reference will now be made in greater detail to a preferred embodiment of the invention , an example of which is illustrated in the accompanying drawings . wherever possible , the same reference numerals will be used throughout the drawings and the description to refer to the same or like parts . fig1 with detail shown in fig2 illustrates stent 500 . fig1 is a plan view of a first embodiment of stent 500 in accordance with the present invention shown in a partially expanded state . as used herein , the term “ plan view ” will be understood to describe an unwrapped plan view . this could be thought of as slicing open a tubular stent along a line parallel to its axis and laying it out flat . it should therefore be appreciated that , in the actual stent , the top edge of fig1 will be joined to the lower edge . stent 500 is comprised of helical strut band 502 interconnected by coil elements 507 . side - by - side coil elements 507 form coil band 510 . coil band 510 is formed as a double helix with helical strut band 502 and progresses from one end of the stent to the other . helical strut band 502 comprises a wave pattern of strut elements 503 that have peaks 508 on either side of the wave pattern and legs 509 between peaks 508 . coil elements 507 interconnect strut elements 503 of helical strut band 502 through or near peaks 508 . nsc portion 505 of helical strut band 502 is defined by the number of strut elements 503 ( nsc ) of helical strut band 502 between coil element 507 as helical strut band 502 progresses around stent 500 . the number of strut elements 503 ( nsc ) in nsc portion 505 of helical strut band 502 is more than the number of strut elements 503 ( n ) in one circumference winding of helical strut band 502 . the number of strut elements 503 ( nsc ) in nsc portion 505 is constant . in this embodiment , stent 500 has n = 12 . 728 helical strut elements 503 in one circumference winding of helical strut band 502 and has nsc = 16 . 5 helical strut elements 503 in nsc portion 505 . ccdn portion 512 of nsc portion 505 of helical strut band 502 is defined by the number of strut elements 503 ( ccdn ) equal to nsc minus n . the number of strut elements 503 ( ccdn ) in ccdn portion 512 and the number of strut elements 503 ( n ) in one circumference winding of helical strut band 502 does not need to be constant at different diameter size states of stent 500 . stent 500 has ccdn = 3 . 772 helical strut elements 503 in ccdn portion 512 . because this connectivity needs to be maintained at any diameter size state a geometric relationship between the helical strut band 502 and coil element 507 can be described by geometric relationship triangle 511 . geometric relationship triangle 511 has a first side 516 with a leg length equal to the effective length ( lc ) 530 of coil element 507 , a second side 513 with a leg length equal to circumferential coil distance ( ccd ) 531 of ccdn portion 512 of helical strut band 502 divided by the sine of an angle a s 535 of helical strut band 502 from the longitudinal axis of stent 500 , a third side 514 with a leg length ( ss ) 532 equal to the longitudinal distance ( pl ) 534 helical strut band 502 progresses in 1 circumference winding minus the effective strut length l s 533 , a first angle 537 of first side 516 is equal to 180 degrees minus angle a s 535 , a second angle 536 of second side 513 is equal to the angle a c 536 of coil element 507 from the longitudinal axis of stent 500 and a third angle 538 of third side 514 equal to angle a s 535 minus angle a c 536 . if the circumferential strut distance ( p s ) 539 of helical strut element 503 is the same for all helical strut elements 503 in ccdn portion 512 , circumferential coil distance ccd 531 is equal to the number of helical strut elements 503 in the ccdn portion 512 multiplied by the circumferential strut distance ( p s ) 539 . the distances in any figure that shows a flat pattern view of a stent represent distances on the surface of the stent , for example vertical distances are circumferential distances and angled distances are helical distances . first side 516 of geometric relationship triangle 511 is drawn parallel to the linear portion of coil element 507 such that the coil angle ac 536 is equal to the angle of the linear portion of coil element 507 . if coil element 507 does not have a substantially linear portion , but progresses about the stent in a helical manner , an equivalent coil angle 536 could be used to construct the geometric relationship triangle 511 . for instance if coil element 507 is a wavy coil element 907 , as shown in fig1 , line 901 could be drawn fitted through the curves of the wavy coil element 907 and line 901 can be used to define coil angle 536 . stent 400 shown in fig3 and 4 is similar to stent 500 in that it is comprised of helical strut band 402 interconnected by coil elements 507 . stent 400 is different in that helical strut band 402 is comprised of two adjacent wave patterns of strut elements 403 a and 403 b that have peaks 508 on either side of the wave pattern . strut element 403 a being connected to strut element 403 b . similar to helical strut band 502 , helical strut band 402 also has a nsc portion 405 and a ccdn portion 412 . helical strut band 402 can be defined as having a number ns of wave patterns of strut elements equal to 2 . helical strut band 502 can be defined as having a number ns of wave patterns of strut elements equal to 1 . in an alternate embodiment , the stent of the present invention can have a helical strut band with a number ns of wave patterns of strut elements equal to 3 , which would be a triple strut band . in an alternate embodiment , the stent of the present invention could have a helical strut band with a number ns of wave patterns of strut elements equal to any integer . stents with helical strut bands having a number ns of wave patterns of strut elements equal to or greater than 2 provide an advantage in that the helical strut band would form a closed cell structure with smaller cell size which is desired when there is additional risk of embolism . stents with smaller cell sizes tend to trap plaque or other potential embolic debris better than stents with larger cell sizes . stent structures described provides the combination of attributes desirable in a stent when the coil - strut ratio , ratio of lc to ls multiplied by the number of wave patterns of strut elements ns in the helical strut band ( lc multiplied by ns divided by ls ), is greater than or equal to 1 . for example the coil - strut ratio for stent 500 is 2 . 06 and for stent 400 is 2 . 02 . stent 200 shown in fig9 has a similar structure to stent 500 . the coil - strut ratio for stent 200 is about 1 . 11 . in order for the stent of the present invention to crimped to a smaller diameter , the geometry of the structure undergoes several changes . because of the helical nature of the helical strut band , strut angle a s must get smaller as the stent diameter decreases . because of the interconnectivity between a first winding of the helical strut band and a second winding of the helical strut band created by the coil element , the angle of the element a c must also get smaller , or become shallower , to accommodate the smaller strut angle a s . if the angle of coil element a c can not become shallower or is difficult to become shallower as the stent crimps and stent angle a s gets smaller , the coil elements will tend to interfere with each other and prohibit crimping or require more force to crimp . the changing of the angle of the coil element during crimping is facilitated if the coil - strut ratio is greater than 1 . coil - strut ratios less than 1 tend to stiffen the coil element such that more force is required to bend the coil element to a shallower angle during the crimping process , which is not desirable . helical strut band 602 of stent 600 , shown in fig5 , transitions to and continues as an end strut portion 622 where the angle of the winding at1 of the wave pattern of strut elements 624 a forming end strut portion 622 is larger than the angle of the helical strut band a s . end strut portion 622 includes a second winding of the wave pattern of strut elements 624 b where the angle at2 of the second winding is larger than the angle of the first winding at1 . strut elements 603 of helical strut band 602 are interconnected to strut elements 624 a of the first winding of end strut portion 622 by a series of transitional coil elements 623 that define transition coil portion 621 . all strut elements 624 a of the first winding of end portion 622 are connected by coil elements 623 to the helical strut band 602 . peaks 620 of helical strut band 602 are not connected to end strut portion 622 . transitional coil portion 621 allows end strut portion 622 to have a substantially flat end 625 . helical strut band 402 of stent 400 transitions to and continues as an end portion where the angle of the first winding at1 of the wave pattern of strut elements forming of the end portion is larger than the angle of the helical strut band as . the angle of the second winding at2 is larger than at1 , and the angle of subsequent windings of the end portion are also increasing ( i . e . at1 & lt ; at2 & lt ; at3 & lt ; at4 ). ( n )— number of helical strut elements in one circumference winding of the helical strut member . ( a s )— angle of helical strut band winding measured from the longitudinal axis of the stent . ( a t )— effective angle of coil element measured from the longitudinal axis of the stent . ( pl )— longitudinal distance ( pitch ) the strut member progresses in 1 circumference winding . equal to the circumference of the stent divided by the arctangent of a s . ( p s )— circumferential distance ( pitch ) between strut legs of a helical strut element of the helical strut band . assuming the circumferential strut pitch is equal for all strut elements of the helical strut band , the circumferential strut pitch is equal to the circumference of the stent divided by n . ( nsc )— number of strut elements of the strut band between a helical element as the strut member progresses ( ccdn )— number of strut elements of the strut band between interconnected strut elements , equal to nsc minus n ( ccd )— circumferential coil distance is the circumferential distance between interconnected strut elements , equal to the ccdn times the p s if the ps is equal for all strut elements in the ccdn portion . ( lc )— effective length of the helical element as defined by the geometric relationship triangle described in table 1 . ( ss )— strut separation as defined in the geometric relationship triangle described in table 1 . ( ls )— effective strut length . equal to pl minus ss . ( ns )— number of adjacent wave patterns of the strut elements forming the helical strut band . coil - strut ratio — ratio of l c to a length l s multiplied by the number of adjacent wave pattern of the strut elements forming the helical strut band , n s . numerically equal to lc / ls * ns . strut length - strut separation ratio — ratio of the effective strut length ( ls ) to the strut separation ( ss ), numerically equal to ls / ss . in one embodiment , the difference between the strut angle , a s , and coil angle , a c , is more than about 20 degrees . because of the necessity of the coil angle to become shallower as the stent is crimped , if the coil angle and the strut angle in the expanded state are too close to each other there is increased difficulty in crimping the stent . for the stent of the present invention the strut length — strut separation ratio is a measure of the relative angle of the strut angle and coil angle . stents with strut length — strut separation ratios less than about 2 . 5 have improved crimping behavior . stent attributes can further be improved if the angle of the strut member is between 55 degrees and 80 degrees and the coil angle is between 45 degrees and 60 degrees in the expanded state . additionally , steeper coil angles a c in the expanded state make crimping the stent of the present invention more difficult . coil angles of less than 60 degrees in the expanded state facilitate crimping the stent of the present invention . for the stent of the present invention , in addition to the coil angle changing during crimping , the helical strut band rotates about the longitudinal axis of the stent to accommodate the connectivity between subsequent windings of helical strut bands during crimping resulting in more windings of the helical strut band along the length of the stent when the stent is crimped . for the stent of the present invention , the geometric relationship triangle can be used to approximate the expected amount of helical strut band rotation during crimping of the stent . if the geometric relationship triangle can be determined for a given diameter size state of the stent , the geometric relationship triangle can be approximated for any other size state based on the following assumptions ; the effective coil length ( l c ), effective strut length ( l s ), and the longitudinal pitch of the helical strut band ( pl ) are a constant for any diameter size state . given the above assumptions and the geometric relationship triangles approximated in the expanded and crimped states , the amount the helical strut band rotates per winding of the helical strut band about the axis of the stent to accommodate the interconnected coil element during crimping can be approximated if the circumferential strut pitch ( p s ) of the strut element of the helical strut band is assumed to be equal for all strut elements in the helical strut band . considering that an increase of helical strut band windings along the length of the stent when the stent is crimped contributes to stent foreshortening it is advantageous for the stent of the present invention to have an approximated increase in the amount of helical strut band windings of less than about 30 % when crimped , preferably less than about 26 %. a 26 % increase in helical strut band winding corresponds to about 20 % foreshortening which is considered the maximum clinically useful amount of foreshortening ( serruys , patrick , w ., and kutryk , michael , j . b ., eds ., handbook of coronary stents , second edition , martin dunitz ltd ., london , 1998 .) hereby incorporated by reference in its entirety into this application . fig6 is a plan view of another embodiment of stent 700 in accordance with the teachings of the present invention . helical strut band 702 progresses helically from one end of stent 700 to the other . each strut element 703 is connected to a strut in a subsequent winding of helical strut band 702 by coil element 707 . strut element 703 includes leg portions 709 . each of leg portions 709 has an equal length . fig7 , with detail shown in fig8 , is a plan view of another embodiment of stent 800 . in this embodiment , coil element 807 includes curved transition portion 852 at ends 853 and 854 . curved transition portion 852 connects to strut element 803 . stent 800 includes transitional helical portions 859 and end strut portions 858 at either end 861 of stent 800 . end strut portions 858 are formed of a pair of connected strut windings 860 . coil element 807 is comprised of two coil portions 807 a and 807 b which are separated by gap 808 , as shown in fig8 . gap 808 can have a size equal to zero where coil portions 807 a and 807 b are touching . gap 808 terminates near ends 853 and 854 . gap 808 can terminate anywhere along the length of coil 807 or at multiple points along coil 807 such that the gap would have interruptions along coil 807 . stents 400 , 500 , 600 , 700 and 800 are made from a common material for self expanding stents , such as nitinol nickel - titanium alloy ( ni / ti ), as is well known in the art . the stents of the present invention may be placed within vessels using procedures well known in the art . the stents may be loaded into the proximal end of a catheter and advanced through the catheter and released at the desired site . alternatively , the stents may be carried about the distal end of the catheter in a compressed state and released at the desired site . the stents may either be self - expanding or expanded by means such as an inflatable balloon segment of the catheter . after the stent ( s ) have been deposited at the desired intralumenal site , the catheter is withdrawn . the stents of the present invention may be placed within body lumen such as vascular vessels or ducts of any mammal species including humans , without damaging the lumenal wall . for example , the stent can be placed within a lesion or an aneurysm for treating the aneurysm . in one embodiment , the flexible stent is placed in a super femoral artery upon insertion into the vessel . in a method of treating a diseased vessel or duct a catheter is guided to a target site of a diseased vessel or duct . the stent is advanced through the catheter to the target site . for example , the vessel can be a vascular vessel , femoropopliteal artery , tibial artery , carotid artery , iliac artery , renal artery , coronary artery , neurovascular artery or vein . stents of the present invention may be well suited to treating vessels in the human body that are exposed to significant biomechanical forces . stents that are implanted in vessels in the human body that are exposed to significant biomechanical forces must pass rigorous fatigue tests to be legally marketed for sale . these tests typically simulate loading in a human body for a number of cycles equivalent to 10 years of use . depending on the simulated loading condition , the number of test cycles may range from 1 to 400 million cycles . for example , stents that are intended to be used in the femorpopliteal arteries may be required to pass a bending test where the stent is bent to a radius of about 20 mm 1 to 10 million times or axially compressed about 10 % 1 to 10 million times . although presently preferred embodiments of the present invention have been disclosed for illustrative purposes , those skilled in the art will appreciate that many additions , modifications , and substitutions are possible without departing from the scope and spirit of the invention as defined by the accompanying claims . for example , a stent could be made with only right - handed or only left - handed helical portions , or the helical strut band could have multiple reversals in winding direction rather than just one . also , the helical strut band could have any number of turns per unit length or a variable pitch , and the strut bands and / or coil bands could be of unequal length along the stent .
the stent of the present invention combines a helical strut band interconnected by coil elements . this structure provides a combination of attributes that are desirable in a stent , such as , for example , substantial flexibility , stability in supporting a vessel lumen , cell size and radial strength . the structure of the stent of the present invention provides a predetermined geometric relationship between the helical strut band and interconnected coil elements in order to maintain connectivity at any diameter size state of the stent .