# Integrated Experimental and Mathematical Exploration of Modular Tissue Cultures for Developmental Engineering

## TL;DR

This paper explores how to grow modular tissues using a mix of experiments and math models to better understand tissue development.

## Contribution

The study introduces an integrated experimental and mathematical framework for modular tissue cultivation and assembly in developmental engineering.

## Key findings

- HDFs formed complex 3D structures in porous scaffolds but remained flattened on solid surfaces.
- Power law models and diffusion simulations captured cell growth and oxygen dynamics during tissue assembly.
- Initial cell density, culture time, and oxygen diffusion significantly influence modular tissue design.

## Abstract

Developmental engineering (DE) involves culturing various cells on modular scaffolds (MSs), yielding modular tissues (MTs) assembled into three-dimensional (3D) tissues, mimicking developmental biology. This study employs an integrated approach, merging experimental and mathematical methods to investigate the biological processes in MT cultivation and assembly. Human dermal fibroblasts (HDFs) were cultured on tissue culture plastics, poly(lactic acid) (PLA) discs with regular open structures, or spherical poly(methyl methacrylate) (PMMA) MSs, respectively. Notably, HDFs exhibited flattened spindle shapes when adhered to solid surfaces, and complex 3D structures when migrating into the structured voids of PLA discs or interstitial spaces between aggregated PMMA MSs, showcasing coordinated colonization of porous scaffolds. Empirical investigations led to power law models simulating density-dependent cell growth on solid surfaces or voids. Concurrently, a modified diffusion model was applied to simulate oxygen diffusion within tissues cultured on solid surfaces or porous structures. These mathematical models were subsequently combined to explore the influences of initial cell seeding density, culture duration, and oxygen diffusion on MT cultivation and assembly. The findings underscored the intricate interplay of factors influencing MT design for tissue assembly. The integrated approach provides insights into mechanistic aspects, informing bioprocess design for manufacturing MTs and 3D tissues in DE.