A mathematical model to predict the evolution of retinal nerve fiber layer thinning in multiple sclerosis patients

Abstract

Multiple sclerosis (MS) is a neurodegenerative disease of the central nervous system (CNS). Many studies of MS patients have described axonal loss in the optic nerve of the retina, and specifically progressive thinning of the retinal nerve fiber layer (RNFL). We hypothesize that RNFL thinning involves the participation of 2 processes that cause CNS damage: autoimmune inflammation and axonal degeneration. To test this hypothesis, we developed a mathematical model based on ordinary differential equations to relate the evolution of RNFL thickness (measured by optical coherence tomography [OCT]) with that of the Expanded Disability Status Scale (EDSS) score in MS patients. Data were obtained from a longitudinal study of 114 MS patients who were followed-up for 10 years. After adjusting the parameters using a genetic algorithm, the model's prediction of the evolution of RNFL thickness accurately reflected the progression revealed by the 10-year clinical data. Our findings suggest that differences in the relative contributions of autoimmune inflammation and axonal degeneration can account for the complex dynamics of MS, which vary from one patient to the next. Moreover, our results show that CNS damage occurs cumulatively from the onset of MS and that most RNFL thinning occurs before the appearance of significant disability. RNFL thickness could therefore serve as a reliable biomarker of MS disease course. Our proposed methodology would enable the use of OCT data from new MS patients to predict the evolution of RNFL thinning and hence the progression of MS in individual patients, and to facilitate the selection of patient-specific therapies.

Keywords: Genetic algorithm; Longitudinal study; Multiple sclerosis; Optic nerve; Optical coherence tomography; Retinal nerve fiber layer.