Patent Publication Number: US-8968320-B2

Title: System and method for manufacturing arthroplasty jigs

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation application of U.S. application Ser. No. 11/959,344 filed Dec. 18, 2007 and entitled System and Method for Manufacturing Arthroplasty Jigs. The &#39;344 application is incorporated by reference herein for all that it discloses or teaches. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to systems and methods for manufacturing customized arthroplasty cutting jigs. More specifically, the present invention relates to automated systems and methods manufacturing such jigs. 
     BACKGROUND OF THE INVENTION 
     Over time and through repeated use, bones and joints can become damaged or worn. For example, repetitive strain on bones and joints (e.g., through athletic activity), traumatic events, and certain diseases (e.g., arthritis) can cause cartilage in joint areas, which normally provides a cushioning effect, to wear down. When the cartilage wears down, fluid can accumulate in the joint areas, resulting in pain, stiffness, and decreased mobility. 
     Arthroplasty procedures can be used to repair damaged joints. During a typical arthroplasty procedure, an arthritic or otherwise dysfunctional joint can be remodeled or realigned, or an implant can be implanted into the damaged region. Arthroplasty procedures may take place in any of a number of different regions of the body, such as a knee, a hip, a shoulder, or an elbow. 
     One type of arthroplasty procedure is a total knee arthroplasty (“TKA”), in which a damaged knee joint is replaced with prosthetic implants. The knee joint may have been damaged by, for example, arthritis (e.g., severe osteoarthritis or degenerative arthritis), trauma, or a rare destructive joint disease. During a TKA procedure, a damaged portion in the distal region of the femur may be removed and replaced with a metal shell, and a damaged portion in the proximal region of the tibia may be removed and replaced with a channeled piece of plastic having a metal stem. In some TKA procedures, a plastic button may also be added under the surface of the patella, depending on the condition of the patella. 
     Implants that are implanted into a damaged region may provide support and structure to the damaged region, and may help to restore the damaged region, thereby enhancing its functionality. Prior to implantation of an implant in a damaged region, the damaged region may be prepared to receive the implant. For example, in a knee arthroplasty procedure, one or more of the bones in the knee area, such as the femur and/or the tibia, may be treated (e.g., cut, drilled, reamed, and/or resurfaced) to provide one or more surfaces that can align with the implant and thereby accommodate the implant. 
     Accuracy in implant alignment is an important factor to the success of a TKA procedure. A one- to two-millimeter translational misalignment, or a one- to two-degree rotational misalignment, may result in imbalanced ligaments, and may thereby significantly affect the outcome of the TKA procedure. For example, implant misalignment may result in intolerable post-surgery pain, and also may prevent the patient from having full leg extension and stable leg flexion. 
     To achieve accurate implant alignment, prior to treating (e.g., cutting, drilling, reaming, and/or resurfacing) any regions of a bone, it is important to correctly determine the location at which the treatment will take place and how the treatment will be oriented. In some methods, an arthroplasty jig may be used to accurately position and orient a finishing instrument, such as a cutting, drilling, reaming, or resurfacing instrument on the regions of the bone. The arthroplasty jig may, for example, include one or more apertures and/or slots that are configured to accept such an instrument. 
     A system and method has been developed for producing customized arthroplasty jigs configured to allow a surgeon to accurately and quickly perform an arthroplasty procedure that restores the pre-deterioration alignment of the joint, thereby improving the success rate of such procedures. Specifically, the customized arthroplasty jigs are indexed such that they matingly receive the regions of the bone to be subjected to a treatment (e.g., cutting, drilling, reaming, and/or resurfacing). The customized arthroplasty jigs are also indexed to provide the proper location and orientation of the treatment relative to the regions of the bone. The indexing aspect of the customized arthroplasty jigs allows the treatment of the bone regions to be done quickly and with a high degree of accuracy that will allow the implants to restore the patient&#39;s joint to a generally pre-deteriorated state. However, the system and method for generating the customized jigs often relies on a human to “eyeball” bone models on a computer screen to determine configurations needed for the generation of the customized jigs. This is “eyeballing” or manual manipulation of the bone modes on the computer screen is inefficient and unnecessarily raises the time, manpower and costs associated with producing the customized arthroplasty jigs. Furthermore, a less manual approach may improve the accuracy of the resulting jigs. 
     There is a need in the art for a system and method for reducing the labor associated with generating customized arthroplasty jigs. There is also a need in the art for a system and method for increasing the accuracy of customized arthroplasty jigs. 
     SUMMARY 
     Disclosed herein is a method of manufacturing an arthroplasty jig. In one embodiment, the method includes: generating two-dimensional images of at least a portion of a bone forming a joint; generating a first three-dimensional computer model of the at least a portion of the bone from the two-dimensional images; generating a second three-dimensional computer model of the at least a portion of the bone from the two-dimensional images; causing the first and second three-dimensional computer models to have in common a reference position, wherein the reference position includes at least one of a location and an orientation relative to an origin; generating a first type of data with the first three-dimensional computer model; generating a second type of data with the second three-dimensional computer model; employing the reference position to integrate the first and second types of data into an integrated jig data; using the integrated jig data at a manufacturing device to manufacture the arthroplasty jig. 
     Disclosed herein is a method of manufacturing an arthroplasty jig. In one embodiment, the method includes: generating two-dimensional images of at least a portion of a bone forming a joint; extending an open-loop contour line along an arthroplasty target region in at least some of the two-dimensional images; generating a three-dimensional computer model of the arthroplasty target region from the open-loop contour lines; generating from the three-dimensional computer model surface contour data pertaining to the arthroplasty target area; and using the surface contour data at a manufacturing machine to manufacture the arthroplasty jig. 
     Disclosed herein is a method of manufacturing an arthroplasty jig. In one embodiment, the method includes: determining from an image at least one dimension associated with a portion of a bone; comparing the at least one dimension to dimensions of at least two candidate jig blank sizes; selecting the smallest of the jig blank sizes that is sufficiently large to accommodate the at least one dimension; providing a jig blank of the selected size to a manufacturing machine; and manufacturing the arthroplasty jig from the jig blank. 
     Disclosed herein are arthroplasty jigs manufactured according to any of the aforementioned methods of manufacture. In some embodiments, the arthroplasty jigs may be indexed to matingly receive arthroplasty target regions of a joint bone. The arthroplasty jigs may also be indexed to orient saw cut slots and drill hole guides such that when the arthroplasty target regions are matingly received by the arthroplasty jig, the saw cuts and drill holes administered to the arthroplasty target region via the saw cut slots and drill hole guides will facilitate arthroplasty implants generally restoring the joint to a predegenerated state. 
     Disclosed herein is a method of computer generating a three-dimensional surface model of an arthroplasty target region of a bone forming a joint. In one embodiment, the method includes: generating two-dimensional images of at least a portion of the bone; generating an open-loop contour line along the arthroplasty target region in at least some of the two-dimensional images; and generating the three-dimensional model of the arthroplasty target region from the open-loop contour lines. 
     Disclosed herein is a method of generating a three-dimensional arthroplasty jig computer model. In one embodiment, the method includes: comparing a dimension of at least a portion of a bone of a joint to candidate jig blank sizes; and selecting from the candidate jig blank sizes a smallest jig blank size able to accommodate the dimensions of the at least a portion of the bone. 
     Disclosed herein is a method of generating a three-dimensional arthroplasty jig computer model. In one embodiment, the method includes: forming an interior three-dimensional surface model representing an arthroplasty target region of at least a portion of a bone; forming an exterior three-dimensional surface model representing an exterior surface of a jig blank; and combining the interior surface model and exterior surface model to respectively form the interior surface and exterior surface of the three-dimensional arthroplasty jig computer model. 
     Disclosed herein is a method of generating a production file associated with the manufacture of arthroplasty jigs. The method includes: generating first data associated a surface contour of an arthroplasty target region of a joint bone; generating second data associated with at least one of a saw cut and a drill hole to be administered to the arthroplasty target region during an arthroplasty procedure; and integrating first and second data, wherein a positional relationship of first data relative to an origin and a positional relationship of second data relative to the origin are coordinated with each other to be generally identical during the respective generations of first and second data. 
     While multiple embodiments are disclosed, still other embodiments of the present invention will become apparent to those skilled in the art from the following detailed description, which shows and describes illustrative embodiments of the invention. As will be realized, the invention is capable of modifications in various aspects, all without departing from the spirit and scope of the present invention. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not restrictive. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a schematic diagram of a system for employing the automated jig production method disclosed herein. 
         FIGS. 1B-1E  are flow chart diagrams outlining the jig production method disclosed herein. 
         FIGS. 1F and 1G  are, respectively, bottom and top perspective views of an example customized arthroplasty femur jig. 
         FIGS. 1H and 1I  are, respectively, bottom and top perspective views of an example customized arthroplasty tibia jig. 
         FIG. 2A  is an anterior-posterior image slice of the damaged lower or knee joint end of the patient&#39;s femur, wherein the image slice includes an open-loop contour line segment corresponding to the targeted region of the damaged lower end. 
         FIG. 2B  is a plurality of image slices with their respective open-loop contour line segments, the open-loop contour line segments being accumulated to generate the 3D model of the targeted region. 
         FIG. 2C  is a 3D model of the targeted region of the damaged lower end as generated using the open-loop contour line segments depicted in  FIG. 2B . 
         FIG. 2D  is an anterior-posterior image slice of the damaged lower or knee joint end of the patient&#39;s femur, wherein the image slice includes a closed-loop contour line corresponding to the femur lower end, including the targeted region. 
         FIG. 2E  is a plurality of image slices with their respective closed-loop contour line segments, the closed-loop contour lines being accumulated to generate the 3D model of the femur lower end, including the targeted region. 
         FIG. 2F  is a 3D model of the femur lower end, including the targeted region, as generated using the closed-loop contour lines depicted in  FIG. 2B . 
         FIG. 2G  is a flow chart illustrating an overview of the method of producing a femur jig. 
         FIG. 3A  is a top perspective view of a left femoral cutting jig blank having predetermined dimensions. 
         FIG. 3B  is a bottom perspective view of the jig blank depicted in  FIG. 3A . 
         FIG. 3C  is plan view of an exterior side or portion of the jig blank depicted in  FIG. 3A . 
         FIG. 4A  is a plurality of available sizes of left femur jig blanks, each depicted in the same view as shown in  FIG. 3C . 
         FIG. 4B  is a plurality of available sizes of right femur jig blanks, each depicted in the same view as shown in  FIG. 3C . 
         FIG. 5  is an axial view of the 3D surface model or arthritic model of the patient&#39;s left femur as viewed in a direction extending distal to proximal. 
         FIG. 6  depicts the selected model jig blank of  FIG. 3C  superimposed on the model femur lower end of  FIG. 5 . 
         FIG. 7A  is an example scatter plot for selecting from a plurality of candidate jig blanks sizes a jig blank size appropriate for the lower end of the patient&#39;s femur. 
         FIG. 7B  is a flow diagram illustrating an embodiment of a process of selecting an appropriately sized jig blank. 
         FIG. 8A  is an exterior perspective view of a femur jig blank exterior surface model. 
         FIG. 8B  is an interior perspective view if the femur jig blank exterior surface model of  FIG. 8A . 
         FIG. 9A  is a perspective view of the extracted jig blank exterior surface model being combined with the extracted femur surface model. 
         FIG. 9B  is a perspective view of the extracted jig blank exterior surface model combined with the extracted femur surface model. 
         FIG. 9C  is a cross section of the combined jig blank exterior surface model and the femur surface model as taken along section line  9 C- 9 C in  FIG. 9B . 
         FIG. 10A  is an exterior perspective view of the resulting femur jig model. 
         FIG. 10B  is an interior perspective view of the femur jig model of  FIG. 10A . 
         FIG. 11  illustrates a perspective view of the integrated jig model mating with the “arthritic model”. 
         FIG. 12A  is an anterior-posterior image slice of the damaged upper or knee joint end of the patient&#39;s tibia, wherein the image slice includes an open-loop contour line segment corresponding to the target area of the damaged upper end. 
         FIG. 12B  is a plurality of image slices with their respective open-loop contour line segments, the open-loop contour line segments being accumulated to generate the 3D model of the target area. 
         FIG. 12C  is a 3D model of the target area of the damaged upper end as generated using the open-loop contour line segments depicted in  FIG. 12B . 
         FIG. 13A  is a top perspective view of a right tibia cutting jig blank having predetermined dimensions. 
         FIG. 13B  is a bottom perspective view of the jig blank depicted in  FIG. 13A . 
         FIG. 13C  is plan view of an exterior side or portion of the jig blank  50 BR depicted in  FIG. 13A . 
         FIG. 14  is a plurality of available sizes of right tibia jig blanks, each depicted in the same view as shown in  FIG. 13C . 
         FIG. 15  is an axial view of the 3D surface model or arthritic model of the patient&#39;s right tibia as viewed in a direction extending proximal to distal. 
         FIG. 16  depicts the selected model jig blank of  FIG. 13C  superimposed on the model tibia upper end of  FIG. 15 . 
         FIG. 17A  is an example scatter plot for selecting from a plurality of candidate jig blanks sizes a jig blank size appropriate for the upper end of the patient&#39;s tibia. 
         FIG. 17B  is a flow diagram illustrating an embodiment of a process of selecting an appropriately sized jig blank. 
         FIG. 18A  is an exterior perspective view of a tibia jig blank exterior surface model. 
         FIG. 18B  is an interior perspective view if the tibia jig blank exterior surface model of  FIG. 18A . 
         FIG. 19A  is a perspective view of the extracted jig blank exterior surface model being combined with the extracted tibia surface model. 
         FIGS. 19B-19D  are perspective views of the extracted jig blank exterior surface model combined with the extracted tibia surface model. 
         FIG. 20A  is an exterior perspective view of the resulting tibia jig model. 
         FIG. 20B  is an interior perspective view of the tibia jig model of  FIG. 20A . 
         FIG. 21  illustrates a perspective view of the integrated jig model mating with the “arthritic model”. 
     
    
    
     DETAILED DESCRIPTION 
     Disclosed herein are customized arthroplasty jigs  2  and systems  4  for, and methods of, producing such jigs  2 . The jigs  2  are customized to fit specific bone surfaces of specific patients. Depending on the embodiment and to a greater or lesser extent, the jigs  2  are automatically planned and generated and may be similar to those disclosed in these three U.S. patent applications: U.S. patent application Ser. No. 11/656,323 to Park et al., titled “Arthroplasty Devices and Related Methods” and filed Jan. 19, 2007; U.S. patent application Ser. No. 10/146,862 to Park et al., titled “Improved Total Joint Arthroplasty System” and filed May 15, 2002; and U.S. patent Ser. No. 11/642,385 to Park et al., titled “Arthroplasty Devices and Related Methods” and filed Dec. 19, 2006. The disclosures of these three U.S. patent applications are incorporated by reference in their entireties into this Detailed Description. 
     a. Overview of System and Method for Manufacturing Customized Arthroplasty Cutting Jigs 
     For an overview discussion of the systems  4  for, and methods of, producing the customized arthroplasty jigs  2 , reference is made to  FIGS. 1A-1E .  FIG. 1A  is a schematic diagram of a system  4  for employing the automated jig production method disclosed herein.  FIGS. 1B-1E  are flow chart diagrams outlining the jig production method disclosed herein. The following overview discussion can be broken down into three sections. 
     The first section, which is discussed with respect to  FIG. 1A  and [blocks  100 - 125 ] of  FIGS. 1B-1E , pertains to an example method of determining, in a three-dimensional (“3D”) computer model environment, saw cut and drill hole locations  30 ,  32  relative to 3D computer models that are termed restored bone models  28 . The resulting “saw cut and drill hole data”  44  is referenced to the restored bone models  28  to provide saw cuts and drill holes that will allow arthroplasty implants to restore the patient&#39;s joint to its pre-degenerated state. 
     The second section, which is discussed with respect to  FIG. 1A  and [blocks  100 - 105  and  130 - 145 ] of  FIGS. 1B-1E , pertains to an example method of importing into 3D computer generated jig models  38  3D computer generated surface models  40  of arthroplasty target areas  42  of 3D computer generated arthritic models  36  of the patient&#39;s joint bones. The resulting “jig data”  46  is used to produce a jig customized to matingly receive the arthroplasty target areas of the respective bones of the patient&#39;s joint. 
     The third section, which is discussed with respect to  FIG. 1A  and [blocks  150 - 165 ] of  FIG. 1E , pertains to a method of combining or integrating the “saw cut and drill hole data”  44  with the “jig data”  46  to result in “integrated jig data”  48 . The “integrated jig data”  48  is provided to the CNC machine  10  for the production of customized arthroplasty jigs  2  from jig blanks  50  provided to the CNC machine  10 . The resulting customized arthroplasty jigs  2  include saw cut slots and drill holes positioned in the jigs  2  such that when the jigs  2  matingly receive the arthroplasty target areas of the patient&#39;s bones, the cut slots and drill holes facilitate preparing the arthroplasty target areas in a manner that allows the arthroplasty joint implants to generally restore the patient&#39;s joint line to its pre-degenerated state. 
     As shown in  FIG. 1A , the system  4  includes a computer  6  having a CPU  7 , a monitor or screen  9  and an operator interface controls  11 . The computer  6  is linked to a medical imaging system  8 , such as a CT or MRI machine  8 , and a computer controlled machining system  10 , such as a CNC milling machine  10 . 
     As indicated in  FIG. 1A , a patient  12  has a joint  14  (e.g., a knee, elbow, ankle, wrist, hip, shoulder, skull/vertebrae or vertebrae/vertebrae interface, etc.) to be replaced. The patient  12  has the joint  14  scanned in the imaging machine  8 . The imaging machine  8  makes a plurality of scans of the joint  14 , wherein each scan pertains to a thin slice of the joint  14 . 
     As can be understood from  FIG. 1B , the plurality of scans is used to generate a plurality of two-dimensional (“2D”) images  16  of the joint  14  [block  100 ]. Where, for example, the joint  14  is a knee  14 , the 2D images will be of the femur  18  and tibia  20 . The imaging may be performed via CT or MRI. In one embodiment employing MRI, the imaging process may be as disclosed in U.S. patent application Ser. No. 11/946,002 to Park, which is entitled “Generating MRI Images Usable For The Creation Of 3D Bone Models Employed To Make Customized Arthroplasty Jigs,” was filed Nov. 27, 2007 and is incorporated by reference in its entirety into this Detailed Description. 
     As can be understood from  FIG. 1A , the 2D images are sent to the computer  6  for creating computer generated 3D models. As indicated in  FIG. 1B , in one embodiment, point P is identified in the 2D images  16  [block  105 ]. In one embodiment, as indicated in [block  105 ] of  FIG. 1A , point P may be at the approximate medial-lateral and anterior-posterior center of the patient&#39;s joint  14 . In other embodiments, point P may be at any other location in the 2D images  16 , including anywhere on, near or away from the bones  18 ,  20  or the joint  14  formed by the bones  18 ,  20 . 
     As described later in this overview, point P may be used to locate the computer generated 3D models  22 ,  28 ,  36  created from the 2D images  16  and to integrate information generated via the 3D models. Depending on the embodiment, point P, which serves as a position and/or orientation reference, may be a single point, two points, three points, a point plus a plane, a vector, etc., so long as the reference P can be used to position and/or orient the 3D models  22 ,  28 ,  36  generated via the 2D images  16 . 
     As shown in  FIG. 10 , the 2D images  16  are employed to create computer generated 3D bone-only (i.e., “bone models”)  22  of the bones  18 ,  20  forming the patient&#39;s joint  14  [block  110 ]. The bone models  22  are located such that point P is at coordinates (X 0-j , Y 0-j , Z 0-j ) relative to an origin (X 0 , Y 0 , Z 0 ) of an X-Y-Z axis [block  110 ]. The bone models  22  depict the bones  18 ,  20  in the present deteriorated condition with their respective degenerated joint surfaces  24 ,  26 , which may be a result of osteoarthritis, injury, a combination thereof, etc. 
     Computer programs for creating the 3D computer generated bone models  22  from the 2D images  16  include: Analyze from AnalyzeDirect, Inc., Overland Park, Kans.; Insight Toolkit, an open-source software available from the National Library of Medicine Insight Segmentation and Registration Toolkit (“ITK”), www.itk.org; 3D Slicer, an open-source software available from www.slicer.org; Mimics from Materialise, Ann Arbor, Mich.; and Paraview available at www.paraview.org. 
     As indicated in  FIG. 1C , the 3D computer generated bone models  22  are utilized to create 3D computer generated “restored bone models” or “planning bone models”  28  wherein the degenerated surfaces  24 ,  26  are modified or restored to approximately their respective conditions prior to degeneration [block  115 ]. Thus, the bones  18 ,  20  of the restored bone models  28  are reflected in approximately their condition prior to degeneration. The restored bone models  28  are located such that point P is at coordinates (X 0-j , Y 0-j , Z 0-j ) relative to the origin (X 0 , Y 0 , Z 0 ). Thus, the restored bone models  28  share the same orientation and positioning relative to the origin (X 0 , Y 0 , Z 0 ) as the bone models  22 . 
     In one embodiment, the restored bone models  28  are manually created from the bone models  22  by a person sitting in front of a computer  6  and visually observing the bone models  22  and their degenerated surfaces  24 ,  26  as 3D computer models on a computer screen  9 . The person visually observes the degenerated surfaces  24 ,  26  to determine how and to what extent the degenerated surfaces  24 ,  26  surfaces on the 3D computer bone models  22  need to be modified to restore them to their pre-degenerated condition. By interacting with the computer controls  11 , the person then manually manipulates the 3D degenerated surfaces  24 ,  26  via the 3D modeling computer program to restore the surfaces  24 ,  26  to a state the person believes to represent the pre-degenerated condition. The result of this manual restoration process is the computer generated 3D restored bone models  28 , wherein the surfaces  24 ′,  26 ′ are indicated in a non-degenerated state. 
     In one embodiment, the above-described bone restoration process is generally or completely automated. In other words, a computer program may analyze the bone models  22  and their degenerated surfaces  24 ,  26  to determine how and to what extent the degenerated surfaces  24 ,  26  surfaces on the 3D computer bone models  22  need to be modified to restore them to their pre-degenerated condition. The computer program then manipulates the 3D degenerated surfaces  24 ,  26  to restore the surfaces  24 ,  26  to a state intended to represent the pre-degenerated condition. The result of this automated restoration process is the computer generated 3D restored bone models  28 , wherein the surfaces  24 ′,  26 ′ are indicated in a non-degenerated state. 
     As depicted in  FIG. 10 , the restored bone models  28  are employed in a pre-operative planning (“POP”) procedure to determine saw cut locations  30  and drill hole locations  32  in the patient&#39;s bones that will allow the arthroplasty joint implants to generally restore the patient&#39;s joint line to it pre-degenerative alignment [block  120 ]. 
     In one embodiment, the POP procedure is a manual process, wherein computer generated 3D implant models  34  (e.g., femur and tibia implants in the context of the joint being a knee) and restored bone models  28  are manually manipulated relative to each other by a person sitting in front of a computer  6  and visually observing the implant models  34  and restored bone models  28  on the computer screen  9  and manipulating the models  28 ,  34  via the computer controls  11 . By superimposing the implant models  34  over the restored bone models  28 , or vice versa, the joint surfaces of the implant models  34  can be aligned or caused to correspond with the joint surfaces of the restored bone models  28 . By causing the joint surfaces of the models  28 ,  34  to so align, the implant models  34  are positioned relative to the restored bone models  28  such that the saw cut locations  30  and drill hole locations  32  can be determined relative to the restored bone models  28 . 
     In one embodiment, the POP process is generally or completely automated. For example, a computer program may manipulate computer generated 3D implant models  34  (e.g., femur and tibia implants in the context of the joint being a knee) and restored bone models or planning bone models  28  relative to each other to determine the saw cut and drill hole locations  30 ,  32  relative to the restored bone models  28 . The implant models  34  may be superimposed over the restored bone models  28 , or vice versa. In one embodiment, the implant models  34  are located at point P′ (X 0-k , Y 0-k , Z 0-k ) relative to the origin (X 0 , Y 0 , Z 0 ), and the restored bone models  28  are located at point P (X 0-j , Y 0-j , Z 0-j ). To cause the joint surfaces of the models  28 ,  34  to correspond, the computer program may move the restored bone models  28  from point P (X 0-j , Y 0-j , Z 0-j ) to point P′ (X 0-k , Y 0-k , Z 0-k ), or vice versa. Once the joint surfaces of the models  28 ,  34  are in close proximity, the joint surfaces of the implant models  34  may be shape-matched to align or correspond with the joint surfaces of the restored bone models  28 . By causing the joint surfaces of the models  28 ,  34  to so align, the implant models  34  are positioned relative to the restored bone models  28  such that the saw cut locations  30  and drill hole locations  32  can be determined relative to the restored bone models  28 . 
     As indicated in  FIG. 1E , in one embodiment, the data  44  regarding the saw cut and drill hole locations  30 ,  32  relative to point P′ (X 0-k , Y 0-k , Z 0-k ) is packaged or consolidated as the “saw cut and drill hole data”  44  [block  145 ]. The “saw cut and drill hole data”  44  is then used as discussed below with respect to [block  150 ] in  FIG. 1E . 
     As can be understood from  FIG. 1D , the 2D images  16  employed to generate the bone models  22  discussed above with respect to [block  110 ] of  FIG. 10  are also used to create computer generated 3D bone and cartilage models (i.e., “arthritic models”)  36  of the bones  18 , forming the patient&#39;s joint  14  [block  130 ]. Like the above-discussed bone models  22 , the arthritic models  36  are located such that point P is at coordinates (X 0-j , Y 0-j , Z 0-j ) relative to the origin (X 0 , Y 0 , Z 0 ) of the X-Y-Z axis [block  130 ]. Thus, the bone and arthritic models  22 ,  36  share the same location and orientation relative to the origin (X 0 , Y 0 , Z 0 ). This position/orientation relationship is generally maintained throughout the process discussed with respect to  FIGS. 1B-1E . Accordingly, movements relative to the origin (X 0 , Y 0 , Z 0 ) of the bone models  22  and the various descendants thereof (i.e., the restored bone models  28 , bone cut locations  30  and drill hole locations  32 ) are also applied to the arthritic models  36  and the various descendants thereof (i.e., the jig models  38 ). Maintaining the position/orientation relationship between the bone models  22  and arthritic models  36  and their respective descendants allows the “saw cut and drill hole data”  44  to be integrated into the “jig data”  46  to form the “integrated jig data”  48  employed by the CNC machine  10  to manufacture the customized arthroplasty jigs  2 . 
     Computer programs for creating the 3D computer generated arthritic models  36  from the 2D images  16  include: Analyze from AnalyzeDirect, Inc., Overland Park, Kans.; Insight Toolkit, an open-source software available from the National Library of Medicine Insight Segmentation and Registration Toolkit (“ITK”), www.itk.org; 3D Slicer, an open-source software available from www.slicer.org; Mimics from Materialise, Ann Arbor, Mich.; and Paraview available at www.paraview.org. 
     Similar to the bone models  22 , the arthritic models  36  depict the bones  18 ,  20  in the present deteriorated condition with their respective degenerated joint surfaces  24 ,  26 , which may be a result of osteoarthritis, injury, a combination thereof, etc. However, unlike the bone models  22 , the arthritic models  36  are not bone-only models, but include cartilage in addition to bone. Accordingly, the arthritic models  36  depict the arthroplasty target areas  42  generally as they will exist when the customized arthroplasty jigs  2  matingly receive the arthroplasty target areas  42  during the arthroplasty surgical procedure. 
     As indicated in  FIG. 1D  and already mentioned above, to coordinate the positions/orientations of the bone and arthritic models  36 ,  36  and their respective descendants, any movement of the restored bone models  28  from point P to point P′ is tracked to cause a generally identical displacement for the “arthritic models”  36  [block  135 ]. 
     As depicted in  FIG. 1D , computer generated 3D surface models  40  of the arthroplasty target areas  42  of the arthritic models  36  are imported into computer generated 3D arthroplasty jig models  38  [block  140 ]. Thus, the jig models  38  are configured or indexed to matingly receive the arthroplasty target areas  42  of the arthritic models  36 . Jigs  2  manufactured to match such jig models  38  will then matingly receive the arthroplasty target areas of the actual joint bones during the arthroplasty surgical procedure. 
     In one embodiment, the procedure for indexing the jig models  38  to the arthroplasty target areas  42  is a manual process. The 3D computer generated models  36 ,  38  are manually manipulated relative to each other by a person sitting in front of a computer  6  and visually observing the jig models  38  and arthritic models  36  on the computer screen  9  and manipulating the models  36 ,  38  by interacting with the computer controls  11 . In one embodiment, by superimposing the jig models  38  (e.g., femur and tibia arthroplasty jigs in the context of the joint being a knee) over the arthroplasty target areas  42  of the arthritic models  36 , or vice versa, the surface models  40  of the arthroplasty target areas  42  can be imported into the jig models  38 , resulting in jig models  38  indexed to matingly receive the arthroplasty target areas  42  of the arthritic models  36 . Point P′ (X 0-k , Y 0-k , Z 0-k ) can also be imported into the jig models  38 , resulting in jig models  38  positioned and oriented relative to point P′ (X 0-k , Y 0-k , Z 0-k ) to allow their integration with the bone cut and drill hole data  44  of [block  125 ]. 
     In one embodiment, the procedure for indexing the jig models  38  to the arthroplasty target areas  42  is generally or completely automated, as discussed in detail later in this Detailed Description. For example, a computer program may create 3D computer generated surface models  40  of the arthroplasty target areas  42  of the arthritic models  36 . The computer program may then import the surface models  40  and point P′ (X 0-k , Y 0-k , Z 0-k ) into the jig models  38 , resulting in the jig models  38  being indexed to matingly receive the arthroplasty target areas  42  of the arthritic models  36 . The resulting jig models  38  are also positioned and oriented relative to point P′ (X 0-k , Y 0-k , Z 0-k ) to allow their integration with the bone cut and drill hole data  44  of [block 125 ]. 
     In one embodiment, the arthritic models  36  may be 3D volumetric models as generated from the closed-loop process discussed below with respect to  FIGS. 2D-2F . In other embodiments, the arthritic models  36  may be 3D surface models as generated from the open-loop process discussed below with respect to  FIGS. 2A-2C  and  12 A- 12 C. 
     As indicated in  FIG. 1E , in one embodiment, the data regarding the jig models  38  and surface models  40  relative to point P′ (X 0-k , Y 0-k , Z 0-k ) is packaged or consolidated as the “jig data”  46  [block  145 ]. The “jig data”  46  is then used as discussed below with respect to [block  150 ] in  FIG. 1E . 
     As can be understood from  FIG. 1E , the “saw cut and drill hole data”  44  is integrated with the “jig data”  46  to result in the “integrated jig data”  48  [block  150 ]. As explained above, since the “saw cut and drill hole data”  44 , “jig data”  46  and their various ancestors (e.g., models  22 ,  28 ,  36 ,  38 ) are matched to each other for position and orientation relative to point P and P′, the “saw cut and drill hole data”  44  is properly positioned and oriented relative to the “jig data”  46  for proper integration into the “jig data”  46 . The resulting “integrated jig data”  48 , when provided to the CNC machine  10 , results in jigs  2 : (1) configured to matingly receive the arthroplasty target areas of the patient&#39;s bones; and (2) having cut slots and drill holes that facilitate preparing the arthroplasty target areas in a manner that allows the arthroplasty joint implants to generally restore the patient&#39;s joint line to its pre-degenerated state. 
     As can be understood from  FIGS. 1A and 1E , the “integrated jig data”  44  is transferred from the computer  6  to the CNC machine  10  [block  155 ]. Jig blanks  50  are provided to the CNC machine  10  [block  160 ], and the CNC machine  10  employs the “integrated jig data” to machine the arthroplasty jigs  2  from the jig blanks  50 . 
     For a discussion of example customized arthroplasty cutting jigs  2  capable of being manufactured via the above-discussed process, reference is made to  FIGS. 1F-1I . While, as pointed out above, the above-discussed process may be employed to manufacture jigs  2  configured for arthroplasty procedures involving knees, elbows, ankles, wrists, hips, shoulders, vertebra interfaces, etc., the jig examples depicted in  FIGS. 1F-1I  are for total knee replacement (“TKR”) procedures. Thus,  FIGS. 1F and 1G  are, respectively, bottom and top perspective views of an example customized arthroplasty femur jig  2 A, and  FIGS. 1H and 1I  are, respectively, bottom and top perspective views of an example customized arthroplasty tibia jig  2 B. 
     As indicated in  FIGS. 1F and 1G , a femur arthroplasty jig  2 A may include an interior side or portion  100  and an exterior side or portion  102 . When the femur cutting jig  2 A is used in a TKR procedure, the interior side or portion  100  faces and matingly receives the arthroplasty target area  42  of the femur lower end, and the exterior side or portion  102  is on the opposite side of the femur cutting jig  2 A from the interior portion  100 . 
     The interior portion  100  of the femur jig  2 A is configured to match the surface features of the damaged lower end (i.e., the arthroplasty target area  42 ) of the patient&#39;s femur  18 . Thus, when the target area  42  is received in the interior portion  100  of the femur jig  2 A during the TKR surgery, the surfaces of the target area  42  and the interior portion  100  match. 
     The surface of the interior portion  100  of the femur cutting jig  2 A is machined or otherwise formed into a selected femur jig blank  50 A and is based or defined off of a 3D surface model  40  of a target area  42  of the damaged lower end or target area  42  of the patient&#39;s femur  18 . 
     As indicated in  FIGS. 1H and 1I , a tibia arthroplasty jig  2 B may include an interior side or portion  104  and an exterior side or portion  106 . When the tibia cutting jig  2 B is used in a TKR procedure, the interior side or portion  104  faces and matingly receives the arthroplasty target area  42  of the tibia upper end, and the exterior side or portion  106  is on the opposite side of the tibia cutting jig  2 B from the interior portion  104 . 
     The interior portion  104  of the tibia jig  2 B is configured to match the surface features of the damaged upper end (i.e., the arthroplasty target area  42 ) of the patient&#39;s tibia  20 . Thus, when the target area  42  is received in the interior portion  104  of the tibia jig  2 B during the TKR surgery, the surfaces of the target area  42  and the interior portion  104  match. 
     The surface of the interior portion  104  of the tibia cutting jig  2 B is machined or otherwise formed into a selected tibia jig blank  50 B and is based or defined off of a 3D surface model  40  of a target area  42  of the damaged upper end or target area  42  of the patient&#39;s tibia  20 . 
     b. Overview of Automated Process for Indexing 3D Arthroplasty Jig Models to Arthroplasty Target Areas 
     As mentioned above with respect to [block  140 ] of  FIG. 1D , the process for indexing the 3D arthroplasty jig models  38  to the arthroplasty target areas  42  can be automated. A discussion of an example of such an automated process will now concern the remainder of this Detailed Description, beginning with an overview of the automated indexing process. 
     As can be understood from  FIG. 1A  and [blocks  100 - 105 ] of  FIG. 1B , a patient  12  has a joint  14  (e.g., a knee, elbow, ankle, wrist, shoulder, hip, vertebra interface, etc.) to be replaced. The patient  12  has the joint  14  scanned in an imaging machine  10  (e.g., a CT, MRI, etc. machine) to create a plurality of 2D scan images  16  of the bones (e.g., femur  18  and tibia  20 ) forming the patient&#39;s joint  14  (e.g., knee). Each scan image  16  is a thin slice image of the targeted bone(s)  18 ,  20 . The scan images  16  are sent to the CPU  7 , which employs an open-loop image analysis along targeted features  42  of the scan images  16  of the bones  18 ,  20  to generate a contour line for each scan image  16  along the profile of the targeted features  42 . 
     As can be understood from  FIG. 1A  and [block  110 ] of  FIG. 1C , the CPU  7  compiles the scan images  16  and, more specifically, the contour lines to generate 3D computer surface models (“arthritic models”)  36  of the targeted features  42  of the patient&#39;s joint bones  18 ,  20 . In the context of total knee replacement (“TKR”) surgery, the targeted features  42  may be the lower or knee joint end of the patient&#39;s femur  18  and the upper or knee joint end of the patient&#39;s tibia  20 . More specifically, the targeted features  42  may be the tibia contacting articulating surface of the patient&#39;s femur  18  and the femur contacting articulating surface of the patient&#39;s tibia  20 . 
     In some embodiments, the “arthritic models”  36  may be surface models or volumetric solid models respectively formed via an open-loop or closed-loop process such that the contour lines are respectively open or closed loops. In one embodiment discussed in detail herein, the “arthritic models”  36  may be surface models formed via an open-loop process. By employing an open-loop and surface model approach, as opposed to a closed-loop and volumetric solid model approach, the computer modeling process requires less processing capability and time from the CPU  7  and, as a result, is more cost effective. 
     The system  4  measures the anterior-posterior extent and medial-lateral extent of the target areas  42  of the “arthritic models”  36 . The anterior-posterior extent and medial-lateral extent may be used to determine an aspect ratio, size and/or configuration for the 3D “arthritic models”  36  of the respective bones  18 ,  20 . In one embodiment of a jig blank grouping and selection method discussed below, the aspect ratio, size and/or configuration of the 3D “arthritic models”  36  of the respective bones  18 ,  20  may be used for comparison to the aspect ratio, size and/or configuration of 3D computer models of candidate jig blanks  50  in a jig blank grouping and selection method discussed below. In one embodiment of a jig blank grouping and selection method discussed below, the anterior-posterior and medial-lateral dimensions of the 3D “arthritic models”  36  of the respective bones  18 ,  20  may be used for comparison to the anterior-posterior and medial-lateral dimensions of 3D computer models of candidate jig blanks  50 . 
     In the context of TKR, the jigs  2  will be femur and tibia arthroplasty cutting jigs  2 A,  2 B, which are machined or otherwise formed from femur and tibia jig blanks  50 A,  50 B. A plurality of candidate jig blank sizes exists, for example, in a jig blank library. While each candidate jig blank may have a unique combination of anterior-posterior and medial-lateral dimension sizes, in some embodiments, two or more of the candidate jig blanks may share a common aspect ratio or configuration. The candidate jig blanks of the library may be grouped along sloped lines of a plot according to their aspect ratios. The system  4  employs the jig blank grouping and selection method to select a jig blank  50  from a plurality of available jig blank sizes contained in the jig blank library. For example, the configurations, sizes and/or aspect ratios of the tibia and femur 3D arthritic models  36  are compared to the configurations, sizes and/or aspect ratios of the 3D models of the candidate jig blanks with or without a dimensional comparison between the arthritic models  36  and the models of the candidate jig blanks. 
     Alternatively, in one embodiment, the anterior-posterior and medial-lateral dimensions of the target areas of the arthritic models  36  of the patient&#39;s femur and tibia  18 ,  20  are increased via a mathematical formula. The resulting mathematically modified anterior-posterior and medial-lateral dimensions are then compared to the anterior-posterior and medial-lateral dimensions of the models of the candidate jig blanks  50 A,  50 B. In one embodiment, the jig blanks  50 A,  50 B selected are the jig blanks having anterior-posterior and medial-lateral dimensions that are the closest in size to the mathematically modified anterior-posterior and medial-lateral dimensions of the patient&#39;s bones  18 ,  20  without being exceeded by the mathematically modified dimensions of the patient&#39;s bones  18 ,  20 . In one embodiment, the jig blank selection method results in the selection of a jig blank  50  that is as near as possible in size to the patient&#39;s knee features, thereby minimizing the machining involved in creating a jig  2  from a jig blank. 
     In one embodiment, as discussed with respect to  FIGS. 1F-1I , each arthroplasty cutting jig  2  includes an interior portion and an exterior portion. The interior portion is dimensioned specific to the surface features of the patient&#39;s bone that are the focus of the arthroplasty. Thus, where the arthroplasty is for TKR surgery, the jigs will be a femur jig and/or a tibia jig. The femur jig will have an interior portion custom configured to match the damaged surface of the lower or joint end of the patient&#39;s femur. The tibia jig will have an interior portion custom configured to match the damaged surface of the upper or joint end of the patient&#39;s tibia. 
     In one embodiment, because of the jig blank grouping and selection method, the exterior portion of each arthroplasty cutting jig  2  is substantially similar in size to the patient&#39;s femur and tibia 3D arthritic models  36 . However, to provide adequate structural integrity for the cutting jigs  2 , the exterior portions of the jigs  2  may be mathematically modified to cause the exterior portions of the jigs  2  to exceed the 3D femur and tibia models in various directions, thereby providing the resulting cutting jigs  2  with sufficient jig material between the exterior and interior portions of the jigs  2  to provide adequate structural strength. 
     As can be understood from [block  140 ] of  FIG. 1D , once the system  4  selects femur and tibia jig blanks  50  of sizes and configurations sufficiently similar to the sizes and configurations of the patient&#39;s femur and tibia computer arthritic models  36 , the system  4  superimposes the 3D computer surface models  40  of the targeted features  42  of the femur  18  and tibia  20  onto the interior portion of the respective 3D computer models of the selected femur and tibia jigs  38 , or more appropriately in one version of the present embodiment, the jig blanks  50 . The result, as can be understood from [block  145 ] of  FIG. 1E , is computer models of the femur and tibia jigs  2  in the form of “jig data”  46 , wherein the femur and tibia jig computer models have: (1) respective exterior portions closely approximating the overall size and configuration of the patient&#39;s femur and tibia; and (2) respective interior portions having surfaces that match the targeted features  42  of the patient&#39;s femur  18  and tibia  20 . 
     The system  4  employs the data from the jig computer models (i.e., “jig data”  46 ) to cause the CNC machine  10  to machine the actual jigs  2  from actual jig blanks. The result is the automated production of actual femur and tibia jigs  2  having: (1) exterior portions generally matching the patient&#39;s actual femur and tibia with respect to size and overall configuration; and (2) interior portions having patient-specific dimensions and configurations corresponding to the actual dimensions and configurations of the targeted features  42  of the patient&#39;s femur and tibia. The systems  4  and methods disclosed herein allow for the efficient manufacture of arthroplasty jigs  2  customized for the specific bone features of a patient. 
     The jigs  2  and systems  4  and methods of producing such jigs are illustrated herein in the context of knees and TKR surgery. However, those skilled in the art will readily understand the jigs  2  and system  4  and methods of producing such jigs can be readily adapted for use in the context of other joints and joint replacement surgeries, e.g., elbows, shoulders, hips, etc. Accordingly, the disclosure contained herein regarding the jigs  2  and systems  4  and methods of producing such jigs should not be considered as being limited to knees and TKR surgery, but should be considered as encompassing all types of joint surgeries. 
     c. Defining a 3D Surface Model of an Arthroplasty Target Area of a Femur Lower End for Use as a Surface of an Interior Portion of a Femur Arthroplasty Cutting Jig. 
     For a discussion of a method of generating a 3D model  40  of a target area  42  of a damaged lower end  204  of a patient&#39;s femur  18 , reference is made to  FIGS. 2A-2G .  FIG. 2A  is an anterior-posterior (“AP”) image slice  208  of the damaged lower or knee joint end  204  of the patient&#39;s femur  18 , wherein the image slice  208  includes an open-loop contour line segment  210  corresponding to the target area  42  of the damaged lower end  204 .  FIG. 2B  is a plurality of image slices ( 16 - 1 ,  16 - 1 ,  16 - 2 , . . .  16 - n ) with their respective open-loop contour line segments ( 210 - 1 ,  210 - 2 , . . .  210 - n ), the open-loop contour line segments  210  being accumulated to generate the 3D model  40  of the target area  42 .  FIG. 2C  is a 3D model  40  of the target area  42  of the damaged lower end  204  as generated using the open-loop contour line segments ( 16 - 1 ,  16 - 2 , . . .  16 - n ) depicted in  FIG. 2B .  FIGS. 2D-2F  are respectively similar to  FIGS. 2A-2C , except  FIGS. 2D-2F  pertain to a closed-loop contour line as opposed to an open-loop contour line.  FIG. 2G  is a flow chart illustrating an overview of the method of producing a femur jig  2 A. 
     As can be understood from  FIGS. 1A ,  1 B and  2 A, the imager  8  is used to generate a 2D image slice  16  of the damaged lower or knee joint end  204  of the patient&#39;s femur  18 . As depicted in  FIG. 2A , the 2D image  16  may be an AP view of the femur  18 . Depending on whether the imager  8  is a MRI or CT imager, the image slice  16  will be a MRI or CT slice. The damaged lower end  204  includes the posterior condyle  212 , an anterior femur shaft surface  214 , and an area of interest or targeted area  42  that extends from the posterior condyle  212  to the anterior femur shaft surface  214 . The targeted area  42  of the femur lower end may be the articulating contact surfaces of the femur lower end that contact corresponding articulating contact surfaces of the tibia upper or knee joint end. 
     As shown in  FIG. 2A , the image slice  16  may depict the cancellous bone  216 , the cortical bone  218  surrounding the cancellous bone, and the articular cartilage lining portions of the cortical bone  218 . The contour line  210  may extend along the targeted area  42  and immediately adjacent the cortical bone and cartilage to outline the contour of the targeted area  42  of the femur lower end  204 . The contour line  210  extends along the targeted area  42  starting at point A on the posterior condyle  212  and ending at point B on the anterior femur shaft surface  214 . 
     In one embodiment, as indicated in  FIG. 2A , the contour line  210  extends along the targeted area  42 , but not along the rest of the surface of the femur lower end  204 . As a result, the contour line  210  forms an open-loop that, as will be discussed with respect to  FIGS. 2B and 2C , can be used to form an open-loop region or 3D computer model  40 , which is discussed with respect to [block  140 ] of  FIG. 1D  and closely matches the 3D surface of the targeted area  42  of the femur lower end. Thus, in one embodiment, the contour line is an open-loop and does not outline the entire cortical bone surface of the femur lower end  204 . Also, in one embodiment, the open-loop process is used to form from the 3D images  16  a 3D surface model  36  that generally takes the place of the arthritic model  36  discussed with respect to [blocks  125 - 140 ] of  FIG. 1D  and which is used to create the surface model  40  used in the creation of the “jig data”  46  discussed with respect to [blocks  145 - 150 ] of  FIG. 1E . 
     In one embodiment and in contrast to the open-loop contour line  210  depicted in  FIGS. 2A and 2B , the contour line is a closed-loop contour line  210 ′ that outlines the entire cortical bone surface of the femur lower end and results in a closed-loop area, as depicted in  FIG. 2D . The closed-loop contour lines  210 ′- 2 , . . .  210 ′- n  of each image slice  16 - 1 , . . .  16 - n  are combined, as indicated in  FIG. 2E . A closed-loop area may require the analysis of the entire surface region of the femur lower end  204  and result in the formation of a 3D model of the entire femur lower end  204  as illustrated in  FIG. 2F . Thus, the 3D surface model resulting from the closed-loop process ends up having in common much, if not all, the surface of the 3D arthritic model  36 . In one embodiment, the closed-loop process may result in a 3D volumetric anatomical joint solid model from the 2D images  16  via applying mathematical algorithms. U.S. Pat. No. 5,682,886, which was filed Dec. 26, 1995 and is incorporated by reference in its entirety herein, applies a snake algorithm forming a continuous boundary or closed-loop. After the femur has been outlined, a modeling process is used to create the 3D surface model, for example, through a Bézier patches method. Other 3D modeling processes, e.g., commercially-available 3D construction software as listed in other parts of this Detailed Description, are applicable to 3D surface model generation for closed-loop, volumetric solid modeling. 
     In one embodiment, the closed-loop process is used to form from the 3D images  16  a 3D volumetric solid model  36  that is essentially the same as the arthritic model  36  discussed with respect to [blocks  125 - 140 ] of  FIG. 1D . The 3D volumetric solid model  36  is used to create the surface model  40  used in the creation of the “jig data”  46  discussed with respect to [blocks  145 - 150 ] of  FIG. 1E . 
     The formation of a 3D volumetric solid model of the entire femur lower end employs a process that may be much more memory and time intensive than using an open-loop contour line to create a 3D model of the targeted area  42  of the femur lower end. Accordingly, although the closed-loop methodology may be utilized for the systems and methods disclosed herein, for at least some embodiments, the open-loop methodology may be preferred over the closed-loop methodology. 
     An example of a closed-loop methodology is disclosed in U.S. patent application Ser. No. 11/641,569 to Park, which is entitled “Improved Total Joint Arthroplasty System” and was filed Jan. 19, 2007. This application is incorporated by reference in its entirety into this Detailed Description. 
     As can be understood from  FIGS. 2B and 2G , the imager  8  generates a plurality of image slices ( 16 - 1 ,  16 - 2  . . .  16 - n ) via repetitive imaging operations [block  1000 ]. Each image slice  16  has an open-loop contour line ( 210 - 1 ,  210 - 2  . . .  210 - n ) extending along the targeted region  42  in a manner as discussed with respect to  FIG. 2A  [block  1005 ]. In one embodiment, each image slice is a two-millimeter 2D image slice  16 . The system  100  compiles the plurality of 2D image slices ( 16 - 1 ,  16 - 2  . . .  16 - n ) and, more specifically, the plurality of open-loop contour lines ( 210 - 1 ,  210 - 2 , . . .  210 - n ) into the 3D femur surface computer model  40  depicted in  FIG. 2C  [block  1010 ]. This process regarding the generation of the surface model  40  is also discussed in the overview section with respect to [blocks  100 - 105 ] of  FIG. 1B  and [blocks  130 - 140 ] of  FIG. 1D . A similar process may be employed with respect to the closed-loop contour lines depicted in  FIGS. 2D-2F . 
     As can be understood from  FIG. 2C , the 3D femur surface computer model  40  is a 3D computer representation of the targeted region  42  of the femur lower end. In one embodiment, the 3D representation of the targeted region  42  is a 3D representation of the articulated tibia contact surfaces of the femur distal end. As the open-loop generated 3D model  40  is a surface model of the relevant tibia contacting portions of the femur lower end, as opposed to a 3D model of the entire surface of the femur lower end as would be a result of a closed-loop contour line, the open-loop generated 3D model  40  is less time and memory intensive to generate. 
     In one embodiment, the open-loop generated 3D model  40  is a surface model of the tibia facing end face of the femur lower end, as opposed a 3D model of the entire surface of the femur lower end. The 3D model  40  can be used to identify the area of interest or targeted region  42 , which, as previously stated, may be the relevant tibia contacting portions of the femur lower end. Again, the open-loop generated 3D model  40  is less time and memory intensive to generate as compared to a 3D model of the entire surface of the femur distal end, as would be generated by a closed-loop contour line. Thus, for at least some versions of the embodiments disclosed herein, the open-loop contour line methodology is preferred over the closed-loop contour line methodology. However, the system  4  and method disclosed herein may employ either the open-loop or closed-loop methodology and should not be limited to one or the other. 
     Regardless of whether the 3D model  40  is a surface model of the targeted region  42  (i.e., a 3D surface model generated from an open-loop process and acting as the arthritic model  22 ) or the entire tibia facing end face of the femur lower end (i.e., a 3D volumetric solid model generated from a closed-loop process and acting as the arthritic model  22 ), the data pertaining to the contour lines  210  can be converted into the 3D contour computer model  40  via the surface rendering techniques disclosed in any of the aforementioned U.S. patent applications to Park. For example, surface rending techniques employed include point-to-point mapping, surface normal vector mapping, local surface mapping, and global surface mapping techniques. Depending on the situation, one or a combination of mapping techniques can be employed. 
     In one embodiment, the generation of the 3D model  40  depicted in  FIG. 2C  may be formed by using the image slices  16  to determine location coordinate values of each of a sequence of spaced apart surface points in the open-loop region of  FIG. 2B . A mathematical model may then be used to estimate or compute the 3D model  40  in  FIG. 2C . Examples of other medical imaging computer programs that may be used include, but are not limited to: Analyze from AnalyzeDirect, Inc. of Overland Park, Kans.; open-source software such as Paraview of Kitware, Inc.; Insight Toolkit (“ITK”) available at www.itk.org; 3D Slicer available at www.slicer.org; and Mimics from Materialise of Ann Arbor, Mich. 
     Alternatively or additionally to the aforementioned systems for generating the 3D model  40  depicted in  FIG. 2C , other systems for generating the 3D model  40  of  FIG. 2C  include the surface rendering techniques of the Non-Uniform Rational B-spline (“NURB”) program or the Bézier program. Each of these programs may be employed to generate the 3D contour model  40  from the plurality of contour lines  210 . 
     In one embodiment, the NURB surface modeling technique is applied to the plurality of image slices  16  and, more specifically, the plurality of open-loop contour lines  210  of  FIG. 2B . The NURB software generates a 3D model  40  as depicted in  FIG. 2C , wherein the 3D model  40  has areas of interest or targeted regions  42  that contain both a mesh and its control points. For example, see Ervin et al., Landscape Modeling, McGraw-Hill, 2001, which is hereby incorporated by reference in its entirety into this Detailed Description. 
     In one embodiment, the NURB surface modeling technique employs the following surface equation: 
                 G   ⁡     (     s   ,   t     )       =         ∑     i   =   0       k   ⁢           ⁢   1       ⁢       ∑     j   =   0       k   ⁢           ⁢   2       ⁢       W   ⁡     (     i   ,   j     )       ⁢     P   ⁡     (     i   ,   j     )       ⁢       b   i     ⁡     (   s   )       ⁢       b   j     ⁡     (   t   )                 ∑     i   =   0       k   ⁢           ⁢   1       ⁢       ∑     j   =   0       k   ⁢           ⁢   2       ⁢       W   ⁡     (     i   ,   j     )       ⁢       b   i     ⁡     (   s   )       ⁢       b   j     ⁡     (   t   )                 ,         
wherein P(i,j) represents a matrix of vertices with nrows=(k1+1) and ncols=(k2+1), W(i,j) represents a matrix of vertex weights of one per vertex point, b i (s) represents a row-direction basis or blending of polynomial functions of degree M 1 , b j (t) represents a column-direction basis or blending polynomial functions of degree M 2 , s represents a parameter array of row-direction knots, and t represents a parameter array of column-direction knots.
 
     In one embodiment, the Bézier surface modeling technique employs the 136zier equation (1972, by Pierre Bézier) to generate a 3D model  40  as depicted in  FIG. 2C , wherein the model  40  has areas of interest or targeted regions  42 . A given Bézier surface of order (n, m) is defined by a set of (n+1)(m+1) control points K ij . It maps the unit square into a smooth-continuous surface embedded within a space of the same dimensionality as (k ij ). For example, if k are all points in a four-dimensional space, then the surface will be within a four-dimensional space. This relationship holds true for a one-dimensional space, a two-dimensional space, a fifty-dimensional space, etc. 
     A two-dimensional Bézier surface can be defined as a parametric surface where the position of a point p as a function of the parametric coordinates u, v is given by: 
               p   ⁡     (     u   ,   v     )       =       ∑     i   =   0     n     ⁢       ∑     j   =   0     m     ⁢         B   i   n     ⁡     (   u   )       ⁢       B   j   m     ⁡     (   v   )       ⁢     k     i   ,   j                   
evaluated over the unit square, where
 
                 B   i   n     ⁡     (   u   )       =       (         n           i         )     ⁢         u   i     ⁡     (     1   -   u     )         n   -   i               
is a Bernstein polynomial and
 
               (         n           i         )     =       n   !         i   !     *       (     n   -   i     )     !               
is the binomial coefficient. See Grune et al,  On Numerical Algorithm and Interactive Visualization for Optimal Control Problems , Journal of Computation and Visualization in Science, Vol. 1, No. 4, July 1999, which is hereby incorporated by reference in its entirety into this Detailed Description.
 
     Various other surface rendering techniques are disclosed in other references. For example, see the surface rendering techniques disclosed in the following publications: Lorensen et al.,  Marching Cubes: A high Resolution  3 d Surface Construction Algorithm , Computer Graphics, 21-3: 163-169, 1987; Farin et al.,  NURB Curves  &amp;  Surfaces: From Projective Geometry to Practical Use , Wellesley, 1995; Kumar et al,  Robust Incremental Polygon Triangulation for Surface Rendering , WSCG, 2000; Fleischer et al.,  Accurate Polygon Scan Conversion Using Half - Open Intervals , Graphics Gems III, p. 362-365, code: p. 599-605, 1992; Foley et al.,  Computer Graphics: Principles and Practice , Addison Wesley, 1990; Glassner,  Principles of Digital Image Synthesis , Morgan Kaufmann, 1995, all of which are hereby incorporated by reference in their entireties into this Detailed Description. 
     d. Selecting a Jig Blank Most Similar in Size and/or Configuration to the Size of the Patient&#39;s Femur Lower End. 
     As mentioned above, an arthroplasty jig  2 , such as a femoral jig  2 A includes an interior portion  100  and an exterior portion  102 . The femoral jig  2 A is formed from a femur jig blank  50 A, which, in one embodiment, is selected from a finite number of femur jig blank sizes. The selection of the femur jig blank  50 A is based on a comparison of the dimensions of the patient&#39;s femur lower end  204  to the dimensions and/or configurations of the various sizes of femur jig blanks  50 A to select the femur jig blank  50 A most closely resembling the patient&#39;s femur lower end  204  with respect to size and/or configuration. This selected femur jig blank  50 A has an outer or exterior side or surface  232  that forms the exterior portion  232  of the femur jig  2 A. The 3D surface computer model  40  discussed with respect to the immediately preceding section of this Detail Description is used to define a 3D surface  40  into the interior side  230  of computer model of a femur jig blank  50 A. 
     By selecting a femur jig blank  50 A with an exterior portion  232  close in size to the patient&#39;s lower femur end  204 , the potential for an accurate fit between the interior portion  230  and the patient&#39;s femur is increased. Also, the amount of material that needs to be machined or otherwise removed from the jig blank  50 A is reduced, thereby reducing material waste and manufacturing time. 
     For a discussion of a method of selecting a jig blank  50  most closely corresponding to the size and/or configuration of the patient&#39;s lower femur end, reference is first made to  FIGS. 3-4B .  FIG. 3A  is a top perspective view of a left femoral cutting jig blank  50 AL having predetermined dimensions.  FIG. 3B  is a bottom perspective view of the jig blank  50 AL depicted in  FIG. 3A .  FIG. 3C  is plan view of an exterior side or portion  232  of the jig blank  50 AL depicted in  FIG. 3A .  FIG. 4A  is a plurality of available sizes of left femur jig blanks  50 AL, each depicted in the same view as shown in  FIG. 3C .  FIG. 4B  is a plurality of available sizes of right femur jig blanks  50 AR, each depicted in the same view as shown in  FIG. 3C . 
     A common jig blank  50 , such as the left jig blank  50 AL depicted in  FIGS. 3A-3C  and intended for creation of a left femur jig that can be used with a patient&#39;s left femur, may include a posterior edge  240 , an anterior edge  242 , a lateral edge  244 , a medial edge  246 , a lateral condyle portion  248 , a medial condyle portion  250 , the exterior side  232  and the interior side  230 . The jig blank  50 AL of  FIGS. 3A-3C  may be any one of a number of left femur jig blanks  50 AL available in a limited number of standard sizes. For example, the jig blank  50 AL of  FIGS. 3A-3C  may be an j-th left femur jig blank, where i=1, 2, 3, 4, . . . m and m represents the maximum number of left femur jig blank sizes. 
     As indicated in  FIG. 3C , the anterior-posterior extent JAi of the jig blank  50 AL is measured from the anterior edge  242  to the posterior edge  240  of the jig blank  50 AL. The medial-lateral extent JMi of the jig blank  50 AL is measured from the lateral edge  244  to the medial edge  246  of the jig blank  50 AL. 
     As can be understood from  FIG. 4A , a limited number of left femur jig blank sizes may be available for selection as the left femur jig blank size to be machined into the left femur cutting jig  2 A. For example, in one embodiment, there are nine sizes (m=9) of left femur jig blanks  50 AL available. As can be understood from  FIG. 3C , each femur jig blank  50 AL has an anterior-posterior/medial-lateral aspect ratio defined as JAI to JMi (e.g., “JAi/JMi” aspect ratio). Thus, as can be understood from  FIG. 4A , jig blank  50 AL- 1  has an aspect ratio defined as “JAi/JMi”, jig blank  50 AL- 2  has an aspect ratio defined as “JA 2 /JM 2 ”, jig blank  50 AL- 3  has an aspect ratio defined as “JA 3 /JM 3 ”, jig blank  50 AL- 4  has an aspect ratio defined as “JA 4 /JM 4 ”, jig blank  50 AL- 5  has an aspect ratio defined as “JA 5 /JM 5 ”, jig blank  50 AL- 6  has an aspect ratio defined as “JA 6 /JM 6 ”, jig blank  50 AL- 7  has an aspect ratio defined as “JA 7 /JM 7 ”, jig blank  50 AL- 8  has an aspect ratio defined as “JA 8 /JM 8 ”, and jig blank  50 AL- 9  has an aspect ratio defined as “JA 9 /JM 9 ”. 
     The jig blank aspect ratio is utilized to design left femur jigs  2 A dimensioned specific to the patient&#39;s left femur features. In one embodiment, the jig blank aspect ratio can be the exterior dimensions of the left femur jig  2 A. In another embodiment, the jig blank aspect ratio can apply to the left femur jig fabrication procedure for selecting the left jig blank  50 AL having parameters close to the dimensions of the desired left femur jig  2 A. This embodiment can improve the cost efficiency of the left femur jig fabrication process because it reduces the amount of machining required to create the desired jig  2  from the selected jig blank  50 . 
     In  FIG. 4A , the N- 1  direction represents increasing jig aspect ratios moving from jig  50 AL- 3  to jig  50 AL- 2  to jig  50 AL- 1 , where “JA 3 /JM 3 ”&lt;“JA 2 /JM 2 ”&lt;“JA 1 /JM 1 ”. The increasing ratios of the jigs  50 AL represent the corresponding increment of JAi values, where the jigs&#39; JMi values remain the same. In other words, since JA 3 &lt;JA 2 &lt;JA 1 , and JM 3 =JM 2 =JM 1 , then “JA 3 /JM 3 ”&lt;“JA 2 /JM 2 ”&lt;“JA 1 /JM 1 ”. One example of the increment level can be an increase from 5% to 20%. 
     The same rationale applies to the N- 2  direction and the N- 3  direction. For example, the N- 2  direction represents increasing jig aspect ratios from jig  50 AL- 6  to jig  50 AL- 5  to jig  50 AL- 4 , where “JA 4 /JM 4 ”&lt;“JA 5 /JM 5 ”&lt;“JA 6 /JM 6 ”. The increasing ratios of the jigs  50 AL represent the corresponding increment of JAi values, where the JMi values remain the same. The N- 3  direction represents increasing jig aspect ratios from jig  50 AL- 9  to jig  50 AL- 8  to jig  50 AL- 7 , where “JA 7 /JM 7 ”&lt;“JA 8 /JM 8 ”&lt;“JA 9 /JM 9 ”. The increasing ratios of the jigs  50 AL represent the corresponding increment of JAi values, where the JMi values remain the same. 
     As can be understood from the plot  300  depicted in  FIG. 7  and discussed later in this Detailed Discussion, the E- 1  direction corresponds to the sloped line joining Group 1, Group 4 and Group 7. Similarly, the E- 2  direction corresponds to the sloped line joining Group 2, Group 5 and Group 8. Also, the E- 3  direction corresponds to the sloped line joining Group 3, Group 6 and Group 9. 
     As indicated in  FIG. 4A , along direction E- 2 , the jig aspect ratios remain the same among jigs  50 AL- 2 ,  50 AL- 5  and jig  50 AL- 8 , where“JA 2 /JM 2 ”=“JA 5 /JM 5 ”=“JA 8 /JM 8 ”. However, comparing to jig  50 AL- 2 , jig  50 AL- 5  is dimensioned larger and longer than jig  50 AL- 2 . This is because the JA 5  value for jig  50 AL- 5  increases proportionally with the increment of its JM 5  value in certain degrees in all X, Y, and Z-axis directions. In a similar fashion, jig  50 AL- 8  is dimensioned larger and longer than jig  50 AL- 5  because the JA 8  increases proportionally with the increment of its JM 8  value in certain degrees in all X, Y, and Z-axis directions. One example of the increment can be an increase from 5% to 20%. 
     The same rationale applies to directions E- 1  and E- 3 . For example, in E- 3  direction the jig ratios remain the same among the jigs  50 AL- 3 ,  50 AL- 6  and jig  50 AL- 9 . Compared to jig  50 AL- 3 , jig  50 AL- 6  is dimensioned bigger and longer because both JM 6  and JA 6  values of jig  50 AL- 6  increase proportionally in all X, Y, and Z-axis directions. Compared to jig  50 AL- 6 , jig  50 AL- 9  is dimensioned bigger and longer because both JM 9  and JA 9  values of jig  50 AL- 9  increase proportionally in all X, Y, and Z-axis. 
     As can be understood from  FIG. 4B , a limited number of right femur jig blank sizes may be available for selection as the right femur jig blank size to be machined into the right femur cutting jig  2 A. For example, in one embodiment, there are nine sizes (m=9) of right femur jig blanks  50 AR available. As can be understood from  FIG. 3 , each femur jig blank  50 AR has an anterior-posterior/medial-lateral aspect ratio defined as JAi to JMi (e.g., “JAi/JMi” aspect ratio). Thus, as can be understood from  FIG. 4B , jig blank  50 AR- 1  has an aspect ratio defined as “JA 1 /JM 1 ”, jig blank  50 AR- 2  has an aspect ratio defined as “JA 2 /JM 2 ”, jig blank  50 AR- 3  has an aspect ratio defined as “JA 3 /JM 3 ”, jig blank  50 AR- 4  has an aspect ratio defined as “JA 4 /JM 4 ”, jig blank  50 AR- 5  has an aspect ratio defined as “JA 5 /JM 5 ”, jig blank  50 AR- 6  has an aspect ratio defined as “JA 6 /JM 6 ”, jig blank  50 AR- 7  has an aspect ratio defined as “JA 7 /JM 7 ”, jig blank  50 AR- 8  has an aspect ratio defined as “JA 8 /JM 8 ”, and jig blank  50 AR- 9  has an aspect ratio defined as “JA 9 /JM 9 ”. 
     The jig blank aspect ratio may be utilized to design right femur jigs  2 A dimensioned specific to the patient&#39;s right femur features. In one embodiment, the jig blank aspect ratio can be the exterior dimensions of the right femur jig  2 A. In another embodiment, the jig blank aspect ratio can apply to the right femur jig fabrication procedure for selecting the right jig blank  50 AR having parameters close to the dimensions of the desired right femur jig  2 A. This embodiment can improve the cost efficiency of the right femur jig fabrication process because it reduces the amount of machining required to create the desired jig  2  from the selected jig blank  50 . 
     In  FIG. 4B , the N- 1  direction represents increasing jig aspect ratios moving from jig  50 AR- 3  to jig  50 AR- 2  to jig  50 AR- 1 , where “JA 3 /JM 3 ”&lt;“JA 2 /JM 2 ”&lt;“JA 1 /JM 1 ”. The increasing ratios of the jigs  50 AR represent the corresponding increment of JAi values, where the jigs&#39; JMi values remain the same. In other words, since JA 3 &lt;JA 2 &lt;JA 1 , and JM 3 =JM 2 =JM 1 , then “JA 3 /JM 3 ”&lt;“JA 2 /JM 2 ”&lt;“JA 1 /JM 1 ”. One example of the increment level can be an increase from 5% to 20%. 
     The same rationale applies to the N- 2  direction and the N- 3  direction. For example, the N- 2  direction represents increasing jig aspect ratios from jig  50 AR- 6  to jig  50 AR- 5  to jig  50 AR- 4 , where “JA 4 /JM 4 ”&lt;“JA 5 /JM 5 ”&lt;“JA 6 /JM 6 ”. The increasing ratios of the jigs  50 AR represent the corresponding increment of JAi values, where the JMi values remain the same. The N- 3  direction represents increasing jig aspect ratios from jig  50 AR- 9  to jig  50 AR- 8  to jig  50 AR- 7 , where “JA 7 /JM 7 ”&lt;“JA 8 /JM 8 ”&lt;“JA 9 /JM 9 ”. The increasing ratios of the jigs  50 AR represent the corresponding increment of JAi values, where the JMi values remain the same. 
     As indicated in  FIG. 4B , along direction E- 2 , the jig aspect ratios remain the same among jigs  50 AR- 2 ,  50 AR- 5  and jig  50 AR- 8 , where“JA 2 /JM 2 ”=“JA 5 /JM 5 ”=“JA 8 /JM 8 ”. However, comparing to jig  50 AR- 2 , jig  50 AR- 5  is dimensioned larger and longer than jig  50 AR- 2 . This is because the JA 5  value for jig  50 AR- 5  increases proportionally with the increment of its JM 5  value in certain degrees in all X, Y, and Z-axis directions. In a similar fashion, jig  50 AR- 8  is dimensioned larger and longer than jig  50 AR- 5  because the JA 8  increases proportionally with the increment of its JM 8  value in certain degrees in all X, Y, and Z-axis directions. One example of the increment can be an increase from 5% to 20%. 
     The same rationale applies to directions E- 1  and E- 3 . For example, in E- 3  direction the jig ratios remain the same among the jigs  50 AR- 3 ,  50 AR- 6  and jig  50 AR- 9 . Compared to jig  50 AR- 3 , jig  50 AR- 6  is dimensioned bigger and longer because both JM 6  and JA 6  values of jig  50 AR- 6  increase proportionally in all X, Y, and Z-axis directions. Compared to jig  50 AR- 6 , jig  50 AR- 9  is dimensioned bigger and longer because both JM 9  and JA 9  values of jig  50 AR- 9  increase proportionally in all X, Y, and Z-axis. 
     The dimensions of the lower or knee joint forming end  204  of the patient&#39;s femur  18  can be determined by analyzing the 3D surface model  40  or 3D arthritic model  36  in a manner similar to those discussed with respect to the jig blanks  50 . For example, as depicted in  FIG. 5 , which is an axial view of the 3D surface model  40  or arthritic model  36  of the patient&#39;s left femur  18  as viewed in a direction extending distal to proximal, the lower end  204  of the surface model  40  or arthritic model  36  may include an anterior edge  262 , a posterior edge  260 , a medial edge  264 , a lateral edge  266 , a medial condyle  268 , and a lateral condyle  270 . The femur dimensions may be determined for the bottom end face or tibia articulating surface  204  of the patient&#39;s femur  18  via analyzing the 3D surface model  40  of the 3D arthritic model  36 . These femur dimensions can then be utilized to configure femur jig dimensions and select an appropriate femur jig. 
     As shown in  FIG. 5 , the anterior-posterior extent fAP of the lower end  204  of the patient&#39;s femur  18  (i.e., the lower end  204  of the surface model  40  of the arthritic model  36 , whether formed via open or closed-loop analysis) is the length measured from the anterior edge  262  of the femoral lateral groove to the posterior edge  260  of the femoral lateral condyle  270 . The medial-lateral extent fML of the lower end  204  of the patient&#39;s femur  18  is the length measured from the medial edge  264  of the medial condyle  268  to the lateral edge  266  of the lateral condyle  270 . 
     In one embodiment, the anterior-posterior extent fAP and medial-lateral extent fML of the femur lower end  204  can be used for an aspect ratio fAP/fML of the femur lower end. The aspect ratios fAP/fML of a large number (e.g., hundreds, thousands, tens of thousands, etc.) of patient knees can be compiled and statistically analyzed to determine the most common aspect ratios for jig blanks that would accommodate the greatest number of patient knees. This information may then be used to determine which one, two, three, etc. aspect ratios would be most likely to accommodate the greatest number of patient knees. 
     The system  4  analyzes the lower ends  204  of the patient&#39;s femur  18  as provided via the surface model  40  of the arthritic model  36  (whether the arthritic model  36  is an 3D surface model generated via an open-loop or a 3D volumetric solid model generated via a closed-loop process) to obtain data regarding anterior-posterior extent fAP and medial-lateral extent fML of the femur lower ends  204 . As can be understood from  FIG. 6 , which depicts the selected model jig blank  50 AL of  FIG. 3C  superimposed on the model femur lower end  204  of  FIG. 5 , the femur dimensional extents fAP, fML are compared to the jig blank dimensional extents jAP, jML to determine which jig blank model to select as the starting point for the machining process and the exterior surface model for the jig model. 
     As shown in  FIG. 6 , a prospective left femoral jig blank  50 AL is superimposed to mate with the left femur lower end  204  of the patient&#39;s anatomical model as represented by the surface model  40  or arthritic model  36 . The jig blank  50 AL covers most of medial condyle  268  and the lateral condyle  270 , leaving small exposed condyle regions including t 1 , t 2 , t 3 . The medial medial-lateral condyle region t 1  represents the region between the medial edge  264  of the medial condyle  268  and the medial edge  246  of the jig blank  50 AL. The lateral medial-lateral condyle region t 2  represents the region between the lateral edge  266  of the lateral condyle  270  and the lateral edge  244  of the jig blank  50 AL. The posterior anterior-posterior region t 3  represents the condyle region between the posterior edge  260  of the lateral condyle  270  and the posterior edge  240  of the jig blank  50 AL. 
     The anterior edge  242  of the jig blank  50 AL extends past the anterior edge  262  of the left femur lower end  204  as indicated by anterior anterior-posterior overhang t 4 . Specifically, the anterior anterior-posterior overhang t 4  represents the region between the anterior edge  262  of the lateral groove of femur lower end  204  and the anterior edge  242  of the jig blank  50 AL. By obtaining and employing the femur anterior-posterior fAP data and the femur medial-lateral fML data, the system  4  can size the femoral jig blank  50 AL according to the following formulas: as jFML=fML−t 1  t 2  and jFAP=fAP−t 3 +t 4 , wherein jFML is the medial-lateral extent of the femur jig blank  50 AL and jFAP is the anterior-posterior extent of the femur jig blank  50 AL. In one embodiment, t 1 , t 2 , t 3  and t 4  will have the following ranges: 2 mm≦t 1 ≦6 mm; 2 mm t 2 ≦6 mm; 2 mm≦t 3 ≦12 mm; and 15 mm≦t 4 ≦25 mm. In another embodiment, t 1 , t 2 , t 3  and t 4  will have the following values: t 1 =3 mm; t 2 =3 mm; t 3 =6 mm; and t 4 =20 mm. 
       FIG. 7A  is an example scatter plot  300  for selecting from a plurality of candidate jig blanks sizes a jig blank size appropriate for the lower end  204  of the patient&#39;s femur  18 . In one embodiment, the X-axis represents the patient&#39;s femoral medial-lateral length fML in millimeters, and the Y-axis represents the patient&#39;s femoral anterior-posterior length fAP in millimeters. In one embodiment, the plot is divided into a number of jig blank size groups, where each group encompasses a region of the plot  300  and is associated with specific parameters JM r , JA r  of a specific candidate jig blank size. 
     In one embodiment, the example scatter plot  300  depicted in  FIG. 7A  has nine jig blank size groups, each group pertaining to a single candidate jig blank size. However, depending on the embodiment, a scatter plot  300  may have a greater or lesser number of jig blank size groups. The higher the number of jig blank size groups, the higher the number of the candidate jig blank sizes and the more dimension specific a selected candidate jig blank size will be to the patient&#39;s knee features and the resulting jig  2 . The more dimension specific the selected candidate jig blank size, the lower the amount of machining required to produce the desired jig  2  from the selected jig blank  50 . 
     Conversely, the lower the number of jig blank size groups, the lower the number of candidate jig blank sizes and the less dimension specific a selected candidate jig blank size will be to the patient&#39;s knee features and the resulting jig  2 . The less dimension specific the selected candidate jig blank size, the higher the amount of machining required to produce the desired jig  2  from the selected jig blank  50 , adding extra roughing during the jig fabrication procedure. 
     As can be understood from  FIG. 7A , in one embodiment, the nine jig blank size groups of the plot  300  have the parameters JM r , JA r  as follows. Group 1 has parameters JM 1 , JA 1 . JM 1  represents the medial-lateral extent of the first femoral jig blank size, wherein JM 1 =70 mm. JA 1  represents the anterior-posterior extent of the first femoral jig blank size, wherein JA 1 =70.5 mm. Group 1 covers the patient&#39;s femur fML and fAP data wherein 55 mm&lt;fML&lt;70 mm and 61 mm&lt;fAP&lt;70.5 mm. 
     Group 2 has parameters JM 2 , JA 2 . JM 2  represents the medial-lateral extent of the second femoral jig blank size, wherein JM 2 =70 mm. JA 2  represents the anterior-posterior extent of the second femoral jig blank size, wherein JA 2 =61.5 mm. Group 2 covers the patient&#39;s femur fML and fAP data wherein 55 mm&lt;fML&lt;70 mm and 52 mm&lt;fAP&lt;61.5 mm. 
     Group 3 has parameters JM 3 , JA 3 . JM 3  represents the medial-lateral extent of the third femoral jig blank size, wherein JM 3 =70 mm. JA 3  represents the anterior-posterior extent of the third femoral jig blank size, wherein JA 3 =52 mm. Group 3 covers the patient&#39;s femur fML and fAP data wherein 55 mm&lt;fML&lt;70 mm and 40 mm&lt;fAP&lt;52 mm. 
     Group 4 has parameters JM 4 , JA 4 . JM 4  represents the medial-lateral extent of the fourth femoral jig blank size, wherein JM 4 =85 mm. JA 4  represents the anterior-posterior extent of the fourth femoral jig blank size, wherein JA 4 =72.5 mm. Group 4 covers the patient&#39;s femur fML and fAP data wherein 70 mm&lt;fML&lt;85 mm and 63.5 mm&lt;fAP&lt;72.5 mm. 
     Group 5 has parameters JM 5 , JA 5 . JM 5  represents the medial-lateral extent of the fifth femoral jig blank size, wherein JM 5 =85 mm. JA 6  represents the anterior-posterior extent of the fifth femoral jig blank size, wherein JA 6 =63.5 mm. Group 5 covers the patient&#39;s femur fML and fAP data wherein 70 mm&lt;fML&lt;85 mm and 55 mm&lt;fAP&lt;63.5 mm. 
     Group 6 has parameters JM 6 , JA 6 . JM 6  represents the medial-lateral extent of the sixth femoral jig blank size, wherein JM 6 =85 mm. JA 6  represents the anterior-posterior extent of the sixth femoral jig blank size, wherein JA 6 =55 mm. Group 6 covers the patient&#39;s femur fML and fAP data wherein 70 mm&lt;fML&lt;85 mm and 40 mm&lt;fAP&lt;55 mm. 
     Group 7 has parameters JM 7 , JA 7 . JM 7  represents the medial-lateral extent of the seventh femoral jig blank size, wherein JM 7 =100 mm. JA 7  represents the anterior-posterior extent of the seventh femoral jig blank size, wherein JA 7 =75 mm. Group 7 covers the patient&#39;s femur fML and fAP data wherein 85 mm&lt;fML&lt;100 mm and 65 mm&lt;fAP&lt;75 mm. 
     Group 8 has parameters JM 8 , JA 8 . JM 8  represents the medial-lateral extent of the eighth femoral jig blank size, wherein JM 8 =100 mm. JA 8  represents the anterior-posterior extent of the eighth femoral jig blank size, wherein JA 8 =65 mm. Group 8 covers the patient&#39;s femur fML and fAP data wherein 85 mm&lt;fML&lt;100 mm and 57.5 mm&lt;fAP&lt;65 mm. 
     Group 9 has parameters JM 9 , JA 9 . JM 9  represents the medial-lateral extent of the ninth femoral jig blank size, wherein JM 9 =100 mm. JA 9  represents the anterior-posterior extent of the ninth femoral jig blank size, wherein JA 9 =57.5 mm. Group 9 covers the patient&#39;s femur fML and fAP data wherein 85 mm&lt;fML&lt;100 mm and 40 mm&lt;fAP&lt;57.5 mm. 
     As can be understood from  FIG. 7B , which is a flow diagram illustrating an embodiment of a process of selecting an appropriately sized jig blank, bone anterior-posterior and medial-lateral extents fAP, fML are determined for the lower end  204  of the surface model  40  of the arthritic model  36  [block  2000 ]. The bone extents fAP, fML of the lower end  204  are mathematically modified according to the above discussed jFML and jFAP formulas to arrive at the minimum femur jig blank anterior-posterior extent jFAP and medial-lateral extent jFML [block  2010 ]. The mathematically modified bone extents fAP, fML or, more specifically, the minimum femur jig blank anterior-posterior and medial-lateral extents jFAP, jFML are referenced against the jig blank dimensions in the plot  300  of  FIG. 7A  [block  2020 ]. The plot  300  may graphically represent the extents of candidate femur jig blanks forming a jig blank library. The femur jig blank  50 A is selected to be the jig blank size having the smallest extents that are still sufficiently large to accommodate the minimum femur jig blank anterior-posterior and medial-lateral extents JFAP, jFML [block  2030 ]. 
     In one embodiment, the exterior of the selected jig blank size is used for the exterior surface model of the jig model, as discussed below. In one embodiment, the selected jig blank size corresponds to an actual jig blank that is placed in the CNC machine and milled down to the minimum femur jig blank anterior-posterior and medial-lateral extents jFAP, jFML to machine or otherwise form the exterior surface of the femur jig  2 A. 
     The method outlined in  FIG. 7B  and in reference to the plot  300  of  FIG. 7A  can be further understood from the following example. As measured in  FIG. 6  with respect to the lower end  204  of the patient&#39;s femur  18 , the extents of the patient&#39;s femur are as follows: fML=79.2 mm and fAP=54.5 mm [block  2000 ]. As previously mentioned, the lower end  204  may be part of the surface model  40  of the arthritic model  36 . Once the fML and fAP measurements are determined from the lower end  204 , the corresponding jig jFML data and jig jFAP data can be determined via the above-described jFML and jFAP formulas: jFML=fML−t 1 −t 2 , wherein VI=3 mm and t 2 =3 mm; and jFAP=fAP−t 3 +t 4 , wherein t 3 =6 mm and t 4 =20 mm [block  2010 ]. The result of the jFML and jFAP formulas is jFML=73.2 mm and jFAP=68.5 mm. 
     As can be understood from the plot  300  of  FIG. 7 , the determined jig data (i.e., jFML=73.2 mm and jFAP=68.5 mm) falls in Group 4 of the plot  300 . Group 4 has the predetermined femur jig blank parameters (JM 4 , JA 4 ) of JM 4 =85 mm and JA 4 =72.5 mm. These predetermined femur jig blank parameters are the smallest of the various groups that are still sufficiently large to meet the minimum femur blank extents jFAP, jFML [block  2020 ]. These predetermined femur jig blank parameters (JM 4 =85 mm and JA 4 =72.5 mm) may be selected as the appropriate femur jig blank size [block  2030 ]. 
     In one embodiment, the predetermined femur jig blank parameters (85 mm, 72.5 mm) can apply to the femur exterior jig dimensions as shown in  FIG. 3C . In other words, the jig blank exterior is used for the jig model exterior as discussed with respect to  FIGS. 8A-9C . Thus, the exterior of the femur jig blank  50 A undergoes no machining, and the unmodified exterior of the jig blank  50 A with its predetermined jig blank parameters (85 mm, 72.5 mm) serves as the exterior of the finished femur jig  2   k    
     In another embodiment, the femur jig blank parameters (85 mm, 72.5 mm) can be selected for jig fabrication in the machining process. Thus, a femur jig blank  50 A having predetermined parameters (85 mm, 72.5 mm) is provided to the machining process such that the exterior of the femur jig blank  50 A will be machined from its predetermined parameters (85 mm, 72.5 mm) down to the desired femur jig parameters (73.2, 68.5 mm) to create the finished exterior of the femur jig  2 A. As the predetermined parameters (85 mm, 72.5 mm) are selected to be relatively close to the desired femur jig parameters (73.2, 68.5 mm), machining time and material waste are reduced. 
     While it may be advantageous to employ the above-described jig blank selection method to minimize material waste and machining time, in some embodiments, a jig blank will simply be provided that is sufficiently large to be applicable to all patient bone extents fAP, fML. Such a jig blank is then machined down to the desired jig blank extents jFAP, jFML, which serve as the exterior surface of the finished jig  2 A. 
     In one embodiment, the number of candidate jig blank size groups represented in the plot  300  is a function of the number of jig blank sizes offered by a jig blank manufacturer. For example, a first plot  300  may pertain only to jig blanks manufactured by company A, which offers nine jig blank sizes. Accordingly, the plot  300  has nine jig blank size groups. A second plot  300  may pertain only to jig blanks manufactured by company B, which offers twelve jig blank size groups. Accordingly, the second plot  300  has twelve jig blank size groups. 
     A plurality of candidate jig blank sizes exist, for example, in a jig blank library as represented by the plot  300  of  FIG. 7B . While each candidate jig blank may have a unique combination of anterior-posterior and medial-lateral dimension sizes, in some embodiments, two or more of the candidate jig blanks may share a common aspect ratio jAP/jML or configuration. The candidate jig blanks of the library may be grouped along sloped lines of the plot  300  according to their aspect ratios jAP/jML. 
     In one embodiment, the jig blank aspect ratio jAP/jML may be used to take a workable jig blank configuration and size it up or down to fit larger or smaller individuals. 
     As can be understood from  FIG. 7A , a series of 98 OA patients having knee disorders were entered into the plot  300  as part of a femur jig design study. Each patient&#39;s femur fAP and fML data was measured and modified via the above-described jFML and jFAP formulas to arrive at the patient&#39;s jig blank data (jFML, jFAP). The patient&#39;s jig blank data was then entered into the plot  300  as a point. As can be understood from  FIG. 7A , no patient point lies outside the parameters of an available group. Such a process can be used to establish group parameters and the number of needed groups. 
     In one embodiment, the selected jig blank parameters can be the femoral jig exterior dimensions that are specific to patient&#39;s knee features. In another embodiment, the selected jig blank parameters can be chosen during fabrication process. 
     e. Formation of 3D Femoral Jig Model. 
     For a discussion of an embodiment of a method of generating a 3D femur jig model  346  generally corresponding to the “integrated jig data”  48  discussed with respect to [block  150 ] of  FIG. 1E , reference is made to  FIGS. 3A-3C ,  FIGS. 8A-8B ,  FIGS. 9A-9C  and  FIG. 10A-10B .  FIGS. 3A-3C  are various views of a femur jig blank  50 A.  FIGS. 8A-8B  are, respectively, exterior and interior perspective views of a femur jig blank exterior surface model  232 M.  FIGS. 9A and 9B  are exterior perspective views of the jig blank exterior model  232 M and bone surface model  40  being combined, and  FIG. 9C  is a cross section through the combined models  232 M,  40  as taken along section line  9 C- 9 C in  FIG. 9B .  FIGS. 10A and 10B  are, respectively, exterior and interior perspective views of the resulting femur jig model  346  after having “saw cut and drill hole data”  44  integrated into the jig model  346  to become an integrated or complete jig model  348  generally corresponding to the “integrated jig data”  48  discussed with respect to [block  1501  of  FIG. 1E . 
     As can be understood from  FIGS. 3A-3C , the jig blank  50 A, which has selected predetermined dimensions as discussed with respect to  FIG. 7 , includes an interior surface  230  and an exterior surface  232 . The exterior surface model  232 M depicted in  FIGS. 8A and 8B  is extracted or otherwise created from the exterior surface  232  of the jig blank model  50 A. Thus, the exterior surface model  232 M is based on the jig blank aspect ratio of the femur jig blank  50 A selected as discussed with respect to  FIG. 7  and is dimensioned specific to the patient&#39;s knee features. The femoral jig surface model  232 M can be extracted or otherwise generated from the jig blank model  50 A of  FIGS. 3A-3C  by employing any of the computer surface rendering techniques described above. 
     As can be understood from  FIGS. 9A-9C , the exterior surface model  232 M is combined with the femur surface model  40  to respectively form the exterior and interior surfaces of the femur jig model  346 . The femur surface model  40  represents the interior or mating surface of the femur jig  2 A and corresponds to the femur arthroplasty target area  42 . Thus, the model  40  allows the resulting femur jig  2 A to be indexed to the arthroplasty target area  42  of the patient&#39;s femur  18  such that the resulting femur jig  2 A will matingly receive the arthroplasty target area  42  during the arthroplasty procedure. The two surface models  232 M,  40  combine to provide a patient-specific jig model  346  for manufacturing the femur jig  2 A. 
     As can be understood from  FIGS. 9B and 9C , once the models  232 M,  40  are properly aligned, a gap will exist between the two models  232 M,  40 . An image sewing method or image sewing tool is applied to the aligned models  232 M,  40  to join the two surface models together to form the 3D computer generated jig model  346  of  FIG. 9B  into a single-piece, joined-together, and filled-in jig model  346  similar in appearance to the integrated jig model  348  depicted in  FIGS. 10A and 10B . In one embodiment, the jig model  346  may generally correspond to the description of the “jig data”  46  discussed with respect [block  145 ] of  FIG. 1E . 
     As can be understood from  FIGS. 9B and 9C , the geometric gaps between the two models  232 M,  40 , some of which are discussed below with respect to thicknesses P 1 , P 2  and P 3 , may provide certain space between the two surface models  232 M,  40  for slot width and length and drill bit length for receiving and guiding cutting tools during TKA surgery. Because the resulting femur jig model  348  depicted in  FIGS. 10A and 10B  may be a 3D volumetric model generated from 3D surface models  232 M,  40 , a space or gap should be established between the 3D surface models  232 M,  40 . This allows the resulting 3D volumetric jig model  348  to be used to generate an actual physical 3D volumetric femur jig  2 . 
     In some embodiments, the image processing procedure may include a model repair procedure for repairing the jig model  346  after alignment of the two models  232 M,  40 . For example, various methods of the model repairing include, but are not limit to, user-guided repair, crack identification and filling, and creating manifold connectivity, as described in: Nooruddin et al.,  Simplification and Repair of Polygonal Models Using Volumetric Techniques  (IEEE Transactions on Visualization and Computer Graphics, Vol. 9, No. 2, April-June 2003); C. Erikson,  Error Correction of a Large Architectural Model: The Henderson County Courthouse  (Technical Report TR95-013, Dept. of Computer Science, Univ. of North Carolina at Chapel Hill, 1995); D. Khorramabdi,  A Walk through the Planned CS Building  (Technical Report UCB/CSD 91/652, Computer Science Dept., Univ. of California at Berkeley, 1991); Morvan et al.,  IVECS: An Interactive Virtual Environment for the Correction of .STL files  (Proc. Conf. Virtual Design, August 1996); Bohn et al.,  A Topology - Based Approach for Shell - Closure , Geometric Modeling for Product Realization, (P. R. Wilson et al., pp. 297-319, North-Holland, 1993); Barequet et al.,  Filling Gaps in the Boundary of a Polyhedron , Computer Aided Geometric Design (vol. 12, no. 2, pp. 207-229, 1995); Barequet et al.,  Repairing CAD Models  ( Proc. IEEE Visualization &#39; 97, pp. 363-370, October 1997); and Gueziec et al.,  Converting Sets of Polygons to Manifold Surfaces by Cutting and Stitching , ( Proc. IEEE Visualization  1998, pp. 383-390, October 1998). Each of these references is incorporated into this Detailed Description in their entireties. 
     As can be understood from  FIGS. 10A and 10B , the integrated jig model  348  may include several features based on the surgeon&#39;s needs. For example, the jig model  348  may include a slot feature  30  for receiving and guiding a bone saw and drill holes  32  for receiving and guiding bone drill bits. As can be understood from  FIGS. 9B and 9C , to provide sufficient structural integrity to allow the resulting femur jig  2 A to not buckle or deform during the arthroplasty procedure and to adequately support and guide the bone saw and drill bits, the gap  350  between the models  232 M,  40  may have the following offsets P 1 , P 2 , and P 3.    
     As can be understood from  FIGS. 9B-10B , in one embodiment, thickness P 1  extends along the length of the anterior drill holes  32 A between the models  232 M,  40  and is for supporting and guiding a bone drill received therein during the arthroplasty procedure. Thickness P 1  may be at least approximately four millimeters or at least approximately five millimeters thick. The diameter of the anterior drill holes  32 A may be configured to receive a cutting tool of at least one-third inches. 
     Thickness P 2  extends along the length of a saw slot  30  between the models  232 M,  40  and is for supporting and guiding a bone saw received therein during the arthroplasty procedure. Thickness P 2  may be at least approximately 10 mm or at least 15 mm thick. 
     Thickness P 3  extends along the length of the posterior drill holes  32 P between the models  232 M,  40  and is for supporting and guiding a bone drill received therein during the arthroplasty procedure. Thickness P 3  may be at least approximately five millimeters or at least eight millimeters thick. The diameter of the drill holes  32  may be configured to receive a cutting tool of at least one-third inches. 
     In addition to providing sufficiently long surfaces for guiding drill bits or saws received therein, the various thicknesses P 1 , P 2 , P 2  are structurally designed to enable the femur jig  2 A to bear vigorous femur cutting, drilling and reaming procedures during the TKR surgery. 
     As indicated in  FIGS. 10A and 10B , the integrated jig model  348  may include: feature  400  that matches the patient&#39;s distal portion of the medial condyle cartilage; feature  402  that matches the patient&#39;s distal portion of the lateral condyle cartilage; projection  404  that can be configured as a contact or a hook and may securely engage the resulting jig  2 A onto the patient&#39;s anterior femoral joint surface during the TKR surgery; and the flat surface  406  that provides a blanked labeling area for listing information regarding the patient, surgeon or/and the surgical procedure. Also, as discussed above, the integrated jig model  348  may include the saw cut slot  30  and the drill holes  32 . The inner portion or side  100  of the jig model  348  (and the resulting femur jig  2 A) is the femur surface model  40 , which will matingly receive the arthroplasty target area  42  of the patient&#39;s femur  18  during the arthroplasty procedure. 
     As can be understood by referring to [block  105 ] of  FIG. 1B  and  FIGS. 2A-2F , in one embodiment when cumulating the image scans  16  to generate the one or the other of the models  40 ,  22 , the models  40 ,  22  are referenced to point P, which may be a single point or a series of points, etc. to reference and orient the models  40 ,  22  relative to the models  22 ,  28  discussed with respect to  FIG. 1C  and utilized for POP. Any changes reflected in the models  22 ,  28  with respect to point P (e.g., point P becoming point P′) on account of the POP is reflected in the point P associated with the models  40 ,  22  (see [block  135 ] of  FIG. 1D ). Thus, as can be understood from [block  140 ] of  FIG. 1D  and  FIGS. 9A-9C , when the jig blank exterior surface model  232 M is combined with the surface model  40  (or a surface model developed from the arthritic model  22 ) to create the jig model  346 , the jig model  346  is referenced and oriented relative to point P′ and is generally equivalent to the “jig data”  46  discussed with respect to [block  145 ] of  FIG. 1E . 
     Because the jig model  346  is properly referenced and oriented relative to point P′, the “saw cut and drill hole data”  44  discussed with respect to [block  125 ] of  FIG. 1E  can be properly integrated into the jig model  346  to arrive at the integrated jig model  348  depicted in  FIGS. 10A-10B . The integrated jig model  348  includes the saw cuts  30 , drill holes  32  and the surface model  40 . Thus, the integrated jig model  348  is generally equivalent to the “integrated jig data”  48  discussed with respect to [block  150 ] of  FIG. 1E . 
     As can be understood from  FIG. 11 , which illustrates a perspective view of the integrated jig model  348  mating with the “arthritic model”  22 , the interior surface  40  of the jig model  348  matingly receives the arthroplasty target area  42  of the femur lower end  204  such that the jig model  348  is indexed to mate with the area  42 . Because of the referencing and orientation of the various models relative to the points P, P′ throughout the procedure, the saw cut slot  30  and drill holes  32  are properly oriented to result in saw cuts and drill holes that allow a resulting femur jig  2 A to restore a patient&#39;s joint to a pre-degenerated condition. 
     As indicated in  FIG. 11 , the integrated jig model  348  may include a jig body  500 , a projection  502  on one side, and two projections  504 ,  506  the other side of jig body  500 . The projections  504 ,  506  match the medial and lateral condyle cartilage. The projections  502 ,  504 ,  506  extend integrally from the two opposite ends of the jig body  500 . 
     As can be understood from [blocks  155 - 165 ] of  FIG. 1E , the integrated jig  348  or, more specifically, the integrated jig data  48  can be sent to the CNC machine  10  to machine the femur jig  2 A from the selected jig blank  50 A. For example, the integrated jig data  48  may be used to produce a production file that provides automated jig fabrication instructions to a rapid production machine  10 , as described in the various Park patent applications referenced above. The rapid production machine  10  then fabricates the patient-specific arthroplasty femur jig  2 A from the femur jig blank  50 A according to the instructions. 
     The resulting femur jig  2 A may have the features of the integrated jig model  348 . Thus, as can be understood from  FIG. 11 , the resulting femur jig  2 A may have the slot  30  and the drilling holes  32  formed on the projections  502 ,  504 ,  506 , depending on the needs of the surgeon. The drilling holes  32  are configured to prevent the possible IR/ER (internal/external) rotational axis misalignment between the femoral cutting jig  2 A and the patient&#39;s damaged joint surface during the distal femur cut portion of the TKR procedure. The slot  30  is configured to accept a cutting instrument, such as a reciprocating slaw blade for transversely cutting during the distal femur cut portion of the TKR. 
     f. Defining a 3D Surface Model of an Arthroplasty Target Area of a Tibia Upper End for Use as a Surface of an Interior Portion of a Tibia Arthroplasty Cutting Jig. 
     For a discussion of a method of generating a 3D model  40  of a target area  42  of a damaged upper end  604  of a patient&#39;s tibia  20 , reference is made to  FIGS. 12A-12C .  FIG. 12A  is an anterior-posterior (“AP”) image slice  608  of the damaged upper or knee joint end  604  of the patient&#39;s tibia  20 , wherein the image slice  608  includes an open-loop contour line segment  610  corresponding to the target area  42  of the damaged upper end  604 .  FIG. 12B  is a plurality of image slices ( 16 - 1 ,  16 - 1 ,  16 - 2 , . . .  16 - n ) with their respective open-loop contour line segments ( 610 - 1 ,  610 - 2 , . . .  610 - n ), the open-loop contour line segments  610  being accumulated to generate the 3D model  40  of the target area  42 .  FIG. 12C  is a 3D model  40  of the target area  42  of the damaged upper end  604  as generated using the open-loop contour line segments ( 16 - 1 ,  16 - 2 , . . .  16 - n ) depicted in  FIG. 12B . 
     As can be understood from  FIGS. 1A ,  1 B and  12 A, the imager  8  is used to generate a 2D image slice  16  of the damaged upper or knee joint end  604  of the patient&#39;s tibia  20 . As depicted in  FIG. 12A , the 2D image  16  may be an AP view of the tibia  20 . Depending on whether the imager  8  is a MRI or CT imager, the image slice  16  will be a MRI or CT slice. The damaged upper end  604  includes the tibia plateau  612 , an anterior tibia shaft surface  614 , and an area of interest or targeted area  42  that extends along the tibia meniscus starting from a portion of the lateral tibia plateau surface to the anterior tibia surface  614 . The targeted area  42  of the tibia upper end may be the articulating contact surfaces of the tibia upper end that contact corresponding articulating contact surfaces of the femur lower or knee joint end. 
     As shown in  FIG. 12A , the image slice  16  may depict the cancellous bone  616 , the cortical bone  618  surrounding the cancellous bone, and the articular cartilage lining portions of the cortical bone  618 . The contour line  610  may extend along the targeted area  42  and immediately adjacent the cortical bone and cartilage to outline the contour of the targeted area  42  of the tibia upper end  604 . The contour line  610  extends along the targeted area  42  starting at point C on the lateral or medial tibia plateau  612  (depending on whether the slice  16  extends through the lateral or medial portion of the tibia) and ends at point D on the anterior tibia shaft surface  614 . 
     In one embodiment, as indicated in  FIG. 12A , the contour line  610  extends along the targeted area  42 , but not along the rest of the surface of the tibia upper end  604 . As a result, the contour line  610  forms an open-loop that, as will be discussed with respect to  FIGS. 12B and 12C , can be used to form an open-loop region or 3D computer model  40 , which is discussed with respect to [block  140 ] of  FIG. 1D  and closely matches the 3D surface of the targeted area  42  of the tibia upper end. Thus, in one embodiment, the contour line is an open-loop and does not outline the entire cortical bone surface of the tibia upper end  604 . Also, in one embodiment, the open-loop process is used to form from the 3D images  16  a 3D surface model  36  that generally takes the place of the arthritic model  36  discussed with respect to [blocks  125 - 140 ] of  FIG. 1D  and which is used to create the surface model  40  used in the creation of the “jig data”  46  discussed with respect to [blocks  145 - 150 ] of  FIG. 1E . 
     In one embodiment and in contrast to the open-loop contour line  610  depicted in  FIGS. 12A and 12B , the contour line is a closed-loop contour line generally the same as the closed-loop contour line  210 ′ discussed with respect to  FIGS. 2D-2E , except the closed-loop contour line pertains to a tibia instead of a femur. Like the femur closed-loop contour line discussed with respect to  FIG. 2D , a tibia closed-loop contour line may outline the entire cortical bone surface of the tibia upper end and results in a closed-loop area. The tibia closed-loop contour lines are combined in a manner similar that discussed with respect to the femur contour lines in  FIG. 2E . As a result, the tibia closed-loop area may require the analysis of the entire surface region of the tibia upper end  604  and result in the formation of a 3D model of the entire tibia upper end  604  in a manner similar to the femur upper end  204  illustrated in  FIG. 2F . Thus, the 3D surface model resulting from the tibia closed-loop process ends up having in common much, if not all, the surface of the 3D tibia arthritic model  36 . In one embodiment, the tibia closed-loop process may result in a 3D volumetric anatomical joint solid model from the 2D images  16  via applying mathematical algorithms. U.S. Pat. No. 5,682,886, which was filed Dec. 26, 1995 and is incorporated by reference in its entirety herein, applies a snake algorithm forming a continuous boundary or closed-loop. After the tibia has been outlined, a modeling process is used to create the 3D surface model, for example, through a Bézier patches method. Other 3D modeling processes, e.g., commercially-available 3D construction software as listed in other parts of this Detailed Description, are applicable to 3D surface model generation for closed-loop, volumetric solid modeling. 
     In one embodiment, the closed-loop process is used to form from the 3D images  16  a 3D volumetric solid model  36  that is essentially the same as the arthritic model  36  discussed with respect to [blocks  125 - 140 ] of  FIG. 1D . The 3D volumetric solid model  36  is used to create the surface model  40  used in the creation of the “jig data”  46  discussed with respect to [blocks  145 - 150 ] of  FIG. 1E . 
     The formation of a 3D volumetric solid model of the entire tibia upper end employs a process that may be much more memory and time intensive than using an open-loop contour line to create a 3D model of the targeted area  42  of the tibia upper end. Accordingly, although the closed-loop methodology may be utilized for the systems and methods disclosed herein, for at least some embodiments, the open-loop methodology may be preferred over the closed-loop methodology. 
     An example of a closed-loop methodology is disclosed in U.S. patent application Ser. No. 11/641,569 to Park, which is entitled “Improved Total Joint Arthroplasty System” and was filed Jan. 19, 2007. This application is incorporated by reference in its entirety into this Detailed Description. 
     As can be understood from  FIGS. 12B and 2G , the imager  8  generates a plurality of image slices ( 16 - 1 ,  16 - 2  . . .  16 - n ) via repetitive imaging operations [block  1000 ]. Each image slice  16  has an open-loop contour line ( 610 - 1 ,  610 - 2  . . .  610 - n ) extending along the targeted region  42  in a manner as discussed with respect to  FIG. 12A  [block  1005 ]. In one embodiment, each image slice is a two-millimeter 2D image slice  16 . The system  100  compiles the plurality of 2D image slices ( 16 - 1 ,  16 - 2  . . .  16 - n ) and, more specifically, the plurality of open-loop contour lines ( 610 - 1 ,  610 - 2 , . . .  610 - n ) into the 3D femur surface computer model  40  depicted in  FIG. 12C  [block  1010 ]. This process regarding the generation of the surface model  40  is also discussed in the overview section with respect to [blocks  100 - 105 ] of  FIG. 1B  and [blocks  130 - 140 ] of  FIG. 1D . A similar process may be employed with respect to tibia closed-loop contour lines. 
     As can be understood from  FIG. 12C , the 3D tibia surface computer model  40  is a 3D computer representation of the targeted region  42  of the tibia upper end. In one embodiment, the 3D representation of the targeted region  42  is a 3D representation of the articulated femur contact surfaces of the tibia proximal end. As the open-loop generated 3D model  40  is a surface model of the relevant femur contacting portions of the tibia upper end, as opposed to a 3D model of the entire surface of the tibia upper end as would be a result of a closed-loop contour line, the open-loop generated 3D model  40  is less time and memory intensive to generate. 
     In one embodiment, the open-loop generated 3D model  40  is a surface model of the femur facing end face of the tibia upper end, as opposed a 3D model of the entire surface of the tibia upper end. The 3D model  40  can be used to identify the area of interest or targeted region  42 , which, as previously stated, may be the relevant femur contacting portions of the tibia upper end. Again, the open-loop generated 3D model  40  is less time and memory intensive to generate as compared to a 3D model of the entire surface of the tibia proximal end, as would be generated by a closed-loop contour line. Thus, for at least some versions of the embodiments disclosed herein, the open-loop contour line methodology is preferred over the closed-loop contour line methodology. However, the system  4  and method disclosed herein may employ either the open-loop or closed-loop methodology and should not be limited to one or the other. 
     Regardless of whether the 3D model  40  is a surface model of the targeted region  42  (i.e., a 3D surface model generated from an open-loop process and acting as the arthritic model  22 ) or the entire femur facing end face of the tibia upper end (i.e., a 3D volumetric solid model generated from a closed-loop process and acting as the arthritic model  22 ), the data pertaining to the contour lines  610  can be converted into the 3D contour computer model  40  via the surface rendering techniques disclosed in any of the aforementioned U.S. patent applications to Park. For example, surface rending techniques employed include point-to-point mapping, surface normal vector mapping, local surface mapping, and global surface mapping techniques. Depending on the situation, one or a combination of mapping techniques can be employed. 
     In one embodiment, the generation of the 3D model  40  depicted in  FIG. 12C  may be formed by using the image slices  16  to determine location coordinate values of each of a sequence of spaced apart surface points in the open-loop region of  FIG. 12B . A mathematical model may then be used to estimate or compute the 3D model  40  in  FIG. 12C . Examples of other medical imaging computer programs that may be used include, but are not limited to: Analyze from AnalyzeDirect, Inc. of Overland Park, Kans.; open-source software such as Paraview of Kitware, Inc.; Insight Toolkit (“ITK”) available at www.itk.org; 3D Slicer available at www.slicer.org; and Mimics from Materialise of Ann Arbor, Mich. 
     Alternatively or additionally to the aforementioned systems for generating the 3D model  40  depicted in  FIG. 12C , other systems for generating the 3D model  40  of  FIG. 12C  include the surface rendering techniques of the Non-Uniform Rational B-spline (“NURB”) program or the B6zier program. Each of these programs may be employed to generate the 3D contour model  40  from the plurality of contour lines  610 . 
     In one embodiment, the NURB surface modeling technique is applied to the plurality of image slices  16  and, more specifically, the plurality of open-loop contour lines  610  of  FIG. 2B . The NURB software generates a 3D model  40  as depicted in  FIG. 12C , wherein the 3D model  40  has areas of interest or targeted regions  42  that contain both a mesh and its control points. For example, see Ervin et al., Landscape Modeling, McGraw-Hill, 2001, which is hereby incorporated by reference in its entirety into this Detailed Description. 
     In one embodiment, the NURB surface modeling technique employs the following surface equation: 
                 G   ⁡     (     s   ,   t     )       =         ∑     i   =   0       k   ⁢           ⁢   1       ⁢       ∑     j   =   0       k   ⁢           ⁢   2       ⁢       W   ⁡     (     i   ,   j     )       ⁢     P   ⁡     (     i   ,   j     )       ⁢       b   i     ⁡     (   s   )       ⁢       b   j     ⁡     (   t   )                 ∑     i   =   0       k   ⁢           ⁢   1       ⁢       ∑     j   =   0       k   ⁢           ⁢   2       ⁢       W   ⁡     (     i   ,   j     )       ⁢       b   i     ⁡     (   s   )       ⁢       b   j     ⁡     (   t   )                 ,         
wherein P(i,j) represents a matrix of vertices with nrows=(k1+1) and ncols=(k2+1), W(i,j) represents a matrix of vertex weights of one per vertex point, b i (s) represents a row-direction basis or blending of polynomial functions of degree MI, b j (t) represents a column-direction basis or blending polynomial functions of degree M 2 , s represents a parameter array of row-direction knots, and t represents a parameter array of column-direction knots.
 
     In one embodiment, the Bézier surface modeling technique employs the Bézier equation (1972, by Pierre Bézier) to generate a 3D model  40  as depicted in  FIG. 12C , wherein the model  40  has areas of interest or targeted regions  42 . A given Bézier surface of order (n, m) is defined by a set of (n+1)(m+1) control points k ij . It maps the unit square into a smooth-continuous surface embedded within a space of the same dimensionality as (k ij ). For example, if k are all points in a four-dimensional space, then the surface will be within a four-dimensional space. This relationship holds true for a one-dimensional space, a two-dimensional space, a fifty-dimensional space, etc. 
     A two-dimensional Bézier surface can be defined as a parametric surface where the position of a point p as a function of the parametric coordinates u, v is given by: 
               p   ⁡     (     u   ,   v     )       =       ∑     i   =   0     n     ⁢       ∑     j   =   0     m     ⁢         B   i   n     ⁡     (   u   )       ⁢       B   j   m     ⁡     (   v   )       ⁢     k     i   ,   j                   
evaluated over the unit square,
 
where
 
                 B   i   n     ⁡     (   u   )       =       (         n           i         )     ⁢         u   i     ⁡     (     1   -   u     )         n   -   i               
is a Bernstein polynomial and
 
               (         n           i         )     =       n   !         i   !     *       (     n   -   i     )     !               
is the binomial coefficient. See Grune et al,  On Numerical Algorithm and Interactive Visualization for Optimal Control Problems , Journal of Computation and Visualization in Science, Vol. 1, No. 4, July 1999, which is hereby incorporated by reference in its entirety into this Detailed Description.
 
     Various other surface rendering techniques are disclosed in other references. For example, see the surface rendering techniques disclosed in the following publications: Lorensen et al.,  Marching Cubes: A high Resolution  3 d Surface Construction Algorithm , Computer Graphics, 21-3: 163-169, 1987; Farin et al.,  NURB Curves  &amp;  Surfaces: From Projective Geometry to Practical Use , Wellesley, 1995; Kumar et al,  Robust Incremental Polygon Triangulation for Surface Rendering , WSCG, 2000; Fleischer et al.,  Accurate Polygon Scan Conversion Using Half - Open Intervals , Graphics Gems III, p. 362-365, code: p. 599-605, 1992; Foley et al.,  Computer Graphics: Principles and Practice , Addison Wesley, 1990; Glassner,  Principles of Digital Image Synthesis , Morgan Kaufmann, 1995, all of which are hereby incorporated by reference in their entireties into this Detailed Description. 
     g. Selecting a Jig Blank Most Similar in Size and/or Configuration to the Size of the Patient&#39;s Tibia Upper End. 
     As mentioned above, an arthroplasty jig  2 , such as a tibia jig  2 B includes an interior portion  104  and an exterior portion  106 . The tibia jig  2 B is formed from a tibia jig blank  50 B, which, in one embodiment, is selected from a finite number of femur jig blank sizes. The selection of the tibia jig blank  50 B is based on a comparison of the dimensions of the patient&#39;s tibia upper end  604  to the dimensions and/or configurations of the various sizes of tibia jig blanks  50 B to select the tibia jig blank  50 B most closely resembling the patient&#39;s tibia upper end  604  with respect to size and/or configuration. This selected tibia jig blank  50 B has an outer or exterior side or surface  632  that forms the exterior portion  632  of the tibia jig  2 B. The 3D surface computer model  40  discussed with respect to the immediately preceding section of this Detail Description is used to define a 3D surface  40  into the interior side  630  of the computer model of a tibia jig blank  50 B. 
     By selecting a tibia jig blank  50 B with an exterior portion  632  close in size to the patient&#39;s upper tibia end  604 , the potential for an accurate fit between the interior portion  630  and the patient&#39;s tibia is increased. Also, the amount of material that needs to be machined or otherwise removed from the jig blank  50 B is reduced, thereby reducing material waste and manufacturing time. 
     For a discussion of a method of selecting a jig blank  50  most closely corresponding to the size and/or configuration of the patient&#39;s upper tibia end, reference is first made to  FIGS. 13A-14B .  FIG. 13A  is a top perspective view of a right tibia cutting jig blank  50 BR having predetermined dimensions.  FIG. 13B  is a bottom perspective view of the jig blank  50 BR depicted in  FIG. 13A .  FIG. 13C  is plan view of an exterior side or portion  232  of the jig blank  50 BR depicted in  FIG. 13A .  FIG. 14A  is a plurality of available sizes of right tibia jig blanks  50 BR, each depicted in the same view as shown in  FIG. 13C .  FIG. 14B  is a plurality of available sizes of left tibia jig blanks, each depicted in the same view as shown in  FIG. 13C . 
     A common jig blank  50 , such as the right jig blank  50 BR depicted in  FIGS. 13A-13C  and intended for creation of a right tibia jig that can be used with a patient&#39;s right tibia, may include a medial tibia foot projection  648  for mating with the medial tibia plateau, a lateral tibia foot projection  650  for mating with the lateral tibia plateau, a posterior edge  640 , an anterior edge  642 , a lateral edge  644 , a medial edge  646 , the exterior side  632  and the interior side  630 . The jig blank  50 BR of  FIGS. 13A-13C  may be any one of a number of right tibia jig blanks  50 BR available in a limited number of standard sizes. For example, the jig blank  50 BR of  FIGS. 13A-13C  may be an i-th right tibia jig blank, where i=1, 2, 3, 4, . . . m and m represents the maximum number of right tibia jig blank sizes. 
     As indicated in  FIG. 13C , the anterior-posterior extent TAi of the jig blank  50 BR is measured from the anterior edge  642  to the posterior edge  640  of the jig blank  50 BR. The medial-lateral extent TMi of the jig blank  50 BR is measured from the lateral edge  644  to the medial edge  646  of the jig blank  50 BR. 
     As can be understood from  FIG. 14A , a limited number of right tibia jig blank sizes may be available for selection as the right tibia jig blank size to be machined into the right tibia cutting jig  2 B. For example, in one embodiment, there are three sizes (m=3) of right tibia jig blanks  50 BR available. As can be understood from  FIG. 13C , each tibia jig blank  50 BR has an anterior-posterior/medial-lateral aspect ratio defined as TAi to TMi (e.g., “TAi/TMi” aspect ratio). Thus, as can be understood from  FIG. 14A , jig blank  50 BR- 1  has an aspect ratio defined as “TA 1 /TM 1 ”, jig blank  50 BR- 2  has an aspect ratio defined as “TA 2 /TM 2 ”, and jig blank  50 BR- 3  has an aspect ratio defined as “TA 3 /TM 3 ”. 
     The jig blank aspect ratio is utilized to design right tibia jigs  2 B dimensioned specific to the patient&#39;s right tibia features. In one embodiment, the jig blank aspect ratio can be the exterior dimensions of the right tibia jig  2 B. In another embodiment, the jig blank aspect ratio can apply to the right tibia jig fabrication procedure for selecting the right jig blank  50 BR having parameters close to the dimensions of the desired right tibia jig  2 B. This embodiment can improve the cost efficiency of the right tibia jig fabrication process because it reduces the amount of machining required to create the desired jig  2  from the selected jig blank  50 . 
     In  FIG. 14A  there is a single jig blank aspect ratio depicted for the candidate tibia jig blank sizes. In embodiments having a greater number of jig blank aspect ratios for the candidate tibia jig blank sizes,  FIG. 14A  would be similar to  FIG. 4A  and would have an N- 1  direction, and potentially N- 2  and N- 3  directions, representing increasing jig blank aspect ratios. The relationships between the various tibia jig blank aspect ratios would be similar to those discussed with respect to  FIG. 4A  for the femur jig blank aspect ratios. 
     As can be understood from the plot  900  depicted in  FIG. 17  and discussed later in this Detailed Discussion, the E- 1  direction corresponds to the sloped line joining Group 1, Group 2 and Group 3 in the plot  900 . 
     As indicated in  FIG. 14A , along direction E- 1 , the jig blank aspect ratios remain the same among jigs blanks  50 BR- 1 ,  50 BR- 2  and  50 BR- 3 , where “TA 1 /TM 1 ”=“TA 2 /TM 2 ”=“TA 3 /TM 3 ”. However, comparing to jig blank  50 BR- 1 , jig blank  50 BR- 2  is dimensioned larger and longer than jig blank  50 BR- 1 . This is because the TA 2  value for jig blank  50 BR- 2  increases proportionally with the increment of its TM 2  value in certain degrees in all X, Y, and Z-axis directions. In a similar fashion, jig blank  50 BR- 3  is dimensioned larger and longer than jig blank  50 BR- 2  because the TA 3  increases proportionally with the increment of its TM 3  value in certain degrees in all X, Y, and Z-axis directions. One example of the increment can be an increase from 5% to 20%. In embodiments where there are additional aspect ratios available for the tibia jig blank sizes, as was illustrated in  FIG. 4A  with respect to the femur jig blank sizes, the relationship between tibia jig blank sizes may be similar to that discussed with respect to  FIGS. 4A and 14A . 
     As can be understood from  FIG. 14B , a limited number of left tibia jig blank sizes may be available for selection as the left tibia jig blank size to be machined into the left tibia cutting jig  2 B. For example, in one embodiment, there are three sizes (m=3) of left tibia jig blanks  50 BL available. As can be understood from  FIG. 13C , each tibia jig blank  50 BL has an anterior-posterior/medial-lateral aspect ratio defined as TAi to TMi (e.g., “TAi/TMi” aspect ratio). Thus, as can be understood from  FIG. 14B , jig blank  50 BL- 1  has an aspect ratio defined as “TA 1 /TM 1 ”, jig blank  50 BL- 2  has an aspect ratio defined as “TA 2 /TM 2 ”, and jig blank  50 BL- 3  has an aspect ratio defined as “TA 3 /TM 3 ”. 
     The jig blank aspect ratio is utilized to design left tibia jigs  2 B dimensioned specific to the patient&#39;s left tibia features. In one embodiment, the jig blank aspect ratio can be the exterior dimensions of the left tibia jig  2 B. In another embodiment, the jig blank aspect ratio can apply to the left tibia jig fabrication procedure for selecting the left jig blank  50 BL having parameters close to the dimensions of the desired left tibia jig  2 B. This embodiment can improve the cost efficiency of the left tibia jig fabrication process because it reduces the amount of machining required to create the desired jig  2  from the selected jig blank  50 . 
     In  FIG. 14B  there is a single jig blank aspect ratio depicted for the candidate tibia jig blank sizes. In embodiments having a greater number of jig blank aspect ratios for the candidate tibia jig blank sizes,  FIG. 14B  would be similar to  FIG. 4B  and would have an N- 1  direction, and potentially N- 2  and N- 3  directions, representing increasing jig blank aspect ratios. The relationships between the various tibia jig blank aspect ratios would be similar to those discussed with respect to  FIG. 4B  for the femur jig blank aspect ratios. 
     As indicated in  FIG. 14B , along direction E- 1 , the jig blank aspect ratios remain the same among jigs blanks  50 BL- 1 ,  50 BL- 2  and  50 BL- 3 , where “TA 1 /TM 1 ”=“TA 2 /TM 2 ”=“TA 3 /TM 3 ”. However, comparing to jig blank  50 BL- 1 , jig blank  50 BL- 2  is dimensioned larger and longer than jig blank  50 BL- 1 . This is because the TA 2  value for jig blank  50 BL- 2  increases proportionally with the increment of its TM 2  value in certain degrees in all X, Y, and Z-axis directions. In a similar fashion, jig blank  50 BL- 3  is dimensioned larger and longer than jig blank  50 BL- 2  because the TA 3  increases proportionally with the increment of its TM 3  value in certain degrees in all X, Y, and Z-axis directions. One example of the increment can be an increase from 5% to 20%. In embodiments where there are additional aspect ratios available for the tibia jig blank sizes, as was illustrated in  FIG. 4B  with respect to the femur jig blank sizes, the relationship between tibia jig blank sizes may be similar to that discussed with respect to  FIGS. 4B and 14B . 
     The dimensions of the upper or knee joint forming end  604  of the patient&#39;s tibia  20  can be determined by analyzing the 3D surface model  40  or 3D arthritic model  36  in a manner similar to those discussed with respect to the jig blanks  50 . For example, as depicted in FIG.  15 , which is an axial view of the 3D surface model  40  or arthritic model  36  of the patient&#39;s right tibia  20  as viewed in a direction extending proximal to distal, the upper end  604  of the surface model  40  or arthritic model  36  may include an anterior edge  660 , a posterior edge  662 , a medial edge  664  and a lateral edge  666 . The tibia dimensions may be determined for the top end face or femur articulating surface  604  of the patient&#39;s tibia  20  via analyzing the 3D surface model  40  of the 3D arthritic model  36 . These tibia dimensions can then be utilized to configure tibia jig dimensions and select an appropriate tibia jig. 
     As shown in  FIG. 15 , the anterior-posterior extent tAP of the upper end  604  of the patient&#39;s tibia  20  (i.e., the upper end  604  of the surface model  40  of the arthritic model  36 , whether formed via open or closed-loop analysis) is the length measured from the anterior edge  660  of the tibia plateau to the posterior edge  662  of the tibia plateau. The medial-lateral extent tML of the upper end  604  of the patient&#39;s tibia  20  is the length measured from the medial edge  664  of the medial tibia plateau to the lateral edge  666  of the lateral tibia plateau. 
     In one embodiment, the anterior-posterior extent tAP and medial-lateral extent tML of the tibia upper end  604  can be used for an aspect ratio tAP/tML of the tibia upper end. The aspect ratios tAP/tML of a large number (e.g., hundreds, thousands, tens of thousands, etc.) of patient knees can be compiled and statistically analyzed to determine the most common aspect ratios for jig blanks that would accommodate the greatest number of patient knees. This information may then be used to determine which one, two, three, etc. aspect ratios would be most likely to accommodate the greatest number of patient knees. 
     The system  4  analyzes the upper ends  604  of the patient&#39;s tibia  20  as provided via the surface model  40  of the arthritic model  36  (whether the arthritic model  36  is an 3D surface model generated via an open-loop or a 3D volumetric solid model generated via a closed-loop process), to obtain data regarding anterior-posterior extent tAP and medial-lateral extent tML of the tibia upper ends  604 . As can be understood from  FIG. 16 , which depicts the selected model jig blank  50 BR of  FIG. 13C  superimposed on the model tibia upper end  604  of  FIG. 15 , the tibia dimensional extents tAP, tML are compared to the jig blank dimensional extents TA, TM to determine which jig blank model to select as the starting point for the machining process and the exterior surface model for the jig model. 
     As shown in  FIG. 16 , a prospective right tibia jig blank  50 BR is superimposed to mate with the right tibia upper end  604  of the patient&#39;s anatomical model as represented by the surface model  40  or arthritic model  36 . In one embodiment, the jig blank  50 BR may cover the anterior approximately two thirds of the tibia plateau, leaving the posterior approximately one third of the tibia exposed. Included in the exposed portion of the tibia plateau are lateral and medial exposed regions of the tibia plateau, as respectively represented by regions q 1  and q 2  in  FIG. 16 . Specifically, exposed region q 1  is the region of the exposed tibia plateau between the tibia and jig blank lateral edges  666 ,  644 , and exposed region q 2  is the region of the exposed tibia plateau between the tibia and jig blank medial edges  664 ,  646 . 
     By obtaining and employing the tibia anterior-posterior tAP data and the tibia medial-lateral tML data, the system  4  can size the tibia jig blank  50 BR according to the following formula: jTML tML−q 1 −q 2 , wherein jTML is the medial-lateral extent of the tibia jig blank  50 BR. In one embodiment, q 1  and q 2  will have the following ranges: 2 mm≦q 1 ≦4 mm; and 2 mm≦q 2 ≦4 mm. In another embodiment, q 1  will be approximately 3 mm and q 2  will approximately 3 mm. 
       FIG. 17A  is an example scatter plot  900  for selecting from a plurality of candidate jig blanks sizes a jig blank size appropriate for the upper end  604  of the patient&#39;s tibia  20 . In one embodiment, the X-axis represents the patient&#39;s tibia medial-lateral length tML in millimeters, and the Y-axis represents the patient&#39;s tibia anterior-posterior length tAP in millimeters. In one embodiment, the plot  900  is divided into a number of jig blank size groups, where each group encompasses a region of the plot  900  and is associated with a specific parameter TM, of a specific candidate jig blank size. 
     In one embodiment, the example scatter plot  900  depicted in  FIG. 17A  has three jig blank size groups, each group pertaining to a single candidate jig blank size. However, depending on the embodiment, a scatter plot  900  may have a greater or lesser number of jig blank size groups. The higher the number of jig blank size groups, the higher the number of the candidate jig blank sizes and the more dimension specific a selected candidate jig blank size will be to the patient&#39;s knee features and the resulting jig  2 . The more dimension specific the selected candidate jig blank size, the lower the amount of machining required to produce the desired jig  2  from the selected jig blank  50 . 
     Conversely, the lower the number of jig blank size groups, the lower the number of candidate jig blank sizes and the less dimension specific a selected candidate jig blank size will be to the patient&#39;s knee features and the resulting jig  2 . The less dimension specific the selected candidate jig blank size, the higher the amount of machining required to produce the desired jig  2  from the selected jig blank  50 , adding extra roughing during the jig fabrication procedure. 
     The tibia anterior-posterior length tAP may be relevant because it may serve as a value for determining the aspect ratio TA i /TM j  for tibia jig blanks  50 B such as those discussed with respect to  FIGS. 13C-14B  and  17 A. Despite this, in some embodiments, tibia anterior-posterior length TA, of the candidate jig blanks may not be reflected in the plot  900  depicted in  FIG. 17A  or the relationship depicted in  FIG. 16  because in a practical setting for some embodiments, tibia jig anterior-posterior length may be less significant than tibia jig medial-lateral length. For example, although a patient&#39;s tibia anterior-posterior distance varies according to their knee features, the length of the foot projection  800 ,  802  (see  FIG. 20A ) of a tibia jig  2 B is simply increased without the need to create a jig blank or jig that is customized to correspond to the tibia anterior-posterior length TA. In other words, in some embodiments, the only difference in anterior-posterior length between various tibia jigs is the difference in the anterior-posterior length of their respective foot projections  800 ,  802 . 
     In some embodiments, as can be understood from  FIGS. 16 and 21 , the anterior-posterior length of a tibia jig  2 B, with its foot projection  800 ,  802 , covers approximately half of the tibia plateau. Due in part to this “half” distance coverage, which varies from patient-to-patient by only millimeters to a few centimeter, in one embodiment, the anterior-posterior length of the jig may not be of a significant concern. However, because the jig may cover a substantial portion of the medial-lateral length of the tibia plateau, the medial-lateral length of the jig may be of substantial significance as compared to the anterior-posterior length. 
     While in some embodiments the anterior-posterior length of a tibia jig  2 B may not be of substantial significance as compared to the medial-lateral length, in some embodiments the anterior-posterior length of the tibia jig is of significance. In such an embodiment, jig sizes may be indicated in  FIG. 17A  by their aspect ratios TA i /TM j  as opposed to just TM j . In other words, the jig sizes may be depicted in  FIG. 17A  in a manner similar to that depicted in  FIG. 7A . Furthermore, in such embodiments,  FIGS. 14A and 14B  may have additional jig blank ratios similar to that depicted in  FIGS. 4A and 4B . As a result, the plot  900  of  17 A may have additional diagonal lines joining the jig blank sizes belonging to each jig blank ratio in a manner similar to that depicted in plot  300  of  FIG. 7A . Also, in  FIG. 17A  and in a manner similar to that shown in  FIG. 7A , there may be additional horizontal lines dividing plot  900  according to anterior-posterior length to represent the boundaries of the various jig blank sizes. 
     As can be understood from  FIG. 17A , in one embodiment, the three jig blank size groups of the plot  900  have parameters TM r , TA r  as follows. Group 1 has parameters TM 1 , TA 1 . TM 1  represents the medial-lateral extent of the first tibia jig blank size, wherein TM 1 =70 mm. TA 1  represents the anterior-posterior extent of the first femoral jig blank size, wherein TA 1 =62 mm. Group 1 covers the patient&#39;s tibia tML and tAP data wherein 55 mm&lt;tML&lt;70 mm and 45 mm&lt;tAP&lt;75 mm. 
     Group 2 has parameters TM 2 , TA 2 . TM 2  represents the medial-lateral extent of the second tibia jig blank size, wherein TM 2 =85 mm. TA 2  represents the anterior-posterior extent of the second femoral jig blank size, wherein TA 2 =65 mm. Group 2 covers the patient&#39;s tibia tML and tAP data wherein 70 mm&lt;tML&lt;85 mm and 45 mm&lt;tAP&lt;75 mm. 
     Group 3 has parameters TM 3 , TA 3 . TM 3  represents the medial-lateral extent of the third tibia jig blank size, wherein TM 3 =100 mm. TA 3  represents the anterior-posterior extent of the second femoral jig blank size, wherein TA 3 =68.5 mm. Group 3 covers the patient&#39;s tibia tML and tAP data wherein 85 mm&lt;tML&lt;100 mm and 45 mm&lt;tAP&lt;75 mm. 
     In some embodiments and in contrast to the selection process for the femur jig blanks discussed with respect to  FIGS. 3A-7B , the tibia jig blank selection process discussed with respect to  FIGS. 13A-17B  may only consider or employ the medial-lateral tibia jig value jTML and related medial-lateral values TM, tML. Accordingly, in such embodiments, the anterior-posterior tibia jig value JTAP and related anterior-posterior values TA, tAP for the tibia jig and tibia plateau are not considered. 
     As can be understood from  FIG. 17B , which is a flow diagram illustrating an embodiment of a process of selecting an appropriately sized jig blank, the bone medial-lateral extent tML is determined for the upper end  604  of the surface model  40  of the arthritic model  36  [block  3000 ]. The medial-lateral bone extent tML of the upper end  604  is mathematically modified according to the above discussed jTML formula to arrive at the minimum tibia jig blank medial-lateral extent jTML [block  3010 ]. The mathematically modified bone medial-lateral extent tML or, more specifically, the minimum tibia jig blank medial-lateral extent jTML is referenced against the jig blank dimensions in the plot  900  of  FIG. 17A  [block  3020 ]. The plot  900  may graphically represent the extents of candidate tibia jig blanks forming a jig blank library. The tibia jig blank  50 B is selected to be the jig blank size having the smallest extents that are still sufficiently large to accommodate the minimum tibia jig blank medial-lateral extent jTML [block  3030 ]. 
     In one embodiment, the exterior of the selected jig blank size is used for the exterior surface model of the jig model, as discussed below. In one embodiment, the selected jig blank size corresponds to an actual jig blank that is placed in the CNC machine and milled down to the minimum tibia jig blank anterior-posterior and medial-lateral extents jTAP, jTML to machine or otherwise form the exterior surface of the tibia jig  2 B. 
     The method outlined in  FIG. 17B  and in reference to the plot  900  of  FIG. 17A  can be further understood from the following example. As measured in  FIG. 16  with respect to the upper end  604  of the patient&#39;s tibia  20 , the extents of the patient&#39;s tibia are as follows: tML=85.2 mm [block  3000 ]. As previously mentioned, the upper end  604  may be part of the surface model  40  of the arthritic model  36 . Once the tML measurement is determined from the upper end  604 , the corresponding jig jTML data can be determined via the above-described jTML formula: jTML=tML−q 1 −q 2 , wherein q 1 =3 mm and q 2 =3 mm [block  3010 ]. The result of the jTML formula is jTML=79.2 mm. 
     As can be understood from the plot  900  of  FIG. 17A , the determined jig data (i.e., jTML=79.2 mm) falls in Group 2 of the plot  900 . Group 2 has the predetermined tibia jig blank parameters (TM 2 ) of TM 2 =85 mm. This predetermined tibia jig blank parameter is the smallest of the various groups that are still sufficiently large to meet the minimum tibia blank extents jTML [block  3020 ]. This predetermined tibia jig blank parameters (TM 2 =85 mm) may be selected as the appropriate tibia jig blank size [block  3030 ]. 
     In one embodiment, the predetermined tibia jig blank parameter (85 mm) can apply to the tibia exterior jig dimensions as shown in  FIG. 13C . In other words, the jig blank exterior is used for the jig model exterior as discussed with respect to  FIGS. 18A-19C . Thus, the exterior of the tibia jig blank  50 B undergoes no machining, and the unmodified exterior of the jig blank  50 B with its predetermined jig blank parameter (85 mm) serves as the exterior of the finished tibia jig  2 B. 
     In another embodiment, the tibia jig blank parameter (85 mm) can be selected for jig fabrication in the machining process. Thus, a tibia jig blank  50 B having a predetermined parameter (85 mm) is provided to the machining process such that the exterior of the tibia jig blank  50 B will be machined from its predetermined parameter (85 mm) down to the desired tibia jig parameter (79.2 mm) to create the finished exterior of the tibia jig  2 B. As the predetermined parameter (85 mm) is selected to be relatively close to the desired femur jig parameter (79.2 mm), machining time and material waste are reduced. 
     While it may be advantageous to employ the above-described jig blank selection method to minimize material waste and machining time, in some embodiments, a jig blank will simply be provided that is sufficiently large to be applicable to all patient bone extents tML. Such a jig blank is then machined down to the desired jig blank extent jTML, which serve as the exterior surface of the finished jig  2 B. 
     In one embodiment, the number of candidate jig blank size groups represented in the plot  900  is a function of the number of jig blank sizes offered by a jig blank manufacturer. For example, a first plot  900  may pertain only to jig blanks manufactured by company A, which offers three jig blank sizes. Accordingly, the plot  900  has three jig blank size groups. A second plot  900  may pertain only to jig blanks manufactured by company B, which offers six jig blank size groups. Accordingly, the second plot  900  has six jig blank size groups. 
     A plurality of candidate jig blank sizes exist, for example, in a jig blank library as represented by the plot  900  of  FIG. 17B . While each candidate jig blank may have a unique combination of anterior-posterior and medial-lateral dimension sizes, in some embodiments, two or more of the candidate jig blanks may share a common aspect ratio tAP/tML or configuration. The candidate jig blanks of the library may be grouped along sloped lines of the plot  900  according to their aspect ratios tAP/tML. 
     In one embodiment, the jig blank aspect ratio tAP/tML may be used to take a workable jig blank configuration and size it up or down to fit larger or smaller individuals. 
     As can be understood from  FIG. 17A , a series of 98 OA patients having knee disorders were entered into the plot  900  as part of a tibia jig design study. Each patient&#39;s tibia tAP and tML data was measured. Each patient tibia tML data was modified via the above-described jTML formula to arrive at the patient&#39;s jig blank data (jFML). The patient&#39;s jig blank data was then entered into the plot  900  as a point. As can be understood from  FIG. 17A , no patient point lies outside the parameters of an available group. Such a process can be used to establish group parameters and the number of needed groups. 
     In one embodiment, the selected jig blank parameters can be the tibia jig exterior dimensions that are specific to patient&#39;s knee features. In another embodiment, the selected jig blank parameters can be chosen during fabrication process. 
     h. Formation of 3D Tibia Jig Model. 
     For a discussion of an embodiment of a method of generating a 3D tibia jig model  746  generally corresponding to the “integrated jig data”  48  discussed with respect to [block  150 ] of  FIG. 1E , reference is made to  FIGS. 13A-13C ,  FIGS. 18A-18B ,  FIGS. 19A-19D  and  FIG. 20A-20B .  FIGS. 13A-13C  are various views of a tibia jig blank  50 B.  FIGS. 18A-18B  are, respectively, exterior and interior perspective views of a tibia jig blank exterior surface model  632 M.  FIGS. 19A-19D  are exterior perspective views of the tibia jig blank exterior model  632 M and bone surface model  40  being combined.  FIGS. 20A and 20B  are, respectively, exterior and interior perspective views of the resulting tibia jig model  746  after having “saw cut and drill hole data”  44  integrated into the jig model  746  to become an integrated or complete jig model  748  generally corresponding to the “integrated jig data”  48  discussed with respect to [block  150 ] of  FIG. 1E . 
     As can be understood from  FIGS. 13A-13C , the jig blank  50 B, which has selected predetermined dimensions as discussed with respect to  FIGS. 17A and 17B , includes an interior surface  630  and an exterior surface  632 . The exterior surface model  632 M depicted in  FIGS. 18A and 18B  is extracted or otherwise created from the exterior surface  632  of the jig blank model  50 B. Thus, the exterior surface model  632 M is based on the jig blank aspect ratio of the tibia jig blank  50 B selected as discussed with respect to  FIGS. 17A and 17B  and is dimensioned specific to the patient&#39;s knee features. The tibia jig surface model  632 M can be extracted or otherwise generated from the jig blank model  50 B of  FIGS. 13A-13C  by employing any of the computer surface rendering techniques described above. 
     As can be understood from  FIGS. 19A-19C , the exterior surface model  632 M is combined with the tibia surface model  40  to respectively form the exterior and interior surfaces of the tibia jig model  746 . The tibia surface model  40  represents the interior or mating surface of the tibia jig  2 B and corresponds to the tibia arthroplasty target area  42 . Thus, the model  40  allows the resulting tibia jig  2 B to be indexed to the arthroplasty target area  42  of the patient&#39;s tibia  20  such that the resulting tibia jig  2 B will matingly receive the arthroplasty target area  42  during the arthroplasty procedure. The two surface models  632 M,  40  combine to provide a patient-specific jig model  746  for manufacturing the tibia jig  2 B. 
     As can be understood from  FIGS. 19B and 19C , once the models  632 M,  40  are properly aligned, a gap will exist between the two models  632 M,  40 . An image sewing method or image sewing tool is applied to the aligned models  632 M,  40  to join the two surface models together to form the 3D computer generated jig model  746  of  FIG. 19B  into a single-piece, joined-together, and filled-in jig model  746  similar in appearance to the integrated jig model  748  depicted in  FIGS. 20A and 20B . In one embodiment, the jig model  746  may generally correspond to the description of the “jig data”  46  discussed with respect [block  145 ] of  FIG. 1E . 
     As can be understood from  FIGS. 19B-19D ,  20 A and  20 B, the geometric gaps between the two models  632 M,  40 , some of which are discussed below with respect to thicknesses VI, V 2  and V 3 , may provide certain space between the two surface models  632 M,  40  for slot width and length and drill bit length for receiving and guiding cutting tools during TKA surgery. Because the resulting tibia jig model  748  depicted in  FIGS. 20A and 20B  may be a 3D volumetric model generated from 3D surface models  632 M,  40 , a space or gap should be established between the 3D surface models  632 M,  40 . This allows the resulting 3D volumetric jig model  748  to be used to generate an actual physical 3D volumetric tibia jig  2 B. 
     In some embodiments, the image processing procedure may include a model repair procedure for repairing the jig model  746  after alignment of the two models  632 M,  40 . For example, various methods of the model repairing include, but are not limit to, user-guided repair, crack identification and filling, and creating manifold connectivity, as described in: Nooruddin et al.,  Simplification and Repair of Polygonal Models Using Volumetric Techniques  (IEEE Transactions on Visualization and Computer Graphics, Vol. 9, No. 2, April-June 2003); C. Erikson,  Error Correction of a Large Architectural Model: The Henderson County Courthouse  (Technical Report TR95-013, Dept. of Computer Science, Univ. of North Carolina at Chapel Hill, 1995); D. Khorramabdi,  A Walk through the Planned CS Building  (Technical Report UCB/CSD 91/652, Computer Science, Dept., Univ. of California at Berkeley, 1991); Morvan et al.,  IVECS: An Interactive Virtual Environment for the Correction of .STL files  (Proc. Conf. Virtual Design, August 1996); Bohn et al.,  A Topology - Based Approach for Shell - Closure , Geometric Modeling for Product Realization, (P. R. Wilson et al., pp. 297-319, North-Holland, 1993); Barequet et al.,  Filling Gaps in the Boundary of a Polyhedron , Computer Aided Geometric Design (vol. 12, no. 2, pp. 207-229, 1995); Barequet et al.,  Repairing CAD Models  ( Proc. IEEE Visualization &#39; 97, pp. 363-370, October 1997); and Gueziec et al.,  Converting Sets of Polygons to Manifold Surfaces by Cutting and Stitching , ( Proc. IEEE Visualization  1998, pp. 383-390, October 1998). Each of these references is incorporated into this Detailed Description in their entireties. 
     As can be understood from  FIGS. 20A and 20B , the integrated jig model  748  may include several features based on the surgeon&#39;s needs. For example, the jig model  748  may include a slot feature  30  for receiving and guiding a bone saw and drill holes  32  for receiving and guiding bone drill bits. As can be understood from  FIGS. 19B and 19C , to provide sufficient structural integrity to allow the resulting tibia jig  2 B to not buckle or deform during the arthroplasty procedure and to adequately support and guide the bone saw and drill bits, the gap between the models  232 M,  40  may have the following offsets V 1 , V 2 , and V 3.    
     As can be understood from  FIGS. 19B-20B , in one embodiment, thickness V 1  extends along the length of the posterior drill holes  32 P between the models  632 M,  40  and is for supporting and guiding a bone drill received therein during the arthroplasty procedure. Thickness V 1  may be at least approximately four millimeters or at least approximately five millimeters thick. The diameter of the posterior drill holes  32 P may be configured to receive a cutting tool of at least one-third inches. 
     Thickness V 2  extends is the thickness of the jig foots  800 ,  802  between the inner and exterior surfaces  40 ,  632 M. The thickness provides adequate structural strength for jig foots  800 ,  802 , to resist buckling and deforming of the jig to manufacture and use. Thickness V 2  may be at least approximately five millimeters or at least eight millimeters thick. 
     Thickness V 3  extends along the length of a saw slot  30  between the models  632 M,  40  and is for supporting and guiding a bone saw received therein during the arthroplasty procedure. Thickness V 3  may be at least approximately 10 mm or at least 15 mm thick. 
     In addition to providing sufficiently long surfaces for guiding drill bits or saws received therein, the various thicknesses V 1 , V 2 , V 2  are structurally designed to enable the tibia jig  2 B to bear vigorous tibia cutting, drilling and reaming procedures during the TKR surgery. 
     As indicated in  FIGS. 20A and 20B , the exterior portion or side  106  of the integrated jig model  748  may include: jig foot or feature  800  that extends over and matches the patient&#39;s medial portion of the tibia plateau; jig foot or feature  802  that extends over and matches the patient&#39;s lateral portion of the tibia plateau; projection  804  that extends downward from the upper exterior surface  632  of the tibia jig  2 B; and a flat portion of the exterior surface  632  that provides a blanked labeling area for listing information regarding the patient, surgeon or/and the surgical procedure. Also, as discussed above, the integrated jig model  748  may include the saw cut slot  30  and the drill holes  32 . The inner portion or side  104  of the jig model  748  (and the resulting tibia jig  2 B) is the tibia surface model  40 , which will matingly receive the arthroplasty target area  42  of the patient&#39;s tibia  20  during the arthroplasty procedure. 
     As can be understood by referring to [block  105 ] of  FIG. 1B  and  FIGS. 12A-12C , in one embodiment when cumulating the image scans  16  to generate the one or the other of the models  40 ,  22 , the models  40 ,  22  are referenced to point P, which may be a single point or a series of points, etc. to reference and orient the models  40 ,  22  relative to the models  22 ,  28  discussed with respect to  FIG. 10  and utilized for POP. Any changes reflected in the models  22 ,  28  with respect to point P (e.g., point P becoming point P′) on account of the POP is reflected in the point P associated with the models  40 ,  22  (see [block  135 ] of  FIG. 1D ). Thus, as can be understood from [block  140 ] of  FIG. 1D  and  FIGS. 19A-19C , when the jig blank exterior surface model  632 M is combined with the surface model  40  (or a surface model developed from the arthritic model  22 ) to create the jig model  746 , the jig model  746  is referenced and oriented relative to point P′ and is generally equivalent to the “jig data”  46  discussed with respect to [block  145 ] of  FIG. 1E . 
     Because the jig model  746  is properly referenced and oriented relative to point P′, the “saw cut and drill hole data”  44  discussed with respect to [block  125 ] of  FIG. 1E  can be properly integrated into the jig model  746  to arrive at the integrated jig model  748  depicted in  FIGS. 20A-20B . The integrated jig model  748  includes the saw cuts  30 , drill holes  32  and the surface model  40 . Thus, the integrated jig model  748  is generally equivalent to the “integrated jig data”  48  discussed with respect to [block  150 ] of  FIG. 1E . 
     As can be understood from  FIG. 21 , which illustrates a perspective view of the integrated jig model  748  mating with the “arthritic model”  22 , the interior surface  40  of the jig model  748  matingly receives the arthroplasty target area  42  of the tibia upper end  604  such that the jig model  748  is indexed to mate with the area  42 . Because of the referencing and orientation of the various models relative to the points P, P′ throughout the procedure, the saw cut slot  30  and drill holes  32  are properly oriented to result in saw cuts and drill holes that allow a resulting tibia jig  2 B to restore a patient&#39;s joint to a pre-degenerated condition. 
     As indicated in  FIG. 21 , the integrated jig model  748  may include a jig body  850 , a medial tibia plateau covering projection  852 , a lateral tibia plateau covering projection  854 , a lower portion  856  extending form the body  850 , posterior drill holes  32 P, anterior drill holes  32 A, a saw slot  30  and an upper flat portion  856  for receiving thereon patient, surgery and physician data. The projections  852 ,  854  extend over their respective medial and lateral tibia plateau portions. The projections  852 ,  854 ,  856  extend integrally from the jig body  850 . 
     As can be understood from [blocks  155 - 165 ] of  FIG. 1E , the integrated jig  748  or, more specifically, the integrated jig data  48  can be sent to the CNC machine  10  to machine the tibia jig  2 B from the selected jig blank  50 B. For example, the integrated jig data  48  may be used to produce a production file that provides automated jig fabrication instructions to a rapid production machine  10 , as described in the various Park patent applications referenced above. The rapid production machine  10  then fabricates the patient-specific arthroplasty tibia jig  2 B from the tibia jig blank  50 B according to the instructions. 
     The resulting tibia jig  2 B may have the features of the integrated jig model  748 . Thus, as can be understood from  FIG. 21 , the resulting tibia jig  2 B may have the slot  30  and the drilling holes  32  formed on the projections  852 ,  854 ,  856 , depending on the needs of the surgeon. The drilling holes  32  are configured to prevent the possible IR/ER (internal/external) rotational axis misalignment between the tibia cutting jig  2 B and the patient&#39;s damaged joint surface during the proximal tibia cut portion of the TKR procedure. The slot  30  is configured to accept a cutting instrument, such as a reciprocating slaw blade for transversely cutting during the proximal tibia cut portion of the TKR. 
     Although the present invention has been described with reference to preferred embodiments, persons skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention.