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

In this study we provide a dynamic non-linear mathematical approach for modeling the course of disease in acquired brain injury (ABI) patients. Data from a multicentric study was used to evaluate the reliability of the Michaelis-Menten (MM) model applied to well-known clinical variables assessing the outcome of ABI patients. The sample consisted of 156 ABI patients admitted to eight neurorehabilitation subacute units (IRU) and evaluated at baseline (T0), after 4 months from the event (T1) and at discharge (T2). The MM model was used to characterize the trend of the first PCA dimension (represented by the variables: feeding modality, RLAS, ERBI_A, Tracheostomy, CRS-r and ERBI-B) to predict the most plausible outcome, in terms of positive or negative GOS at discharge. Exploring the evolution over time of the PCA Dimension 1, after day 86 the MM model was able to better discriminate the time course for individuals with positive with respect to negative GOS (Accuracy: 85%; Sensitivity: 90.6%; Specificity: 62.5%). Using a non-linear dynamic mathematical model, we can provide more comprehensive trajectories of the clinical evolution of ABI patients during the rehabilitation period. Our model can be used to select patients for interventions designed for a specific outcome trajectory.