Medical Biomathematics and Biometrics Commons^™

Tumor–Immune Dynamics With Memory And Time Delay: A Fractional-Order Model With Ctla-4 Regulation, Mutaz Mohammad, Mohyeedden Sweidan, Alexander Trounev, Fathalla Rihan

Mathematical Modelling and Numerical Simulation with Applications

This study develops a fractional-order tumor-immune interaction model incorporating Caputo memory effects, delayed immune activation, and CTLA-4 checkpoint regulation. The model describes the coupled dynamics of tumor cells, CD4$^{+}$ T cells, IFN-$\gamma$, and CTLA-4, and extends classical integer-order tumor-immune models by accounting for hereditary immune responses and biologically motivated latency effects. Theoretical properties, including positivity, boundedness, equilibrium structure, and fractional-order stability, are examined to establish the biological and mathematical consistency of the model. The delayed fractional system is then investigated computationally by comparing several numerical methods, including finite difference discretization, Daubechies wavelet collocation, Euler wavelet collocation, and a predictor-corrector scheme. …

A Probabilistic Modeling Analysis Of The Longitudinal Immune Response To Infection And Vaccination Across Demographic Groups And Pulmonary Symptoms, James O'Hanlon, Kaitlyn Sullivan, Lyndsey M. Muehling, Glenda Canderan, Jie Sun, Judith A. Woodfolk, Jeffrey M. Wilson, Rayanne A. Luke

Spora: A Journal of Biomathematics

Antibody and cytokine kinetics describe the dynamic response to immune events such as infection and vaccination. These dynamics are not fully understood, and mathematical characterization may help explain variability across demographic groups and pulmonary symptoms post-acute infection. We fit time-dependent probability models to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data to obtain distributions of longitudinal antibody response and cytokine values. To assess differences between groups, an overlap metric is applied to the modeled response curves. Our antibody models suggest significant differences between male and female populations and demonstrate deficient antibody responses of less-healthy groups such as smokers. Our cytokine …

Managing Multi-Drug Resistance: An Evolutionary Game Theory And Optimal Control Approach, Shukhrat Nasrulloev

Theses and Dissertations

Multi-drug resistance is an evolutionary process in which treatment eliminates sensitive cells, allowing resistant clones to dominate. This thesis investigates this process using a framework integrating population dynamics, evolutionary game theory, and optimal control theory. We develop a two-population logistic growth model describing competition between drug-sensitive and drug-resistant cells under treatment, construct dose-dependent payoff matrices and replicator dynamics to characterize evolutionary competition, and derive a critical drug level D_crit = (r_S - rR)/(dS - d_R) at which resistant cells gain a fitness advantage. An optimal control problem is formulated via Pontryagin's Maximum Principle to identify schedules …

A Bayesian Late-Fusion Supportability Framework For Rare-Disease Severity Prediction In Glut1 Deficiency Syndrome, Jordan M. Rodriguez

Mathematics Dissertations

Glucose transporter type 1 deficiency syndrome (GLUT1-DS) is a rare neurometabolic disorder with heterogeneous neurological and developmental severity. Because patient-level severity is not observed as a single validated outcome, this dissertation develops a Bayesian late-fusion supportability framework for constructing and predicting an ordered latent severity phenotype from clinical, genetic, and EEG-derived evidence. The primary target was constructed in a larger clinical cohort using age-5 symptom burden and learning cognition, then assigned to an aligned multimodal prediction cohort. Target-defining variables were excluded from supervised predictors, and models were evaluated using patient-exclusive cross-validation with training-fold preprocessing and fold-wise EEG PCA.

The primary …

Probabilistic Modeling Of Antibody Kinetics Post Infection And Vaccination, Rayanne Luke, Prajakta Bedekar, Anthony J. Kearsley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Overview Of Video Game Biometrics Collection And Considerations For Cyberbiosecurity, Lucas Potter, Christen Westberry, Xavier-Lewis Palmer

Electrical & Computer Engineering Faculty Publications

Over the past fifty years, the global cost of consumer electronics has significantly decreased, leading to greater accessibility to both biosensing systems and interactive entertainment platforms. This increased access has naturally resulted in higher usage of medical and entertainment electronics. However, the intersection of these technologies, combined with invasive data harvesting practices, has raised concerns about the potential misuse of biological signals to manipulate individuals' behavior both within and beyond the video game environment. Currently, biometric data in video games are employed in various ways, such as using Heart Rate Variability (HRV) as a performance metric and integrating eye tracking …

Assessing The Adequacy Of A Prediction Model, Abhaya Indrayan, Sakshi Mishra Ms

COBRA Preprint Series

No abstract provided.

Effect Of Specific Data Variations On Automated Speaker Recognition, Ethan David Meighen

Graduate Theses, Dissertations, and Problem Reports (ETD)

Speaker recognition is not a new biometric modality but there are still many obstacles in the way in order for it to become as used as fingerprint recognition, facial recognition, and iris recognition. Many real-world environmental conditions, hardware device variations, and human behavior present serious challenges to the use of opportunistic voice or speaker samples for identification purposes. Non-idealities, identified as nuisance factors, include environmental noise, input device quality, length of utterance, sample rate variation, and unscripted data are common nuisance factors that can impact speaker recognition match score performance. The impact of the nuisance factors listed above were evaluated …

A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd

Mathematics Dissertations - Archive

In this dissertation, we first present a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune responses. A stochastic process that captures the system's inherent randomness determines the dynamics of colon cancer. The stochastic framework is based on the Fokker-Planck equation, which represents the evolution of the probability density function corresponding to the stochastic process. We formulate an optimization problem that takes individual patient data with randomness present and solves it to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, we perform a sensitivity analysis of the optimal parameter set to identify the …

Scalar-On-Function Regression: Estimation And Inference Under Complex Survey Designs, Ekaterina Smirnova, Erjia Cui, Lucia Tabacu, Andrew Leroux

Mathematics & Statistics Faculty Publications

Increasingly, large, nationally representative health and behavioral surveys conducted under a multistage stratified sampling scheme collect high dimensional data with correlation structured along some domain (eg, wearable sensor data measured continuously and correlated over time, imaging data with spatiotemporal correlation) with the goal of associating these data with health outcomes. Analysis of this sort requires novel methodologic work at the intersection of survey statistics and functional data analysis. Here, we address this crucial gap in the literature by proposing an estimation and inferential framework for generalizable scalar-on-function regression models for data collected under a complex survey design. We propose to: …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison Of Brain- Cousens And Cedergreen Models For A Biochemical Dataset, Venkat D. Abbaraju, Tamaraty L. Robinson, Brian P. Weiser

Rowan-Virtua School of Osteopathic Medicine Departmental Research

Biphasic, non-sigmoidal dose-response relationships are frequently observed in biochemistry and pharmacology, but they are not always analyzed with appropriate statistical methods. Here, we examine curve fitting methods for “hormetic” dose-response relationships where low and high doses of an effector produce opposite responses. We provide the full dataset used for modeling, and we provide the code for analyzing the dataset in SAS using two established mathematical models of hormesis, the Brain-Cousens model and the Cedergreen model. We show how to obtain and interpret curve parameters such as the ED50 that arise from modeling, and we discuss how curve parameters might change …

Modeling The Immune Response To Immunotherapy And Triple Negative Breast Cancer In Mice, Dayton J. Syme, Angelica Davenport, Yun Lu, Anna G. Sorace, Nicholas G. Cogan

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimizing Tumor Xenograft Experiments Using Bayesian Linear And Nonlinear Mixed Modelling And Reinforcement Learning, Mary Lena Bleile

Statistical Science Theses and Dissertations

Tumor xenograft experiments are a popular tool of cancer biology research. In a typical such experiment, one implants a set of animals with an aliquot of the human tumor of interest, applies various treatments of interest, and observes the subsequent response. Efficient analysis of the data from these experiments is therefore of utmost importance. This dissertation proposes three methods for optimizing cancer treatment and data analysis in the tumor xenograft context. The first of these is applicable to tumor xenograft experiments in general, and the second two seek to optimize the combination of radiotherapy with immunotherapy in the tumor xenograft …

Adaptive Critic Network For Person Tracking Using 3d Skeleton Data, Joseph G. Zalameda, Alex Glandon, Khan M. Iftekharuddin, Mohammad S. Alam (Ed.), Vijayan K. Asari (Ed.)

Electrical & Computer Engineering Faculty Publications

Analysis of human gait using 3-dimensional co-occurrence skeleton joints extracted from Lidar sensor data has been shown a viable method for predicting person identity. The co-occurrence based networks rely on the spatial changes between frames of each joint in the skeleton data sequence. Normally, this data is obtained using a Lidar skeleton extraction method to estimate these co-occurrence features from raw Lidar frames, which can be prone to incorrect joint estimations when part of the body is occluded. These datasets can also be time consuming and expensive to collect and typically offer a small number of samples for training and …

A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang

Faculty Publications

Immunotherapy is an innovative treatment that enlists the patient's immune system to battle tumors. The optimal dose for treating patients with an immunotherapeutic agent may differ according to their biomarker status. In this article, we propose a biomarker-based phase I/II dose-finding design for identifying subgroup-specific optimal dose for immunotherapy (BSOI) that jointly models the immune response, toxicity, and efficacy outcomes. We propose parsimonious yet flexible models to borrow information across different types of outcomes and subgroups. We quantify the desirability of the dose using a utility function and adopt a two-stage dose-finding algorithm to find the optimal dose for each …

Decoding Clinical Biomarker Space Of Covid-19: Exploring Matrix Factorization-Based Feature Selection Methods, Farshad Saberi-Movahed, Mahyar Mohammadifard, Adel Mehrpooya, Mohammad Rezaei-Ravari, Kamal Berahmand, Mehrdad Rostami, Saeed Karami, Mohammad Najafzadeh, Davood Hajinezhad, Mina Jamshidi, Farshid Abedi, Mahtab Mohammadifard, Elnaz Farbod, Farinaz Safavi, Mohammadreza Dorvash, Shahrzad Vahedi, Mahdi Eftekhari, Farid Saberi-Movahed, Iman Tavassoly

Publications and Research

One of the most critical challenges in managing complex diseases like COVID-19 is to establish an intelligent triage system that can optimize the clinical decision-making at the time of a global pandemic. The clinical presentation and patients’ characteristics are usually utilized to identify those patients who need more critical care. However, the clinical evidence shows an unmet need to determine more accurate and optimal clinical biomarkers to triage patients under a condition like the COVID-19 crisis. Here we have presented a machine learning approach to find a group of clinical indicators from the blood tests of a set of COVID-19 …

Testing The Effect Of Acetaminophen Overdose On The Liver And The Role Of Biomarkers To Predict Death Or Survival, Christine Brasic

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Differential Geometry-Based Machine Learning Algorithm For The Brain Age Problem, Justin Asher, Khoa Tan Dang, Maxwell Masters

The Journal of Purdue Undergraduate Research

No abstract provided.

Automatic Recognition, Segmentation, And Sex Assignment Of Nocturnal Asthmatic Coughs And Cough Epochs In Smartphone Audio Recordings: Observational Field Study, Filipe Barata, Peter Tinschert, Frank Rassouli, Claudia Steurer-Stey, Elgar Fleisch, Milo Puhan, Martin Brutsche, David Kotz, Tobias Kowatsch

Dartmouth Scholarship

Background: Asthma is one of the most prevalent chronic respiratory diseases. Despite increased investment in treatment, little progress has been made in the early recognition and treatment of asthma exacerbations over the last decade. Nocturnal cough monitoring may provide an opportunity to identify patients at risk for imminent exacerbations. Recently developed approaches enable smartphone-based cough monitoring. These approaches, however, have not undergone longitudinal overnight testing nor have they been specifically evaluated in the context of asthma. Also, the problem of distinguishing partner coughs from patient coughs when two or more people are sleeping in the same room using contact-free audio …

Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk

Department of Mathematics: Faculty Publications

One quarter of veterans returning from the 1990–1991 Persian Gulf War have developed Gulf War Illness (GWI) with chronic pain, fatigue, cognitive and gastrointestinal dysfunction. Exertion leads to characteristic, delayed onset exacerbations that are not relieved by sleep. We have modeled exertional exhaustion by comparing magnetic resonance images from before and after submaximal exercise. One third of the 27 GWI participants had brain stem atrophy and developed postural tachycardia after exercise (START: Stress Test Activated Reversible Tachycardia). The remainder activated basal ganglia and anterior insulae during a cognitive task (STOPP: Stress Test Originated Phantom Perception). Here, the role of attention …

Deepcon-Pre: Improved Protein Contact Map Prediction Using Inverse Covariance And Deep Residual Networks, Nachammai Palaniappan

Theses

As with most domains where machine learning methods are applied, correct feature engineering is critical when developing deep learning algorithms for solving the protein folding problem. Unlike the domains such as computer vision and natural language processing, feature engineering is not rigorously studied towards solving the protein folding problem. A recent research has highlighted that input features known as precision matrix are most informative for predicting inter-residue contact map, the key for building three-dimensional models. In this work, we study the significance of the precision matrix feature when very deep residual networks are trained. Using a standard dataset of 3456 …

Mathematics Saves Lives: Models And Signals Enabling Medicine And Biology, Raina Robeva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Transient Dynamics Of Infection Transmission In An Intensive Care Unit, Christopher Short, Matthew S. Mietchen, Eric T. Lofgren

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Analysis Of The Rajasthan Public Health System’S Response To The 2019 Dengue Insurgence, Luke Bryan

Independent Study Project (ISP) Collection

Dengue virus is in a pandemic status and is a major public health issue in the modern world. The mosquito-borne disease is largely prevalent in Asia and specifically India, where more than half of the states are considered to have complete presence of the dengue virus. The intricate infrastructure of the Indian public health system looks for dengue cases at all levels and reports to the integrated disease surveillance programme (IDSP).

Analyses of the IDSP and trends of dengue cases was done in response to dengue outbreaks throughout the state. Geographic information system (GIS) maps were created to evaluate a …

Seeing Eye To Eye: A Machine Learning Approach To Automated Saccade Analysis, Maigh Attre

Honors Scholar Theses

Abnormal ocular motility is a common manifestation of many underlying pathologies particularly those that are neurological. Dynamics of saccades, when the eye rapidly changes its point of fixation, have been characterized for many neurological disorders including concussions, traumatic brain injuries (TBI), and Parkinson’s disease. However, widespread saccade analysis for diagnostic and research purposes requires the recognition of certain eye movement parameters. Key information such as velocity and duration must be determined from data based on a wide set of patients’ characteristics that may range in eye shapes and iris, hair and skin pigmentation [36]. Previous work on saccade analysis has …

Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli

Masters Theses & Specialist Projects

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that …

A Mathematical Model Of The Inflammatory Response To Pathogen Challenge, Lester Caudill, Fiona Lynch

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Bayesian Analytical Approaches For Metabolomics : A Novel Method For Molecular Structure-Informed Metabolite Interaction Modeling, A Novel Diagnostic Model For Differentiating Myocardial Infarction Type, And Approaches For Compound Identification Given Mass Spectrometry Data., Patrick J. Trainor

Electronic Theses and Dissertations

Metabolomics, the study of small molecules in biological systems, has enjoyed great success in enabling researchers to examine disease-associated metabolic dysregulation and has been utilized for the discovery biomarkers of disease and phenotypic states. In spite of recent technological advances in the analytical platforms utilized in metabolomics and the proliferation of tools for the analysis of metabolomics data, significant challenges in metabolomics data analyses remain. In this dissertation, we present three of these challenges and Bayesian methodological solutions for each. In the first part we develop a new methodology to serve a basis for making higher order inferences in metabolomics, …