Implantable artificial ligament, and method for manufacturing such an artificial ligament
The artificial ligament with a braided hollow sheath and deformable insert addresses the issue of disrupted spinal load distribution post-fusion by providing flexible and rigid behaviors, reducing the risk of PJK and PJF through improved load redistribution.
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- COUSIN BIOTECH R L
- Filing Date
- 2022-11-09
- Publication Date
- 2026-06-12
Smart Images

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Abstract
Description
Title of the invention: Implantable artificial ligament, and method for manufacturing such an artificial ligament technical field
[0001] The present invention relates to the technical field of implantable artificial ligaments, in particular for the prevention and / or treatment of spinal pathology, more particularly for the prevention and / or treatment of pathology(ies) occurring following the fusion of one or more vertebrae of the spine, preferably for the prevention and / or treatment of proximal junctional kyphosis (PJK).
[0002] The present invention also relates to the technical field of manufacturing processes for such artificial ligaments. Previous technique
[0003] Following spinal surgery to fuse one or more vertebrae, spinal deformities during patient movement, particularly flexion, are distributed across the remaining unfused vertebrae, which are located near the fused area. This distribution concentrates the loads on the unfused vertebrae, thus altering the natural load distribution gradient observed in a spine without a fused area. Naturally, the facet joints prevent posterior spinal migration, and the intervertebral discs prevent anterior spinal migration. Furthermore, these spinal structures include joint capsules containing synovial fluid, which acts as a lubricant for the facet joints to prevent bone wear. Following vertebral fusion, the facet joints near the fused area no longer function correctly.The loads are thus transferred to the ligaments, which are not naturally designed to withstand such a high cumulative load. The resulting imbalances in the spine cause kyphosis, or even spondylolisthesis in the most severe cases.
[0004] Proximal junction kyphosis (PJK) can lead to proximal junction failure (PJF), which is a serious early complication of spinal surgery in adults and may require revision surgery. Risk factors for spinal surgery include overcorrection, undercorrection, excessive ligament dissection, and osteoporosis. These spinal pathologies (PJK, PJF) generally occur within three months of spinal surgery in approximately 66% of cases. It has been observed that up to 40% of adult patients who have undergone spinal surgery have developed PJK. The progression from PJK to PJF must be avoided, because PJF requires revision surgery, which represents additional discomfort and risks for the patient, and generates additional costs.
[0005] Following vertebral fusion(s), the aim is to recreate a natural gradient of load distribution and relieve the non-fused vertebrae, in particular to avoid an anterior collapse of the fused area.
[0006] It is known to use braided textile ligaments to eliminate the abrupt transition between thoracic rigidity after vertebral fusion, particularly lumbar vertebral fusion, and the flexibility of the unfused vertebral segments. However, the proposed textile ligaments exhibit very rigid behavior and are not sufficiently elastic.
[0007] There is a need for an artificial ligament that has a rigid behavior according to certain deformation plates and an elastic behavior in other deformation ranges in order to compensate for the thoracic rigidity compared to the flexibility of the non-fused vertebral segments. Description of the invention
[0008] The present invention relates, according to a first aspect, to an artificial ligament, in particular for the treatment of proximal junctional kyphosis (PJK), alleviating all or part of the aforementioned problems in that it comprises, advantageously is essentially made up of, even more advantageously is made up of, a long-span braided hollow sheath having an internal volume, and a deformable insert housed in the internal volume of the braided hollow sheath and this over at least a part of the length of said hollow sheath.
[0009] Advantageously, the artificial ligament has: - a deformation phase A in which the slope coefficient ka measured on a tensile force (N) - elongation (%) curve Cia of said artificial ligament is less than or equal to 6 Newtons / %, advantageously less than or equal to 5 Newtons / %; and - a deformation phase B in which the slope coefficient kb measured on said curve Cia of tensile force (N) - elongation (%) of said artificial ligament is greater than or equal to 4 Newtons / %, advantageously greater than or equal to 5 Newtons / %, and less than or equal to 40 Newtons / %, the elongation of said artificial ligament in said deformation phase B is greater than or equal to 2% and less than or equal to 15%, in particular less than or equal to 10%; - a deformation phase C in which the slope coefficient kc measured on said curve Cia of tensile force (N) - elongation (%) of said artificial ligament is greater than the slope coefficient kb of phase B. Advantageously, the placement of a deformable insert along all or part of the length of the hollow duct's internal volume allows for modification of the duct's mechanical behavior. In particular, this deformable, elastic insert allows to increase the sheath's capacity, and therefore ultimately the ligament's, to lengthen and create a range of rigidity, particularly conducive to the treatment of CJP.
[0010] Advantageously, in phase A, corresponding to low deformations, in particular to an elongation (%) less than or equal to 5% or 2%, a low elongation is observed under a low load on the artificial ligament, then an elongation that increases slightly for a high load.
[0011] A non-exhaustive and non-limiting technical explanation of the present invention is that in phase A, the behavior of the artificial ligament is dominated and therefore largely attributable to the deformable insert. Then, in phase B, the threads of the hollow textile sheath continue to slide relative to each other and thus compress the deformable insert, increasing the applied force and the resulting elongation. Finally, in the last phase, namely phase C, the deformable insert is completely compressed / crushed by the threads of the hollow sheath, and the behavior of the artificial ligament is determined by said threads of the hollow sheath. The behavior in phase C corresponds to the so-called rigid behavior phase of the artificial ligament.
[0012] The deformable insert thus makes it possible to shift the rigid behavior of the hollow sheath to large elongations, and to maintain a flexible / elastic behavior at small, or even very small, elongations. This arrangement makes it possible to provide flexibility to the levels of the unfused vertebrae located near those that are fused for small amplitude movements, and rigidity for larger movements.
[0013] Advantageously, the artificial ligament is implantable, in particular it is suitable for insertion into a living organism (human or animal) for a prolonged period, for example from a few days to several months or years.
[0014] In one embodiment, the Ck curve of the tensile force-elongation of said artificial ligament is measured on a Lyod Lrx machine, with a tensile speed of 100 mm / minute, particularly at ambient temperature, for example, at a temperature ranging from 19°C to 23°C, without any particular relative humidity conditions. Optionally, a preload of 10 N is applied, particularly at a preload speed of 50 mm / min. The artificial ligament comprises, in particular, first and second ends. A first end is disposed in first jaws, and a second end is disposed in second jaws. The first jaws are fixed, while the second jaws move in translation at a speed of 100 mm / minute. Preferably, the initial test length of the artificial ligament is 395 mm ± 5 mm.
[0015] In one embodiment, the deformable insert is elastic.
[0016] The tensile force applied to said insert or ligament or to said braided hollow sheath is always considered in this text as applied in the direction longitudinal of said insert or ligament or braided hollow sheath.
[0017] Preferably, the elongation (%) and tensile force values measured and indicated in this text on the Ck curve of tensile force (N) - elongation (%) of said artificial ligament are obtained during the first traction cycle, i.e. after the first traction, carried out on the artificial ligament after removal from its sterilized packaging.
[0018] Preferably, the tensile and elongation forces (%) indicated in this text are not tensile forces causing rupture, and therefore elongations at rupture, of the ligament, unless otherwise specified.
[0019] In this text, an elastic insert is defined as an insert having a residual deformation of 10% or less for a longitudinally applied force of 300 N or less. The elastic insert thus deforms longitudinally under an applied force of a maximum of 300 N and recovers its initial undeformed length or with a variation of no more than 10%, advantageously no more than 8%, even more advantageously no more than 5%, and in particular no more than 3%. The deformation can be calculated as follows: (Residual length of the deformable insert after at least one longitudinal deformation - Initial length of the deformable insert having undergone no longitudinal deformation) / Initial length of the deformable insert having undergone no longitudinal deformation. Artificial ligament
[0020] Preferably, the artificial ligament comprises first and second ends, in particular free, between which the longitudinal body of said artificial ligament extends. Preferably, the artificial ligament comprises a length L, and a width 1 (if it is flat) or a diameter d (if it is substantially round).
[0021] Preferably, the length L of the artificial ligament is greater than or equal to 50 mm and less than or equal to 400 mm, more preferably greater than or equal to 100 mm and less than or equal to 300 mm.
[0022] Preferably, the width 1 or the diameter d of the artificial ligament is greater than or equal to 3 mm and less than or equal to 20 mm, more preferably less than or equal to 15 mm, preferably less than or equal to 10 mm.
[0023] Preferably, the artificial ligament has a longitudinal axis Lk, advantageously extending between its first and second ends, in particular free. Preferably, the artificial ligament has a transverse axis Tk substantially intersecting the axis Lk, in particular substantially perpendicular to the axis Lk.
[0025] The artificial ligament can be elongated and flat or elongated and substantially round. hollow sheath
[0026] Preferably, the hollow sheath comprises first and second ends, further preferably between which the longitudinal body of the hollow sheath extends.
[0027] Preferably, the hollow sheath comprises a length Lgc and a width lgc (if it is flat) or a diameter dgc (if it is substantially round).
[0028] Preferably, the length Lgc of the hollow sheath is greater than or equal to 50 mm and less than or equal to 400 mm, more preferably greater than or equal to 100 mm and less than or equal to 300 mm.
[0029] Preferably, the width lgc or the diameter dgc of the hollow sheath is greater than or equal to 3 mm and less than or equal to 20 mm, more preferably less than or equal to 15 mm, preferably less than or equal to 10 mm. Preferably, the hollow sheath has a longitudinal axis Lgc and transverse axis Tgc, in particular substantially perpendicular to the axis Lgc.
[0031] The hollow sheath can be elongated and flat or elongated and substantially round.
[0032] The hollow sheath is braided and comprises several braided wires.
[0033] Preferably, the hollow sheath comprises, advantageously is made up essentially of, even more advantageously is made up of, one or more monofilamentary wire(s), and / or one or more spun fiber(s), and / or one or more multifilamentary wire(s), preferably one or more multifilamentary wire(s).
[0034] The hollow sheath comprises an internal volume, in particular delimited by its inner wall, substantially opposite its outer wall. Said internal volume receives, along all or part of its length Lgc, said insert.
[0035] The hollow sheath comprises, advantageously is made up essentially of, even more advantageously is made up of, at least one or more wires which is / are totally bioresorbable, or only partially bioresorbable, preferably non-resorbable.
[0036] Preferably, the hollow braided sheath comprises, advantageously is made up essentially of, even more advantageously is made up of, several braided strands, in particular a braided strand is supported by a spindle on the braiding loom, each braided strand comprising one or more yarn(s), in particular as described in this text.
[0037] Preferably, the hollow braided sheath comprises, advantageously is made up essentially of, even more advantageously is made up of, a number of braided strands ranging from 8 to 64, even more preferably ranging from 12 to 52 strands, preferably comprises from 16 to 48 strands.
[0038] Preferably, the hollow sheath, particularly braided, comprises, advantageously is made essentially of, even more advantageously is made of, one or more yarns comprising at least one material selected from the list including: polyethylene terephthalate, high-tenacity polyethylene terephthalate, polybutylene terephthalate, high molecular weight polyethylene, very high molecular weight polyethylene molecular, polyamide 4-6 or 6-6,... or a mixture of the latter, preferably from the list including: polyethylene terephthalate, in particular high toughness, high or very high molecular weight polyethylene.
[0039] In the present text, bioresorbable means the ability of a material (for example, a textile, a thread, a foam, or a coating, etc.) to be degraded by a living organism in which it is implanted so as to disappear after a determined period, for example after 10 days or after several months, for example after 6 months. Deformable insert
[0040] Preferably, the insert comprises first and second ends, even more preferably between which the longitudinal body of the insert extends.
[0041] The insert can be continuous or discontinuous. When the insert is discontinuous, the insert comprises several insert sections arranged adjacently or spaced apart within the internal volume of the hollow sheath.
[0042] Preferably, the insert comprises a length L; and a width 1; (if it is flat) or a diameter d; (if it is substantially round).
[0043] Preferably, the length L of the insert is greater than or equal to 50 mm and less than or equal to 400 mm, more preferably greater than or equal to 100 mm and less than or equal to 300 mm.
[0044] Preferably, the width h or the diameter d of the hollow sheath is greater than or equal to 3 mm and less than or equal to 20 mm, more preferably less than or equal to 15 mm, preferably less than or equal to 10 mm.
[0045] Preferably, L; is less than or equal to Lgc.
[0046] Preferably, h or d; is less than or equal to lgc or dgc. Preferably, the insert has a longitudinal axis L; and transverse axis T;, in particular sen possibly perpendicular to the L axis;
[0048] The insert can be elongated and flat or elongated and substantially round.
[0049] The insert is not preferably a braid.
[0050] Preferably, the insert comprises (in particular is) an elongated element comprising one or more yarn(s), and / or one or more polymer foam cord(s), and / or one or more rod(s), and / or one or more extruded polymer profile(s), and / or one or more woven and / or knitted textile strip(s) / cord(s), and / or one or more nonwoven strip(s) / cord(s).
[0051] The insert is preferably a rod or a set of several rods, in particular each having a substantially cylindrical cross-section. When the insert is a set of several rods, said rods are arranged parallel to each other.
[0052] Preferably, said at least rush, or each of said rushes, comprises, before- geusement is made up essentially of, even more advantageously is made up of, one or more material(s) chosen from: polyurethane, polycarbonate-urethane, or polydimethylsiloxane, or even a mixture of the latter.
[0053] Preferably, the polycarbonate-urethane (PCU) has a shore A hardness ranging from about 80 to about 90. In a preferred example, the polycarbonate-urethane is chosen from those marketed by DSM under the Bionate® brand.
[0054] Preferably, polydimethylsiloxane is an elastomer, more preferably has a Shore A hardness ranging from about 20 to about 80. In a preferred example, polydimethylsiloxane is marketed by the company Nusil.
[0055] In one embodiment, the deformable insert does not occupy all the internal volume of the hollow sheath.
[0056] In one embodiment, the hollow sheath comprises an internal volume Vint, and the solid volume occupied by the deformable insert represents at most 95%, preferably at most 90%, even more preferably at most 85%, preferably at most 80%, in particular at most 75%, more particularly at most 70%, of the internal volume Vint of the hollow sheath.
[0057] The solid volume of the deformable insert is understood to mean any volume occupied by the deformable insert which does not include any void, for example not including the orifices of a foam.
[0058] Preferably, the volume Vint of the hollow sheath is calculated theoretically as a function of the dimensions (mm) of the hollow sheath (internal diameter or internal width and internal height, internal length).
[0059] In one embodiment, the hollow sheath comprises an internal volume Vint, and the solid volume occupied by the deformable insert represents at least 25%, preferably at least 35%, even more preferably at least 45%, preferably at least 55%, in particular at least 65%, more particularly at least 75%, of the internal volume Vint of the hollow sheath.
[0060] Advantageously, since the internal volume is not filled by the deformable insert, there remain voids in the internal volume which will be compressed during a longitudinal deformation of the ligament, thus delaying the engagement of the hollow sheath in the longitudinal deformation and putting stress on the insert first.
[0061] The deformable insert may be totally bioresorbable, or only partially bioresorbable, or non-resorbable, preferably non-resorbable.
[0062] In a first embodiment, the deformable insert and / or the braided sheath comprises (each) (advantageously is / are each essentially made of, even more advantageously is / are each made of) one or more yarns, preferably multifilamentary, of high-tenacity polyethylene (in particular, very high molecular weight polyethylene, or UHMWPE), preferably having at least one of the following characteristics:
[0063] - a linear density (dtex) ranging from 200 dtex to 600 dtex, in particular ranging from 300 dtex to 550 dtex, more specifically ranging from 400 dtex to 500 dtex; and / or
[0064] - a tenacity (cN / dtex) ranging from 25 cN / dtex to 50 cN / dtex, in particular ranging from 30 cN / dtex to 45 cN / dtex, more specifically ranging from 30 cN / dtex to 40 cN / dtex; and / or
[0065] - an elongation at break of less than or equal to 30%, preferably less than or equal to 20%, preferably less than or equal to 10%, preferably less than or equal to 5%; and / or
[0066] - a breaking force greater than or equal to 80 N, preferably greater than or equal to 100 N, preferably greater than or equal to 140 N, preferably greater than or equal to 160 N, in particular less than or equal to 1000 N.
[0067] In a second embodiment, possibly in combination with the first embodiment, the deformable insert and / or the braided sheath comprises (each) (advantageously is / are each made essentially of, even more advantageously is / are each made essentially of) one or more yarns, preferably multifilamentary, made of polyethylene terephthalate, preferably having at least one of the following characteristics:
[0068] - a linear density (dtex) ranging from 25 dtex to 150 dtex, in particular ranging from 25 dtex to 100 dtex, more specifically ranging from 25 dtex to 65 dtex; and / or
[0069] - a tenacity (cN / dtex) ranging from 25 cN / dtex to 100 cN / dtex, in particular ranging from 40 cN / dtex to 90 cN / dtex, more specifically ranging from 60 cN / dtex to 90 cN / dtex; and / or
[0070] - an elongation at break of less than or equal to 50%, preferably less than or equal to 40%, preferably less than or equal to 30%, preferably less than or equal to 20%; and / or
[0071] - a breaking force greater than or equal to 150 cN, preferably greater than or equal to at 250 cN, preferably greater than or equal to 300 cN, in particular less than or equal to 1000 cN.
[0072] Preferably, linear density is measured using standard EN 13392, in particular dating from 2001 when it is a monofilamentary yarn, or according to standard EN ISO 2060 dating from 1995 when it is a multifilamentary yarn.
[0073] Preferably, the elongation at break, the toughness and the breaking strength are measured using the EN 13895 standard, in particular dating from 2003 when it is a monofilamentary yarn, or according to the EN ISO 2062 standard dating from 1993 when it is a multifilamentary yarn.
[0074] Preferably, the insert is long and even more preferably the length of the insert is substantially equal to the length of the braided hollow sheath.
[0075] Preferably, the insert and the braided hollow sheath have central longitudinal axes Lin and Lgc respectively.
[0076] Preferably, the deformable insert and the braided hollow sheath are coaxial.
[0077] Preferably, the deformation phases take place in this order, A, then B and finally C, the forces and elongations being increasing from phase A to phase B and then to phase C.
[0078] Preferably, phases A, B and C are distinct from each other.
[0079] Preferably, the artificial ligament has deformation phases A, then B and finally C under the application of an increasing force (N).
[0080] Preferably, the curve Ck is the curve LAI 1, or LAI 2, or LAI3, or even LAI 4 or LAI5.
[0081] The slope coefficient (ka) is understood to be the slope coefficient of a line TA tangent at any point of the curve C in phase A, preferably at any point of the curve Ck whose elongation is less than or equal to 5% or 2%.
[0082] The slope coefficient (kb) is understood to be the slope coefficient of a line TB tangent at any point of the curve Cia in phase B, preferably at any point of the curve Cia whose elongation is greater than or equal to 5% or 2% and less than or equal to 15%, advantageously less than or equal to 10%.
[0083] The slope coefficient (kc) is understood to be the slope coefficient of a line TC tangent at any point of the curve C in phase C, preferably at any point of the curve C whose elongation is greater than or equal to 5%, preferably greater than or equal to 7%, even more preferably greater than or equal to 10%, possibly greater than or equal to 15%.
[0084] It is understood by "is essentially made up of" that the element(s) introduced by this expression is / are present in majority, it is possible that other element(s) (not described) may be present but it / they are not in majority. In one embodiment, the deformable insert is a rod comprising a thermoplastic or thermosetting elastomer, preferably comprising (advantageously consisting mainly of, even more advantageously consisting of) one or more polymer(s) selected from: a polyurethane, a polycarbonate-urethane, a polydimethylsiloxane, or a mixture of these.
[0085] In this text, thermoplastic elastomer means that said elastomer present in the insert can be transformed by heating it (in particular molded, extruded or injected), in particular said elastomer has a softening or melting temperature allowing it to be shaped by heat.
[0086] In this text, the term "thermosetting elastomer" means that the elastomer present in the insert cannot be transformed by heating it, in particular said elastomer has no melting point.
[0087] In one embodiment, the insert is a rod or a set of rod(s), and each rod is essentially made up of, in particular is made up of, one or more polymer(s) chosen from the following polymers: polyurethane, poly-carbonate-urethane, polydimethylsiloxane or a mixture of the latter.
[0088] In particular, said polymer is a polyurethane or a polycarbonate-urethane or a polydimethylsiloxane.
[0089] In one embodiment, said insert is a rod or a set of rod(s), in particular said rod or each of said rods is extruded.
[0090] The cross-section of said rod or of each of said rod(s) has for its largest dimension (d), or for diameter (d) when the cross-section is substantially circular, d being greater than or equal to 1 mm and less than or equal to 5 mm.
[0091] In one embodiment, said artificial ligament has an elongation less than or equal to 15%, possibly less than or equal to 10%, under the effect of a tensile force of the order of 250 Newtons, preferably after at least 10 cycles of traction, each cycle of traction comprising the application of a tensile force of the order of 250 Newtons.
[0092] In one embodiment, the difference (%) between the residual elongation (%) obtained after a traction cycle (n) of the ligament and the residual elongation (%) obtained after a traction cycle (n+1) of the ligament, with n is an integer other than 0, preferably n is equal to 10, is less than or equal to 15%, preferably less than or equal to 10%, more preferably less than or equal to 8%, preferably less than or equal to 5%, more preferably less than or equal to 3%, each traction cycle comprising the application of a traction force of the order of 250 Newtons.
[0093] The tensile force of the order of 250 Newtons is less than the tensile rupture force of the artificial ligament.
[0094] A traction cycle in the present text includes the application of the traction force, here of the order of 250 N, then the return to the resting state of the ligament, i.e. without exerting any traction force on the ligament. In this text, residual elongation (%) is understood to mean: the difference between the residual length (mm) of the artificial ligament after one traction cycle (n) and the initial length (mm) of the artificial ligament (advantageously before the application of any traction cycle) divided by the initial length (mm) of the artificial ligament ((residual length of the ligament - initial length of the ligament) / initial length of the ligament).
[0095] In one embodiment, in phase A of deformation, the elongation of said artificial ligament is less than or equal to 5%, possibly less than or equal to 2%, under the application of a tensile force less than or equal to 200 Newtons; and in phase C of deformation, the elongation of said artificial ligament is greater than or equal to 5%, preferably greater than or equal to 10%, even more preferably greater than or equal to 15%, under the application of a tensile force greater than or equal to 200 Newtons and less than or equal to 800 Newtons.
[0096] In a first embodiment, in phase A of deformation, the elongation of said artificial ligament is less than or equal to 5%, possibly 2%, under the application of a tensile force less than or equal to 150 Newtons, preferably less than or equal to 100 Newtons, even more preferably less than or equal to 50 Newtons.
[0097] Advantageously, in phase A of deformation, the elongation of said artificial ligament is less than or equal to 5%, possibly to 2%, under the application of a tensile force greater than 0 Newtons, advantageously greater than or equal to 10 Newtons.
[0098] In a second embodiment, possibly in combination with the second embodiment, in phase C of deformation, the elongation of said artificial ligament is greater than or equal to 5%, advantageously greater than or equal to 10%, even more advantageously greater than or equal to 15%, under the application of a tensile force greater than or equal to 300 Newtons.
[0099] In one embodiment, kb is greater than ka, in particular kb is greater than or equal to twice ka, more particularly kb is greater than or equal to three times ka.
[0100] The foot of the curve is very important when transitioning from phase A to phase B because the force applied in phase A for very small elongations (on the order of a few %) is close to 0 Newtons.
[0101] In one embodiment, kc is greater than kb, in particular kc is greater than or equal to twice kb, more particularly kc is greater than or equal to three times kb, even more particularly kc is greater than or equal to four times kb.
[0102] An increase in stiffness is observed in phase C of the artificial ligament deformation, in which essentially the mechanical properties of the sheath wires are expressed. The toe of the curve is very significant during the transition from phase B to phase C.
[0103] In one embodiment, in phase B of deformation, the tensile force applied to the artificial ligament is less than or equal to 200 Newtons, preferably less than or equal to 100 Newtons.
[0104] In one embodiment, the internal volume of said at least a part of the braided hollow sheath receiving said insert comprises one or more compressible empty cavity(ies) so as to crush during the passage from deformation phase A to deformation phase B.
[0105] Advantageously, the empty cavities are reversibly compressible so that during the transition from phase B to phase A, and possibly at rest, said cavities recover their initial volumes.
[0106] The said cavity(ies) may each have a dimension on the order of a micrometer or a millimeter.
[0107] In one embodiment, the insert has a void ratio greater than or equal to 30%, preferably less than or equal to 90%, more preferably less than or equal to 80%, preferably less than or equal to 70%
[0108] The void ratio of the insert is preferably calculated with the following formula: 100x[l(P / (MxS))] in which P is the linear mass of the insert in grams / cm, M is the density of the material forming the insert in grams / cm3 (for example of the polymer material in which the insert is formed), and S is the cross-sectional area of the insert in cm2.
[0109] In one embodiment, the solid surface area of the cross-section of the insert is less than the total surface area (mm2) of the cross-section of said at least a part of the braided hollow sheath receiving said insert in its internal volume.
[0110] Advantageously, the artificial ligament includes empty spaces that can be crushed during its progressive elongation under the application of a longitudinal traction force.
[0111] In one embodiment, the insert is chosen from: a tube, a foam cord, a deformable profile, and at least one long, multilobed element, in particular trilobed or quadrilobed, for example at least one multilobed monofilament.
[0112] Advantageously, the insert has an irregular structure capable of creating cavities and / or comprises a foamed material comprising cavities.
[0113] Preferably, the deformable profile is a spring profile.
[0114] In one variant, the insert is chosen from: a tube, a foam, and at least one long-lined element, in particular at least one rod or at least one monofilamentary thread, more particularly multilobed.
[0115] In one embodiment, the insert is a long, extruded, foamed or three-dimensionally printed element, in particular by additive or subtractive manufacturing or a combination thereof.
[0116] In one embodiment, said insert comprises at least one polymer material having a Shore A hardness ranging from 5 to 90, in particular from 5 to 50, more particularly from 20 to 50.
[0117] Preferably, Shore A hardness is determined with the NF EN ISO 868 standard dating from 2003.
[0118] Preferably, said insert has a Shore A hardness ranging from 5 to 90, in particular from 5 to 50, more specifically from 20 to 50.
[0119] Preferably, at least 50% by mass of said insert is made essentially of said at least one polymer material having a Shore A hardness of 5 to 90, more preferably at least 80% or 90% by mass of said insert is made essentially of said at least one polymer material having a Shore A hardness of 5 to 90.
[0120] In one embodiment, the braided hollow sheath comprises, advantageously is made up essentially, even more advantageously is made up of, at least 10 strands, preferably at least 14 strands, braided, each of the strands comprising at least one multifilamentary wire.
[0121] In one embodiment, the hollow braided sheath comprises, advantageously is made essentially, even more advantageously is made, one or more wires comprising one or more material(s) selected from: very high molecular weight polyethylene, polyethylene terephthalate, polypropylene, polyetheretherketone (PEEK), polyetherketoneketone (PEKK), polytrimethylene terephthalate (PTT), or a combination thereof.
[0122] In one embodiment, the height of a braided helix pitch of the braided hollow sheath is greater than or equal to 4 mm, preferably greater than or equal to 8 mm, in particular between 4 mm and 25 mm.
[0123] A braided helix pitch corresponds to the distance separating two crossings of a determined braided wire with the longitudinal axis of the hollow braided sheath. In one embodiment, the external diameter of the insert is greater than or equal to 2 mm and less than or equal to 15 mm, preferably less than or equal to 10 mm, and even more preferably less than or equal to 8 mm.
[0124] The present invention relates, according to a second aspect, to a method for manufacturing an artificial ligament, in particular according to any one of the variants / embodyments in reference to the first aspect of the invention, advantageously comprising: a) the supply of a deformable insert, b) a step of braiding a hollow sheath having an internal volume, at least a portion of which is overbraided around said deformable insert, said deformable insert being housed within the internal volume of the braided hollow sheath and over at least a portion of the length of said hollow sheath, and in that the ligament has: - a deformation phase A in which the slope coefficient ka measured on a tensile force (N) - elongation (%) curve Cia of said artificial ligament is less than or equal to 6 Newtons / %, preferably less than or equal to 5 Newtons / %; and - a deformation phase B in which the slope kb measured on said curve Cia of tensile force (N) - elongation (%) of said artificial ligament is greater than or equal to 4 Newtons / %, preferably greater than or equal to 5 Newtons / %, and less than or equal to 40 Newtons / %, the elongation of said artificial ligament in said phase B of deformation is greater than or equal to 2 and less than or equal to 15%; - a deformation phase C in which the slope coefficient kc measured on said curve Ck of tensile force (N) - elongation (%) is greater than the slope coefficient kb of phase B.
[0125] In one embodiment, said method comprises a heat-fixing step including the application of a temperature ranging from 90°C to 300°C, in particular around 130°C, for at least 1 minute, in particular for a period ranging from 2 minutes to 10 minutes. Preferably, a load (applied to the free ends of said artificial ligament) ranging from 1 daN to 10 daN is applied to the artificial ligament during the heat-fixing step.
[0126] In one embodiment, the braided hollow sheath comprises (in particular is made essentially of) one or more polyethylene wire(s), and the temperature applied during the heat-setting step is greater than or equal to 90°C and less than or equal to 300°C.
[0127] In one embodiment, the braided hollow sheath comprises (in particular is made essentially of) one or more polyethylene terephthalate or polybutylene terephthalate yarn(s), and the temperature applied during the heat-setting step is greater than or equal to 150°C and less than or equal to 230°C. Description of the drawings
[0128] The present invention will be better understood upon reading the following embodiments, cited by way of non-limiting example, and illustrated by the figures in which:
[0129] [Fig-1] [Fig.1] schematically represents a first example of an ar ligament special equipment according to the invention;
[0130] [Fig.2] [Fig.2] schematically represents, in enlarged view, the height of a braided helix pitch of the braided hollow sheath of the artificial ligament shown in [Fig.1];
[0131] [Fig.3] [Fig.3] schematically represents a second example of an artificial ligament according to the invention;
[0132] [Fig.4] [Fig.4] schematically represents a second example of a deformable insert suitable for implementing the invention;
[0133] [Fig.5] [Fig.5] schematically represents a third example of a deformable insert suitable for implementing the invention;
[0134] [Fig.6] [Fig.6] schematically represents a fourth example of a deformable insert suitable for implementing the invention;
[0135] [Fig.7] [Fig.7] schematically represents a fifth example of a deformable insert suitable for implementing the invention;
[0136] [Fig-8] [Fig.8] schematically represents different Ck curves in which the applied tensile force is indicated on the ordinate, and the elongation obtained (%) is indicated on the abscissa for flat artificial ligaments according to the invention and a hollow braided sheath without insert forming a comparative artificial ligament;
[0137] [Fig.9] [Fig.9] schematically represents different Ck curves in which the applied tensile force is indicated on the ordinate, and the elongation obtained (%) is indicated on the abscissa for substantially tubular artificial ligaments according to the invention and two hollow braided sheaths without insert forming comparative artificial ligaments.
[0138] The curves shown in Figures 8 and 9 are obtained for traction cycles that do not lead to ligament rupture but for a maximum applied traction force of approximately 250 Newtons. These Ck traction force-elongation curves of said artificial ligament are measured as described above in this text, i.e. on a Lyod Lrx machine, with a traction speed of 100 mm / minute, in particular at ambient temperature, for example at a temperature ranging from 19°C to 23°C, without any particular relative humidity conditions, optionally a preload of 10N is applied, in particular at a preload speed of 50 mm / min.The artificial ligament comprises, in particular, first and second ends; a first end is disposed in first jaws, and a second end is disposed in second jaws; the first jaws are fixed while the second jaws move in translation at a speed of 100 mm / minute. Preferably, the initial test length of the artificial ligament is 395 mm + / - 5 mm. Description of the implementation methods
[0139] The first example of an artificial ligament 10 according to the invention comprises a hollow braided sheath 20 defining an internal volume 22 and having a determined length Lgci as well as first and second opposing ends (24, 26). The artificial ligament 10 also comprises a deformable insert 30 having a length Lnet of the first and second opposing ends (34, 36). In this specific example, the deformable insert 30 is a polyurethane foam cord having a Shore A hardness of approximately 40. In particular, the length Lu is less than Lgci but could be equal to Lgd.
[0140] The helix pitch Ph[ of the hollow braided sheath 20 is in this specific example on the order of 11 mm. The braided helix pitch corresponds to the distance Ph[ separating two adjacent crossings of a braided wire - colored in black for identification purposes on [Fig.2] - with the longitudinal axis of the hollow braided sheath 20.
[0141] In this specific example, the artificial ligament 10 comprises 16 strands comprising each a multifilament polyethylene terephthalate yarn of 435 dtex and 120 filaments, said strands being braided on a 16-spindle braiding loom (one strand / spindle).
[0142] The second example of an artificial ligament 100 according to the invention comprises a hollow braided sheath 120 defining an internal volume 122 and having a determined length Lgc2 as well as opposing first and second ends (124, 126). The artificial ligament 100 also comprises a deformable insert 130 having a length Li2 and opposing first and second ends (134, 136). In this particular example, the deformable insert 130 is a polyurethane foam cord having a Shore A hardness of approximately 40. In particular, the length Li2 is less than Lgc2 but could be equal to Lgc2.
[0143] The helix pitch Ph2 of the hollow braided sheath 120 is in this specific example of the order of 19 mm.
[0144] In this specific example, the artificial ligament 100 comprises 48 strands, each consisting of 4 multifilament polyethylene terephthalate yarns, each yarn having a fineness of 138 dtex and comprising 32 filaments. The 48 strands are braided on a 48-spindle braiding machine (one strand / spindle).
[0145] In this text, the number of braided strands corresponds to the number of spindles supporting one or more threads (a strand may include one or more threads) which are braided on the braiding loom.
[0146] The braided sheath 120 has more braided strands and is thus less tight around the insert 130 than the braided sheath 20 which is very tight around the insert 30.
[0147] In order to offset the rigid behavior of the hollow braided sheath under the effect of longitudinal tension, particularly in phase C of deformation, the wires of the sheath are braided so as to penetrate / engage with the surface of the insert, i.e. with a helix pitch large enough for the wires to slide relative to each other.
[0148] In the examples shown in Figures 1 to 3, the insert (30, 130) is a cord made of elastic and deformable polyurethane foam. This insert can alternatively be, for example, an extruded or foamed polymer profile 200 having a trilobed cross-section as shown in [Fig. 4] or a quadrilobed cross-section 210 as shown in [Fig. 5]. The diameters dini and din2 of the inserts 200 and 210, respectively (i.e., the diameter of the circle receiving the cross-section of said insert), are, for example, each on the order of 4 mm. The insert according to the invention can also be a spring profile 220 having a height hin3 ranging from 2 mm to 8 mm, for example on the order of 4 mm, and a width lin3 ranging from 1 mm to 8 mm, for example on the order of 5 mm. The thickness of a wall ein3 ranges from 0.1 mm to 2 mm; for example, it is on the order of 0.4 mm. The insert according to the invention can also be a nested textile strip 230 knitted bee wire, wound around itself to form a tube around which the hollow sheath is braided.
[0149] Alternatively, the insert according to the invention can be a rod made of polyurethane or polycarbonate-urethane (PCU), or even of polydimethylsiloxane (PDMS).
[0150] Fig. 8 represents the longitudinally applied tensile force (N) and elongation (%) curves obtained for a comparative artificial ligament LAC1 and three artificial ligaments according to the invention whose hollow braided sheaths are substantially flat LAI1, LAI2, and LAI3, for a maximum applied tensile force of 250 Newtons. Example LAC1
[0151] This comparative artificial ligament comprises a hollow textile sheath braided on a 48-spindle braiding loom, and therefore comprises 48 textile strands, each textile strand comprising 4 polyethylene terephthalate yarns, each yarn comprising 32 filaments and having a density of 138 dtex. A total density of 552 dtex is obtained per strand. The helix pitch is approximately 19.64 mm. Example LAI1
[0152] This artificial ligament according to the invention comprises a hollow textile sheath braided on a 48-spindle braiding loom, and therefore comprises 48 textile strands. Each textile strand comprises 4 polyethylene terephthalate yarns, each yarn comprising 32 filaments and having a count of 138 dtex. This results in 552 dtex per strand. The helix pitch is approximately 19.64 mm. This artificial ligament includes an insert formed from a polyurethane foam cord with a Shore A hardness of approximately 40, having a length (lin) of approximately 13.5 cm, a width (lin) of approximately 6.5 mm, and a thickness of approximately 4 mm. The length of the hollow textile sheath (Lgc) is substantially equal to the length (lin) of the insert. Example LAI2
[0153] This artificial ligament according to the invention comprises a hollow textile sheath braided on a 48-spindle braiding loom, and therefore comprises 48 textile strands. Each textile strand comprises 4 polyethylene terephthalate yarns, each yarn comprising 32 filaments and having a count of 138 dtex. This results in 552 dtex per strand. The helix pitch is approximately 19.64 mm. This artificial ligament includes an insert formed from a polyurethane foam cord with a Shore A hardness of approximately 40, having a length (lin) of approximately 10.5 cm, a width (lin) of approximately 5 mm, and a thickness of approximately 4 mm. The length of the hollow textile sheath (Lgc) is substantially equal to the length (lin) of the insert. Example LAI3
[0154] This artificial ligament according to the invention comprises a hollow textile sheath braided on a 48-spindle braiding loom, and therefore comprises 48 textile strands, each strand The textile comprises four polyethylene terephthalate yarns, each yarn containing 32 filaments and having a count of 138 dtex. This results in 552 dtex per strand. The helix pitch is approximately 19.64 mm. This artificial ligament includes an insert formed from a polyurethane foam cord with a Shore A hardness of approximately 40, having a length of approximately 10.5 cm, a width of approximately 5 mm, and a thickness of approximately 4 mm. The length of the hollow textile sheath is approximately equal to the length of the insert.
[0155] Ligaments LAC1, LAI1, LAI2, and LAI3 all undergo a calendering step during which they are calendered and heated, notably at 110°C for 45 seconds, to flatten them and fix their shape. Ligaments LAC1, LAI1, and LAI2 also undergo a heat-setting step, unlike ligament LAI3, which does not undergo a heat-setting step.
[0156] In these specific examples, and without limitation, the heat-setting step includes heating the artificial ligament under tension (preferably applied to the free ends of said artificial ligament) ranging from 1 daN to 10 daN, in particular 10 daN. The heating time is greater than or equal to 2 minutes and less than or equal to 10 minutes, and the heating temperature is greater than or equal to 90°C and less than or equal to 300°C. When the hollow braided sheath is composed of polyethylene yarns, the heating, and therefore heat-setting, temperature is preferably greater than or equal to 80°C and less than or equal to 120°C. When the hollow braided sheath is made primarily of polyethylene terephthalate or polybutylene terephthalate yarn(s), the heating, and therefore heat-setting, temperature is greater than or equal to 150°C and less than or equal to 230°C.
[0157] It is observed that ligament LAC1 does not include A and B phases and enters the most rigid phase C almost immediately after the application of the tensile force (N). Ligaments according to the invention LAI1, LAI2, and LAI3 have their C deformation phases offset by the A and B deformation phases. Phase A occurs as a deformation plateau in which the ligament elongates for a near-zero tensile force with a small elongation, in particular substantially less than or equal to 2%.
[0158] Phase B of deformation, intermediate between phases A and C, exhibits an elongation that remains moderate, less than or equal to 4% for a still fairly modest applied force, in particular less than or equal to 100 N. Finally, in phase C of deformation, the ligaments LAI1, LAI2 and LAI3 elongate much more but for much higher applied forces, for example greater than or equal to 100 N.
[0159] For example, on the LAI1 curve, we measure a slope coefficient ka of the order of 4 N / %, a slope coefficient kb of the order of 5.5 N / %, and a slope coefficient kc at a first point (bottom of the curve) of 27.07 N / % and at a second point (middle of the curve) of 41.68 N / %.
[0160] Fig. 9 represents the longitudinally applied tensile force curves (N) and the elongations obtained (%) for two comparative artificial ligaments LAC2 and LAC3, and two artificial ligaments according to the invention LAI4, LAI5, whose hollow braided sheaths are substantially round, for a maximum applied tensile force of 240 Newtons. Example LAC2
[0161] This comparative artificial ligament comprises a hollow textile sheath braided on a 16-spindle braiding loom, and therefore comprises 16 textile strands. Each textile strand comprises one very high molecular weight polyethylene yarn, for example, Spectra brand. Each yarn comprises 120 filaments and has a density of 435 dtex. This ligament does not include a deformable insert. The helix pitch (ph) is 11 mm. Example LAC3
[0162] This comparative artificial ligament is similar to the LAC2 ligament except that the helix pitch Ph is 5 mm. Example LAI4
[0163] This artificial ligament according to the invention comprises a hollow textile sheath braided on a 16-spindle braiding loom, and therefore comprises 16 textile strands, each textile strand comprising 1 very high molecular weight polyethylene yarn, for example of the Spectra brand, each yarn comprising 120 filaments and having a density of 435 dtex. The helix pitch (ph) is 11 mm.
[0164] This artificial ligament comprises a laminate having a length Lin of approximately 10 cm and a width Lin of approximately 6 mm. The length of the hollow textile sheath Lgc is substantially equal to the length Lin of the insert. The pre-tension applied before the establishment of the force-stretch curve is 200 g. Example LAI5
[0165] This artificial ligament according to the invention comprises a hollow textile sheath braided on a 16-spindle braiding loom, and therefore comprises 16 textile strands, each textile strand comprising 1 very high molecular weight polyethylene yarn, for example of the Spectra brand, each yarn comprising 120 filaments and having a density of 435 dtex. The helix pitch (ph) is 11 mm.
[0166] This artificial ligament comprises a laminette (an openwork knit, such as that shown in [Fig. 7]) having a length of approximately 10 cm and a width of approximately 6 mm. The length of the hollow textile sheath Lgc is substantially equal to the length of the insert. The pre-tension applied before the establishment of the force-stretch curve is 300 g.
[0167] For example, on the LAI4 curve, we measure a slope coefficient ka of almost 0 N / %, a slope coefficient kb of around 12 N / %, and a slope coefficient kc of the order of 133.
[0168] The behavior of the artificial ligaments LAI4 and LAI5 is similar to that of the ligaments LAI1-3: a phase A of deformation similar to a plateau is observed, followed by the beginning of a foot of the curve in phase B in which the elongation remains moderate under a moderate force, and a stiffness which increases sharply in the deformation phase C. The direction coefficient kb is thus greater than or equal to 3 times the direction coefficient ka, and likewise the direction coefficient kc is greater than or equal to 3 times the direction coefficient kb.
Claims
Demands
1. An implantable artificial ligament (10,100) for the treatment of proximal junctional kyphosis, characterized in that said artificial ligament (10,100) comprises a long, braided hollow sheath (20,120) having an internal volume (22,122), said braided hollow sheath comprising one or more non-absorbable thread(s), and a deformable insert (30,130,200,210,220,230) housed within the internal volume (22,122) of the braided hollow sheath (20,120) over at least a portion of the length of said hollow sheath (20,120), in that the artificial ligament (10,100) has: - a deformation phase A in which the slope coefficient ka measured on a Ck curve of tensile force (N) - elongation (%) of said artificial ligament (10,100) is less than or equal to 6 Newtons / %;and - a deformation phase B in which the slope kb measured on said Ck curve of tensile force (N) - elongation (%) of said artificial ligament (10,100) is greater than or equal to 4 Newtons / % and less than or equal to 40 Newtons / %, the elongation of said artificial ligament (10,100) in said deformation phase B is greater than or equal to 2% and less than or equal to 15%; - a deformation phase C in which the slope kc measured on said Ck curve of tensile force (N) - elongation (%) of said artificial ligament (10,100) is greater than the slope kb of phase B; and in that the artificial ligament has an elongation less than or equal to 15% under the effect of a tensile force of approximately 250 newtons; in that kb is greater than ka; and in that the slope ka is the slope of a straight line TA tangent at any point of the curve Cia whose elongation is less than or equal to 5%.;
2. Artificial ligament (10,100) according to claim 1, characterized in that the deformable insert (30,130,200,210,220,230) is a rod comprising a thermoplastic or thermosetting elastomer, preferably comprising one or more polymer(s) selected from: a polyurethane, a polycarbonate-urethane, a polydimethylsiloxane, or a mixture thereof.
3. Artificial ligament (10,100) according to either of claims 1 and 2, characterized in that the difference (%) between the residual elongation (%) obtained after a traction cycle n of said ligament (10,100) and the residual elongation (%) obtained after a traction cycle n+1 of said ligament, with n is an integer other than 0, preferably n is equal to 10, is less than or equal to 15%, each traction cycle including the application of a traction force of the order of 250 Newtons.
4. Artificial ligament (10,100) according to any one of claims 1 to 3, characterized in that: - in the deformation phase A, the elongation of said artificial ligament (10,100) is less than or equal to 5% for a tensile force greater than 0 Newtons and less than or equal to 200 Newtons; and - in the deformation phase C, the elongation of said artificial ligament (10,100) is greater than or equal to 5% for a tensile force greater than or equal to 200 newtons and less than or equal to 800 Newtons.
5. Artificial ligament (10,100) according to any one of claims 1 to 4, characterized in that the slope kc is greater than or equal to 3 times the slope kb.
6. Artificial ligament (10,100) according to any one of claims 1 to 5, characterized in that in the deformation phase B, the tensile force applied to the artificial ligament (10,100) is less than or equal to 200 Newtons.
7. Artificial ligament (10,100) according to any one of claims 1 to 6, characterized in that the internal volume (22,122) of said at least a part of the braided hollow sheath (20,120) receiving said insert (30,130,200,210,220,230) comprises one or more compressible empty cavity(ies) so as to crush during the passage from deformation phase A to deformation phase B.
8. Artificial ligament (10,100) according to any one of claims 1 to 7, characterized in that the solid surface area (mm2) of the cross-section of the insert is less than the total surface area (mm2) of the cross-section of said at least a part of the braided hollow sheath (20,120) receiving said insert (30,130,200,210,220,230) in its internal volume (22,122).
9. Artificial ligament (10,100) according to any one of claims 1 to 8, characterized in that the insert (30,130,200,210,220,230) is selected from: a tube, a foam, and at least one long element, in particular at least one rod or at least one monofilamentary thread, more particularly multilobed.
10. Artificial ligament (10,100) according to any one of claims 1 to 9, characterized in that the insert (30,130,200,210,220,230) is an extruded, foamed or three-dimensionally printed elongated element, in particular by additive or subtractive manufacturing or a combination thereof.
11. Artificial ligament (10,100) according to any one of claims 1 to 10, characterized that said insert (30,130,200,210,220,230) comprises one or more polymer material(s) having a Shore A hardness ranging from 5 to 90, in particular ranging from 5 to 50, more particularly ranging from 20 to 50.
12. Artificial ligament (10,100) according to any one of claims 1 to 11, characterized in that the braided hollow sheath (20,120) comprises at least 10 strands, preferably at least 14 strands, braided, each of the strands comprising at least one multifilamentary yarn.
13. Artificial ligament (10,100) according to any one of claims 1 to 12, characterized in that the hollow braided sheath (20,120) comprises one or more yarn(s) comprising at least one material selected from: very high molecular weight polyethylene, polyethylene terephthalate, polypropylene, polyetheretherketone (PEEK), polyetherketone-neketone (PEKK), polytrimethylene terephthalate (PTT).
14. Artificial ligament (10,100) according to any one of claims 1 to 13, characterized in that the height of a braided helix pitch of the braided hollow sheath (20,120) is greater than or equal to 4 mm, preferably greater than or equal to 8 mm, in particular is greater than or equal to 4 mm and less than or equal to 25 mm.
15. Artificial ligament (10,100) according to any one of claims 1 to 14, characterized in that the external diameter of the insert (30,130,200,210,220,230) is greater than or equal to 2 mm and less than or equal to 15 mm.
16. A method for manufacturing an implantable artificial ligament (10, 100) for the treatment of proximal junctional kyphosis, in particular according to any one of claims 1 to 15, characterized in that it comprises: a) the provision of a deformable insert (30, 130, 200, 210, 220, 230), b) a step of braiding a hollow sheath (20, 120), having an internal volume (22, 122), around said deformable insert (30, 130, 200, 210, 220, 230), said braided hollow sheath comprising one or more non-absorbable thread(s), said deformable insert being housed in the internal volume (22,122) of the braided hollow sheath (20,120) and this over at least a part of the length of said hollow sheath, and in that the ligament has: - a deformation phase A in which the slope coefficient ka measured on a Ck curve of tensile force (N) - elongation (%) of said artificial ligament (10,100) is less than or equal to 6 Newtons / %; and - a deformation phase B in which the slope coefficient kb measured on said Ck curve of tensile force (N) - elongation (%) of said artificial ligament (10,100) is greater than or equal to 4 Newtons / % and less than or equal to 40 Newtons / %, the elongation of said artificial ligament (10,100) in said deformation phase B is greater than or equal to 2% and less than or equal to 15%; - a deformation phase C in which the slope kc measured on said curve Cia of tensile force (N) - elongation (%) of said artificial ligament (10,100) is greater than the slope kb of phase B; and in that the artificial ligament has an elongation less than or equal to 15% under the effect of a traction force of the order of 250 newtons; in that kb is greater than ka; and in that the slope coefficient ka is the slope coefficient of a straight line TA tangent at any point of the curve Ck whose elongation is less than or equal to 5%.