Modelling motion energy in psychotherapy: A dynamical systems approach

In this study we introduce an innovative mathematical and statistical framework for the analysis of motion energy dynamics in psychotherapy sessions. Our method combines motion energy dynamics with coupled linear ordinary differential equations and a measurement error model, contributing new clinical parameters to enhance psychotherapy research. Our approach transforms raw motion energy data into an interpretable account of therapist–patient interactions, providing novel insights into the dynamics of these interactions. A key aspect of our framework is the development of a new measure of synchrony between the motion energies of therapists and patients, which holds significant clinical and theoretical value in psychotherapy. The practical applicability and effectiveness of our modelling and estimation framework are demonstrated through the analysis of real session data. This work advances the quantitative analysis of motion dynamics in psychotherapy, offering important implications for future research and therapeutic practice.