Modelling and inference of interacting cell dynamics using single time-point images

Abstract

Understanding cell dynamics, such as migration, proliferation, and interactions are central in cancer biology, particularly for modeling invasive tumors like glioblastoma. High-throughput in vitro assays frequently rely on single time-point (endpoint) im- ages, which lack direct temporal data, presenting a significant methodological chal- lenge for parameter estimation. This thesis develops a comprehensive computational pipeline to infer interacting cell dynamics exclusively from endpoint phase-contrast microscopy images using Approximate Bayesian Computation (ABC). The workflow integrates a robust U-Net segmentation model with a ResNet34 back- bone and boundary-aware probability shaping, alongside a velocity-predictive track- ing algorithm to mitigate survival bias and extract unbiased biological features. We evaluate an agent-based model utilizing overdamped Langevin dynamics proposed and used in against an advanced Fractional Brownian Motion (fBm) framework de- signed to capture directional persistence. Our results demonstrate that while the fBm model accurately captures the super-diffusive memory inherent to glioblastoma motility, this increased model capacity introduces parameter degeneracy at a sin- gle temporal endpoint. To navigate the resulting non-linear parameter manifolds, Sequential Monte Carlo (SMC-ABC) proved strictly superior to standard Rejection and Regression-Adjusted ABC variants. Furthermore, we expose an important "Sim-to-Real Gap" regarding summary statis- tics: while continuous Topological Data Analysis (TDA) via Persistence Images excels on idealized in vitro data, it suffers from ”topological fragility” when ex- posed to real-world biological noise and segmentation artifacts. Consequently, a hybrid summary statistic combining the Pair Correlation Function (PCF) with dis- crete Betti curves emerged as the most robust metric for experimental inference. Ultimately, this work establishes that extracting complex dynamic memory from static snapshots is mathematically viable, provided that physical model capacity is carefully balanced with robust spatial statistics and adaptive, non-linear Bayesian algorithms.