Uncertainty plays a major role in using mathematics to address biological and medical questions, specifically when analyzing real-world data. This minisymposium features recent mathematical and computational advances in solving inverse problems and quantifying uncertainties for a wide variety of biological and biomedical applications. Topics include development of numerical methods, model reduction, parameter estimation, and data-driven approaches for applications such as safety pharmacology, cell metabolism, tumor growth, and blood coagulation.
08:30
Quantifying Uncertainty in Time-Varying Parameters for Biological Systems
Andrea Arnold | Worcester Polytechnic Institute | United States
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Andrea Arnold | Worcester Polytechnic Institute | United States
Estimating and quantifying uncertainty in system parameters remains a big challenge in many biological applications. In particular, many biological systems involve parameters that are known to vary with time but have unknown dynamics and cannot be measured. This talk will address aspects of uncertainty in Monte Carlo filtering estimates of time-varying parameters, with particular emphasis on how uncertainty in the parameter estimates affects the corresponding model output predictions. Results will be demonstrated on examples from biological systems, including estimating the time-varying applied current in the Hodgkin-Huxley model for neuron spiking dynamics.
09:00
UQ and estimation of Quantities of Interest in Safety Pharmacology applications
Fabien Raphel | Sorbonne Université | France
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Damiano Lombardi | Inria | France
Fabien Raphel | Sorbonne Université | France
The main goal of cardio-toxicity studies is to assess the impact of molecules on the electrical activity of cardiac cells. In experiments, groups of cells are monitored in a control state and when a given concentration of a molecule is injected; an electro graph is recorded (called Field Potential). The main goal is to determine, based on the recorded signals, the electrical conductivity of the different ionic channels and how they are altered by the molecule. The intrinsic variability, the heterogeneities and the parametric uncertainty of the system have to be taken into account in order to perform a robust estimation of the ionic channel properties. To this end, some methods are investigated: first, numerical strategies to account for the uncertainties of the system and build an in-silico population of experiments are presented; second, a greedy dimension reduction strategy for classification in high-dimensional setting is detailed. Several realistic test cases are presented.
09:30
- CANCELED - Exploring posterior samples of highly underdetermined models
Daniela Calvetti | Case Western Reserve University | United States
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Daniela Calvetti | Case Western Reserve University | United States
Complex biological systems such as cell metabolism are characterized by models in which the degrees of freedom are significantly larger than the data. A way to explore the possible states that satisfy the data is to create a virtual data set by Markov Chain Monte Carlo methods. Due to the high dimensionality, the MCMC sample is hard to analyze beyond the usual low order statistics such as the mean and variance. In this talk, some data mining methods for extracting pertinent information of the virtual data are discussed.
10:00
Equation learning and uncertainty quantification for biological transport models of glioblastoma growth
Kevin Flores | North Carolina State University | United States
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Kevin Flores | North Carolina State University | United States
A recent area of research is applying machine learning methods towards learning mathematical models from data. These methods have shown promise in physical applications in which data quality and quantity is high, however, testing and extending equation learning methodology to biological settings with high noise levels and few data points has been less well investigated. We adapted and tested equation learning methods in a biologically realistic setting using the Fisher-KPP model, a commonly utilized model for describing spatiotemporal glioblastoma tumor growth and invasion. We simulated glioblastoma patient data with 1%, 5%, and 10% noise levels, generating only a few time points (either 3, 5, or 10) which could be used for equation learning. We used bootstrapping to assess parameter uncertainty in the learned equations. We found that the ability of equation learning methods to recover the correct equation and parameters was sensitive to the parameter domain, i.e., the proliferation and diffusion rates describing the tumor growth. We found that the correct equations and parameters for slower growing tumors could be recovered with as few as 3 time points.