We present a novel framework for analyzing dynamic vocal tract deformations by integrating volumetric Magnetic Resonance Imaging (MRI) data and real-time MRI (rtMRI) boundary constraints within an iterative Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. More precisely, we apply LDDMM to morph volumetric vocal tract shapes using rtMRI boundary constraints that enable a smooth and anatomically plausible articulatory transformation. We demonstrate the method and discuss the issues involved using a vowel-consonant-vowel sequence. We show the influence of varying the number of rtMRI images on the resulting articulatory transformation.