Image-Based Scientific Machine Learning for Theories of Biological Dynamics Across Scales – Equation discovery of tissue and organ dynamics

In this focused workshop, we focus on the upper end of the Long Program ladder of scales, beyond individual cells towards tissues and organs. Example systems of interest include blood vessels, cardiac tissue, and cancerous tumors, where the dynamics are dominated by mechanobiology and the complex interplay of elastic forces against tissue growth and remodeling. Data-driven mathematical modeling of these dynamics, such as differential equations, would allow discovery and interpretation of causal mechanisms, individual-organism forecasting, risk stratification, and design of medical and surgical interventions. Raw empirical data on morphology can be obtained with medical imaging such as Computed Tomography, but needs to be further processed into informative features. Modeling here takes both bottom-up forms like Finite Element Analysis and top-down forms like sparse equation discovery. In both bottom-up and top-down modeling, the data on both healthy and pathological dynamics of organisms is often noisy, irregular, and limited due to its clinical origins.

In order to integrate this array of questions, we plan to bring in clinical scientists, experimental biologists, mathematicians, computer scientists, physicists, and bioengineers. Specific discussion focal points are: 1. discovery of relevant features and coordinates from data, 2. model selection among candidate dynamical equations, 3. biomechanical simulations, and 4. challenges of sparse and irregular clinical data. The discussions would be focused on creation of both benchmark and challenge datasets, shared methods and software packages, and mechanistic interpretation and disambiguation.