# Mathematical model and numerical simulation for tissue growth on bioscaffolds

Hyun Geun Lee, Jintae Park, Sungha Yoon, Chaeyoung Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

## Abstract

Tissue growth on bioscaffolds can be controlled using substrate geometry such as substrate curvature. In this study, we present a mathematical model and numerical simulation method for tissue growth on a bioscaffold to investigate the effect of local curvature on tissue growth. The mathematical model is based on the Allen-Cahn (AC) equation, which has been extensively used to model many problems involving motion by mean curvature. By solving the AC equation using the explicit Euler method, the proposed method is simple and fast. Numerical simulations on various geometries are presented to demonstrate the applicability of the proposed framework on tissue growth on a bioscaffold.

Original language English 4058 Applied Sciences (Switzerland) 9 19 https://doi.org/10.3390/app9194058 Published - 2019 Oct 1

### Bibliographical note

Funding Information:
The authors thank the reviewers for their constructive and helpful comments on the revision of this article.The first author (H.G.L.) was supported by the Research Grant of Kwangwoon University in 2019 and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1C1C1011112). The corresponding author (J.K.) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03933243).

## Keywords

• Allen-Cahn equation
• Bioscaffold
• Tissue growth
• Triply periodic minimal surface

## ASJC Scopus subject areas

• General Materials Science
• Instrumentation
• General Engineering
• Process Chemistry and Technology
• Computer Science Applications
• Fluid Flow and Transfer Processes

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