Advection-diffusion-reaction equations based tumor cells growth modeling

Lu Jun Zhang, Ming Yan Jiang, An De Bao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Cancer has been one of the major diseases threatening human life. Considering various factors influencing tumor invasion to construct a rational tumor growth model, through integrating mathematical and physical theories with computer technology, it is important to understand the invasion procedure of cancerous tissue and help for optimizing clinical tumor therapy plan. Based on an advection-diffusion-reaction equation which describes the mass conservation laws, this paper detailed the modeling of the tumor cells growth and analyzed its rationality and practical significance by considering many factors including tumor cells adhesion energy, cell moving velocity, solid pressure, mass exchange and nutrition distribution. The simulation results showed the effects of some factors in the model, including the lowest nutrition concentration supporting viable tumor cells, adhesion energy parameter and initial tumor shape, on tumor cells growth, and proved that our model can simulate the evolution of tumors growing outward expansion trend; and according to the nutrient concentration changes and other conditions alterations, the corresponding evolution results can be obtained; simulating tumor cells growth results appear the protuberant structures, which is consistent with the actual tumor growth. This study is significant for predicting tumor growth evolution and assisting clinical tumor therapy.

Original languageEnglish (US)
Pages (from-to)679-689
Number of pages11
JournalChinese Journal of Biomedical Engineering
Issue number5
StatePublished - Oct 20 2012


  • Advection-diffusion-reaction equations
  • Diffusion-reaction equations
  • Mathematical modeling
  • Tumor cells growth

ASJC Scopus subject areas

  • Medicine (miscellaneous)
  • Bioengineering
  • Biomedical Engineering


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