Bayesian Uncertainty Quantification in Biological Models

In these research projects, we utilize the Pi4U framework to perform Bayesian UQ on various biological networks. Pi4U is a highly parrallel framework that uses Transitional Markov Chain Monte Carlo (TMCMC) to sample the parameter space and find approximations for the posterior distributions of the parameters. As a byproduct, TMCMC calculates the evidence for the model conditioned on the measured data. Thus, the Pi4U framework is used in Bayesian model selection. Below are a few of the applications that we have been studying.

Blood Flow Model

In this project, we are interested in understanding the parameters that influence blood flow profiles. Using a one-diminensional blood flow model derived from conservation laws, we can approximate velocity, cross sectional area, and internal pressure, which determine the flow profile. However, different arterial stiffness can greatly effect the resulting flows and these are not known. In the first part of the project, we use Pi4U to approximate the parameters of the flow. We are also interested in discovering which artery has irregular stiffness, and use the Bayesian model selection aspect of Pi4U to discover what artery has abnormal stiffness. Currently we are focused on proof of concept that Pi4U works on our blood flow model, but intend to extend this further to real medical data and adding oxygen transport to the blood flow model.

In this project, we are interested in understanding the structure of bilipid membranes. In particular, we have been studying what angles the upper layer and the bottom layer of the membranes prefer to create membranes of different curvature. The membranes are modeled using a dissipitve particle dynamics (DPD) simulation. Since DPD models involve a random force, we have an additional level required for approximating the posterior distributions, as each model run for the same parameters will result in similar, but slightly different curvatures.

In this project, we are interested in understanding epidemic spread. We have been studying how changing various parameters influence the development of a disease in a population.