Transcatheter aortic valve implantation (TAVI) is becoming the standard choice of care for non-operable patients suffering from severe aortic valve stenosis. As there is no direct view or access to the affected anatomy, accurate preoperative planning is crucial for a successful outcome. The most important decision during planning is selecting the proper implant type and size. Due to the wide variety in device sizes and types and non-circular annulus shapes, there is often no obvious choice for the specific patient. Most clinicians base their final decision on their previous experience. As a first step towards a more predictive planning, we propose an integrated method to estimate the aortic apparatus from CT images and compute implant deployment. Aortic anatomy, which includes aortic root, leaflets and calcifications, is automatically extracted using robust modeling and machine learning algorithms. Then, the finite element method is employed to calculate the deployment of a TAVI implant inside the patient-specific aortic anatomy. The anatomical model was evaluated on 198 CT images, yielding an accuracy of 1.30 +/- 0.23 mm. In eleven subjects, pre- and post-TAVI CT images were available. Errors in predicted implant deployment were of 1.74 +/- 0.40 mm in average and 1.32 mm in the aortic valve annulus region, which is almost three times lower than the average gap of 3 mm between consecutive implant sizes. Our framework may thus constitute a surrogate tool for TAVI planning.