Safety & Efficacy Study of the Medtronic CoreValve® System-Treatment of Symptomatic Severe Aortic Stenosis With Significant Comorbidities in Extreme Risk Subjects Who Need Aortic Valve Replacement

Inclusion Criteria: * Subject must have co-morbidities such that one cardiologist and two cardiac surgeons agree that medical factors preclude operation, based on a conclusion that the probability of death or serious morbidity exceeds the probability of meaningful improvement. Specifically, the predicted operative risk of death or serious, irreversible morbidity is ≥ 50% at 30 days. * Subjects must meet all of the criteria under at least one of the sub-groups 2a-c: a. Senile degenerative aortic valve stenosis and i. At least one of the following co-morbid conditions: 1. Severe (≥3-4+) mitral valve regurgitation as measured by echocardiography 2. Severe (≥3-4+) tricuspid valve regurgitation as measured by echocardiography 3. End-stage renal disease requiring renal replacement therapy (Stage 5 of the KDOQI CKD Classification) or creatinine clearance \<20cc/min but not requiring renal replacement therapy AND ii. mean gradient \> 40 mmHg or jet velocity greater than 4.0 m/sec by either resting or dobutamine stress echocardiogram (if the LVEF \< 50%), or simultaneous pressure recordings at cardiac catheterization either resting or with dobutamine stress (if the LVEF \< 50%) AND iii. an initial aortic valve area of ≤ 0.8 cm2 (or aortic valve area index ≤0.5 cm2/m2) by resting echocardiogram or simultaneous pressure recordings at cardiac catheterization AND/OR b. Low gradient, low output aortic stenosis as defined by the presence of all three of the following i. In the presence of LVEF \<50%, absence of contractile reserve, a mean gradient ≥25mmHg and \<40mmHg AND jet velocity less than 4.0m/sec with dobutamine stress echocardiography or simultaneous pressure recordings at cardiac catheterization OR In the presence of LVEF ≥50%, a mean gradient ≥25mmHg and \<40mmHg AND jet velocity less than 4.0 m/sec, by echocardiography or simultaneous pressure recordings at cardiac catheterization AND ii. an initial aortic valve area of ≤0.8 cm2 (or aortic valve area index ≤0.5 cm2/m2) by resting echocardiogram or simultaneous pressure recordings at cardiac catheterization AND iii. radiographic evidence of severe aortic valve calcification AND/OR c. Failed bioprosthetic surgical aortic valve * Subject is symptomatic from his/her aortic valve stenosis, as demonstrated by New York Heart Association (NYHA) Functional Class II or greater. * The subject or the subject's legal representative has been informed of the nature of the study, agrees to its provisions and has provided written informed consent as approved by the IRB of the respective clinical site. * The subject and the treating physician agree that the subject will return for all required post-procedure follow-up visits. Exclusion Criteria: Clinical * Evidence of an acute myocardial infarction ≤30 days before the MCS TAVI procedure. * Any percutaneous coronary or peripheral interventional procedure performed within 30 days prior to the MCS TAVI procedure * Blood dyscrasias as defined: leukopenia (WBC \<1000mm3), thrombocytopenia (platelet count \<50,000 cells/mm3), history of bleeding diathesis or coagulopathy. * Untreated clinically significant coronary artery disease requiring revascularization. * Cardiogenic shock manifested by low cardiac output, vasopressor dependence, or mechanical hemodynamic support. * Need for emergency surgery for any reason. * Severe ventricular dysfunction with left ventricular ejection fraction (LVEF) \<20% as measured by resting echocardiogram. * Recent (within 6 months) cerebrovascular accident (CVA) or transient ischemic attack (TIA). * Active Gastrointestinal (GI) bleeding that would preclude anticoagulation. * A known hypersensitivity or contraindication to all anticoagulation/antiplatelet regimens (including ability to be anticoagulated for the index procedure), nitinol, or \[allergic\] sensitivity to contrast media which cannot be adequately pre-medicated. * Ongoing sepsis, including active endocarditis. * Subject refuses a blood transfusion. * Life expectancy \<12 months due to associated non-cardiac co-morbid conditions. * Other medical, social, or psychological conditions that in the opinion of an Investigator precludes the subject from appropriate consent. * Severe dementia (resulting in either inability to provide informed consent for the study/procedure, prevents independent lifestyle outside of a chronic care facility, or will fundamentally complicate rehabilitation from the procedure or compliance with follow-up visits). * Currently participating in an investigational drug or another device study. * Symptomatic carotid or vertebral artery disease. Anatomical Subject has a: * Native aortic annulus size \<18 mm or \>29 mm per the baseline diagnostic imaging (not applicable for TAV in SAV subjects) OR * Surgical bioprosthetic annulus \<17mm or \>29mm i. Stented SAV per the manufactured labeled inner diameter OR ii. Stentless SAV per the baseline diagnostic imaging * Subject has a pre-existing prosthetic heart valve with a rigid support structure in either the mitral or pulmonic position: 1. that could affect the implantation or function of the study valve OR 2. the implantation of the study valve could affect the function of the pre-existing prosthetic heart valve * Moderate to severe mitral stenosis. * Mixed aortic valve disease: aortic stenosis and aortic regurgitation with predominant aortic regurgitation, (AR is moderate-severe to severe (≥3-4+))(except for failed surgical bioprothesis) * Hypertrophic obstructive cardiomyopathy. * Echocardiographic evidence of new or untreated intracardiac mass, thrombus or vegetation. * Severe basal septal hypertrophy with an outflow gradient. * Aortic root angulation (angle between plane of aortic valve annulus and horizontal plane/vertebrae) \>70° (for femoral and left subclavian/axillary access) and \>30° (for right subclavian/axillary access). * Ascending aorta that exceeds the maximum diameter for any given native or surgical bioprosthetic\* aortic annulus size (see table below) Aortic Annulus Diameter/ Ascending Aorta Diameter, 18 mm\* - 20 mm/ \>34 mm, 20 mm - 23 mm/ \>40 mm, 23 mm - 27 mm/ \>43 mm, 27 mm - 29 mm/ \>43 mm, \* 17mm for surgical bioprosthetic aortic annulus * Congenital bicuspid or unicuspid valve verified by echocardiography (Not applicable for TAV in SAV subjects). * Sinus of valsalva anatomy that would prevent adequate coronary perfusion. * Degenerated surgical bioprothesis presents with a significant concomitant perivalvular leak (between prothesis and native annulus), is not securely fixed in the native annulus, or is not structurally intact (e.g. wireform frame fracture) (ONLY FOR TAV in SAV subjects) * Degenerated surgical bioprothesis presents with a partially detached leaflet that in the aortic position may obstruct a coronary ostium (ONLY FOR TAV in SAV subjects) Vascular * Transarterial access not able to accommodate an 18Fr sheath.