Equipment for bone surgery, including an osteosynthesis plate and at least one drilling barrel

Abstract

The present invention relates to a device (1) for bone surgery, particularly adapted to an osteotomy technique generating two bone fragments (S1, S2) separated by a cutting line (T), for example, a femoral derotation osteotomy. The device (1) comprises an osteosynthesis plate (2) including a combination of through holes (3), fixation screws (5), and at least one drill barrel (6). A contact surface (311) of at least one of said through holes (3), referred to as a monoplanar through hole (3c), and the contact surface (611) of said at least one drill barrel (6) are configured to define a pivot joint between said drill barrel (6) and said monoplanar through hole (3c). Figure for the abstract: 3

Description

Title of the invention: Equipment for bone surgery, comprising an osteosynthesis plate and at least one drilling barrel Technical field of the invention

[0001] The present invention relates to the technical field of equipment for bone surgery, in particular adapted to an osteotomy technique generating two bone fragments separated by a cutting line, for example a femoral derotation osteotomy. State of the art

[0002] Certain bone surgery materials are particularly suitable for an osteotomy technique aimed at consolidating two bone fragments separated by a cutting line, for example a femoral derotation osteotomy.

[0003] For this, the material includes:

[0004] - an osteosynthesis plate comprising a combination of through holes which are intended to accommodate fixing screws intended to be implanted in the two bone fragments,

[0005] - the fixing screws, and

[0006] - at least one drilling gun, intended to guide the drilling determining the orientation fixing screws through the through holes.

[0007] It may be advantageous to tilt the axis of at least some of the fixing screws, in an appropriate manner.

[0008] For this, certain osteosynthesis plates include:

[0009] - through holes adapted to fixing screws of said “mono-axial”, with a predefined orientation, and / or

[0010] - through holes adapted to so-called “poly-axial” fixing screws, that is, the angle of implantation in the bone can be adjusted within a predetermined permissible inclination range.

[0011] "Poly-axial" type systems offer the surgeon a choice of screw placement. The surgeon can in fact choose the inclination of the fixation screws that he considers most optimal.

[0012] However, during their implantation, some of these fixing screws are likely to come into conflict within the bone material (conflicting crossing).

[0013] There is thus a need for a technical solution which would allow optimal positioning on a biomechanical level, without risk of conflict between the fixing screws within the bone material. Presentation of the invention

[0014] In order to overcome the aforementioned drawback of the state of the art, the present invention provides equipment for bone surgery, in particular adapted to an osteotomy technique generating two bone fragments separated by a cutting line, for example a femoral derotation osteotomy.

[0015] This material includes:

[0016] - an osteosynthesis plate comprising a combination of through holes each presenting a longitudinal axis:

[0017] — a first group of through holes, arranged in a first section of the osteosynthesis plate and intended to accommodate fixing screws intended to be implanted in at least one first bone fragment,

[0018] — a second group of through holes, arranged in a second section of the osteosynthesis plate and intended to accommodate fixing screws intended to be implanted in at least one second bone fragment,

[0019] - said fixing screws, intended to be inserted through said holes tra slopes of said osteosynthesis plate and to be implanted in the bone fragments, and

[0020] - at least one drilling barrel, one free end of which has a surface of contact intended to cooperate by fitting with a complementary contact surface provided at the level of said through holes.

[0021] The contact surface of at least one of said through-holes, called monoplanar through-hole, and the contact surface of said at least one drilling barrel are configured to define a pivot connection between said drilling barrel and said monoplanar through-hole.

[0022] The pivot connection is defined by an axis of rotation which is oriented perpendicular to the longitudinal axis of said at least one monoplanar through-orifice, with a rotational clearance extending over an angular sector on either side of the longitudinal axis of said at least one monoplanar through-orifice.

[0023] This material according to the invention is thus interesting in that it allows the installation of a fixing screw while offering a compromise between, on the one hand, a possibility of play in angulation relative to the longitudinal axis of said at least one monoplanar through-orifice and, on the other hand, prevention of any risk of conflict with the other fixing screws attached to the osteosynthesis plate.

[0024] This technical solution is also interesting for ensuring an optimal position of the fixing screw on a biomechanical level.

[0025] Other non-limiting and advantageous characteristics of the product according to the invention, taken individually or in all technically possible combinations, are the following:

[0026] - the contact surface of said at least one monoplanar through-orifice and the surface contact of at least one drilling barrel are configured to allow rotation of said at least one drilling barrel around its longitudinal axis;

[0027] - the contact surface of said at least one monoplanar through-orifice and the surface contact of said at least one drilling barrel comprises: first complementary portions, defining a ball joint, and second complementary portions, removing a degree of freedom in rotation perpendicular to the longitudinal axis of said at least one monoplanar through-orifice;

[0028] - the contact surface of said at least one monoplanar through-orifice comprises: a first portion in the form of a spherical cap or a truncated cone, and a second portion having an oblong section, perpendicular to the longitudinal axis, defined by two side walls, parallel to a major axis and perpendicular to said axis of rotation, and two divergent end walls; preferably, the osteosynthesis plate comprises an upper face and a lower face, and said first portion is provided on the side of said upper face and said second portion is provided on the side of said lower face; more preferably, on the side of the upper face, said first portion is extended by a third portion having an oblong section perpendicular to the longitudinal axis, defined by two side walls, parallel to a major axis and perpendicular to said axis of rotation, and two divergent end walls;

[0029] - the contact surface of said at least one drilling barrel comprises a first portion in the shape of a spherical cap, and a second portion of cylindrical shape, said second portion preferably being provided at one end of said drilling barrel;

[0030] - the angular sector, on each side of the longitudinal axis, is at least 5°, preferably 5° to 15°;

[0031] - said at least one monoplanar through-orifice is provided in said first section ;

[0032] - said fixing screw consists of a polyaxial fixing screw comprising a head provided with a spherical portion capable of cooperating with the contact surface of said at least one monoplanar through-orifice, where appropriate with the first portion of the contact surface of said at least one monoplanar through-orifice.

[0033] Generally speaking, a bone surgery method, using equipment according to the invention, comprises the following successive steps:

[0034] - positioning of said osteosynthesis plate against said two fragments bony,

[0035] - the implantation of at least one fixation screw in a first bone fragment at through the first group of through holes and at least one fixation screw into a second bone fragment through the second group of through holes,

[0036] - a drilling of at least one bone fragment, possibly through the line of cutting, guided by a drilling gun positioned on said at least one monoplanar through-hole,

[0037] - the implantation of said at least one fixing screw through said at least one monoplanar through-hole, preferably oriented to be implanted in said bone fragments and to cross said cutting line.

[0038] Of course, the various features, variants and embodiments of the invention may be combined with each other in various combinations to the extent that they are not incompatible or mutually exclusive. Detailed description of the invention

[0039] Furthermore, various other characteristics of the invention emerge from the appended description given with reference to the drawings which illustrate non-limiting forms of embodiment of the invention and where:

[0040] [Fig-1] is a general and perspective view of an osteosynthesis plate constituting bone surgery equipment according to the invention;

[0041] [Fig.2] represents a monoplanar through-hole which is illustrated by three views different: a front view (part A), a longitudinal sectional view along plane AA of the front view (part B) and a cross-sectional view along plane BB of the front view (part C);

[0042] [Fig.3] is a schematic view, along a longitudinal section, which illustrates the connection pivot between the monoplanar through hole and the drilling barrel;

[0043] [Fig.4] is a schematic view, in cross-section, which illustrates the connection pivot between the monoplanar through hole and the drilling barrel;

[0044] [Fig.5] illustrates the cooperation between the monoplanar through-hole and a screw of fixing, view along the longitudinal section plane (part A.) and view along the transverse section plane (part B.);

[0045] [Fig.6] is a schematic view illustrating an osteosynthesis plate which is attached to bone fragments and which receives a drilling barrel positioned on said at least one monoplanar through orifice;

[0046] [Fig.7] is a schematic view illustrating an implantation (according to different possible orientations) of a fixing screw through said at least one monoplanar through-hole;

[0047] [Fig.8] is another schematic view illustrating the implantation of the fixing screw through said at least one monoplanar through-hole.

[0048] It should be noted that, in these figures, the structural and / or functional elements common to the different variants may have the same references.

[0049] The present invention thus relates to equipment 1 for bone surgery (figures 1 to 5).

[0050] As described below in relation to figures 6 and following, this material 1 is in particular adapted to an osteotomy technique intended to consolidate at least two bone fragments SI, S2 separated by a cutting line T, for example during a femoral derotation osteotomy.

[0051] For this purpose, in general, the material 1 comprises:

[0052] - an osteosynthesis plate 2 comprising a combination of through holes 3,

[0053] - fixing screws 5, and

[0054] - at least one drilling gun 6 (also referred to as a “drill guide” in English). Osteosynthesis plate

[0055] The osteosynthesis plate 2 comprises a combination of through holes 3 (also called “pads”).

[0056] Generally speaking, the osteosynthesis plate 2 advantageously comprises two opposite faces:

[0057] - a lower face 21, intended to come to bear on the bone fragments SI, S2, and

[0058] - an upper face 22, opposite.

[0059] Each through-orifice 3 advantageously has a longitudinal axis 3', passing between the lower face 21 and the upper face 22.

[0060] The through holes 3 are divided into at least two groups:

[0061] - a first group of through holes 3a, arranged in a first section 2a of the osteosynthesis plate 2 and intended to accommodate fixing screws 5 intended to be implanted in at least a first bone fragment SI,

[0062] - a second group of through holes 3b, arranged in a second section 2b of the osteosynthesis plate 2 and intended to accommodate fixing screws 5 intended to be implanted in at least a second bone fragment S2.

[0063] The sections 2a, 2b are each intended to cooperate with at least one of the bone fragments S1, S2.

[0064] Generally, the through-orifices 3 comprise a contact surface 311 intended to cooperate with a complementary contact surface 611 of said at least one drilling barrel 6.

[0065] The contact surface 311 of the through holes 3 is advantageously located on the side of the upper face 22 of the osteosynthesis plate 2.

[0066] According to the invention and as developed subsequently, at least one of the through orifices 3c is intended to cooperate with the drilling barrel 6 with a possibility of angular play which is limited / guided in a plane of orientation P.

[0067] Generally speaking and for the sake of understanding, this through orifice 3c is also referred to as “monoplanar through orifice 3c”. Fixing screws

[0068] The fixing screws 5 are intended to be inserted through the through holes 3 of the osteosynthesis plate 2 and to be implanted in the bone fragments SI, S2.

[0069] These fixing screws 5, and in particular the fixing screw 5 intended to be fitted through the monoplanar through-hole 3c, advantageously consist of polyaxial fixing screws.

[0070] As illustrated in [Fig.5], such a polyaxial fixing screw 5 comprises in particular:

[0071] - a head 51, provided with a spherical portion 511, intended to cooperate with the orifice crossing 3 of the osteosynthesis plate 2, and

[0072] - a threaded body 52, intended to be implanted in at least one bone fragment SI, S2 and intended to extend on the side of the lower face 21 of the osteosynthesis plate 2. Drilling barrel

[0073] A drilling gun 6 (or “drill guide”) is advantageously intended to guide the drilling equipment (surgical motor and drill) to generate the pilot holes which are intended for the implantation of the fixing screws 5.

[0074] This drilling barrel 6 can also serve as a guide for the fixing screws 5 when they are put in place.

[0075] The drilling barrel 6 comprises in particular a free end 61 which comprises a contact surface 611 (preferably male) intended to cooperate by fitting with a complementary contact surface 311 (preferably female), formed at the level of the through-orifices 3.

[0076] This drilling barrel 6 also advantageously comprises a longitudinal axis 6'. Contact surfaces

[0077] According to the invention, the contact surface 311 of the monoplanar through-orifice 3c and the contact surface 611 of said at least one drilling barrel 6 are configured to define a pivot connection between the drilling barrel 6 and the monoplanar through-orifice 3c.

[0078] This cooperation allows a choice of drilling orientation, with oscillating guidance of the drilling gun 6 on either side of the longitudinal axis 3' of said at least one monoplanar through-orifice 3c, according to an orientation plane P.

[0079] Generally speaking and as illustrated schematically in Figures 3 and 4, the pivot connection is defined by an axis of rotation R which is oriented perpendicular to the longitudinal axis 3' of said at least one monoplanar through-orifice 3c.

[0080] This pivot connection then defines a rotational clearance extending over an angular sector G on either side of the longitudinal axis 3' of said at least one monoplanar through-orifice 3c.

[0081] The drilling gun 6, cooperating with the monoplanar through-orifice 3c, is thus guided in rotation (or in oscillation) in a plane of orientation P passing through the longitudinal axis 3' of said at least one monoplanar through-orifice 3c (illustrated in particular in FIGS. 3, 4 and 8). The longitudinal axis 6' of the drilling gun 6 then extends in the plane of orientation P throughout its authorized stroke.

[0082] Preferably, the angular sector G (or the angular travel), on each side of the longitudinal axis 3' of said at least one monoplanar through-orifice 3c (or on either side of the longitudinal axis 3'), is at least 5°, preferably from 5° to 15°.

[0083] Generally, the contact surface 311 of said at least one monoplanar through-orifice 3c and the contact surface 611 of at least one drilling barrel 6 may also be configured to allow rotation of said at least one drilling barrel 6 around its longitudinal axis 6'.

[0084] Generally speaking and according to a preferred embodiment, the contact surface 311 of said at least one monoplanar through-orifice 3c and the contact surface 611 of said at least one drilling barrel 6 comprise two complementary portions:

[0085] - first portions 3111, 6111, complementary, defining a ball joint, And

[0086] - second portions 3112, 6112, complementary, removing a degree of freedom rotating perpendicularly to the longitudinal axis 3' of said at least one monoplanar through-orifice 3c.

[0087] In other words, the first portions 3111, 6111 center the drilling barrel 6 relative to the monoplanar through-orifice 3c (advantageously at the level of its longitudinal axis 3').

[0088] And the second portions 3112, 6112 guide the trajectory of the drilling gun 6, with:

[0089] - an amplitude of rotation in the plane of orientation P, and

[0090] - a zero rotation amplitude, or at least less than 1°, in a plane normal to this orientation plan P.

[0091] For this, preferably, the contact surface 311 of said at least one monoplanar through-orifice 3c comprises:

[0092] - a first portion 3111 (advantageously concave or female) in the shape of spherical or truncated cone-shaped cap, and

[0093] - a second portion 3112 having an oblong section (perpendicular to the longitudinal axis 3' and of which a major axis 3112' extends in the orientation plane P).

[0094] The second portion 3112 is defined by a belt of walls:

[0095] - two side walls 3112a, parallel to a major axis 3112' and to the orientation plane P (axis AA on part A. on [Fig.2]) and perpendicular to the axis of rotation R (part C of [Fig.2]), and

[0096] - two diverging end walls 3112b, diverging from each other towards the lower face 21 (part B of [Fig.2]).

[0097] The orientation of the major axis 3112' of the second portion 3112 defines the aforementioned orientation plane P.

[0098] More preferably, in the thickness of the osteosynthesis plate 2:

[0099] - the first portion 3111 is provided on the side of the upper face 22, and

[0100] - the second portion 3112 is provided on the side of the lower face 21.

[0101] Still preferably, the second portion 3112 is arranged between the first portion 3111 and the lower face 21.

[0102] Still generally, the first portion 3111 is advantageously extended by a third portion 3113 having an oblong section perpendicular to the longitudinal axis 3'.

[0103] Here again, this third portion 3113 is defined by a belt of walls:

[0104] - two side walls 3113a, parallel to a major axis 3113' (axis AA on the part A.) and perpendicular to the axis of rotation R, and

[0105] - two diverging end walls 3113b, diverging from each other towards the upper face 22 (part B. of [Fig.2]).

[0106] This third portion 3113 extends here between the first portion 3111 and the upper face 22.

[0107] Furthermore, in general and as illustrated in Figures 3 and 4, the contact surface 611 of said at least one drilling barrel 6 comprises:

[0108] - a first portion 6111 (here convex or male) in the form of a spherical cap, and

[0109] - a second portion 6112 of cylindrical shape,

[0110] - and preferably a cylindrical body 6113.

[0111] The second portion 6112 is preferably provided at the free end 61 of the drilling barrel 6.

[0112] Preferably, the first portion 6111 of the contact surface 611 of said at least one drilling barrel 6 is intended to match the first portion 3111 of the contact surface 311 of said at least one monoplanar through-orifice 3c, to together define the ball joint.

[0113] And the second portion 6112 of the contact surface 611 of said at least one drilling barrel 6 has a diameter which corresponds, apart from the clearance, to the distance separating the two side walls 3112a of the second portion 3112 of the contact surface 311 of said at least one monoplanar through-orifice 3c.

[0114] This particular dimension ensures guidance in oscillation around the axis of rotation R which extends:

[0115] - perpendicular to the major axis 3112' of this second portion 3112, and

[0116] - perpendicular to the longitudinal axis 3' of the monoplanar through-orifice 3c.

[0117] Furthermore, the cylindrical body 6113 of said at least one drilling barrel 6 advantageously has a diameter which corresponds, apart from the clearance, to the distance separating the two side walls 3113a of the third portion 3113 of the contact surface 311 of said at least one monoplanar through-orifice 3c.

[0118] This particular dimension contributes to the oscillation guidance of the drilling gun 6 around the axis of rotation R.

[0119] Generally speaking, said at least one monoplanar through-orifice 3c is advantageously provided in the aforementioned first section 2a of the osteosynthesis plate 2.

[0120] This monoplanar through-orifice 3c is then oriented so that the orientation plane P is free from conflict with respect to the fixing screws 3 intended to be implanted in the other through-orifices 3 of the osteosynthesis plate 2 ([Fig.8] in particular).

[0121] Still generally, the spherical portion 511 at the head 51 of the polyaxial fixing screw 5 (intended to be fitted through the monoplanar through-hole 3c) is capable of cooperating with the contact surface 311 of said at least one monoplanar through-hole 3c, where appropriate with the first portion 3111 of the contact surface 311 of said at least one monoplanar through-hole 3c.

[0122] A section of the body 52, on the side of the head 51, is intended to cooperate with the second portion 3112 of the contact surface 311 of said at least one monoplanar through-orifice 3c. Bone surgery procedure

[0123] A bone surgery method, using the equipment 1, is illustrated in Figures 6 to 8.

[0124] The method comprises positioning the osteosynthesis plate 2 against the two bone fragments S1, S2.

[0125] These bone fragments SI, S2 are possibly separated by a cutting line T.

[0126] This cutting line T, with the bone fragments SI, S2 which result from it, is for example used in the context of a femoral derotation osteotomy.

[0127] In this case, the incision is advantageously made along the longitude axis of the distal femur on the medial or lateral part of the thigh. The osteotomy is performed: the distal femur is subjected to external or internal rotation, in accordance with the pre-planning in order to adjust the rotational alignments of the femoro-patellar joint.

[0128] Generally, the method is continued by positioning the osteosynthesis plate 2 against the bone fragments SI, S2.

[0129] The osteosynthesis plate 2 is arranged so that:

[0130] - the first section 2a of the osteosynthesis plate 2 rests on a first bone fragment SI, and

[0131] - the second section 2b of the osteosynthesis plate 2 rests on a second fragment S2 bone.

[0132] The implantation of at least some of the fixing screws 5 is then implemented:

[0133] - at least one fixing screw 5 is implanted in a first bone fragment SI, through the first group of through holes 3a, and

[0134] - at least one fixing screw 5 is implanted in a second bone fragment S2, at through the second group of through holes 3b.

[0135] The method then comprises a step of drilling at least one bone fragment S1, S2, guided by a drilling gun 6 positioned on said at least one monoplanar through-orifice 3c, possibly through the cutting line T.

[0136] In this case, the orientation of the drilling barrel 6 can be adjusted in an angular sector G, according to an orientation plane P, without risk of conflict with the other fixing screws 3 attached to the osteosynthesis plate 2 while seeking an optimal position of the fixing screw 3 on the biomechanical level.

[0137] In the context of a femoral derotation osteotomy, the drilling barrel 6 is adjusted so that the drilling passes through the two bone fragments SI, S2, through the cutting line T.

[0138] This method also comprises an implantation of at least one fixing screw 5 through said at least one monoplanar through-orifice 3c.

[0139] For example, this fixing screw 5 is oriented to be implanted in the two bone fragments S1, S2 and to cross the cutting line T, according to the orientation defined by the drilling barrel 6.

[0140] Other fixing screws 5 may also be added (possibly polyaxial fixing screws 5), without risk of interaction with the fixing screw 5 which passes through said at least one monoplanar through-hole 3c.

[0141] Of course, various other modifications may be made to the invention within the scope of the appended claims.

Claims

Claims

1. Material (1) for bone surgery, in particular adapted to an osteotomy technique generating two bone fragments (SI, S2) separated by a cutting line (T), for example a femoral derotation osteotomy, which material (1) comprises: - an osteosynthesis plate (2) comprising a combination of through holes (3) each having a longitudinal axis (3'): — a first group of through holes (3a), arranged in a first section (2a) of the osteosynthesis plate (2) and intended to accommodate fixing screws (5) intended to be implanted in at least a first bone fragment (SI), — a second group of through holes (3), provided in a second section (2b) of the osteosynthesis plate (2) and intended to accommodate fixing screws (5) intended to be implanted in at least one second bone fragment (S2), - said fixing screws (5), intended to be inserted through said through holes (3) of said osteosynthesis plate (2) and to be implanted in the bone fragments (SI, S2), and - at least one drilling barrel (6) of which a free end (61) comprises a contact surface (611) intended to cooperate by fitting with a complementary contact surface (311) arranged at the level of said through-holes (3), characterized in that the contact surface (311) of at least one of said through-holes (3), called monoplanar through-hole (3c), and the contact surface (611) of said at least one drilling barrel (6) are configured to define a pivot connection between said drilling barrel (6) and said monoplanar through-hole (3c), which pivot connection is defined by an axis of rotation (R) which is oriented perpendicular to the longitudinal axis (3') of said at least one monoplanar through-hole (3c), with a rotational clearance extending over an angular sector (G) on either side of the longitudinal axis (3') of said at least one monoplanar through-hole (3c).

2. Material (1) for bone surgery according to claim 1, characterized in that the contact surface (311) of said at least one monoplanar through-orifice (3c) and the contact surface (611) of at least one drilling barrel (6) are configured to allow rotation of said at least one drilling barrel (6) around its longitudinal axis. (6').

3. Equipment (1) for bone surgery according to any one of claims 1 or 2, characterized in that the contact surface (311) of said at least one monoplanar through-hole (3c) and the contact surface (611) of said at least one drilling barrel (6) comprise: - first complementary portions (3111, 6111), defining a ball joint, and - second complementary portions (3112, 6112), eliminating a degree of freedom in rotation perpendicular to the longitudinal axis (3') of said at least one monoplanar through-hole (3c).

4. Material (1) for bone surgery according to any one of claims 1 to 3, characterized in that the contact surface (311) of said at least one monoplanar through-orifice (3c) comprises: - a first portion (3111) in the form of a spherical cap or of a truncated cone shape, and - a second portion (3112) having an oblong section, perpendicular to the longitudinal axis (3'), defined by: — two side walls (3112a), parallel to a major axis 3112' and perpendicular to said axis of rotation (R), and — two diverging end walls (3112b).

5. Material (1) for bone surgery according to claim 4, characterized in that the osteosynthesis plate (2) comprises an upper face (22) and a lower face (21), and in that said first portion (3111) is provided on the side of said upper face (22) and in that said second portion (3112) is provided on the side of said lower face (21).

6. Material (1) for bone surgery according to claim 5, characterized in that, on the side of the upper face (22), said first portion (3111) is extended by a third portion (3113) having an oblong section perpendicular to the longitudinal axis (3'), defined by: - ​​two side walls (3113a), parallel to a major axis (3112') and perpendicular to said axis of rotation (R), and - two diverging end walls (3113b).

7. Material (1) for bone surgery according to any one of claims 1 to 6, characterized in that the contact surface (611) of said at least one drilling barrel (6) comprises: - a first portion (6111) in the form of a spherical cap, and - a second portion (6112) of cylindrical shape, said second portion (6112) preferably being provided at one end of said drilling barrel (6).

8. Material (1) for bone surgery according to any one of claims 1 to 7, characterized in that the angular sector (G), on each side of the longitudinal axis (3'), is at least 5°, preferably 5° to 15°

9. 1J. Material (1) for bone surgery according to any one of claims 1 to 8, characterized in that said at least one monoplanar through-orifice (3c) is provided in said first section (2a).

10. Material (1) for bone surgery according to any one of claims 1 to 9, characterized in that said fixing screw (5) consists of a polyaxial fixing screw comprising a head (51) provided with a spherical portion (511) capable of cooperating with the contact surface (311) of said at least one monoplanar through-hole (3c), where appropriate with the first portion (3111) of the contact surface (311) of said at least one monoplanar through-hole (3c).

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