Patent Publication Number: US-2023137909-A1

Title: Prosthetic heart valve

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     The present application is a Continuation-In-Part of:
         International patent application PCT/IL2018/050725 to Hariton et al., filed Jul. 4, 2018, and entitled “Prosthetic heart valve,” which is a Continuation-In-Part of U.S. patent application Ser. No. 15/956,956 to Jamberger et al., filed Apr. 19, 2018, and entitled “Prosthetic heart valve;”   U.S. patent application Ser. No. 16/135,969 to Hariton et al., filed Sep. 19, 2018, and entitled “Prosthetic valve with inflatable cuff configured for radial extension.” which claims benefit of U.S. provisional patent application 62/560,384 to Hariton et al., filed Sep. 19, 2017, and entitled “Prosthetic valve and methods of use;” and   U.S. patent application Ser. No. 16/135,979 to Hariton et al., filed Sep. 19, 2018, and entitled “Prosthetic valve with inflatable cuff configured to fill a volume between atrial and ventricular tissue anchors,” which claims benefit of U.S. provisional patent application 62/560,384 to Hariton et al., filed Sep. 19, 2017, and entitled “Prosthetic valve and methods of use.”       

     All of the above applications are incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     Some applications of the present invention relate in general to valve replacement. More specifically, some applications of the present invention relate to prosthetic valves for replacement of a cardiac valve. 
     BACKGROUND 
     Ischemic heart disease causes regurgitation of a heart valve by the combination of ischemic dysfunction of the papillary muscles, and the dilatation of the ventricle that is present in ischemic heart disease, with the subsequent displacement of the papillary muscles and the dilatation of the valve annulus. 
     Dilation of the annulus of the valve prevents the valve leaflets from fully coapting when the valve is closed. Regurgitation of blood from the ventricle into the atrium results in increased total stroke volume and decreased cardiac output, and ultimate weakening of the ventricle secondary to a volume overload and a pressure overload of the atrium. 
     SUMMARY OF THE INVENTION 
     For some applications, an implant is provided having a valve body that defines a lumen, an upstream support portion, and a plurality of legs. The implant is percutaneously deliverable to a native heart valve in a compressed state, and is expandable at the native valve. The implant comprises an inner frame and an outer frame. Typically, the upstream support portion is at least partly defined by the inner frame, and the legs are at least partly defined by the outer frame. The implant is secured at the native valve by sandwiching tissue of the native valve between the upstream support portion and the legs. For some applications, a flexible pouch extends radially outward from the valve body. For some such applications, the arms and the legs narrow the pouch therebetween to form a narrowed portion of the pouch, thereby dividing an interior space of the pouch into (a) an inner portion, radially inward from the narrowed portion, and in fluid communication with the lumen, and (b) an outer portion, radially outward from the narrowed portion, and in fluid communication with the inner portion via the narrowed portion. 
     There is therefore provided, in accordance with an application of the present invention, apparatus, including: 
     a frame assembly that includes:
         a valve body that circumscribes a longitudinal axis and defines a lumen along the axis;   a plurality of upstream arms that are coupled to the valve body at a first axial level with respect to the longitudinal axis, each of the arms extending radially outward from the valve body to a respective arm-tip; and   a plurality of downstream legs that are coupled to the valve body at a second axial level with respect to the longitudinal axis, and that extend radially outward from the valve body and toward the plurality of arms;       

     a plurality of prosthetic leaflets, disposed within the lumen, and arranged to facilitate one-way upstream-to-downstream fluid flow through the lumen, the first axial level being upstream of the second axial level; and 
     a flexible pouch that defines an interior space therein, the pouch shaped and coupled to the frame assembly such that:
         the pouch extends radially outward from the valve body, and   the arms and the legs narrow the pouch therebetween to form a narrowed portion of the pouch, so as to define:
           an inner portion of the interior space, radially inward from the narrowed portion, and in fluid communication with the lumen, and   an outer portion of the interior space, radially outward from the narrowed portion, and in fluid communication with the inner portion via the narrowed portion.   
               

     In an application, at the narrowed portion, the legs extend in an upstream direction past the arms. 
     In an application, the arms are disposed inside the pouch. 
     In an application, the arms and the legs are arranged such that, at the narrowed portion, the arms and the legs alternate circumferentially. 
     In an application, the inner portion of the interior space is in fluid communication with the lumen via a plurality of discrete windows defined by the apparatus. 
     In an application, the apparatus further includes a belt wrapped around the frame assembly downstream of the windows, circumscribing the lumen, each of the windows being bounded, at a downstream edge of the window, by the belt. 
     In an application, the leaflets are arranged to form a plurality of commissures therebetween, and are attached to the frame assembly at the commissures, and the belt is disposed over the commissures. 
     In an application: 
     the pouch has an upstream surface and a downstream surface, and, 
     at the narrowed portion, each of the legs pushes the downstream surface toward the upstream surface. 
     In an application, at the narrowed portion, each of the legs pushes the downstream surface into contact with the upstream surface. 
     In an application, at the narrowed portion, each of the legs forms a respective bulge in the upstream surface by pressing the downstream surface against the upstream surface. 
     In an application, the pouch is stitched to the arms. 
     In an application, at the narrowed portion, the pouch is stitched to the arms but not to the legs. 
     In an application, the frame assembly includes (i) a valve frame that defines the valve body and the plurality of upstream arms, and (ii) an outer frame that circumscribes the valve frame, and defines the plurality of downstream legs. 
     In an application, an upstream portion of the pouch is attached to the valve frame, and a downstream portion of the pouch is attached to the outer frame. 
     In an application, the apparatus further includes at least one coagulation component. disposed within the outer portion of the interior space, and configured to promote blood coagulation within the outer portion of the interior space. 
     In an application, the coagulation component is annular, and, within the outer portion of the interior space, circumscribes the longitudinal axis. 
     There is further provided, in accordance with an application of the present invention, apparatus, including: 
     a frame assembly that includes:
         a valve body that circumscribes a longitudinal axis and defines a lumen along the axis:   a plurality of upstream arms that are coupled to the valve body at a first axial level with respect to the longitudinal axis, each of the arms extending radially outward front the valve body to a respective arm-tip; and   a plurality of downstream legs that are coupled to the valve body at a second axial level with respect to the longitudinal axis, and that extend radially outward from the valve body and toward the plurality of arms;       

     a tubular liner that lines the lumen, and that has an upstream end and a downstream end; 
     a plurality of prosthetic leaflets, disposed within the lumen, attached to the liner, and arranged to facilitate one-way upstream-to-downstream fluid flow through the lumen, the first axial level being upstream of the second axial level; 
     a first sheet of flexible material, the first sheet having (i) a greater perimeter, and (ii) a smaller perimeter that defines an opening, the first sheet being attached to the plurality of arms with the opening aligned with the lumen of the valve body; and 
     a second sheet of flexible material:
         the second sheet having a first perimeter and a second perimeter,   the first perimeter being attached to the greater perimeter of the first sheet around the greater perimeter of the first sheet.   the second sheet extending from the first perimeter radially inwards and downstream toward the second perimeter, the second perimeter circumscribing, and attached to the valve body al a third axial level that is downstream of the first axial level. and:       

     the first sheet, the second sheet, and the liner define an inflatable pouch therebetween, the inflatable pouch defining an interior space therein, the first sheet defining an upstream wall of the pouch, the second sheet defining a radially-outer wall of the pouch, and the liner defining a radially-inner wall of the pouch, and 
     each of the legs presses the second sheet into contact with the first sheet. 
     In an application, the arms are disposed inside the pouch. 
     In an application, each of the legs forms a respective bulge in the first sheet by pressing the second sheet against the first sheet. 
     In an application, the legs extend in an upstream direction past the arms. 
     In an application, the frame assembly includes (i) a valve frame that defines the valve body and the plurality of upstream arms, and (ii) an outer frame that circumscribes the valve frame, and defines the plurality of downstream legs. 
     In an application, an upstream portion of the pouch is attached to the valve frame, and a downstream portion of the pouch is attached to the outer frame. 
     In an application, the plurality of legs forms a narrowed portion of the pouch by pressing the second sheet into contact with the first sheet, the narrowed portion of the pouch circumscribing the valve body. 
     In an application, at the narrowed portion, the second sheet is not stitched to the legs. 
     In an application, the arms and the legs are arranged such that, at the narrowed portion. the arms and the legs alternate circumferentially. 
     In an application, the narrowed portion of the pouch shapes the pouch to define:
         an inner portion of the interior space, radially inward From the narrowed portion, and in fluid communication with the lumen, and   an outer portion of the interior space, radially outward from the narrowed portion, and in fluid communication with the inner portion via the narrowed portion.       

     In an application, the apparatus further includes at least one coagulation component, disposed within the outer portion of the interior space, and configured to promote blood coagulation within the outer portion of the interior space. 
     In an application, the coagulation component is annular, and, within the outer portion of the interior space, circumscribes the longitudinal axis. 
     In an application, the interior space is in fluid communication with the lumen via a plurality of discrete windows defined by the apparatus. 
     In an application, the apparatus further includes a belt wrapped around the frame assembly downstream of the windows, circumscribing the lumen, each of the windows being bounded, at a downstream edge of the window, by the belt. 
     In an application, the leaflets are arranged to form a plurality of commissures therebetween, and are attached to the frame assembly at the commissures, and the belt is disposed over the commissures. 
     The present invention will be more fully understood from the following detailed description of applications thereof, taken together with the drawings, in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS.  1 A-E  and  2  are schematic illustrations of an implant and a frame assembly of the implant, in accordance with some applications of the invention; 
         FIGS.  3 A-F  are schematic illustrations showing the implantation of the implant at a native valve of a heart of a subject, in accordance with some applications of the invention; 
         FIGS.  4 ,  5 A -C, and  6  are schematic illustration of implants and their frames, in accordance with some applications of the invention; 
         FIG.  7    is a schematic illustration of an outer frame of a frame assembly of an implant, in accordance with some applications of the invention; 
         FIG.  8    is a schematic illustration of a frame assembly, in accordance with some applications of the invention; 
         FIGS.  9 A-B  are schematic illustrations of an inner frame, and an implant comprising the inner frame, in accordance with some applications of the invention; 
         FIGS.  10 A-B  are schematic illustrations of an inner frame, and an implant comprising the inner frame, in accordance with some applications of the invention; 
         FIGS.  11 A-B  are schematic illustrations of an inner frame, and an implant comprising the inner frame, in accordance with some applications of the invention; 
         FIGS.  12 A-H  are schematic illustrations of a technique for use with a frame of a prosthetic valve, in accordance with some applications of the invention; 
         FIGS.  13 A-E ,  14 A-D,  15 A-C,  16 A-C,  17 ,  18 A-C, and  19  are schematic illustrations of an implant, and steps in the assembly of the implant, in accordance with some applications of the invention: and 
         FIGS.  20 , and  21 A -C are schematic illustrations of an implant, in accordance with some applications of the invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Reference is made to  FIGS.  1 A-E  and  2 , which are schematic illustrations of an implant  20  and a frame assembly  22  of the implant, in accordance with some applications of the invention. Implant  20  serves as a prosthetic valve for use at a native heart valve of a subject typically the mitral valve. Implant  20  has a compressed state for minimally-invasive (typically transluminal, e.g., transfemoral) delivery, and an expanded state into which the implant is transitioned at the native heart valve, and in which the implant provides prosthetic valve functionality. Implant  20  comprises frame assembly  22 , flexible sheeting  23 , and a valve member, such as prosthetic leaflets  58 . 
       FIGS.  1 A-E  show implant  20  and frame assembly  22  in the expanded state. For clarity,  FIGS.  1 A-D  show frame assembly  22  alone.  FIG.  1 A  shows an isometric exploded view of frame assembly  22 , and  FIG.  1 B  shows a side exploded view of the frame assembly.  FIGS.  1 C and  1 D  are side- and top-views, respectively, of frame assembly  22 , assembled.  FIG.  1 E  is a perspective view of implant  20 , including sheeting  23  and leaflets  58 . 
     Implant  20  has an upstream end  24 , a downstream end  26 , and defines a central longitudinal axis ax 1  therebetween. Frame assembly  22  comprises a valve frame  30  that comprises a valve body (which is a generally tubular portion)  32  that has an upstream end  34  and a downstream end  36 , and is shaped to define a lumen  38  through the valve body from its upstream end to its downstream end. Valve body  32  circumscribes axis ax 1 , and thereby defines lumen  38  along the axis. Throughout this application, including the specification and the claims, unless stated otherwise, “upstream” and “downstream,” e.g., with respect to the ends of implant  20 , are defined with respect to the longitudinal axis or implant  20 , by the Orientation and functioning of leaflets  58 , which facilitate one-way upstream-to-downstream fluid flow through lumen  38 . 
     Valve frame  10  further comprises a plurality of arms  46  each of which, in the expanded state. extends radially outward from valve body  32 . In this context, the term “extends radially outward” is not limited to extending in a straight line that is orthogonal to axis ax 1 , but rather, and as shown for arms  46 , includes extending away from axis ax 1  while curving in an upstream and/or downstream direction. Typically, and as shown, each arm  46  extends from valve body  32  in an upstream direction, and curves radially outward. That is, the portion of arm  46  closest to valve body  32  extends primarily upstream away from the valve body (e.g., extending radially outward only a little, extending not at all radially outward, or even extending radially inward a little), and the arm then curves to extend radially outward. The curvature of arms  46  is described in more detail hereinbelow. 
     Valve body  32  is defined by a repeating pattern of cells that extends around central longitudinal axis ax 1 . In the expanded state of each tubular portion, these cells are typically narrower at their upstream and downstream extremities than midway between these extremities. For example, and as shown, the cells may be roughly diamond or astroid in shape. Typically, and as shown. valve body  32  is defined by two stacked, tessellated rows of cells an upstream row  29   a  of first-row cells, and a downstream row  29   b  of second-row cells. Frame  30  is typically made by cutting (e.g., laser-cutting) its basic (i.e., raw) structure from a tube of, for example, Nitinol (followed by re-shaping and heat treating to form its shape-set structure). Although valve body  32  is therefore typically monolithic, because the resulting cellular structure of valve body  32  resembles an open lattice, it may be useful to describe it as defining a plurality of joists  28  that connect at nodes  100  to form the cellular structure. 
     Typically, and as shown, each arm  46  is attached to and extends from a site  35  that is at the connection between two adjacent cells of upstream row  29   a.  That is, site  35  is a connection node between first-row cells. The tessellation between rows  29   a  and  29   b  is such that site  35  may alternatively be described as the upstream extremity of cells of downstream row  29   b.  That is, the upstream extremity of each second-row cell is coincident with a respective connection node between first-row cells. Site  35  is therefore a node  100  that connects four joists  28 . Upstream end  34  of valve body  32  may be described as defining alternating peaks and troughs, and sites  35  are downstream of the peaks (e.g., at the troughs). 
     It is hypothesized by the inventors that connecting arm  46  to valve body  32  at site  35  (instead of at upstream end  34 ) maintains the length of the lumen of the tubular portion, but also advantageously reduces the distance that the tubular portion extends into the ventricle of the subject, and thereby reduces a likelihood of inhibiting blood flow out of the ventricle through the left ventricular outflow tract. It is further hypothesized by the inventors that because each site  35  is a node  100  that connects four joists (whereas each node  100  that is at upstream end  34  connects only two joists), sites  35  are inure rigid, and therefore connecting arms  46  to valve body  32  at sites  35  provides greater rigidity to each arm. 
     Sheeting  23  may comprise one or more individual sheets, which may or may not be connected to each other. The individual sheets may comprise the same or different materials. Typically, sheeting  23  comprises a fabric, e.g., comprising a polyester, such as polyethylene terephthalate. Arms  46  are typically covered with sheeting  23 . Typically, and as shown in  FIG.  1 E , an annular sheet  25  of sheeting  23  is disposed over arms  46 , extending between the arms, e.g., so as to reduce a likelihood of paravalvular leakage. For some such applications, excess sheeting  23  is provided between arms  46 , so as to facilitate movement of arms  46  independently of each other. Annular sheet  25  typically covers the upstream side of arms  46 , but may alternatively or additionally cover the downstream side of the arms. 
     Alternatively, each arm  46  may be individually covered in a sleeve of sheeting  23 , thereby facilitating independent movement of the arms. 
     Arms  46 , and typically the sheeting that covers the arms, define an upstream support portion  40  of implant  20 . 
     Other surfaces of frame assembly  22  may also be covered with sheeting  23 . Typically, sheeting  23  covers at least part of valve body  32 , e.g., defining a liner  27  that lines an inner surface of the valve body, and thereby defining lumen  38 . 
     Support  40  has an upstream surface, and a downstream surface. Each arm  46  is typically curved such that a downstream surface of support  40  defines an annular concave region  152 , and an annular convex region  154  radially outward from the concave region. That is, in region  152  the downstream surface of support  40  (e.g., the downstream surface of each arm  46  thereof) is concave, and in region  154  the downstream surface of the support is convex. 
     Concave region  152  extends radially between a concave-region inner radius r 1  and a concave-region outer radius r 2 . Convex region  154  extends radially between a convex-region inner radius r 3  and a concave-region outer radius r 4 . It is to be noted that in this context (including the specification and the claims), the term “radius” means a radial distance from axis ax 1 . 
     For some applications, and as shown, each arm  46  has a serpentine shape, such that there is no discernable gap between concave region  152  and convex region  154 . For such applications, each arm  46  has an inflection point where region  152  transitions into region  154 . For such applications, radius r 2  and radius r 3  are coincident, and collectively define an inflection radius at which the inflection point of each arm lies. 
     For some applications, radius r 1  is the radius of tubular portion  32 . For some applications, there is a discernable gap between regions  152  and  154 . For example, each arm may be curved in regions  152  and  154 , but have a straight portion between these regions. 
     Although regions  152  and  154  may be locally defined with respect to one or more particular arms  46 , these regions typically completely circumscribe axis ax 1 . 
     Frame assembly  22  further comprises a plurality of legs  50 , each of which, in the expanded state, extends radially outward and in an upstream direction from a respective leg-base  66  to a respective leg-tip  68 . Each leg  50  defines a tissue-engaging flange  54 , which is typically the most radially outward part of the leg, and includes leg-tip  68 . Typically, legs  50  are defined by an outer frame (or “leg frame”)  60  that circumscribes and is coupled to valve frame  30 . 
     Frames  30  and  60  define respective coupling elements  31  and  61 , which are fixed with respect to each other at coupling points  52 . For some applications, frames  30  and  60  are attached to each other only at coupling points  52 . Although frames  30  and  60  are attached to each other at coupling points  52 , radial forces may provide further coupling between the frames, e.g., frame  30  pressing radially outward against frame  60 . 
     Typically, coupling points  52  are circumferentially aligned with legs  50  (and flanges  54  thereof), but circumferentially offset with respect to arms  46 . That is, the coupling points are typically at the same rotational position around axis ax 1  as the legs, but are rotationally  21 ) staggered with respect to the rotational position of the arms. 
     Coupling points  52  are typically disposed circumferentially around frame assembly  22  on a transverse plane that is orthogonal to axis ax 1 . That is, coupling points  52  are typically all disposed at the same longitudinal position along axis ax 1 . Typically, coupling points  52  are disposed longitudinally between upstream end  24  and downstream end  26  of frame assembly  22 , but not at either of these ends. Further typically, coupling points  52  are disposed longitudinally between upstream end  34  and downstream end  36  of tubular portion  32 , but not at either of these ends. As shown, tubular portion  32  is typically barrel-shaped—i.e., slightly wider in the middle than at either end. For some applications, and as shown, coupling points  52  are disposed slightly downstream of the widest part of tubular portion  32 . For example, coupling points  52  may be 0.5-3 mm downstream of the widest part of tubular portion  32 . Alternatively or additionally, the longitudinal distance between the widest part of tubular portion  32  and coupling points  52  may be 20-50 percent (e.g., 20-40 percent) of the longitudinal distance between the widest part of the tubular portion and downstream end  36 . 
     Coupling elements  31  are typically defined by (or at least directly attached to) legs  50 . Therefore legs  50  are fixedly attached to frame  30  at coupling points  52 . Despite the fixed attachment of legs  50  to frame  30 , frame  60  comprises a plurality of struts  70  that extend between, and connect, adjacent legs. Struts  70  are typically arranged in one or more rings  72 , e.g., a first (e.g., upstream) ring  74  and a second (e.g., downstream) ring  76 . For some applications, and as shown, frame  60  comprises exactly two rings  72 . Each ring is defined by a pattern of alternating peaks  64  and troughs  62 , the peaks being further upstream than the troughs. Each ring is typically coupled to legs  50  at troughs  62 —i.e., such that peaks  64  are disposed circumferentially between the legs. Peaks  64  are therefore typically circumferentially aligned with arms  46 . That is, peaks  64  are typically at the same rotational position around axis ax 1  as arms  46 . 
     The elongate element of frame  60  that defines leg  50  continues in a downstream direction past ring  74  and coupling element  61 , and couples ring  74  to ring  76 . However, throughout this patent application, leg  50  itself is defined as the free portion of this elongate element that extends from ring  74 . Leg-base  66  may be defined as the region of leg  50  that is coupled to the remainder of frame  60  (e.g., to ring  74 ). Because each leg  50  extends in a generally upstream direction, leg-base  66  may also be defined as the most downstream region of leg  50 . 
     In the expanded state, the leg-tip  68  of each leg is typically disposed radially between radius r 3  and radius r 4 . That is, the leg-tip  68  of each leg is aligned with convex region  154 . 
     Frame  60  is typically cut from a single tube, e.g., of Nitinol. Therefore, the radial thickness of the frame is typically consistent throughout—e.g., it is the wall thickness of the tube from which it was cut. However, the circumferential width of components of frame  60  (i.e., the width of the component measured around the circumference of the frame) may differ. For example, for some applications, a circumferential thickness W 2  of legs  50  may be at least three times greater than a circumferential thickness W 1  of struts  70 . Greater circumferential thickness typically provides the component with greater rigidity. 
     Valve frame  30  and outer frame  60  are typically each cut from respective metallic tubes, e.g., of Nitinol. This is typically the case for each of the implants described herein. More specifically, for each of the implants described herein:
         (1) the valve frame is typically cut from a metallic tube to form a raw valve-frame structure in which the arms and the projections extend axially from the valve body, and the raw valve-frame structure is subsequently shape-set to form a shape-set valve-frame structure in which (i) the valve body is wider than in the raw valve-frame structure, and (ii) the arms extend radially outward from the valve body; and   (2) the outer frame is typically cut from a metallic tube to form a raw outer-frame structure in which the legs (including the flanges) extend axially, and the raw outer-frame structure is subsequently shape-set to form a shape-set outer-frame structure in which (i) the rings are wider than in the raw outer-frame structure, and (ii) the flanges extend radially outward from the rings.       

     Prosthetic leaflets  58  are disposed within lumen  38 , and are configured to facilitate one-way liquid flow through the lumen from upstream end  34  to downstream end  36 . Leaflets  58  thereby define the orientation of the upstream and downstream ends of valve body  32 , and of implant  20  in general. 
     Typically, implant  20  is biased (e.g., shape-set) to assume its expanded state. For example, frames  30  and  60  may be constructed from a shape-memory metal such as Nitinol or a shape-memory polymer. Transitioning of implant  20  between the respective states is typically controlled by delivery apparatus, such as by constraining the implant in a compressed state within a capsule and/or against a control rod, and selectively releasing portions of the implant to allow them to expand. 
       FIG.  2    shows implant  20  in its compressed state, for delivery to the heart of the subject, e.g., within a capsule  170  or delivery tube. Capsule  90  may be a capsule or a catheter. For clarity, only frame assembly  22  of implant  20  is shown. In the compressed state, arms  46  define a ball  18  at an end of valve body  32 . It is to be noted that in this context, the term “ball” (including the specification and the claims) means a substantially bulbous element. The ball may be substantially spherical, spheroid, ovoid, or another bulbous shape. 
     In the compressed state, frame assembly  22  defines a waist  56  (i.e., is waisted) at a longitudinal site between the valve body and the ball. For some applications, and as shown, waist  56  is longitudinally upstream of frame  60 , and is therefore primarily defined by valve frame  30 . However, for some such applications, the downstream limit of the waist may be defined by the upstream limit of frame  60  (e.g., flanges  54  thereof). 
     It is to be noted that, typically, the bulbous shape of ball  48  is interrupted at waist  56 , i.e., where the frame transitions from the ball to the waist. For some applications, and as shown, valve frame  30  is monolithic (e.g., cut from a single metal tube), and defines both valve body  32  and arms  46 . For some applications, and as shown, in the compressed state, the overall shape of valve frame  30  resembles that of an air rifle pellet or a shuttlecock (e.g., see the cross-section in  FIG.  2   ). For some applications, a longitudinal cross-section of frame  30  has an overall shape that resembles a keyhole. 
     For some applications, at waist  56 , frame  30  (and typically frame assembly  22  overall) has a transverse diameter ( 110  that is less than 5 mm (e.g., 2-4 mm). For some applications, ball  48  has a greatest transverse diameter d 11  of 8-12 mm (e.g., 9-11 mm). For some applications, transverse diameter d 10  is less than 10 percent (e.g., less than 30 percent, such as 10-30 percent) of transverse diameter d 11 . 
     Due to waist  56 , while implant  20  is in its compressed state and disposed within capsule  90 , the implant and capsule define a toroidal gap  57  therebetween. Toroidal gap  57  circumscribes longitudinal axis ax 1  of the implant around waist  56 . Therefore, valve body  32  extends in a first longitudinal direction (i.e., in a generally downstream direction) away from gap  57 , and arms  16  extend in a second longitudinal direction (i.e., in a generally upstream direction) away from the gap. For applications in which implant  20  is delivered to the native valve transfemorally, valve body  32  is closer to the open end of capsule  90  than is gap  57 , and arms  46  (e.g., ball  48 ) are further from the open end of capsule  90  than is gap  57 . For some applications, and as shown, a downstream limit of gap  57  is defined by the tips of flanges  54 . For some applications, and as shown, an upstream limit of gap  57  is defined by the downstream side of arms  46 . 
     It is to be noted that, typically, frame  60  is disposed only downstream of toroidal gap  57 , but the frame  30  is disposed both upstream and downstream of the toroidal gap. 
     Reference is again made to  FIG.  1 E . For some applications, implant  20  comprises a polytetrafluoroethylene (e.g., Teflon) ring  78  attached to downstream end  26 . Ring  78  circumscribes lumen  38  at downstream end  36  of valve body  32 , and typically at downstream end  26  of implant  20 . Therefore ring  78  serves as a downstream lip of lumen  38 . Typically, ring  78  is attached (e.g., stitched) to both frame  30  and frame  60 . For example, ring  78  may be attached to frame  60  at troughs  62 . For some applications, ring  78  is stitched to downstream end  36  of valve body  32  by stiches  99  that wrap around the ring (i.e., through the opening of the ring and around the outside of the ring) but do not pierce the ring (i.e., the material of the ring). 
     Typically, ring  78  covers downstream end  26  of the implant (e.g., covers the frames at the downstream end). It is hypothesized by the inventors that ring  78  advantageously protects tissue (e.g., native leaflets and/or chordae tendineae) from becoming damaged by downstream end  26  of implant  20 . There is therefore provided, in accordance with some applications of the invention, apparatus comprising:
         a valve body, having an upstream end and a downstream end, shaped to define a lumen from the upstream end to the downstream end, the lumen defining a longitudinal axis of the prosthetic valve, and the downstream end of the valve body having;   a fabric liner, lining the lumen;   a valve member, disposed within the lumen of the valve body; and   a polytetrafluoroethylene ring coupled to the downstream end of the valve body such that the ring circumscribes the lumen at the downstream end of the valve body.       

     Reference is made to  FIGS.  3 A-F , which are schematic illustrations showing the implantation of implant  20  at a native valve  10  of a heart  4  of a subject, in accordance with some applications of the invention. Valve  10  is shown as a mitral valve of the subject, disposed between a left atrium  6  and a left ventricle  8  of the subject. However, implant  20  may be implanted at another heart valve of the subject, mutatis mutandis. Similarly, although  FIGS.  3 A-F  show implant  20  being delivered transseptally via a sheath  88 , the implant may alternatively be delivered by any other suitable route, such as transatrially, or transapically. 
     Implant  20  is delivered, in its compressed state, to native valve  10  using a delivery tool  160  that is operable from outside the subject ( FIG.  3 A ). Tool  160  typically comprises an extracorporeal controller  162  (e.g., comprising a handle) at a proximal end of the tool, and a shall  164  extending from the controller to a distal portion of the tool. At the distal portion of tool  160 , the tool typically comprises a capsule  170  comprising one or more capsule portions  172 ,  174  (described below), and a mount  166 . Mount  166  is coupled (typically fixed) to shaft  164 . Controller  162  is operable to control deployment of implant  20  by transitioning the tool between a delivery state ( FIG.  3 A ), an intermediate state ( FIG.  3 E ), and an open state ( FIG.  3 F ). Typically, implant  20  is delivered within capsule  170  of tool  160  in its delivery state, the capsule retaining the implant in the compressed state. Implant  20  typically comprises one or more appendages  80  at downstream end  26 . each appendage typically shaped to define a catch or other bulbous element at the end of the appendage, and to engage mount  166 , e.g., by becoming disposed within notches in the mount. Appendages  80  are typically defined by valve frame  30 , but may alternatively be defined by outer frame  60 . Capsule  170  retains appendages  80  engaged with mount  166  by retaining implant  20  (especially downstream end  26  thereof) in its compressed state. A transseptal approach, such as a transfemoral approach, is shown. At this stage, frame assembly  22  of implant  20  is as shown in  FIG.  2   . 
     Subsequently, flanges  54  are deployed—i.e., are allowed to protrude radially outward, e.g., by releasing them from capsule  170  ( FIG.  3 B ). For example, and as shown, capsule  170  may comprise a distal capsule-portion  172  and a proximal capsule-portion  174 , and the distal capsule-portion may be moved distally with respect to implant  20 , so as to expose flanges  54  while continuing to restrain upstream end  24  and downstream end  26  of implant  20 . In  FIG.  3 B , upstream support portion  40  (e.g., arms  46 ) is disposed within capsule-portion  174 , and downstream end  36  of tubular portion  32  is disposed within capsule-portion  172 . 
     Typically, and as shown in  FIGS.  3 A-B , tool  160  is positioned such that when flanges  54  are deployed, they are deployed within atrium  6  and/or between leaflets  12  of the subject. Subsequently, the tool is moved downstream (distally, for a transseptal approach) until the leaflets are observed to coapt upstream of flanges  54  ( FIG.  3 C ). It is hypothesized by the inventors that this reduces how far into ventricle  8  the flanges become disposed, and therefore reduces the distance that the deployed flanges must be moved in an upstream direction in order to subsequently engage the leaflets, and therefore reduces the likelihood of inadvertently or prematurely ensnaring tissue such as chordae tendineae. This is described in more detail, mutatis mutandis, in WO 2016/125160 to Hariton et al., filed Feb. 3, 2016, which is incorporated herein by reference. 
     Alternatively, flanges  54  may be initially deployed within ventricle  8 . 
     Subsequently, implant  20  is moved upstream, such that flanges  54  engage leaflets  12  of valve  10  ( FIG.  3 D ). 
     Subsequently, delivery tool  160  is transitioned into its intermediate state, thereby allowing implant  20  to assume a partially-expanded state in which upstream support portion  40  is expanded. e.g., by releasing the upstream support portion from capsule  170  ( FIG.  3 E ). For example, and as shown, proximal capsule-portion  174  may be moved proximally with respect to mount  166  and/or implant  20 , so as to expose upstream support portion  40  (e.g., arms  46 ). Typically, in this state, upstream support portion  40  has expanded to have a diameter that is at least 80 percent (e.g., at least 90 percent, e.g., at least 95 percent) of its diameter in the expanded state of implant  20  (e.g., the diameter after implantation is complete), while downstream end  26  of the implant remains compressed. For some applications, in the partially-expanded state, upstream support portion  40  has expanded to its fully-expanded diameter. That is, downstream end  36  of tubular portion  32  remaining disposed within capsule-portion  172  typically does not inhibit, by more than 20 percent, if at all, the expansion of upstream support portion  40 . However, in the partially-expanded state of implant  20 , legs  50  are partially inhibited from expanding, such that each leg-lip  68  is radially aligned with concave region  152 . That is, each leg-tip  68  is disposed radially between concave-region inner radius r 1  and concave-region outer radius r 2 . 
     In the intermediate state, leaflets  12  of native valve  10  are sandwiched between upstream support portion  40  (e.g., annular sheet  25  thereof) and legs  50  (e.g., flanges  54  thereof). It is to be noted that appendages  80  remain engaged with mount  166 . 
     Subsequently, delivery tool  160  is transitioned into its open state, thereby allowing implant  20  to expand toward its expanded state (i.e., such that tubular portion  32  widens to its fully-expanded state) ( FIG.  3 F ). For example, capsule-portion  172  may be moved distally with respect to mount  166  and/or implant  20 . The resulting expansion of downstream end  26  of implant  20  disengages appendages  80 , and thereby implant  20  as a whole, from mount  166 . Appendages  80  are not visible in  FIG.  3 F  (or  FIG.  3 C ) because they are obscured by ring  78 . 
     In the expanded state of implant  20 , each leg-tip  68  is radially aligned with convex region  154 . That is, each leg-tip  68  is disposed radially between convex-region inner radius r 3  and convex-region outer radius r 4 . This is also illustrated in  FIG.  1 C . 
     Tool  160  (e.g., capsule-portion  172  thereof) may then be withdrawn via lumen  38  of implant  20 , and removed from the body of the subject. 
     Reference is made to  FIGS.  4 , and  5 A -C, which are schematic illustrations of implants, in accordance with some applications of the invention.  FIG.  4    shows an implant  120 .  FIG.  5 A  shows an implant  220 ,  FIG.  5 B  shows a frame assembly  222  of implant  220  after shape-setting, and  FIG.  5 C  shows a valve frame  230  of frame assembly  222  prior to shape-setting (i.e., the shape-set valve-frame structure). 
     Implants  120  and  220  are typically the same as implant  20 , described hereinabove, except where noted. Sheeting  23  forms annular sheet  25  that is disposed over and typically stitched to arms  46 . Implant  120  thereby comprises valve body  32  (e.g., as described hereinabove), and an upstream support portion  140  that itself comprises arms  46  and annular sheet  25 . Similarly, implant  220  comprises valve body  32  and an upstream support portion  240  that itself comprises arms  46  and annular sheet  25 . 
     Implants  120  and  220  each further comprises a respective plurality of elongate projections  146  or  246 . Whereas arms  46  are covered by sheeting  23 , the projections extend in an upstream direction through sheeting  23 . For some applications, and as shown for projections  146 , the projections extend through annular sheet  25 . For some applications, and as shown for projections  246 , the projections extend between annular sheet  25 , and a portion of sheeting  23  that lines valve body  32  (e.g., at a seam where these two portions of sheeting  23  are joined). The projections and arms  46  are both configured to be positioned in atrium  6  of the heart. For some applications, and as shown for projections  146 , the projections extend through annular sheet  25 . 
     It is to be noted that projection  146  and  246  are distinct from appendages  80 , which are disposed at the other end of the valve body. 
     Each projection terminates in a nub  148  or  248  that facilitates snaring of the projection using a transcatheter snare, lasso, or similar tool. It is to be understood that the shapes shown for the nubs are merely examples, and that the scope of the invention includes any suitably shaped nub. It is hypothesized by the inventors that the projections facilitate repositioning and/or retrieval of the implant during and/or after implantation, using a snare, lasso, or similar tool. The projections are typically positioned and/or shaped such that nubs  148  or  248  are not in contact with annular sheet  25  or atrial tissue (e.g., are disposed at least 5 mm away (e.g., 5-25 mm away) from annular sheet  25  or atrial tissue). For some applications, and as shown for projections  146  of implant  120 , the projections curve outwards and then inwards toward the central longitudinal axis of the implant (i.e., are shaped to be concave toward the axis). For some applications, and as shown for projections  246  of implant  220 , the projections do not extend radially outward from the valve body. Projections  246  typically extend axially in an upstream direction away from the valve body (i.e., generally parallel to axis ax 1 , i.e., within  10  degrees of axis ax 1 ). 
     Regarding implant  120  ( FIG.  4   ), projections  146  extend from sites  35  in a similar way to arms  46 . Projections  146  may be structurally similar to arms  46 , and may even be identically cut when frame  30  is initially cut from the original metal tube (i.e., in the raw valve-frame structure). However, projections  146  have a different curvature to arms  46  (e.g., they may be bent differently post-cutting), and are curved such that they extend through annular sheet  25 . Whereas at least some of arms  46  typically reach and press against the atrial wall, projections  146  are typically shaped such that nubs  148  are not in contact with the atrial wall. Typically, each projection  146  replaces an arm  46 , such that the cumulative sum of arms and projections is twelve.  FIG.  4    shows an embodiment comprising six arms  46  and six projections  146 , but the scope of the invention includes other ratios, such as nine arms  46  and three projections  146 . 
       FIG.  5 A  shows implant  220 , comprising a frame assembly  222 , leaflets  58 , and sheeting  23 .  FIG.  5 B  shows frame assembly  222  alone, the frame assembly comprising (i) a valve frame  230  that defines valve body  32 , and (ii) an outer frame  260 .  FIG.  5 C  shows the basic structure of valve frame  230 , as it is initially cut from a tube (typically a metallic tube, such as a Nitinol tube), e.g., before the frame is shape-set into the shape shown in  FIG.  5 B . Although this basic structure is tubular,  FIG.  5 C  depicts the structure two-dimensionally, as though the cut-out structure were cut longitudinally, and unrolled to become flat. 
     Except where noted, frame assembly  222 , valve frame  230 , and outer frame  260  are typically identical to frame assembly  22 , valve frame  30 , and outer frame  60 , mutatis mutandis. For some applications, implant  220  is identical to implant  20  except for projections  246 . 
     In contrast to projections  146  of implant  120 , each projection  246  of implant  220  extends from a respective site  37  that is at the upstream extremity (i.e., peak) of a respective first-row cell of upstream row  29   a  or valve body  32  (i.e., from upstream end  34  of the valve body). Projections  246  thereby alternate with, rather than replace, arms  46 . Therefore, it is possible for implant  220  to comprise projections  246  in addition to twelve arms  46 . Implant  220  may comprise an equal number of projections  246  and arms  46 , but typically, the implant comprises fewer projections than arms. For example, implant  220  may comprise half as many, or fewer, projections  246  than arms  46 —e.g., a third as many, or a quarter as many projections as arms. Projections  246  and arms  46  are typically evenly distributed circumferentially, and therefore typically at least two arms (e.g., at least three arms, such as at least four arms) are disposed circumferentially between each projection and each of its circumferentially-neighboring projections.  FIGS.  5 A-C  show implant  220  comprising three projections  246  and twelve arms  46 , with four arms disposed circumferentially between each projection and each of its circumferentially-neighboring projections.  FIGS.  11 A-B , described hereinbelow, show an implant in which three arms are disposed circumferentially between each projection and each of its circumferentially-neighboring projections. 
     Each projection  246  has a projection-length d 13 , measured from the upstream extremity of the respective first-row cell (i.e., from site  37 ). Each of the arms has an arm-length d 14 , measured from the upstream extremity of the respective second-row cell (i.e., site  35 ). Arm-length d 14  is greater than projection-length d 13  (e.g., 2-20 times greater, e.g., 4-20 times greater, such as 4-10 times greater). For some applications, arm-length d 14  is 20-28 mm, such as 22-26 mm (e.g., 22-23 mm, 23.5-24.5 mm, or 25-26 mm). For some applications, projection-length d 13  is 2-10 mm (e.g., 3-8 mm, e.g., 4-6 mm, such as about 5 mm). 
     Typically, each arm  46  (i) has a narrow portion  46   a  that is attached to, and extends from, the upstream extremity of the respective second-row cell, and (ii) at a widening zone  46   b,  widens into a wide portion  46   c  that extends from the narrow portion, and is wider than the narrow portion. Narrow portion  46   a  has a narrow-portion length d 20  that is typically at least 30 percent of arm-length (e.g., at least 40 percent, such as 40-80 percent, such as 40-60 percent). Wide portion  46   c  has a wide-portion length that is at least 30 percent of arm-length d 14  (e.g., at least  40  percent, such as 40-80 percent, such as 40-60 percent). 
     Wide portion  46   c  has a width d 15  that is typically 1.5-6 times greater (e.g., 2-4 times greater, such as 2.5-3.5 times greater) than a width d 16  of narrow portion  46   a.  For some applications width d 15  is 1-2 mm (e.g., 1.4-1.8 mm, such as 1.6 mm). Width d 16  is typically 0.2-0.8 mm (e.g., 0.4-0.6 mm, such as 0.5 mm). It is to be noted that, although individual parts of arm  46  within portion  46   c  may be narrower than within portion  46   a,  these individual parts form a back-and-forth pattern that results in wide portion  46   c  being, overall, wider than narrow portion  46   a.  Typically, wide portion  46   c  is more flexible, in at least one plane, than narrow portion  46   a.  Therefore, wide portion  46   c  is also a flexible portion of arm  46 . 
     Each projection  246  has a width d 17  that is typically 0.2-0.8 mm (e.g., 0.4-0.6 mm, such as 0.5 mm). Each nub has a nub-width d 18  that is typically 1-2 mm (e.g., 1.4-1.8 mm, such as 1.6 mm), and a nub-length d 19  that is typically 0.5-1 mm (e.g., 0.7-0.9 mm, such as 0.8 mm). Wide portion  46   c  is typically at least 3 times (e.g., at least 10 times) longer than nub-length d 19 . 
     As described hereinabove, the valve frame is typically monolithic, cut from a single tube. Typically, and as shown in  FIG.  5 C , while valve frame  230  is in its raw valve-frame structure (e.g., described hereinabove with reference to  FIGS.  1 A-E , mutatis mutandis), nubs  248  are disposed between arms  46 . As shown in  FIG.  5 C , arms  46  and projections  246  may be dimensioned such that, while valve frame  230  is in its raw valve-frame structure, nubs  248  are disposed between narrow portions  46   a  of arms  46 . That is, nubs  248  may be disposed axially closer than wide portion  46   c  to valve body  32 . Thereby, arms  46  and projections  246  efficiently fit adjacently to each other within a single cutout from tube of a particular diameter. Narrow-portion length d 20  is typically greater than projection-length d 13  (e.g., at least 1.5 times greater, such as 1.5-3 times greater). 
     Reference is now made to  FIG.  6   , which shows the basic structure of a variant  230   a  of valve frame  230 , in accordance with some applications of the invention.  FIG.  6    shows variant  230   a  as it is initially cut from a tube (typically a metallic tube, such as a Nitinol tube), e.g., before the frame is shape-set.  FIG.  6    shows a two-dimensional view, as though the cut-out structure were cut longitudinally, and unrolled to become flat. Similarly to with frame  230  ( FIG.  5 C ), nubs  248  of variant  230   a  are disposed between arms  46 . However, projections  246   a  of variant  230   a  are longer than projections  246  of frame  230 , and nubs  248   a  are therefore disposed between wide portions  46   c  of arms  46 . In order to accommodate this, in frame  230   a.  at least the arms  46  that are adjacent to nubs  248   a  are deflected circumferentially (which is represented two-dimensionally as being laterally deflected) compared to their positions in frame  230 , and are typically unevenly spaced. During subsequent shape setting, arms  46  are typically circumferentially displaced, e.g., such that they are evenly spaced. Variant  230   a  may be used in place of any other valve frame described herein, mutatis mutandis. Similarly, variant  230   a  may be used in combination with other technologies described herein, mutatis mutandis. 
     Reference is made to  FIG.  7   , which is a schematic illustration of an outer frame  60   a,  in accordance with some applications of the invention. Outer frame  60   a  is typically identical to outer frame  60  except that peaks  64   a  of frame  60   a  have a larger radius of curvature than do peaks  64  of frame  60 . Outer frame  60   a  may be used in place of any other outer frame described herein, mutatis mutandis. Similarly, frame  60   a  may be used in combination with other technologies described herein, mutatis mutandis. 
     Reference is made to  FIG.  8   , which is a schematic illustration of a frame assembly  22   b , in accordance with some applications of the invention. Frame assembly  22   b  comprises a valve frame  30   b  and an outer frame  60   b.  Except where noted, frame assembly  22   b,  valve frame  30   b , and outer frame  60   b  are as described for frame assembly  22 , valve frame  30 , and outer frame  60 , respectively. 
     Outer frame  60   b  comprises (or defines) (1) a first (e.g., upstream) ring  74   b  defined by a pattern of alternating first-ring peaks and first-ring troughs, (2) a second (e.g., downstream) ring  76   b  defined by a pattern of alternating second-ring peaks and second-ring troughs, and a plurality of legs  50 , each of the legs coupled to the first ring and the second ring, and extending radially outward. 
     Valve frame  3011  comprises a tubular portion (e.g., a tubular frame) that has a cellular structure defined by a plurality of metallic elements with spaces therebetween a e.g., as described for valve frame  30 , mutatis mutandis. 
     The cellular structure of the valve frames described herein may also be viewed as defining rings of alternating peaks and troughs, the rings circumscribing the longitudinal axis of the implant. Whereas the waveform (i.e., the peak-trough waveform) of the rings of the outer frame are in phase with each other, the phase of the waveform of the rings of the valve frame typically alternate with respect to each other. That is, for the valve frame, the waveform of one ring is out of phase (e.g., is in antiphase) with that of its axially-adjacent rings. For example, and with reference to  FIG.  1 B , valve frame  30  defines a first (e.g., upstream) ring  182 , a second (e.g., middle) ring  184 , and a third (e.g., downstream) ring  186 , and ring  184  is in antiphase with rings  182  and  184 . Valve frame  30   b  similarly defines a first (e.g., upstream) ring  182   b,  a second (e.g., middle) ring  184   b,  and a third (e.g., downstream) ring  186   b,  and ring  184   b  is in antiphase with rings  182   b  and  184   b.    
     Typically, and as shown for each of the implants described herein, when the frame assembly is assembled, (1) the waveform of one of outer frame rings is in-phase with the waveform of the inner frame ring with which it is axially aligned, and (2) the waveform of one of outer frame rings is out of phase (e.g., is in antiphase) with the waveform of the inner frame ring with which it is axially aligned. For example, and with reference to  FIG.  1 C , ring  74  is in-phase with the ring of the inner frame with which it is axially aligned (ring  184 ), whereas ring  76  is in antiphase with the ring of the inner frame with which it is axially aligned (ring  186 ). Similarly, for frame assembly  22   b,  ring  741 ) is in-phase with the ring of the inner frame with which it is axially aligned (ring  184   b ), whereas ring  76   b  is in antiphase with the ring of the inner frame with which it is axially aligned (ring  186   b ). 
     Because ring  76   b  is in antiphase with ring  186   b,  the peaks of ring  76   b  are not disposed directly radially outward from respective parts of frame  30   b,  and therefore are not in contact with frame  30   b.  However, despite ring  74   b  being in phase with ring  184   b,  and the peaks of ring  74   b  being disposed directly radially outward from respective parts of frame  30   b,  the peaks of ring  74   b  are also not in contact with frame  30   b.  That is, frame assembly  22  defines a radial gap  188  between frames  30  and  60  at the peaks of ring  74   b.  Typically, therefore, none of the peaks of the rings of frame  60   b  is in contact with inner frame  30   b.  In contrast, for frame assembly  22 , although the peaks of ring  76  are not in contact with frame  30 , the peaks of ring  74  typically are in contact with frame  30 . 
     The features of frame assembly  22   b  may be used in combination with other implants described herein. For example, other frame assemblies described herein may be shaped to define gap  188 , mutatis mutandis. 
     Reference is made to  FIGS.  9 A-B , which are schematic illustrations of an inner frame  330   a,  and an implant  320   a  comprising inner frame  330   a,  in accordance with some applications of the invention. Inner frame  330   a  may be used in place of other inner frames of implants described herein, mutatis mutandis. Similarly, frame  330   a  may be used in combination with other technologies described herein, mutatis mutandis. Inner frame  330   a  comprises a valve body (which is a generally tubular portion)  332   a  that has an upstream end  334   a  and a downstream end  336   a,  and is shaped to define a lumen through the valve body from its upstream end to its downstream end. Valve frame  330   a  further comprises a plurality of arms  46 , each of which, in the expanded state, extends radially outward from valve body  332   a.    
     Valve body  332   a  has a cellular structure defined by a plurality of joists  28  connected at a plurality of nodes  102 , the joists and nodes delimiting cells of the cellular structure. Except where noted, inner frame  330   a  is generally the same as inner frame  230  (or inner frame  30 ), mutatis mutandis, and valve body  332   a  is generally the same as valve body  32 , mutatis mutandis. Compared to valve body  32 , valve body  332   a  comprises additional joists  28 , which are hypothesized by the inventors to increase strength and rigidity. In particular, the additional joists are hypothesized by the inventors to increase the resistance of the valve body to compression toward axis ax 1 , including resistance to circumferential compression (e.g., compression that would otherwise reduce the diameter of the valve body, but that would retain the valve body in a generally cylindrical shape) and localized compression (e.g., compression that would otherwise reduce the diameter of the valve body at only certain locations, causing the valve body to become more oval in transverse cross-section). 
     Referring back to  FIGS.  1 A-B , the cellular structure of valve body  32  is such that its nodes  100  typically connect 2-4 of its joists. For example, a node  100   a  connects two joists, and a node  100   b  connects four joists. (In this context, neither arms  46  nor projections  246  are joists of the valve body&#39;s cellular structure, and so sites  35  and  34  are also nodes that connect 2-4 joists.) In contrast, the cellular structure of valve body  332   a  is such that some of its nodes  102  are minor nodes  104 , and some are major nodes  106 . Minor nodes  104  connect 2-4 joists, whereas major nodes  106  connect 6-8 joists. Typically, and as shown, major nodes  106  connect  6  joists (again, excluding arms  46 , which are not joists of the valve body&#39;s cellular structure). Typically, and as shown, minor nodes  104  connect 2 joists. Therefore, for some applications, none of the nodes  102  of the cellular structure of valve body  332   a  connects 4 joists. 
     Similarly to valve body  32  of frame  30 , the cells of the cellular structure of valve body  332   a  comprise a first circumferential row  109   a  of cells, and a second circumferential row  109   b  of cells. That is, row  109   a  is a row of first-row cells, and row  109   b  is a row of second-row cells. Each of the cells of row  109   a  is connected to each of its circumferentially-adjacent first-row cells at a respective major node  106 . Typically, and as shown, each of the cells of row  109   a  is longitudinally delimited by two minor nodes  104  (i.e., the upstream end and the downstream end of each cell is at a respective minor node). It is to be noted that, typically, each of the cells of row  109   a  is not connected to another cell at these minor nodes  104  (i.e., the minor nodes that longitudinally delimit the first-row cell). 
     Each of the cells of row  109   b  is connected to each of its circumferentially-adjacent second-row cells at a respective major node  106 . Typically, and as shown, each of the cells of row  109   b  is longitudinally delimited by at least one major node  106  (e.g., is delimited by one major node at an upstream end of the cell). Typically, and as shown, each of the cells of row  109   b  is also longitudinally delimited by a minor node  104  (e.g., at a downstream end of the cell). For some applications, and as shown, each of the major nodes  106  at which circumferentially-adjacent first-row cells are connected is also the major node that longitudinally-delimits a respective second-row cell (e.g., at the upstream end of the second-row cell). In the example shown, that common major node  106  is also site  35 , at which arms  46  are attached to the valve body. 
     The cells of the cellular structure of valve body  332   a  are typically delimited by exactly four nodes  102 . 
     Frame  330   a  defines coupling elements  31 , which are fixed to coupling elements  61  of frame  60  at coupling points, as described hereinabove for frame assembly  22 , mutatis mutandis. For some applications, and as shown, coupling elements  31  are defined by respective major nodes  106 . Therefore, for some applications, a frame assembly comprises (i) inner frame  330   a  that defines valve body  332   a,  and (ii) an outer frame (e.g., frame  60 ) that circumscribes the valve body, and is coupled to the inner frame by being fixed to major nodes of the valve body. For such applications, coupling elements  31  are typically defined by the major nodes at which circumferentially-adjacent second-row cells are connected. 
     For some applications, and as shown, valve body  332   a  is defined by exactly two stacked, tessellated rows  109  of cells. That is, typically, first row  109   a  is the most upstream row, second row  108   b  is the most downstream row, and these two rows are tessellated with each other. Therefore, for some applications, all the cells of the cellular structure of valve body  332   a  are either first-row cells or second-row cells. 
     Valve body  332   a  may be described as comprising pairs  108  of joists  28  that run generally parallel to each other. In the expanded state of the valve body (i.e., the state shown in  FIG.  7   ) the joists  28  of each pair  108  are disposed 0.1-1 mm (e.g., 0.25-0.9 mm, such as 0.25-0.65 mm) from each other. Although the joists  28  of each pair  108  run generally parallel to each other, they typically only share one node  102  in common. That shared common node is typically a major node  106 . That is, at a first end of each pair  108 , both joists  28  are typically connected to each other at a major node. In some cases, at a second end of each pair  108 , one of the joists connects to another major node  106 , but the other joist connects to a minor node  104  that is disposed a distance d 12  away from the major node at the second end of the pair. In other cases, at the second end of each pair  108 . one of the joists connects to a first minor node, and the other joist connects to another minor node that is disposed a distance d 12  away from the first minor node. Distance d 12  is typically 0.1-1 mm (e.g., 0.25-0.9 mm, such as 0.25-0.65 mm). 
     For some applications, and as shown, the arrangement of joists  28  in pairs  108  results in the joists that delimit the cells of first row  109   a  not delimiting the cells of second row  1091 ). That is, for some applications, no individual joist  28  delimits both a first-row cell and a second-row cell. 
     Another aspect of valve body  332   a  is as follows: Major nodes  106  are typically arranged in major-node rows, each major-node row circumscribing longitudinal axis ax 1  at a respective major-node-row longitudinal site, and minor nodes  104  are typically arranged in minor-node rows, each minor-node row circumscribing the longitudinal axis at a respective minor-node-row longitudinal site. Along at least part of axis ax 1 , the minor-node-row longitudinal sites alternate with the major-node-row longitudinal sites. For some applications, along at least this part of axis ax 1 , at least 3 minor-node-row longitudinal sites alternate with at least 2 major-node-row longitudinal sites, e.g., in the order minor-major-minor-major-minor, as shown. 
     Reference is now made to  FIGS.  10 A-B  which are schematic illustrations of an inner frame  330   b,  and an implant  320   b  comprising inner frame  330   b,  in accordance with some applications of the invention. Inner frame  330   b  may be used in place of other inner frames of implants described herein, mutatis mutandis. 
     Inner frame  330   b  comprises a valve body (which is a generally tubular portion)  332   b  that has an upstream end  334   b  and a downstream end  336   b,  and is shaped to define a lumen through the valve body from its upstream end to its downstream end. Valve frame  330   b  further comprises a plurality of anus  46 , each of which, in the expanded state, extends radially outward from valve body  332   b.  Inner frame  330   b  is typically the same as inner frame  330   a,  except where noted. Compared to inner frame  330   a,  inner frame  330   b  comprises additional joists  28  at upstream end  334   b.  That is, in contrast to inner frame  330   a,  for inner frame  330   b  pairs  108  of joists are also disposed at the upstream side of the upstream row of cells. 
     In frame  330   a,  sites  37  are coincident with the upstream extremity of a respective upstream-row cell. In contrast, in frame  330   b,  sites  37  are not coincident with the upstream extremity of a respective upstream-row cell. Rather, sites  37  are coincident with a minor node that joins the joists that are paired with (e.g., that are parallel with) the joists of the respective upstream-row cell. 
     Implant  320   b  is typically the same as implant  320   a,  except that it comprises inner frame  330   b  instead of inner frame  330   a.    
     Reference is now made to  FIGS.  11 A-B , which are schematic illustrations of an inner frame  330   c,  and an implant  320   c  comprising inner frame  330   c,  in accordance with some applications of the invention. Inner frame  330   c  may be used in place of other inner frames of implants described herein, mutatis mutandis. 
     Inner frame  330   c  comprises a valve body (which is a generally tubular portion)  332   c  that has an upstream end  334   c  and a downstream end  336   c,  and is shaped to define a lumen through the valve body from its upstream end to its downstream end. Valve frame  330   c  further comprises a plurality of arms  46 , each of which, in the expanded state, extends radially outward from valve body  332   c.  Inner frame  330   c  is typically the same as inner frame  330   b,  except where noted. 
     In general, for implants having an expandable cellular structure, such as the valve bodies described herein, for a given size of the implant, a cellular structure that defines fewer, larger cells, advantageously facilitates radial compression (i.e., “crimping”) to a smaller diameter than does a comparable cellular structure that defines more, smaller cells. However, this is typically at the expense of strength and rigidity of the expanded valve. As described hereinabove, the presence of additional joists  28  (e.g., in inner frames  330   a,    330   b,  and  330   c ) to form pairs  108  is hypothesized to increase strength and rigidity, in particular with respect to compression toward the central longitudinal axis. As a result, it is further hypothesized by the inventors that using such a paired joist cellular structure facilitates reducing the number, and increasing the size, of the cells of the valve body, in order to achieve a valve body that is radially compressible to a smaller diameter while maintaining sufficient strength and rigidity. 
     Accordingly, valve body  332   c  of inner frame  330   c  has fewer, larger cells compared to valve body  32  of inner frame  30 , and is therefore radially compressible to a smaller diameter. Whereas each row of cells of valve body  32  includes 12 cells, each row of cells of valve body  332   c  includes 9 cells. More generally, whereas the rotationally-symmetrical pattern of valve body  32  has 12 repeats (e.g., 12 cells per cell row, 12 minor nodes per minor-node row, 12 major nodes per major-node row, 12 coupling elements, 12 arms  46 ), the rotationally-symmetrical pattern of valve body  132   c  has only 9 repeats. (Both valve body  32  and valve body  332   c  typically have 3 appendages  80  and 3 projections  246 .) Both valve body  32  and valve body  332   c  define two rows of cells. Therefore, whereas valve body  32  defines 24 cells in total, valve body  332   c  defines 18 cells in total. Whereas valve body  32  defines exactly 24 major nodes, valve body  332   c  defines exactly 18 major nodes. 
     For some applications, and as shown, inner frame  330   c  comprises additional joists  28  at upstream end  334   c  (e.g., similarly to inner frame  330   b ). That is, for such applications, pairs  108  of joists are typically also disposed at the upstream side of the upstream row of cells of inner frame  330   c.  For such applications, implant  320   c  is typically the same as implant  320   b,  except that implant  320   c  comprises 9 rotationally-symmetrical repeats, rather than 12. 
     For some applications, inner frame  330   c  does not comprise additional joists  28  at upstream end  334   c,  and is instead more like inner frame  330   a  in this regard. 
     Reference is again made to  FIGS.  9 A- 11 B . It is to be noted that although the above-described arrangements of joists connected at major and minor nodes are described in the context of a prosthetic heart valve, the scope of the invention includes using such arrangements in other implants or components thereof that comprise a cellular structure, such as stents. 
     Reference is made to  FIGS.  12 A-H , which are schematic illustrations of a technique for use with a frame of a prosthetic valve, in accordance with some applications of the invention. The technique is for augmenting a tissue-engaging flange of the frame with a soft pad  300 . To illustrate the technique.  FIGS.  12 A-H  show the technique being used to augment flanges  54  of outer frame  60  with soft pads  300 , hut it is to be noted that the technique may be used with any suitable frame, mutatis mutandis. 
       FIG.  12 A  shows frame  60 , which has tissue-engaging flanges  54 . A model  302  of a soft pad  300  with which each flange  54  is to be augmented is affixed to the respective flange ( FIG.  12 B ). Subsequently, a mold  304  is formed by (i) positioning frame  60  such that models  302  are supported within a fluid  310   f  of a first substance  310  while the first substance solidifies, and (ii) subsequently, removing the models from the first substance, leaving a cavity in the solidified first substance. For example, and as shown in  FIGS.  12 C-E , a bath  306  of fluid  310   f  may be prepared, and frame  60  may be inverted and lowered into the bath such that models  302  are supported within the fluid ( FIG.  12 C ). First substance  310  is allowed to solidify into solidified first substance  310   s  ( FIG.  12 D ). Subsequently, frame  60  is withdrawn from the bath, thereby removing models  302  from solidified first substance  310   s,  such that each model leaves a respective cavity  308  in solidified first substance  310   s  ( FIG.  12 E ). 
     Models  302  are then removed from flanges  54  ( FIG.  12 F ). Pads  300  are then formed by: (i) placing flanges  54  in contact with a second substance  312  by repositioning the frame such that each flange is supported within a respective cavity  308 , and introducing a fluid  312   f  of the second substance to the cavity ( FIG.  12 G ), and (ii) while the flange remains in contact with the second substance, allowing the second substance to solidify into solidified second substance  312   s  and to become affixed to the flange. Subsequently, flanges  54  are removed from cavities  308  with formed pads  300  (comprising solidified second substance  312   s ) affixed to the flanges ( FIG.  12 H ). 
     The technique described with reference to  FIGS.  12 A-H  may be used with a frame that has a single tissue-engaging flange. However, as shown, the technique is typically used with a frame that has a plurality of flanges, e.g., to augment all the flanges simultaneously. It is to be noted that flanges  54  are not all disposed on the same side of frame assembly  22  (i.e., after frames  30  and  60  have been attached to each other). For example, flanges  54  are not all at the upstream end of the prosthetic valve or at the downstream end of the prosthetic valve. Rather, they are disposed downstream of the tips of arms  46  and upstream of downstream end  26 . 
     Furthermore, flanges  54  are arranged circumferentially around the longitudinal axis of the prosthetic valve. Flanges  54  (and eventually pads  300 ) are arranged circumferentially around frame  30  longitudinally between the upstream end and the downstream end of frame  30 , exclusive. For some applications, the flanges being not all disposed on the same side might inhibit the use of the technique of  FIGS.  12 A-H  to simultaneously augment all of the flanges. 
     For example, it may be difficult to place all of models  302  into the fluid first substance, or to place all of flanges  54  into the fluid second substance, without also placing other portions of the frame assembly into the fluid substance. The two-frame nature of frame assembly  22  advantageously allows flanges  54  to be augmented with pads before frame  60  is attached to frame  30 . Because all of flanges  54  are disposed at the same side (e.g., the upstream side) of frame  60 , they can all be placed into the fluid substances simultaneously. 
     An alternative solution is also contemplated by the inventors, in which an annular bath is positioned circumscribing the central portion of the prosthetic valve or frame assembly, such that all flanges can be placed into the fluid substances even when the flanges are not all disposed on the same side of a prosthetic valve or frame assembly. 
     For some applications, substance  310  and/or substance  312  may be a mixture of constituents that is initially fluid upon mixing, and that solidifies as the constituents react with each other. For some applications, fluid substance  310   f  and/or fluid substance  312   f  is fluid because it is in a molten state, and solidifies as it cools. When solidified, second substance  312  is typically soft, flexible, and/or resilient. For some applications, second substance  312  (or at least solidified second substance  312   s ) is a foam. For some applications, second substance  312  comprises silicone, polyurethane, a thermoplastic elastomer such as Santoprene (™), and/or polyether block amide. 
     For some applications, the techniques described with reference to  FIGS.  12 A-H  are alternatively or additionally used, mutatis mutandis, to augment the downstream end of the implant with one or more pads, e.g., to serve a similar function to ring  78  described hereinabove. 
     Reference is made to  FIGS.  13 A-E ,  14 A-D,  15 A-C,  16 A-C,  17 ,  18 A-C, and  19 , which are schematic illustrations of an implant  420 , and steps in the assembly of the implant, in accordance with some applications of the invention. In particular, these figures illustrate steps in the attachment of various flexible components to the frame assembly of the implant, such as steps in the dressing of the frame assembly with various sheets of flexible material. Implant  420  is shown as comprising frame assembly  222 , and is typically identical to implant  220  except for where described otherwise. However, it is to be noted that the steps described with reference to  FIGS.  13 A- 18 C  may be used, mutatis mutandis, to assemble other implants, including the other implants described herein. 
       FIGS.  13 A-E  show flexible components of implant  420 .  FIGS.  13 A-B  are perspective and side views, respectively. of a valvular assembly  430 , comprising leaflets  58  arranged to serve as a check valve. In valvular assembly  430 , each leaflet  58  defines (i) an upstream surface  457 , past which blood will flow through implant  420  in an upstream-to-downstream direction, and (ii) a downstream surface  459 , against which blood will press when the valvular assembly closes and inhibits blood flow in a downstream-to-upstream direction. Valvular assembly  430  typically further comprises a liner  427  and/or a plurality of connectors  432 . Liner  427  of implant  420  generally corresponds to liner  27  of implant  20 , mutatis mutandis. Typically, valvular assembly  430  comprises three leaflets  58  and three connectors  432 . Connectors  432  couple the leaflets to each other to form commissures, and are used to secure the leaflets, at the commissures, to frame assembly  222 . Connectors  432  are arranged circumferentially, and leaflets  58  extend radially inward from the connectors. For some applications, valvular assembly  430 , and connectors  432  in particular, are as described in PCT patent application publication WO 2018/029680 to Hariton et al., and/or U.S. patent application Ser. No. 15/878,206 to Hariton et al. both of which are incorporated herein by reference. 
     Each leaflet  58  is attached (e.g., stitched) to liner  427  along a line (e.g., a stitch line)  437 . Each leaflet  58  defines a free edge  458 , which is typically straight, and at which the leaflet coapts with the other leaflets  58 . Stitch line  437  is typically curved. Each leaflet typically defines a curved edge (e.g., an upstream edge)  456  at which the leaflet is attached to liner  427 . The curve of edge  456  and/or stitch line  437  is concave toward the downstream end of valvular assembly  430 , such that edge  456  and/or stitch line  437  (i) become closer to the downstream end of the valvular assembly at connectors  432 , and (ii) are closest to the upstream end of the valvular assembly about midway circumferentially between the connectors. That is, edge  456  has an apex about midway circumferentially between connectors  432 . 
     Typically, and as shown, leaflets  58  extend further axially downstream (i.e., downstream with respect to axis ax 1 ) than does liner  427 . Therefore, a downstream portion of each leaflet  58  is typically circumferentially expose d from liner  427 . For some applications, and as shown, liner  427  is shaped to define regions  428  at which a downstream edge  436  of the liner recedes from the downstream end of valvular assembly  430 . At each region  428 , more of the respective leaflet  58  is circumferentially exposed. Each region  428  is typically circumferentially aligned with the concavity defined by edge  456  and/or stitch line  437 . At regions  428 , downstream edge  436  of liner  427  is typically stitched to ring  182  of frame  230 . Therefore, for some applications, the most upstream parts of downstream edge  436  of liner  427  are closer to the upstream end of the implant than is the most downstream parts of arms  46 . As described in more detail hereinbelow, in implant  420 , regions  428  of liner  427  facilitate the provision of windows  482  into a pouch  490 . 
       FIG.  13 C  shows a sheet  440  of flexible material. Typically, and as shown, sheet  440  is provided flat, and in the shape of a major are of an annulus, having a first are-end  442   a  and a second are-end  442   b.  Sheet  440  of implant  420  generally corresponds to annular sheet  25  of implant  20 , mutatis mutandis. 
       FIG.  3 D  shows a sheet  450  of flexible material. Sheet  450  is annular, and defines an inner perimeter  452 , an outer perimeter  454 , and a radial dimension d 21  therebetween. 
       FIG.  13 E  shows a sheet  460  of flexible material. Sheet  460  is shaped to define a belt  462  and a plurality of elongate strips  461 . Each strip  464  defines a respective central strip-axis ax 2 , and extends along its strip-axis from belt  462  to the end  466  of the strip. Typically, belt  462  is linear and defines a belt-axis ax 3 , and strip-axis ax 2  is orthogonal to the belt-axis. Typically, strips  464  are parallel to each other. Each strip  464  has first and second edges  468  (e.g., a first edge  468   a  and a second edge  468   b ), which extend on either side of axis ax 2 , between belt  462  and end  466 . 
     As indicated by the reference numeral  23 , sheets  440 ,  450 , and  460  may all be considered components of sheeting  23 . For some applications, liner  427 , sheet  440 , sheet  450 , and/or  460  comprise (e.g., consist of) the same material as each other. Typically, sheets  440 ,  450 , and  460  are provided as flat, and are subsequently shaped during assembly of implant  420 , e.g., as described hereinbelow. 
     For applications in which sheet  440  is provided flat and in the shape of a major are of an annulus, sheet  440  is shaped into an open frustum by attaching (e.g., stitching) ends  442   a  and  4421 ) together ( FIGS.  14 A-B ). This is represented by a stitch line  444  in  FIG.  14 B . Alternatively, sheet  440  may be provided in the open frustum shape. The open frustum shape has a greater perimeter  446  at a first base of the frustum, and a smaller perimeter  448  at a second base of the frustum. Perimeter  448  defines an opening, and sheet  440  is stitched to arms  46  such that the opening is aligned with the lumen defined by valve body  32  of frame  30  ( FIG.  14 C ), and typically such that the sheet covers an upstream side of the arms.  FIG.  14 D  shows valvular assembly  430  having been coupled to frame assembly  222 . This step may be performed after sheet  440  is stitched to arms  46  (as shown) or beforehand. Valvular assembly  430  is placed inside valve body  32  of frame  30 , and is attached by stitching connectors  432  and liner  427  to frame assembly  222 . Connectors  432  are typically stitched to ring  184  and/or ring  186 . For some applications, the attachment of connectors  432  to frame assembly  222  is as described in PCT patent application publication WO 2018/029680 to Hariton et al., and/or U.S. patent application Ser. No. 15/878,206 to Hariton et al., both of which are incorporated herein by reference. 
     Smaller perimeter  448  of sheet  440  is stitched to an upstream edge  434  of liner  427 , to form a substantially sealed channel through implant  420 . This stitching is represented by a stitch line  435 . Typically, and as shown, projections  246  extend between, and are sandwiched between, perimeter  448  of sheet  440  and upstream edge  434  of liner  427 . Upstream edge  434  is typically circular. 
     Downstream edge  436  of liner  427  is stitched to valve body  32  of frame  30 . Typically, downstream edge  436  is shaped and positioned to approximately conform to rings  182  and  184 , and is stitched to these rings. 
     It is to be noted that throughout this patent application (including the specification and the claims) stitching of a perimeter or edge of a sheet to a perimeter or edge of another sheet, does not necessarily mean that the sheets are stitched at their absolute edges (i.e., their free edges). Rather, in this context, the “perimeter” or “edge” also includes the adjacent area of the sheet, as is understood by one of ordinary skill in the stitching art, and as is typically required for effective stitching. 
     Valvular assembly  430  is typically positioned within frame assembly such that the apex of curved edge  456  of each leaflet  58  is disposed axially close to (e.g., axially within 2 mm of, e.g., within 1 mm of) an upstream end  34  of valve body  32 . Valvular assembly  430  is also typically positioned within frame assembly such that free edge  458  of each leaflet  58  is disposed downstream of leg  50 . 
     Subsequently, sheet  450  is attached to frame assembly  222  ( FIGS.  15 A-C ). Outer perimeter  454  of sheet  450  is stitched to greater perimeter  446  of the sheet  440  ( FIG.  15 A ). This is represented by stitch line  455 . Typically, perimeter  454  is larger than perimeter  446 , and is brought inwards to be stitched to perimeter  446  (e.g., making sheet  450  frustoconical), with inner perimeter  452  disposed axially away from frame assembly  222  (e.g., further axially away than outer perimeter  454  from the frame assembly). 
     Subsequently, sheet  450  is everted by bringing inner perimeter  452  toward frame assembly  222 , and passing the inner perimeter around the tips of arms  46 —i.e., axially past the tips of all of the arms ( FIG.  15 B ). Typically, and as shown, arms  46  collectively define an arm-span ( 123  that is wider than perimeter  452 . That is, the tips of arms  46  typically define a perimeter that is greater than perimeter  452 . For some applications, the passage of inner perimeter  452  around the tips of arms  46  is facilitated by bending (e.g., temporarily) one or more of arms  46 . 
     Inner perimeter  452  is advanced over at least part of valve body  32  toward a downstream end of frame assembly  222 , and is stitched in place. Typically, perimeter  452  is advanced between the valve body and legs  50 , such that perimeter  452  circumscribes valve body  32 , and legs  50  are disposed radially outside of sheet  150 . As described hereinabove, each leg  50  extends radially outward and in an upstream direction from a respective leg-base  66  to a respective leg-tip  68 . Each leg therefore extends at an acute angle to define a respective cleft  250  between the leg and valve body  32  (e.g., the tubular portion), the cleft open to the upstream direction. Typically, perimeter  452  is tucked into clefts  250 , and is stitched into place. Frame assembly  222  defines a distance d 22 , measured along a straight line, between the ends of arms  46  and clefts  250 . For clarity, distance d 22  may be defined as a distance between (i) an imaginary ring described by the ends of arms  46 , and (ii) an imaginary ring described by clefts  250 . 
     The dimensions and positioning of sheet  450  defines an inflatable pouch  490  that is bounded by sheet  450  (e.g., defining an outer and/or downstream wall of the pouch), sheet  440  (e.g., defining an upstream wall of the pouch), and liner  427  (e.g., defining an inner wall of the pouch). Pouch  490  typically circumscribes the longitudinal axis of the implant and/or the valve body of frame assembly  222  (e.g., the pouch is a cuff), and further typically extends radially outward from the valve body. Typically, an upstream portion of pouch  490  is attached to valve frame  30  (e.g., and is not attached to outer frame  60 ), and a downstream portion of the pouch is attached to the outer frame. As described in more detail hereinbelow, at least one respective window  482  into pouch  490  is defined between each leaflet  58  and perimeter  452 . 
       FIG.  16 A-C  show steps in dressing frame assembly  222  with sheet  460 , in accordance with some applications of the invention. Each strip  461  is formed into a respective pocket  478  ( FIGS.  16 A-B ). Each strip is folded over itself, about a fold-line  463  that is orthogonal to strip-axis ax 2 , thereby forming (i) a first strip-portion  464   a  that extends from belt  462  to the fold-line, and (ii) a second strip-portion  464   b  that extends from fold-line hack toward the belt. First strip-portion  464   a  and second strip-portion  464   b  are stitched together at first edge  468   a  and second edge  468   b.  The resulting pocket  478  is typically elongate, and has (i) an opening  470  defined at least in part by end  466  of the strip, and (ii) a tip  472  at the fold-line. 
     For some applications, a soft pad  476  is provided in each pocket  478 , typically at tip  472 . For some such applications, and as shown in  FIG.  15 B , pad  476  is formed from a piece of foam  474  (e.g., comprising polyurethane). Piece of foam  474  may initially be generally cubic. For some applications, and as shown, piece of foam  474  is folded to form a niche  477  in pad  476 , typically after having been at least partly flattened by compression. Pad  476  may be introduced into pocket  478  before the pocket is fully formed (e.g., as shown), or may be subsequently introduced into the pocket via opening  470 . 
     Alternatively, pads  300  may be used in place of pads  476 , and may be added to flanges  54  as described with reference to  FIGS.  12 A-H , mutatis mutandis. 
     For applications in which pad  476  is used, each strip-portion  464   a  and  464   b  typically defines a widened region  479  adjacent to fold-line  463 , such that when pockets  478  are formed, a receptacle for pad  476  is formed. 
     Pockets  478  are subsequently slid onto legs  50 , and belt  462  is wrapped around frame assembly  222  downstream of legs  50  (e.g., downstream of the axial level at which the legs are coupled to the valve body). Belt  462  is typically positioned such that it is disposed over the commissures of leaflets  58  and/or over connectors  432 . That is, the belt is typically wrapped around the frame assembly at an axial level such t For applications in which pads  476  are used, flanges  54  of legs  50  are typically advanced into niches  477  of the pads. Belt  462  (e.g., the edge of the belt from which pockets  478  extend) is stitched to sheet  450 . More specifically, the upstream edge of belt  462  is stitched circumferentially to perimeter  452  of sheet  450 . This is represented by a stitch line  465 . Therefore, once implant  420  is assembled, the edge of belt  462  from which pockets  478  extend is an upstream edge of the belt, while the edge that is closest to the downstream end of the implant is a downstream edge of the belt. Legs  50 , within pockets  478 , extend radially outward from between belt  462  and sheet  450  (e.g., at stitch line  465 ). 
     For some applications, tips  472  and/or pads  476  are further secured to flanges  54  by stitching  475 , which may pass through a hole  55  (labeled in  FIG.  1 A ) defined in each flange  54 . Stitching  475  is visible in  FIGS.  18 A-C . 
     As shown in  FIG.  16 C , for some applications, polytetrafluoroethylene ring  78  is typically also attached to frame assembly  222 . For some such applications, in addition to being stitched to frame assembly  222 , ring  78  is also stitched to belt  462  (e.g., to the edge of the belt opposite pockets  478 —i.e., the downstream edge of the belt). 
       FIG.  17    shows a ribbon  480  being wrapped around the leg-base  66  of each leg  50 , in accordance with some applications of the invention. For some applications, the ends of ribbon  480  overlap. Ribbons  480  are stitched in place, but the stitches are typically not disposed in cleft  250 . As shown, ribbons  480  may be stitched to belt  462 . Although ribbons  480  are shown being used in combination with pockets  478  (and are therefore wrapped around the pockets at leg-base  66 ), it is to be noted that ribbons  480  may alternatively be used for applications in which legs  50  are generally uncovered. Ribbon  480  covers cleft  250 , and is hypothesized by the inventors to reduce a likelihood of tissue (e.g., leaflet or chordae tissue) from becoming wedged in and/or damaged by the cleft. 
       FIGS.  18 A-C  show implant  420  alter its assembly.  FIG.  18 A  is an upper perspective view (e.g., showing upstream surfaces of the implant),  FIG.  18 B  shows a side view, and  FIG.  18 C  shows a lower perspective view (e.g., showing downstream surfaces of the implant). 
     As described with reference to  FIGS.  3 E-F , implant  20  (which comprises frame assembly  22 ) is secured in place at the native valve by sandwiching tissue of the native valve between the implant&#39;s upstream support portion  40  and flanges  54 . Implants that comprise frame assembly  222 , such as implant  220 , are typically secured in the same way, mutatis mutandis. Implants that further comprise pouch  490 , such as implant  420 , are typically secured similarly, but with pouch  490  disposed between the upstream support portion and the tissue of the native valve. Therefore in at least some regions of implant  420 , the tissue of the native valve is sandwiched between flanges  54  and pouch  490 , e.g., as shown in  FIG.  19   . 
     Windows  482  open into pouch  490  from the lumen of the valve body. Once implant  420  has been implanted at the native valve, windows  482  are disposed functionally within ventricle  8 , whereas at least portions of pouch  490  are disposed functionally within atrium  6 . Therefore, during ventricular systole, ventricular pressure (which is much greater than atrial pressure) forces blood into pouch  490 , thereby inflating the pouch. This inflation presses pouch  490  against the tissue of the native valve, it is hypothesized by the inventors that this inhibits paravalvular leakage of blood, especially during ventricular systole. For example, the pouch may seal a paravalvular gap at the commissures of the native valve. For some applications, inflation of pouch  490  squeezes tissue of the native valve (e.g., native leaflets) between the pouch and flanges  54 . Pouch  490  is typically dimensioned such that if, in a particular region, tissue is not disposed between a flange  54  and pouch  490 , inflation of the pouch presses the pouch against the flange. 
     There is therefore provided, in accordance with an application of the present invention, apparatus, comprising:
         a frame assembly (e.g., frame assembly  222 ) that comprises: (i) a valve body that circumscribes a longitudinal axis and defines a lumen along the axis; (ii) a plurality of arms (e.g., arms  46 ) that are coupled to the valve body at a first axial level with respect to the longitudinal axis (e.g., defined by sites  35 ), each of the arms extending radially outward from the valve body to a respective arm-tip; and (iii) a plurality of ventricular legs (e.g., legs  50 ) that (a) are coupled to the valve body at a second axial level with respect to the longitudinal axis (e.g., defined by coupling points  52 ), the second axial level being downstream of the first axial level, and that (b) extend radially outward from the valve body and toward the plurality of arms;   a tubular liner (e.g., liner  427 ) that lines the lumen, and that has an upstream end and a downstream end;   a plurality of prosthetic leaflets (e.g., leaflets  58 ), disposed within the lumen, attached to the liner, and arranged to facilitate one-way upstream-to-downstream fluid flow through the lumen;   a first sheet of flexible material (e.g., sheet  440 ), the first sheet having (i) a greater perimeter, and (ii) a smaller perimeter that defines an opening, the first sheet being attached to the plurality of arms with the opening aligned with the lumen of the valve body; and   a second sheet of flexible material (e.g., sheet  450 ):
           the second sheet having a first perimeter and a second perimeter,   the first perimeter being attached to the greater perimeter of the first sheet around the greater perimeter of the first sheet,   the second sheet extending from the first perimeter radially inwards and downstream toward the second perimeter, the second perimeter circumscribing,   and attached to, the valve body at a third axial level that is downstream of the first axial level.   
               

     The first sheet, the second sheet, and the liner define inflatable pouch  490  therebetween, the first sheet defining an upstream wall of the pouch, the second sheet defining a radially-outer wall of the pouch, and the liner defining a radially-inner wall of the pouch. The apparatus defines a plurality of windows (e.g., windows  482 ) from the lumen into the pouch, each of the windows bounded by the liner at upstream edges of the window, and bounded by the second perimeter and/or belt  462  at a downstream edge of the window. Each window  482  is typically discrete—i.e., bounded on all sides, and separate from other windows. For some applications in which downstream edge  436  of liner  427  is stitched to ring  182  of frame  230 , the most upstream parts of windows  482  are closer to the upstream end of the implant than are the most downstream parts of arms  46 . 
     Typically, and as shown, pouch  490  circumscribes the valve body of implant  420 . 
     Typically, and as shown in  FIG.  18 C , each window  482  spans more than one cell of the valve body. This is represented by the multiple instances of reference numeral  482  in  FIG.  18 C . 
     For some applications, and as shown, each window spans at least partly of five cells of the valve body. For some such applications, and as shown. each window spans substantially all of two cells (e.g., two cells of row  29   a ) and about half (e.g., 40-60 percent) of each of three cells (e.g., three cells of row  29   b ). Each window  482  is bounded by liner  127  at an upstream edge of the window. Typically, and as shown, the upstream edge of each window  482  is defined at rings  182  and  184  of valve frame  230 , at which region  428  of liner  427  is stitched to the valve frame. At the downstream edge of each window, the window is bounded by perimeter  452 , and also by belt  462 . Therefore, at the downstream edge of each window  482 , the window may be considered to be hounded by stitch line  465 . 
     For some applications, the upstream edge of each window  482  is the shape of a capital letter M, e.g., with the apices of the letter M at upstream end  34  of the valve body, and with the vertex of the letter M at a site  35 . Because region  428  of liner  427  follows, and is stitched to, the joists of valve frame  230  at region  428  of the liner, it is hypothesized by the inventors that this arrangement reinforces the upstream edge of window  482 , e.g., increasing durability compared to an arrangement in which the upstream edge of the window crosses between joists of the valve frame. 
     As described hereinabove, sheet  440  typically covers an upstream side of arms  46 . Once pouch  490  has been formed, at least most of each arm  46  is therefore disposed inside the pouch. As also described hereinabove, sheet  440  is stitched to arms  46 . Once pouch  490  has been formed, the pouch (i.e., the part of the pouch defined by sheet  440 ) is therefore stitched to arms  46 . 
     For some applications, a circumferential stitch line  445  is used to stitch sheet  440  to sheet  450  at a radius smaller than the overall radius of upstream support portion  40  (i.e., radially inward from the tips of arms  46 ), typically sandwiching arms  46  between these two sheets. Stitch line  445  is typically radially aligned with region  154  and/or wide (and flexible) portion  46   c  of arm  46 . This typically creates a region  484  in which the portions of sheets  440  and  450  that are disposed radially outward from stitch line  445  are isolated front pouch  490 . For such applications, the ends of arms  46  are therefore typically disposed in region  484 , and are isolated from pouch  490 . 
     For some applications, and as shown, sheet  450  is sufficiently baggy that the sheet (e.g., pouch  490 ) may extend radially outward beyond arms  46 , particularly if uninhibited by tissue of the native valve. This may be achieved by radial dimension d 21  of sheet  450  being greater than distance d 22  between the ends arms  46  and clefts  250 . For some applications, dimension d 21  is more than 30 percent greater (e.g., more than 50 percent greater) than distance d 22 . For example, dimension d 21  may be 30-100 percent greater (e.g., 30-80 percent greater, e.g., 40-80 percent greater, such as 50-70 percent greater) than distance d 22 . As shown, pouch  490  may extend radially outward beyond arms  46  irrespective of the presence of stitch line  445 , which is disposed radially-inward from the ends of arms  46 . 
     Regarding the axial position (i.e., the position along the longitudinal axis of implant  420 ) of pouch  490  and windows  482 . For some applications, pouch  490  extends, with respect to the longitudinal axis of implant  420 , further upstream than the leaflets. That is, for some applications, upstream regions of pouch  490  (e.g., those closest to prosthetic valve support  40 ) are situated further upstream than even the apex of curved edge  456  of leaflets  58 . For some applications, and as shown, each of leaflets  58  is attached to liner  427  upstream of windows  482 . That is, at least the apex of curved edge  456  of leaflets  58  is disposed upstream of windows  482 . Free edge  458  of each leaflet  58  is typically disposed downstream of the third axial level—i.e., the axial level at which perimeter  452  of sheet  450  is attached to frame assembly  222 . That is, leaflets  58  typically extend further downstream than pouch  490 . For some applications. 
     and as shown, the third axial level (i.e., the axial level at which perimeter  452  of sheet  450  is attached to frame assembly  222 ) is upstream of the second axial level (i.e., the axial level at which legs  50  are attached to the valve body). 
     It is to be noted that, whereas liner  427  is disposed on the inside of valve body  32 , sheet  450  and belt  462  are disposed on the outside of the valve body. Axially downstream of windows  482 , valve body  32  is typically not lined i.e., no liner is typically disposed between leaflets  58  and frame  30 . However, belt  462  circumscribes valve body  32  and serves a similar function to a liner—channeling fluid through the lumen of the valve body. 
     It is to be noted that projections  246  are not visible in  FIG.  18 B . For some applications, and as shown, the projection-length of projections  246  (e.g., see projection-length d 13  in  FIG.  5 C ) is such that the projections do not extend further upstream than the tips of arms  46 . For some applications, and as shown, projections  246  extend further upstream than the highest part of arms  46  within concave region  152 . For some applications, and as shown, projections  246  extend to an axial height that is between (a) that of the tips of arms  46 , and (b) that of the highest part of arms  46  within concave region  152 . This is illustrated perhaps most clearly in  FIG.  9 A , which shows inner frame  330   a,  but is applicable to each of the inner frames described herein, mutatis mutandis. 
     Reference is made to  FIGS.  20 , and  21 A -C, which are schematic illustrations of implant  420 , in accordance with some applications of the invention. Pouch  490  defines an interior space  500 . For some applications, and as shown, arms  46  and legs  50  (e.g., flanges  54  thereof) narrow pouch  490  therebetween to form a narrowed portion  510  of the pouch. Narrowed portion  510  typically circumscribes valve body  32  and/or the longitudinal axis of the implant e.g., the narrowed portion being annular. This thereby defines (i) an inner portion  502  of the interior space, radially inward from narrowed portion  510 , and in fluid communication with lumen  38  of the implant (e.g., via windows  482 ), and (ii) an outer portion  504  of the interior space, radially outward from the narrowed portion, and in fluid communication with inner portion  502  via the narrowed portion. At narrowed portion  510  each leg  50  (e.g., flange  54  thereof) typically pushes sheet  450  (which defines a downstream surface of pouch  490 ) toward sheet  440  (which defines an upstream surface of the pouch), such as pressing sheet  450  into contact with sheet  440 . 
     Typically, and as shown, arms  46  and legs  50  alternate circumferentially. That is, when viewed from above, an arm  46  is disposed circumferentially on either side of each leg  50 , and a leg is disposed circumferentially on either side of each arm. This is illustrated for implant  22  in  FIG.  1 D , mutatis mutandis. For applications in which arms  46  and legs  50  alternate circumferentially, at narrowed portion  510  each leg  50  (e.g., flange  54  thereof) forms a respective bulge  506  in sheet  440  (i.e., the upstream surface of pouch  490 ) by pressing sheet  450  (i.e., the downstream surface of the pouch) against the upstream surface (see  FIG.  18 A ). Bulges  506  are therefore disposed circumferentially between arms  46 . It is typically the tip of each leg  50  that presses into sheet  450 , and therefore bulges  506  are typically compact (e.g., as opposed to being elongate). 
     It is to be noted that narrowed portion  510  is therefore formed without pouch  490  being sandwiched directly between arms  46  and legs  50 . It is also to be noted that, at narrowed portion  510 , pouch  490  is stitched to arms  46  but not to legs  50 . For some applications, at narrowed portion  510 , legs  50  extend in an upstream direction past arms  46 . (This can be understood from  FIG.  1 C , mutatis mutandis). For some applications, this configuration results in sheet  450  billowing between legs  50 , e.g., as indicated by reference numeral  508  in  FIG.  18 C . 
     It is to be noted that the configuration described hereinabove exists in implant  420  even prior to implantation—i.e., even in the absence of tissue captured between arms  46  and flanges  54 . 
     For some applications of the invention, narrowed portion  510  impedes fluid communication between outer portion  504  and inner portion  502  (and thereby between the outer portion and the lumen of the implant). It is hypothesized by the inventors that, for some such applications, this advantageously inhibits blood that has entered outer portion  504 , from exiting the outer portion. During ventricular systole, ventricular pressure forces blood through windows  482  into pouch  490  (i.e., inner portion  502  thereof). At least some of this blood typically enters outer portion  504 , e.g., due to the relatively high ventricular pressure. It is hypothesized by the inventors that, at least in part due to narrowed portion  510 , during ventricular diastole, pressure in the opposite direction is insufficient to force as much blood back out of outer portion  504 . It is further hypothesized by the inventors that, for some applications, this results in a net increase in the volume of blood within outer portion  504  during each cardiac cycle. e.g., until resistance inhibits further inflation of outer portion  504 . This is illustrated by the sequence of frames A-F in  FIG.  20   , which represent the state of implant  420  over time.  FIG.  20    shows blood  14  entering outer portion  504  only after inner portion  502  has become substantially filled (frames C-D), but for some applications blood may begin to enter outer portion  504  earlier. 
     It is hypothesized by the inventors that such a configuration of pouch  490  further improves paravalvular sealing provided by the pouch. It is further hypothesized by the inventors that, for some applications of the invention, such a configuration of pouch  490  facilitates the pouch (e.g., outer portion  504  thereof) conforming to the tissue surrounding implant  420 , and therefore further facilitating sealing. For example.  FIGS.  21 A-C  show implant  420  disposed at native valve  10 , when the anatomy of the native valve (e.g., the annulus and/or leaflets) are uneven with respect to the implant. For example, the anatomy itself may be particularly uneven. 
     or the implant may have been implanted at a sub-optimal angle with respect to the anatomy. In the example shown, at a zone  520   a  the anatomy is relatively close to upstream support portion  40 , whereas at a zone  520   b,  the anatomy is relatively spaced apart from the upstream support portion, e.g., resulting in a gap  522  ( FIG.  21 A ). Over time (e.g., between ten seconds and one hour), outer portion  504  fills, in each zone, according to the mechanical constraints of that region ( FIGS.  21 B-C ). In the example shown, in zone  520   a  outer portion  504  inflates with blood until space between upstream support portion  40  and the anatomy (e.g., annulus or leaflet tissue) is filled, and the anatomy resists further inflation of the outer portion ( FIG.  21 B ). In zone  520   b  outer portion  504  continues to inflate with blood because, in this zone, the space between the upstream support portion and the anatomy is larger ( FIG.  21 C ). In this way, it is hypothesized by the inventors that implant  420  advantageously adapts to the native anatomy, providing improved paravalvular sealing. 
     For some applications, at least one coagulation component  530  is disposed within outer portion  504 , and is configured to promote blood coagulation within the outer portion. For some applications, coagulation component  530  is annular and, within outer portion  504 , circumscribes the longitudinal axis of the implant. For some applications, coagulation component  530  comprises a fabric (e.g., comprising polyethylene terephthalate). For some applications, coagulation component  530  comprises polytetrafluoroethylene (e.g., expanded polytetrafluoroethylene), e.g., in the form of a membrane or ribbon. For some applications, coagulation component  530  comprises a metallic (e.g., nitinol or stainless steel) wire, membrane. or mesh, covered by a fabric or expanded polytetrafluoroethylene. For applications, coagulation component comprises a coagulation-inducing drug coated thereon or embedded therein (e.g., within a fabric). For some applications, coagulation component  530  comprises pericardial tissue (e.g., bovine or porcine). 
     For some applications of the invention, the scope of the invention includes using one or more of the apparatus and techniques described in this patent application in combination with one or more of the apparatus and techniques described in one or more of the following documents, each of which is incorporated herein by reference:
         U.S. patent application Ser. No. 15/541,783 to Hariton et al., tiled Jul. 6, 2017, and entitled “Prosthetic valve with axially-sliding frames,” which published as US 2018/0014930 (now U.S. Pat. No. 9,974,651)   U.S. patent application Ser. No. 15/668,659 to Hariton et al., filed Aug. 3, 2017, and entitled “Techniques for deployment of a prosthetic valve,” which published as US 2017/0333187   U.S. patent application Ser. No. 15/668,559 to Jamberger et al., filed Aug. 3, 2017, and entitled “Prosthetic heart valve”   U.S. patent application Ser. No. 15/956,956 to Jamberger et al., filed Apr. 19, 2018, and entitled “Prosthetic heart valve”   PCT patent application IL2018/050725 to Hariton et al., filed Jul. 4, 2018, and entitled “Prosthetic heart valve”   U.S. patent application Ser. No. 16/135,969 to Hariton et al., filed Sep. 19, 2018, and entitled, “Prosthetic valve with inflatable cuff configured for radial extension”   U.S. patent application Ser. No. 16/135,979 to Hariton et al., tiled Sep. 19, 2018, and entitled, “Prosthetic valve with inflatable cuff configured to fill a volume between atrial and ventricular tissue anchors”   U.S. provisional patent application 62/560,384 to Hariton et al., filed Sep. 19, 2017, and entitled “Prosthetic valve and methods of use.”       

     (Some elements in the present patent application are also described in U.S. 62/560,384, U.S. patent application Ser. Nos. 16/135,969, or 16/135,979, but are named differently. For the sake of clarity, element names used in the present application supersede those used in U.S. 62/560,384, U.S. patent application Ser. Nos. 16/135,969, or 16/135,979.) 
     It will be appreciated by persons skilled in the art that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof that are not in the prior art, which would occur to persons skilled in the art upon reading the foregoing description.