Mathematical Modelling and Simulations of Complex Breathing Patterns Detected by RADAR Sensors

We present a mathematical model for chest and abdomen motion during breathing, where a radar-based sensor records the superposition of the signals coming from chest and abdominal regions. The oscillatory movement of abdomen does not necessarily need to be synchronous to that of a chest. The degree of asynchrony between these two motions, called thoracoabdominal asynchrony can be described by the phase-lag angle. A large value of the phase-lag angle indicates the presence of certain breathing abnormalities, such as bronchopulmonary dysplasia, airway obstruction or the presence of certain neuromuscular diseases. Using a simple mathematical model, we show that different values for the phase lag lead to different complex shapes in the in-phase versus quadrature signal plane (complex plane). In the limit of large carrier wavelength (when the carrier wavelength is much larger than the typical chest/abdomen displacement amplitude during breathing), these shapes reduce to Lissajous figures. We present Matlab simulation results, where thoracoabdominal asynchrony was simulated using a radar simulation and analysis tool that models the entire signal chain from RF to IF domain.