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

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3 Citations (Scopus)

Abstract

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 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 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 (a) a possible explanation for the ambiguity found in prior analyses, and (b) present a potentially clinically useful model for RA disease progression based upon radiographic assessment of joint damage. (C) 2000 Elsevier Science Ltd.

Original languageEnglish (US)
Pages (from-to)31-38
Number of pages8
JournalMathematical and Computer Modelling
Volume31
Issue number2-3
DOIs
StatePublished - Jan 2000

Fingerprint

Rheumatoid Arthritis
Erosion
Progression
Mathematical Model
Mathematical models
Modeling
Damage
Kinetics
Curve fitting
Second-order Model
Chronic Disease
Kinetic Model
Square root
Incidence
Arthritis
Mathematical model
Model
First-order
Unknown
Evaluate

Keywords

  • Disease modeling
  • Inflammation
  • Joint erosion
  • Mathematical modeling
  • Nonlinear models
  • Radiographic damage
  • Rheumatoid arthritis
  • Simulation

ASJC Scopus subject areas

  • Information Systems and Management
  • Control and Systems Engineering
  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

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title = "Modeling the progression of articular erosion in rheumatoid arthritis (RA): Initial mathematical models",
abstract = "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 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 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 (a) a possible explanation for the ambiguity found in prior analyses, and (b) present a potentially clinically useful model for RA disease progression based upon radiographic assessment of joint damage. (C) 2000 Elsevier Science Ltd.",
keywords = "Disease modeling, Inflammation, Joint erosion, Mathematical modeling, Nonlinear models, Radiographic damage, Rheumatoid arthritis, Simulation",
author = "Witten, {T. M.} and {Del Rincon}, Inmaculada and Agustin Escalante",
year = "2000",
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AU - Witten, T. M.

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N2 - 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 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 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 (a) a possible explanation for the ambiguity found in prior analyses, and (b) present a potentially clinically useful model for RA disease progression based upon radiographic assessment of joint damage. (C) 2000 Elsevier Science Ltd.

AB - 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 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 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 (a) a possible explanation for the ambiguity found in prior analyses, and (b) present a potentially clinically useful model for RA disease progression based upon radiographic assessment of joint damage. (C) 2000 Elsevier Science Ltd.

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KW - Simulation

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