reference is now made to fig1 a - e , which are schematic illustrations of a mitral valve 20 and a left ventricle 22 being reshaped via a transapical approach , in accordance with some applications of the present invention . as shown in fig1 a , a p1 - anchor p1 , a p2 - anchor p2 , and a p3 - anchor p3 are coupled to tissue in the vicinity of , respectively , the p1 , p2 and p3 segments of the posterior mitral valve leaflet . for example , the clips may be coupled to tissue on , or posterior to the p1 , p2 , and p3 segments ( e . g ., to respective locations of the mitral annulus ). anchors p1 , p2 and p3 typically include any anchors , clips , and / or pledgets , as are known in the art . for example , the anchors may include clips that comprise a shape - memory alloy , such as nitinol . for some applications , anchors as described in u . s . pat . no . 7 , 056 , 325 to makower , which is incorporated herein by reference , are used . for some applications , clips ( e . g ., the u - clip ® manufactured by medtronic ( minneapolis , minn .)) are used as anchors , for example , as described hereinbelow with reference to fig3 a - f . for some applications , a mitral ring that includes self - suturing clips , as described hereinbelow with reference to fig8 - 10 , is used for anchors p1 , p2 and p3 . typically , a tissue penetrating sheath penetrates the cardiac muscle behind the posterior leaflet , so as to place the anchors on the atrial side of the posterior leaflet , as described in further detail hereinbelow , with reference to fig4 - 7 . the penetrating sheath is inserted via a delivery catheter 24 , shown in fig1 a , for example . as shown in fig1 b , a tether 30 , which passes through anchors p1 , p2 , and p3 is pulled and anchored to an anchoring location 32 that is at a cardiac site that is anterior and inferior to the posterior leaflet , e . g ., the outside surface of the heart in the vicinity of the apex of the heart , as shown . typically , the tether is pulled and anchored to location 32 such that : the circumference of the mitral annulus decreases ( due to the p1 , p2 , and p3 anchors being pulled anteriorly ) a ratio of the anteroposterior diameter of the annulus to the lateral diameter of the annulus decreases ( due to the p1 , p2 , and p3 anchors being pulled anteriorly ) the distance d ( shown in fig1 a and 1c ) from the papillary muscles to the posterior leaflet decreases ( due to tension in tether 30 pulling the inferior wall of the left ventricle toward the posterior leaflet ). typically , tether 30 is fixedly coupled to anchor p2 , e . g ., via a knot 34 , as shown in fig1 d . the tether is slidably coupled to the p1 and p3 anchors . for some applications , this results in the p1 and p3 anchors being pulled inferiorly with respect to the p2 anchor , when tether 30 is pulled , as shown in fig1 e . typically , this restores a saddle - shape to a mitral annulus 36 that has become misshapen due to dilation of the annulus . as described hereinabove , the saddle - shape of the annulus further reduces the circumference of the annulus , and / or reduces tension in the mitral valve leaflets , relative to a flattened mitral annulus . for some applications , tether 30 is pulled through the anchors during a beating heart procedure , such that the degree of functional change can be controlled during the procedure , and observed under functional imaging ( e . g ., echocardiography ). typically , the tether is pulled and anchored in response to the real - time functional imaging , for example , such that an optimal hemodynamic response is achieved . reference is now made to fig2 a - d , which are schematic illustrations of mitral valve 20 and left ventricle 22 being reshaped via a transaortic retrograde approach , in accordance with some applications of the present invention . as shown in fig2 a , for some applications , anchors p1 , p2 , and p3 , and tether 30 are inserted into the subject &# 39 ; s heart via a transaortic retrograde approach . the placement of the anchors is generally similar to that described hereinabove , with reference to fig1 a - e , except that delivery catheter 24 is inserted via the aorta , rather than via the apex of the heart . subsequent to the placement of the anchors , tether is pulled , and is anchored to anchoring location 32 , which may be on the inner surface of the myocardium , for example , in the vicinity of the apex of the heart , as shown in fig2 b - d . reference is now made to fig3 a - f , which are schematic illustrations of mitral valve 20 and left ventricle 22 being reshaped , using clips as the p1 , p2 , and p3 anchors , in accordance with some applications of the present invention . fig3 a - f shows the clips being used in a transaortic retrograde technique , although the clips can also be used in combination with the other techniques described herein , mutatis mutandis . typically , delivery catheter 24 inserts the clips into tissue from a ventricular side of the valve . the clips are typically inserted such that the clips penetrate the tissue and the tips of the clips enter atrium 40 . tether 30 passes through the clips , and the ends of the tether are anchored to anchoring location , as described hereinabove , and as shown in fig3 b - d . typically , anchor p2 is fixedly coupled to tether 30 , e . g ., via knot 34 , as shown in fig3 e . further typically , the tether is slidably coupled to the p1 and p3 anchors , as indicated by arrow 42 in fig3 e . thus , when the tether is pulled toward anchoring site 32 , which is anterior and inferior to the posterior leaflet , anchors p1 and p3 slide toward anchor p2 , and are pulled inferiorly with respect to anchor p2 . as described hereinabove , with reference to fig3 a - e , for some applications , clips are inserted from the ventricle into the posterior mitral valve leaflet , such that the clips penetrate the leaflet . alternatively , anchors are placed on the atrial side of the posterior mitral valve leaflet . for some applications , the anchors are placed on the atrial side of the posterior valve leaflet via a transmyocardial approach , in accordance with the techniques described with reference to fig4 - 7 . reference is now made to fig4 a - c , which are schematic illustrations of anchors p1 , p2 , and p3 being applied to tissue in the vicinity of the posterior mitral valve leaflet via a transmyocardial approach , in accordance with some applications of the present invention . a penetrating sheath 50 is inserted into the left ventricle , via delivery catheter 24 . the penetrating sheath is advanced such that the sheath penetrates the myocardium , and the distal tip of the sheath is disposed in atrium 40 , as shown in fig4 a . subsequently , an anchor - delivery sheath 52 is advanced out of the distal end of penetrating sheath 50 . the p1 , p2 and p3 anchors are delivered and anchored to atrial tissue that is in the vicinity of ( e . g ., on or posterior to ) the posterior leaflet of the mitral valve , via the anchor - delivery sheath . fig4 c illustrates the delivery and placement of the p1 anchor via anchor - delivery sheath 52 . reference is now made to fig5 a - d , which are schematic illustrations of anchors p1 , p2 , and p3 being applied to tissue in the vicinity of the posterior mitral valve leaflet via a transmyocardial approach , in accordance with alternative applications of the present invention . for some applications , penetrating sheath 50 is inserted into left ventricle 22 via anchor - delivery sheath 52 , which , in turn , is inserted via delivery catheter 24 , as shown in fig5 a . the penetrating sheath is advanced such that the sheath penetrates the myocardium , and the distal tip of the sheath is disposed in atrium 40 , as shown in fig5 b . subsequently , penetrating sheath is withdrawn from anchor - delivery sheath 52 ( shown in fig5 c ), and the anchors are delivered to the left atrium via the anchor - delivery sheath . fig5 d illustrates the delivery and placement of the p1 anchor via anchor - delivery sheath 52 . reference is now made to fig6 a - c , which are schematic illustrations of anchors p1 , p2 , and p3 being applied to the posterior mitral valve leaflet via a transmyocardial approach , in accordance with further alternative applications of the present invention . for some applications , a single sheath 50 penetrates the myocardium , and delivers the anchors to the tissue of the left atrium . as shown in fig6 a - c , for some applications , penetrating sheath 50 defines openings 54 , 56 , and 58 , via which , respectively , p1 , p2 , and p3 anchors are delivered . the distal tip of the penetrating sheath is advanced from the distal end of delivery catheter 24 , such that the penetrating sheath penetrates the myocardium , as shown in the transition from fig6 a - 6b . subsequently , the penetrating sheath is advanced , such that opening 54 is facing tissue in the vicinity of the p1 segment of the posterior leaflet of mitral valve 20 . anchor p1 is anchored to the aforementioned tissue , via opening 54 , as shown in fig6 c . subsequently , p2 and p3 anchors are anchored to tissue in the vicinity of , respectively , the p2 and p3 segments of the posterior leaflet of mitral valve 20 , via openings 56 and 58 ( not shown ). reference is now made to fig7 , which is a schematic illustration of anchors p1 , p2 , and p3 being applied to tissue in the vicinity of the posterior mitral valve leaflet via a transaortic retrograde transmyocardial approach , in accordance with some applications of the present invention . it is noted that in the techniques described hereinabove , with reference to fig4 - 6 , penetrating sheath is inserted into the atrium via a penetration site that is in the vicinity of the anterior commissure of the mitral valve . anchor - delivery sheath 52 or penetrating sheath 50 is then advanced from the aforementioned penetration site to the p1 , p2 and p3 segments of the posterior mitral valve . for alternative applications , penetrating sheath 50 penetrates the myocardium at a penetrating site that is in the vicinity of the posterior commissure of the mitral valve , as shown in fig7 . in all other respects delivery of the anchors via the penetrating sheath ( and , optionally , via the anchor - delivery sheath ) is generally in accordance with the techniques described with reference to fig4 - 6 . reference is now made to fig8 a - h , which are schematic illustrations of a mitral ring 60 , self - suturing anchors 62 being disposed inside the mitral ring , in accordance with some applications of the present invention . mitral ring 60 is typically made of a polymer , a plastic , titanium , stainless steel , and / or other similar materials . anchors 62 are elongate elements that are shaped to define openings 63 . a mandrel 64 is reversibly disposed through the openings , as shown in fig8 a - b . in response to the mandrel being withdrawn from the openings , ends 66 of the anchors automatically move outwardly , via openings 68 in the mitral ring ( typically , due to the anchors being elastically loaded ), as shown in fig8 c . typically , while mandrel 64 is disposed inside openings 63 defined by anchors 62 , the anchors are placed adjacent to tissue that is in the vicinity of the mitral valve ( or other tissue as described hereinbelow ). in response to the mandrel being withdrawn from the openings , ends 66 of the anchors move outwardly , thereby entering the tissue . ends 66 are typically sharp , so as to facilitate penetration of the tissue . for some applications , in response to mandrel being reinserted via the openings that are defined by the anchors , the anchors exit the tissue via exit routes that are the reverse of the entry routes of the anchors . thus , if the anchors have been inaccurately placed , the anchors may be removed from the tissue without causing an additional wound to the tissue , during the removal of the anchors . typically , a guidewire 65 passes through openings 63 , and the mandrel is advanced and withdrawn over the guidewire . thus , the guidewire facilitate reinsertion if the mandrel via the openings , if necessary . typically , a tether ( e . g ., tether 30 described hereinabove ) passes through the anchors , and is used to tether the anchors to each other . it is noted that for some applications , mitral ring 60 includes flexible regions 70 between adjacent anchors . the function of the flexible regions is described in further detail hereinbelow . fig8 d , 8 e , and 8 f show a single anchor , respectively , configured as when the mandrel is inserted through opening 63 ( fig8 d , mandrel not shown ), configured as when the mandrel is removed from opening 63 ( fig8 e ), and disposed inside mitral ring 60 ( fig8 f ). it is noted that even in the configuration shown in fig8 e ( i . e ., as when mandrel 64 has been withdrawn ), the anchor defines an opening 63 , via which the mandrel can be reinserted . fig8 g - h are schematic illustrations that demonstrate the principle by which self - suturing anchors operate . each anchor is configured such that when mandrel 64 is inserted via opening 63 , the anchor is elastically loaded , i . e ., it is as if there was a loaded spring 72 ( shown in dashed lines in fig8 g - h ) disposed above the anchor . the spring is prevented from expanding by the mandrel . upon removal of the mandrel from opening , the spring is released , thereby causing the diameter of opening 63 to decrease , and pushing ends 66 outward . for some applications , the anchors comprise a shape - memory alloy , such as nitinol . each anchor is shaped in the closed configuration of the anchor . the mandrel is inserted through the opening in the anchor , such that the shape - memory alloy is biased open . thus , insertion of the mandrel through the opening causes the anchor to become elastically loaded . upon removal of the mandrel from the opening of the anchor , the anchor reverts to the closed shape thereof . for some applications , the anchors comprise a metal , such as stainless steel . each anchor is shaped into the closed configuration of the anchor and becomes elastically loaded due to the insertion of the mandrel through the opening in the anchor , as described hereinabove . reference is now made to fig9 a - i , which are schematic illustrations of mitral ring 60 being implanted on the atrial side of the posterior mitral valve , in accordance with some applications of the present invention . for some applications , mitral ring is inserted into left atrium 40 via delivery catheter 24 ( fig9 a ), via the inter - atrial septum , as shown . alternatively , the mitral ring is inserted directly into the atrium ( e . g ., via a minimally invasive surgical approach ). the most distal of self suturing anchors 62 of ring 60 is placed adjacent to tissue in the vicinity of ( e . g ., on or posterior to ) the p3 segment of the posterior mitral valve leaflet ( fig9 b ). mandrel 64 is withdrawn from opening 63 defined by the distal self - suturing anchor , such that the anchor automatically becomes anchored to the tissue , due the ends of the anchors penetrating the tissue , as described hereinabove ( fig9 c ). subsequently , a second one of self suturing anchors 62 of ring 60 is placed adjacent to tissue in the vicinity of ( e . g ., on or posterior to ) the p2 segment of the posterior mitral valve leaflet ( fig9 d ). mandrel 64 is withdrawn from opening 63 defined by the self - suturing anchor , such that the anchor automatically becomes anchored to the tissue , due the ends of the anchors penetrating the tissue , as described hereinabove ( fig9 e ). further subsequently , a third one of self suturing anchors 62 of ring 60 is placed adjacent to tissue in the vicinity of ( e . g ., on or posterior to ) the p1 segment of the posterior mitral valve leaflet ( fig9 f ). mandrel 64 is withdrawn from opening 63 defined by the self - suturing anchor , such that the anchor automatically becomes anchored to the tissue , due the ends of the anchors penetrating the tissue , as described hereinabove ( fig9 g ). a tether 80 passes through the anchors , and is tied to mitral ring 60 in a vicinity of a first end 82 of the ring that is closest to the posterior commissure . the tether is tightened , so as to pull the anchors toward each other ( fig9 h ). the tether is then anchored in its tightened configuration , for example , by tying the tether to a second end 84 of the mitral ring that is closest to the anterior commissure ( fig9 i ). flexible regions 70 of the mitral ring facilitate the movement of the anchors toward each other , in response to the tightening of tether 80 , by flexing , and / or by becoming compressed . the tightening of the tether causes a decrease in the circumference of the mitral annulus . it is noted that , although not shown , for some applications , mitral ring 60 is placed on the atrial aspect of the posterior mitral valve , as described with reference to fig9 a - i , and is combined with the techniques described hereinabove , with reference to fig1 - 7 , for tethering the posterior leaflet to anchoring location 32 , which is at a cardiac site that is anterior and inferior to the posterior leaflet . reference is now made to fig1 a - j , which are schematic illustrations of mitral ring 60 being implanted on the ventricular side of the posterior mitral valve via a transaortic retrograde approach , in accordance with some applications of the present invention . it is noted that although the mitral ring is shown as being delivered via a transaortic retrograde approach ( via delivery catheter 24 ), for some applications , the mitral ring is delivered to the ventricular side of the posterior mitral valve via a transapical approach . the mitral ring is passed along the groove between the posterior mitral valve leaflet and the left ventricular wall , such that first end 82 of the mitral ring is in the vicinity of the posterior commissure of the mitral valve , as shown in fig1 a - c . it is noted , for some applications , as shown , a first end of tether 30 passes out of the first end of the mitral ring . typically , the mitral ring is placed such that first , second , and third self - suturing anchors 62 are adjacent to tissue in the vicinity of ( e . g ., on or posterior to ) the p3 , p2 , and p1 segments of the posterior mitral valve leaflet . mandrel 64 is withdrawn from the openings defined by self - suturing anchors , such that the anchors become anchored to the tissue and act as p1 , p2 , and p3 anchors , in accordance with the techniques described hereinabove , and as shown in fig1 d - f . subsequently , the distal tip of delivery catheter is moved toward anchoring location 32 ( fig1 g ), which , as described hereinabove , is at a cardiac site that is anterior and inferior to the posterior mitral valve leaflet . tether 30 is tightened and anchored to anchoring location 32 , in accordance with the techniques described hereinabove , as shown in fig1 h - j . as shown in fig1 j , flexible regions 70 of the mitral ring facilitate flexing and compression of the mitral ring , such that the anchors are able to move toward each other , and such that the p1 and p3 anchors are able to move inferiorly , relative to the p2 anchor . it is noted that although self - suturing anchors 62 and ring 60 are described hereinabove as being anchored to tissue associated with the mitral valve , the scope of the present invention includes anchoring self - suturing anchors ( and , optionally , a housing ) to natural or prosthetic tissue of other portions of a subject &# 39 ; s body , mutatis mutandis . for example , the anchors may anchor a ring to tissue of a subject &# 39 ; s gastrointestinal tract . for some applications , the anchors and the ring are anchored to tissue in the vicinity of the sphincter muscles that are at the junction between the esophagus and the stomach and the ring is tightened in accordance with the techniques described hereinabove , e . g ., in order to treat gastroesophageal reflux disease ( gerd ). alternatively , the anchors anchor a ring to the inside of a subject &# 39 ; s stomach , and the ring is tightened in accordance with the techniques described hereinabove , in order to treat obesity . further alternatively , the anchors may be used to treat an atrial or a ventricular septal defect , to close a patent foramen ovale , and / or to treat an abdominal aortic aneurysm . 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 .
apparatus and methods are provided , including a plurality of anchoring elements , each of the anchoring elements being an elongate element that is curved to define an opening . a housing holds each of the anchoring elements . a mandrel is reversibly disposable through the openings defined by the anchoring elements . the anchoring elements are configured such that , in response to removal of the mandrel from the openings , ends of the anchoring elements automatically move outwardly , and diameters of the openings decrease , due to elastic loading of the anchoring elements . other embodiments are also described .