Hybrid Mathematical-Computational Models for Tissue Engineering

Abstract

Tissue engineering -- the in vitro fabrication of functional tissue constructs from cells, biomaterials, and biological signals -- is guided by complex mathematical relationships governing nutrient transport, mechanical loading, cell growth, ECM deposition, and tissue maturation. Mathematical models of individual processes (reaction-diffusion equations for oxygen transport in scaffolds, continuum mechanics for scaffold deformation, kinetic models for ECM crosslinking) have been developed independently, but the integration of these mathematical descriptions with computational cell-level simulations into coherent hybrid models that can guide tissue engineering bioreactor design and protocol optimisation has remained a challenge. This paper proposes the Tissue Engineering Hybrid Mathematical-Computational (TEHMC) framework, integrating continuum partial differential equation (PDE) models for transport and mechanics with agent-based cell simulations and machine learning surrogate models into a unified tissue engineering design tool, comprising four modelling components: a nutrient transport and reaction PDE solver (NTRPS) modelling oxygen and glucose diffusion and consumption in 3D scaffolds; a scaffold mechanics model (SMM) predicting stress-strain distributions and mechanosensing signals in engineered constructs under bioreactor loading conditions; a hybrid cell-continuum integrator (HCCI) coupling CITRA-style cell agents with the PDE fields from NTRPS and SMM; and a machine learning design surrogate (MLDS) emulating TEHMC simulation outputs for rapid scaffold and protocol design space exploration. TEHMC is evaluated on three tissue engineering applications: cartilage construct maturation in perfusion bioreactors, bone scaffold vascularisation under mechanical loading, and cardiac patch electromechanical maturation. NTRPS oxygen distribution predictions agree with experimental microelectrode measurements with r = 0.948 (SD = 0.018). SMM mechanical stress predictions agree with finite element reference solutions with r = 0.964 (SD = 0.014). MLDS emulation of full TEHMC simulations achieves R2 = 0.944 (SD = 0.022) at 1,200x speedup. MLDS-guided scaffold design optimisation identifies configurations that improve construct maturation score by 32.4% (SD = 6.8%) vs. empirical standard designs. The study contributes the TEHMC specification, three validated tissue engineering models, and an ML surrogate-accelerated design framework.