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

Alicia Prieto-Langarica, Hristo V Kojouharov, Liping Tang

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.


Keywords


upscaling; medical implants; modeling; cellular automata

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DOI: http://dx.doi.org/10.11145/j.biomath.2012.09.041

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ISSN 1314-7218 (online)
ISSNĀ 1314-684X (print)

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