Constructing One-Dimensional Continuous Models from Two-Dimensional Discrete Models of Medical Implants

Authors

  • Alicia Prieto-Langarica Youngstown State University
  • Hristo V Kojouharov The University of Texas at Arlington
  • Liping Tang The University of Texas at Arlington

DOI:

https://doi.org/10.11145/j.biomath.2012.09.041

Keywords:

upscaling, medical implants, modeling, cellular automata

Abstract

Medically implanted devices are becoming increasingly important in medical practice. Over 4 million people in the United States have long-term biomedical implants. However, many medical implants have to be removed because of infection or because their protein coating causes excessive inflammation and decrease in the immune system response. In this work, a discrete two-dimensional model of blood cells and bacteria interactions on the surface of a medical implant is transformed into a discrete one-dimensional model. This one-dimensional model is then upscaled into a partial differential equation model. The results from the discrete two-dimensional model and the continuous one-dimensional model are then compared for different protein coating mixtures. Two medical treatment alternatives are also explored and the two models are compared again.

Author Biographies

Alicia Prieto-Langarica, Youngstown State University

Assistant Professor

Department of Mathematics and Statistics

Hristo V Kojouharov, The University of Texas at Arlington

Professor

Department of Mathematics

Liping Tang, The University of Texas at Arlington

Professor

Department of Bioengineering

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Published

2012-10-08

Issue

Section

Original Articles