in antibiotic classes, we also analyze the effects of the method of administration of the new antibiotic. Simulations suggest a need in the long term for the development of new classes of antibiotics administered in a very structured, targeted manner.

Information Content in Data Sets: A Review of Methods for Interrogation and Model Comparison

Abstract In this review we discuss methodology to ascertain the amount of information in given data sets with respect to determination of model parameters with desired levels of uncertainty. We do this in the context of least squares (ordinary, weighted, iterative reweighted weighted or “generalized”, etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in the biological and environmental sciences.

Spatio-temporal analysis of foraging behaviors of Anelosimus studiosus utilizing mathematical modeling of multiple spider interaction on a cooperative web.

In this paper, we develop a model for predation movements of a subsocial spider species, Anelosimus studiosus. We expand on a previous model to include multiple spider interaction on the web as well as a latency period during predation. We then use the model to test different spatial configurations to determine the optimal spacing of spiders within a colony for successful capture during predation. The model simulations indicate that spiders uniformly spacing out along the edge of the web results in the most successful predation strategy. This is similar to the behavior observed by Ross (2013) in which it was determined to be statistically significant that during certain times of the day, spiders were positioned along the edge more than expected under complete spatial randomness.

A physiologically-based pharmacokinetic model for the antibiotic ertapenem.

Ertapenem is an antibiotic commonly used to treat a broad spectrum of infections, which is part of a broader class of antibiotics called carbapenem. Unlike other carbapenems, ertapenem has a longer half-life and thus only has to be administered once a day. A physiologically-based pharmacokinetic (PBPK) model was developed to investigate the uptake, distribution, and elimination of ertapenem following a single one gram dose. PBPK modeling incorporates known physiological parameters such as body weight, organ volumes, and blood flow rates in particular tissues. Furthermore, ertapenem is highly bound in human blood plasma; therefore, nonlinear binding is incorporated in the model since only the free portion of the drug can saturate tissues and, hence, is the only portion of the drug considered to be medicinally effective. Parameters in the model were estimated using a least squares inverse problem formulation with published data for blood concentrations of ertapenem for normal height, normal weight males. Finally, an uncertainty analysis of the parameter estimation and model predictions is presented.