A Phase-Field Model for Articular Cartilage Regeneration in Degradable Scaffolds

Ana Yun, Soon Hyuck Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Degradable scaffolds represent a promising solution for tissue engineering of damaged or degenerated articular cartilage which due to its avascular nature, is characterized by a low self-repair capacity. To estimate the articular cartilage regeneration process employing degradable scaffolds, we propose a mathematical model as the extension of Olson and Haider's work (Int. J. Pure Appl. Math. 53:333-353, 2009). The simulated tissue engineering procedure consists in (i) the explant of a cylindrical sample, (ii) the removal of the inner core region, and (iii) the filling of the inner region with hydrogels, degradable scaffolds enriched with nutrients, such as oxygen and glucose. The phase-field model simulates the cartilage regeneration process at the scaffold-cartilage interface. It embeds reaction-diffusion equations, which are used to model the nutrient and regenerated extracellular matrix. The equations are solved using an unconditionally stable hybrid numerical scheme. Cartilage repair processes with full-thickness defects, which are controlled by properties of hydrogel materials and cartilage explant culture based on biological interest are observed. The implemented mathematical model shows the capability to simulate cartilage repairing processes, which can be virtually controlled evaluating hydrogel and cartilage material properties including nutrient supply and defected magnitude. In particular, the adopted methodology is able to explain the regeneration time of cartilage within hydrogel environments. With the numerical scheme, the numerical simulations are demonstrated for the potential improvement of hydrogel structures.

Original languageEnglish
Pages (from-to)2389-2409
Number of pages21
JournalBulletin of Mathematical Biology
Issue number12
Publication statusPublished - 2013 Dec


  • Articular cartilage regeneration
  • Hydrogel
  • Phase-field model
  • Reaction-diffusion model

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics


Dive into the research topics of 'A Phase-Field Model for Articular Cartilage Regeneration in Degradable Scaffolds'. Together they form a unique fingerprint.

Cite this