Sensitivity analysis of biologically informed neural networks for collective cell migration

Mentors:
Lead: Kevin Flores (Mathematics, NCSU)
Collaborator: Jason Haugh (Chemical and Biological Engineering, NCSU)

Intellectual merit and significance:
Flores recently developed biologically informed neural networks (BINNs) to automatically discover reaction and diffusion terms in PDEs from data to model collective cell migration accurately [1]. Developing methods for sensitivity analysis of the BINN models, a hybrid of neural networks and PDEs, will enable us to investigate the contribution of intercellular interaction, proliferation, and diffusion rates to collective cell migration.

Objectives:
We will develop and validate sensitivity analysis methods for BINNs by utilizing directional derivatives with respect to “infinite dimensional” parameter sets, sets of functions that lie in an appropriate topological vector space, e.g., bounded continuous functions. We will investigate suitable choices for perturbations, including constant linear and nonlinear functions describing the shape of the discovered reaction and diffusion inside the learned PDE. Sensitivity analysis will investigate biological questions, including diffusion, proliferation, and death processes depending on cell density using cell monolayer data.

Outcomes:
This project will produce a validated model for sensitivity analysis of hybrid neural network- PDE BINN models derived directly from experimental data. The methods are flexible and can be used as the basis to study more complex mechanisms at play in cell migration, such as cell cycle progression.

References:
1. Lagergren J, Nardini J, Baker R, Simpson M, Flores K. Biologically informed neural networks guide mechanistic modeling from sparse experimental data. PLoS Comp Biol. 2020;16:e1008462.