Abstract:
A vertebral rod has 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.

Description:
BACKGROUND  
       [0001]     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.  
         [0002]     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.  
         [0003]     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.  
       SUMMARY  
       [0004]     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. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0005]      FIG. 1  is a perspective view of first and second assemblies comprising spinal rods attached to vertebral members according to one or more embodiments;  
         [0006]      FIG. 2  is a lateral view of a spinal rod according to one or more embodiments; and  
         [0007]      FIGS. 3-20  are axial views of a spinal rod illustrating cross sections according to different embodiments. 
     
    
     DETAILED DESCRIPTION  
       [0008]     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  in  FIG. 1 .  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 . In the example assembly  20  shown, 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 .  
         [0009]     In one embodiment as illustrated in  FIG. 1 , 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. Thus, the exemplary assemblies  12  shown in  FIG. 1  are merely representative of one type of attachment mechanism.  
         [0010]     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.  
         [0011]      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. Other Figures described below show various embodiments of a spinal rod  10  characterized by different cross sections viewed according to the view lines illustrated in  FIG. 2 . For instance,  FIG. 3  shows one example cross section of the spinal rod  10   a . In this embodiment, 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 . In one embodiment, the outer surface  22   a  and inner surface  32   a  are uniformly consistent along the entire length L of the rod  10   a . That is, 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. In one or more embodiments, the cross section of a rod  10  may vary along the length L of the rod  10 .  
         [0012]     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 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&#39;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. 
 
         [0013]     In general, an object&#39;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&#39;s centroid C, the larger the moment of inertia. In  FIG. 3 , the moments of inertia about the x-axis I x  and the y-axis I y  for the area inside the elliptical outer shape  22   a  (ignoring the inner aperture  30   a  for now) may be determined according to the following equations:
 
 I   x   =∫y   2 dA  (2)
 
 I   y   =∫x   2 dA  (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 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. 
 
         [0014]     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. 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 I xo  and I xi  are the moments of inertia about the x-axis for the outer and inner areas, respectively. Similarly, I yo  and I yi  are the moments of inertia about the y-axis for the outer and inner areas, respectively. 
 
         [0015]     In the present embodiment of the rod  10   a  shown in  FIG. 3 , 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. For example, 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. Conversely, 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.  
         [0016]     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 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. Thus, the overall size of the rods  10  may be limited by this constraint.  
         [0017]      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 . Using the equations above, one is able to determine that the overall flexural rigidity about the x and y axes is greater for rod  10   a  as compared to rod  10   b . 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.  
         [0018]     The internal aperture  30  may be asymmetric as well. For example, 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 . However, 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.  
         [0019]     The rods  10  may also have multiple inner apertures  30 . For instance, 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 . Notably, the exemplary apertures  30   d ,  130   d  are disposed within the interior of the rod  10   d . Further, the apertures  30   d ,  130   d  are offset from the centroid C.  
         [0020]     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 in  FIG. 7 . This particular rod  10   e  has a square outer surface  22   e  that is substantially symmetric relative to axes X and Y. However, 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. Therefore, 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.  
         [0021]     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 . However, 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.  
         [0022]     The rod  10  may also have substantially triangular outer surfaces  22  as evidenced by the embodiments  10   h ,  10   i , and  10   j . In  FIG. 10 , 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. By comparison, the rod  10   i  shown in  FIG. 11  comprises a triangular outer surface  22   i  that is substantially equilateral. The rod  10   j  shown in  FIG. 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.  
         [0023]     Other 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.  
         [0024]     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 . In  FIG. 15 , the rod  10   n  comprises two apertures  30   n ,  130   n  that are defined by inner surfaces  32   n ,  132   n . As indicated, 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. By way of comparison, 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.    
         [0025]     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 . In each case, the outer 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 the outer 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 asymmetric inner aperture  30   q - s.    
         [0026]     In  FIG. 17 , the inner aperture  30   q  defined by inner 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)). In  FIG. 18 , 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. Thus, 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.  
         [0027]      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 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.  
         [0028]      FIG. 20  shows the same rod  10   q  as illustrated in  FIG. 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). 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.    
         [0029]     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.  
         [0030]     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.  
         [0031]     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 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.