My research interest focus mainly on two principals: learning something new to me and explaining things through math. Although vague, they encompass all my past and current research interests. Math modeling is made possible by learning about the system one is describing. Another reason I enjoy math modeling is it easily lends itself to cross-functional collobration. Working with others from various backgrounds can lead to new ideas and better understanding.
My PhD research focused on inverse problems and lung modeling. Specifically, solving an inverse problem using medical images and patient data. Working with people across various disciplines, we were able to collect multiple sets of real world data. We collected mechanical ventilation data to determine the wide ranging airway resistance values in the bronchial tree. Using the overall lung volume from the ventilators as well as regional lung information from electrical impedance tomography (EIT) data, a medical imaging technique, we solved an inverse problem and determined the airway resistance with asymetric flow of a lung. Python scripts and MATLAB functions were used to help solve our inverse problem.
Papers
Estimation of airway resistance throughout the bronchial tree from mechanical ventilation output data with Emily Heavner, Jennifer L. Mueller, Kim McFann, Julie Dunn, Omar Alnachoukati, Corey Mohnike. Accepted to appear in Applied Mathematics for Modern Challenges (AMMC), September 2024.
An inverse problem and multi-compartment lung model for the estimation of lung airway resistance throughout the bronchial tree, Colorado State University Libraries, December 2022.
Assurance Arguments for
the Non-graphically-inclined: Two Approaches with Michael C. Holloway, NASA/TM-2017-219650, July, 2017.
Poster
Computational Estimation of Airway Resistance Throughout the Bronchial Tree,
Joint Mathematics Meeting, Virtual, April 2022.
Investigating Airway Resistance Values in the Alveolar Tree using an Inverse Problem and a Dynamical System Lung Model,
Conference on Modern Challenges in Imaging
In the Footsteps of Allan MacLeod Cormack
On the Fortieth Anniversary of his Nobel Prize, Tufts University, August 2019.
Talks
An Inverse Problem and Multi-Compartment Lung Model for the
Estimation of Lung Airway Resistance throughout the Bronchial Tree, Public Thesis Defense, CSU, October 2022.
Estimating Airway Resistance in the Bronchial Tree Using an Inverse Problem and an Asymmetric
Multi-Compartment Lung Model , Guest Lecture in Math 676: Inverse Problems: a Data Science
Perspective, Colorado State University, April 2022
Estimation of Airway Resistance Throughout the Bronchial Tree using an Inverse Problem and an Asymmetric Multi-Compartment Lung Model ,
Joint Mathematics Meeting, Virtual, April 2022.
Introduction to an Asymmetric Multi-compartment Lung Model and Parameter Estimation,
Greenslopes
Seminar, Colorado State University, April 2022.
Estimation of airway resistance throughout the bronchial tree from mechanical ventilation output data ,
Society for Mathematical Biology Annual Meeting, Virtual, June 2021.
Introduction to Inverse Problems and their Applicationsin the Medical Field ,
Greenslopes
Seminar, Colorado State University, March 2020.
What is Regularization and Why Do We Care?,
Data Science Seminar,
Colorado State University, November 2019.
Inverse Problems and their Applications,
Solving Problems
in Applied Math Lab, Colorado State University, November 2019.
Derivation of Shallow Water Equations,
Solving Problems
in Applied Math Lab, Colorado State University, March 2019.
Introduction and Numerical Simulation of a Dynamical System Lung Model,
SIAM Front Range Applied Math
Conference , University of Colorado Denver, March 2019.
Lung Model Using Switched Dynamical System and EIT,
Greenslopes
Seminar, Colorado State University, October 2018.
Stochastic Traffic Flow Model Based on Hampton Roads, VA, Christopher Newport University, December 2016
Species Competition in a Lotka Volterra Model Using Netlogo , Christopher Newport University, March 2016