# Differential Equations Seminar

## Justin Brooks, Army Research Laboratory

Monday, May 8, 2017

11:00 AM - 12:00 PM

11:00 AM - 12:00 PM

Mathematics/Psychology : 401

**Title:**A Framework for Dynamical Systems Modeling of Continuous Internal Human State

**Abstract:**The necessity to accurately predict human behavior in order to design functional, adaptive systems is increasing with the complexity of technology. Virtual/augmented reality, gesture/voice recognition, and similar technologies rely on accurately interpreting human behavioral and/or physiological signals for optimal function. In current system designs, variability in these signals is often interpreted as human error; however, this variability is often not an error, but instead, indicates a change in the internal state (e.g. stress, boredom, fatigue) of the human. Thus, to improve adaptive system performance, we must improve our ability to decipher and quantify dynamic human states. An attractive theoretical perspective to understand human state arises from a dynamical systems framework. Here, states are defined as attractor basins that emerge from the interaction between several subsystems including: peripheral physiology, the autonomic nervous system (ANS), the central nervous system (CNS), and the environment. While conceptually appealing, dynamical system models of internal state exist as abstractions and have not been developed in a modeling framework that could be used to interpret empirical observations. In this two year effort, we propose the development of such a mathematical model and examine the model’s predictions to empirical data.

First, we propose to construct a two state attractor landscape to model internal state using simulations. We extend existing equations that govern the interaction of the ANS and peripheral physiology with equations that represent the influence of the CNS and environment on these systems. We will examine the evolution of the entire model through phase space. In this model, the environment and CNS are represented heuristically as an excursion in the energy landscape which the ANS seeks to minimize. After determining the physiological boundaries for the parameters in the model, we examine variability in state stability and transitions.

Second, we propose to analyze fMRI and impedance cardiography data collected during a mental math task which has been shown to induce changes in arousal. With these data, we operationally define state as a correlation between blood-oxygen level dependent (BOLD) signal in specific brain regions and heart rate as continuous measure of state consistent with existing anatomical and functional observations. The time series of these correlations serve as a link between our mathematical model and empirical data. By minimizing the difference between the predicted and actual correlation time series we are then able to numerically estimate the models parameters.

In sum, this research provides a modular model system to quantify human states. The model is flexible, and is able to incorporate additional parameters and equations to further refine and more accurately assess human state that ultimately can be used to better understand, characterize, and ultimately predict human behavior for adaptive systems.