Method, system and computer program for determining the porosity of a flexible porous structure subjected to deformation

Abstract

A method, system and computer program are provided for determining the porosity of a flexible porous structure when it is subjected to deformation. The method performs the following steps by processing representative data of the flexible porous structure: a) generates a first function (F.sub.s) defining how the flexible porous structure changes shape when it is subjected to deformation; b) generates a second function (F.sub.p) defining how a covered surface of the flexible porous structure changes when it is subjected to changes in shape, wherein the second function (F.sub.p) is directly linked with porosity of the flexible porous structure; c) obtains reference porosity values of a reference region (CU-R) of the flexible porous structure in a reference configuration via the first function (F.sub.s); and d) calculates the porosity of at least one deformed region (CU-D) of the flexible porous structure, from said reference porosity values and from the second function (F.sub.p).

Claims

1. A method for determining the porosity of a flexible porous structure when it is subjected to deformation, comprising performing the following steps by means of processing representative data of said flexible porous structure: a) generating a first function (F.sub.s) defining how at least one part of the flexible porous structure, given its coordinates, changes shape when it is subjected to one or more geometric deformations, wherein said change of the shape is determined in two directions, one in a cross-section of the flexible porous structure (F.sub.s1) and the other in a longitudinal direction (F.sub.s2); b) generating a second function (F.sub.p) defining how a covered surface, and/or a variable associated with same, for at least one part of the flexible porous structure, changes when it is subjected to one or more changes in shape, said second function (F.sub.p) being directly linked with porosity of the flexible porous structure; c) obtaining, by means of said first function (F.sub.s), reference porosity values of at least one reference region (CU-R) of the flexible porous structure in a reference configuration; and d) calculating the porosity of at least one deformed region (CU-D) of the flexible porous structure corresponding with said reference region (CU-R) but for a deformed configuration different from said reference configuration, from said obtained reference porosity values of the reference region (CU-R) and from at least said second function (F.sub.p).

2. The method according to claim 1, wherein said data makes up respective three-dimensional representations of the flexible porous structure for each of the configurations: the reference configuration and the deformed configuration, wherein the data making up said three-dimensional representations are obtained by means of simulation or are obtained directly on a real flexible porous structure placed covering an outer surface of a solid or hollow element, or an inner surface demarcating a hollow region of an element.

3. The method according to claim 1, wherein said variable associated with porosity is relative to the occupancy of the material forming the flexible porous structure.

4. The method according to claim 1, wherein said variable associated with porosity is relative to the degree of interstitial space, or free space of the material forming the flexible porous structure.

5. The method according to claim 1, further comprising: x1) selecting, before said step c), at least said deformed region (CU-D) of the flexible porous structure in said deformed configuration; and x2) calculating, after said step c), the shape of at least said reference region (CU-R) of the flexible porous structure using said first function (F.sub.s), using the coordinates corresponding to the deformed region (CU-D), wherein said second function (F.sub.p) generated in step b) defines how the occupancy of the material forming the flexible porous structure changes for at least said part of the flexible porous structure; after said step x2) and prior to the calculation of porosity of the flexible porous structure in the deformed region (CU-D) of said step d), the method comprises calculating the occupancy of the material forming the flexible porous structure for at least said reference region (CU-R), from said reference porosity values; and said step d) comprises: d1) calculating the occupancy of the material forming the flexible porous structure for at least said deformed region (CU-D) using the second function (F.sub.p) and the calculated occupancy of the reference region (CU-R); and d2) calculating the porosity in the deformed region (CU-D) from said occupancy of same calculated in d1) and from its total dimension.

6. The method according to claim 5, wherein said step d2) comprises calculating the degree of interstitial space, or free space of the material forming the flexible porous structure, from said occupancy, and carrying out said calculation of porosity from said degree of interstitial space by calculating the quotient between interstitial space and total space of the deformed region (CU-D).

7. The method according to claim 1, wherein both said parts of the flexible porous structure and said deformed region (CU-D) and reference region (CU-R) are area elements on a perimetral surface of the flexible porous structure.

8. The method according to claim 1, wherein said flexible porous structure is tubular.

9. The method according to claim 8, wherein: said first function (F.sub.s) defines how a perimetral surface of the flexible porous structure changes shape when it is subjected to one or more geometric deformations; and said second function (F.sub.p) defines how the covered surface and/or said variable associated with same for the perimetral surface of the flexible porous structure, changes when it is subjected to one or more changes in shape.

10. The method according to claim 5, wherein: the deformed regions (CU-D) are not superimposed on one another; or the deformed regions (CU-D) completely occupy a perimetral surface of the flexible porous structure, where the method comprises dividing said perimetral surface into said deformed regions (CU-D) prior to step x1).

11. The method according to claim 10, further comprising processing the several porosity values obtained in the corresponding steps d) to perform at least one of the following actions: determining the spatial distribution of porosity throughout the flexible porous structure; obtaining a porosity value combining at least several of said porosity values for a zone of the flexible porous structure that includes several deformed regions (CU-D); and visually representing on a three-dimensional model of the flexible porous structure the spatial distribution of porosity for individual deformed regions (CU-D) and/or groups of deformed regions (CU-D), Wherein the reference configuration corresponds to a situation in which the flexible porous structure is released into a medium in which it is not subject to external stresses deforming it, or wherein the reference configuration corresponds to a situation in which the flexible porous structure is deformed but with a reference deformation that is different from that of said deformed configuration.

12. The method according to claim 11, wherein said reference deformation is a deformation that keeps the flexible porous tubular structure straight and with a uniform radius along its entire length, wherein said flexible porous structure is tubular.

13. The method according to claim 1, wherein the flexible porous structure adopts, for said deformed configuration, a heterogeneous radius and a heterogeneous three-dimensional morphology, where said heterogeneous three-dimensional morphology includes at least one curvature and/or at least one twist.

14. The method according to claim 2, further comprising carrying out said calculation of porosity for several deformed spatial configurations, with different deformations, corresponding to several respective positions adopted by the flexible porous structure in said simulation or in relation to said element.

15. The method according to claim 1, wherein said flexible porous structure is a stent.

16. The method according to claim 1, wherein in said deformed configuration the flexible porous structure adopts a conical shape.

17. The method according to claim 1, wherein said reference porosity values of said reference region (CU-R) are known and are recorded in a memory, where the method performs said obtaining of said porosity values of said reference region (CU-R) by accessing same in said memory.

18. A system for determining the porosity of a flexible porous structure when it is subjected to deformation, comprising a data processing unit with access to reference porosity values of at least one reference region (CU-R) of the flexible porous structure in a reference configuration, and which implement an algorithm for processing representative data of said flexible porous structure for the calculation of porosity by: a) generating a first function (F.sub.s) defining how at least one part of the flexible porous structure, given its coordinates, changes shape when it is subjected to one or more geometric deformations, wherein said change of the shape is determined in two directions, one in the cross-section of the flexible porous structure (F.sub.s1) and the other in the longitudinal direction (F.sub.s2); b) generating a second function (F.sub.p) defining how a covered surface, and/or a variable associated with same, for at least one part of the flexible porous structure, changes when it is subjected to one or more changes in shape, said second function (F.sub.p) being directly linked with porosity of the flexible porous structure; c) obtaining, by means of said first function (F.sub.s), reference porosity values of at least one reference region (CU-R) of the flexible porous structure in a reference configuration; and d) calculating the porosity of at least one deformed region (CU-D) of the flexible porous structure corresponding with said reference region (CU-R) but for a deformed configuration different from said reference configuration, from said obtained reference porosity values of the reference region (CU-R) and from at least said second function (F.sub.p).

19. The system according to claim 18, further comprising: a computing unit including said processing unit; a display unit configured for, under the control of said computing unit, showing a three-dimensional representation of the flexible porous structure for the deformed configuration with the spatial distribution of porosity calculated for individual deformed regions (CU-D) and/or groups of deformed regions (CU-D), wherein the computing unit being further configured for carrying out said calculation of porosity for several deformed configurations, with different deformations, corresponding to several respective positions adopted by the flexible porous structure, and for controlling the display unit so that they show a three-dimensional representation of the flexible porous structure for said deformed configurations with their respective spatial distributions of porosity for individual deformed regions (CU-D) and/or groups of deformed regions (CU-D).

20. A computer program product including code instructions which when they are run in a computer implement a method for determining the porosity of a flexible porous structure when it is subjected to deformation by performing the following steps: a) generating a first function (F.sub.s) defining how at least one part of the flexible porous structure, given its coordinates, changes shape when it is subjected to one or more geometric deformations, wherein said change of the shape is determined in two directions, one in the cross-section of the flexible porous structure (F.sub.s1) and the other in the longitudinal direction (F.sub.s2); b) generating a second function (F.sub.p) defining how a covered surface, and/or a variable associated with same, for at least one part of the flexible porous structure, changes when it is subjected to one or more changes in shape, said second function (F.sub.p) being directly linked with porosity of the flexible porous structure; c) obtaining, by means of said first function (F.sub.s), reference porosity values of at least one reference region (CU-R) of the flexible porous structure in a reference configuration; and d) calculating the porosity of at least one deformed region (CU-D) of the flexible porous structure corresponding with said reference region (CU-R) but for a deformed configuration different from said reference configuration, from said obtained reference porosity values of the reference region (CU-R) and from at least said second function (F.sub.p).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The preceding and other advantages and features will be better understood from the following detailed description of embodiments with reference to the attached drawings, which must be interpreted in an illustrative and non-limiting manner, in which:

(2) FIG. 1 shows a perspective view of a stent released in the air adopting a tubular structure (a), as well as a cross-section view thereof (b) and a detail of the interweaving (c).

(3) FIG. 2 shows, on the left, the detail of view (c) of FIG. 1, and, on the right, an enlarged view of part of same corresponding to the cross point between two wires of the stent, in which the difference of covered area in two cross point positions is observed.

(4) FIG. 3 shows, on the left, the development of a stent cut along the length thereof and extended on a plane and, on the right, a detail of the structure and the area occupied by a wire element connecting two cross points.

(5) FIG. 4 corresponds to a detail of a stent in a deformed configuration when it is implanted in a vessel in the body, on the left, and of the same stent deployed in a reference position or configuration, on the right.

(6) FIG. 5 is a graph showing the relation of change in porosity for each area element of the stent, according to Example 4, which will be described in the following section.

DETAILED DESCRIPTION OF EMBODIMENTS

(7) As described up until now, the authors of the present invention have developed a method for determining the porosity and distribution thereof for a flexible porous structure. Said method allows determining in a very accurate manner the final porosity and the spatial distribution and variation thereof for a stent based on deformation with respect to a reference position or configuration.

(8) In the present section, the term reference radius refers to the radius adopted by the stent in a reference configuration and expressed as a function of any of the design variables, or another feature of the stent, in said reference configuration, and the term reference length refers to the length adopted by the stent in the reference position. Therefore, the stent adopts the reference length when it has its reference radius.

(9) This section will focus on the description of the method for the case in which the flexible porous structure is a stent placed or to be placed in a vascular structure, and the CU-R and CU-D regions are area elements, the term CU-D being used to refer to any element on the surface of the stent once it is implanted, and the term CU-R being used to refer to the element equivalent to CU-D in the reference position or configuration.

(10) In the present section, each of the different angles the wires of the stent have with respect to the longitudinal direction thereof is referred to as interweaving angle, the surface covered by the wires of the stent is referred to as occupied area, the surface not covered by the wires of the stent is referred to as free area, and the relation between the ratio of free area for a total given area on the surface of the stent is referred to as porosity.

(11) As described in a previous section, the method of the present invention is based on the analysis of local deformation of the structure of the stent once it is placed. This calculation requires defining a relation of the change in area of the stent as a function of the change in its geometric configuration, which relation is defined by the aforementioned function F.sub.s. It is also necessary to define a function that describes in what way the occupied area (or directly the porosity) is modified on the surface of the stent when said surface is deformed, which is carried out by means of the function F.sub.p, described in a preceding section.

(12) The function determining the change in total area of the stent with the variations in its geometry is determined in two directions defining that transformation between surfaces, i.e.: F.sub.s=F.sub.s1*F.sub.s2.

(13) On one hand, in the cross-section of the stent, F.sub.s1, the change in total area of the stent is defined by the change in its perimeter due to radial expansion. For deformations of the stent without circular symmetry, the transformation is defined by the ratio between the arc length in the reference position and the arc length once the stent is adapted to the surface in which it is deployed.

(14) On the other hand, in the longitudinal direction, F.sub.s2, the change in area is determined by the change in length of the stent when it expands in the tubular structure delimiting it. This function can be determined with different methodologies. One way, with a constant value along the entire stent, is to define this function as the ratio between the length in the measurement position and the length in the reference position. Another way can be by considering the different degrees of expansion the stent experiences as a function of its position in the vessel, as described in detail in patent document ES2459244B1. The greater the degree of detail used to define this function, the greater the approximation that is obtained in the result with respect to the real case.

(15) The function defining the change in occupied area with respect to deformations on the surface of the stent, F.sub.p, can be defined by several methods. This function can be determined empirically by measuring the area of the stent and the amount of visible wire when the device is deployed in various straight cylinders of variable radius. In an analytical manner, it can be defined by calculating the variation in the occupied area in the stent. For this purpose, a distribution for the wires on the surface is assumed and for said distribution, it is calculated how the overlapping surface changes between pairs of wires given different stent diameters. In each case, the occupied surface in the stent is the surface occupied by each wire multiplied by the number of wires minus the overlapping wire surface at the cross points. Another way to extract this function in an analytical manner is to define an area element in the stent such that, under rigid transformations of this element, the surface of the stent can be covered. The calculation of the function of the change in occupied area is determined by deforming the surface element and determining how its occupied area is adapted to the new configuration.

(16) Once the functions F.sub.s and F.sub.p are determined, according to one embodiment the method of the present invention for determining the porosity of a stent when it is placed in a 3D structure comprises the following steps: E1. Obtaining a tubular representation of the stent in the reference position (20 in FIG. 4) with known porosity, or reference porosity, values. E2. Obtaining a tubular representation of the stent in its deployed position object of study (21 in FIG. 4). E3. Dividing the surface of the stent into a set of area elements CU-D such that they cover the entire surface thereof and preferably do not overlap one another (CU-D: element 23 in FIG. 4). E4. Calculating CU-R (22 in FIG. 4), i.e., its shape, in the reference configuration R by means of using F.sub.s (step 24 in FIG. 4), where CU-R is equivalent to CU-D. E5. Calculating the covered area in the element CU-R given the reference porosity in the position CU-R. E6. Calculating the covered area in CU-D from the function F.sub.p relating the covered areas in CU-D and CU-R (step 25 in FIG. 4). E7. Calculating porosity in the element CU-D as the quotient between the non-covered area and the total area of CU-D; E8. Repeating the step 4), 5), 6) and 7) for all the CU-Ds.

(17) For another embodiment, some of the preceding steps can be omitted, as described in a preceding section, particularly when for the calculation of porosity it is not necessary to first determine the occupied area. Specifically, for such embodiment, the function F.sub.p defines how porosity of the flexible porous structure changes, and therefore steps E5 and E6 are not necessary and are replaced with a single step that comprises calculating the porosity of CU-D directly using the function F.sub.p and the reference porosity values of CU-R.

(18) FIGS. 1 to 4 show different representations of the stent and of parts thereof, in a more or less schematic manner.

(19) Particularly, FIG. 1 shows a perspective view of the stent (a), formed by a series of interwoven wires, a cross-section view of the stent (b) and an enlarged portion thereof with a detail of the interweaving of the wires of the stent (c). The length of the stent -1-, the diameter -2-, the braiding angle -3-, the length between two cross points of the stent -4-, the longitudinal and transverse projection, along the perimeter, of the distance between cross points -5- and -6-, the distance between cross points along the perimeter -7- and the thickness of the wire -8- are shown in detail in said FIG. 1.

(20) The detailed view (c) of FIG. 1 is also depicted in FIG. 2 (view on the left) together with an enlargement thereof (view on the right) illustrating the cross point between two wires and how the area thereof changes when the stent is subjected to deformation. The figure shows in detail: braiding angle -3-, length between two cross points of the stent -4-, longitudinal and transverse projection, along the perimeter, of the distance between cross points -5- and -6-, distance between cross points along the perimeter -7- and thickness of the wire -8-, the crossing angle when the wires are perpendicular -17-, the crossing angles for an arbitrary position -15 and -16- (and the complementary angle thereof -18-), as well as the length of the overlap zone for an arbitrary position -14-.

(21) The development of a stent like that shown in FIG. 1 is illustrated in the view on the left of FIG. 3, which, on the right, shows a detail of the structure and the area occupied by a wire element connecting two cross points of the stent. Said figure shows in detail the length of the stent -1-, the length of the perimeter -19-, the thickness of the wire -8-, the crossing angles, along the braiding, and the complementary angle thereof, -3- and -9-, the areas not occupied by metal -10- and -11-, two dimensions indicative of the measurements of the wire -12- and -13- and the length of wire between two cross points -4-.

(22) Finally, and in a more schematic manner (because the wires of the stent are not illustrated), FIG. 4 illustrates, in the view on the left, the stent inserted in a vessel -26- in the body, adopting a deformed configuration -21-, and in the view on the right, it illustrates the stent in a reference configuration -20- in which, in this case, the stent is deployed adopting a cylindrical shape. The figure shows a deformed region CU-D of a selected area of the stent -23- in the deformed stent -21-, and in the stent in the reference configuration -20-, the corresponding region in the reference position, or reference region CU-R -22-, as well as the schematic depiction of the steps for determining the calculation of porosity in CU-D, determining CU-R from the area CU-D using Fs -24- (step E4), and determining the amount of metal occupied in CU-D once it is known in CU-R through Fp -25- (step E6).

(23) In the method of the present invention, the representation of the stent and advantageously of the vessel in which it will be placed, is provided in the form of three-dimensional surfaces which can be obtained by means of any method known in the art, for example, by means of image segmentation of an angiographic image (Antiga, L. et al. An image-based 5 modeling Framework for patient-specific computational hemodynamics. Medical and biological engineering and computing, 2008, 46(11), 1097-1112) and subsequent reconstruction of the surface (Lorensen, W. E. and Cline, H. E. Marching Cubes: A high resolution 3D Surface construction algorithm. Computer Graphics, 1987, 21, 4). The three-dimensional surfaces of the structure of the stent and of the vessel can be depicted by means of polygon meshes, in which the resolution can be adjusted to obtain relevant information about the morphology thereof. As mentioned above, said techniques are known in the literature, and any of them can be used provided that it allows describing the morphology of the vessel in the region in which the stent will be placed and the morphology of the stent itself. It is also possible to apply it to a three-dimensional simulation of the positioning of the stent, provided that the initial and final positions in the vessel and the radii thereof are known.

(24) With the method of the present invention not only is it possible to predict the porosity of a real or simulated stent once it is placed inside a vessel, but it is also possible to detect regions in which there may be a poor positioning of the stent in the walls of the vascular structure, such as in the case of blocking or complete or partial coverage of branched vessels.

(25) With the use of the method of the present invention it is possible for the neurointerventional radiologist to plan the treatment and to know the porosity in each position of the stent before performing said treatment and, therefore, selecting the most suitable stent and the site where said stent should be placed.

(26) Furthermore, according to the third aspect of the invention, the method of the present invention is implemented by means of a computer program which allows performing the determining of the final porosity of the stent more quickly and precisely.

(27) A series of examples for determining the porosity or associated variables by applying the method proposed by the present invention are described below.

EXAMPLES

Example 1

(28) Determining the relation of change in area covered by metal of the unit cell for a reference configuration. The selected configuration is one in which the stent is released without being subject to external stresses. In this position the unit cell can be defined as the entire stent for a single braiding angle. It is thereby possible to calculate the relation of change in area covered by metal with the total area from radially deforming the unit cell, the entire stent in this case, taking into account that the length of each wire is constant and that the amount of metal covering the surface is equal to the surface occupied by each wire (length times thickness) minus the amount of metal overlapping at the cross points.

(29) The total area occupied by the stent can be calculated from the diameter and the length L.sub.stent of the stent.
A.sub.total=.Math..Math.L.sub.stent

(30) The amount of metal in the cross points is calculated based on the area occupied by the rhombus of FIG. 2 multiplied by the number of cross points of the stent; this relation can be expressed as:

(31) $A_{\mathrm{cross}\mathrm{points}}=\left(\frac{N_{\mathrm{wires}}}{2}\right).Math.\frac{L_{\mathrm{stent}}}{L_c}.Math.\frac{l^2}{\sin \left(\right)}$$L_c=L.Math.\cos /2$

(32) In this case A.sub.total represents the total area occupied by the surface of the stent, A.sub.cross points defines the area in the cross points between wires, N.sub.wires is the number of wires of the stent, L.sub.stent defines the length of the stent, I is the thickness of each wire, is the angle between wires (i.e. twice the angle -3- indicated in FIG. 1) and L.sub.c is the longitudinal component of the distance between two consecutive cross points, element -4- in FIG. 3.

(33) The following table shows the values of the area occupied by the surface of the stent with respect to the area of metal for a stent consisting of 48 wires with of diameter 4 mm, length of 16 mm, 0.04 mm of thickness in each wire and 1560 cross points and a distance between consecutive cross points along the wire of 0.3611, for different deformed positions of the stent, and therefore different angles :

(34) TABLE-US-00001 TABLE 1 Total area [mm.sup.2] Occupied area [mm.sup.2] 20.7931 20.6476 75.3745 38.3293 138.5351 41.4003 182.9858 42.2906 202.7232 42.5608 195.0818 42.4627 161.0934 41.9136 105.3486 40.2458

Example 2

(35) Determining the relation of change in the unit cell for a reference configuration. The rectangle occupied by the portion of wire between two consecutive cross points as shown in FIG. 3 is selected as a unit cell. The rotation and translational movement of this pattern generates a complete stent with a single braiding angle for the selected nominal position. The total area and the occupied area can be determined in a geometric manner from angle /2, which is generated by the stent with the longitudinal direction, indicated as -3- in FIG. 3.

(36) $A_{\mathrm{total}}=L^2.Math.\frac{\sin \left(\right)}{2}$$A_{\mathrm{occupied}}=L^2.Math.\frac{\sin \left(\right)}{2}-{\left(L-\frac{l}{\sin \left(\right)}\right)}^2.Math.\frac{\sin \left(\right)}{2}$

(37) The following table shows the area occupied by the stent with respect to the total area for a stent consisting of 48 wires with diameter of 4 mm, length of 16 mm, wires with a thickness of 0.04 mm and 1560 cross points with a distance between cross points of 0.3611, for different deformed positions of the stent:

(38) TABLE-US-00002 TABLE 2 Total area [mm.sup.2] Occupied Area [mm.sup.2] 0.006664 0.006617 0.024158 0.012285 0.039808 0.013134 0.055772 0.013509 0.064203 0.013632 0.063963 0.013629 0.055085 0.013497 0.038767 0.013099

Example 3

(39) Calculation of porosity for a stent consisting of 48 wires with diameter of 4 mm, length of 16 mm, wire thickness of 0.04 mm, 1560 cross points and a homogenous porosity of 0.79 in its nominal position, i.e., in its reference configuration; it is deployed in a homogenous cylinder of 2 mm in diameter, in its deformed configuration.

(40) The stent adopts a length of 21.84 mm when it is adapted inside the homogenous cylinder of 2 mm. The surface of the cylinder is divided into elements of 1 mm in the longitudinal direction and 1.26 mm on the perimeter. Therefore, the selected area element CU-D will have a surface of 1.26 mm.sup.2. To calculate the surface element CU-R in the nominal configuration, i.e., in the reference configuration, the function F.sub.s is calculated. For this purpose, the transformation of area in the direction of the perimeter and in the longitudinal direction is calculated. In the direction of the perimeter, the transformation is determined by the difference of arcs for two radii of 2 mm and 4 mm, that is, an arc element of 1.26 mm on a radius of 2 mm corresponds to 2.52 mm of arc on a radius of 4 mm. The relation in the longitudinal direction is determined by the ratio between the lengths of the stent in its reference position and final position, 16 mm compared to 21.84 mm, so a length of 1 mm in the stent in its final position corresponds to 0.73 mm in its reference position, so the corresponding area in the nominal position corresponds to 2.520.73=1.83 mm.sup.2. Therefore, once the porosity in the reference position is known, in this case 0.79, the occupied area in this position is (10.79)1.26=0.38 mm.sup.2.

(41) The occupied area in the final position can be related with the reference area by calculating the variations in area of occupied metal with the variations in total area set forth in Tables 1 and 2. The total area of the stent in the deployed position and in the reference position can be calculated from its diameters and lengths. In this case, it corresponds to 202 mm.sup.2 in the reference position and 138 mm.sup.2 in the deployed position. Taking into account the occupied area values for each position, it is estimated that the variation in occupied area with the variation in total area (difference of the occupied area divided by the difference in total area) is in the order of 1/50, which in this case is calculated as (41.442.6)/(202138)=0.01875, that is, when the variation in the selected total area is positive one (+1), the occupied area decreases 1/50 that amount. In the present case, the variation in the total area is 1.261.83=0.62 mm.sup.2, so the occupied area in the deployed position is 0.380.62*0.01875=0.368 mm.sup.2, giving rise to a porosity of (10.368/1.26)=0.708.

Example 4

(42) Calculation of porosity for a stent consisting of 48 wires with diameter of 4 mm, length of 16 mm, 0.04 mm of thickness in each wire and 1560 cross points and a homogenous porosity in its nominal (reference) position of 0.79 when it is deployed in a conical cylinder the diameter of which ranges from 4 mm to 1.5 mm.

(43) The stent has a length of 19.7 mm when it is adapted inside the conical cylinder, which entails a change in length of 23%. The surface of the cylinder is divided into area elements of 1 mm in the longitudinal direction and of the total perimeter in the direction of the perimeter. The relation of change in length of the stent with the circumference can be experimentally estimated by deploying the stent on cylinders the diameters of which range from 4 mm to 1.5 mm, or analytically by taking into account that the stent is a spring-type structure having a known equation. The same calculations as those in the preceding example are performed in each 1 mm segment, taking into account that in this case the variations in occupied area with total area will be different for each segment of the cone of different radius being taken. The porosity in each segment is calculated again from the difference in area of the segment in the cone and of the equivalent section of segment over the nominal position, as well as in the corresponding occupied areas.

(44) The calculation of porosity of one of these segments is described below. Firstly, it is assumed that each element of 1 mm in length has a constant diameter within that order of magnitude (the variation in the diameter in each segment is in the order of 0.13 mm). Therefore, the area of the stent is reconstructed by applying the Riemann sum concept. In addition, the variation in diameter from the start, 4 mm, until the end, 1.5 mm, is established through a linear equation, =4(2.5/19.7)x, where x is an integer taking values of 0 to 20. Finally, the change in length can be calculated by applying the equation of the helix. A stent with 48 wires means that in a perimeter in which the wires thereof cross, there are 24 cross points, which gives rise to 65 cross points in the longitudinal direction for a stent of 1560 cross points in total. Therefore, the number of turns of each wire along a length will be 65/48=1.35 turns per wire. The equation of the helix is expressed mathematically as:
L.sub.wire.sup.2=L.sub.helix.sup.2+(n.Math..Math.).sup.2
where n is the number of turns and L.sub.helix is the longitudinal dimension of the helix, in the present case the length of the stent. Therefore, for each 1 mm segment and known diameter, it is possible to calculate what the length will be when it occupies its nominal diameter, 4 mm, by simply applying the changes in length determined by the equation of the helix, note that the length of the wire is constant for any diameter and length adopted by the stent and that it can be calculated from the nominal position of the length of helix and known diameters.

(45) The first segment has a nominal radius of 4 mm, as there is no change in length associated with its diameter or with the morphology to which it is adapted, its porosity coincides with the nominal porosity.

(46) The fourteenth segment of the stent in its deployed position in the conical cylinder has a diameter of 2.22 mm, which entails an area of 2.22*pi*1=6.97 mm.sup.2 on a segment having 1 mm in length. For the purpose of calculating the length of the segment when the stent is in its nominal position, or nominal length, the equation of the helix is applied as follows.

(47) Firstly, and given that the length of the wire is constant, the equation is balanced for two positions of known diameter, in this case for a diameter of 4 mm (nominal position) for which L.sub.helix is equal to the nominal length of the stent, i.e., 16 mm, and for a diameter of 2.22 mm (deployed position), for n=1.35. Therefore:
16.sup.2+(1.35.Math..Math.4).sup.2=L.sub.deployed helix.sup.2+(1.35.Math..Math.2.22).sup.2
where L.sub.deployed helix is the length of the helix corresponding to the deployed position for a diameter of 2.22 mm. Therefore:
L.sub.deployed helix=(16.sup.2+(1.35.Math..Math.4).sup.2(1.35.Math..Math.2.22).sup.2).sup.0.5=(16.sup.2+(1.35.Math.).sup.2*(4.sup.22.22.sup.2)).sup.0.5
which gives a value for L.sub.deployed helix of 21.33 mm.

(48) Considering that the length of the helix is reduced from 21.33 mm to 16 mm when it transitions from the deployed position to the nominal position, by applying a rule of 3 a segment of 1 mm in length in its deployed position will be reduced to a segment of nominal length equal to (21.33 mm*1 mm)/16 mm, i.e., of a value equal to 0.74 mm, so it corresponds to an area of 0.74*4*=9.30 mm.sup.2, which for a nominal porosity of 0.79 implies an occupied area of (10.79)*9.30=1.95 mm.sup.2. Assuming that the corrective factor with the area is constant, equivalent to that calculated in Example 3, the occupied area in the fourteenth position will be 1.95+(6.979.30)/50=1.9 mm.sup.2, which gives rise to a porosity of 1(1.9/6.97)=0.72.

(49) The relation of the change in porosity for each element of the stent inserted in the conical cylinder is shown in FIG. 5, where for the distance of 19 mm indicated in the graph the stent is adapted to the portion of the conical cylinder of 1.59 mm of diameter.

(50) The present invention can also be applied to determining the porosity of a non-tubular shaped, braided or non-braided flexible porous structure, the surface of which is generated by elements of a known shape and placed in a given order, such as a WEB system. When this type of porous structure is subjected to a deformation, it modifies both its shape and its porosity on the surface of the structure based on a new arrangement of the elements forming it.

(51) A person skilled in the art will be able to introduce changes and modifications to the described embodiments without departing from the scope of the invention as it is defined in the attached claims.