MMPB Subgroup Contributed Talks

Brendan Fry

Metropolitan State University of Denver

"A hybrid model for metabolic signaling in the human retinal microcirculation"

Impaired blood flow regulation and oxygenation have been implicated as contributors to glaucomatous damage in the retina. Here, a mathematical model is presented that combines an image-based heterogeneous representation of the retinal arteriolar vasculature with a compartmental description of the downstream capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. This hybrid model is used to predict blood flow and oxygenation throughout the entire retinal microcirculation; in addition, a metabolic wall signal is calculated in each vessel from blood and tissue oxygen levels, and is conducted upstream to communicate the metabolic status of the retina to the arterioles. Model results predict a wide range of metabolic signals generated throughout the microvascular network, dependent both on oxygen levels and vascular path lengths. Overall, the model predicts that a higher metabolic wall signal is generated in pathways with a lower oxygen level at the terminal arteriole. This model framework will be used in the future to simulate blood flow regulation in a realistic, spatially non-uniform representation of the human retina, in order to assess the role of metabolic blood flow dysregulation in glaucoma.

Thomas Bury

McGill University

"Long ECGs reveal rich and robust dynamical regimes in patients with frequent premature ventricular complexes."

Heart disease is one of the leading causes of disability and death. One manifestation of heart disease is abnormal heart rhythms, called arrhythmia. A very common arrhythmia consists of abnormal extra heart beats called premature ventricular complexes (PVCs). Though considered benign in most cases, recent studies have shown that frequent PVCs pose an increased risk for more serious arrhythmia that can lead to sudden cardiac death. Risk stratification for these patients remains a significant challenge in part since the mechanism generating the PVCs is usually unknown. In this talk, we will show how analysis of multi-day ECGs reveal robust dynamical regimes in PVC dynamics that vary as a function of heart rate and hour of the day. This analysis facilitates the development of basic mathematical models that can help reveal the underlying mechanism of PVCs. With the current advances in wearable technology and corresponding influx of ECG data, such approaches can bring about a dynamics-based personalised medicine.

Jeungeun Park

University of Cincinnati

"A swimming strategy of polarly-flagellated bacteria"

Flagellar bacteria swim through fluid by rotating their flagella that are connected to rotary motors in their cell wall. The physical, geometrical, and material properties of flagella characterize bacterial swimming patterns. In this talk, we present a mathematical model of a lophotrichous bacterium swimming through fluid. We introduce a recently reported swimming mode in which a bacterium undergoes a slow swimming phase by wrapping its flagella around the cell body. By using our mathematical model, we investigate the mechanism of wrapping motion, and suggest benefits of the motion in bacterial native habitats. Furthermore, we compare our numerical examples with experimental observations.

Dongheon Lee

Department of Biomedical Engineering, Duke University

"Hybrid Data-driven Mechanistic Modeling Approach to Describe Uncertain Intracellular Signaling Pathways"

Developing an accurate mechanistic model is important in analyzing an intracellular signaling pathway. However, a model is difficult to be developed since it requires in-depth understandings. Since underlying mechanisms are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a mechanistic model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability.