US20070191841A1 - Spinal rods having different flexural rigidities about different axes and methods of use - Google Patents
Spinal rods having different flexural rigidities about different axes and methods of use Download PDFInfo
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- US20070191841A1 US20070191841A1 US11/342,195 US34219506A US2007191841A1 US 20070191841 A1 US20070191841 A1 US 20070191841A1 US 34219506 A US34219506 A US 34219506A US 2007191841 A1 US2007191841 A1 US 2007191841A1
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- axis
- rod
- cavity
- vertebral rod
- bending
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B17/00—Surgical instruments, devices or methods, e.g. tourniquets
- A61B17/56—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor
- A61B17/58—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor for osteosynthesis, e.g. bone plates, screws, setting implements or the like
- A61B17/68—Internal fixation devices, including fasteners and spinal fixators, even if a part thereof projects from the skin
- A61B17/70—Spinal positioners or stabilisers ; Bone stabilisers comprising fluid filler in an implant
- A61B17/7001—Screws or hooks combined with longitudinal elements which do not contact vertebrae
- A61B17/7002—Longitudinal elements, e.g. rods
- A61B17/7019—Longitudinal elements having flexible parts, or parts connected together, such that after implantation the elements can move relative to each other
- A61B17/7026—Longitudinal elements having flexible parts, or parts connected together, such that after implantation the elements can move relative to each other with a part that is flexible due to its form
- A61B17/7029—Longitudinal elements having flexible parts, or parts connected together, such that after implantation the elements can move relative to each other with a part that is flexible due to its form the entire longitudinal element being flexible
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B17/00—Surgical instruments, devices or methods, e.g. tourniquets
- A61B17/56—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor
- A61B17/58—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor for osteosynthesis, e.g. bone plates, screws, setting implements or the like
- A61B17/68—Internal fixation devices, including fasteners and spinal fixators, even if a part thereof projects from the skin
- A61B17/70—Spinal positioners or stabilisers ; Bone stabilisers comprising fluid filler in an implant
- A61B17/7001—Screws or hooks combined with longitudinal elements which do not contact vertebrae
- A61B17/7002—Longitudinal elements, e.g. rods
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B17/00—Surgical instruments, devices or methods, e.g. tourniquets
- A61B17/56—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor
- A61B17/58—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor for osteosynthesis, e.g. bone plates, screws, setting implements or the like
- A61B17/68—Internal fixation devices, including fasteners and spinal fixators, even if a part thereof projects from the skin
- A61B17/70—Spinal positioners or stabilisers ; Bone stabilisers comprising fluid filler in an implant
- A61B17/7001—Screws or hooks combined with longitudinal elements which do not contact vertebrae
- A61B17/7002—Longitudinal elements, e.g. rods
- A61B17/701—Longitudinal elements with a non-circular, e.g. rectangular, cross-section
Definitions
- Spinal or vertebral rods are often used in the surgical treatment of spinal disorders such as degenerative disc disease, disc herniations, scoliosis or other curvature abnormalities, and fractures. Different types of surgical treatments are used. In some cases, spinal fusion is indicated to inhibit relative motion between vertebral bodies. In other cases, dynamic implants are used to preserve motion between vertebral bodies. For either type of surgical treatment, spinal rods may be attached to the exterior of two or more vertebrae, whether it is at a posterior, anterior, or lateral side of the vertebrae. In other embodiments, spinal rods are attached to the vertebrae without the use of dynamic implants or spinal fusion.
- Spinal rods may provide a stable, rigid column that encourages bones to fuse after spinal-fusion surgery. Further, the rods may redirect stresses over a wider area away from a damaged or defective region. Also, a rigid rod may restore the spine to its proper alignment. In some cases, a flexible rod may be appropriate. Flexible rods may provide some advantages over rigid rods, such as increasing loading on interbody constructs, decreasing stress transfer to adjacent vertebral elements while bone-graft healing takes place, and generally balancing strength with flexibility.
- a surgeon may wish to control anatomic motion after surgery. That is, a surgeon may wish to inhibit or limit one type of spinal motion following surgery while allowing a lesser or greater degree of motion in a second direction. As an illustrative example, a surgeon may wish to inhibit or limit motion in the flexion and extension directions while allowing for a greater degree of lateral bending.
- conventional rods tend to be symmetric in nature and may not provide this degree of control.
- Illustrative embodiments disclosed herein are directed to a vertebral rod having an elongated body extending along a longitudinal axis.
- the rod also includes a cavity extending the length of the body.
- Either the body or the cavity may have an asymmetrical shape about a centroid in a plane perpendicular to the longitudinal axis. Alternatively, both may have the symmetrical shape about the centroid.
- the body of the rod may be bounded by an exterior surface and the cavity.
- the body has a first bending axis that is perpendicular to longitudinal axis.
- the body also has a second bending axis that is perpendicular to the longitudinal axis and to the first bending axis.
- the body of the rod may be distributed asymmetrically about the first and second bending axes.
- the rod may have a different bending stiffness about the first and second bending axes.
- the cavity may be contained within or intersect the exterior surface.
- FIG. 1 is a perspective view of first and second assemblies comprising spinal rods attached to vertebral members according to one or more embodiments;
- FIG. 2 is a lateral view of a spinal rod according to one or more embodiments.
- FIGS. 3-20 are axial views of a spinal rod illustrating cross sections according to different embodiments.
- FIG. 1 shows a perspective view of first and second spinal rod assemblies 20 in which spinal rods 10 are attached to vertebral members V 1 and V 2 .
- the rods 10 are positioned at a posterior side of the spine, on opposite sides of the spinous processes S.
- Spinal rods 10 may be attached to a spine at other locations, including lateral and anterior locations.
- Spinal rods 10 may also be attached at various sections of the spine, including the base of the skull and to vertebrae in the cervical, thoracic, lumbar, and sacral regions. In one embodiment, a single rod 10 is attached to the spine. Thus, the illustration in FIG. 1 is provided merely as a representative example of one application of a spinal rod 10 .
- the spinal rods 10 are secured to vertebral members V 1 , V 2 by pedicle assemblies 12 comprising a pedicle screw 14 and a retaining cap 16 .
- the outer surface of spinal rod 10 is grasped, clamped, or otherwise secured between the pedicle screw 14 and retaining cap 16 .
- Other mechanisms for securing spinal rods 10 to vertebral members V 1 , V 2 include hooks, cables, and other such devices. Examples of other types of retaining hardware include threaded caps, screws, and pins.
- Spinal rods 10 are also attached to plates in other configurations.
- the exemplary assemblies 12 shown in FIG. 1 are merely representative of one type of attachment mechanism.
- the rod 10 may be constructed from a variety of surgical grade materials. These include metals such as stainless steels, cobalt-chrome, titanium, and shape memory alloys. Non-metallic rods, including polymer rods made from materials such as PEEK and UHMWPE, are also contemplated. Further, the rod 10 may be straight, curved, or comprise one or more curved portions along its length.
- FIG. 2 shows a spinal rod 10 of the type used in the exemplary assembly 20 in FIG. 1 .
- the rod 10 has a length between a first end 17 and a second end 18 extending along a longitudinal axis A.
- FIG. 3 shows one example cross section of the spinal rod 10 a .
- the spinal rod 10 a is comprised of an oval or elliptical outer surface 22 a and an interior cavity or aperture 30 a defined by an inner surface 32 a .
- the outer surface 22 a and inner surface 32 a are uniformly consistent along the entire length L of the rod 10 a .
- the cross section shown in FIG. 3 may be the same at all points along the length L of the rod 10 a .
- the same may also be true of other cross sections described below.
- the cross section of a rod 10 may vary along the length L of the rod 10 .
- the structural characteristics of the rod 10 may be dependent upon several factors, including the material choice and the cross section shape of the rod 10 .
- the modulus of elasticity varies by material and reflects the relationship between stress and strain for that material.
- titanium alloys generally possess a modulus of elasticity in the range between about 100-120 GPa.
- implantable grade polyetheretherketone (PEEK) possesses a modulus of elasticity in the range between about 3-4 Gpa, which, incidentally, is close to that of cortical bone.
- an object's moment of inertia depends on its shape and the distribution of mass within that shape. The greater the concentration of material away from the object's centroid C, the larger the moment of inertia.
- centroid C The intersection of the x-axis and y-axis is called the centroid C of rotation.
- the centroid C may be the center of mass for the shape assuming the material is uniform over the cross section. Since dimension h in FIG. 3 is larger than dimension b, it follows that the moment of inertia about the x-axis I x is larger than the moment of inertia about the y-axis I y . This means that the oval shape defined by the outer surface 22 a has a greater resistance to bending about the x-axis as compared to the y-axis.
- the actual bending stiffness of the rod 10 a shown in FIG. 3 may also depend upon the moment of inertia of the inner aperture 30 a . Determining the overall flexural rigidity of the rod 10 a requires an analysis of the composite shape of the rod 10 a . Generally, the moment of inertia of a composite area with respect to a particular axis is the sum (or difference in the case of a void) of the moments of inertia of its parts with respect to that same axis. Thus, for the rod 10 a shown in FIG.
- I x I xo ⁇ I xi (4)
- I y I yo ⁇ I yi (5)
- I xo and I xi are the moments of inertia about the x-axis for the outer and inner areas, respectively.
- I yo and I yi are the moments of inertia about the y-axis for the outer and inner areas, respectively.
- the inner aperture 30 a is symmetric about the centroid C. Consequently, the moments of inertia about the x and y axes for the area inside the outer surface 22 a are reduced by the same amount according to equations (4) and (5). Still, the overall flexural rigidity of the rod 10 a is greater about the x-axis as compared to the y-axis. Accordingly, a surgeon may elect to install the rod 10 a in a patient to correspondingly control flexion, extension, or lateral bending. One may do so by orienting the rod 10 a with the x-axis positioned perpendicular to the motion that is to be controlled.
- a surgeon who elects to control flexion and extension may orient the rod 10 a with the stiffer bending axis (x-axis in FIG. 3 ) approximately parallel to the coronal plane of the patient.
- a surgeon who elects to control lateral bending may orient the rod 10 a with the stiffer bending axis (x-axis in FIG. 3 ) approximately parallel to the sagittal plane of the patient.
- the surgeon may also elect to install the rod 10 a with the x and y axes oriented at angles other than aligned with the sagittal and coronal planes of the patient.
- a surgeon may elect to use the rods 10 disclosed herein with existing mounting hardware such as pedicle screws or hook saddles (not shown).
- Some exemplary rod sizes that are commercially available range between about 4-7 mm.
- the overall size of the rods 10 may be limited by this constraint.
- FIG. 4 shows a rod 10 b similar to rod 10 a (i.e., outer surface 22 b is substantially similar to surface 22 a ) with the exception that the inner aperture 30 b defined by inner surface 32 b is larger than the inner aperture 30 a of rod 10 a .
- Rods 10 a and 10 b may be available as a set with a common outer surface 22 a , 22 b . However, since the rods have a different internal aperture 30 a , 30 b configuration, a surgeon may select between the rods 10 a , 10 b to match a desired bending stiffness.
- the internal aperture 30 may be asymmetric as well.
- the rod 10 c shown in FIG. 5 includes an outer surface 22 c that is substantially similar to the outer surface 22 a of rod 10 a .
- the inner aperture 30 c defined by surface 32 c is elliptical or oval shaped.
- the inner aperture 30 c has a height h 1 parallel to the x-axis that is less than the width b 1 parallel to the y-axis. That is, the moment of inertia of the inner aperture 30 c is greater about the y-axis than about the x-axis. This is in contrast to the outer surface 22 c , which has a larger moment of inertia about the x-axis.
- the rods 10 may also have multiple inner apertures 30 .
- the rod 10 d shown in FIG. 6 comprises a plurality of apertures 30 d , 130 d defined by inner surfaces 32 d , 132 d .
- the outer surface 22 d may be substantially similar to the outer surface 22 a of rod 10 a .
- the exemplary apertures 30 d , 130 d are disposed within the interior of the rod 10 d .
- the apertures 30 d , 130 d are offset from the centroid C.
- the embodiments described above have all had a substantially similar, oval shaped outer surface 22 .
- This particular rod 10 e has a square outer surface 22 e that is substantially symmetric relative to axes X and Y.
- the inner aperture 30 e defined by inner surface 32 e is asymmetric relative to these same X and Y axes.
- Inner surface 32 e is substantially rectangular and defined by dimensions b and h. Specifically, dimension b (parallel to the Y-axis) is not equal to dimension h (parallel to the X-axis). In the embodiment shown, dimension b is larger than dimension h.
- the aperture 30 e has a larger moment of inertia relative to the Y-axis as compared to the X-axis. Consequently, according to equations (4) and (5), the rod 10 e has a greater bending strength about the X-axis as compared to the Y-axis.
- the rod 10 f shown in FIG. 8 has rectilinear inner 32 f and outer 22 f surfaces. However, in contrast to rod 10 e , the inner surface 32 f is substantially square and outer surface 22 f is substantially rectangular.
- This configuration is analogous to rod 10 a shown in FIG. 3 in that the inner aperture 30 f is symmetric about the X and Y axes while the outer surface 22 f is asymmetric about the X and Y axes.
- the rod 10 g shown in FIG. 9 has both an inner aperture 30 g and an outer surface 22 g that are asymmetric about the X and Y axes. The same is true of the rod 10 c shown in FIG. 5 .
- rod 10 g has an inner aperture 30 g and an area inside the outer surface 22 g that have larger moments of inertia about the same X-axis. This is due, in part, to the fact that the rectangular inner aperture 30 g and outer surface 22 g are substantially aligned.
- the rod 10 may also have substantially triangular outer surfaces 22 as evidenced by the embodiments 10 h , 10 i , and 10 j .
- the outer surface 22 h is shown as an isosceles triangle that has a larger height h (parallel to the X-axis) than base b (parallel to the Y-axis). This may tend to yield a rod 10 h having a greater moment of inertia about the X-axis.
- the rod 10 i shown in FIG. 11 comprises a triangular outer surface 22 i that is substantially equilateral.
- the 12 comprises a substantially triangular outer surface 22 j that is substantially equilateral, albeit with non-linear sides.
- the inner apertures 30 h , 30 i , 30 j may be shaped as shown in FIGS. 10-12 or as desired in accordance with the discussion provided above.
- rods 10 may have polygonal shapes such as the embodiments illustrated in FIGS. 13 and 14 .
- the rod 10 k shown in FIG. 13 comprises a hexagonal outer surface 22 k while rod 10 m in FIG. 14 comprises a pentagonal outer surface 22 m .
- the rods 10 may have more sides if desired.
- the embodiments described thus far have included an aperture 30 that is substantially contained within the interior of the outer surface 22 .
- the aperture 30 may intersect with the outer surface 22 .
- the rod 10 n comprises two apertures 30 n , 130 n that are defined by inner surfaces 32 n , 132 n .
- the inner surfaces 32 n , 132 n intersect the outer surface 22 n resulting in open apertures 30 n , 130 n .
- the rod 10 n is shaped similar to an I-beam that has a greater moment of inertia and bending stiffness about the X-axis.
- the rod 10 p shown in FIG. 16 also has a single open aperture 30 p defined by an inner surface 32 p that intersects with the outer surface 22 p.
- the rods 10 may also have a substantially circular outer surface 22 similar to many conventional rods, thus accommodating existing rod securing hardware (not shown). This is illustrated by the exemplary rods 10 q , 10 r , and 10 s shown in FIGS. 17, 18 , and 19 .
- the outer surface 22 q - s of the rod 10 q - s is substantially circular and/or characterized by a substantially constant radius.
- the moment of inertia about axes X and Y is substantially the same for the areas within the outer surface 22 q - s .
- the moment of inertia about the X and Y axes for the rod 10 q - s may be altered by including an asymmetric inner aperture 30 q - s.
- the inner aperture 30 q defined by inner surface 32 q has a larger moment of inertia about the X-axis.
- the rod 10 q has a larger moment of inertia about the Y-axis (pursuant to equations (4) and (5)).
- the inner aperture 30 r defined by inner surface 32 r is also substantially circular. However, the inner aperture 30 r is offset from centroid C. Further, the inner surface 32 r is tangent to the Y-axis, but spaced away from the X-axis.
- the moment of inertia of the inner aperture 30 r is larger with respect to the X-axis as compared to the Y-axis. Consequently, the moment of inertia and bending stiffness of the overall rod 10 r is larger about the Y-axis.
- FIG. 19 shows another embodiment of a rod 10 s having an open inner aperture 30 s .
- the inner surface 32 s has a substantially constant radius and intersects the substantially circular outer surface 22 s .
- the inner aperture 30 s is offset from the centroid C, but aligned with the Y-axis in the orientation shown. Therefore, the inner aperture 30 s has a larger moment of inertia about the X-axis. The bending stiffness of the overall rod 10 s is therefore greater about the Y-axis.
- FIG. 20 shows the same rod 10 q as illustrated in FIG. 17 .
- the rod 10 q comprises a first set of markings 34 (the ⁇ sign in the embodiment shown) and a second set of markings 36 (the + sign in the embodiment shown).
- the markings 34 , 36 may be stamped, engraved, or otherwise included on the rod as an indication of the bending stiffness in the direction of the marking.
- the markings 34 , 36 may be included on an end 17 , 18 of the rod 10 q as shown or on the outer surface 22 q.
- inventions described above have contemplated one or two inner apertures 30 to modify the moments of inertia about one axis relative to another.
- the rods 10 do not need to be limited to this number of apertures.
- the moment of inertia equations provided herein allow one to calculate moments of inertia for any number of apertures and flexural rigidity of the overall rod 10 .
- the present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.
Abstract
Description
- Spinal or vertebral rods are often used in the surgical treatment of spinal disorders such as degenerative disc disease, disc herniations, scoliosis or other curvature abnormalities, and fractures. Different types of surgical treatments are used. In some cases, spinal fusion is indicated to inhibit relative motion between vertebral bodies. In other cases, dynamic implants are used to preserve motion between vertebral bodies. For either type of surgical treatment, spinal rods may be attached to the exterior of two or more vertebrae, whether it is at a posterior, anterior, or lateral side of the vertebrae. In other embodiments, spinal rods are attached to the vertebrae without the use of dynamic implants or spinal fusion.
- Spinal rods may provide a stable, rigid column that encourages bones to fuse after spinal-fusion surgery. Further, the rods may redirect stresses over a wider area away from a damaged or defective region. Also, a rigid rod may restore the spine to its proper alignment. In some cases, a flexible rod may be appropriate. Flexible rods may provide some advantages over rigid rods, such as increasing loading on interbody constructs, decreasing stress transfer to adjacent vertebral elements while bone-graft healing takes place, and generally balancing strength with flexibility.
- Aside from each of these characteristic features, a surgeon may wish to control anatomic motion after surgery. That is, a surgeon may wish to inhibit or limit one type of spinal motion following surgery while allowing a lesser or greater degree of motion in a second direction. As an illustrative example, a surgeon may wish to inhibit or limit motion in the flexion and extension directions while allowing for a greater degree of lateral bending. However, conventional rods tend to be symmetric in nature and may not provide this degree of control.
- Illustrative embodiments disclosed herein are directed to a vertebral rod having an elongated body extending along a longitudinal axis. The rod also includes a cavity extending the length of the body. Either the body or the cavity may have an asymmetrical shape about a centroid in a plane perpendicular to the longitudinal axis. Alternatively, both may have the symmetrical shape about the centroid. The body of the rod may be bounded by an exterior surface and the cavity. The body has a first bending axis that is perpendicular to longitudinal axis. The body also has a second bending axis that is perpendicular to the longitudinal axis and to the first bending axis. The body of the rod may be distributed asymmetrically about the first and second bending axes. Also, the rod may have a different bending stiffness about the first and second bending axes. The cavity may be contained within or intersect the exterior surface.
-
FIG. 1 is a perspective view of first and second assemblies comprising spinal rods attached to vertebral members according to one or more embodiments; -
FIG. 2 is a lateral view of a spinal rod according to one or more embodiments; and -
FIGS. 3-20 are axial views of a spinal rod illustrating cross sections according to different embodiments. - The various embodiments disclosed herein are directed to spinal rods that are characterized by a cross section that provides different flexural rigidities in different directions. Various embodiments of a spinal rod may be implemented in a spinal rod assembly of the type indicated generally by the
numeral 20 inFIG. 1 .FIG. 1 shows a perspective view of first and secondspinal rod assemblies 20 in whichspinal rods 10 are attached to vertebral members V1 and V2. In theexample assembly 20 shown, therods 10 are positioned at a posterior side of the spine, on opposite sides of the spinous processes S.Spinal rods 10 may be attached to a spine at other locations, including lateral and anterior locations.Spinal rods 10 may also be attached at various sections of the spine, including the base of the skull and to vertebrae in the cervical, thoracic, lumbar, and sacral regions. In one embodiment, asingle rod 10 is attached to the spine. Thus, the illustration inFIG. 1 is provided merely as a representative example of one application of aspinal rod 10. - In one embodiment as illustrated in
FIG. 1 , thespinal rods 10 are secured to vertebral members V1, V2 bypedicle assemblies 12 comprising apedicle screw 14 and aretaining cap 16. The outer surface ofspinal rod 10 is grasped, clamped, or otherwise secured between thepedicle screw 14 and retainingcap 16. Other mechanisms for securingspinal rods 10 to vertebral members V1, V2 include hooks, cables, and other such devices. Examples of other types of retaining hardware include threaded caps, screws, and pins.Spinal rods 10 are also attached to plates in other configurations. Thus, theexemplary assemblies 12 shown inFIG. 1 are merely representative of one type of attachment mechanism. - The
rod 10 may be constructed from a variety of surgical grade materials. These include metals such as stainless steels, cobalt-chrome, titanium, and shape memory alloys. Non-metallic rods, including polymer rods made from materials such as PEEK and UHMWPE, are also contemplated. Further, therod 10 may be straight, curved, or comprise one or more curved portions along its length. -
FIG. 2 shows aspinal rod 10 of the type used in theexemplary assembly 20 inFIG. 1 . Therod 10 has a length between afirst end 17 and asecond end 18 extending along a longitudinal axis A. Other Figures described below show various embodiments of aspinal rod 10 characterized by different cross sections viewed according to the view lines illustrated inFIG. 2 . For instance,FIG. 3 shows one example cross section of thespinal rod 10 a. In this embodiment, thespinal rod 10 a is comprised of an oval or ellipticalouter surface 22 a and an interior cavity oraperture 30 a defined by aninner surface 32 a. In one embodiment, theouter surface 22 a andinner surface 32 a are uniformly consistent along the entire length L of therod 10 a. That is, the cross section shown inFIG. 3 may be the same at all points along the length L of therod 10 a. The same may also be true of other cross sections described below. In one or more embodiments, the cross section of arod 10 may vary along the length L of therod 10. - The structural characteristics of the
rod 10 may be dependent upon several factors, including the material choice and the cross section shape of therod 10. The flexural rigidity, which is a measure of bending stiffness, is given by the equation:
Flexural Rigidity=E×I (1)
where E is the modulus of elasticity or Young's Modulus for the rod material and I is the moment of inertia of a rod cross section about the bending axis. The modulus of elasticity varies by material and reflects the relationship between stress and strain for that material. As an illustrative example, titanium alloys generally possess a modulus of elasticity in the range between about 100-120 GPa. By way of comparison, implantable grade polyetheretherketone (PEEK) possesses a modulus of elasticity in the range between about 3-4 Gpa, which, incidentally, is close to that of cortical bone. - In general, an object's moment of inertia depends on its shape and the distribution of mass within that shape. The greater the concentration of material away from the object's centroid C, the larger the moment of inertia. In
FIG. 3 , the moments of inertia about the x-axis Ix and the y-axis Iy for the area inside the ellipticalouter shape 22 a (ignoring theinner aperture 30 a for now) may be determined according to the following equations:
I x =∫y 2dA (2)
I y =∫x 2dA (3)
where y is the distance between a given portion of the elliptical area and the x-axis and x is the distance between a given portion of the elliptical area and the y-axis. The intersection of the x-axis and y-axis is called the centroid C of rotation. The centroid C may be the center of mass for the shape assuming the material is uniform over the cross section. Since dimension h inFIG. 3 is larger than dimension b, it follows that the moment of inertia about the x-axis Ix is larger than the moment of inertia about the y-axis Iy. This means that the oval shape defined by theouter surface 22 a has a greater resistance to bending about the x-axis as compared to the y-axis. - The actual bending stiffness of the
rod 10 a shown inFIG. 3 may also depend upon the moment of inertia of theinner aperture 30 a. Determining the overall flexural rigidity of therod 10 a requires an analysis of the composite shape of therod 10 a. Generally, the moment of inertia of a composite area with respect to a particular axis is the sum (or difference in the case of a void) of the moments of inertia of its parts with respect to that same axis. Thus, for therod 10 a shown inFIG. 3 , the overall flexural rigidity is given by the following:
I x =I xo −I xi (4)
I y =I yo −I yi (5)
where Ixo and Ixi are the moments of inertia about the x-axis for the outer and inner areas, respectively. Similarly, Iyo and Iyi are the moments of inertia about the y-axis for the outer and inner areas, respectively. - In the present embodiment of the
rod 10 a shown inFIG. 3 , theinner aperture 30 a is symmetric about the centroid C. Consequently, the moments of inertia about the x and y axes for the area inside theouter surface 22 a are reduced by the same amount according to equations (4) and (5). Still, the overall flexural rigidity of therod 10 a is greater about the x-axis as compared to the y-axis. Accordingly, a surgeon may elect to install therod 10 a in a patient to correspondingly control flexion, extension, or lateral bending. One may do so by orienting therod 10 a with the x-axis positioned perpendicular to the motion that is to be controlled. For example, a surgeon who elects to control flexion and extension may orient therod 10 a with the stiffer bending axis (x-axis inFIG. 3 ) approximately parallel to the coronal plane of the patient. Conversely, a surgeon who elects to control lateral bending may orient therod 10 a with the stiffer bending axis (x-axis inFIG. 3 ) approximately parallel to the sagittal plane of the patient. The surgeon may also elect to install therod 10 a with the x and y axes oriented at angles other than aligned with the sagittal and coronal planes of the patient. - It may be desirable to adjust the bending stiffness of the
rod 10 by varying the size and shape of the inner aperture 30. For instance, a surgeon may elect to use therods 10 disclosed herein with existing mounting hardware such as pedicle screws or hook saddles (not shown). Some exemplary rod sizes that are commercially available range between about 4-7 mm. Thus, the overall size of therods 10 may be limited by this constraint. -
FIG. 4 shows arod 10 b similar torod 10 a (i.e.,outer surface 22 b is substantially similar to surface 22 a) with the exception that theinner aperture 30 b defined byinner surface 32 b is larger than theinner aperture 30 a ofrod 10 a. Using the equations above, one is able to determine that the overall flexural rigidity about the x and y axes is greater forrod 10 a as compared torod 10 b.Rods outer surface internal aperture rods - The internal aperture 30 may be asymmetric as well. For example, the rod 10 c shown in
FIG. 5 includes anouter surface 22 c that is substantially similar to theouter surface 22 a ofrod 10 a. However, the inner aperture 30 c defined by surface 32 c is elliptical or oval shaped. The inner aperture 30 c has a height h1 parallel to the x-axis that is less than the width b1 parallel to the y-axis. That is, the moment of inertia of the inner aperture 30 c is greater about the y-axis than about the x-axis. This is in contrast to theouter surface 22 c, which has a larger moment of inertia about the x-axis. - The
rods 10 may also have multiple inner apertures 30. For instance, therod 10 d shown inFIG. 6 comprises a plurality ofapertures inner surfaces 32 d, 132 d. The outer surface 22 d may be substantially similar to theouter surface 22 a ofrod 10 a. Notably, theexemplary apertures rod 10 d. Further, theapertures - The embodiments described above have all had a substantially similar, oval shaped outer surface 22. Certainly, other shapes are possible as illustrated by the embodiment of the
rod 10 e shown inFIG. 7 . Thisparticular rod 10 e has a square outer surface 22 e that is substantially symmetric relative to axes X and Y. However, theinner aperture 30 e defined by inner surface 32 e is asymmetric relative to these same X and Y axes. Inner surface 32 e is substantially rectangular and defined by dimensions b and h. Specifically, dimension b (parallel to the Y-axis) is not equal to dimension h (parallel to the X-axis). In the embodiment shown, dimension b is larger than dimension h. Therefore, theaperture 30 e has a larger moment of inertia relative to the Y-axis as compared to the X-axis. Consequently, according to equations (4) and (5), therod 10 e has a greater bending strength about the X-axis as compared to the Y-axis. - The
rod 10 f shown inFIG. 8 has rectilinear inner 32 f and outer 22 f surfaces. However, in contrast torod 10 e, theinner surface 32 f is substantially square andouter surface 22 f is substantially rectangular. This configuration is analogous torod 10 a shown inFIG. 3 in that theinner aperture 30 f is symmetric about the X and Y axes while theouter surface 22 f is asymmetric about the X and Y axes. Therod 10 g shown inFIG. 9 has both aninner aperture 30 g and anouter surface 22 g that are asymmetric about the X and Y axes. The same is true of the rod 10 c shown inFIG. 5 . However,rod 10 g has aninner aperture 30 g and an area inside theouter surface 22 g that have larger moments of inertia about the same X-axis. This is due, in part, to the fact that the rectangularinner aperture 30 g andouter surface 22 g are substantially aligned. - The
rod 10 may also have substantially triangular outer surfaces 22 as evidenced by theembodiments FIG. 10 , theouter surface 22 h is shown as an isosceles triangle that has a larger height h (parallel to the X-axis) than base b (parallel to the Y-axis). This may tend to yield arod 10 h having a greater moment of inertia about the X-axis. By comparison, therod 10 i shown inFIG. 11 comprises a triangularouter surface 22 i that is substantially equilateral. Therod 10 j shown inFIG. 12 comprises a substantially triangularouter surface 22 j that is substantially equilateral, albeit with non-linear sides. Theinner apertures FIGS. 10-12 or as desired in accordance with the discussion provided above. -
Other rods 10 may have polygonal shapes such as the embodiments illustrated inFIGS. 13 and 14 . Therod 10 k shown inFIG. 13 comprises a hexagonalouter surface 22 k whilerod 10 m inFIG. 14 comprises a pentagonalouter surface 22 m. Therods 10 may have more sides if desired. - The embodiments described thus far have included an aperture 30 that is substantially contained within the interior of the outer surface 22. In other embodiments, the aperture 30 may intersect with the outer surface 22. This can be seen in the exemplary embodiments shown in
FIGS. 15 and 16 . InFIG. 15 , therod 10 n comprises twoapertures 30 n, 130 n that are defined byinner surfaces inner surfaces outer surface 22 n resulting inopen apertures 30 n, 130 n. Therod 10 n is shaped similar to an I-beam that has a greater moment of inertia and bending stiffness about the X-axis. By way of comparison, therod 10 p shown inFIG. 16 also has a singleopen aperture 30 p defined by aninner surface 32 p that intersects with theouter surface 22 p. - The
rods 10 may also have a substantially circular outer surface 22 similar to many conventional rods, thus accommodating existing rod securing hardware (not shown). This is illustrated by theexemplary rods 10 q, 10 r, and 10 s shown inFIGS. 17, 18 , and 19. In each case, theouter surface 22 q-s of the rod 10 q-s is substantially circular and/or characterized by a substantially constant radius. As such, the moment of inertia about axes X and Y is substantially the same for the areas within theouter surface 22 q-s. However, the moment of inertia about the X and Y axes for the rod 10 q-s may be altered by including an asymmetricinner aperture 30 q-s. - In
FIG. 17 , theinner aperture 30 q defined byinner surface 32 q has a larger moment of inertia about the X-axis. Thus, the rod 10 q has a larger moment of inertia about the Y-axis (pursuant to equations (4) and (5)). InFIG. 18 , theinner aperture 30 r defined byinner surface 32 r is also substantially circular. However, theinner aperture 30 r is offset from centroid C. Further, theinner surface 32 r is tangent to the Y-axis, but spaced away from the X-axis. Thus, the moment of inertia of theinner aperture 30 r is larger with respect to the X-axis as compared to the Y-axis. Consequently, the moment of inertia and bending stiffness of theoverall rod 10 r is larger about the Y-axis. -
FIG. 19 shows another embodiment of a rod 10 s having an open inner aperture 30 s. In this embodiment, the inner surface 32 s has a substantially constant radius and intersects the substantially circularouter surface 22 s. The inner aperture 30 s is offset from the centroid C, but aligned with the Y-axis in the orientation shown. Therefore, the inner aperture 30 s has a larger moment of inertia about the X-axis. The bending stiffness of the overall rod 10 s is therefore greater about the Y-axis. -
FIG. 20 shows the same rod 10 q as illustrated inFIG. 17 . In this particular view, the rod 10 q comprises a first set of markings 34 (the − sign in the embodiment shown) and a second set of markings 36 (the + sign in the embodiment shown). Themarkings markings end outer surface 22 q. - Spatially relative terms such as “under”, “below”, “lower”, “over”, “upper”, and the like, are used for ease of description to explain the positioning of one element relative to a second element. These terms are intended to encompass different orientations of the device in addition to different orientations than those depicted in the figures. Further, terms such as “first”, “second”, and the like, are also used to describe various elements, regions, sections, etc and are also not intended to be limiting. Like terms refer to like elements throughout the description.
- As used herein, the terms “having”, “containing”, “including”, “comprising” and the like are open ended terms that indicate the presence of stated elements or features, but do not preclude additional elements or features. The articles “a”, “an” and “the” are intended to include the plural as well as the singular, unless the context clearly indicates otherwise.
- The present invention may be carried out in other specific ways than those herein set forth without departing from the scope and essential characteristics of the invention. For example, embodiments described above have contemplated one or two inner apertures 30 to modify the moments of inertia about one axis relative to another. The
rods 10 do not need to be limited to this number of apertures. The moment of inertia equations provided herein allow one to calculate moments of inertia for any number of apertures and flexural rigidity of theoverall rod 10. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.
Claims (24)
Priority Applications (4)
Application Number | Priority Date | Filing Date | Title |
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US11/342,195 US20070191841A1 (en) | 2006-01-27 | 2006-01-27 | Spinal rods having different flexural rigidities about different axes and methods of use |
EP07701232A EP1978879A1 (en) | 2006-01-27 | 2007-01-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
PCT/US2007/060477 WO2007087476A1 (en) | 2006-01-27 | 2007-01-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
US13/181,474 US8945187B2 (en) | 2006-01-27 | 2011-07-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
Applications Claiming Priority (1)
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US11/342,195 US20070191841A1 (en) | 2006-01-27 | 2006-01-27 | Spinal rods having different flexural rigidities about different axes and methods of use |
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US13/181,474 Division US8945187B2 (en) | 2006-01-27 | 2011-07-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
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Also Published As
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US20110270313A1 (en) | 2011-11-03 |
WO2007087476A1 (en) | 2007-08-02 |
US8945187B2 (en) | 2015-02-03 |
EP1978879A1 (en) | 2008-10-15 |
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