Modeling outcome trajectories in patients with acquired brain injury using a non-linear dynamic evolution approach

Abstract This study describes a dynamic non-linear mathematical approach for modeling the course of disease in acquired brain injury (ABI) patients. Data from a multicentric study were used to evaluate the reliability of the Michaelis–Menten (MM) model applied to well-known clinical variables that assess the outcome of ABI patients. The sample consisted of 156 ABI patients admitted to eight neurorehabilitation subacute units and evaluated at baseline (T0), 4 months after the event (T1) and at discharge (T2). The MM model was used to characterize the trend of the first Principal Component Analysis (PCA) dimension (represented by the variables: feeding modality, RLAS, ERBI-A, Tracheostomy, CRS-r and ERBI-B) in order to predict the most plausible outcome, in terms of positive or negative Glasgow outcome score (GOS) at discharge. Exploring the evolution of the PCA dimension 1 over time, after day 86 the MM model better differentiated between the time course for individuals with a positive and negative GOS (accuracy: 85%; sensitivity: 90.6%; specificity: 62.5%). The non-linear dynamic mathematical model can be used to provide more comprehensive trajectories of the clinical evolution of ABI patients during the rehabilitation period. Our model can be used to address patients for interventions designed for a specific outcome trajectory.