Modeling the progression of articular erosion in rheumatoid arthritis (RA): Initial mathematical models

Rheumatoid Arthritis (RA) is a chronic inflammatory disease of unknown cause 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 with age. The inflammatory process that characterizes RA, centers in and around articular structures and is characterized by destruction that progresses over time. Attempts to apply curve fitting to the analysis of the progression of radiographie 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 signficiant degree 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 interventions to ameliorate joint destruction. In this paper, we present a rigorously derived second-order kinetics model and propose 1. possible explanation for the ambiguity found in prior analyses, and esent a potentially clinically useful model for RA disease progression based upon radiographic assessment of joint damage.