In fact, S3 is filled out by a family of nested tori in this manner (with two degenerate circles), a fact which is important in the study of S3 as a fiber bundle over S2 (the Hopf bundle). The surface described above, given the relative topology from R3, is homeomorphic to a topological torus as long as it does not intersect its own axis. A particular homeomorphism is given by stereographically projecting the topological torus into R3 from the north pole of S3.
A phase 3 trial of statin intolerant patients called ODYSSEY ran for 65 weeks. Results were presented at the 2014 European Society of Cardiology meeting. A 78-week study of alirocumab in 2341 people taking statins who were at high risk for cardiovascular events and had high LDL cholesterol levels was published in April 2015. This study showed a significant reduction of LDL cholesterol levels in patients taking both Alirocumab and oral statins compared to placebo patients solely taking oral statins. Studies are ongoing to assess the effects of alirocumab in normocholesterolemic individuals.In July 2014, Regeneron and Sanofi announced that they had purchased a priority review voucher that BioMarin had won for a recent rare disease drug approval for $67.5 million; the voucher cut four months off the regulatory review time for alirocumab and was part of their strategy to beat Amgen to market with the first approval of a PCSK9 inhibitor.In July 2015, the FDA approved alirocumab as a second-line treatment to lower LDL cholesterol for adults who have hereditary high cholesterol and people with atherosclerosis who require additional lowering of LDL cholesterol when diet and statin treatment have not worked. This was the first approval of a PCSK9 inhibitor. The FDA approval was contingent on the completion of further clinical trials to better determine efficacy and safety.Regeneron and Amgen had each filed for patent protection on their monoclonal antibodies and the companies ended up in patent litigation in the U.S.