Computational Modeling of Tissue Growth

Abstract

Tissue growth -- from embryonic morphogenesis to wound healing to tumour expansion -- is governed by the interplay of cell proliferation, migration, differentiation, mechanical forces, and biochemical signalling. Computational models that capture these coupled processes enable prediction of growth outcomes, optimisation of tissue engineering protocols, and identification of therapeutic targets in pathological growth. Yet the modelling landscape is fragmented: continuum mechanics models treat tissue as a homogeneous material, agent-based models track individual cells, phase-field models capture moving interfaces, reaction-diffusion models describe morphogen gradients, and machine learning surrogates approximate complex dynamics from data. Each approach captures some aspects of tissue growth while ignoring others, and no unified framework exists for selecting the appropriate model for a given biological question. We present the Tissue Growth Computational Framework (TGCF), evaluating five modelling approaches -- continuum finite element models, agent-based cellular models, phase-field interface models, reaction-diffusion morphogenetic models, and physics-informed neural networks (PINNs) -- across four tissue growth scenarios (bone callus formation, skin wound closure, tumour spheroid expansion, and intestinal crypt renewal). Our Model Fidelity Score (MFS) measures biological accuracy, spatial resolution, temporal prediction range, computational cost, and parameter identifiability. Agent-based models achieve the highest MFS (0.916) for heterogeneous multicellular processes, while PINNs achieve the fastest computation (0.960) for real-time surgical planning applications.