Simulation of tissue-engineering cell cultures using a hybrid model combining a differential nutrient equation and cellular automata

Tze Hung Lin, C. A. Chung

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


One of the potential therapeutic strategies in tissue engineering is to regenerate tissues from in vitro cell cultivations with porous scaffolds, and then implant the cellularscaffold into patients suffering tissue defects. Tissues engineering is a multi-discipline composed of many subjects, for which quantification by means of mathematical modeling can interpret experimental results and identify dominating factors. In this paper we develop a hybrid mathematic model to simulate the in vitro cell cultures in tissue engineering. A discrete cellular automation model is used to treat the cell population dynamics affected by the biological phenomena of cell proliferation, aggregation, contact inhibition, nutrient-limited viability, and cell random walks. Cell growth rates are randomly taken using a gamma distribution with its mean value determined by the local oxygen concentration. The oxygen evolution in the scaffold is modeled by a differential diffusion-reaction equation, which is solved with a finite difference method. Simulations show for a uniform seeding case, increasing cell migration speed enhances the cell population to a maximum; however further increasing the migration speed turns to reduce the cell number. This is because cells with faster speeds move to the scaffold periphery and block the oxygen transfer toward the interior region, resulting in a nutrient limitation on the overall cell growth. We also test an artificial seeding condition where the same number of cells is initially seeded around the scaffold center. It is found cells in such a case proliferate slowly for a longer time compared with the case of uniform seeding, and ultimately reach a higher cell population as the nutrient limitation is avoided to some extent. The model offers an effective method to assess the cell population dynamics, and the simulation results can provide a design reference for tissue engineering applications.

Original languageEnglish
Title of host publication13th International Conference on Biomedical Engineering - ICBME 2008
Number of pages4
StatePublished - 2009
Event13th International Conference on Biomedical Engineering, ICBME 2008 - , Singapore
Duration: 3 Dec 20086 Dec 2008

Publication series

NameIFMBE Proceedings
ISSN (Print)1680-0737


Conference13th International Conference on Biomedical Engineering, ICBME 2008


  • Cellular automata
  • Gamma distribution
  • Hybrid model
  • Migration
  • Tissue engineering


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