Modeling, prediction and control methods for tumor dynamics

Cancer cell dynamics can be seen as a complex, multiscale dynamical system whose behavior emerges from interactions among heterogeneous cells, their microenvironment, and external inputs. This thesis proposes a set of systems-theoretic methods for modeling, prediction, and control of tumor dynamics. Thanks to the combination of theoretical control and optimization tools with data and testbeds from experimental oncology, three novel approaches for cancer system scenarios are presented. First, a novel multi-cell tracking algorithm is proposed for time-lapse microscopy data. By modeling cell dynamics as an open multi-agent dynamical system, simultaneous prediction, tracking, and inference of biological cell-to-cell interaction parameters is performed. This method considers cells heterogeneity, migration, and proliferation within a single estimator that connects single-cell dynamics to population observables. Second, a systems-theoretic analysis of Extended Cellular Potts Models (ECPMs) investigates how haptotaxis, extracellular-matrix degradation, and stochasticity drive cancer invasion. Viewing ECPMs through the lens of feedback control, the work derives analytical results for tumor invasion times and related probabilities, energy evolution, and steady-state behaviors in simplified configurations, clarifying how microscopic local interaction rules determine macroscopic invasion speed and morphology. Third, an \emph{in silico} Nonlinear Model Predictive Control (NMPC) approach regulates non-small cell lung cancer growth under multi-drug low-dose protocols. Built upon experimentally identified growth and pharmacodynamics models from \emph{in vitro} imaging, dose-response assays, and viability tests, the NMPC framework explores constrained, multi-drug low-dose combination strategies while accounting for uncertainties. Together, these works contribute toward a unified research direction that integrates data acquisition, modeling, parameter identification, theoretical analysis, and model-based optimal control. By demonstrating how systems and control principles can quantify, predict, and regulate tumor behavior across scales, this work contributes to the emerging field of cybergenetics, thus aiming at bridging control and optimization methods with experimental oncology.