Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.

The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.

Quantitative model of the phase behavior of recombinant pH-responsive elastin-like polypeptides.

Quantitative models are required to engineer biomaterials with environmentally responsive properties. With this goal in mind, we developed a model that describes the pH-dependent phase behavior of a class of stimulus responsive elastin-like polypeptides (ELPs) that undergo reversible phase separation in response to their solution environment. Under isothermal conditions, charged ELPs can undergo phase separation when their charge is neutralized. Optimization of this behavior has been challenging because the pH at which they phase separate, pHt, depends on their composition, molecular weight, concentration, and temperature. To address this problem, we developed a quantitative model to describe the phase behavior of charged ELPs that uses the Henderson-Hasselbalch relationship to describe the effect of side-chain ionization on the phase-transition temperature of an ELP. The model was validated with pH-responsive ELPs that contained either acidic (Glu) or basic (His) residues. The phase separation of both ELPs fit this model across a range of pH. These results have important implications for applications of pH-responsive ELPs because they provide a quantitative model for the rational design of pH-responsive polypeptides whose transition can be triggered at a specified pH.

Real-Time Decision Making and Aggressive Behavior in Youth: A Heuristic Model of Response Evaluation and Decision (RED).

Considerable scientific and intervention attention has been paid to judgment and decision-making systems associated with aggressive behavior in youth. However, most empirical studies have investigated social-cognitive correlates of stable child and adolescent aggressiveness, and less is known about real-time decision making to engage in aggressive behavior. A model of real-time decision making must incorporate both impulsive actions and rational thought. The present paper advances a process model (response evaluation and decision; RED) of real-time behavioral judgments and decision making in aggressive youths with mathematic representations that may be used to quantify response strength. These components are a heuristic to describe decision making, though it is doubtful that individuals always mentally complete these steps. RED represents an organization of social-cognitive operations believed to be active during the response decision step of social information processing. The model posits that RED processes can be circumvented through impulsive responding. This article provides a description and integration of thoughtful, rational decision making and nonrational impulsivity in aggressive behavioral interactions.

Mechanistic Models of Anti-HIV Microbicide Drug Delivery

A new modality for preventing HIV transmission is emerging in the form of topical microbicides. Some clinical trials have shown some promising results of these methods of protection while other trials have failed to show efficacy. Due to the relatively novel nature of microbicide drug transport, a rigorous, deterministic analysis of that transport can help improve the design of microbicide vehicles and understand results from clinical trials. This type of analysis can aid microbicide product design by helping understand and organize the determinants of drug transport and the potential efficacies of candidate microbicide products.

Microbicide drug transport is modeled as a diffusion process with convection and reaction effects in appropriate compartments. This is applied here to vaginal gels and rings and a rectal enema, all delivering the microbicide drug Tenofovir. Although the focus here is on Tenofovir, the methods established in this dissertation can readily be adapted to other drugs, given knowledge of their physical and chemical properties, such as the diffusion coefficient, partition coefficient, and reaction kinetics. Other dosage forms such as tablets and fiber meshes can also be modeled using the perspective and methods developed here.

The analyses here include convective details of intravaginal flows by both ambient fluid and spreading gels with different rheological properties and applied volumes. These are input to the overall conservation equations for drug mass transport in different compartments. The results are Tenofovir concentration distributions in time and space for a variety of microbicide products and conditions. The Tenofovir concentrations in the vaginal and rectal mucosal stroma are converted, via a coupled reaction equation, to concentrations of Tenofovir diphosphate, which is the active form of the drug that functions as a reverse transcriptase inhibitor against HIV. Key model outputs are related to concentrations measured in experimental pharmacokinetic (PK) studies, e.g. concentrations in biopsies and blood. A new measure of microbicide prophylactic functionality, the Percent Protected, is calculated. This is the time dependent volume of the entire stroma (and thus fraction of host cells therein) in which Tenofovir diphosphate concentrations equal or exceed a target prophylactic value, e.g. an EC50.

Results show the prophylactic potentials of the studied microbicide vehicles against HIV infections. Key design parameters for each are addressed in application of the models. For a vaginal gel, fast spreading at small volume is more effective than slower spreading at high volume. Vaginal rings are shown to be most effective if inserted and retained as close to the fornix as possible. Because of the long half-life of Tenofovir diphosphate, temporary removal of the vaginal ring (after achieving steady state) for up to 24h does not appreciably diminish Percent Protected. However, full steady state (for the entire stromal volume) is not achieved until several days after ring insertion. Delivery of Tenofovir to the rectal mucosa by an enema is dominated by surface area of coated mucosa and whether the interiors of rectal crypts are filled with the enema fluid. For the enema 100% Percent Protected is achieved much more rapidly than for vaginal products, primarily because of the much thinner epithelial layer of the mucosa. For example, 100% Percent Protected can be achieved with a one minute enema application, and 15 minute wait time.

Results of these models have good agreement with experimental pharmacokinetic data, in animals and clinical trials. They also improve upon traditional, empirical PK modeling, and this is illustrated here. Our deterministic approach can inform design of sampling in clinical trials by indicating time periods during which significant changes in drug concentrations occur in different compartments. More fundamentally, the work here helps delineate the determinants of microbicide drug delivery. This information can be the key to improved, rational design of microbicide products and their dosage regimens.