In previous work we have used patient-specific data to build a computational model of the blood flow in the left ventricle of the heart, in which we analysed the mechanical stresses in the blood flow, with a focus on turbulent flow structures. The computational model was based on solving the Navier-Stokes equations with a finite element method on a deforming mesh, and the mechanical stresses were analyzed using the triple decomposition of the velocity gradient of the flow. Here we present recent work in which the existing model of the mitral valve, a simple inlet boundary condition, is replaced by a three dimensional model that represents the papillary mus- cles and leaflets by a unified continuum fluid-structure interaction model, and the chordae tendinae by a porous medium. Turbulent flow structures in the new model are analyzed by the triple decomposition of the velocity gradient tensor, and are compared with previous results using a simplified mitral valve model.