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Physical Sciences and Mathematics Commons™
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- Keyword
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- Agent-based models (2)
- Antibiotic resistance (2)
- Immune response (2)
- Mathematical model (2)
- Mean and variance modulations (2)
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- Nosocomial infection (2)
- Ant (1)
- Antimicrobial stewadship; Mathematical modeling; Healthcare-associated infection; Nosocomial infection; Epidemiology; Antibiotic resistance (1)
- Antimicrobial stewardship (1)
- Apoptosis (1)
- Conductance-based neuron models (1)
- Contrast (1)
- Dendritic cells (1)
- Differential equations (1)
- Differential equations model (1)
- Differential equations models (1)
- Epidemiology (1)
- Healthcare-associated infection (1)
- Imaging corrosion (1)
- Immune cells (1)
- Immunology (1)
- Immunotherapy (1)
- Inflammation (1)
- Inflammatory diseases (1)
- Integrate-and-fire models (1)
- Inversion procedure (1)
- Leaky integrate-and-fire (1)
- Macrophages (1)
- Mathematical & computational biology (1)
- Mathematical modeling (1)
Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds
Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds
Department of Math & Statistics Faculty Publications
In an inflammatory setting, macrophages can be polarized to an inflammatory M1 phenotype or to an anti-inflammatory M2 phenotype, as well as existing on a spectrum between these two extremes. Dysfunction of this phenotypic switch can result in a population imbalance that leads to chronic wounds or disease due to unresolved inflammation. Therapeutic interventions that target macrophages have therefore been proposed and implemented in diseases that feature chronic inflammation such as diabetes mellitus and atherosclerosis. We have developed a model for the sequential influx of immune cells in the peritoneal cavity in response to a bacterial stimulus that includes macrophage …
Developing A Minimally Structured Mathematical Mode Of Cancer Treatment With Oncolytic Viruses And Dendritic Cell Injections, Jane L. Gevertz, Joanna R. Wares
Developing A Minimally Structured Mathematical Mode Of Cancer Treatment With Oncolytic Viruses And Dendritic Cell Injections, Jane L. Gevertz, Joanna R. Wares
Department of Math & Statistics Faculty Publications
Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of …
A Unified Inter-Host And In-Host Model Of Antibiotic Resistance And Infection Spread In A Hospital Ward, Lester Caudill, Barry Lawson
A Unified Inter-Host And In-Host Model Of Antibiotic Resistance And Infection Spread In A Hospital Ward, Lester Caudill, Barry Lawson
Department of Math & Statistics Faculty Publications
As the battle continues against hospital-acquired infections and the concurrent rise in antibiotic resistance among many of the major causative pathogens, there is a dire need to conduct controlled experiments, in order to compare proposed control strategies. However, cost, time, and ethical considerations make this evaluation strategy either impractical or impossible to implement with living patients. This paper presents a multi-scale model that offers promise as the basis for a tool to simulate these (and other) controlled experiments. This is a “unified” model in two important ways: (i) It combines inter-host and in-host dynamics into a single model, and (ii) …
Evaluating Infection Prevention Strategies In Out-Patient Dialysis Units Using Agent-Based Modeling, Joanna R. Wares, Barry Lawson, Douglas Shemin, Erika M. C. D'Agata
Evaluating Infection Prevention Strategies In Out-Patient Dialysis Units Using Agent-Based Modeling, Joanna R. Wares, Barry Lawson, Douglas Shemin, Erika M. C. D'Agata
Department of Math & Statistics Faculty Publications
Patients receiving chronic hemodialysis (CHD) are among the most vulnerable to infections caused by multidrug-resistant organisms (MDRO), which are associated with high rates of morbidity and mortality. Current guidelines to reduce transmission of MDRO in the out-patient dialysis unit are targeted at patients considered to be high-risk for transmitting these organisms: those with infected skin wounds not contained by a dressing, or those with fecal incontinence or uncontrolled diarrhea. Here, we hypothesize that targeting patients receiving antimicrobial treatment would more effectively reduce transmission and acquisition of MDRO. We also hypothesize that environmental contamination plays a role in the dissemination of …
The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares
The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares
Department of Math & Statistics Faculty Publications
Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and sub-optimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study …
The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares
The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares
Department of Math & Statistics Faculty Publications
Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and suboptimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study …
A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill
A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill
Department of Math & Statistics Faculty Publications
The human immune response to bacterial pathogens is a remarkably complex process, involving many different cell types, chemical signals, and extensive lines of communication. Mathematical models of this system have become increasingly high-dimensional and complicated, as researchers seek to capture many of the major dynamics. In this paper, we argue that, in some important instances, preference should be given to low-dimensional models of immune response, as opposed to their high-dimensional counterparts. One such model is analyzed and shown to reflect many of the key phenomenological properties of the immune response in humans. Notably, this model includes a single parameter values, …
The Dynamics Of Integrate-And-Fire: Mean Vs. Variance Modulations And Dependence On Baseline Parameters, Joanna R. Wares, Todd W. Troyer
The Dynamics Of Integrate-And-Fire: Mean Vs. Variance Modulations And Dependence On Baseline Parameters, Joanna R. Wares, Todd W. Troyer
Department of Math & Statistics Faculty Publications
The leaky integrate-and-fire (LIF) is the simplest neuron model that captures the essential properties of neuronal signaling. Yet common intuitions are inadequate to explain basic properties of LIF responses to sinusoidal modulations of the input. Here we examine responses to low - and moderate-frequency modulations of both the mean and variance of the input current and quantify how these responses depend on baseline parameters. Across parameters, responses to modulations in the mean current are low pass, approaching zero in the limit of high frequencies. For very low baseline firing rates, the response cutoff frequency matches that expected from membrane integration. …
Complementary Responses To Mean And Variance Modulations In The Perfect Integrate-And-Fire Model, Joanna R. Wares, Todd W. Troyer
Complementary Responses To Mean And Variance Modulations In The Perfect Integrate-And-Fire Model, Joanna R. Wares, Todd W. Troyer
Department of Math & Statistics Faculty Publications
In the perfect integrate-and-fire model (PIF), the membrane voltage is proportional to the integral of the input current since the time of the previous spike. It has been shown that the firing rate within a noise free ensemble of PIF neurons responds instantaneously to dynamic changes in the input current, whereas in the presence of white noise, model neurons preferentially pass low frequency modulations of the mean current. Here, we prove that when the input variance is perturbed while holding the mean current constant, the PIF responds preferentially to high frequency modulations. Moreover, the linear filters for mean and variance …
Temporal Processing In The Exponential Integrate-And-Fire Model Is Nonlinear, Joanna R. Wares, Todd W. Troyer
Temporal Processing In The Exponential Integrate-And-Fire Model Is Nonlinear, Joanna R. Wares, Todd W. Troyer
Department of Math & Statistics Faculty Publications
The exponential integrate-and-fire (EIF) model was introduced by Fourcaud-Trocme et al. (2003) as an extension of the standard leaky integrate-and-fire model (LIF). Here, the nonlinearity in the EIF model’s temporal response to square-wave inputs is investigated. Comparing the time course of onset and offset responses revealed that offset responses have a steeper initial slope, but a slower approach to equilibrium. A linear systems analysis performed for these square-wave inputs indicates that at frequencies above ~40 Hz, gain was slightly smaller for square-wave inputs, but phase did not change significantly relative to simulations in which the corresponding sinusoids were presented in …
A Contrast-Based Neural Control System For Ant Navigation, Joanna R. Wares, Predrag-Peter Ilich, Daniel P. Dougherty
A Contrast-Based Neural Control System For Ant Navigation, Joanna R. Wares, Predrag-Peter Ilich, Daniel P. Dougherty
Department of Math & Statistics Faculty Publications
A mathematical model for a neural control system of ant locomotion was developed. Contrast-based detectors using excitation and inhibition were tuned to specific contrast orientations. A control system using multiple orientation contrast detectors was then developed and optimized for a model ant, which could move via a biased random walk. The system allowed sufficient control to guide the ant through various mazes.
Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan
Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan
Department of Math & Statistics Faculty Publications
This paper examines an inverse problem which arises in thermal imaging. We investigate the problem of detecting and imaging corrosion in a material sample by applying a heat flux and measuring the induced temperature on the sample's exterior boundary. The goal is to identify the profile of some inaccessible portion of the boundary. We study the case in which one has data at every point on the boundary of the region, as well as the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for …