Patent Publication Number: US-2023157807-A1

Title: Stents with increased flexibility

Description:
PRIORITY CLAIM 
     This application is a continuation of U.S. patent application Ser. No. 17/575,595, filed Jan. 13, 2022, titled “STENTS WITH INCREASED FLEXIBILITY,” now U.S. Patent Application Publication No. 2022/0133464, which is a continuation of International Patent Application No. PCT/US2020/042409, filed Jul. 16, 2020, titled “STENTS WITH INCREASED FLEXIBILITY,” which claims priority to U.S. Provisional Patent Application No. 62/874,890, titled “STENTS WITH INCREASED FLEXIBILITY” filed on Jul. 16, 2019. 
    
    
     INCORPORATION BY REFERENCE 
     All publications and patent applications mentioned in this specification are herein incorporated by reference in their entirety to the same extent as if each individual publication or patent application was specifically and individually indicated to be incorporated by reference. 
     FIELD 
     Described herein are expandable intraluminal grafts (“stents”) for use within a body passageway or duct which are particularly useful for repairing blood vessels narrowed or occluded by disease. The stents described herein are configured to change size over a large range, while minimizing the strain on the stent. 
     BACKGROUND 
     Intravascular stents may be used in coronary arteries and other body lumens of human patients. Stents are generally tubular-shaped devices which function to hold open a segment of a blood vessel or other body lumen such as a coronary artery. They also are suitable for use to support and hold back a dissected arterial lining that can occlude the fluid passageway. At present, there are numerous commercial stents being marketed throughout the world. For example, prior art stents typically have multiple cylindrical rings connected by one or more connecting links. While some of these stents are flexible and have the appropriate radial rigidity needed to hold open a vessel or artery, there typically is a tradeoff between flexibility and radial strength and the ability to tightly compress or crimp the stent onto a catheter so that it does not move relative to the catheter or dislodge prematurely prior to controlled implantation in a vessel. 
     Intravascular stents are known and there are numerous structural designs in commercial use. One well known structural pattern includes a tubular stent having rings connected by links. Typically, there are two or more links connecting adjacent rings. While stents having two links between adjacent rings (two-link stents) offer the benefit of low crimp profile and high flexibility, these benefits come with a trade-off in terms of longitudinal stability. Further, peak-to-peak stent patterns (in which the peaks on adjacent rings point toward each other and are essentially axially aligned) offer dense packing of stent rings, which in turn allows for a stent pattern with high radial strength and high radial stiffness. One stent pattern that incorporates these design features is the 2 link offset peak-to-peak style stent. While this stent pattern performs well in terms of traditional stent metrics, it experiences one key tradeoff, namely it will excessively shorten under modest longitudinal compressive loads. 
     Two-link stents, specifically offset peak-to-peak, where the peaks of adjacent rings point toward each other but are slightly offset circumferentially, excessively shorten under modest (clinically relevant) longitudinal compressive loads. This creates unwanted implications for safety and efficacy of the stent implant. Offset and angled link designs lend readily to collapse behavior, as links do not provide resistance in direction of load, and in addition offset link designs create a bending moment effect, which encourages the bar arms adjacent to link structures to bend and swing excessively (stress is focused in these bar arms). 
     The methods and apparatuses described herein may be used with and may incorporate features from International Application No. PCT/US2019/013843, filed on Jan. 16, 2019, entitled “STENTS WITH INCREASED FLEXIBILITY,” claiming priority to U.S. Provisional Application No. 62/618,007, filed on Jan. 16, 2018, entitled “STENTS WITH INCREASED FLEXIBILITY,” each of which is herein incorporated by reference in its entirety. 
     SUMMARY OF THE DISCLOSURE 
     The present disclosure relates to stents, such as balloon-expandable vascular prosthesis. In addition to vascular applications, these devices may be used for tracheal, bronchial patency and/or in iliac or renal arteries. 
     The stents described herein have greater flexibility than prior art stents and expand with less foreshortening, based in part upon a combination of factors, including the configuration of one or more portions of the stent, material properties, and dimensions of one or more portions of the stents. 
     The stents can include a plurality of annular supports (rings) that are adjacent and extend transversely (e.g., at 90 degrees, but including +/−15 degrees) to the longitudinal distal-to-proximal axis of the device. The rings may be coupled together by one or more crosslink connectors (and in particular, S-shaped crosslink or omega-shaped crosslink, which may also be referred to herein as ring connectors). 
     At least some of the supports (e.g., rings) may have a configuration that has a repeating pattern (e.g., a biphasic pattern) of a pair of flat-ended, open trapezoidal shapes (which may be rounded at the corners) that are circumferential offset but face each other and may be connected at their ends by connecting members that may be straight or curved (e.g., sigmoid shaped). The trapezoidal shapes may be square, rectangular, isosceles (e.g., a wide-mouthed isosceles in which the open end of the trapezoid would be the longer parallel side, or narrow-mouthed isosceles, in which the open end of the trapezoid would be the shorter parallel side). 
     Typically, as the stent device is expanded, the flat end of the open trapezoidal shapes stay approximately the same (e.g., same length, and may remain substantially parallel with each other), while the connecting members may bend relative to the flat ends. In some variations, the legs of the open trapezoidal shapes (the legs forming the open ends) may bend relative to the connecting members and/or the flat end(s). 
     In some variations, the crosslink connectors may be configured as S-shaped connectors, (e.g., the ring connector has an S-shape). An S-shaped ring connector may offer decreased strain when connecting adjacent rings. In some other variations, the crosslink connectors may be configured as omega-shaped crosslink connectors, which may include an arc region (e.g., semi-circular or 180 degree arc, 170 degree arc, 190 degree arc, 200 degree arc, 210 degree arc, etc.) from which a pair of straight legs may extend from either side of the ends of the arc region, e.g., in a single line. For example, each omega-shaped ring connector may include includes an arc region and a pair of linear sections extending from the arc regions on either side of the arc region. One or both ends of the ring connector may be L-shaped. For example, the omega-shaped ring connector may include a first an L-shaped end connecting to the second side of one of the first open trapezoidal portions of the plurality of biphasic cells and a second L-shaped end connecting to the fifth side of one of the second open trapezoidal portions of the plurality of biphasic cells. IN some variations a combination of both s-shaped and omega-shaped connectors may be used in different regions and/or intermixed. 
     In general, the apparatuses described herein may be configured as balloon-expandable stent grafts that may be used in percutaneous transluminal angioplasty (PTA) procedures, including in particular in peripheral arteries such as tibial, femoral and iliac. Balloon-expandable stents are Endovascular prostheses and may be metallic tubular meshes that expand radially by means of inflation of a balloon. The stent grafts describe here may have a frame (e.g., a cobalt chrome tubular frame/mesh, Nitinol tubular frame/mesh, stainless steel tubular frame/mesh, etc.), embedded into sleeve formed from a polymer matrix. The sleeve may be porous. 
     For example, this apparatuses and methods described herein relate to stent grafts (“stents”) having radiused struts that may be embedded and/or enveloped in a polymer matrix. The stent graft may comprise rings that form radiused struts in sinusoidally (“s-shaped”) shaped segments. The rings may be connected by omega-shaped crosslinks, e.g., crosslinks or crosslinks that may have an S-shape or an omega (Ω) shape. The stent struts may be embedded and/or enveloped into a polymer matrix of a composite, such as a composite of PTFE that may enhance its mechanical properties. The improved properties may permit the stent to go through tortuous paths of injured peripheral arteries with the required flexibility and with the proper radial stability to open the vascular vessel and recover the blood flow. 
     For example, described herein are stent devices having a length extending in a distal to proximal direction, the device comprising: a plurality of adjacent rings arranged transverse to a length of the device, wherein each ring is a ring comprising length of material arranged radially around the length of the stent device as a plurality of repeating biphasic cells, each biphasic cell comprising a first open trapezoidal portion having a first side, a second side and a third side forming a proximal-facing opening, and a second open trapezoidal portion having a fourth side, a fifth side and a sixth side forming a distal-facing opening, wherein the second side and the fifth side are parallel, further wherein the third side of the first open trapezoidal portion is connected to the fourth side of the second open trapezoidal portion by a first connector region extending at a first angle relative to the third side, and wherein the first side of the first open trapezoidal portion connects to a sixth side of an adjacent biphasic cell in the ring by a second connector extending at a second angle relative to the first side; and a plurality of crosslink (e.g., omega-shaped and/or S-shaped) connecting each ring that is adjacent to a more distal ring to the more distal ring, wherein in some variations each ring connector connects the second side of one of the first open trapezoidal portions of the plurality of biphasic cells in the ring that is adjacent to the more distal ring to the fifth side of one of the second open trapezoidal portions of the plurality of biphasic cells of the more distal ring; wherein the stent device has a first configuration in which the plurality of adjacent rings have a first diameter, and the stent device has a second configuration in which the plurality of adjacent rings have a second diameter that is greater than the first diameter, and wherein the second side and the fifth side remain parallel as the stent device is expanded from the first configuration to the second configuration. Each of the plurality of rings and a respective subset of the plurality of crosslinks connecting each ring to a more distal ring may be referred to as a connecting portion. The respective subset of the plurality of crosslink connectors of a first connecting portion may be aligned diagonally with a respective subset of the plurality of crosslink connectors in and adjacent connecting portion. 
     In some variations, each of the crosslink connectors (e.g., S-shaped crosslink connectors) may connect between a second and third sides of one of a first open trapezoidal portions of a plurality of biphasic cells in a first ring that is proximally adjacent to a more distal ring and may connect between a fourth and a fifth side of one of the second open trapezoidal portions of the plurality of biphasic cells of the more distal ring. 
     Each of a first subset of crosslink connectors of a first connecting portion may be radially offset from a respective one of a second subset of crosslink connectors of a second connecting portion that is adjacent to the first connecting portion. The subset of crosslink of a connecting portion, connected to the flattened tops of the ring of the connecting portion, may not be connected to adjacent flattened tops of the ring. 
     In general, as described herein, an S-shape may refer to a double-curved shape, having an inflection point at about (e.g., near) the midpoint of the curve with curved regions extending in opposite directions of curvature on either side of the inflection point. The curved regions on either side may be symmetric (e.g., may have radiuses of curvature that are the same or nearly the same) or they may be different (e.g., the first curved region may have a radius of curvature that is larger than the second radius of curvature, including larger by between 0.1%-50%, between 0.1%-40%, 0.1% to 30%, 0.1% to 25%, 0.1% to 20%, etc.). This may apply to the unit cell and crosslinks connector design separately. 
     A stent device having a length extending in a distal to proximal direction may include: a plurality of adjacent rings arranged transverse to a length of the device, wherein each ring is a ring comprising length of material arranged radially around the length of the stent device as a plurality of repeating biphasic cells, each biphasic cell comprising a first open trapezoidal portion having a first side, a second side and a third side forming a proximal-facing opening, and a second open trapezoidal portion having a fourth side, a fifth side and a sixth side forming a distal-facing opening, wherein the second side and the fifth side are parallel, further wherein the first open trapezoidal portion is radially offset from the second open trapezoidal portion and the third side of the first open trapezoidal portion is connected to the fourth side of the second open trapezoidal portion by a first connector region extending at a first angle relative to the third side, and wherein the first side of the first open trapezoidal portion connects to a sixth side of an adjacent biphasic cell in the ring by a second connector extending at a second angle relative to the first side; and between one and three crosslinks connecting each ring omega-shaped connector connects the second side of one of the first open trapezoidal portions of the plurality of biphasic cells in the ring that is adjacent to the more distal ring to the fifth side of one of the second open trapezoidal portions of the plurality of biphasic cells of the more distal ring, further wherein an omega-shape of each of the omega-shaped connectors connecting the plurality of adjacent rings is oriented in the same distal to proximal direction; wherein the stent device has a first configuration in which a first diameter of the plurality of adjacent rings is between 0.5 mm and 4 mm and a second configuration in which a second diameter of the plurality of adjacent rings is between 2 mm and 12 mm, and wherein the second side and the fifth side remain parallel but the first and second angles change as the stent device expands from the first configuration to the second configuration. Each ring that is adjacent to a more distal ring and the between 1 to 6 crosslinks connected to the flattened tops of the ring is a connecting portion. The respective crosslinks of a first connecting portion are aligned diagonally with respective crosslink connectors in an adjacent more proximal connecting portion. 
     The between 1 and 6 crosslinks connected to the flattened top of each ring may not be connected to adjacent flattened tops of the ring. The between 1 to 6 crosslinks of a first connecting portion may be radially offset from between 1 to 6 crosslinks of a second connecting portion. 
     The plurality of crosslink connectors may comprise between 1 and 10 crosslink connectors (e.g., between 1 and 7, between 1 and 6, between 1 and 5 between 1 and 4, between 1 and 3, etc.). In some variations, the plurality of omega-shaped or/and S-Shape connectors has a maximum of 2 crosslink connectors. 
     Typically, the first open trapezoidal portion (or at least the flattened top of the open trapezoidal portion) is radially offset from the second open trapezoidal portion (e.g., the flattened top of the open trapezoidal portion). This offset may increase as the device transitions from the first (un-expanded configuration) into the second (expanded) configuration, while the flattened top remains essentially the same shape and size. Thus, the radial offset between the first open trapezoidal portion and the second open trapezoidal portion may increase as the stent device transitions from the first configuration to the second configuration. 
     In general, the length of any of the devices described herein may be between about 10 mm and about 80 mm (e.g., between about 12 mm to about 80 mm, between about 18 mm and about 79 mm, between about 16 mm and 78 mm, e.g., 80 mm or less, 79 mm or less, 78 or less, etc.). The first diameter (e.g., the outer diameter of each ring in the un-expanded configuration) may be between about 0.5 mm and about 4 mm and the second diameter (e.g., the outer diameter of the rings in the expanded configuration) may be between about 2 mm and about 12 mm (e.g., between about 3 mm and about 7 mm, etc.). 
     The frame (e.g., the length of material) may comprises one or more of: an alloy of chromium cobalt, a nickel titanium alloy (e.g., Nitinol), a stainless steel and a magnesium alloy. 
     Any of these devices may include a sleeve bonded to and/or encapsulating the frame (e.g., the plurality of connected rings). The sleeve may be a polymeric matrix in which the plurality of rings is encapsulated. For example, the sleeve may be PTFE. The sleeve material may be electrospun onto the frame. The sleeve may comprise a porous material. In some variations, the sleeve may have a thickness of between about 0.05 and 0.5 mm. 
     In any of the stent devices described herein the crosslink connectors may be oriented so that an —S-shape or an omega-shape (the approximately “Ω” shape) of each of the crosslink connectors connecting the plurality of adjacent rings are all in the same distal to proximal direction, e.g., so that they all face distally or proximally. In some variations, the crosslinks may all be S-shaped crosslink connectors. In some other variations, the crosslink connectors may all be omega-shaped crosslinks. In other variation the crosslink connectors can be a combination of both omega-shaped and S-shaped connectors. 
     As mentioned above, the first open trapezoidal portion may be an open rectangle, open isosceles trapezoid, etc. The open trapezoidal portions (first and second) may generally include a flattened end with square or rounded corners extending into a pair of legs. The legs forming the open end may be straight or curved (including sinusoidal). The legs may bend as the device expands from the first (un-expanded) to the second (expanded) configuration. In some variations the second open trapezoidal portion may be the same shape as the first open trapezoidal shape, or different. For example, the first and third sides may be parallel and in some variations the fourth and sixth sides are not parallel. The first and second open trapezoidal shapes have opposite open ends that face different each other (e.g., one faces distally while the other faces proximally). Either or both the first open trapezoidal portion and the second open trapezoidal portion may have rounded edges. In general, the trapezoidal shapes may have different sizes and shapes (e.g., the angles between the walls of the shapes may be different (see, e.g.,  FIGS.  20 D and  20 E , etc.). 
     The width of the length of material forming the repeating biphasic cells (the rings) may be constant or it may vary. For example, the width may be between about 0.05 and about 0.5 mm (e.g., between about 0.1 and about 0.3, between about 0.1 and about 0.2, etc.). 
     The plurality of adjacent rings are typically separated from each other by a ring offset. The crosslink connector (e.g., the S-shaped crosslink connector or omega-shaped crosslink connector) may sit within this ring offset. The ring offset may be a distance of between 0.1 and 1.5 mm (e.g., between about 0.1 mm and about 1.4 mm, between about 0.1 mm and 1.2 mm, etc.) along the distal to proximal length of the stent device. In general, the distal to proximal height of each ring may be between about 0.5 mm and about 4 mm (e.g., between about 0.5 mm and about 3.5 mm, between about 1 mm and about 3 mm, etc.). 
     The stent devices described herein, because of the dimensions and arrangement of the frame (e.g., the repeating biphasic cell configuration) and the crosslink connectors (e.g., the S-shaped crosslink connectors or the omega-shaped crosslink connectors) may permit the device to have particularly advantageous properties, including resistance to kinking. For example, the stent device may bend at least 90 degrees along its length in the first configuration without kinking. The device may foreshortens less than 8.5% (e.g., less than 8.4%, less than 8.0%, less than 7.5%, less than 6%, less than 5.5%, etc.) when expanding from the first configuration to the second configuration. For example, the device may foreshorten less than 7% (e.g., less than 6%, less than 5.5%, etc.) when the second diameter of the plurality of adjacent rings is greater than 2.9 times the first diameter of the plurality of adjacent rings. 
     The first open trapezoidal portions of the repeating biphasic cells in each of the rings may be aligned with the first open trapezoidal portions in the other rings along the proximal to distal length of the device. Similarly the second open trapezoidal portion of the repeating biphasic cells may be aligned with each other along the length (proximal to distal) of the device. 
     The patterns forming the rings may alternatively be described herein as a repeating pattern of alternating flattened tops and flattened bottoms, wherein the flattened tops extend transverse to the length of the device and wherein the flattened bottoms extend transverse to the length of the device and further wherein the flattened tops and flattened bottoms are connected by sigmoid-shaped connectors so that each flattened top forms part of a proximal facing U-shape and each flattened bottom forms part of a distal facing U-shape. Each flattened top and a portion each of two sigmoid-shaped connectors to which it is attached may form a first open trapezoidal portion having a proximal-facing opening and each flattened bottom and a portion each of two sigmoid-shaped connectors to which it is attached forms a second open trapezoidal portion having a distal-facing opening. 
     Thus, described herein are stent devices comprising: a plurality of adjacent rings arranged transverse to a length of the device in a proximal to distal direction, wherein each ring comprises a length of material arranged radially around the length of the stent device in a repeating pattern of alternating flattened tops and flattened bottoms, wherein the flattened tops extend transverse to the length of the device and wherein the flattened bottoms extend transverse to the length of the device and further wherein the flattened tops and flattened bottoms are connected by sigmoid-shaped connectors so that each flattened top forms part of a proximal facing U-shape and each flattened bottom forms part of a distal facing U-shape; a plurality of crosslinks connecting each ring that is adjacent to a more distal ring to the more distal ring, wherein each ring connector connects one of the flattened tops the ring that is adjacent to the more distal ring to a flattened bottom of the more distal ring; wherein the stent device has a first configuration in which the plurality of adjacent rings have a first diameter, and the stent device has a second configuration in which the plurality of adjacent rings have a second diameter that is greater than the first diameter, and wherein the flattened tops and the flattened bottoms remain parallel to each other as the stent device is expanded from the first configuration to the second configuration. Each of the plurality of rings and a respective subset of the plurality of crosslink connectors connecting each ring may be in a connecting portion. The respective subset of the plurality of crosslink connectors of a first connecting portion may be aligned diagonally with a respective subset of the plurality of crosslink connectors in an adjacent more proximal connecting portion. In some variations the pattern is an ABAB repeat pattern; an ABCBA repeat pattern, or an ABCABC repeat pattern, etc. 
     The plurality of crosslink connectors may comprise, for example, between 1 and 10 crosslink connectors in each connecting portion (e.g., between 1 and 3, between 1 and 4, between 1 and 5, between 1 and 6, between 1 and 7, between 1 and 8, between 1 and 9, etc.). The plurality of crosslink connectors may have a maximum of 2 crosslink connectors in each connecting portion. The flattened tops of each ring may be radially offset from the flattened bottoms. The radial offset may increase as the stent device transitions from the first configuration to the second configuration. As mentioned above, a shape of each of the crosslink connectors connecting the plurality of adjacent rings may be oriented in the same proximal to distal direction. Each of the first subsets of crosslink connectors of a first connecting portion may be radially offset from a respective one of the second subset of crosslink connectors of a second connecting portion that is adjacent to the first connecting portion. The respective subset of the plurality of crosslink connectors of a first connecting portion connected to the flattened tops of each ring may not be connected to adjacent flattened tops of the ring. In some examples, all or a subset of the plurality of crosslink connectors of a first connecting portion may connect to the lateral portion of the inferior U-shape in the biphasic unit cell with the opposite lateral of superior U-shape in the biphasic unit cell. 
     For example, a stent device may include: a plurality of adjacent rings arranged transverse to a length of the device in a proximal to distal direction, wherein each ring comprises a length of material arranged radially around the length of the stent device in a repeating pattern of alternating flattened tops and flattened bottoms, wherein the flattened tops extend transverse to the length of the device and wherein the flattened bottoms extend transverse to the length of the device and further wherein the flattened tops and flattened bottoms may be connected by sigmoid-shaped connectors so that each flattened top forms part of a distal-facing U-shape and each flattened bottom forms part of a proximal-facing U-shape; between one and three crosslinks connecting each ring that is adjacent to a more distal ring to the more distal ring, wherein each ring connector connects one of the flattened tops of the ring that is adjacent to the more distal ring to a flattened bottom of the more distal ring, further wherein a shape of each of the crosslinks is oriented in the same proximal to distal direction; wherein the stent device has a first configuration in which the plurality of adjacent rings have a first diameter, and the stent device has a second configuration in which the plurality of adjacent rings have a second diameter that is greater than the first diameter, and wherein the flattened tops and the flattened bottoms remain parallel to each other and the shape of the sigmoid-shaped connectors extends radially as the stent device is expanded from the first configuration to the second configuration. Each ring that is adjacent to a more distal ring and the between 1 and 3 crosslinks connected to the flattened tops of the ring may comprise a connecting portion. The respective crosslinks of a first connecting portion may be aligned diagonally with respective crosslinks in an adjacent more proximal connecting portion. The respective crosslinks of a first connecting portion may be radially offset from respective crosslinks in an adjacent connecting portion. 
     As mentioned above, the first diameter may be between 0.5 mm and 4 mm and the second diameter may be between 2 mm and 12 mm. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The novel features of the invention are set forth with particularity in the claims that follow. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings of which: 
         FIG.  1 A  is a side view illustrating a delivery configuration of an exemplary stent that comprises a plurality of supports coupled together by connecting regions. 
         FIG.  1 B  illustrates an end view of the stent from  FIG.  1 A . 
         FIG.  1 C  illustrates a highlighted view of detail of region A shown in  FIGS.  1 A and  1 D . In any of the images and examples provided herein, the dimensions shown are exemplary only, and are intended to provide illustrations of a range of dimensions that may work (e.g., +/− about 50%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, 5%, etc.). In  FIG.  1 C , the dimensions are in mm. 
         FIG.  1 D  illustrates the stent from  FIG.  1 A  in a flattened, planar, configuration. Exemplary dimensions (in mm) are shown; as mentioned, the dimensions may be +/− about 50%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, 5%, etc. 
         FIG.  1 E  illustrates the stent from  FIG.  1 A  in an initial (unexpanded, bottom) configuration and an expanded (top) configuration. Shading indicates relative strain on the frame of the stent shown. 
         FIG.  1 F  overlays the two configurations shown side-by-side in  FIG.  1 E . 
         FIGS.  2 A- 2 C  illustrate view of an exemplary stent similar to the exemplary stent shown in  FIGS.  1 A- 1 F . A side view of the stent is shown in  FIG.  2 A .  FIG.  2 B  shows an end view of the stent device of  FIG.  2 A  with exemplary dimensions (in mm) of the inner and outer un-expanded diameters.  FIG.  2 C  is an “unrolled” configuration of the stent device of  FIG.  2 A , if the device of  FIG.  2 A  were cut along the longitudinal (e.g. proximal to distal) axis and unrolled to be flat. 
         FIGS.  3 A- 3 C  illustrate view of an exemplary stent similar to the exemplary stent shown in  FIGS.  1 A- 1 F and  2 A- 2 C . A side view of the stent device is shown in  FIG.  3 A .  FIG.  3 B  is an end vie of the stent device of  FIG.  3 A .  FIG.  3 B  is an “unrolled” configuration of the stent device of  FIG.  3 A , if the device of  FIG.  3 A  were cut along the longitudinal (e.g. proximal to distal) axis and unrolled to be flat. 
         FIG.  4 A  is a graph illustrating an example of an applied pressure vs. diameter profile of one example of a stent apparatus as described herein. 
         FIG.  4 B  is a graph illustrating an example of a stress-strain profile of one example of a stent apparatus as described herein. 
         FIG.  5    illustrates an exemplary stent device including an optional sleeve (covering). 
         FIG.  6    illustrates an exemplary catheter system for delivering any of the stents devices herein. Any of these stent devices may be included with all or some of the delivery components shown in  FIG.  6   . 
         FIG.  7    shows an example of an apparatus as described herein, configured as a balloon-expandable chrome cobalt stent, including plurality of adjacent crosslink connected together by 3 or fewer omega-shaped connectors (e.g., two connectors) between adjacent rings. The stent device in  FIG.  7    shows a lateral view. 
         FIG.  8 A  is an example of a portion of a stent apparatus, showing an open trapezoidal region including a flattened surface to which an omega-shaped connector is attached. 
         FIG.  8 B  shows a schematic of a plurality of repeated biphasic shapes (unit cell) including a first open trapezoidal portion having a flattened top side (e.g., a second side) and a proximal-facing opening, and a second open trapezoidal portion having a flattened top side (e.g., a fifth side) forming a distal-facing opening. 
         FIG.  8 C  shows a schematic of an example of a portion of the first open trapezoidal shape having the flattened top, two sides forming the proximal-facing opening, showing the angle formed between a connector region (connecting the first open trapezoidal shape to the second open trapezoidal shape) and the first open trapezoidal shape. 
         FIG.  9 A- 9 C  illustrate expansion of another example of a portion of a ring of a stent device including a repeating pattern of biphasic cells, each biphasic cell comprising a first open trapezoidal portion having a first side, a second side and a third side forming a proximal-facing opening, and a second open trapezoidal portion having a fourth side, a fifth side and a sixth side forming a distal-facing opening, in which the first open trapezoidal portion is connected to the second open trapezoidal portion.  FIG.  9 A  shows the exemplary biphasic cell configuration in an un-expanded configuration, while  FIGS.  9 B and  9 C  show a progressively more expanded configurations. 
         FIG.  10 A  is an example of another variation of a plurality of repeated biphasic shapes (unit cell) including a first open trapezoidal portion having a flattened top side (e.g., a second side) and a proximal-facing opening, and a second open trapezoidal portion having a flattened top side (e.g., a fifth side) forming a distal-facing opening. In this example, the first and second open trapezoidal portions have the same shape (e.g. rounded isosceles trapezoids in which the sides of the trapezoid forming the opening are angled in). 
         FIG.  10 B  shows a schematic of an example of a portion of the first open trapezoidal shape having the flattened top, two sides forming the proximal-facing opening, showing the angle (α′) formed between a connector region (connecting the first open trapezoidal shape to the second open trapezoidal shape) and the first open trapezoidal shape. 
         FIG.  11    illustrates one example of a portion of two rings of an exemplary stent apparatus including an omega-shaped crosslink that may be used to join the rings of repeated biphasic shapes (open trapezoidal shapes) forming the stent. Adjacent rings may be interconnected through two (or in some variations, more) crosslinks placed between peaks between adjacent rings. 
         FIG.  12    shows an example of a stent device as described herein in an expanded configuration. In this example, the flat top regions remain flat, and although the unit shapes are foreshortened slightly, this is compensated at least in part by the expansion of the omega-shaped crosslinks. 
         FIG.  13    is an example of a stent apparatus as described herein including a cover having a pores encapsulating the metallic frame of the stent as described herein. 
         FIG.  14 A  is a graph showing an example of crush with parallel plates (radial compression) for an example of a stent apparatus as described herein (force×displacement), showing the compression at 50% of the diameter of the stent of about 7.5 N. 
         FIG.  14 B  is a graph showing an example of crush resistance for an example of a stent apparatus with radially applied loads for an example of a stent apparatus as described herein (force×distance). 
         FIGS.  15 A- 15 C  illustrate examples of prior art stents showing kinking during bending at 90 degrees.  FIG.  15 A  is an 8×58 mm stent,  FIG.  15 B  is an 8×59 mm stent, and  FIG.  15 C  is an 8×57 mm stent. 
         FIGS.  16 A and  16 B  illustrate examples of the stent apparatuses described herein in 90 degree bending, showing smooth (unkinked) bending over the same experimental parameters as the prior art stents shown in  FIGS.  15 A- 15 C , but with substantially less kinking or reduction in diameter.  FIG.  16 A  is an 8×38 mm stent and  FIG.  16 B  is a 10×58 mm stent. 
         FIG.  17 A  illustrates an example of a navigability test jig that may be used to characterize a stent apparatus as described herein, having regions (“arteries” of 3, 4, 6 and 8 mm diameters, at angles of between 30-90 degrees and various radius of curvatures. 
         FIG.  17 B  is an example of one variation of a stent apparatus as described herein shown navigating a test jig such as the one shown in  FIG.  17 A . 
         FIGS.  18 A- 18 D  are tables illustrating properties of different examples of stents as described herein.  FIG.  18 A  shows initial and final lengths and diameters of a 5×18 mm stent graft apparatus.  FIG.  18 B  shows initial and final lengths and diameters of a 5×38 mm stent graft apparatus.  FIG.  18 C  shows initial and final lengths and diameters of a 6×18 mm stent graft apparatus.  FIG.  18 D  shows initial and final lengths and diameters of a 6×38 mm stent graft apparatus. 
         FIGS.  19 A- 19 F  show different variations of stent apparatuses having different distribution and ring connector shapes. 
         FIGS.  20 A- 20 C  show exemplary dimensions of one variation of a stent apparatus according to some embodiments of the disclosure. 
         FIGS.  20 D and  20 E  show an enlarged view of a unit cell of an exemplary apparatus such as the one shown in  FIG.  20 A .  FIG.  20 E  shows a skeletonized version of the region, including a unit cell, of  FIG.  20 D . 
         FIG.  21    shows exemplary dimensions and features of a stent apparatus according to some embodiments of the disclosure. 
         FIGS.  22 A- 22 B  show details of two examples of ring connector shapes;  FIG.  22 A  shows an omega-shaped connector while  FIG.  22 B  shows a S-shaped connector. 
         FIGS.  23 A- 23 B  show stress distributions compared between different stent apparatus having different ring connector shapes. 
         FIGS.  24 A- 24 B  show stress distributions compare between different unit cell configurations. 
         FIGS.  25 A- 25 C  show exemplary dimensions of a stent apparatus according to some embodiments of the disclosure. 
         FIGS.  26 A- 26 C  show exemplary dimensions of a stent apparatus according to some embodiments of the disclosure. 
         FIGS.  27 A- 27 C  show exemplary dimensions of a stent apparatus according to some embodiments of the disclosure. 
         FIGS.  28 A- 28 C  show exemplary dimensions of a stent apparatus according to some embodiments of the disclosure. 
         FIGS.  29 A- 29 C  show exemplary dimensions of a stent apparatus according to some embodiments of the disclosure. 
         FIG.  30    shows a finite element model (FEM) simulation of a stent apparatus. 
         FIGS.  31 A- 31 C  show exemplary dimensions of a stent apparatus according to some embodiments of the disclosure. 
         FIGS.  32 A- 32 B  illustrate the results of radial compression testing of three examples of stents (with or without graft material on the stent) having a plurality of adjacent rings formed of alternating flattened tops and flattened bottoms that are transverse to the length of the device and are connected by sigmoid-shaped connectors aligned in a helically winding arrangement around the length of the device as described herein (e.g.,  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C ).  FIG.  32 A  shows the average crush resistance (between parallel plates) following ISO 25539 testing, showing an average of between about 3N and about 6.5 N.  FIG.  32 B  is a graph showing a comparison of the radial compression strength (e.g., crush resistance) of the stents as descried herein (indicated by *), and prior art stents. 
         FIGS.  33 A- 33 B  shows the results of longitudinal compression testing of three examples of stents (with or without graft material on the stent) having a plurality of adjacent rings formed of alternating flattened tops and flattened bottoms that are transverse to the length of the device and are connected by sigmoid-shaped connectors aligned in a helically winding arrangement around the length of the device as described herein (e.g.,  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C ).  FIG.  33 A  shows the average longitudinal stent resistance following ISO 25539 testing.  FIG.  33 B  is a graph showing a comparison of the longitudinal stent resistance (e.g., the force needed to achieve 15% longitudinal compression) between prior art stents and examples of stents as descried herein (indicated by *) having different dimensions. 
         FIGS.  34 A and  34 B  illustrate the results of performance testing for crimped testing (e.g., crimped stent profile testing).  FIG.  34 A  is a table showing the results of crimp testing on three different sizes of the stents described herein, e.g., stents having a plurality of adjacent rings formed of alternating flattened tops and flattened bottoms that are transverse to the length of the device and are connected by sigmoid-shaped connectors aligned in a helically winding arrangement around the length of the device.  FIG.  34 B  graphically illustrates a comparison between the results of crimp testing for the stent devices as described herein (e.g., in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C , indicated by an “*” in  FIG.  34 B ) and prior art stent devices. 
         FIGS.  35 A and  35 B  illustrate the results of performance testing for recoil (e.g., recoil testing).  FIG.  35 A  is a table showing the results of recoil testing on two different sizes of the stents as described herein, e.g., stents having a plurality of adjacent rings formed of alternating flattened tops and flattened bottoms that are transverse to the length of the device and are connected by sigmoid-shaped connectors aligned in a helically winding arrangement around the length of the device (similar to that shown in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C ).  FIG.  35 B  graphically illustrates a comparison between the results of recoil testing for the stent devices as described herein (e.g., in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C , indicated by an “*” in  FIG.  35 B ) and prior art stent devices. 
         FIG.  36    is a graph illustrating the stent foreshortening of the stent configurations described herein. In  FIG.  36   , the stents examined are similar to those shown in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C  (with or without a graft material included). Foreshortening was typically less than about 8.5%. 
         FIGS.  37 A- 37 C  illustrate one example of a stent as described herein, including a sleeve encapsulating the rings.  FIG.  37 A  shows the stent arranged on a balloon that has been inflated to expand the stent into the second, expanded, configuration.  FIG.  37 B  shows the expanded stent removed from the balloon.  FIG.  37 C  shows the distal end opening of the stent. 
     
    
    
     DETAILED DESCRIPTION 
     Described herein are stent apparatuses with improved flexibility for greater expansion without fracture. This allows the stents to be expanded to greater diameter sizes when in use, which provides an exemplary benefit of being able to use a single stent for a greater variety of uses (e.g., different vessel sizes) without having to use a differently sized stent. The stents described herein are also adapted such that foreshortening of the stent during expansion is reduced, preventing a variety of complications. 
     The stents herein generally have a collapsed delivery configuration, and are adapted to be expanded. The “collapsed” configurations may be referred to herein as delivery, collapsed, initial, or other similar term. The delivery configuration can be the configuration the stent has after being manufactured, such as by laser cutting a tubular element or 3-D printing the stent. The stents herein are described as being expanded by balloon expansion, but the stents could be adapted to be able to at least partially self-expand. 
     Any of the stents herein can include one or more coverings over any portion of the stent. 
     The stents include a plurality of supports, optionally annular, wherein each of the plurality of supports are connected to at least one adjacent support by one or more connecting portions, which can include one or more connectors. 
     There are several factors that influence the flexibility of the stents herein and provide the stents with the ability to expand to larger outer dimensions without fracturing. The following are examples of factors that can influence the flexibility of the stents: the configuration of the annular supports and connectors; the dimensions of the annular supports and connectors; and the materials of the annular supports and connectors. 
       FIG.  1 A  illustrates a side view of exemplary stent  10  in an un-expanded (e.g., delivery) configuration, stent  10  having a first end  12  (e.g., proximal end) and a second end  14  (e.g., distal end) and a length, L; thus stent  10  has a longitudinal axis L extending through a lumen defined by the stent. Stent  10  includes a plurality of annular supports  22  (“rings”) transverse to the long axis and generally axially spaced from at each other; the individual regions are connected by at least one crosslink connector  20  (in this example, an omega crosslink connector). In this example, an annular support is “adjacent” to another annular support if it is the next annular support when moving towards either the first end  12  or the second end  14 . In this example, the annular supports  22  (which may also be referred to herein as “rings”) are connected to at least one adjacent support  22  by a ring connector  20  (i.e., omega connector). The rings  22  may be described herein as being “connected” to adjacent rings; it is understood that this may include one or more (e.g., two) ring connectors  20  that may be integrally formed with the rings, such as if the entire stent may be manufactured from a single piece of starting material, e.g., by laser cutting a cylindrical piece. Each of the rings  22  in this embodiment has a wave configuration, with a plurality of peaks and valleys, repeating in a pattern (only some peaks and valleys are labeled for clarity). In this embodiment, peaks of the supports may extend to the same location along the length of the stent. Valleys of supports (rings) also extend to the same location along the length of the stent. Thus, the peaks (e.g., the flattened top regions  24 ) may be aligned along the length of the stent device, shown, and the valleys (e.g., the flattened bottom regions  24 ′) may also be aligned along the length of the stent. Peaks and valleys of the waves may define flattened, or squared, ends. Between the peaks and valley are intermediate sections  28  (connecting regions), and in this embodiment the intermediate sections have S-shapes (or may have sigmoid shapes), as can be seen in the side view of  FIG.  1 A . This embodiment is an example of at least one annular support with a repeating wave pattern having flattened ends connected by curvilinear intermediate sections, such as S-shape intermediate regions. For simplicity of discussion, a repeating unit of a ring and the plurality of crosslinks attached to the flattened tops of the ring can be referred to as a connecting portion. The apparatus thus includes a plurality of connecting portions forming the stent. 
     In this embodiment, the annular supports all have the same configuration along the length of the stent. Peaks  24  (which are described in additional detail below, and may be referred to herein as a first open trapezoidal portion having a first side, a second side and a third side forming a proximal-facing opening) of adjacent rings may therefore be circumferentially aligned, and valleys (which are described in additional detail below and may be referred to herein as a second open trapezoidal portion having a fourth side, a fifth side and a sixth side) of adjacent rings may be circumferentially aligned. 
     In alternative embodiments, not every annular support has the same configuration as every other annular support. 
     Adjacent annular supports  22  are connected together by ring connector  20 .  FIG.  1 D  illustrates a flattened/planar view of an example of a stent device  10 , which illustrates the connections between adjacent rings. In this embodiment, the crosslink  20  (e.g., omega crosslink between adjacent rings  22  include at least two crosslinks, shown in  FIG.  1 C  as Detail A shown in  FIGS.  1 A and  1 D .  FIG.  1 C  illustrates a ring connector that connects adjacent rings  22  (only a portion of rings are shown). The ring connector has a configuration, at least a portion of which may have a general “omega” configuration. In this embodiment, the general “omega” configuration is defined by arc region (e.g., dome region)  32  and radial regions  33  generally extending radially outward from arc or domed region  32 . In this embodiment, radial regions have linear configurations and may be L-shaped, but in other embodiments they could include some curvature. The ring connector (i.e., an omega ring connector) may also include axial regions  34  which may extend generally axially from radial regions  33  and may be parallel to the longitudinal axis LA of the device (e.g., forming the L-shaped ends, mentioned above). Axial regions  33  of the ring connector are linear but could, in some embodiments, have some curvature to them. One of the axial regions  34  extends further toward first end  12  than the other axial region  34 . Radial regions of a ring connector may generally be aligned when they have linear configurations (and are also aligned with other radial regions of the other ring connector that connects the two adjacent supports), and axial regions  34  are parallel to each other, and to the longitudinal axis LA. 
     The “omega” shape is generally defined by an arc or domed region  32  and radial regions  33 . While domed region  32  and radial regions  33  do not form an exact, traditional, “omega” Greek letter, it is understood that they form a general “omega” shape of the ring connector. Domed regions  32  and radial sections  33  can have slightly varying configurations and that portion of the ring connector can still have a general “omega” configuration as that term is used herein. 
     The crosslink extends from a flattened top region (e.g., of the open trapezoidal ‘peak’ region  24 ) of a first ring  22  to a flattened top (e.g., of the next open trapezoidal ‘valley’ region  24 ′) of an adjacent ring  22 , as can be seen in  FIGS.  1 A and  1 D . The first open trapezoidal portion (e.g., peak) and second open trapezoidal portion (valley) from which the ring connector extends are not circumferential aligned. For example, a ring connector extends from a first open trapezoidal portion  24  on a first ring  22  to a second open trapezoidal portion  24 ′ on an adjacent ring, as shown in  FIGS.  1 A,  1 C and  1 D . 
     As can be seen in  FIG.  1 D , the arc regions of all of the omega-shaped crosslink have similar configurations, and are all oriented in the same direction. In this embodiment, each pair of adjacent supports is coupled together by two omega-shaped crosslinks, each of which has the configuration shown in  FIG.  1 C . As can be seen in  FIG.  1 D , the omega-shaped crosslink in any given connecting portion are not circumferentially aligned with the crosslink in the adjacent connecting portion, but they are circumferentially aligned with the crosslink in the next adjacent connecting portion. In this embodiment, the position of the omega crosslink are in an A-B-A-B pattern, with every-other ring having crosslink that are circumferentially aligned. 
     The first and second open trapezoidal potions of the repeating biphasic shapes forming each ring are connected by an intermediate section (e.g., connecting the peak and a valley regions) as described above. In  FIG.  1 D , the connecting intermediate section is a length that extends in an angle between the open trapezoidal portions; this may be straight or curved (e.g., sinusoidal, including s-shaped). As will be described in greater detail below, this intermediate section, and in some variations the ‘legs’ of the open trapezoidal portions (forming the openings) may change their angle relative to the flattened top region when the stent devices expand (e.g., when driven by a balloon to expand). 
     In  FIG.  1 D , the two omega-shaped crosslink  20  extend from adjacent peaks  24 ′ and  20 , on adjacent rings, connecting the two rings. In this embodiment, the two crosslinks extend from adjacent flattened top (or bottom) regions. In the example shown in  FIGS.  1 A- 1 D , there are three flattened top regions (peaks) between some of the omega-shaped crosslink (from which no crosslink extends), and one flattened top region (peak) on the other side (radially) between the two omega-shaped connectors. Thus, in the space between each set of rings, two omega-shaped crosslinks connect the adjacent rings, and the connecting pattern is offset and alternating with every other ring, as shown in  FIGS.  1 A- 1 D . 
     In some variations, only three or fewer (e.g., two) crosslink are used to connect adjacent rings. For example, by having only two crosslinks in each space between each set of rings, there is less area of material than in some other stent designs. This smaller area may allow the stent to have more flexibility and can expand to a greater extent when forces are applied on the stent such as by an expansion balloon. In alternative embodiments, however, there could be more than two crosslinks in a connecting portion, and the desired flexibility could still be maintained by modifying one or more other aspects, such as, for example without limitation, one or more dimensions (e.g., thickness, radius), configuration, or material. 
     In general, each ring may be formed of a length of material, such as a metal (e.g., a nickel titanium alloy, a chromium alloy, a stainless-steel alloy, etc.). The length of material may be a strip of material formed into a rectangular or square cross-section (e.g., which may be formed by laser cutting from a tube of the material), or in some variation it may be formed of a wire. 
     The dimensions of the rings are one factor that may influence the flexibility and may provide for greater expansion of the stents herein. Less area of the stent material generally increases the flexibility and allows the stent to expand to greater outer dimensions without fracture.  FIG.  1 D  shows exemplary dimensions and radii for portions of at least one of the rings. In some embodiments the thickness of the support material is from 0.05 mm to 2 mm, such as from 0.05 to 1 mm, such as from 0.1 mm to 0.8 mm, such as from 0.06 mm to 0.09 mm (e.g., 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.6 mm 0.7 mm, 0.8 mm, 0.9 mm, 1 mm). 
     The configuration of the ring, including the arrangement of the repeating biphasic cells (e.g., the first and second open trapezoidal portions) of the rings is another factor that influences the flexibility and provides for greater expansion of the stents herein. The plurality of adjacent rings (e.g., annular supports)  22  generally have a wave-like configuration, with squared (flattened) end and S-shaped intermediate sections in between these flattened ends (forming peaks and valleys). As shown in the exemplary  FIG.  1 D , the connecting regions  28  between the open trapezoidal portions (or more specifically, between the flattened tops) are not aligned with the longitudinal axis of the stent. That is, they are at an angle relative to the longitudinal axis. This angle can increase the flexibility of the stent and allow for greater expansion. 
     As mentioned above, the dimensions of the omega-shaped crosslink connectors are an additional factor influences the flexibility and provides for greater expansion of the stents herein.  FIG.  1 C  shows exemplary dimensions (e.g., thicknesses and radii) that can be used for any of the omega-shaped crosslink connectors described herein. In some embodiments, one or more omega-shaped crosslink connectors has a thickness from about 0.02 mm to about 1 mm, such as about 0.02 mm to about 0.8 mm (e.g., about 0.02 mm about 0.03 mm, about 0.04 mm, about 0.05 mm, about 0.06 mm, about 0.07 mm, about 0.08 mm, etc.). 
     The configuration and number of the omega-shaped crosslink connectors are other factors that influence the flexibility and provides for greater expansion of the stents herein. As set forth herein, at least a portion of the omega-shaped crosslink connectors may have a general omega configuration, including an arc (e.g., domed) section. The omega configuration provides for added flexibility in the connecting portions. Additionally, in some embodiments the connecting portions only include two omega-shaped crosslinks connectors, which reduces the area of the connecting portions and increases the flexibility. 
       FIG.  1 E  illustrates an expanded configuration (top) of the stent  10  from  FIGS.  1 A- 1 D . The bottom configuration in  FIG.  1 E  is the same stent device  10  as shown in  FIG.  1 A . The top in  FIG.  1 E  illustrates the stent  10  (which has an initial, unexpanded outer diameter of approximately 2.76 mm—see  FIG.  1 B ) expanded to an outer diameter of about 8 mm, about 2.9 times the initial outer dimension.  FIG.  1 E  also illustrates the foreshortening that the stent undergoes as it is expanded. The initial length is 18 mm, and the length when expanded is about 16.9 mm, shortening by about 1.1 mm. In this embodiment the stent foreshortened by not more than about 6.2% when expanded to about 2.9 times an initial outer diameter. The ability to expand this much with so little foreshortening is due in part to the configuration of the rings and omega-shaped crosslink connectors, the dimensions of the rings and omega-shaped crosslink connectors, and the material(s) forming the stent. 
     As can also be seen in the top view of  FIG.  1 E , when the stent is expanded, the flattened top of the first open trapezoidal portion (peak)  24  is rotated along the radius of the stent, e.g., away from the longitudinal axis of the stent, with the flattened tops (or bottoms) of the next open trapezoidal portion (valley)  24 ′ also rotated, but still parallel with the first flattened top  24 . The plane of each ring is shown rotated by angle (β) relative to the long axis (LA) compared to the initial configuration shown in the bottom of  FIG.  1 E , showing the unexpanded configuration. The flattened tops of peaks  24  and may be individually flared radially outward relative to the flattened tops of the valleys  24 ′ when the device is expanded. The angle of rotation can be anywhere from 5 degrees to 60 degrees, such as from 10 to 45 degrees. 
     As is also shown in the bottom of  FIG.  1 E , each ring may have an axis or plane E′ that is orthogonal to the longitudinal axis (LA). When the stent is expanded, in this example the annular supports (rings) expand in such a manner than the axis rotates with respect to the longitudinal axis, and as shown in the expanded top configuration, the plane of the rings has rotated relative to the longitudinal axis. The angle β is less than 90 degrees (compared with the original angle of β′ which is approximately 90 degrees in this example). 
       FIG.  1 F  illustrates the initial  80  and expanded  82  configurations from  FIG.  1 E  overlaid on top of each other, which can further highlight the disclosure described with respect to  FIG.  1 E . 
     It is understood that not every features show in the embodiments herein is necessary to increase the flexibility of the stents herein. For example, in alternative embodiments, some connecting portions can have three crosslink connectors, and the stent may still be able to expand to desired outer dimensions for some applications. 
     As set forth above, one of the exemplary advantages of stents herein is that they can be mounted on different diameter expansion balloons and can be expanded to a greater variety of outer dimensions. This can reduce the number of stents that must be available for use for a particular medical application. 
       FIGS.  2 A- 2 C  illustrate an exemplary stent that is similar in many ways to the exemplary stent in  FIGS.  1 A- 1 E . The general configurations of the annular supports and crosslink connectors is the same to those in  FIGS.  1 A- 1 E . One difference is that the initial outer dimension of the stent is shown as 2.83 mm (see, e.g.,  FIG.  2 B ), as opposed to 2.76 mm in the embodiment in  FIG.  1 A- 1 E . The initial larger outer dimension allows the stent in this embodiment to be expanded to larger outer dimensions without fracturing. Another difference is the distance between peaks in one circumferential region of the stent. As shown in  FIG.  2 C , one distance between the peaks in the center of the stent is 1.90 mm, whereas in  FIG.  1 A- 1 E  it was 1.70 mm (see  FIG.  1 D ). Any of the other features described with respect to the embodiment in  FIGS.  1 A- 1 E  can be incorporated in this embodiment as well. 
       FIGS.  3 A- 3 C  illustrate an exemplary stent that is similar in many ways to the exemplary stent in  FIGS.  1 A- 1 E and  2 A- 2 C , and any feature therein can be incorporated into this embodiment as well. This embodiment is longer than the embodiments in  FIGS.  1 A- 1 E and  2 A- 2 C , with the exemplary length of 38 mm. The outer dimension of 2.76 mm shown in  FIG.  3 D  is the same as in the embodiment in  FIG.  1 A- 1 E . The distance between adjacent peaks is slightly different than the embodiments in  FIGS.  1 A- 1 E and  2 A -C, as shown in  FIG.  3 C . The crosslink connectors can have any of the dimensions of any of the crosslink connectors herein. Other exemplar dimensions are also provided in  FIG.  3 C . 
     The stents can generally be any appropriate length and have any appropriate initial outer dimension. 
     Exemplary materials for any of the stents herein include cobalt-chrome alloys (e.g., L605) y 316 L stainless steel. Expandable polytetrafluorethylene (ePTFE) and polyester (PET, dracon) are examples of materials that can be used for one or more sleeves, coatings or coverings on the stent, if included. 
       FIG.  4 A  illustrates a pressure versus diameter graph for the stent shown in  FIGS.  1 A- 1 E , illustrating a pressure applied by an internal expansion balloon. When plotting applied pressure vs corresponding outer diameter values, stent expansion progresses gradually until reaching approximately 7.5 bar pressure. From this pressure, more accelerated expansion starts, being more susceptible to expansion as pressure increases, until reaching about 8 mm, a maximum expansion value. It is noted that this exemplary stent is configured to be able increase its diameter in approximately 2.9 times without showing fracture hazard. When removing applied pressure, a slight stent recovery occurs due to initial elastic deforming. Similarly,  FIG.  4 B  shows an example of a stress vs. strain curve for a stent device such as those shown in  FIGS.  1 A- 1 F,  2 A- 2 C and  3 A- 3 C . In this example, the stress (in MPa) vs. strain (mm/mm) follows a similar profile to that shown in  FIG.  4 A  for applied pressure vs. diameter over the ranges examined. 
     As mentioned, any of the stent devices descried herein may include a sleeve, cover, coating or the like. For example,  FIG.  5    illustrates an exemplary stent device (which can be any of the stents described herein), at least a portion of which is covered by a sleeve  505 . In this example, the ends of the stent frame  503  are uncovered by the sleeve. Examples of sleeves that may be used are described in greater detail below. The sleeve may be referred to herein as a graft material. 
       FIG.  6    is a perspective view illustrating an exemplary catheter system  600  for delivering any of the stents  601  described herein. This system may include a connector  603  connected to an elongate lumen  605  for inserting the stent device  601  over an expandable balloon  607 . The balloon may be inflated by applying fluid through the catheter (e.g., one of the lumen of the catheter  605 ). One or more imaging markers  609  may be included to aid in visualizing the stent when in the body, e.g., using fluoroscopy. The tip  611  of the device may be open and a lumen through the device may be used for advancement over a guidewire (not shown). 
     The devices described herein may be used anywhere appropriate in the body, including, but not limited to, the peripheral vasculature. For example, a merely exemplary location for placement of the stents herein can be in tibial arteries, such as for injury to such arteries. The primitive iliac artery has a diameter between about 5 and 8 mm, and may be well suited for stents herein. 
     Although many of the stents described herein are shown having a plurality of parallel rings that are arranged transverse to the length of the stent, any of these devices may be configured as one or more helically arranged spirals of the unit cells that are coupled via crosslink connectors. In this case each “ring” refers to a ring per unit axil length. For example, a stent may include a single helically arranged (e.g., spiral) row of unit cells forming a plurality of coils (one ring per ×units, e.g., mm, of axial length) that are connected by crosslink connectors, including s-shaped or omega-shaped crosslink connectors. 
     EXAMPLES 
       FIG.  7    shows another example of a stent  700  as described herein. The stent may include a sheath or cover  703 . For example the stent device frame, formed of a plurality of interconnected rings, as described above, may be embedded in a polymeric matrix  703 , such as Bioweb® (Zeus Industrial Products Inc). The layers of this polymeric matrix may be applied, e.g., by electrospinning to the entire structure of the stent frame, providing a great deal of flexibility and structural stability. This may also improve its radial proprieties and allow the vascular vessel to open and recover the blood flow. 
       FIG.  13    illustrates one example of a sleeve encapsulating a stent frame. In this example, the sleeve is formed of a porous material (such as PTFE) that is applied to the frame in an average thickness of between, e.g., about 0.02 mm to about 5 mm (e.g., between about 0.05 mm to about 1 mm, between about 0.05 mm to about 0.25 mm, between about 50 micrometers to about 500 micrometers, between about 60 to about 80 micrometers, between about 50 to about 70 micrometers, etc.). The pores may be a variety of different sizes, depending upon the needs. In some variations the sleeve may be formed by electrospinning the material onto the stent frame, using polymer fibers with thicknesses ranging from nanoscale to microscale. Fabrics with complex shapes can be electrospun from solutions, producing a broad range of fiber and fabric properties. This technique has the ability to create encapsulation technology, spin membrane/sheet, and develop 3-D structures for coating substrates of varying shapes and sizes. 
     Returning to  FIGS.  8 A- 8 C , in general, the rings are formed of a length of material (e.g., metallic and or polymeric material) that forms, around the radius of the stent, a pattern of repeating biphasic cells, as shown in  FIG.  8 B . The repeating biphasic cells  801  typically include a pair of flattened top regions  803 ,  805  that are connected by an intermediate region  807 . In some variations the flattened top region forms a pair of open trapezoidal portions, such as shown in  FIG.  8 C . In  FIG.  8 C , the open trapezoidal portion (dashed box  809 ) includes a first side or leg  811 , a second side (corresponding to the flattened top  803 ), and a third side or leg  815 . This open trapezoidal portion has a distal-facing opening  817 . Similarly, a second open trapezoidal portion  819 , oriented 180 degrees off of the first open trapezoidal portion  809 , includes a fourth side  821 , a fifth side (corresponding to the flattened top  805 ), and a sixth side or leg  823 . The second open trapezoidal portion has a proximal-facing opening  818 . The first and second open trapezoidal portions may be connected by intermediate regions  807 . For example, the third side  815  of the first open trapezoidal portion may be connected to the fourth side of the second open trapezoid portion by a connector region  807 , as shown, and the first side of the first open trapezoidal portion is connected to the sixth side of a second open trapezoidal portion of the next biphasic cell. 
     The first open trapezoidal portion and the second open trapezoidal portion may have different ‘trapezoidal’ shapes. For example, in  FIG.  8 B , the first and second open trapezoidal shape is approximately rectangular  809 , and open on one side, as shown in  FIG.  8 C . Both the first and second open trapezoidal portions in the exemplary biphasic cell shown in  FIG.  8 C  are the same general shape.  FIGS.  9 A- 9 C  illustrate another example of a repeating biphasic cell forming a ring of a stent device as described herein, in which the first biphasic cell is an open trapezoidal portion having an isosceles (or keystone) shape  905 , while the second open trapezoidal portion  907  has a more rectangular shape, at least in the un-expanded shape (shown in  FIG.  9 A ). The dimensions of the open trapezoidal portions (e.g., the lengths of the flattened top regions  901 ,  903 ) are approximately the same. 
       FIGS.  10 A- 10 B  illustrate another example of a repeating biphasic cell  1001  in with the first and second open trapezoidal portions  1005 ,  1007  are approximately the same (e.g., isosceles) shape. As shown in  FIG.  10 B , the open trapezoidal portion  1005  in this example includes first  1009 , second (flattened top  1011 ) and third  1013  sides. The first  1009  and third  1013  sides are angled inwards forming the open isosceles trapezoidal shape. The angle (a) shown provides and angle of the first or third sides relative to the intermediate connector  1017 . 
     As shown in all of these examples the open trapezoidal shapes may have rounded (curved) edges. In some variations the open trapezoidal shapes may have straight edges (e.g., angled edges). In addition, the flattened tops (e.g.,  803 ,  805 ,  901 ,  903 ) may be flat or approximately flat, as shown. Thus, they may be curved slightly (typically &lt;15 degrees of curvature, e.g., &lt;12 degrees, &lt;10 degrees, &lt;8 degrees, etc.). The flattened tops of the first and second open trapezoidal portions shown are parallel, where in the context of the flattened (e.g., slightly curved) tops, the term parallel means substantially, parallel, so that an average vector through the flattened top portion of the first open trapezoidal portion (see, e.g.,  832 ,  FIG.  8 A ) is parallel to an average vector through the flattened top portion of the second open trapezoidal portion. 
       FIGS.  8 B- 8 C,  9 A- 9 C and  10 A- 10 B  schematically illustrate the repeating biphasic cells; in practice the cells may be formed of a length of material having a width, w, as shown in  FIG.  8 A . In this example, the width is constant; in some variations the width may be narrower, e.g., in the intermediate region connecting the open trapezoidal regions. In  FIG.  8 A , the exemplary portion of the repeating biphasic cell shows an open trapezoidal portion  819  having a proximal-facing opening  818  and half of the adjacent open trapezoidal portions  809  having distal-facing openings.  FIG.  8 A  also shows an example of an omega-shaped ring connector  851  that is connecting to the flattened top of the open trapezoidal portion  819  at a middle region. The omega ring connector includes an arc (“domed”) region  853  and two laterally extending arms extending from the arc  855 . The ends of the omega-shaped crosslink connectors may be L-shaped  857 ,  857 ′ so as to connect perpendicularly to the flattened top(s). 
     In general, the repeating biphasic cells forming the rings may have a generally interconnected “U” shape, with the U-shapes alternating as distal-facing and proximal facing radially around the circumference of the stent in each ring. As shown and described above, the generally U-shaped geometry may also be described an open trapezoidal portion. Thus, the U-shapes may have an inwards curved part in the beginning of the figure and afterwards an outwards curve. The tops of the U&#39;s may be connected to each other by an intermediate region, which may be angled or curved, as shown. Thus, the repeating biphasic cell may be formed of a pair of connected U-shapes. 
     The repeating biphasic cell shapes allow the stent to expand adequately and give the stent enough stability to expand and maintain the peripheral vascular vessel open. The radial stability and homogeneity of the stent may be improved by including a sheath, e.g., embedding it in a membrane, as described above. 
       FIGS.  9 A- 9 C  illustrate the effect of expansion of the stent on a portion of a ring, showing the movement of the intermediate region  909  and/or the legs of the open trapezoidal region(s) as the device transitions from an unexpanded configuration (shown in  FIG.  9 A ) to an expanded configuration (shown in  FIG.  9 C ). For example, in  FIG.  9 A  the repeating biphasic cell pattern is shown in the unexpanded configuration, and the first and second open trapezoidal portions  905 ,  907  are shown with the first  911  and third  913  sides and fourth  915  and sixth  917  sides angled slightly inwards and the first and second open trapezoidal portions  905 ,  907  are connected to each other by an intermediate region  909  (adjacent repeating biphasic cells are also connected by intermediate regions  909 ′).  FIG.  9 B  shows a schematic of the repeating biphasic cell of  FIG.  9 A  after the ring formed by the repeating biphasic cell has begun to expand, e.g., by applying an expansion force from a balloon. In  FIG.  9 B , the first and third sides of the proximal-facing open trapezoidal portion  901  have opened slightly (e.g., expanding the open trapezoidal shape) and the angle of the intermediate regions  909 ,  909 ′ has changed as well. Similarly, the fourth  915  and sixth  917  sides have also opened slightly. As expansion continues, in  FIG.  9 C  the first  911  and third  913  sides and the fourth  915  and sixth  917  sides have opened relative to the flattened tops  901 ,  903  even more, resulting in the expansion (without substantial foreshortening) of the repeating biphasic cells. 
       FIGS.  11  and  12    illustrate an example of a stent device similar to those described above. In  FIG.  11   , a portion of a stent frame  1100  encapsulated in a sleeve  1103  is shown. The frame is in an un-expanded configuration.  FIG.  11    shows an omega-shaped ring connector  1104  connected via an L-shaped connector  1101  to a flattened top of a first open trapezoidal portion  1111  having a distal-facing opening (the distal direction  1121  is ‘up’ in  FIG.  11   ). The opposite end of the omega-shaped ring connector  1109  is a second L-shaped connector (e.g., a right-angled connector) that is connected to a flattened top of another open trapezoidal portion  1113  having a proximal-facing opening on an adjacent ring of the stent. 
     A stent such as the one shown in  FIG.  11    is shown in an expanded view in  FIG.  12   . In this example, similar to that shown in  FIG.  9 C , above, the stent frame  1200  is expanded so that the sides of the open trapezoidal portions forming the distal- and proximal-facing openings are spread further apart and the angle between the interconnecting intermediate regions and the flattened top regions is larger, while the flattened top regions remain parallel, and essentially unchanged from the un-expanded configuration. In  FIG.  12   , the distance between the flattened ends  1203  is much larger than in the un-expanded configuration. The omega-shaped crosslink(s)  1205  continue to connect the adjacent rings together, while bending to minimize foreshortening of the stent, even when the diameter of the stent increases more than twice its un-expanded diameter. 
     As described above, the rings forming the stent are interconnected through the omega-shaped crosslink connectors that build up the stent. Every cylindrical ring, other than the most proximal and the most distal rings, may be connected to adjacent cylindrical rings through two sets of crosslink connectors, one set of crosslink connectors connecting from a more proximal to the cylindrical ring, and the second set of crosslink connectors connecting from the cylindrical ring to a more distal ring. The crosslink connectors may be placed at spaced locations, as shown in  FIG.  1 A- 1 F , above. The crosslink connectors are not typically placed on the same connection point as the adjacent rings, but (as shown) may repeat the pattern every other ring. The omega shape or S-shape may give the stent flexibility when it has to expand. For example, the crosslinks design may allow them to be embedded in a material (e.g., ePTFE or PTFE) as well as to be crimped and uniformly expanded without ruptures. This type of crosslinks may allow the stent to crimp in the catheter without overlapping each other. As will be described below in  FIGS.  16 A- 16 B , the rings may not overlap when the stent is compressed and/or bent in the catheter. The crosslink connectors may be identical and may have the same organization (orientation) along the stent&#39;s length. The stent can be compressed to a diameter that is smaller than the one it was designed in, in order to be placed correctly on the balloon, to obtain a thin profile when placed on the catheter and/or to avoid the stent migration when introduced in the tortuous paths of the vascular vessels. 
     Thus, in some variations, the membrane, together with the repeating biphasic cell pattern that forms the stent, may make the stent flexible, and the position of the crosslink connectors may improve the stent&#39;s flexibility, giving a uniform flexibility in the whole structure when the stent graft is bent or kinked. The uniform flexibility may be assisted by the sleeve (e.g., membrane) and the link between the rings through the omega-shaped crosslink connectors. 
     The stent devices described herein are highly flexible, and may be bent over a tight radius of bending without kinking. For example,  FIGS.  14 A and  14 B  illustrate the resistance to crushing of these stents. In  FIG.  14 A , the graph illustrates compression at 50% of the dimeter of the stent, which occurs when a force of about 7.5 N is applied. The test shown in  FIG.  14 A  was performed until the stent was compressed approximately 50% of its length. As shown in  FIG.  14 B , the maximum force reached was about 9.5 N. 
     The mechanical properties, including the flexibility and resistance to kinking, was apparent when compared to other prior art stents having similar dimensions. For example,  FIG.  15 A- 15 C  illustrate various prior art stents in which the flexibility was examined when bending the stents 90 degrees with a very short radius of bending (bending at almost a right angle). For example,  FIG.  15 A  shows bending of a first prior art stent  1501 , showing an 8×58 mm stent (“LifeStream” covered stent by CR Bard, having a sinusoidal stent pattern with an offset connector between adjacent rows of sinusoids). This stent kinked  1503  at tight bend radius, as shown. Similarly,  FIG.  15   , showing an 8×59 mm prior art stent  1505  (“Advanta V12” covered stent by Getinge is a PTFE covered stent having an open cell pattern of adjacent zig-zags interconnected by longitudinal links); this stent also kinked  1507 . The prior art stent  1509  in  FIG.  15 C  (“BeGraft” covered stent by Bentley, having a repeating pattern of curly bracket-shapes) also kinked  1511 , though less than the devices in  FIGS.  15 A and  15 B . 
     In contrast the stent devices described herein do not appreciably kink. For example a covered stent device having a plurality of adjacent rings arranged transverse to a length of the device, wherein each ring is a ring comprising length of material arranged radially around the length of the stent device as a plurality of repeating biphasic cells, as described above, when bent 90 degrees over the same bend radius did not kink, as shown in  FIGS.  16 A and  16 B . In  FIG.  16 A , the 5×38 mm stent  1601  did not kink at the bend  1603 , in contrast to the prior art devices. Similar result were seen with a 10×58 mm stent  1605 , as shown in  FIG.  16 B  and with 5×38 mm and 8×38 mm stents (not shown). The stent devices described herein flexed without kinking or exhibiting a diameter reduction of greater than 50% when bent up to at least 90 degrees over a short length, as shown, in contrast to prior art devices. 
     Because the stents described herein also have both a high flexibility, high resilience and a high resistance to kinking, these stents are highly navigable, able to navigate even the most tortious vessels. Navigability testing was performed on the exemplary stent devices described herein. The navigability test consists of introducing a catheter with the stent covered with PTFE in a device that simulates the peripheral arterial vasculature, such as the device (“jig”) shown schematically in  FIG.  17 A . The test was performed by a physician specialized in stenting technique. The result of the tests is qualitative, but showed extremely high degrees of navigability and flexibility. The devices described herein were successfully deployed in vessels having diameters of between 3-8 mm (e.g., 3, 4, 6 and 8 mm respectively). For example,  FIG.  17 B  shows an example of a navigability test in which a catheter including a stent  1701  was navigated through a tortious model of a vessel relatively easily. The model used has more complex trajectories than typical peripheral human anatomy. A catheter with a stent graft was navigated smoothly through the device, including through regions of high tortuosity without damage and remained positioned in the catheter. The stent graft has adequate flexibility to traverse complex trajectories, including 30 degree, 45 degree, 60 degree and 90 degree bends. 
     In general, the stents described herein may be any appropriate size (e.g., unexpanded diameter, expanded diameter, and length). The configuration of repeating biphasic cells and crosslink connectors, including both S-shaped and omega shaped, described herein may be particularly well suited for smaller diameter (e.g., 7m or less) and/or smaller length (e.g., 40 mm or shorter) devices.  FIGS.  18 A- 18 D  each provide example parameters for four different examples of stents as described herein. All of these exemplary stents were made as covered stents, with an ePTFE sheath (in this case the sheath encapsulated the stent frame as described above). For example,  FIG.  18 A  describes a 5×18 mm stent graft having an initial (unexpanded) diameter of 2.1 mm and final (30 seconds after removal of the balloon) diameter of 5.0 mm.  FIG.  18 B  describes a similar 5×38 mm device, having a starting diameter of about 2.2 mm and a final (30 seconds after removal of the balloon) of about 4.9 mm.  FIG.  18 C  shows an example of a 6×18 mm stent, and  FIG.  18 D  shows an example of a 6×38 mm stent device. In general, all of these devices went from an unexpanded configuration to an expanded configuration of greater than 2×the unexpanded configuration yet had less than 7% foreshortening (e.g., less than 6.5%, less than 6%, less than 5.5%, etc.). 
       FIGS.  19 A- 19 C  compares the relative positions of crosslink connectors and differing types of crosslink connectors in different exemplary stent devices, where each stent is oriented with the distal end of the device at the top of the figure, and the proximal end of the device at the bottom of the figure, shown vertically here. In  FIG.  19 A , the exemplary stent device  1910 , similar to that of  FIG.  1 D , is shown. The repeating biphasic cells (unit cell) are as described above in  FIG.  1 D , and may have similar dimensions. The crosslink connectors in this embodiment are omega shaped crosslink connectors, which further include L-segments, permitting the connection with each flattened top/bottom to be perpendicular. The distribution of the crosslink connectors for each connecting portion, which comprises a ring and the crosslink connectors connected thereto, varies in an A-B-A-B pattern, and also is distributed around the center point radially. That is, viewing down a vertical center line  1907  of the stent, the crosslink connectors are distributed in a symmetrical or mirrored arrangement about the center line  1907 . In  FIG.  19 A , the ring connector arrangement for the most proximal ring  1905  and the more distal adjacent ring  1903  is specifically pointed out. For this exemplary device, each ring has 5 repeating units with alternating open trapezoids facing distally and proximally. For ring  1905 , ring connector  1902  is connected from a center point of a flattened top of ring  1905  to a center point of a flattened bottom of ring  1903 , where the flattened top is of ring  1905  is the second flattened top from the center line. The other ring connector  1904  of this connecting portion similarly connects from the center of a second flattened top to the right of the center line  1907 , to a center point on a flattened bottom of ring  1903 , which is offset further away from the center line  1907  than the site of connection on the flattened top on ring  1905 . Looking at the crosslink connectors between ring  1901  and  1903 , the connection points of ring connector  1906  are shifted one flattened top/flattened bottom unit closer to the right towards the center line  1907 . The corresponding ring connector  1908  is symmetrically shifted to connect between the rings  1901  and  1903  one flattened top/flattened bottom unit closer to the left towards the center line  1907 . As shown in  FIG.  19 D , the patterns  1941 ,  1943  repeat each alternating row throughout the length of the stent in the A-B-A-B pattern about the center line  1907  and are symmetrical with respect to a centerline of stent  1930 . 
       FIG.  19 B  shows a different exemplary stent  1920 , which has the same dimensions and has the same crosslink connectors, e.g., omega shaped crosslink connectors. However, in this device, the distribution of the crosslink connectors is configured differently. Ring connector  1912  connects from a center point of a flattened top of ring  1915  to a center point on a flattened bottom of ring  1913  offset away from the center line  1917  relative to the point of connection of ring connector  1912  onto ring  1915 , which itself is the second flattened top of ring  1915  to the left of the center line  1917 . Ring connector  1914 , also connecting from ring  1915  and connecting to ring  1913 , is now designed to connect from a center point of a flattened top of ring  1915  just to the right of the centerline  1917 , and connects to a center point on a flattened bottom of ring  1915 , which is offset, and is located right along the centerline  1917 . The connector  1916  connects from ring  1913  to ring  1911 , and connects from a center point on a flattened top of ring  1913  just to the left of the center line to a center point on a flattened bottom of ring  1911  offset and further to the left away from the centerline, relative to the connection point on ring  1913 . The connector  1918  connects from a center point on the second flattened top to the right of the center line of ring  1913 , to a center point on a flattened bottom of ring  1911 , which is offset to the left of the connection point on ring  1913 . The pattern of ring connector connection points between ring  1913  and ring  1911  is shifted diagonally compared to the connection points of crosslink connectors between ring  1915  and ring  1913 , as shown in  FIG.  19 E . In this example, the diagonal shift is one unit cell shift to the right, proceeding from distal to proximal, for patterns  1945 ,  1947 . The distribution can also be described as shifting radially (e.g., circumferentially) by one unit cell. As shown in the additional rings, the patterns  1945 ,  1947  shifts to the right, then reverses to the left, yielding an ABCBA pattern, looking from distal to proximal. 
       FIG.  19 C  shows yet another exemplary stent device  1930 . This device includes unit cells having a different shape from that of device  1910 ,  1920 . Each flattened top and bottom are connected via intermediate or connecting regions having a more pronounced curve such as a pair of sigmoid curves, and the unit cell is more symmetrically shaped from flattened top to flattened bottom. The length of the unit cell, from the top of the flattened top to the base of the flattened bottom is longer, e.g., 3 mm compared to 2 mm for the same dimension in device  1910 ,  1920 . The width, radially or circumferentially, of the unit cell of device  1930  is smaller (1.49 mm) compared to that of devices  1910 ,  1920  (1.70 mm). In this exemplary stent, the length, proximally to distally, is 16.6 mm. The crosslink connectors of this device are S-shape crosslink connectors and attach to a point offset from the center point of a flattened top or flattened bottom. The offset point may be at the curved region defining one end of the flattened top or flattened bottom. The space between successive rings for device  1930  is larger (0.4 mm) compared to the space between successive rings for device  1910 ,  1920  (0.28 mm). Further, the S-shape crosslink connectors connect to the adjacent ring in a direction aligned parallel to the center line of the device, and are not connected in an offset direction, ring to ring. In this exemplary device, two S shape crosslink connectors also are used to connect a ring to an adjacent ring. The S-shape crosslink connectors  1922 ,  1924 , which connect from ring  1929  to ring  1925 , are connected to flattened bottoms along the ring  1925 , separated by two other flattened bottoms. S-shape crosslink connectors  1922 ,  1924  are non-symmetrically disposed relative to the centerline  1927 . The S shape crosslink connectors  1926 ,  1928  which connect from ring  1925  to ring  1923 , are connected to two flattened bottoms shifted by one-unit cell to the left, relative to crosslink connectors  1922 ,  1924 , and are symmetrically disposed relative to the centerline and are separated from each other by the same distance of two flattened bottoms separation. The same shift to by one unit cell to the left, distal to proximal is seen in the positions of the S shape connectors  1932 ,  1934 , which connect ring  1923  to ring  1921 , and shown in  FIG.  19 F , marked as patterns  1951 ,  1953 ,  1955 . The pattern for this stent device is an ABC repeat, and is directed in a leftward direction, from distal to proximal. Without wishing to be bound by theory, this design affords a less rigid stent, due at least to the non-offset nature of the connections made by the crosslink connectors, ring to ring, and to the increased length of the unit cells, e.g. a given length of stent will have fewer crosslink connectors connecting adjacent rings. 
       FIGS.  20 A-C  show another exemplary stent  2010 .  FIG.  20 A  illustrates a side view of exemplary stent  2010  in an un-expanded (e.g., delivery) configuration, stent  2010  having a first end  12  (e.g., proximal end) and a second end  14  (e.g., distal end) and a length, L; thus stent  2010  has a longitudinal axis LA extending through a lumen defined by the stent. Stent  2010  includes a plurality of annular supports  2022  (“rings”) transverse to the long axis and generally axially spaced from at each other; the individual regions are connected by at least one ring connector  2020  (e.g., S-shape ring connector). In this example, an annular support is “adjacent” to another annular support if it is the next annular support when moving towards either the first end  12  (proximal) or the second end  14  (distal). In this example, the annular supports  2022  (which may also be referred to herein as “rings”) are connected to at least one adjacent support  2022  by a ring connector  2020  (S-shape ring connector). The rings  2022  may be described herein as being “connected” to adjacent rings; for ease of discussion a ring and a plurality of crosslink connectors, e.g., one or more S-shape crosslink connectors, which connect the ring to an adjacent ring may be referred to as a connecting portion. In this example, there are two S-shape crosslink connectors connecting each ring to the ring adjacent to it. The rings and the crosslink connectors are understood to be integrally formed with the rings, such as where the entire stent may be manufactured from a single piece of starting material, e.g., by laser cutting a cylindrical piece. 
     Each of the rings  2022  in this embodiment has a wave configuration, with a plurality of two peaks and two valleys, repeating in a pattern (only some peaks and valleys are labeled for clarity). In this embodiment, peaks of the supports  2022  may extend to the same location along the length of the stent. Valleys of supports (rings) also extend to the same location along the length of the stent. Thus, the peaks (e.g.,  2024  and  2025 ) may be aligned along the length of the stent device, shown, and the valleys (e.g.,  2024 ′ and  2025 ′) may also be aligned along the length of the stent. Peaks and valleys of the waves may define flattened, or squared, ends  2028 . This embodiment is an example of at least one annular support with a repeating wave pattern having flattened ends connected by curvilinear intermediate sections. 
     In this embodiment, the annular supports all have the same configuration along the length of the stent. Two peaks  2025  produce a closed head (top)  2026 , enclosing a shape with a proximal-facing opening, and two valleys  24 ′ define the interior of a closed head (bottom)  2027 , having a distal-facing opening. In some variations, not every annular support has the same configuration as every other annular support.  FIG.  20 B  shows the inner diameter of stent  2010  is 2.53 mm and the outer diameter is 2.77 mm. 
       FIG.  20 C  illustrates an expanded, flattened/planar view of the region A of a stent device  2010  of  FIG.  20 A , which illustrates the connections between adjacent rings. In this embodiment, the region between two adjacent rings  2022  are connected by at least two crosslink connectors, e.g., S-connectors), and only a portion of the rings  2022  are shown. The ring connector  2020  has a “S” configuration. In this embodiment, the general “S” configuration is defined by two arcs  2031  and  2033  connected by a linear region  32 . The S-shape ring connector  2020  and adjacent annular supports  2022  are connected along a lateral radius of heads (flattened tops)  2026  and  2027 . The proximal part of the S-shaped ring connector  2020  connects with a downward-directed radius of the closed head  2026  however the distal part of the S-shape ring connector  2020  connects with a upward-directed radius of the bottom closed head  2027 . 
     The “S” shape may include two arcs  2031  and  2033  connected by a midpoint (which may include a linear region and/or a point of inflexion  2032  between the two curving regions. Curves  2031  and  2033  can have slightly varying configurations and the S-shape ring connector can still have a general “S” configuration as used herein. 
     As can be seen in  FIG.  20 A , the S-shaped connectors may all have similar configurations, and may all be oriented in the same direction. Alternatively in some variations the S-shaped connectors may have different configurations (shapes, radius of curvatures for the first and second arcs, etc.), including different thicknesses. In this embodiment, each pair of adjacent supports  2022  is coupled together by two S-shaped crosslink connectors  2020 , each of which has the configuration shown in  FIG.  20 C . 
       FIGS.  20 D and  20 E  illustrate an enlarged view of a unit cell that may be repeated to form the rings of a stent such as the stent example shown in  FIGS.  19 C,  19 F,  20 A,  21 ,  25 A,  26 A,  27 A,  28 A,  30  and  31 A . In  FIG.  20 E , the rings of  FIG.  20 A  may be formed of a length of material (e.g., metallic and or polymeric material) that forms, around the radius of the stent, a pattern of repeating biphasic cells, as shown in  FIG.  20 E . The repeating biphasic cells  2001  typically include a pair of flattened top regions  2003 ,  2005  that are connected by an intermediate region  2007 . In some variations the flattened top regions each form an open trapezoidal portion. In  FIG.  20 E , the first open trapezoidal portion includes a first side or leg  2009 , a second side (corresponding to the flattened top  2003 ), and a third side or leg  2015 . This open trapezoidal portion has a distal-facing opening  2017 . Similarly, a second open trapezoidal portion, oriented 180 degrees off of the first open trapezoidal portion, includes a fourth side  2019 , a fifth side (corresponding to the flattened top  2005 ), and a sixth side or leg  2023 . The second open trapezoidal portion has a proximal-facing opening  2018 . The first and second open trapezoidal portions may be connected by intermediate regions  2007 . For example, the third side  2015  of the first open trapezoidal portion may be connected to the fourth side  2019  of the second open trapezoid portion by a connector region  2007 , as shown, and the first side of the first open trapezoidal portion  2009  is connected to the sixth side of a second open trapezoidal portion of the next biphasic cell. The connector regions may be generally straight, and/or may be curved including s-shaped, so as to connect to the side of two trapezoidal regions. 
     As mentioned above, the trapezoidal regions may be referred to as trapezoidal as they have a flattened top, two generally straight sides, and an open bottom. The connections between the top and bottom may be rounded, as shown in  FIG.  20 E . 
     The first open trapezoidal portion and the second open trapezoidal portion may have different ‘trapezoidal’ shapes, as mentioned above. For example, in  FIG.  20 E , the first and second open trapezoidal shape is approximately isosceles trapezoidal, and open on one side. Both the first and second open trapezoidal portions in the exemplary biphasic cell shown in  FIGS.  20 D and  20 E  are the same general shape, although the trapezoidal portion having a proximal-facing opening has walls that are more angled relative to the flat top(s). 
     As can be seen in  FIG.  21   , the S-shaped crosslink connectors  2020  in any given connecting portion of stent  2010  are not circumferentially aligned with the connectors in the adjacent connecting portion, but they are circumferentially aligned with the connectors in the third adjacent connecting portion. In this embodiment, the position of the S-shape crosslink connectors  2020  are in an A-B-C-A-B-C pattern, with every third ring  2022  where the respective crosslink connectors are circumferentially aligned. Additionally, for stent  2010  of  FIGS.  20 A- 20 C , and  FIG.  21   , the unit cell high is 2.2 mm and the width are 1.45 mm. 
     In some variations, only three or fewer (e.g., two) connectors are used to connect adjacent rings. For example, by having only two connectors in each connecting region, there may be less area of material than in some other stent designs. This smaller area may allow the stent to have more flexibility and can expand to a greater extent when forces are applied on the stent such as by an expansion balloon. In alternative embodiments, however, there could be more than two connectors in a connecting portion, and the desired flexibility could still be maintained by modifying one or more other aspects, such as, for example without limitation, one or more dimensions (e.g., thickness, radius), configuration, or material. 
     The stent apparatuses described herein, an in particular, the stent apparatuses having an s-shaped connector (and in some variation the longer unit cells such as those shown in  FIGS.  20 A- 20 E ) may expand to a radial diameter that is slightly larger than others. For example, in some variations, the radial expansion may be up to 12 mm or more (e.g., up to 11 mm, up to 10 mm, etc.). 
       FIGS.  22 A and  22 B  compare dimensions for the respective detail region A for the device of  FIGS.  19 A- 19 B  and  FIG.  19 C ,  FIGS.  20 A-C ,  FIG.  21    respectively. In  FIG.  22 A , detail region  2210  shows the width  2213  of omega shaped crosslink connectors is 0.05 mm, and the length of perpendicular portion  2215  of the L-segment of the omega shape ring connector permitting perpendicular connection to the flattened bottom or flattened top is 0.12 mm. The other cross-wise portion  2217  of the L-segment is 0.32 mm. In  FIG.  22 B , the S-shape ring connector of the stent device of  FIGS.  20 A-C ,  FIG.  21    has a much simpler design, and the detail region  2220  shows that the S shape ring connector has a width  2223  that is 0.06 mm. The additional dimensions are described as above. For all of devices of  FIG.  19 A- 19 C .  FIGS.  20 A-C ,  FIG.  21   , the width of the materials forming the unit cells is the same for all of these stent devices at 0.14 mm. 
       FIGS.  23 A and  23 B  show stress distribution models for the omega-shape ring connector and the S shape ring connector respectively. In  FIG.  23 A , region  2303  shows a lighter colored region which indicates increased stress at the inside curve of the “omega” portion of the omega shape ring connector. A larger region  2305  on the underside of L-shaped portion of the omega curve, shows stress from torque exerted by its connection to the two rings. A central region  2307  has a more intense region of stress. In contrast,  FIG.  23    B shows the S-shape ring connector. There are no regions of stress at all, and the darker colors represent lower stress than the medium coloration. 
       FIGS.  24 A and  24 B  show stress distribution models for the unit cell shown of devices of  FIG.  19 A,  19 B  and  FIGS.  19 C,  20 A -C,  21  respectively.  FIG.  24 A  shows regions  2403  and  2405 , located at the center of flattened bottoms/flattened tops of unit cells of  FIG.  19 A,  19 B  having increased stress both at the inside edge  2403  and outside edge  2405  of the feature. The area near the union between the unit cell and the omega shaped ring connector is an area where high stresses values can be observed. In the stent  1930  of  FIG.  19 C  and other stents like it (FIGS.  20 A- 20 C,  21 , incorporating the change in the location of the connection, between the unit cell and the ring connector, eliminates stress in the unit cell. 
     In contrast,  FIG.  23 B  shows a model of the flattened top/flattened bottom of the unit cell of  FIG.  19 C ,  FIGS.  20 A- 20 C , where no stress at all develops. 
       FIG.  25 A  shows an exemplary stent device  2310  like the stent device of  FIG.  19 C , and has similar dimensions and features as described for device  1930 ,  2010 . Two S-shape crosslink connectors are used to connect one ring to the ring adjacent, and span a distance of 0.4 mm. The pattern of crosslink connections is similar to device  1930 ,  2010 , having an ABC repeat pattern, and non-offset connection between rings. The dimensions of the stent  2510  is 10 mm by 16.6 mm long. Region A of  FIG.  25 A  is shown in greater detail in  FIG.  25 B  and has the same dimensions of width of the material forming the unit cells (flattened top/flattened bottom) of 0.14 mm and the width of the S shape ring connector of 0.06 mm, as that of stent  1930 .  FIG.  25 C  shows the inner diameter  2513  (2.61 mm) and outer diameter  2515  (2.85 mm) of the unexpanded stent  2510 . 
     The initial outer dimension  2515  of the stent is shown as 2.83 mm (see, e.g.,  FIG.  25 C ), as opposed to 2.76 mm in the embodiment in  FIGS.  20 A-B . The initial larger outer dimension allows the stent in this embodiment to be expanded to larger outer dimensions without fracturing. Another difference is the height and the width of the unit cell. As shown in  FIGS.  20 A-B , the unit cell high is 2.2 mm and the width are 1.45 mm however in the case of the  FIGS.  25 A- 25 C , the unit cell is 3 mm high and 1.49 mm wide. 
       FIGS.  26 A- 26 C  show another exemplary stent device  2610 , having dimensions of 10 mm by 23.4 mm. The unit cells are similar to the unit cells of stent devices  1930 ,  2010  and  2510 , having the same dimensions, same number of S shape crosslink connectors, distance connected across by the crosslink connectors, and pattern of ring connector location, and alignment (ABC repeat). The location of contact with the flattened bottom and flattened top is the mirror image of devices  1930 ,  2510 , connecting from the left side of the flattened top to the right side of the flattened bottom of unit cells on each ring.  FIG.  26 B  shows the detail region A from  FIG.  26 A , and shows the same dimensions for the length of material forming the unit cells and the S shape crosslink connectors as for device  1930 ,  2010 ,  2310 .  FIG.  26 C  shows the dimensions of the unexpanded stent  2610 , having an inner diameter  2613  of 2.61 mm, and an outer diameter  2615  of 2.85 mm. 
       FIGS.  27 A- 27 C  show another exemplary stent device  2710 , having dimensions of 10 mm by 26.8 mm long. The unit cells are similar to the unit cells of stent devices  1930 ,  2510 ,  2610 , having the same dimensions, same number of S shape crosslink connectors, distance connected across by the crosslink connectors, and pattern of ring connector location, and alignment (ABC repeat). The location of contact with the flattened bottom and flattened top is the same as for stent device  2610 .  FIG.  27 B  shows the detail region A from  FIG.  27 A , and shows the same dimensions for the length of material forming the unit cells and the S shape crosslink connectors as for device  1930 ,  2510 ,  2610 .  FIG.  27 C  shows the dimensions of the unexpanded stent  2710 , having an inner diameter  2713  of 2.61 mm, and an outer diameter  2715  of 2.85 mm. 
       FIGS.  28 A- 28 C  show another exemplary stent device  2810 , having dimensions of 10 mm by 33.6 mm long. The unit cells are similar to the unit cells of stent devices  1930 ,  2510 ,  2610 ,  2710  having the same dimensions, same number of S shape crosslink connectors, distance connected across by the crosslink connectors, and pattern of ring connector location, and alignment (ABC repeat). The location of contact with the flattened bottom and flattened top is the same as for stent device  2610 ,  2710 .  FIG.  28 B  shows the detail region A from  FIG.  28 A , and shows the same dimensions for the length of material forming the unit cells and the S shape crosslink connectors as for device  1930 ,  2510 ,  2610 ,  2710 .  FIG.  28 C  shows the dimensions of the unexpanded stent  2610 , having an inner diameter  2813  of 2.61 mm, and an outer diameter  2815  of 2.85 mm. 
       FIGS.  29 A- 29 C  show another exemplary stent device  2910 , having dimensions of 10 mm by 57.4 mm long. The unit cells are similar to the unit cells of stent devices  1930 ,  2510 ,  2610 ,  2710 ,  2810 , having the same dimensions, same number of S shape crosslink connectors, distance connected across by the crosslink connectors, and pattern of ring connector location, and alignment (ABC repeat). The location of contact with the flattened bottom and flattened top is the same as for stent device  2610 ,  2710 ,  2810 .  FIG.  29 B  shows the detail region A from  FIG.  29 A , and shows the same dimensions for the length of material forming the unit cells and the S shape crosslink connectors as for device  1930 ,  2510 ,  2610 ,  2710 ,  2810 .  FIG.  29 C  shows the dimensions of the unexpanded stent  2910 , having an inner diameter  2913  of 2.61 mm, and an outer diameter  2915  of 2.85 mm. 
       FIG.  30    shows a finite-element simulation of stent expansion for the stent  2910  of  FIGS.  29 A- 29 C , having expanded dimensions of 10 mm by 57.4 mm long. 
       FIGS.  31 A- 31 C  show another exemplary stent device  3110 , having dimensions of 10 mm by 77.8 mm long. The unit cells are similar to the unit cells of stent devices  1930 ,  2510 ,  2610 ,  2710 ,  2710 .  2910 , having the same dimensions, same number of S shape crosslink connectors, distance connected across by the crosslink connectors, and pattern of ring connector location, and alignment (ABC repeat). The location of contact with the flattened bottom and flattened top is the same as for stent device  2610 ,  2710 ,  2810 ,  2910 .  FIG.  31 B  shows the detail region A from  FIG.  31 A , and shows the same dimensions for the length of material forming the unit cells and the S shape crosslink connectors as for device  1930 ,  2510 ,  2610 ,  2710 ,  2610 ,  2810 .  FIG.  31 C  shows the dimensions of the unexpanded stent  3110 , having an inner diameter  3113  of 2.61 mm, and an outer diameter  3115  of 2.85 mm. 
     Performance Testing 
     In general, the biphasic arrangement of trapezoidal unit cells forming each ring of the stent, as well as the configuration and arrangement of the s-shaped connectors connecting adjacent rings of the stent, may allow these devices to expand while maintaining their radial compression strength and longitudinal compression strength with a minimal recoil and stent foreshortening.  FIGS.  32 A- 36    illustrate the result of performance testing of the stents described herein and comparisons with other (e.g., prior art) stents. The results show an improvement in performance for all sizes of the improved stents described herein as compared to prior art stents of comparable sizes. This testing was done to ISO standards, such as ISO 25539. 
     A variety of differently-sized stents having a plurality of rings formed of biphasic open trapezoidal shapes (alternating distal-facing and proximal-facing trapezoidal shapes), such as shown in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C , in which the rings are connected by s-shaped connectors in a helical pattern were characterized and compared to each other as well as to known stents (such as the GORE TIGRIS vascular stent, BARD LIFESTENT Vascular stent, CORDIS S.M.A.R.T CONTROL stent, COVIDIEN PROTÉGÉ EVERFELX stent, Abbott ABSOLUTE PRO LL vascular stent, OptiMed SINUS-SUPERFLEX stent, COOK ZILVER PTX stent, and IDEV SUPERA stent). 
       FIGS.  37 A- 37 C  illustrate an example of a stent  3700  similar to that shown in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C , described above. In the example of a stent shown in  FIG.  37 A , the stent  3700  is expanded into the second configuration by the expansion of a balloon  3703 . The stent includes a plurality of rings  3705  that are adjacent to each other and connected by s-shaped connectors; in  FIGS.  37 A- 37 C  the stent is covered by a sleeve  3709  (e.g., graft) material. The rings are arranged transverse to the length (distal-to-proximal length) of the stent. The plane of each ring is transverse and perpendicular to the length. Each ring is formed of a repeating pattern of alternating flattened tops and flattened bottoms extending transverse to the length of the device, wherein the flattened tops are connected to the flattened bottoms by sigmoid-shaped region (connector) so that each flattened top forms part of a proximal-facing U-shape and each flattened bottom forms part of a distal-facing U-shape. The top, bottom and sigmoid-shaped regions are all continuous regions of the same length of material (e.g., wire, laser-cut tube, etc.). These shapes may also be described as a plurality of repeating biphasic cells, in which each biphasic cell includes a first open trapezoidal portion having a first side, a second side (e.g., top), and a third side forming a proximal-facing opening, and a second open trapezoidal portion having a fourth side, a fifth side (e.g., bottom) and a sixth side forming a distal-facing opening. The second side and the fifth side may be arranged in parallel (e.g., the top and bottom may be transverse to the length of the stent in the relaxed configuration). The first open trapezoidal portion is radially offset from the second open trapezoidal portion and the third side of the first open trapezoidal portion is connected to the fourth side of the second open trapezoidal portion by a first connector region. The first side, fourth side and connector region correspond to the sigmoidal connector. The first side of the first open trapezoidal portion connects to a sixth side of an adjacent biphasic cell in the ring by a second connector, so that the biphasic trapezoidal pattern repeats to form the ring. 
     The s-shaped connectors connecting adjacent rings, as described above, may connect a region between one of the flattened tops and one of the sigmoid-shaped connectors (e.g., between a first and second side) on one of the rings to a region between one of the fattened bottoms and one of the sigmoid-shaped connectors (e.g., between a fourth and fifth side) on an adjacent ring. 
     The stents described herein may be formed of a metallic and/or polymeric material. For example, in some variations the stent may be formed of a Co—Cr Alloy (e.g., L605) which may be coated/covered with a sleeve of graft material (e.g., PTFE, such as “BIOWEB”) that may be electrospun coated, e.g., to an average weight of between about 10 g/m 2  and 15 g/m 2 . The diameter (e.g., outer diameter, OD) may be between 5 mm and 10 mm (e.g., between about 6-7 F) and may have a length of between about 18 mm and 59 mm. The crimped profile may be small (e.g., approximately 2 mm), and the stent may have a high retention force and high flexibility, even when coated on both the inside and outside with the graft material (e.g., PTFE). Without the particular configuration of the rings and crosslink connectors (e.g., s-shaped connectors) described herein, these properties may be difficult or impossible to achieve. 
     Thus, the arrangement of the stent components, and in particular the combination of shapes forming the rings and the s-shaped connectors, may provide a stent with advantageous properties as compared to other configurations, including more traditional prior art stents. For example, the radial compressive properties may be superior, providing a high crush strength. For example,  FIG.  32 A  shows the results of radial compression testing on three different sizes (5×18 mm, 8×38 mm and 10×58 mm), with and without a graft (e.g., sleeve) of the improved stent described herein, and shown generally in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C , above. The average crush resistance is estimated by the necessary force to provide some percentage (e.g., 25%, 50%, etc.) of radial compression. In these examples the radial compression testing (e.g., performed between parallel plates) showed an average of crush resistances (radial stiffness) that was between about 3N (e.g., about 3.1 N, about 3.5 N, etc.) or about 300 grams force (gf) (e.g., about 310 gf, about 350 gf, etc.) and about 6.5 N (e.g., about 6.2 N, about 6.0 N, about 5.9 N, etc.) or about 650 gf (e.g., about 620 gf, about 600 gf, about 590 gf, etc.) to cause 25% radial compression. This range may provide advantages in compressing without kinking (see, e.g.,  FIGS.  16 A- 16 B , described above), or reducing the diameter less than 2 mm, while still remaining highly flexible and compliant. In comparison, prior art devices, as shown in  FIG.  32 B  in the same radial compression testing had a necessary force to radial compression (e.g., necessary force to 25% radial compression, per ISO 25539 testing) that was substantially less than this range (e.g., less than about 3 N for the GORE TIGRIS vascular stent, BARD LIFESTENT Vascular stent, CORDIS S.M.A.R.T CONTROL stent, COVIDIEN PROTEGE EVERFELX stent, Abbott ABSOLUTE PRO LL vascular stent, OptiMed SINUS-SUPERFLEX stent, COOK ZILVER PTX stent and BARD LUMINEXX stent) or much higher than this range (e.g., greater than 10 N for the IDEV SUPERA stent). In  FIG.  32 B , the lower values typically represent lower radial stiffness, while the higher values represent higher radial stiffness. 
     Similar testing for longitudinal compression is shown in  FIGS.  33 A and  33 B . In this example, the same stent designs and sizes tested in  FIG.  33 A  were examined to determine average longitudinal stent compression. The graph in  FIG.  33 A  represents the necessary force to cause 15% longitudinal compression following standard (ISO 25539) testing.  FIG.  33 B  shows a comparison to the same prior art stents described in  FIG.  32 B . The lower values represent a lower compression force while higher values show a higher compression force. The longitudinal compression forces for the stents described herein (shown by “*” for 5×18 mm, 8×38 mm and 10×58 mm stents in  FIG.  33 B ) are comparable to those of the prior art stents tested (having similar ranges of lengths). 
     The crimping and expanding of the stents described herein were also examined and compared to prior art stents. As shown in  FIGS.  34 A- 34 B , the stents described herein (e.g., 5×18 mm, 8×38 mm, and 10×58 mm) all showed stent crimp profiles that were equivalent or superior to those of prior art stents (see,  FIG.  34 B ), having a crimp stent diameter of less than about 2.25 mm (e.g., less than 2.2 mm, less than 2.15 mm, less than 2.10 mm, etc.) and greater than about 1.5 mm (e.g., 1.7 mm 1.8 mm, etc.). Thus, the improved stents described herein may be crimped down onto a balloon for later expansion at narrower diameters while expanding to equivalent diameters with relatively low force. 
     In addition, the stents described herein (e.g., as shown in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C, and  37 A- 37 C ) typically have a much lower stent recoil following balloon expansion than prior art stents. This was tested for different dimensions of the stents described herein, including 5×18 mm and 10×58 mm stents, as shown in the table of  FIG.  35 A .  FIG.  35 B  illustrates the formula for calculating the percentage of stent recoil (e.g., the difference between the inflated outer diameter and the final outer diameter divided by the inflated outer diameter, expressed as a percentage). In  FIG.  35 B  the percent recoil of these new (indicated by “*”) stents of different dimensions is shown compared to a typical range of prior art stents. The percent stent recoil for the new stents is less than 5% (e.g., less than 4.8%, less than 4.6%, etc.), which may be advantageous in maintaining placement and stability when using the stent. 
     Similarly, the improved stents described herein (e.g., as shown in  FIGS.  20 A- 20 E,  21 ,  22 B,  23 B,  25 A- 31 C, and  37 A- 37 C ) have a relatively low percent of stent foreshortening from the compressed (crimped) to the expanded configuration, as graphically illustrated in  FIG.  36   .  FIG.  36    also shows the equation for estimating percent foreshortening (e.g., the difference between crimped stent length and expanded stent length, divided by the crimped stent length, and expressed as a percentage). In general, the percent foreshortening was less than 8.5% (e.g., less than about 8.4%). This also compares favorably to existing prior art stents, which may shorten more when transitioning between crimped and expanded configurations, resulting in a less predictable and stable implantation into the vessel. 
     When a feature or element is herein referred to as being “on” another feature or element, it can be directly on the other feature or element or intervening features and/or elements may also be present. In contrast, when a feature or element is referred to as being “directly on” another feature or element, there are no intervening features or elements present. It will also be understood that, when a feature or element is referred to as being “connected”, “attached” or “coupled” to another feature or element, it can be directly connected, attached or coupled to the other feature or element or intervening features or elements may be present. In contrast, when a feature or element is referred to as being “directly connected”, “directly attached” or “directly coupled” to another feature or element, there are no intervening features or elements present. Although described or shown with respect to one embodiment, the features and elements so described or shown can apply to other embodiments. It will also be appreciated by those of skill in the art that references to a structure or feature that is disposed “adjacent” another feature may have portions that overlap or underlie the adjacent feature. 
     Terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. For example, as used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and/or groups thereof. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items and may be abbreviated as “/”. 
     Spatially relative terms, such as “under”, “below”, “lower”, “over”, “upper” and the like, may be used herein for ease of description to describe one element or feature&#39;s relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is inverted, elements described as “under” or “beneath” other elements or features would then be oriented “over” the other elements or features. Thus, the exemplary term “under” can encompass both an orientation of over and under. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. Similarly, the terms “upwardly”, “downwardly”, “vertical”, “horizontal” and the like are used herein for the purpose of explanation only unless specifically indicated otherwise. 
     Although the terms “first” and “second” may be used herein to describe various features/elements (including steps), these features/elements should not be limited by these terms, unless the context indicates otherwise. These terms may be used to distinguish one feature/element from another feature/element. Thus, a first feature/element discussed below could be termed a second feature/element, and similarly, a second feature/element discussed below could be termed a first feature/element without departing from the teachings of the present disclosure. 
     Throughout this specification and the claims which follow, unless the context requires otherwise, the word “comprise”, and variations such as “comprises” and “comprising” means various components can be co-jointly employed in the methods and articles (e.g., compositions and apparatuses including device and methods). For example, the term “comprising” will be understood to imply the inclusion of any stated elements or steps but not the exclusion of any other elements or steps. 
     In general, any of the apparatuses and methods described herein should be understood to be inclusive, but all or a sub-set of the components and/or steps may alternatively be exclusive, and may be expressed as “consisting of” or alternatively “consisting essentially of” the various components, steps, sub-components or sub-steps. 
     As used herein in the specification and claims, including as used in the examples and unless otherwise expressly specified, all numbers may be read as if prefaced by the word “about” or “approximately,” even if the term does not expressly appear. The phrase “about” or “approximately” may be used when describing magnitude and/or position to indicate that the value and/or position described is within a reasonable expected range of values and/or positions. For example, a numeric value may have a value that is +/−0.1% of the stated value (or range of values), +/−1% of the stated value (or range of values), +/−2% of the stated value (or range of values), +/−5% of the stated value (or range of values), +/−10% of the stated value (or range of values), etc. Any numerical values given herein should also be understood to include about or approximately that value, unless the context indicates otherwise. For example, if the value “10” is disclosed, then “about 10” is also disclosed. Any numerical range recited herein is intended to include all sub-ranges subsumed therein. It is also understood that when a value is disclosed that “less than or equal to” the value, “greater than or equal to the value” and possible ranges between values are also disclosed, as appropriately understood by the skilled artisan. For example, if the value “X” is disclosed the “less than or equal to X” as well as “greater than or equal to X” (e.g., where X is a numerical value) is also disclosed. It is also understood that the throughout the application, data is provided in a number of different formats, and that this data, represents endpoints and starting points, and ranges for any combination of the data points. For example, if a particular data point “10” and a particular data point “15” are disclosed, it is understood that greater than, greater than or equal to, less than, less than or equal to, and equal to 10 and 15 are considered disclosed as well as between 10 and 15. It is also understood that each unit between two particular units are also disclosed. For example, if  10  and  15  are disclosed, then 11, 12, 13, and 14 are also disclosed. 
     Although various illustrative embodiments are described above, any of a number of changes may be made to various embodiments without departing from the scope of the disclosure as described by the claims. For example, the order in which various described method steps are performed may often be changed in alternative embodiments, and in other alternative embodiments one or more method steps may be skipped altogether. Optional features of various device and system embodiments may be included in some embodiments and not in others. Therefore, the foregoing description is provided primarily for exemplary purposes and should not be interpreted to limit the scope of the disclosure as it is set forth in the claims. 
     The examples and illustrations included herein show, by way of illustration and not of limitation, specific embodiments in which the subject matter may be practiced. As mentioned, other embodiments may be utilized and derived there from, such that structural and logical substitutions and changes may be made without departing from the scope of this disclosure. Such embodiments of the inventive subject matter may be referred to herein individually or collectively by the term “invention” merely for convenience and without intending to voluntarily limit the scope of this application to any single invention or inventive concept, if more than one is, in fact, disclosed. Thus, although specific embodiments have been illustrated and described herein, any arrangement calculated to achieve the same purpose may be substituted for the specific embodiments shown. This disclosure is intended to cover any and all adaptations or variations of various embodiments. Combinations of the above embodiments, and other embodiments not specifically described herein, will be apparent to those of skill in the art upon reviewing the above description.