Left ventricular diastolic dysfunction (LVDD) is any abnormality in the filling of the left ventricle (LV).  Despite the prevalence of this disease, it remains difficult to diagnose, mainly due to inherent compensatory mechanisms and a limited physical understanding of the filling process.  LV filling can be non-invasively imaged using color m-mode echocardiography which provides a spatio-temporal map of inflow velocity.  These filling patterns, or waves, are conventionally used to qualitatively assess the filling pattern, however, this work aims to physically quantify the filling waves to improve understanding of diastole and develop robust, reliable, and quantitative parameters. This work reveals that LV filling waves in a normal ventricle act as dispersive waves and not only propagate along the length of the LV but also spread and disperse in the direction of the apex.  In certain diseased ventricles, this dispersion is limited due to changes in LV geometry and wall motion.  This improved understanding could aid LVDD diagnostics not only for determining health and disease, but also for distinguishing between progressing disease states. This work also identifies a limitation in a current LVDD parameter, intra ventricular pressure difference (IVPD), and presents a new methodology to address this limitation.  This methodology is also capable of synthesizing velocity information from a series of heartbeats to generating one representative heartbeat, addressing inaccuracies due to beat-to-beat variations.  This single beat gives a comprehensive picture of that specific patient's filling pattern.  Together, these methods improve the clinical utility of IVPD, making it more robust and limiting the chance for a misdiagnosis. / Master of Science