Modeling the progression of articular erosion in Rheumatoid Arthritis (RA): Initial mathematical models

Rheumatoid Arthritis (RA) is a chronic inflammatory disease of unknown caus e that affects around 1% of the adult population in the U.S. Women are more often affected than men by a ratio of 3 to 1, and although the disease can appear at any age in adult life, the incidence and prevalence increase wit h age. The inflammatory process that characterizes RA, centers in and aroun d articular structures and is characterized by destruction that progresses over time. Attempts to apply curve fitting to the analysis of the progressi on of radiographic damage in RA have lead to numerous forms of mathematical models (linear, quadratic, cubic, square root, first-order kinetics, etc.) . None of these models has been very successful in that a significant degre e of ambiguity of the appropriate model form still remains. A mathematical model of the progression of RA would be useful to evaluate the effect of in terventions to ameliorate joint destruction. In this paper, we present a ri gorously derived second-order kinetics model and propose (a) a possible explanation for the ambiguity found in prior analyses, and (b) present a potentially clinically useful model for RA disease progressio n based upon radiographic assessment of joint damage. (C) 2000 Elsevier Science Ltd. All rights reserved.