Analysis of a mathematical model of rheumatoid arthritis.

Journal of Mathematical Biology
Avner Friedman, King-Yeung Lam

Abstract

Rheumatoid arthritis is an autoimmune disease characterized by inflammation in the synovial fluid within the synovial joint connecting two contiguous bony surfaces. The inflammation diffuses into the cartilage adjacent to each of the bony surfaces, resulting in their gradual destruction. The interface between the cartilage and the synovial fluid is an evolving free boundary. In this paper we consider a two-phase free boundary problem based on a simplified model of rheumatoid arthritis. We prove global existence and uniqueness of a solution, and derive properties of the free boundary. In particular it is proved that the free boundary increases in time, and the cartilage shrinks to zero as [Formula: see text], even under treatment by a drug. It is also shown in the reduced one-phased problem, with cartilage alone, that a larger prescribed inflammation function leads to a faster destruction of the cartilage.

References

Feb 16, 2008·Journal of Mathematical Biology·Frédéric Frank Weller
Oct 7, 2009·Proceedings of the National Academy of Sciences of the United States of America·Chuan XueChandan K Sen
Jun 3, 2011·Mathematical Biosciences and Engineering : MBE·Avner Friedman, Chuan Xue
Apr 15, 2014·Archive for Rational Mechanics and Analysis·A FriedmanChuan Xue
Sep 11, 2014·Bulletin of Mathematical Biology·Avner Friedman, Wenrui Hao
Mar 18, 2016·PloS One·Wenrui HaoAvner Friedman
Oct 30, 2016·Journal of Theoretical Biology·Nourridine SieweAvner Friedman
Feb 18, 2017·PloS One·Wenrui HaoDai Zhu
May 8, 2018·Proceedings of the National Academy of Sciences of the United States of America·Xiulan LaiAvner Friedman
Oct 23, 2018·Journal of Theoretical Biology·Nicolae Moise, Avner Friedman

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