Modeling and parameter estimation of tumor spheroids from bottom-view imaging: beyond the spherical assumption

Tumor spheroids are widely used in vitro models for studying tumor growth and treatment response, yet their analysis is often limited by incomplete geometric measurements. In practice, only a two-dimensional bottom view is available, which can lead to strong biases when spheroids deviate from an ideal spherical shape, in particular for flattened aggregates. We propose a mechanistic modeling and data assimilation framework that accounts for both poor data quality and model uncertainty. A biologically motivated partial differential equations model with axial symmetry is introduced and reduced to a low-dimensional system compatible with sparse observations and ellipsoidal shapes. Uncertainties in initial conditions and parameters are handled using a Luenberger-type observer coupled with a reduced-order unscented Kalman filter. The approach is validated on synthetic data and applied to experimental in vitro spheroid data under propranolol treatment, illustrating how model-based integration of limited measurements improves the interpretation of spheroid growth dynamics and treatment-induced morphological changes.