Dynamic Modeling of Clinical Depression and Treatment Responsiveness Identification

Abstract

The Major Depressive Disorder (MDD) represents one of the major public rising health care problems worldwide according to the World Health Organization. In this work we introduce a novel dynamic model for the analysis of clinimetric data obtained from the follow-up assesment in depressed patients, and the identification of its parameters and analysis of its equilibria and stability, that also helps to evaluate the effectiveness of some given treatments. The resulting reduced model is a positive nonlinear system with two parameters to identify the intensity of the treatment and the dynamics of the depression levels in a Hamilton Rating Scale for Depression. In order to verify the validity of the the model, a group of 39 participants diagnosed with MDD meeting DSM-IV criteria was divided in four groups, including a controlled clinical trial, randomly assigned to one of four treatment options: a) repetitive transcranial magnetic stimulation (rTMS) + escitalopram; b) rTMS+ placebo, c) sham rTMS + escitalopram and sham rTMS and placebo. Clinical assesments were done weekly using HDRS as main outcome measure in order to identify the parameters of the model using a Least-Squares algorithm. The results show that the intensity and the dynamics of clinical depression can be established with a simple nonlinear model.