Our research focuses on the advancement of theoretical and computational methods to quantify complex fluid flow. Much of our research is geared towards modeling and analyzing hemodynamic conditions in the cardiovascular system. This multidisciplinary research combines advances in medical imaging, mathematical modeling, and computational mechanics. Our motivations for this research are 3-fold: (1) to uncover biomechanical interactions underlying disease initiation and progression, (2) to improve diagnosis of cardiovascular deficiencies, and (3) to better engineer interventions and devices. We also develop computational dynamical systems methods to better understand the physics of fluids and the material structures that organize fluid transport.