A computational reaction–diffusion model for biosynthesis and linking of cartilage extracellular matrix in cell-seeded scaffolds with varying porosity

  • Sarah D. Olson
  • Mansoor A. Haider
Original Paper


Cartilage tissue engineering is commonly initiated by seeding cells in porous materials such as hydrogels or scaffolds. Under optimal conditions, the resulting engineered construct has the potential to fill regions where native cartilage has degraded or eroded. Within a cell-seeded scaffold supplied by nutrients and growth factors, extracellular matrix accumulation should occur concurrently with scaffold degradation. At present, the interplay between cell-mediated synthesis and linking of matrix constituents and the evolving scaffold properties is not well understood. We develop a computational model of extracellular matrix accumulation in a cell-seeded scaffold based on a continuum reaction–diffusion system with inhomogeneous inclusions representing individual cells. The effects of porosity on engineered tissue outcomes is accounted for via the use of mixture variables capturing the spatiotemporal dynamics of both bound and unbound system constituents. The unbound constituents are the nutrients and unlinked extracellular matrix, while the bound constituents are the scaffold and the linked extracellular matrix. The linking model delineates binding of matrix constituents to either existing bound extracellular matrix or to scaffold. Results on a representative domain exhibit bound matrix trapping (vs spreading) around cells in scaffolds with lower (vs higher) initial porosity, similar to experimental results obtained by Erickson et al. (Osteoarthr Cartil 17:1639–1648, 2009). Significant alterations in the spatiotemporal accumulation of bound matrix are observed when, among the set of all model parameters, only the initial scaffold porosity is varied. The model presented herein proposes a methodology to investigate coupling between cell-mediated biosynthesis and linking of extracellular matrix in porous, cell-seeded scaffolds that has the potential to aid in the design of optimal tissue-engineered cartilage constructs.


Scaffold porosity Tissue-engineered cartilage Extracellular matrix linking Reaction–diffusion Computational model 



This study was funded in part by the National Science Foundation (Olson—1455270, Haider—1615820).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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