WiMB: Mathematical modeling and its application

Thursday, June 17 at 11:30am (PDT)
Thursday, June 17 at 07:30pm (BST)
Friday, June 18 03:30am (KST)

SMB2021 SMB2021 Follow Thursday (Friday) during the "MS20" time block.
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Qimin Huang (Case Western Reserve University, USA), Katie Storey (University of Michigan, USA)


This mini-symposium will present a variety of biological and medical questions using mathematical models to understand complex system dynamics. Mathematical modeling and analysis of problems originating in biological and life sciences is of fundamental importance to both scientific research and health policy. All four speakers are from the collaborative teams of Women in Mathematical Biology. We aim to illustrate our significant progress with research projects (e.g., antibiotic-resistance bacteria and phage therapy, cancer treatment, polarization of a single macrophage, and photoreceptors) and to foster innovation in the application of mathematical, statistical, and computational methods in the resolution of problems in mathematical biology. In addition to presenting our work, we aim to foster research collaboration among women in mathematical biology.

Atanaska Dobreva

(Arizona State University, USA)
"Investigating pathological mechanisms in cone photoreceptor vitality and the timing of rescue strategies via bifurcation analysis and time-varying sensitivity analysis"
Photoreceptors are the sensory cells of the eye, which perform the most essential role in vision. There are two types of photoreceptors: rods for night and peripheral vision and cones for color vision. Glucose is the main fuel for photoreceptors, and they break it down to form lactate, lipids and other metabolites needed to create energy and to renew the light-absorbing outer segments, which are periodically shed. Thus, properly functioning metabolic processes ensure the structural integrity and vitality of photoreceptors. The progression of degenerative retinal diseases such as age-related macular degeneration (AMD) and retinitis pigmentosa (RP) has been linked to nutrient deprivation. We analyzed a mathematical model for the metabolic dynamics of a cone photoreceptor via bifurcation analysis and time-varying global sensitivity analysis (GSA) in order to identify factors that increase the risk of cone degeneration in AMD and RP when glucose supply to photoreceptors is low. Our results indicate that the factors of greatest importance include glucose availability and transport, utilization of lipids for photoreceptor outer segment renewal and -oxidation of fatty acids to provide auxiliary metabolites for energy production. In addition, the GSA helped to uncover insights into timing of intervention strategies to rescue the cone cell.

Katie Storey

(University of Michigan, USA)
"A Framework for Performing Data-Driven Modeling of Tumor Growth with Radiotherapy Treatment"
Recent technological advances make it possible to collect detailed information about tumors, and yet clinical assessments about treatment responses are typically based on sparse datasets. In this work, we propose a workflow for choosing an appropriate model, verifying parameter identifiability, and assessing the amount of data necessary to accurately calibrate model parameters. We compare tumor growth models of varying complexity in an effort to determine the level of complexity needed to accurately predict tumor growth dynamics and response to radiotherapy. We consider a simple, one-compartment ordinary differential equation model which tracks tumor volume and a two-compartment model that accounts for tumor volume and the fraction of necrotic cells within the tumor. We investigate the structural and practical identifiability of these models, and the impact of noise on identifiability. We also generate synthetic data from a complex, spatially- resolved, cellular automaton model (CA), investigating the fit of the ODE models to tumor volume data generated by the CA, using sequential model calibration. Our results suggest that if tumor volume data alone is provided then a tumor with a large necrotic volume is the most challenging case to fit. However, supplementing data on total tumor volume with additional necrotic information enables the two-compartment ODE model to perform significantly better than the one-compartment model, in terms of parameter convergence and predictive power.

Qimin Huang

(Case Western Reserve University, USA)
"Investigating the impact of combination phage and antibiotic therapy: A modeling study"
Antimicrobial resistance (AMR) is a serious threat to global health today. The spread of AMR, along with the lack of new drug classes in the antibiotic pipeline, has resulted in a renewed interest in phage therapy, which is the use of bacteriophages to treat pathogenic bacterial infections. This therapy, which was successfully used to treat a variety of infections in the early twentieth century, had been largely dismissed due to the discovery of easy-to-use antibiotics. However, the continuing emergence of antibiotic resistance has motivated new interest in the use of phage therapy to treat bacterial infections. We have modeled an ODE system to investigate the effect of immune system on combination treatment of the phage and antibiotic. Our result shows the frequency and concentration of dose as well as the timing of phage administration are important factors of the combination phage therapy.

Hwayeon Ryu

(Elon University, USA)
"Bifurcation and sensitivity analysis reveal key drivers of multistability in a model of macrophage polarization"
We analyze a mathematical model for polarization of a single macrophage which, despite its simplicity, exhibits complex dynamics in terms of multistability. In particular, we demonstrate that an asymmetry in the regulatory mechanisms and parameter values is important for observing multiple phenotypes. Bifurcation and sensitivity analyses show that external signaling cues are necessary for macrophage commitment and emergence to a phenotype, but that the intrinsic macrophage pathways are equally important. Based on our numerical results, we formulate hypotheses that could be further investigated by laboratory experiments to deepen our understanding of macrophage polarization.

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Virtual conference of the Society for Mathematical Biology, 2021.