Abstract:
A method of determining a center of curvature of the spherical outer surface of an object using a computer system is provided. The method includes defining at least one contact region on the spherical outer surface in a plane substantially tangential to a circumference thereof and a first reference axis normal to said plane. Spatial coordinates of at least one of a first and a second geometric parameter are determined, the first geometric parameter including at least two points located on the spherical outer surface and the second geometric parameter including a second reference axis normal to the spherical outer surface. The center of curvature of the spherical outer surface is then calculated using the first reference axis and at least one of the first and second geometric parameters. An associated system and calibration device is also provided.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application claims priority on U.S. Provisional Patent Application Ser. No. 60/682,852 filed May 20, 2005, the entire contents of which is incorporated herein by reference. 

   TECHNICAL FIELD 
   The invention relates generally to a calibrating device for use in conjunction with a computer system, and more particularly to an improved method and apparatus for determining the center point of a spherical object. 
   BACKGROUND OF THE ART 
   Proper calibration of tools, bone structures, implants and other components used in computer assisted surgery (CAS) procedures is vital. 
   In particular, determining the center of rotation (COR) of a spherically shaped object for use during a CAS surgery is a fairly common, but nonetheless important procedure. For example, during a total hip replacement (THR) surgery, determining the COR of the partially spherical femoral head and/or the corresponding cup-shaped acetabulum within which it is received, is typically required in order to ensure proper relative positioning of the respective femoral head and acetabular cup implants. 
   At least two known methods are currently employed for determining the COR of such a spherical object using a CAS system. For simplicity, these methods will be briefly described with reference to calculating the center of rotation of a femoral head. The first method involves rotating the femur between several positions, and capturing position and orientation information at each of the positions using the CAS system, from which the CAS system is able to determine the center point about which the femur is rotating by extrapolating lines from each of the captured positions and determining an intersection point thereof. More specifically, the femur is first maintained in a stable position such that the CAS system is able to register its position in space. The femur is then rotated to another position, and the position capturing procedure is repeated. This is repeated in order to permit the CAS system to identify and capture at least three distinct positions of the femur, from which the CAS system can define and calculate an imaginary cone having a tip coincident with the COR of the femoral head about which the femur was rotated between measured positions. Alternately, another method involves gradually rotating the femur in space during which time the CAS system automatically collects position and orientation information of the femur at predetermined regular intervals. These methods are simple, however have certain drawbacks. Particularly, if only three points are captured, the error margin remains relatively high. However, capturing a plurality of points, while improving accuracy, can be overly time consuming. Additionally, if the surgeon or user is not careful to displace the limb through its full rotational envelope and the points are captured too close to each other (i.e. linearly or quasi-linearly), then the resulting cone calculated by the CAS system will be skewed and not representative of the true COR of the limb. Further, another disadvantage of this method is the fact that it requires the surgeon to hold and rotate the limb of the patient through a relatively large region above the operating table, which in certain cases can at the very least be quite awkward. Other possibility for errors exists with these methods. For example, any displacement of the femoral head within the acetabulum as it is rotated therewithin, additionally adds error to the calculation of the tip of the cone and therefore the calculated center of rotation can differ from the true center of rotation of the limb by a significant amount. 
   A second method which as been employed to determine the COR of a spherical object using a CAS system involves using a tracked pointer or digitizer to collect a number of points on the spherical surfaces itself. Given a sufficient number of points on the surface, the CAS system is then able to reconstruct or digitize the surface, from which it can calculate an estimated center of rotation thereof. This method, however, requires relatively complex calculations on the part of the CAS system and further can result in imprecise results caused by an imperfectly digitized surface. This method also requires that a plurality of points on the surface of the spherical surfaces be digitized in order to provide accurate results. 
   Accordingly, there remains nonetheless a need for an improved device and method for determining the center of rotation of a spherical object using a CAS system. 
   SUMMARY OF THE INVENTION 
   It is therefore an object of this invention to provide an improved method and apparatus for determining the center point of a special object using a computer system. 
   In one aspect, the present invention provides a method of determining at least a center of curvature of a spherical outer surface of an object, the method comprising the steps of: defining at least one contact region on said spherical outer surface in a plane substantially tangential to a circumference thereof and a first reference axis normal to said plane; determining spatial coordinates of at least one of a first and a second geometric parameter, the first geometric parameter including at least two points located on said spherical outer surface and the second geometric parameter including a second reference axis normal to said spherical outer surface; and calculating the center of curvature of said spherical outer surface using said first reference axis and at least one of said first and second geometric parameters. 
   In another aspect, the present invention provides a method of determining a center of rotation of an object using a computer system, the object having an at least partially spherical outer surface and a diameter, the method comprising: providing a calibration device having a tracking member thereon which is in communication with the computer system, the calibration device including a tubular tip portion having a remote end defining an annulus and a central longitudinal axis, said annulus having a known diameter and being located a known distance from said tracking member; locating and tracking the calibration device in three dimensional space using the computer system; abutting said annulus against said spherical outer surface of said object to define an annular contact region therebetween and a first reference axis defined by said central longitudinal axis, said annular contact region defining a plane tangential to a circumference of the spherical outer surface and normal to said first reference axis; determining the spatial coordinates of at least two points on said spherical outer surface within said annular contact region using the computer system; and calculating a center of rotation of said object using at least said two points and said first reference axis. 
   In another aspect, the present invention provides a system for determining a center of curvature of a spherical outer surface of an object, the system comprising: a computer system operable to locate and track in three dimensional space at least one tracking member communicable with the computer system; a calibration device having a tip portion defining a longitudinal axis and having one of said tracker members engaged thereto, said tip portion defining an object contacting element at a remote end thereof, said object contacting element being located a known distance from said tracking member such that the position and orientation of the object contacting element in three dimensional space is determined by the computer system; and a calculation module for calculating the center of curvature of the spherical outer surface using at least the determined position and orientation of the longitudinal axis and the object contacting element, the object contacting element being adapted to abut against the outer spherical surface in at least three points and such that said longitudinal axis is normal to said spherical outer surface. 
   There is also provided, in accordance with another aspect of the present invention, a calibration device for determining a center of curvature of a spherical outer surface of an object using a computer system, the calibration device comprising: a body having a tip portion defining at least one object contacting element at a remote end thereof, the tip portion defining a central longitudinal axis therethrough, the object contacting element of said tip portion defining a contact plane substantially orthogonal to said longitudinal axis when abutted against said spherical outer surface; a tracking member engaged to said body, the tracking member being locatable and trackable in three dimensional space by the computer system; and wherein the object contacting element and the central longitudinal axis of the tip portion are disposed in known locations relative to said tracking member to permit their position and orientation in three dimensional space to be determined by the computer system, such that spatial coordinates of at least two points on the spherical outer surface of the object and a reference axis normal to the spherical outer surface are determinable by the computer system when the object contacting element is abutted thereagainst. 
   Further details of these and other aspects of the present invention will be apparent from the detailed description and figures included below. 

   
     DESCRIPTION OF THE DRAWINGS 
     Reference is now made to the accompanying figures depicting aspects of the present invention, in which: 
       FIG. 1  is schematic perspective view of a calibration device, for use with a CAS system, in accordance with one embodiment of the present invention; 
       FIG. 2  is a schematic perspective view of the calibration device of  FIG. 1  and the CAS system; 
       FIG. 3   a  is a partial cross-sectional view of a tip of the calibration device of  FIG. 1 , shown abutted against a convex outer surface of a spherical object; 
       FIG. 3   b  is a partial cross-sectional view of a tip of the calibration device of  FIG. 1 , shown abutted against a concave inner surface of a spherical object; 
       FIG. 4   a  is a schematic view of a tip portion of the calibration device of  FIG. 1  shown for demonstration purposes simultaneously in two locations on a spherical object, in accordance with an alternate method of the present invention; 
       FIG. 4   b  is a partial cross-sectional view of the calibration device and spherical object of  FIG. 4   a;    
       FIG. 5  is a side elevation view of a calibration device in accordance with an alternate embodiment of the present invention; and 
       FIG. 6  is a side elevation view of a calibration device in accordance with another embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Computer assisted surgery (CAS) systems are capable of real time location and tracking of a plurality of discrete objects in a surgical field. A variety of systems are used, however most require the patient bone elements to be identified and registered to pre-operatively taken anatomical scans or intra-operatively taken images of the same bone elements. Therefore, by using trackable members which can be located and tracked in space by the CAS system, the surgeon is able to use the CAS system as an aid when conducting procedures on the identified bone element. In order to ensure accuracy and repeatability, all tracked tools, prosthetic implants, bone elements and or other surgical objects employed in conjunction with such a CAS system must therefore be precisely calibrated. Although the embodiments described below all relate to such as CAS system, it is to be understood that the calibration device and method of the present invention may be employed with a computer system used in alternate fields other than surgical ones. For example, other applications may benefit from being able to use a computer system capable of monitoring, in real time, the position and movement of objects which are identifiable by the computer system. For example, in various manufacturing industries, tracking members may be fixed to displacing machines, tools, workpieces and/or other objects used in the manufacturing process, such that the positions of these objects may be located and tracked by a corresponding computer system. Automobile manufacturing may also employ such a computer system to identify, locate and track objects during the production process. In any of such alternate applications, a spherical object which might be employed would need to be properly calibrated, particularly in order to determine the exact center thereof. As such, the calibration device, system and method of the present invention, although preferably used in surgical applications, can similarly be employed in environments such as those described above. 
   The calibration device  10  ( FIG. 1 ) of the present invention is particularly adapted to be used with a computer assisted surgery (CAS) system  90 , as schematically depicted in  FIG. 2 , in order to calibrate an at least partially spherical object. 
   The term “spherical object” as used herein is defined as an object having at least a portion thereof which is at least partially spherically shaped and therefore has either a concave and/or convex spherical surface and a center of curvature relative to the spherical surface. For example, such a spherical object can include a hollow hemispherical cup, a spherical ball, the head of a femur (whether natural bone or prosthetic implant), an acetabular cup (whether natural bone or prosthetic implant), and the like. Such objects may include circular, hemispherical, cup-shaped and other similar objects which comprise at least a curved or spherical outer surface having a center about which this surface is rotatable. The term “spherical object” used throughout is intended to include all such objects. These may include either portion of a ball and socket joint, whether bone or prosthetic implant. For example, the femoral head and/or the acetabulum within which it is received for rotation therewithin. Although both concave and convex spherical objects  40  ( FIG. 3   a ),  50  ( FIG. 3   b ) are schematically depicted herein as a perfect sphere and cup respectively, it is to be understood that these represent other spherical or at least partially spherical objects as identified above. In the embodiment described in detail herein, the spherical object is used in conjunction with a CAS system which permits the center thereof, and therefore the center of rotation of the object in three dimensional space, to be determined. The term “center of rotation” as used herein is intended to include a center of curvature of the spherical surface of the object, whether or not rotation of the object itself, or a mating/correspond element, occurs about this point. 
   Referring now to  FIG. 1 , the calibration device  10  is preferably a relatively small, hand held CAS calibrator which permits the instant determination of a spherical object&#39;s center of rotation. The calibration device  10  comprises generally a main body  12  and at least a tip portion  14  fastened to the main body  12  and projecting therefrom. The tip portion  14  may be either permanently fixed to the main body  12 , or alternately detachable therefrom such that once the tip portion  14  has been used on a patient, it may be either disposed of and replaced with a new tip portion or cleaned and replaced for subsequent use. It is to be understood that the main body portion  12  may be relatively larger than the tip portion  14 , or vice versa as depicted in  FIG. 1 . In one embodiment, the tip portion  14  is formed of a hollow cylindrical tube  16 , the remote end  18  of which may define an annulus  20 . Although the tip portion  14  is depicted in  FIG. 1  as being a significant length relative to the main body portion  12 , it is to be understood that the main body  12  can be much larger, longer, etc. than the tip portion  14 , wherein the tip portion  14  is relatively smaller tubular tip at one end thereof. Further, although the tip portion  14  has an object contacting element at its remote end that is tubular in the first embodiment described herein, alternate configurations of this remote tip end are similarly possible, provided they comprise an object contacting element at the tip thereof for abutment against a spherical surface of the object to be calibrated. Such alternate tip portion configurations may include, for example, a solid cylinder with a concave tip, a ring spaced from but fastened to the main body of the calibration device, and a tubular tip element without a full annulus at the remote end thereof. Two other alternate embodiments of the tip portion of the calibration device of the present invention are also described in more detail below with reference to  FIGS. 5 and 6 . 
   A tracking member  13 , which is located and tracked in three dimensional space by the CAS system  90  (as depicted in  FIG. 2 ) used in conjunction with the calibration device  10 , is fixed to the main body  12  of the calibration device  10  by a projecting support rod  21 . The tracking member  13  generally comprises a tracker head element  15 , preferably having three detectable element (i.e. CAS identification markers)  19  engaged, preferably removably, thereto. Each identification marker or detectable element  19  is identifiable by the CAS system employed, such that the three detectable elements  19  identify the location and orientation of the tracking member  13 , and therefore the rest of the calibration device to which the tracking member  13  is fixed, in space. The detectable elements  19  are preferably optically detectable spheres, preferably coated with a retro-reflective layer, which are visible by, for example, at least two cameras and/or infrared sensors  92  of the optically-based CAS system  90 . The cameras/sensors  92  of the CAS system  90  can therefore detect the position of each optically detectable sphere  19  illuminated by infrared light. Each detectable marker element  19  can alternately be any other type of position indicator such as a light emitting diode (LED) or a detectable electromagnetic indicator, provided each can be detected by the type of sensor used by the specific CAS system. Although the present calibration device  10  is most preferably adapted for use with an optically based CAS system  90 , one skilled in the art will appreciate that in addition to the optical system mentioned above, other types of CAS tracking systems can equivalently be used, such as, for example, those which use electromagnetic, ultrasound or laser as a means for position identification. In such cases, it is to be understood that the detectable marker elements  19  will be such that they are able to indicate to, and/or be detected by, the particular CAS system used. 
   The annulus  20  defined by the remote tip end  18  of the tip portion  14  depicted is adapted to be abutted directly against an outer spherical surface of the spherical object for which the center is to be determined, as described in further detail below. As the tip portion is fixed in place to the main body  12  of the calibration device  10 , the annulus  20  at the remote tip  18  of the tip portion  14  is therefore disposed in a known location relative to the tracking member  13  fixed to the main body  12 . The inside and outside diameters of the tube  16  of the tip portion  14  are also known, as is the location of the central longitudinal axis  26  thereof. Although the annulus  20  depicted has slightly rounded edges, the tip  18  can also define an annulus which has non-rounded edges (i.e. wherein the outer surface of the tube  16  and the flat end surface of the annulus  20  meet at right angles). 
   Although preferably the remote tip end  18  and the annulus  20  formed thereon is of a fixed diameter and is fixed in place and immovable relative to the main body  12  of the calibration device  10 , it remains possible that the remote tip end  18  is displaceable, such as to pivot relative to the main body  12  via an articulated joint therebetween or alternately to expand and/or contract such that the diameter of the annulus  20  is variable in order to be able to accept spherical objects of varying sizes for example. However, if the remote tip end  18  is displaceable relative to the tracking member  13  or has a variable diameter, the relative position between the tracking member  13  and the remote tip end  18 , and therefore the annulus  20  formed thereby, as well as the adjusted diameter of the annulus  20  must be able to be determined by the CAS system  90  or identified thereto manually by a user. 
   The method of determining the center of rotation of a spherical object using the calibration device  10  will now be described with reference to  FIGS. 3   a - 3   b.  The use of the calibration device  10  with the CAS system  90  ( FIG. 2 ) permits the determination of the center of rotation of the spherical object, whether the diameter of the spherical surface of the object is known or unknown. 
   A first method is used when the diameter of the spherical surface of the object is known, or at least predetermined prior to calibrating the spherical object using the calibration device  10  and the CAS system  90 . As depicted in  FIGS. 3   a - 3   b,  the remote end  18  of the tube  16  which comprises the tip portion  14  of the calibration device  10  is abutted directly against the spherical surface of the spherical object to be calibrated, such that the annulus  20  defined at the remote tip end  18  mates with the spherical object about an annular contact region therebetween. In  FIG. 3   a,  the spherical object  40  is a convex sphere (representing for example a femoral head) which comprises an outer spherical surface  42  against which the annulus  20  at the remote end  18  of the tubular tip portion is directly abutted. In  FIG. 3   b,  the spherical object  50  is a concave cup (representing for example an acetabular socket) defining an inner concave spherical surface  52  therewithin, against which the remote end  18  of the tubular tip portion  14  is abutted to ensure an annular contact region therebetween. It is to be understood that when the spherical object being calibrated is a bone element of a patient, such as a femoral head or acetabulum for example, this bone element is separately tracked by the CAS using a bone tracking member fastened thereto (but not shown). 
   When the remote end  18  of the tubular tip portion  14 , the location of which is known by the CAS system, is placed against one of the spherical surfaces  42 / 52 , the annulus  20  at the tip end  18  in contact with the spherical surface  42 / 52  defines an imaginary plane  24  which is tangential to the circumference of the spherical surface  42 / 52  and substantially orthogonal to the longitudinal axis  26  of the tube  16  which at least partially comprises the tip portion  14 . At least one contact point  35 , between the spherical surface  42 / 52  and the annular tip  20  of the calibration device within the annular contact region therebetween, is captured be identified by the CAS system in a single reading. As the diameter of the spherical object  40 / 50  is known, the CAS system is able to determine the location of the center of rotation (COR)  39  of the spherical object, which lies along the known central longitudinal axis  26  at a distance away from the spherical surface  42 / 52  equal to the predetermined radius of the object. Thus, the exact location of the COR  39  is able to be determined by the CAS system. In an alternate means of calculating the COR, the CAS system is able to extrapolate an imaginary line  37  originating at each of at least one point  35  identified on the surface  42 / 52  and having a length equal to the known radius (i.e. half the known diameter) of the spherical surface  42 / 52 . The lines  37  intersect one another and the longitudinal axis  26  of the tubular tip portion  14  at a single point  39 . This intersection point  39  defines the COR of the spherical object being calibrated. The CAS system is thus able to determine the location in space of this COR point  39  of the spherical object. 
   Accordingly, the calibration device  10  may be used with the CAS system  90  in order to simply and quickly determine the COR of almost any spherical object (whether concave or convex), by merely abutting the end  18  of the tip portion  14  once (i.e. for a single reading) against the spherical surface, and acquiring points using the CAS system. Further, due to the annular shape of the tubular tip portion of the calibration device, when abutted against a spherical surface the center of rotation of the surface is self-centered in alignment with the known longitudinal axis  26  of the tubular portion  16  of the device. 
   A second method in accordance with another embodiment of the present invention, as depicted in  FIG. 4   a - 4   b,  is used when the diameter of the spherical object being calibrated is unknown. The same calibration device  10  is employed, and the method is similar to that described above when the diameter of the spherical object is known, this second method however involves an additional step. Namely, once the annular remote end  18  of the tubular tip portion  14  has been abutted a first time against the spherical outer surface  42  of the convex spherical object  40  as described above (i.e. in a first position) in order to capture points on the spherical surface in a first reading, the calibration device  10  is then displaced by the user and abutted a second time in a different position (i.e. a second position) against another region of the spherical surface  42  for a second reading by the CAS system. (The tubular tip portion  14  of the calibration device  10  is depicted for ease of explanation in both the first and second positions in  FIG. 4   a - 4   b,  however only one calibration device is used for both readings.) In each position of the calibration device  10 , the CAS system determines the positional information of the annular tip  18  thereof, and therefore points in the annular contact region on the outer surface  42 . Thus, at each of the first and second positions, a reference line  45  is defined which is collinear with the longitudinal axis  26  of the tubular tip portion  14  of the calibration device  10 . Each of these two reference lines  45  interests in space at a single point  39  which defines the center of rotation of the spherical object. The CAS system can therefore calculate the diameter of the spherical object being calibrated, using trigonometry as the location of the abutment points  35  between the tip  18  and the surface  42  and the determined center of rotation  39 . 
   Therefore, the calibration device, when used in accordance with the methods described above  10  and the CAS system  90 , permits the quick and easy determination of the center of rotation of a spherical object for subsequent use in a computer assisted surgical procedure. 
   Referring to  FIGS. 5 and 6 , two alternate embodiments of the tip portion of the calibration device of the present invention are depicted. In  FIG. 5 , the calibration device  110  comprises a main body  112 , defining a handle portion, and having a tracking member  13  fastened thereto. The tip portion  114  of the calibration device  110  comprises an object contacting element that includes at least three projecting individual fingers or tip ends  118 , which are preferably evenly angularly spaced apart. Each tip end  118  is adapted to abut the spherical object  40  at distinct points on the spherical surface  42  thereof. Therefore, much as the annulus  20  of the tip portion  14 , the individual tip ends  118  abut the spherical surface within an annular region therearound, however only at three discrete points. The position of the these three points abutted by the tip ends  118  is captured by the CAS system in a single reading, in order to determine the location of the center of the spherical object (when the diameter thereof is known). As described above, when the diameter is unknown, the tip ends  118  must be displace such that a second reading may be taken. In  FIG. 6 , the calibration device  210  comprises a main body  212 , which may define a handle portion, to which is fastened the tracking member  13 . The tip portion  214  of the calibration device  210  comprises an object contacting element having a structure  216  defining at least three notches  217  at the remote end  218  thereof. (Only one such notch  217  is visible in  FIG. 5 .) These notches  217  act much as the fingers or tip ends  118 , wherein the edges at the remote end tips  218  abutting the outer spherical surface  42  of the spherical object  40 . The tip portions  114  and  214  act and are operable much as per the tip portion  14  described above, in order to determine the center of the spherical object being calibrated by the calibration device. 
   The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without department from the scope of the invention disclosed. Still other modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure, and such modifications are intended to fall within the appended claims.