Mathematical modelling of tissue formation in chondrocyte filter cultures.
Abstract: In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.
Publication Date: 2011-12-17 PubMed ID: 22179936DOI: 10.22203/ecm.v022a28Google Scholar: Lookup
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- Journal Article
Summary
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The research article presents a mathematical model that helps understand the processes involved in in vitro growth and development of tissue in chondrocyte filter cultures, which is a common three-dimensional differentiation model in cartilage tissue engineering.
Objective of the Study
- One of the primary aims of the study was to better characterize the processes governing in vitro growth and tissue development in chondrocyte filter cultures.
- This was pursued through a multidisciplinary approach that integrated experimental and applied mathematical methods.
Methodology
- A mathematical model was constructed using partial differential equations. This model predicted aspects such as the distribution of cells and glycosaminoglycans (GAGs) and overall thickness of the tissue.
- Healthy mature equine chondrocytes were expanded and placed on collagen-coated filters, then cultured for up to 7 weeks to obtain experimental data.
- This data was examined biochemically and histologically to then be used for comparison with the simulation predictions, allowing refinement of the initial models.
Findings of the Study
- The simulations offered a reasonable depiction of the experimentally obtained cell and matrix distribution within cultures.
- The model clearly showed that the experimental GAG and cell distribution heavily depends on the cell differentiation rate. This finding is crucial for the interpretation of experimental outcomes.
- The research revealed that large swathes of the tissue were inactive in terms of proliferation and growth of the layer, inferring that increasing seeding densities would not significantly affect the growth rate.
Conclusions and Implications
- The researchers developed a simple mathematical model to predict the experimental data that were observed, providing an interpretation of the principal underlying mechanisms steering growth-related changes in tissue composition.
- The findings of this study have far-reaching implications for our understanding of tissue growth, particularly in the field of cartilage tissue engineering. They provide valuable insights for optimizing and controlling conditions for successful tissue formation in chondrocyte filter cultures.
Cite This Article
APA
Catt CJ, Schuurman W, Sengers BG, van Weeren PR, Dhert WJ, Please CP, Malda J.
(2011).
Mathematical modelling of tissue formation in chondrocyte filter cultures.
Eur Cell Mater, 22, 377-392.
https://doi.org/10.22203/ecm.v022a28 Publication
Researcher Affiliations
- School of Mathematics, University of Southampton, UK.
MeSH Terms
- Algorithms
- Animals
- Cartilage, Articular / cytology
- Cartilage, Articular / growth & development
- Cartilage, Articular / metabolism
- Cell Count
- Cell Differentiation
- Cell Movement
- Cell Proliferation
- Cells, Cultured
- Chondrocytes / metabolism
- Chondrocytes / physiology
- Collagen / metabolism
- Extracellular Matrix / metabolism
- Glycosaminoglycans / metabolism
- Horses
- Models, Biological
- Tissue Engineering
Citations
This article has been cited 6 times.- Eskelinen ASA, Tanska P, Florea C, Orozco GA, Julkunen P, Grodzinsky AJ, Korhonen RK. Mechanobiological model for simulation of injured cartilage degradation via pro-inflammatory cytokines and mechanical stimulus.. PLoS Comput Biol 2020 Jun;16(6):e1007998.
- Pearce D, Fischer S, Huda F, Vahdati A. Applications of Computer Modeling and Simulation in Cartilage Tissue Engineering.. Tissue Eng Regen Med 2020 Feb;17(1):1-13.
- Kar S, Smith DW, Gardiner BS, Grodzinsky AJ. Systems Based Study of the Therapeutic Potential of Small Charged Molecules for the Inhibition of IL-1 Mediated Cartilage Degradation.. PLoS One 2016;11(12):e0168047.
- Sarig U, Nguyen EB, Wang Y, Ting S, Bronshtein T, Sarig H, Dahan N, Gvirtz M, Reuveny S, Oh SK, Scheper T, Boey YC, Venkatraman SS, Machluf M. Pushing the envelope in tissue engineering: ex vivo production of thick vascularized cardiac extracellular matrix constructs.. Tissue Eng Part A 2015 May;21(9-10):1507-19.
- Fu AS, Solorio LD, Alsberg E, Saidel GM. Mathematical modelling of glycosaminoglycan production by stem cell aggregates incorporated with growth factor-releasing polymer microspheres.. J Tissue Eng Regen Med 2017 Feb;11(2):481-488.
- Halloran JP, Sibole S, van Donkelaar CC, van Turnhout MC, Oomens CW, Weiss JA, Guilak F, Erdemir A. Multiscale mechanics of articular cartilage: potentials and challenges of coupling musculoskeletal, joint, and microscale computational models.. Ann Biomed Eng 2012 Nov;40(11):2456-74.
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