Abstract:
One aspect of the invention provides an artificial, flexible valve including: a stent defining a wall and a plurality of leaflets extending from the wall of the stent. The plurality of leaflets form a plurality of coaptation regions between two adjacent leaflets. The coaptation regions include extensions along a z-axis and adapted and are configured to form a releasable, but substantially complete seal when the leaflets are in a closed position. Another aspect of the invention provides an artificial, flexible valve including: a stent defining a wall and a plurality of leaflets extending from the wall of the stent. Each of the plurality of leaflets terminates in a commissure line. The commissure lines deviate from a hyperbola formed in the x-y plane by at least one deviation selected from the group consisting of: a deviation in the z-direction and one or more curves relative to the hyperbola.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to U.S. Provisional Patent Application Ser. No. 61/989,820, filed May 7, 2014. The entire content of this application is hereby incorporated by reference herein. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Valves exist in the body (e.g., in the heart and the systemic veins) to allow unidirectional blood flow. A variety of congenital conditions, infectious diseases (e.g., rheumatic heart disease), endocarditis, and age-related impairments (e.g., senile stenosis) can necessitate implantation of an artificial valve. 
       SUMMARY OF THE INVENTION 
       [0003]    One aspect of the invention provides an artificial, flexible valve including: a stent defining a wall and a plurality of leaflets extending from the wall of the stent. The plurality of leaflets form a plurality of coaptation regions between two adjacent leaflets. The coaptation regions include extensions along a z-axis and adapted and are configured to form a releasable, but substantially complete seal when the leaflets are in a closed position. 
         [0004]    This aspect of the invention can have a variety of embodiments. The extensions can have a length along the z-axis between about 1 mm and about 10 mm. The extensions can have a curved profile. The curved profile can lie in an x-y plane. The curved profile can be a variance in extension length along the z-axis. 
         [0005]    The coaptation regions can have a substantially hyperbolic profile. Each of the plurality of leaflets can have a substantially elliptical leaflet-stent attachment line. The stent can be an expandable, cylindrical stent. The leaflets can be reinforced with one or more selected from the group consisting of: reinforcing materials and directional fibers. One or more selected from the group consisting of: coaptation regions and leaflet-stent attachment lines can be reinforced with one or more selected from the group consisting of: additional polymer thickness, reinforcing materials, and directional fibers. 
         [0006]    Adjacent leaflets can be coupled to a wide post of the stent. The wide post can include one or more windows. The wide post can have a width between about 0.5 mm and about 3 mm. 
         [0007]    The stent can include metal or plastic. The metal can be selected from the group consisting of: stainless steel, 316L stainless steel, cobalt-chromium alloys, and nickel-titanium alloys. 
         [0008]    The leaflets can be formed from a first polymer. The first polymer can be selected from the group consisting of: polytetrafluoroethylene, polyethylene, polyurethane, silicone, and copolymers thereof. 
         [0009]    The stent can be dip-coated in a second polymer. The second polymer can be selected from the group consisting of: polytetrafluoroethylene, polyethylene, polyurethane, silicone, and copolymers thereof. The leaflets can be coupled to the second polymer. The leaflets can be mechanically coupled to the second polymer. The leaflets can be chemically coupled to the second polymer. The leaflets can be coupled to the second polymer by one or more techniques selected from the group consisting of: gluing, chemical fusing, thermal fusing, sonic welding, stitching, and mechanical fastening. 
         [0010]    A leaflet-stent attachment line for each of the plurality of leaflets can substantially approximate a frame of the stent. The leaflet-stent attachment line can lie within about 3 mm of the frame of the stent. 
         [0011]    The stent can include one or more anchor points. The anchor points can contain a radio-opaque material. 
         [0012]    The valve can be adapted and configured for replacement of one or more cardiac valves selected from the group consisting of: aortic, mitral, tricuspid, and pulmonary. 
         [0013]    The valve can be adapted and configured for insertion in a subject&#39;s veins in order to treat venous insufficiency. The valve can be adapted and configured for serial expansion as the subject ages. 
         [0014]    Another aspect of the invention provides an artificial, flexible valve including: a stent defining a wall and a plurality of leaflets extending from the wall of the stent. Each of the plurality of leaflets terminates in a commissure line. The commissure lines deviate from a hyperbola formed in the x-y plane by at least one deviation selected from the group consisting of: a deviation in the z-direction and one or more curves relative to the hyperbola. 
         [0015]    This aspect of the invention can have a variety of embodiments. The leaflets can further include extensions beyond the commissure lines along a z-axis. The extensions can have a length along the z-axis between about 1 mm and about 10 mm. The extensions can have a curved profile. The curved profile can lie in an x-y plane. The curved profile can be a variance in extension length along the z-axis. 
         [0016]    Each of the plurality of leaflets can have a substantially elliptical leaflet-stent attachment line. The stent can have an expandable, cylindrical stent. The leaflets can be reinforced with one or more selected from the group consisting of: reinforcing materials and directional fibers. 
         [0017]    One or more selected from the group consisting of: coaptation regions and leaflet-stent attachment lines can be reinforced with one or more selected from the group consisting of: additional polymer thickness, reinforcing materials, and directional fibers. 
         [0018]    Adjacent leaflets can be coupled to a wide post of the stent. The wide post can include one or more windows. The wide post can have a width between about 0.5 mm and about 3 mm. 
         [0019]    The stent can include metal or plastic. The metal can be selected from the group consisting of: stainless steel, 316L stainless steel, cobalt-chromium alloys, and nickel-titanium alloys. 
         [0020]    The leaflets can be formed from a first polymer. The first polymer can be selected from the group consisting of: polytetrafluoroethylene, polyethylene, polyurethane, silicone, and copolymers thereof. 
         [0021]    The stent can be dip-coated in a second polymer. The second polymer can be selected from the group consisting of: polytetrafluoroethylene, polyethylene, polyurethane, silicone, and copolymers thereof. The leaflets can be coupled to the second polymer. The leaflets can be mechanically coupled to the second polymer. The leaflets can be chemically coupled to the second polymer. The leaflets can be coupled to the second polymer by one or more techniques selected from the group consisting of: gluing, chemical fusing, thermal fusing, sonic welding, stitching, and mechanical fastening. 
         [0022]    A leaflet-stent attachment line for each of the plurality of leaflets can substantially approximate a frame of the stent. The leaflet-stent attachment line can lie within about 3 mm of the frame of the stent. 
         [0023]    The stent can include one or more anchor points. The anchor points can contain a radio-opaque material. 
         [0024]    The valve can be adapted and configured for replacement of one or more cardiac valves selected from the group consisting of: aortic, mitral, tricuspid, and pulmonary. 
         [0025]    The valve can be adapted and configured for insertion in a subject&#39;s veins in order to treat venous insufficiency. The valve can be adapted and configured for serial expansion as the subject ages. 
         [0026]    Another aspect of the invention provides an artificial, flexible valve including: an expandable, cylindrical stent defining a wall and a plurality of leaflets extending from the wall of the stent. Adjacent leaflets can be coupled to a relatively wide post of the stent. 
         [0027]    The leaflets can further include extensions beyond the commissure lines along a z-axis. The extensions can have a length along the z-axis between about 1 mm and about 10 mm. The extensions can have a curved profile. The curved profile can lie in an x-y plane. The curved profile can be a variance in extension length along the z-axis. 
         [0028]    The coaptation regions can have a substantially hyperbolic profile. Each of the plurality of leaflets can have a substantially elliptical leaflet-stent attachment line. The leaflets can be reinforced with one or more selected from the group consisting of: reinforcing materials and directional fibers. 
         [0029]    One or more selected from the group consisting of: coaptation regions and leaflet-stent attachment lines can be reinforced with one or more selected from the group consisting of: additional polymer thickness, reinforcing materials, and directional fibers. 
         [0030]    The relatively wide post can include one or more windows. The relatively wide post can have a width between about 0.5 mm and about 3 mm. 
         [0031]    The stent can include metal or plastic. The metal can be selected from the group consisting of: stainless steel, 316L stainless steel, cobalt-chromium alloys, and nickel-titanium alloys. 
         [0032]    The leaflets can be formed from a first polymer. The first polymer can be selected from the group consisting of: polytetrafluoroethylene, polyethylene, polyurethane, silicone, and copolymers thereof. 
         [0033]    The stent can be dip-coated in a second polymer. The second polymer can be selected from the group consisting of: polytetrafluoroethylene, polyethylene, polyurethane, silicone, and copolymers thereof. The leaflets can be coupled to the second polymer. The leaflets can be mechanically coupled to the second polymer. The leaflets can be chemically coupled to the second polymer. The leaflets can be coupled to the second polymer by one or more techniques selected from the group consisting of: gluing, chemical fusing, thermal fusing, sonic welding, stitching, and mechanical fastening. 
         [0034]    A leaflet-stent attachment line for each of the plurality of leaflets can substantially approximate a frame of the stent. The leaflet-stent attachment line can lie within about 3 mm of the frame of the stent. 
         [0035]    The stent can include one or more anchor points. The anchor points can contain a radio-opaque material. 
         [0036]    The valve can be adapted and configured for replacement of one or more cardiac valves selected from the group consisting of: aortic, mitral, tricuspid, and pulmonary. The valve can be adapted and configured for insertion in a subject&#39;s veins in order to treat venous insufficiency. The valve can be adapted and configured for serial expansion as the subject ages. The valve may not contain any animal-derived materials. 
         [0037]    Another aspect of the invention provides a mandrel including: a cylindrical profile and a plurality of recesses adapted and configured to define a plurality of leaflets forming a plurality of coaptation regions between two adjacent leaflets. The coaptation regions can include extensions along a z-axis and be adapted and configured to form a releasable, but substantially complete seal when the leaflets are in a closed position. 
         [0038]    This aspect of the invention can have a variety of embodiments. The mandrel can include one more cutting guides located between the plurality of recesses. The mandrel can include one or more heating elements. 
         [0039]    Another aspect of the invention provides a mandrel including: a cylindrical profile and a plurality of recesses adapted and configured to define a plurality of leaflets. Each of the plurality of leaflets terminate in a commissure line. The commissure lines deviate from a hyperbola formed in the x-y plane by at least one deviation selected from the group consisting of: a deviation in the z-direction and one or more curves relative to the hyperbola. 
         [0040]    This aspect of the invention can have a variety of embodiments. The mandrel can include one more cutting guides located between the plurality of recesses. The mandrel can include one or more heating elements. 
         [0041]    Another aspect of the invention provides a method for fabricating an artificial, flexible valve. The method includes: dip coating a cylindrical mandrel having a plurality of recesses each approximating a profile of a leaflet and coupling the leaflets to an inner wall of a stent. 
         [0042]    This aspect of the invention can have a variety of embodiments. The method can further include dip coating the stent prior to coupling the leaflets to the inner wall of the stent. The stent and the mandrel can have larger diameters than a target location for the valve. The method can further include separating adjacent leaflets from each other. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0043]    For a fuller understanding of the nature and desired objects of the present invention, reference is made to the following detailed description taken in conjunction with the accompanying drawing figures wherein like reference characters denote corresponding parts throughout the several views and wherein: 
           [0044]      FIGS. 1A and 1B  provide perspective (in which fluid flows from the bottom of the stent toward the top of the stent) and top (in which fluid flows out of the page when the valve is open and flows down into the page to close the valve) views of a valve according to an embodiment of the invention; 
           [0045]      FIG. 2  depicts a stent according to an embodiment of the invention; 
           [0046]      FIGS. 3A-3F  depict various stent geometries according to embodiments of the invention; 
           [0047]      FIG. 4  depicts various vertical post geometries according to embodiments of the invention; 
           [0048]      FIGS. 5A-5D  depict the positioning of a leaflet joint adjacent to a window of a vertical post according to an embodiment of the invention; 
           [0049]      FIG. 6  depicts a stent prior to expansion, dip coating, and leaflet installation according to an embodiment of the invention; 
           [0050]      FIG. 7  depicts a stent including one or more anchor points according to an embodiment of the invention; 
           [0051]      FIG. 8  depicts the engagement of a stent with a holder for dipping and rotation according to an embodiment of the invention; 
           [0052]      FIGS. 9A-9E  depict a mandrel according to an embodiment of the invention; 
           [0053]      FIG. 9F  depicts the positioning of a hyperbolic commissure line relative to defined asymptotes according to embodiments of the invention; 
           [0054]      FIG. 10A  depicts a comparison of elliptical vs. parabolic geometries leaflet valley lines according to embodiments of the invention; 
           [0055]      FIGS. 10B and 10C  depict a comparison of elliptical vs. parabolic leaflet stent attachment lines according to embodiments of the invention; 
           [0056]      FIGS. 11A-11D  depict mandrels for forming coaptation regions of varying height according to embodiments of the invention; 
           [0057]      FIGS. 12A-12D  depict mandrels for forming coaptation regions of varying radial length according to embodiments of the invention; 
           [0058]      FIGS. 12E-12H  depict mandrels for forming commissure lines having variable depths along the z-axis according to embodiments of the invention; 
           [0059]      FIGS. 12I-12K  depict mandrels for forming coaptation regions having curved profiles in an x-y plane, resulting in increased coaptation length, according to embodiments of the invention; 
           [0060]      FIGS. 12L-12N  depict mandrels for forming commissure lines having curved profiles in an x-y plane, resulting in increased coaptation length, according to embodiments of the invention; 
           [0061]      FIG. 13A  depicts a mandrel according to an embodiment of the invention; 
           [0062]      FIGS. 13B and 13C  depict the positioning of reinforcing zones on a mandrel according to an embodiment of the invention; 
           [0063]      FIGS. 14A-14C  depict various top profiles according to an embodiment of the invention; 
           [0064]      FIGS. 15A and 15B  depict the fabrication of valves according to embodiments of the invention; 
           [0065]      FIG. 16  depict the fabrication of valves according to an embodiment of the invention; 
           [0066]      FIGS. 17A and 17B  depict the compression of a valve after assembly in order to bring leaflets into contact with each other according to embodiments of the invention; 
           [0067]      FIG. 17C  is a high-speed photograph of a closed valve under pressure according to embodiments of the invention; 
           [0068]      FIG. 18  depicts a method of implanting a valve according to embodiments of the invention; and 
           [0069]      FIG. 19  depicts a method of expanding an implanted valve according to embodiments of the invention. 
       
    
    
     DEFINITIONS 
       [0070]    The instant invention is most clearly understood with reference to the following definitions. 
         [0071]    As used herein, the singular form “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. 
         [0072]    Unless specifically stated or obvious from context, as used herein, the term “about” is understood as within a range of normal tolerance in the art, for example within 2 standard deviations of the mean. “About” can be understood as within 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, 0.5%, 0.1%, 0.05%, or 0.01% of the stated value. Unless otherwise clear from context, all numerical values provided herein are modified by the term about. 
         [0073]    As used in the specification and claims, the terms “comprises,” “comprising,” “containing,” “having,” and the like can have the meaning ascribed to them in U.S. patent law and can mean “includes,” “including,” and the like. 
         [0074]    Unless specifically stated or obvious from context, the term “or,” as used herein, is understood to be inclusive. 
         [0075]    Ranges provided herein are understood to be shorthand for all of the values within the range. For example, a range of 1 to 50 is understood to include any number, combination of numbers, or sub-range from the group consisting 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, or 50 (as well as fractions thereof unless the context clearly dictates otherwise). 
       DETAILED DESCRIPTION OF THE INVENTION 
       [0076]    Aspects of the invention provide a novel platform that allows development of polymeric valves of any size and shape. Aspects of the invention can be applied to valves designed for surgical implantation (e.g., through a sternotomy or thoracotomy) or valves designed for percutaneous, transcatheter implantation. Additionally, embodiments of the invention allow for possible percutaneous replacement of a dysfunctional valve, whether in adults or in small children. In addition, if implanted in a child, embodiments of the invention allow the valve to be serially expanded to accompany the child&#39;s growth. 
       Cardiac Applications 
       [0077]    Multiple types of congenital heart defects require heart valve replacement surgery in infancy or childhood. In adults, the most commonly replaced valves are aortic and mitral, whereas in children, the pulmonary valve is the most commonly replaced valve. Heart valves are currently replaced using tissue valves (homograft or xenograft) or mechanical metal valves, each having their shortcomings. Homograft valves are in short supply, particularly in sizes suitable for use in children, and biologic tissue-based valves (whether bovine, porcine, or homograft) tend to induce an immunologic reaction which leads to failure of these valves. Mechanical valves generally require anticoagulation, and are almost never used in the pulmonary position due to an increased risk of thrombosis. 
         [0078]    Furthermore, none of the surgically implanted valves can adapt to growing patients. The rapid growth of pediatric patients leads them to outgrow their implanted valves within a few years and induces a cycle of frequent surgical valve replacements during childhood. Aspects of the invention provide valves having improved biocompatibility, durability, and hemodynamic performance and would reduce the frequency of recurrent open heart surgeries for valve replacement. 
       Venous Applications 
       [0079]    Additionally, aspects of the invention can be used for venous valve replacement in patients having venous disease such as chronic venous insufficiency (leading to leg swelling). Because the polymer leaflets can be made extremely thin, the valves can even open under extremely low venous pressure gradients. 
       Artificial, Flexible Valves 
       [0080]    Referring now to  FIGS. 1A and 1B , one aspect of the invention provides an artificial, flexible valve  100 . The valve includes an expandable, cylindrical stent  102  defining a wall  104 . Valve  100  further includes a plurality of leaflets  106   a - 106   c . Wall  104  can be formed by dip coating stent  102  in a polymer as further described herein. Leaflets  106  can be coupled to wall  104  along seams  108  using a variety of approaches (e.g., glue) as discussed further herein. Stent  102  can include one or more vertical posts  110 ,  112 , which can be relatively narrow posts  110  or relatively wide posts  112 . Preferably leaflet joints between adjacent leaflets  106  are positioned on or close to a vertical post  110 ,  112  of the stent  102 . 
         [0081]    The valve  100  will now be described in the context of its components and methods of fabrication. 
       Stents 
       [0082]    Referring now to  FIG. 2 , stent  102  can be a metallic stent having plurality of wires, strips, and the like  202  defining a plurality of cells  204 ,  206  of various sizes. Stent  102  can be fabricated from a variety of malleable materials such as stainless steel, 316L stainless steel, cobalt-chromium alloys, nickel-titanium alloys (colloquially known as “nitinol”), and the like. Stent  102  can also be formed from various non-metallic materials such as plastics such as polyethylene, polyurethane, polytetrafluoroethylene (PTFE), silicone, poly(propylene) (PP), polyethylene terephthalate (PET), and the like. 
         [0083]    Stent  102  can be completely enveloped by a polymer dip coating. Stent  102  and/or wall  104  can also be fabricated from a biocompatible material. 
         [0084]    The stent  102  can be manufactured by laser cutting or wire forming. To increase bonding strength between metal and polymer, roughness of stent surface can be controlled. Some or all open cells  204 ,  206  of the stent can be covered as the bare  102  stent is dipped into the polymer solution. 
         [0085]      FIG. 6  depicts a stent  102  prior to expansion, dip coating, and leaflet installation. Stents  102  typically have a diameter of between about 2 mm and 6 mm prior to expansion and can be expanded to between about 5 mm and about 30 mm for implantation into a subject. 
         [0086]    The components of stent  102  can have a variety of dimensions that can be selected to achieve a desired flexibility, rigidity, resilience, and the like. For example, the thickness and width of components of the stent  102  can be between about 0.1 mm and about 2 mm. 
         [0087]    As discussed above, stent  102  can include one or more vertical posts  110   a - 110   c  to enhance bonding with leaflets  106 . 
         [0088]    Stent  102  can include a plurality of vertical posts  110  that can serve a variety of functions. Some vertical posts  110  can include additional structure and are referred to herein as wide posts  112 . Wide posts  112  are preferably located at leaflet joints where two leaflets  106  meet. For example, in a valve  100  having a three leaflets  106 , wide posts  112  can be positioned at 120° intervals within cylindrical stent  102 . 
         [0089]    Wide posts  112  provide mechanical support to leaflets and prevent or substantially limit inward deformation of wall  104  due to tensile forces applied to leaflets  106  transferred to wall  104 . Without being bound by theory, it is believed that the wide posts  112  provide increased strength and resiliency due to formation of polymer wall  104  through windows  206  and around wide posts  112 , thus providing cohesive holding of the polymer to itself around the stent  102  instead of relying solely on adhesive bonding of the polymer wall  104  to the stent  102 . 
         [0090]    Wide posts  112  advantageously allow for relaxed tolerances in positioning leaflets  106  relative to wide posts  112 . For example, window  208  can have a width of between about 0.5 mm and about 3 mm (e.g., about 1 mm) and a height of between about 1 mm and about 10 mm (e.g., about 5 mm). 
         [0091]    A variety of additional wide post geometries are depicts in  FIGS. 3A-3F . In  FIG. 3A , the wide posts have a solid architecture without any windows. In  FIG. 3B , the wide posts have a substantially rectangular architecture defining a single, long window as in  FIGS. 1A, 1B, and 2 . In  FIG. 3C , the wide posts define a plurality of coaxial substantially rectangular windows. In  FIG. 3D , the wide posts define a plurality of coaxial, substantially parallel windows. In  FIG. 3E , the wide posts define a plurality of coaxial, substantially rectangular windows in a 2×3 arrangement. In  FIG. 3F , the wide posts include a plurality of circular windows. These wide post architectures are further depicted in  FIG. 4 . Although substantially circular and rectangular window geometries are depicted, any geometry can be utilized including windows having a profile approximating a triangle, a square, an n-gon (e.g., a hexagon, an octagon, and the like), and the like. 
         [0092]    Referring now to  FIGS. 5A-5D , the positioning of a leaflet joint  502  (formed, e.g., on mandrel  900  as discussed herein) adjacent to window  206  of wide post  112  is depicted. (The polymer dip-coated wall  104  is completely transparent for ease and clarity in viewing, but can be transparent, translucent, or opaque.)  FIG. 5B-5D  further depict how a geometry of the stent  102  can be selected to substantially approximate the leaflet-stent attachment seam  108  discussed herein in order to provide added mechanical support and resiliency. 
         [0093]    Referring now to  FIG. 7 , stent  102  can include one or more anchor points  702 . Anchor points  702  advantageously facilitate holding, dipping, and rotation of the stent  102  during the dip coating process without interfering with the dip coating of the remainder of the stent architecture. Accordingly, the entire stent  102  can be dip coated in a single dipping, although multiple dippings can be utilized to control coating density, thickness, and the like. Anchor points  702  can also receive one or more radio-opaque materials such as platinum to aid in placement and visualization of the valve. 
         [0094]    In one embodiments depicted in  FIG. 8 , stent  102  can be engaged with a holder  802  (e.g., by posts  804 ) for dipping and rotation. Once the polymer (again depicted as, but not necessarily, transparent) is wet on the stent  102 , the stent can be positioned horizontally and rotated axially. 
       Leaflets 
       [0095]    Leaflets  106  can be formed using a variety of techniques including dip coating, 3D-printing (also known as additive manufacturing), molding, and the like. 
         [0096]    Referring now to  FIG. 9A , leaflets  106  can be fabricated by dip coating a mandrel  900  with a polymer. The mandrel  900  can be made with a solid such as a metal (e.g., stainless steel, titanium, aluminum, and the like), a plastic (e.g., polyethylene, polypropylene, polyvinyl chloride, polytetrafluoroethylene, polyoxymethylene, and the like), and the like. Since the coated polymer leaflets  106  will be removed from the mandrel  900  after the polymer dries, roughness of mandrel surface can be controlled using known machining and other manufacturing techniques. The mandrel  900  can be made from a cylinder. Preferably, the diameter of the mandrel  900  is a slightly (e.g., between about 0.05 and about 0.4 mm) smaller than inner diameter of stent  102  after expansion. 
         [0097]    The mandrel  900  for the leaflets  106  can have novel features, including edges representing the leaflet attachment points that are mathematically defined and leaflet tips that are extended in order to increase the coaptation length of the leaflets. The mandrel  900  can be dimensioned to produce leaflets  106  having different regional thickness and supplementary materials such as directional fibers or reinforcing particles inserted between layers or mixed into the polymer solution in order to increase durability. For example, polymer interaction with particles on the nanoscale or microscale can greatly improve the physical properties or tear resistance of the polymer leaflets  106 . 
         [0098]    Mandrel  900  can be designed to have a complementary geometry to the desired leaflet shape and permits easier viewing of leaflet geometry. Although mandrel  900  is utilized to describe the geometry of the leaflet  106 , it should be recognized that the upstream surface of the resulting leaflets will have this geometry when formed by dip coating and that the complementary geometry of the leaflet(s)  106  can be produced using techniques other than dip coating. Mandrel  900  is preferably cylindrical and can have an outer profile substantially approximating an inner profile of stent  102 . Mandrel  900  can define a plurality of pockets  902  that each define a leaflet  106  as it hangs from wall  104  via attachment line  108 . Each leaflet  106  terminates in a commissure line  904  often, but not necessarily lying in a plane at the point where the elliptical or parabolic curve ends and where the leaflet often contacts the other leaflets. A substantially vertical coaptation region  906  can extend beyond the commissure line  904  to an extended commissure line  912  for improved sealing as will be discussed herein. 
         [0099]    Referring now to  FIGS. 9B and 9C , mandrel can be cast, machined, printed, or otherwise fabricated so that pockets  902  have a desired geometry. In one embodiment of the invention, the commissure line  904  (and optionally the coaptation region  906  and extended commissure line  912 ) has a substantially hyperbolic profile when viewed in the x-y plane. Additionally or alternatively, leaflet-stent attachment line  108  and/or a leaflet valley line  908  (formed by taking a cross-section in a z plane) can have substantially elliptical profiles. Although other quadratic profiles (e.g., parabolic) could be used, elliptical profiles better promote a secure pocket shape and the closure of the leaflet-stent attachment line  108  to the contour of the cylindrical mandrel  900 . A comparison of elliptical vs. parabolic leaflet valley lines is provided in  FIG. 10A . A comparison of elliptical vs. parabolic leaflet-stent attachment lines is provided in  FIGS. 10B and 10C . 
         [0100]    Referring now to  FIG. 9D , mandrel  900  can define a gap  910  between adjacent leaflets. Advantageously, leaflets  106  with a hyperbolic profile can produce smaller gaps than leaflets with parabolic profiles. For example, gaps  910  can be less than 1 mm or between about 0.1 mm and about 1 mm (e.g., between about 0.1 mm and about 0.2 mm, between about 0.2 mm and about 0.3 mm, between about 0.3 mm and about 0.4 mm, between about 0.4 mm and about 0.5 mm, between about 0.5 mm and about 0.6 mm, between about 0.6 mm and about 0.7 mm, between about 0.7 mm and about 0.8 mm, about 0.8 mm and about 0.9 mm, about 0.9 mm and about 1 mm, and the like). 
         [0101]    As seen in  FIG. 9E , the length of hyperbolic commissure line  904  is about twice the radius of the stent or mandrel. The positioning of a hyperbolic commissure line  904  relative to defined asymptotes is depicted in  FIG. 9F . 
         [0102]    Referring now to  FIG. 11A , coaptation region can have minimal height in the z-axis so as to consist only of the commissure line  904 . Alternatively, coaptation region  906  can have a vertical extension in the z-axis to an extended commissure line  912  as depicted in  FIGS. 11B-11D . The height of the coaptation region  906  can be selected to reduce the amount of regurgitation, while still allowing the valve to open. For example the coaptation region  906  can have a height between about 1 mm and about 10 mm (e.g., about 3 mm). Although  FIGS. 11B-11D  depict extensions of coaptation region  904  that extend solely in the z-axis, the same effect can be achieved using a smooth leaflet-stent attachment line that extends in the z-axis so that the adjacent leaflet-stent attachment lines (and/or the regions of leaflets hanging therebetween) approach and/or contact each other to form an extended coaptation region. 
         [0103]    The zone of coaptation is affected by the pressure placed upon the closed valve  100 . The higher the pressure, the more downward tension is placed on the leaflets  106 , possibly leading to a failure of coaptation with consequent regurgitation. Proper coaptation also allows the leaflets  106  to support each other, so there is less stress placed on any individual leaflet  106 . Another benefit of enhancing height of the coaptation zone is that this allows the valve  100  to be re-dilated to a larger diameter late after implantation (such as to accommodate growth of a pediatric patient), while still maintaining competence of the valve  100 . 
         [0104]    Options for enhancing the height of the coaptation zone include creating excess length of the leaflet free edges, so that the free edge length is greater than twice the radius of the stent or mandrel depicted in  FIG. 9E . Lengthening of the leaflet free edges can be accomplished by curved edges in the x-y plane, or in the z-axis, or in all 3 axes. 
         [0105]    Referring now to  FIGS. 12A-12D , coaptation regions  906  can have varying heights in the z-axis between the commissure line  904  and extended commissure line  912 . For example, the height of coaptation region  906  can increase toward the outside of the mandrel as depicted in  FIG. 12B . In another embodiment, the height of the coaptation region  906  can dip to form a trough between the outside and the center of the mandrel  900  as depicted in  FIG. 12C . 
         [0106]    Referring now to  FIGS. 12E-12H , the same profiles can be applied to commissure line  904  without any coaptation region  906 . 
         [0107]    Referring now to  FIGS. 12I-12K , the commissure lines  904 , coaptation regions  906  and/or extended commissure lines  912  can have curved profiles in an x-y plane (as opposed to a substantially hyperbolic profile) in order to increase the length of the commissure line  904 , coaptation region  906 , and/or extended commissure line  912 . For example, the mandrel  900  can be thicker between the perimeter and the center as depicted in  FIG. 12I  to produce one or more scallops. In  FIGS. 12J and 12K , the mandrel  900  can have either a single curve or multiple curves. 
         [0108]    Referring now to  FIGS. 12L-12N , the same profiles can be applied to commissure line  904  without any coaptation region  906 . 
         [0109]    In order to increase tear-resistance of the leaflets  106  and enhance bonding strength between leaflets  106  and stent  102 , the thickness of the leaflets  106  can be controlled regionally. Because the most common failure points are at the outer edges of the leaflets  106  (such as commissure line  904  or extended commissure line  912  and leaflet-stent attachment line  108 ), increased thickness at outer areas of the leaflets  106  can improve the strength and durability. Also, if local areas are expected to have concentrated stress, the areas can be locally reinforced (e.g., made thicker than other areas). The thickness can be smoothly increased. The width of thickened area along leaflet-stent attachment line  108  can be large enough to cover the glued area for bonding the leaflets  106  and the covered stent  102 . In some embodiments, the thickness of thickened areas of the leaflets is between about 0.1 mm and about 1 mm. 
         [0110]    Multiple dippings can be performed to produce leaflets with a desired thickness. In some embodiments, the thickness of the leaflets is between about 0.01 mm and about 0.2 mm. 
         [0111]    Different reinforcing materials such as strips, fibers and particles can be placed between the layers, or directly mixed into the polymer solution. The inserted material(s) can prevent tearing and reduce propagation of the tear if it occurs. The materials can have directional properties and can be layered onto, or embedded into, the leaflets in an optimal direction to prevent or limit tears. 
         [0112]    Referring now to  FIG. 13A , a photograph of a mandrel  900  is provided. Referring now to  FIG. 13B , a reinforcing zone  1302  can be formed on the mandrel  900  prior either by removing mandrel material to allow for additional thickness in certain (e.g., outer) regions of leaflets  106  or by introducing one or more reinforcing fibers prior to, during, or after dip coating. Suitable reinforcing materials include fibers (e.g., polymers, nanotubules, aramids, para-aramids, and the like), wires, and the like. Transitions between reinforced and non-reinforced areas can be smooth in order to minimize any turbulence in the implanted valve  100 . 
         [0113]    After dipping the mandrel  900  into the polymer solution, the coated polymer dries in order to form the leaflet(s)  106 . Because the formed leaflets  106  are connected, they need to be separated from each other. These can be cut by a sharp cutter (e.g., a knife, a scalpel, a razor blade, a utility knife, and the like), a heated iron, a laser, a rotary tool, and the like. A guide on the top surface of the mandrel for cutting provides a clear, easy, and safe cutting path. The guide can be grooved/concave or convex. Also, the commissure edges of the mandrel can be sharp like a blade to facilitate leaflet separation and to improve on the quality of the cut edges. 
         [0114]    Referring now to  FIG. 14A-14C , the gap portion  910  of the mandrel can have various top profiles to facilitate sealing of the leaflets and/or separation of the leaflets prior to removal from mandrel  900 . For example, the gap portion  910  can have a grooved profile as depicted in  FIG. 14A , a concave profile as depicted in  FIG. 14B , or an angled profile as depicted in  FIG. 14C . Additionally or alternatively, a heating element (e.g., an Ohmic or resistive heating element such as a wire) can be included in the mandrel and can be actuated to melt the polymer to separate the leaflets and/or relax the polymer to facilitate removal of the leaflets from the mandrel  900 . 
         [0115]    The stent-mounted valve  100  can be implanted with smaller diameter than its manufactured diameter for reducing leakage and improving durability. 
       Methods of Fabricating Valves 
       [0116]    Referring now to  FIGS. 15A, 15B, and 16 , a method for fabricating a valve is depicted. A bare stent  102  and a bare mandrel  900  are provided. 
         [0117]    In some embodiments, the stent  102  can be first coated with a polymer such as PEEK or other metal surface modifier prior to further dip coating of the stent  102  in another polymer in order to improve adhesion of the leaflet polymer  106  to the metal stent  102 . 
         [0118]    The bare mandrel  900  can optionally be coated with a release agent to promote separation of the polymer leaflets from the mandrel  900 . 
         [0119]    Both the bare stent  102  and the mandrel  900  are dip coated separately in a polymer, which may be the same or different for the bare stent  102  and the mandrel  900 . 
         [0120]    The leaflets  106  formed on the mandrel  900  can be removed prior to introduction to the coated stent. Alternatively, the coated mandrel  900  can be introduced into the coated stent, the leaflets  106  can be bonded to the coated stent, and the mandrel  900  can be then be removed to leave the assembled valve  100 . 
         [0121]    Leaflets  106  can be bonded to the dip-coated stent using a variety of techniques including gluing, chemical fusing (i.e., dissolving the polymers) thermal fusing, sonic welding, stitching, mechanical fastening, and the like. For example, the same polymer solution used to coat either bare stent  102  and/or mandrel  900  can be applied to bond the leaflets  106  to the dip-coated stent. 
         [0122]    Although separate fabrication of the polymer-coated stent and the leaflets  106  are currently preferred as a means of avoiding or minimizing air bubbles, the entire valve could be formed in a single dip coating (or series of dip coatings) through use of production-grade manufacturing techniques and other optimizations. 
         [0123]    Although dipcoating was successfully used to fabricate prototypes of the valves described herein, any other manufacturing technique capable of producing flexible leaflets can be utilized. Exemplary techniques include injection molding and additive manufacturing or 3D printing. 
         [0124]    Referring now to  FIGS. 17A and 17B , stent  102  and leaflets  106  can be fabricated based on a diameter that is slightly larger than the placement location as depicted in  FIG. 17A . When deployed to a location having a smaller diameter than the manufactured diameter, the leaflets  106  will be held in tight contact with each other as seen in  FIG. 17B  to form a tight seal. (In order to form a press fit with the vessel wall, the deployed diameter will be greater than the vessel diameter, but less than the manufactured diameter.) 
         [0125]    As can be seen in  FIGS. 17A and 17B , the coaptation regions of leaflets  106  have a substantially hyperbolic profile both at the manufactured diameter and the deployed diameter. 
         [0126]    Referring now to  FIG. 17C , a high-speed photograph of a closed valve under pressure during in vitro testing in a hemodynamic pulse duplicator is provided. 
       Polymers 
       [0127]    The leaflets  106  can be formed from the same or different polymer with which the stent  102  is coated to form wall  104 . For example, the leaflets  106  can be formed from polymers such as polyethylene, polyurethane, silicone, and the like. Wall  104  can be formed from polyethylene, polyurethane, silicone, and the like. 
         [0128]    Supplementary materials such as directional fibers can mixed into the polymer solution or applied to the leaflets between coatings in order to increase durability 
         [0129]    The selected polymer can be dissolved by a solvent such as tetrahydrofuran or dimethylacetamide. The thickness of the coated polymer can be controlled as a function of the density of the polymer solution and total number of dippings. When the polymer becomes dry after dipping, the coated stent and mandrel can be placed horizontally and axially rotated in order to produce a constant thickness and prevent the polymer from dripping. 
       Implantation of Valves 
       [0130]    Referring now to  FIG. 18 , a method  1800  of implanting an artificial valve is provided. The valve to be implanted can be a valve  100  as described herein. 
         [0131]    In step S 1802 , the valve is placed over an expander and within a sheath. Various surgical expanders and access devices exist in the cardiac surgery field. For example, a balloon catheter could be introduced into a patient&#39;s femoral artery and guided to the location of the implanted valve (e.g., within the patient&#39;s heart or systemic veins). 
         [0132]    In step S 1804 , the sheath (containing the valve and the expander) is introduced into a vessel of the subject. 
         [0133]    In step S 1806 , the valve and the expander are advanced from the sheath and positioned in the desired location. 
         [0134]    In step S 1808 , the desired positioning can be verified using various imaging techniques such as fiber optics, ultrasound, X-ray, and the like. 
         [0135]    In step S 1810 , the expander is actuated within the valve to expand the valve to form a press fit against the vessel in which the valve is implanted. For example, a balloon catheter can be expanded by introducing gas or a liquid into the balloon. 
         [0136]    In step S 1812 , the desired positioning and expansion can be verified using various imaging techniques such as fiber optics, ultrasound, X-ray, and the like. 
         [0137]    In step S 1814 , the expander and sheath can be retracted according to standard surgical techniques. 
       Expansion of Implanted Valves 
       [0138]    Referring now to  FIG. 19 , a method  1900  of expanding an implanted valve is provided. The implanted valve can be a valve  100  as described herein. 
         [0139]    In step S 1902 , an expander is introduced into the implanted valve. 
         [0140]    In step S 1904 , the expander is actuated within the implanted valve to increase the diameter of the implanted valve. 
         [0141]    In step S 1906 , the desired expansion can be verified using various imaging techniques. 
         [0142]    In step S 1908 , the expander can be retracted according to standard surgical techniques. 
       Surgically-Implanted Valves 
       [0143]    Although embodiments of the invention are described and depicted in the context of percutaneous, transcatheter valves having expandable, cylindrical stents, embodiments of the invention described herein can be applied to surgically-implanted valves that generally include anchors having fixed-diameter anchors supporting a plurality of leaflets (e.g., the CARPENTIER-EDWARDS™ series of valves available from Edwards Lifesciences Corporation of Irvine, Calif.). In such embodiments, the anchor replaces the expandable, cylindrical stents described herein. 
       EQUIVALENTS 
       [0144]    Although preferred embodiments of the invention have been described using specific terms, such description is for illustrative purposes only, and it is to be understood that changes and variations may be made without departing from the spirit or scope of the following claims. 
       INCORPORATION BY REFERENCE 
       [0145]    The entire contents of all patents, published patent applications, and other references cited herein are hereby expressly incorporated herein in their entireties by reference.