Mathematical Model and Numerical Simulation for Tissue Growth on Bioscaffolds

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

doi:10.3390/app9194058

Hyun Geun Lee, Jintae Park + Show 3 more

Open Access

https://doi.org/10.3390/app9194058

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Journal: Applied Sciences	Publication Date: Sep 28, 2019
Citations: 11	License type: CC BY 4.0

Affiliation: Korea University, Kwangwoon University

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.

Highlights

In some fracture patients, the bone defects do not get well in the ordinary recuperation period or do not mend at all
The main purpose of this study is to present a mathematical model and numerical simulation for tissue growth on a bioscaffold in two-dimensional (2D) and three-dimensional (3D) space
We propose a simple mathematical model for tissue growth on scaffolds using features of the AC equation, that is, motion by mean curvature

Summary

Introduction

The bone defects do not get well in the ordinary recuperation period or do not mend at all. Simulations of tissue growth on scaffold have been performed [9,10,11,12] and applied in many fields [13,14,15,16,17]. The authors in [18] performed in vitro cell growth studies with osteogenic cells grown on biologically inductive substrate, hydroxylapatite. The main purpose of this study is to present a mathematical model and numerical simulation for tissue growth on a bioscaffold in two-dimensional (2D) and three-dimensional (3D) space. We propose a simple mathematical model for tissue growth on scaffolds using features of the AC equation, that is, motion by mean curvature.

Mathematical Model

Numerical Solution

Numerical Experiments

Simulation of Tissue Growth on Scaffold In 2D

Simulation of Tissue Growth on Scaffold In 3D

Comparison between Experiments and Simulations

Conclusions