This paper focuses on computer simulation aspects of Digital Twin models in the medical framework. In particular, it addresses the need of fast and accurate simulators for the mechanical response at tissue and organ scale and the capability of integrating patient-specific anatomy from medical images to pinpoint the individual variations from standard anatomical models.We propose an automated procedure to create mechanical models of the human liver with patient-specific geometry and real time capabilities. The method hinges on the use of Statistical Shape Analysis to extract the relevant anatomical features from a database of medical images and Model Order Reduction to compute an explicit parametric solution for the mechanical response as a function of such features. The Sparse Subspace Learning, coupled with a Finite Element solver, was chosen to create low-rank solutions using a non-intrusive sparse sampling of the feature space.In the application presented in the paper, the statistical shape model was trained on a database of 385 three dimensional liver shapes, extracted from medical images, in order to create a parametrized representation of the liver anatomy. This parametrization and an additional parameter describing the breathing motion in linear elasticity were then used as input in the reduced order model. Results show a consistent agreement with the high fidelity Finite Element models built from liver images that were excluded from the training dataset. However, we evidence in the discussion the difficulty of having compact shape parametrizations arising from the extreme variability of the shapes found in the dataset and we propose potential strategies to tackle this issue.A method to represent patient-specific real-time liver deformations during breathing is proposed in linear elasticity. Since the proposed method does not require any adaptation to the direct Finite Element solver used in the training phase, the procedure can be easily extended to more complex non-linear constitutive behaviors - such as hyperelasticity - and more general load cases. Therefore it can be integrated with little intrusiveness to generic simulation software including more sophisticated and realistic models.