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 useDownload PDFInfo
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- US20070191841A1 US20070191841A1US11/342,195US34219506AUS2007191841A1US 20070191841 A1US20070191841 A1US 20070191841A1US 34219506 AUS34219506 AUS 34219506AUS 2007191841 A1US2007191841 A1US 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
- 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 or setting implements
- 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, e.g. 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
- 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 or setting implements
- 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, e.g. 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
- 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 or setting implements
- 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, e.g. 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 rodsare 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 rodsmay 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 surgeonmay 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 rodstend to be symmetric in nature and may not provide this degree of control.
- Illustrative embodiments disclosed hereinare directed to a vertebral rod having an elongated body extending along a longitudinal axis.
- the rodalso includes a cavity extending the length of the body.
- Either the body or the cavitymay 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 rodmay be bounded by an exterior surface and the cavity.
- the bodyhas a first bending axis that is perpendicular to longitudinal axis.
- the bodyalso has a second bending axis that is perpendicular to the longitudinal axis and to the first bending axis.
- the body of the rodmay be distributed asymmetrically about the first and second bending axes.
- the rodmay have a different bending stiffness about the first and second bending axes.
- the cavitymay be contained within or intersect the exterior surface.
- FIG. 1is a perspective view of first and second assemblies comprising spinal rods attached to vertebral members according to one or more embodiments;
- FIG. 2is a lateral view of a spinal rod according to one or more embodiments.
- FIGS. 3-20are axial views of a spinal rod illustrating cross sections according to different embodiments.
- FIG. 1shows 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 10are positioned at a posterior side of the spine, on opposite sides of the spinous processes S.
- Spinal rods 10may be attached to a spine at other locations, including lateral and anterior locations.
- Spinal rods 10may 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 10are 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 10is 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 2include hooks, cables, and other such devices. Examples of other types of retaining hardware include threaded caps, screws, and pins.
- Spinal rods 10are also attached to plates in other configurations.
- the exemplary assemblies 12 shown in FIG. 1are merely representative of one type of attachment mechanism.
- the rod 10may 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. 2shows a spinal rod 10 of the type used in the exemplary assembly 20 in FIG. 1 .
- the rod 10has a length between a first end 17 and a second end 18 extending along a longitudinal axis A.
- FIG. 3shows one example cross section of the spinal rod 10 a .
- the spinal rod 10 ais 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 aare uniformly consistent along the entire length L of the rod 10 a .
- the cross section shown in FIG. 3may be the same at all points along the length L of the rod 10 a .
- the samemay also be true of other cross sections described below.
- the cross section of a rod 10may vary along the length L of the rod 10 .
- the structural characteristics of the rod 10may be dependent upon several factors, including the material choice and the cross section shape of the rod 10 .
- the modulus of elasticityvaries by material and reflects the relationship between stress and strain for that material.
- titanium alloysgenerally 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 inertiadepends 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 CThe intersection of the x-axis and y-axis is called the centroid C of rotation.
- the centroid Cmay 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. 3may 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 xI xo ⁇ I xi (4)
- I yI yo ⁇ I yi (5)
- I xo and I xiare the moments of inertia about the x-axis for the outer and inner areas, respectively.
- I yo and I yiare the moments of inertia about the y-axis for the outer and inner areas, respectively.
- the inner aperture 30 ais 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 extensionmay 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 bendingmay 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 surgeonmay 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 surgeonmay 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 availablerange between about 4-7 mm.
- the overall size of the rods 10may be limited by this constraint.
- FIG. 4shows 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 bmay 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 30may be asymmetric as well.
- the rod 10 c shown in FIG. 5includes 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 cis elliptical or oval shaped.
- the inner aperture 30 chas 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 10may also have multiple inner apertures 30 .
- the rod 10 d shown in FIG. 6comprises a plurality of apertures 30 d , 130 d defined by inner surfaces 32 d , 132 d .
- the outer surface 22 dmay be substantially similar to the outer surface 22 a of rod 10 a .
- the exemplary apertures 30 d , 130 dare disposed within the interior of the rod 10 d .
- the apertures 30 d , 130 dare offset from the centroid C.
- the embodiments described abovehave all had a substantially similar, oval shaped outer surface 22 .
- This particular rod 10 ehas 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 eis asymmetric relative to these same X and Y axes.
- Inner surface 32 eis 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 ehas 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. 8has 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 configurationis 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. 9has 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 ghas 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 10may also have substantially triangular outer surfaces 22 as evidenced by the embodiments 10 h , 10 i , and 10 j .
- the outer surface 22 his 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. 11comprises a triangular outer surface 22 i that is substantially equilateral.
- the 12comprises a substantially triangular outer surface 22 j that is substantially equilateral, albeit with non-linear sides.
- the inner apertures 30 h , 30 i , 30 jmay be shaped as shown in FIGS. 10-12 or as desired in accordance with the discussion provided above.
- rods 10may have polygonal shapes such as the embodiments illustrated in FIGS. 13 and 14 .
- the rod 10 k shown in FIG. 13comprises a hexagonal outer surface 22 k while rod 10 m in FIG. 14 comprises a pentagonal outer surface 22 m .
- the rods 10may have more sides if desired.
- the embodiments described thus farhave included an aperture 30 that is substantially contained within the interior of the outer surface 22 .
- the aperture 30may intersect with the outer surface 22 .
- the rod 10 ncomprises two apertures 30 n , 130 n that are defined by inner surfaces 32 n , 132 n .
- the inner surfaces 32 n , 132 nintersect the outer surface 22 n resulting in open apertures 30 n , 130 n .
- the rod 10 nis 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. 16also has a single open aperture 30 p defined by an inner surface 32 p that intersects with the outer surface 22 p.
- the rods 10may 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 - sis substantially circular and/or characterized by a substantially constant radius.
- the moment of inertia about axes X and Yis 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 - smay be altered by including an asymmetric inner aperture 30 q - s.
- the inner aperture 30 q defined by inner surface 32 qhas a larger moment of inertia about the X-axis.
- the rod 10 qhas 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 ris 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 ris 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. 19shows another embodiment of a rod 10 s having an open inner aperture 30 s .
- the inner surface 32 shas a substantially constant radius and intersects the substantially circular outer surface 22 s .
- the inner aperture 30 sis 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. 20shows the same rod 10 q as illustrated in FIG. 17 .
- the rod 10 qcomprises 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 , 36may 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 , 36may be included on an end 17 , 18 of the rod 10 q as shown or on the outer surface 22 q.
- inventions described abovehave contemplated one or two inner apertures 30 to modify the moments of inertia about one axis relative to another.
- the rods 10do not need to be limited to this number of apertures.
- the moment of inertia equations provided hereinallow one to calculate moments of inertia for any number of apertures and flexural rigidity of the overall rod 10 .
- the present embodimentsare, 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.
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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; andFIGS. 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 10a. In this embodiment, thespinal rod 10ais comprised of an oval or ellipticalouter surface 22aand an interior cavity oraperture 30adefined by aninner surface 32a. In one embodiment, theouter surface 22aandinner surface 32aare uniformly consistent along the entire length L of therod 10a. That is, the cross section shown inFIG. 3 may be the same at all points along the length L of therod 10a. 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 Ixand the y-axis Iyfor the area inside the ellipticalouter shape 22a(ignoring theinner aperture 30afor now) may be determined according to the following equations:
Ix=∫y2dA (2)
Iy=∫x2dA (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 Ixis larger than the moment of inertia about the y-axis Iy. This means that the oval shape defined by theouter surface 22ahas a greater resistance to bending about the x-axis as compared to the y-axis. - The actual bending stiffness of the
rod 10ashown inFIG. 3 may also depend upon the moment of inertia of theinner aperture 30a. Determining the overall flexural rigidity of therod 10arequires an analysis of the composite shape of therod 10a. 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 10ashown inFIG. 3 , the overall flexural rigidity is given by the following:
Ix=Ixo−Ixi (4)
Iy=Iyo−Iyi (5)
where Ixoand Ixiare the moments of inertia about the x-axis for the outer and inner areas, respectively. Similarly, Iyoand Iyiare the moments of inertia about the y-axis for the outer and inner areas, respectively. - In the present embodiment of the
rod 10ashown inFIG. 3 , theinner aperture 30ais symmetric about the centroid C. Consequently, the moments of inertia about the x and y axes for the area inside theouter surface 22aare reduced by the same amount according to equations (4) and (5). Still, the overall flexural rigidity of therod 10ais greater about the x-axis as compared to the y-axis. Accordingly, a surgeon may elect to install therod 10ain a patient to correspondingly control flexion, extension, or lateral bending. One may do so by orienting therod 10awith 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 10awith 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 10awith 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 10awith 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 aperture30. 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 10bsimilar torod 10a(i.e.,outer surface 22bis substantially similar to surface22a) with the exception that theinner aperture 30bdefined byinner surface 32bis larger than theinner aperture 30aofrod 10a. Using the equations above, one is able to determine that the overall flexural rigidity about the x and y axes is greater forrod 10aas compared torod 10b.Rods outer surface internal aperture rods - The internal aperture30 may be asymmetric as well. For example, the rod10cshown in
FIG. 5 includes anouter surface 22cthat is substantially similar to theouter surface 22aofrod 10a. However, the inner aperture30cdefined by surface32cis elliptical or oval shaped. The inner aperture30chas a height h1parallel to the x-axis that is less than the width b1parallel to the y-axis. That is, the moment of inertia of the inner aperture30cis greater about the y-axis than about the x-axis. This is in contrast to theouter surface 22c, which has a larger moment of inertia about the x-axis. - The
rods 10 may also have multiple inner apertures30. For instance, therod 10dshown inFIG. 6 comprises a plurality ofapertures inner surfaces 32d,132d. The outer surface22dmay be substantially similar to theouter surface 22aofrod 10a. Notably, theexemplary apertures rod 10d. Further, theapertures - The embodiments described above have all had a substantially similar, oval shaped outer surface22. Certainly, other shapes are possible as illustrated by the embodiment of the
rod 10eshown inFIG. 7 . Thisparticular rod 10ehas a square outer surface22ethat is substantially symmetric relative to axes X and Y. However, theinner aperture 30edefined by inner surface32eis asymmetric relative to these same X and Y axes. Inner surface32eis 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 30ehas a larger moment of inertia relative to the Y-axis as compared to the X-axis. Consequently, according to equations (4) and (5), therod 10ehas a greater bending strength about the X-axis as compared to the Y-axis. - The
rod 10fshown inFIG. 8 has rectilinear inner32fand outer22fsurfaces. However, in contrast torod 10e, theinner surface 32fis substantially square andouter surface 22fis substantially rectangular. This configuration is analogous torod 10ashown inFIG. 3 in that theinner aperture 30fis symmetric about the X and Y axes while theouter surface 22fis asymmetric about the X and Y axes. Therod 10gshown inFIG. 9 has both aninner aperture 30gand anouter surface 22gthat are asymmetric about the X and Y axes. The same is true of the rod10cshown inFIG. 5 . However,rod 10ghas aninner aperture 30gand an area inside theouter surface 22gthat have larger moments of inertia about the same X-axis. This is due, in part, to the fact that the rectangularinner aperture 30gandouter surface 22gare substantially aligned. - The
rod 10 may also have substantially triangular outer surfaces22 as evidenced by theembodiments FIG. 10 , theouter surface 22his 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 10hhaving a greater moment of inertia about the X-axis. By comparison, therod 10ishown inFIG. 11 comprises a triangularouter surface 22ithat is substantially equilateral. Therod 10jshown inFIG. 12 comprises a substantially triangularouter surface 22jthat 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 10kshown inFIG. 13 comprises a hexagonalouter surface 22kwhilerod 10minFIG. 14 comprises a pentagonalouter surface 22m. Therods 10 may have more sides if desired.- The embodiments described thus far have included an aperture30 that is substantially contained within the interior of the outer surface22. In other embodiments, the aperture30 may intersect with the outer surface22. This can be seen in the exemplary embodiments shown in
FIGS. 15 and 16 . InFIG. 15 , therod 10ncomprises twoapertures 30n,130nthat are defined byinner surfaces inner surfaces outer surface 22nresulting inopen apertures 30n,130n. Therod 10nis 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 10pshown inFIG. 16 also has a singleopen aperture 30pdefined by aninner surface 32pthat intersects with theouter surface 22p. - The
rods 10 may also have a substantially circular outer surface22 similar to many conventional rods, thus accommodating existing rod securing hardware (not shown). This is illustrated by theexemplary rods 10q,10r, and10sshown inFIGS. 17, 18 , and19. In each case, theouter surface 22q-sof the rod10q-sis 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 22q-s. However, the moment of inertia about the X and Y axes for the rod10q-smay be altered by including an asymmetricinner aperture 30q-s. - In
FIG. 17 , theinner aperture 30qdefined byinner surface 32qhas a larger moment of inertia about the X-axis. Thus, the rod10qhas a larger moment of inertia about the Y-axis (pursuant to equations (4) and (5)). InFIG. 18 , theinner aperture 30rdefined byinner surface 32ris also substantially circular. However, theinner aperture 30ris offset from centroid C. Further, theinner surface 32ris tangent to the Y-axis, but spaced away from the X-axis. Thus, the moment of inertia of theinner aperture 30ris larger with respect to the X-axis as compared to the Y-axis. Consequently, the moment of inertia and bending stiffness of theoverall rod 10ris larger about the Y-axis. FIG. 19 shows another embodiment of a rod10shaving an open inner aperture30s. In this embodiment, the inner surface32shas a substantially constant radius and intersects the substantially circularouter surface 22s. The inner aperture30sis offset from the centroid C, but aligned with the Y-axis in the orientation shown. Therefore, the inner aperture30shas a larger moment of inertia about the X-axis. The bending stiffness of the overall rod10sis therefore greater about the Y-axis.FIG. 20 shows the same rod10qas illustrated inFIG. 17 . In this particular view, the rod10qcomprises a first set of markings34 (the − sign in the embodiment shown) and a second set of markings36 (the + sign in the embodiment shown). Themarkings markings end outer surface 22q.- 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 apertures30 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)
1. A vertebral rod comprising:
a body extending along a first axis and having a length along the first axis between a first end and a second end;
a cavity extending the length of the body;
at least one of the body and the cavity having an asymmetrical shape about a centroid in a plane perpendicular to the first axis.
2. The vertebral rod ofclaim 1 wherein the cavity is centered about the first axis.
3. The vertebral rod ofclaim 1 wherein the body is centered about the first axis.
4. The vertebral rod ofclaim 1 wherein the body and the cavity are centered about the first axis.
5. The vertebral rod ofclaim 1 wherein the cavity is defined by an inner surface having a first shape and the body is defined by an outer surface having a second shape, first and second shapes being different.
6. The vertebral rod ofclaim 1 wherein the cavity is defined by an inner surface having a first shape and the body is defined by an outer surface having a second shape, first and second shapes being the same.
7. The vertebral rod ofclaim 1 further comprising markings indicating an orientation of the asymmetrical shape.
8. A vertebral rod comprising:
a body having a cavity, each extending along a first axis and each having a length along the first axis between a first end and a second end, the body bounded by an exterior surface and the cavity;
the body having a first bending axis that is perpendicular to the first axis and a second bending axis that is perpendicular to the first axis and to the first bending axis, the body being distributed asymmetrically about the first and second bending axes.
9. The vertebral rod ofclaim 8 wherein the exterior surface is asymmetric about the first and second bending axes.
10. The vertebral rod ofclaim 8 wherein the cavity is asymmetric about the first and second bending axes.
11. The vertebral rod ofclaim 8 wherein the exterior surface and the cavity are each asymmetric about the first and second bending axes.
12. The vertebral rod ofclaim 8 wherein the cavity is interior to the exterior surface.
13. The vertebral rod ofclaim 8 wherein the cavity intersects with the exterior surface.
14. The vertebral rod ofclaim 8 further comprising markings indicating an orientation of the asymmetric distribution of the body.
15. A vertebral rod comprising:
a body extending along a first axis and having a length along the first axis between a first end and a second end, the body having a first cross sectional shape substantially perpendicular to the first axis;
a cavity extending the length of the body, the cavity having a second cross sectional shape substantially perpendicular to the first axis; and
the first cross sectional shape and the second cross sectional shape being different.
16. The vertebral rod ofclaim 15 wherein the second cross sectional shape is interior to the first cross sectional shape.
17. The vertebral rod ofclaim 15 wherein the second cross sectional shape intersects the first cross sectional shape.
18. A vertebral rod comprising:
a body having a cavity, each extending along a first axis and each having a length along the first axis between a first end and a second end, the body bounded by an exterior surface and the cavity;
the body having a first bending axis that is perpendicular to the first axis and a second bending axis that is perpendicular to the first axis and to the first bending axis, the body having different area moments of inertia about the first and second bending axes.
19. The vertebral rod ofclaim 18 wherein the exterior surface defines an area having different area moments of inertia about the first and second bending axes.
20. The vertebral rod ofclaim 18 wherein the cavity has different area moments of inertia about the first and second bending axes.
21. The vertebral rod ofclaim 18 wherein the exterior surface and the cavity each have different area moments of inertia about the first and second bending axes.
22. The vertebral rod ofclaim 18 wherein the cavity is interior to the exterior surface.
23. The vertebral rod ofclaim 18 wherein the cavity intersects with the exterior surface.
24. The vertebral rod ofclaim 18 further comprising markings indicating an orientation of the asymmetric area moments of inertia.
Priority Applications (4)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US11/342,195US20070191841A1 (en) | 2006-01-27 | 2006-01-27 | Spinal rods having different flexural rigidities about different axes and methods of use |
| EP07701232AEP1978879A1 (en) | 2006-01-27 | 2007-01-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
| PCT/US2007/060477WO2007087476A1 (en) | 2006-01-27 | 2007-01-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
| US13/181,474US8945187B2 (en) | 2006-01-27 | 2011-07-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US11/342,195US20070191841A1 (en) | 2006-01-27 | 2006-01-27 | Spinal rods having different flexural rigidities about different axes and methods of use |
Related Child Applications (1)
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| US13/181,474DivisionUS8945187B2 (en) | 2006-01-27 | 2011-07-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
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| US20070191841A1true US20070191841A1 (en) | 2007-08-16 |
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| US13/181,474Active2028-02-27US8945187B2 (en) | 2006-01-27 | 2011-07-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| US13/181,474Active2028-02-27US8945187B2 (en) | 2006-01-27 | 2011-07-12 | Spinal rods having different flexural rigidities about different axes and methods of use |
Country Status (3)
| Country | Link |
|---|---|
| US (2) | US20070191841A1 (en) |
| EP (1) | EP1978879A1 (en) |
| WO (1) | WO2007087476A1 (en) |
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Also Published As
| Publication number | Publication date |
|---|---|
| US8945187B2 (en) | 2015-02-03 |
| US20110270313A1 (en) | 2011-11-03 |
| EP1978879A1 (en) | 2008-10-15 |
| WO2007087476A1 (en) | 2007-08-02 |
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