Research
My research interests include mathematical modeling of human physiological processes (inflammation, cardiovascular function, and stress responses), sensitivity analysis, parameter estimation, bifurcation analysis, and simulation of therapeutic treatments. My Ph.D. advisor is Mette Olufsen, and I am a member of the Cardiovascular Dynamics Group at NCSU.
Studying the mechanisms of the immune system and its response to a stimulant is a relevant and important research area relating to various diseases involving human inflammation. Prolonged inflammation effects are common in individuals with conditions such as sepsis, one of the leading causes of death in U.S. hospitals. The most common experimental way to study the human immune response is through an endotoxin challenge. During this experimental procedure, healthy humans are given endotoxin (lipopolysaccharide, LPS), by either bolus injection or continuous infusion and immune, thermal, hormonal, and cardiovascular markers are measured for several hours after administration before measurements return to baseline.
My primary research focus is on studying human inflammation from a mathematical modeling perspective and using my results to investigate clinically-relevant scenarios of inflammation. Through sensitivity analysis, subset selection, and parameter estimation techniques, I have calibrated a complex mathematical model (nonlinear ordinary differential equations) to experimental data from a continuous infusion of endotoxin (thought of as a better experimental setup to study systemic inflammatory diseases such as sepsis compared to bolus endotoxin administration). Using the resulting model, we form a hypothesis about the underlying physiological mechanisms that cause different release profiles of cytokines and lingering flu-like symptoms seen during different endotoxin administration methods. We adapt our calibrated model to simulate sepsis and investigate the bifurcation from a healthy state to a septic state, providing insight on potential focuses for sepsis treatment. We also use our sepsis model to uncover the potential impacts of upcoming sepsis treatment methods such as vitamin C therapy.
Using the inflammation model, I also study the dynamics of the interactions of the human immune response with other important regulatory processes in the body. The immune system and other systems such as the hypothalamic-pituitary-adrenal (HPA) axis and the cardiovascular system have all been studied in detail individually, but the dynamics of their relationship with each other lacks understanding. Each of the systems’ mechanisms also act on various time scales, making it difficult to study their couplings. Using dynamical systems calibrated to experimental data from endotoxin challenges, I study the effects of changes in endotoxin administration time, dosing amount, and method on the whole-body response. In this more comprehensive model, we can simulate clinically-relevant scenarios related to inflammation that are unethical to do experimentally in humans and predict a larger picture of cardiovascular, hormonal, temporal, and immune responses. The simulation results of the model and gained understanding of the couplings between various bodily systems could help guide treatments to improve mortality in patients with systemic inflammatory diseases.
Publications:
- Windoloski, K.A., Janum, S., Berg, R.M.G., Olufsen, M.S. (2023) Characterization of differences in immune responses during bolus and continuous infusion endotoxin challenges using mathematical modeling. Submitted. [Preprint] arXiv:2308.01495
- Windoloski, K.A., Bangsgaard, E.O., Dobreva, A., Ottesen, J.T., Olufsen, M.S. (2023). A unified computational model for the human response to lipopolysaccharide-induced inflammation. In: Mathematics Online First Collections. Springer, Cham. https://doi.org/10.1007/16618_2022_39
- Windoloski, K.A., Ottesen, J.T., Olufsen, M.S. (2022) In Silico modeling of immune-cardiovascular-endocrine interactions. J Cardiovasc Med Cardiol 9(4): 037-041. https://dx.doi.org/10.17352/jcmc
- Levy, B, Windoloski, K, & Ludlam, J (2021). Matrix and agent-based modeling of threats to a diamond-backed terrapin population. Math Biosci, 340, 108672. https://doi.org/10.1016/j.mbs.2021.108672
In Preparation:
- Windoloski, K.A., Berg, R.M.G, Olufsen, M.S. Dynamical systems modeling of sepsis and potential therapeutic treatment impact. In preparation.
Supplementary Documents: