Collaborative Research: Efficient Methods for Identifiability of Dynamic Models

Cuny Queens College, Flushing NY

Investigators

Abstract

The goal of the project is to analyze and improve the calibration of dynamic models developed by researchers in biology and other sciences to model real-world processes. Mathematical models are used broadly across biology to understand mechanisms, make predictions, and guide intervention strategies. To do so, the model parameters often must be calibrated using data; the estimated parameters can have significant implications for reliability of insights generated from the model and data. This raises the important question of whether the calibration process is well posed, i.e. is it possible to uniquely estimate model parameters from a given type or set of data? Identifiability analysis is the study of these issues, and this project will improve and expand the currently available set of algebraic identifiability methods to set them on a firmer theoretical basis and address new types of models used broadly in many biological settings. Beyond academia, the algorithms to be developed will allow researchers to successfully link models and experiments to generate model-based insights that improve real-world treatment strategies. Training will be provided to two Ph.D. students working on research for this project. The training component will also include interdisciplinary course development as well as a conference with tutorial lectures and problem sessions to educate industrial and academic participants in the theory, algorithms, and software developed in this project. This project is supported jointly by the Division of Mathematical Sciences Mathematical Biology and Division of Computing and Communication Foundations Algorithmic Foundations programs. More specifically, the investigators will develop, analyze, and implement symbolic and symbolic-numeric algorithms that perform identifiability analysis of dynamic models (including ordinary differential (ODE), delay, and difference equation models) that appear in biology and other sciences. Using these algorithms, they will also carry out identifiability analysis for a range of models drawn from cellular signaling and physiology applications. The proposed algorithms will be based on differential-difference algebra, which connects to identifiability in the common case of rational ODEs/delay/difference equations by applying differential-difference elimination algorithms to the model equations. Such symbolic methods for ODE models have proven to be productive in the area of parameter identifiability. The proposed methods would allow a large class of models to be analyzed for structural identifiability, allowing one to assess which parameters can be estimated and tailor experiment design to answer the questions of interest for treatment strategies and mechanistic insights. For the first time, rigorously justified and analyzed efficient algorithms will be available for identifiability problems in delay and difference equation models. Certified and more efficient algorithms will appear for global identifiability problems in ODE models. To carry out the proposed research, new advances in the algebraic theory of differential/difference equations will be made. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.