Applied Mathematics Commons^™

Hemodynamic Analysis Of Fast And Slow Aneurysm Occlusions By Flow Diversion In Rabbits, Bong Jae Chung, Fernando Mut, Ramanathan Kadirvel, Ravi Lingineni, David F. Kallmes, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Purpose: To assess hemodynamic differences between aneurysms that occlude rapidly and those occluding in delayed fashion after flow diversion in rabbits. Methods: Thirty-six elastase-induced aneurysms in rabbits were treated with flow diverting devices. Aneurysm occlusion was assessed angiographically immediately before they were sacrificed at 1 (n=6), 2 (n=4), 4 (n=8) or 8 weeks (n=18) after treatment. The aneurysms were classified into a fast occlusion group if they were completely or near completely occluded at 4 weeks or earlier and a slow occlusion group if they remained incompletely occluded at 8 weeks. The immediate post-treatment flow conditions in aneurysms of each …

Wall Mechanical Properties And Hemodynamics Of Unruptured Intracranial Aneurysms, J. R. Cebral, X. Duan, Bong Jae Chung, C. Putman, Khaled Aziz, A. M. Robertson

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Aneurysm progression and rupture is thought to be governed by progressive degradation and weakening of the wall in response to abnormal hemodynamics. Our goal was to investigate the relationship between the intra-aneurysmal hemodynamic conditions and wall mechanical properties in human aneurysms. MATERIALS AND METHODS: A total of 8 unruptured aneurysms were analyzed. Computational fluid dynamics models were constructed from preoperative 3D rotational angiography images. The aneurysms were clipped, and the domes were resected and mechanically tested to failure with a uniaxial testing system under multiphoton microscopy. Linear regression analysis was performed to explore possible correlations between hemodynamic …

A Framework For Inferring Unobserved Multistrain Epidemic Subpopulations Using Synchronization Dynamics, Eric Forgoston, Leah B. Shaw, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A new method is proposed to infer unobserved epidemic subpopulations by exploiting the synchronization properties of multistrain epidemic models. A model for dengue fever is driven by simulated data from secondary infective populations. Primary infective populations in the driven system synchronize to the correct values from the driver system. Most hospital cases of dengue are secondary infections, so this method provides a way to deduce unobserved primary infection levels. We derive center manifold equations that relate the driven system to the driver system and thus motivate the use of synchronization to predict unobserved primary infectives. Synchronization stability between primary and …

Penalized Function-On-Function Regression, Andrada Ivanescu, Ana Maria Staicu, Fabian Scheipl, Sonja Greven

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A general framework for smooth regression of a functional response on one or multiple functional predictors is proposed. Using the mixed model representation of penalized regression expands the scope of function-on-function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional response as well as multiple functional predictors that are observed on the same or different domains than the functional response, on a dense or sparse grid, and with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals as a by-product of the …

Predicting Successful Long-Term Weight Loss From Short-Term Weight-Loss Outcomes: New Insights From A Dynamic Energy Balance Model (The Pounds Lost Study), Diana Thomas, W Andrada Ivanescu, Corby K. Martin, Steven B. Heymsfield, Kaitlyn Marshall, Victoria E. Bodrato, Donald Williamson, Stephen Anton, Frank M. Sacks, Donna Ryan, George A. Bray

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background: Currently, early weight-loss predictions of long-term weight-loss success rely on fixed percent-weight-loss thresholds.

Objective: The objective was to develop thresholds during the first 3 mo of intervention that include the influence of age, sex, baseline weight, percent weight loss, and deviations from expected weight to predict whether a participant is likely to lose 5% or more body weight by year 1.

Design: Data consisting of month 1, 2, 3, and 12 treatment weights were obtained from the 2-y Preventing Obesity Using Novel Dietary Strategies (POUNDS Lost) intervention. Logistic regression models that included covariates of age, height, sex, baseline weight, …

Modeling Contagion In The Eurozone Crisis Via Dynamical Systems, Giuseppe Castellacci, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We recently (Castellacci and Choi, 2013) formulated a theoretical framework for the modeling of financial instability contagion using the theories of dynamical systems. Here, our main goal is to model the Eurozone financial crisis within that framework. The underlying system comprises many economic agents that belong to several subsystems. In each instantiation of this framework, the hierarchy and nesting of the subsystems is dictated by the nature of the problem at hand. We describe in great detail how a suitable model can be set up for the Eurozone crisis. The dynamical system is defined by the evolution of the wealths …

The Coupled Within- And Between-Host Dynamics In The Evolution Of Hiv/Aids In China, Jie Lou, Hongna Zhou, Dong Liang, Zhen Jin, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this work, we develop and analyze mathematical models for the coupled within-host and between-host dynamics caricaturing the evolution of HIV/AIDS. The host population is divided into susceptible, the infected without receiving treatment and the infected receiving ART treatment in accordance with China’s Four-Free-One-Care Policy. The within-host model is a typical ODE model adopted from literatures. The between-host model incorporates age-since-infection described by a system of integrodifferential equations. The two models are coupled via the viral load and number of CD4+ T cells of within the hosts. For the between-host model with an arbitrarily selected HIV infected individual, we focus …