Abstract:
A joint prosthesis device comprises a head configured to fit within a cup and in one embodiment includes a first member for attachment to a first bone in a joint and including a first articulation surface portion defined by a first radius of curvature and a second member for attachment to a second bone in the joint and including a second articulation surface portion defined by a second radius of curvature and a third articulation surface defined by a third radius of curvature, wherein each of the second radius of curvature and the third radius of curvature has a length that is different from the length of the first radius of curvature by less than 0.05 millimeters and wherein the origin of the second radius of curvature is not coincident with the origin of the third radius of curvature.

Description:
FIELD 
       [0001]    This application relates to the field of prosthetic devices, and particularly joint prostheses comprising head and cup arrangements. 
       BACKGROUND  
       [0002]    A common orthopedic joint prosthesis includes a ball and cup arrangement. For example, hip joints typically comprise a rounded femoral head and an acetabular cup. The rounded femoral head is provided on a stem that is configured to engage the intramedullary cavity of the femor and secure the head on the femor. The rounded femoral head includes a convex surface configured to engage a concave surface on the acetabular cup. The acetabular cup is configured for implantation on the acetabulum of the pelvis. When the rounded femoral head is received within the acetabular cup, a ball and socket joint is provided. 
         [0003]    In order to reduce wear between the components of the joint prosthesis, the components are manufactured such that the clearance between the bearing surfaces is minimized. The term “clearance” is often used in reference to a “diametral clearance” of the joint prosthesis. The diametral clearance between bearing surfaces is generally considered to be the difference in the diameter defining the bearing surface of the ball and the diameter defining the bearing surface of the cup. 
         [0004]    While minimal diametral clearance between the bearing surfaces is desired, at least two factors limit the reduction of clearances. First, manufacturing tolerances generally limit the extent to which clearances may be reduced. For example, for diametral clearances below the 15-30 micron range, it has been observed that imperfect formation of the femoral head and the acetabular cup contributes to local interferences and small deformations that result in wear. 
         [0005]    Second, acetabular cup deformation during implantation into the acetabulum also limits the degree to which clearances may be reduced in a hip joint prosthesis. This deformation generally occurs near the equatorial lip of the acetabular cup. For substantially spherical cup and head arrangements, reduction in clearances near the pole of the head also means reduction in clearances near the equatorial lip. In other words, when the head and the cup of a hip prosthesis are substantially spherical, the small clearances near the pole of the head are also found in the region near the equatorial lip of the cup. Thus, when cup deformation occurs near the equatorial lip in a low clearance spherical design, interference is likely to occur between the equatorial lip of the cup and the ball. 
         [0006]    One way to reduce clearance complications resulting from acetabular cup deformation is to provide a conformal region having a small clearance near the center of the primary articulation area of the femoral head, and a peripheral region surrounding the conformal region, wherein the peripheral region has a significantly greater clearance than the conformal region, including a significantly greater clearance near the lip of the cup. With this arrangement, deformations near the equatorial lip of the acetabular cup are less likely to result in obstruction with the femoral head because of the increased clearance near the equatorial lip. Although several of these arrangements have been provided in the past, they have not provided optimal solutions. In particular, many of these arrangements include peripheral regions surrounding the conformal region where the clearances in these peripheral regions quickly diverge from the relatively small clearances in the conformal zone. However, when the clearance in the peripheral region is too great, significant wear may result. 
         [0007]    Accordingly, what is needed is a joint prosthesis configured to avoid interference between the ball and cup even if the equatorial region of the cup is deformed during implantation. It would also be advantageous if the clearance between the ball and cup could remain relatively low even in a peripheral region surrounding the conformal region. 
       SUMMARY  
       [0008]    A joint prosthesis device comprises a head configured to fit within a cup and in one embodiment includes a first member for attachment to a first bone in a joint and including a first articulation surface portion defined by a first radius of curvature and a second member for attachment to a second bone in the joint and including a second articulation surface portion defined by a second radius of curvature and a third articulation surface defined by a third radius of curvature, wherein each of the second radius of curvature and the third radius of curvature has a length that is different from the length of the first radius of curvature by less than 0.05 millimeters and wherein the origin of the second radius of curvature is not coincident with the origin of the third radius of curvature. 
         [0009]    In another embodiment, a prosthetic device includes a cup including a concave surface defining a cavity, the concave surface defined by at least one radius of curvature (R C ), and a head including an outer surface and configured to fit at least partially within the cavity, the outer surface including a cap portion defined by a cap radius of curvature (R P ) and a toroidal portion located about the cap portion and defined by a toroidal radius of curvature (R T ), wherein the cap portion is configured to conform with the concave cup surface and the R C  is less than 0.05 millimeters longer than the R T . 
         [0010]    In a further embodiment, a prosthetic device includes a cup including a concave surface defining a cavity, the concave surface defined by at least one radius of curvature (R C ), and a head including an articulation portion configured to fit at least partially within the cavity, the articulation portion including a toroidal portion defined by a toroidal radius of curvature (R T ) having a circular origin and a cap portion defined by a cap radius of curvature (R P ), wherein the R C  is less than 0.05 millimeters longer than the R T . 
         [0011]    In yet another embodiment, a prosthetic ball for use in a ball and cup joint system includes a spherical cap articulation portion defined by a radius of curvature, and a toroidal articulation portion defined by a portion of the inner surface of a spindle torus. 
         [0012]    The above described features and advantages, as well as others, will become more readily apparent to those of ordinary skill in the art by reference to the following detailed description and accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]      FIG. 1  shows a perspective view of various components of a hip prosthesis including an acetabular cup, a femoral head, and a femoral stem in accordance with principles of the invention; 
           [0014]      FIG. 2  shows a cutaway view of the hip prosthesis of  FIG. 1  assembled and implanted in a pelvis and femur; 
           [0015]      FIG. 3  shows a cross-sectional view of the femoral head and acetabular cup of  FIG. 1 ; 
           [0016]      FIG. 4  shows a diagrammatic representation of the radii which define the inner surface of the cup, a primary contact zone and a toroidal zone in accordance with principles of the invention; 
           [0017]      FIG. 5  depicts a perspective view of a slice of the femoral head of  FIG. 3  showing the relative positions of the origin for the radius of curvature of the cap portion of the femoral head and the circular origin of the radius of curvature of the toroidal section; 
           [0018]      FIG. 6  shows a cross sectional view of a spindle torus; 
           [0019]      FIG. 7  shows a three-dimensional representation of the bottom half of the torus of  FIG. 6  including the apple shaped or outer surface and the lemon shaped or inner surface of the torus; 
           [0020]      FIG. 8  shows a diagrammatic representation of the definition of the outer surface of a femoral ball using the lemon shape or inner surface of a spindle torus and an arc of a circle centered below the axis defined by the center of the circle (the circular origin) which defines the spindle torus; 
           [0021]      FIG. 9  shows a diagrammatic representation of the circles of  FIG. 8  with the center of the circle used to define the arc or cap portion closer to the axis defined by the center of the circle (the circular origin) thereby decreasing the size of the cap portion as compared with  FIG. 8 ; 
           [0022]      FIG. 10  shows a diagrammatic representation of the circles of  FIG. 8  with the center of the circle used to define the arc or cap portion at the same distance away from the axis defined by the center of the circle (the circular origin) as shown in  FIG. 8  but with the diameter of the circular origin reduced (i.e. the apple shaped portion is more circular) thereby increasing the size of the cap portion as compared with  FIG. 8 ; 
           [0023]      FIG. 11  shows a cross-sectional view of the femoral head and acetabular cup of  FIG. 1  with the femoral head rotated within the acetabular cup and contacting the acetabular cup at the opening of the acetabular cup; 
           [0024]      FIG. 12  shows a cross-sectional view of an alternative embodiment of an acetabular cup with a diagrammatic overlay showing the use of a toroidal surface within the acetabular cup in accordance with principles of the invention; and 
           [0025]      FIG. 13  shows a cross-sectional view of an alternative embodiment of an acetabular cup with a diagrammatic overlay showing the use of a toroidal surface within the acetabular cup wherein the cap portion and toroidal portion of the acetabular cup are not centered within the acetabular cup in accordance with principles of the invention. 
       
    
    
     DESCRIPTION  
       [0026]    With reference to  FIG. 1 , a prosthetic device in the form of a prosthetic hip joint  100  is shown in a disassembled configuration. The prosthetic hip joint  100  includes an acetabular cup  102  and a femoral component  104 . The femoral component  104  includes a femoral head  106  (or “ball”), and a femoral stem  108 . The femoral head  106  is configured for attachment to the femoral stem  108 . The femoral head  106  is also configured to slideably engage the acetabular cup  102 . 
         [0027]    The acetabular cup  102  is the part of the prosthetic hip joint  100  that forms the socket of a ball-and-socket structure. The acetabular cup  102  includes a convex outer surface  110  configured for engagement with a patient&#39;s acetabulum and a concave interior surface  112  configured to engage the femoral head  106 . The cup  102  includes a lip  114  which defines a rim in a peripheral region and which extends between the convex outer surface  110  and the concave interior surface  112 . 
         [0028]    The convex outer surface  110  of the acetabular cup  102  may be provided as part of a shell including a biocompatible material. In at least one embodiment, the shell is comprised of a relatively rigid material, such as a biocompatible metal or ceramic. For example, the shell may be comprised of titanium or cobalt chrome. The concave interior surface  112  of the cup  102  may be in the form of a liner that provides a bearing surface for the acetabular cup  102 . The liner may be comprised of a biocompatible material that offers a low coefficient of friction, such as polyethylene. Alternatively, the liner may be comprised of a metal or ceramic. While exemplary materials for the acetabular cup  102  have been offered herein, one of skill in the art will recognize that numerous other biocompatible materials may be used as are known in the art. 
         [0029]    The femoral component  104  is used to replace the natural head of a femur. To this end, the femoral head  106  includes a generally ball-shaped outer surface  116  designed and dimensioned to be received at least partially within the cavity defined by the concave interior surface  112  of the acetabular cup  102 . The femoral head  106  includes a generally conical bore  118  which is used to fix femoral head  106  to a Morse taper  120  on the neck  122  which extends from the femoral stem  108 . The femoral component  104  is comprised of a relatively rigid biocompatible material such as a ceramic or metal. For example, the ball  106  may be comprised of cobalt chrome or stainless steel. While exemplary materials for the femoral component  104  have been offered herein, one of skill in the art will recognize that numerous other biocompatible materials may be used as are known in the art. 
         [0030]    As shown in  FIG. 2 , the prosthetic hip joint  100  may be implanted in a patient by securing the acetabular cup  102  in the acetabulum  124  of the pelvis  126 . Also, the femoral component  104  is secured to the femur  128  by inserting the femoral stem  108  within the intramedullary cavity  130  of the femur  128 . The femoral head  106  which extends from the neck  122  is brought into slideable contact with the acetabular cup  102  such that the femoral head  106  is allowed to articulate within the acetabular cup  102 . This slideable relationship provides for a ball and socket type joint. 
         [0031]    An enlarged cutaway view of the acetabular cup  102  showing the femoral head  106 , with the head  106  slightly removed from engagement with the cup  102  is shown in  FIG. 3 . The configuration of the head  106  defines different zones or regions for the prosthesis, including a primary contact zone A and a toroidal zone T. 
         [0032]    The term “primary contact zone” refers to a region of the head  106  which provides the main contact area between the head  106  and the cup  102  for most joint movements once implanted in a patient. Accordingly, with reference to  FIG. 3 , the convex bearing surface  116  of the head  106  primarily articulates with the concave bearing surface  112  of the cup  102  within the primary contact zone A. Some contact, however, occurs between the head  106  and the cup  102  within the toroidal zone T, particularly with certain extra-ordinary movements by the patient. 
         [0033]    The primary contact zone A is shown as lying within the region subtended by the angle a having a vertex at an origin  140  of the spherical cap portion. This means that the primary contact zone A is provided within a perimeter defined by the intersection of a cone  142  with the convex outer surface  116  of the head  106 , the cone  142  having an apex  144  at the origin  140  and an aperture (or “opening angle”) of α. As shown in  FIG. 3 , the cone  142  is symmetric about an axis  146  extending through the origin  140 . The toroidal zone T extends from the primary contact zone A to the conical bore  118 . 
         [0034]    Studies such as Bergmann, et al., “Hip contact forces and gait patterns from routine activities,” J. Biomech., 2001, 34(7), 859-871, have shown that contact predominantly occurs in an area defined by opening angles between 85 and 145 degrees. Accordingly, while the α in this embodiment is 95 degrees other opening angles between 85 and 145 degrees may be used. Selection of opening angles between 95 and 125 degrees provide for good radial clearance which is discussed below. 
         [0035]    The acetabular cup  102  is shown in  FIG. 3  centered upon and symmetric with respect to an apex  148 , which is the deepest portion of the cup  102 , in the coronal plane. In particular, the apex  148  of the concave bearing surface  112  of the cup  102  is shown in  FIG. 3  aligned with the axis  146 . When the cup  102  is in this position relative to the head  106 , it is considered to be in a centered position. In practice, the cup  102  and head  106  are generally aligned in the implanted position such that the apex  148  of the cup  102  is about thirty degrees off the axis  146  of the head  106  in the coronal plane and about fifteen degrees off the axis  146  of the head  106  in the sagittal plane. For a spherical cup geometry, the articulation area on the head is independent of the cup orientation. 
         [0036]    With continued reference to  FIG. 3 , the outer surface  116  of the head  106  at any given point is defined by a radius of curvature (R H ). The head  106  does not form a perfect sphere, however, and the radius of curvature R H  is different at different points on the surface  116  of the head  106  as shown in  FIG. 4 . The radius of curvature in the primary contact zone (R P ) in the embodiment of  FIG. 3  is 18.035 mm, while the radius of curvature in the toroidal zone (R T ) is 18.0120 mm. 
         [0037]    Moreover, as shown in  FIG. 4 , the origin of the R P  is located at the origin  140 . The origin of the R T , however, is defined by a circle  150  shown in  FIG. 5 .  FIG. 5  depicts a slice of the femoral head  106  taken along the plane defined by the axis  146  and an axis  152  which is perpendicular to the axis  146  and which intersects the origin  140 . The portion of the circle  150  which is behind the slice of the ball  106  as depicted in  FIG. 5  is shown as a dashed line. The circle  150  has a radius of 0.0155 mm and lies within a plane that is located 0.0510 mm above the origin  140  and positioned perpendicular to the axis  152 . 
         [0038]    Any given point on the outer surface  116  in the toroidal zone T is defined by an R T  having an origin located on the point of the circle  150  farthest away from the point being defined. For example, the arc  154  of the surface  116  shown in  FIG. 5  is defined by sweeping R T  from the position shown as R T1  to the position of R T1′  while maintaining the origin of the R T  at the point  156 . Similarly, the arc  158  of the surface  116  of  FIG. 5  is defined by sweeping R T  from the position shown as R T2  to the position of R T2′  while maintaining the origin of the R T  at the point  160 . Thus, the origin of the R T  shown in  FIG. 4  is located at a point 0.0510 mm above the axis  152  and 0.0155 to the left of the axis  146 . 
         [0039]    From a mathematical construct, the toroidal zone T is thus formed as the lemon of a spindle torus. A spindle torus is formed by the revolution of a circle about an axis coplanar with the circle. A cross sectional view of a torus  162  is shown in  FIG. 6  while  FIG. 7  is a three-dimensional representation of the bottom half of the torus  162 . The torus  162  in cross-section presents two overlapping circles  164  and  166 . The centers  168  and  170  of the circles  164  and  166  are points on a circle  172 . The circle  172  is thus the circular origin of the torus  162  having a radius of curvature  174  which is the radius of the circles  164  and  166 . The outer surface  178  of the torus is referred to as the “apple” shape while the inner surface  180  is referred to as the “lemon” shape. 
         [0040]    As shown in  FIG. 8 , the lemon  180  and a circle  182  having a center  184  located below the axis  186  defined by the centers  168  and  170  of the circles  164  and  166 , respectively can be used to define a cap  192 .  FIG. 9  is identical to  FIG. 8  with the exception that the origin  184  of the circle  182  has been positioned closer to the axis  186  defined by the circular origin of the outer surface  178 . As is apparent from comparing  FIG. 9  with  FIG. 8 , as the origin  184  of the circle  182  approaches the axis  186 , the cap portion  192  becomes smaller. The shape can be further modified by moving the origin  184  closer to one or the other of the centers  168  and  170 . Consequently, the location and extent of the discontinuity between the cap portion  192  and the outer surface  180  can be modified. 
         [0041]    Thus, by moving the origin or center  184  closer to the axis defined by the circular origin, the spherical cap portion  192  becomes smaller. For example, given a circular origin diameter of 0.031 millimeters, an R P  of 18.035 millimeters and an R T  of 18.0120 millimeters, a cap portion with a 95 degree opening angle is obtained by positioning the origin of the spherical cap portion 0.051 millimeters below the plane of the circular origin. In the event a cap portion with a 125 degree opening angle is desired using the same radii, one need only position the origin of the spherical cap portion at about 0.08 millimeters below the plane of the circular origin. 
         [0042]      FIG. 10  is identical to  FIG. 8  with the exception that the diameter of the circular origin  172  of the outer surface  178  is reduced. Thus, two centers  168  and  170  of the circles  164  and  166  are positioned more closely together. As is apparent from comparing  FIG. 10  with  FIG. 8 , as the two centers  168  and  170  of the circles  164  and  166  converge, that is, as the diameter of the circular origin  172  is shortened, the shape of the inner surface  180  becomes more circular, thereby increasing the size of the cap portion  192 . Consequently, the location and extent of the discontinuity between the cap portion  192  and the outer surface  180  can be modified. 
         [0043]    Moreover, while the circles  164 ,  166  and  182  are shown with identical radii, the radius of the circle  182  may be shorter or longer than the radii of the circles  164  and  166  in certain embodiments. Similarly, the radius of the circle  182  may be the same, shorter or longer than the radius or radii of a particular cup. 
         [0044]    Returning to  FIG. 3 , the acetabular cup  102  is defined by a radius of curvature (R C ). The R C  extends from the virtual center of the cup  102 , which as depicted in  FIG. 3  is coincident with the origin  140 , to the concave inner surface  112  of the acetabular cup  102 . The R C  is constant for all points on the concave inner surface  112  such that the concave inner surface  112  of the cup forms a hemisphere. The R C  in this embodiment is 18.050 mm. 
         [0045]    The radial clearance (R CL ) or difference between R C  and R H  at a given point on the head  106  and the opposing point on the cup  102  (i.e., on a given ray extending from the origin  140  of the head  106  to the concave surface  112  of the cup  102 ) does not necessarily translate directly into a spatial clearance between the head  106  and the cup  102 . For example, when the prosthesis  100  is implanted and the head  106  is in a centered position, the head  106  is in contact with the cup  102 , even though the R CL  is 0.015 mm (R C (18.050 mm)−R P (18.035 mm)). The value of R CL , however, is useful in quantifying the conformity between the surface of the ball  106  and the cup  102  which are in contact. For example, a small R CL  for a given contact area, i.e. less than 0.05 mm, generally provides lower wear rates. Accordingly, the prosthetic hip joint  100  maintains an R CL  less than 0.050 mm throughout the primary contact zone A. 
         [0046]    Additionally, the toroidal zone T provides increased clearance between the ball  106  and the cup  102  at the lip  114 . With reference to the embodiment of  FIG. 3 , the acetabular cup  102  is exactly hemispherical. Thus, the width of the cup  102  at the plane defined by the lip  114  is the widest portion of the cup  102 . Accordingly, when the ball  106  is centered within the cup  102  and in contact with the cup  102  along the axis  146 , the origin  140  is located 0.015 mm above the plane defined by the lip  114 . Thus, the widest diameter defined by the toroidal zone T will be located on a plane positioned 0.066 mm above the plane defined by the lip  114 . At this location, the width of the toroidal zone is 35.993 mm. The width of the cup  102  on a plane located 0.066 mm above the plane defined by the lip  114  is 36.0998 mm. Thus, the clearance is 0.1068 mm. 
         [0047]    At the plane defined by the lip  114 , however, the width of the toroidal zone T decreases to 35.9927 mm while the width of the cup increases to 36.1 mm resulting in a clearance of 0.1073 mm. In contrast, a precisely circular ball with a radius of 18.035 mm would result in a clearance at the plane defined by the lip  114  of 0.0300 mm. 
         [0048]    Referring to  FIG. 11 , the femoral ball  106  is rotated within the acetabular cup  102  to the maximum amount possible before dislocation would occur in an implanted device. The contact area between the ball  106  and the cup  102  for purposes of this example is centered at location  196 . This configuration, which is not a normally occurring configuration, provides insight into the smallest expected clearance for the embodiment of  FIG. 3 . That is, as the contact area is located more fully within the cup  102  with the ball  106  rotated as shown in  FIG. 6 , the origin  140  of the spherical cap portion moves off of the plane defined by the lip  114 , thereby increasing the clearance at the lip  114 . The width of the ball  106  in the plane defined by the lip  114  in the configuration of  FIG. 6  is 36.04699 mm resulting in a clearance of 0.0530 mm. In contrast, a precisely circular ball with a radius of 18.035 mm in the configuration of  FIG. 6  would result in a clearance at the plane defined by the lip  114  of 0.0300 mm. 
         [0049]    Thus, while the configuration of the prosthetic hip joint  100  provides the desired conformity between the ball  106  and the cup  102  regardless of the orientation of the ball  106  within the cup  102 , the conformity is achieved while providing increased clearance on the plane defined by the lip  114 . 
         [0050]    An alternative embodiment of an acetabular cup  200  is shown in  FIG. 12 . The acetabular cup  200  includes an outer surface  202  and an inner surface  204 . The inner surface  204  includes a cap portion  206  formed on a circle  208  with a center  210  and a toroidal portion  212 . The toroidal portion  212  is shown in cross-section as formed on two circles  214  and  216  having centers  218  and  220 , respectively. The center  208  is located above the axis  222  defined by the centers  218  and  220 . In this embodiment, the toroidal portion  212  is formed on the apple or outer surface of the torus defined by the rotation of the circles  214  and  216 . Accordingly, even if each of the circles  208 ,  214  and  216  have the same diameter, the diameter of the cup  200  in the toroidal portion  212  will be greater than the diameter in the cap portion  206 . 
         [0051]    As noted above, a cup and head are generally aligned in the implanted position such that the apex of the cup is about thirty degrees off the axis of the head in the coronal plane and about fifteen degrees off the axis of the head in the sagittal plane. Accordingly, it may be desired to modify the location of the cap portion of a cup. For example,  FIG. 13  shows an acetabular cup  230  includes an outer surface  232  and an inner surface  234 . The inner surface  234  includes a cap portion  236  formed on a circle  238  with a center  240  and a toroidal portion  242 . The toroidal portion  242  is shown in cross-section as formed on two circles  244  and  246  having centers  248  and  250 , respectively. The center  238  is located above the axis  252  defined by the centers  248  and  250 . 
         [0052]    In this embodiment, the toroidal portion  242  is formed on the apple or outer surface of the torus defined by the rotation of the circles  244  and  246 . Accordingly, even if each of the circles  238 ,  244  and  246  have the same diameter, the diameter of the cup  230  in the toroidal portion  242  will be greater than the diameter in the cap portion  236 . Additionally, the cap portion  236  is centered at a location  254  which is offset from the apex  256  or deepest portion of the cup  230 . Thus, the cap portion  236  is centered on the normal contact area between a ball and the cup  230  when the ball and cup  230  are implanted. Accordingly, most of the contact between a ball and the cup  236  when implanted will occur within the cap portion  236 . 
         [0053]    Although the present invention has been described with respect to certain preferred embodiments, it will be appreciated by those of skill in the art that other implementations and adaptations are possible. Moreover, there are advantages to individual advancements described herein that may be obtained without incorporating other aspects described above. Therefore, the spirit and scope of the appended claims should not be limited to the description of the preferred embodiments contained herein.