Abstract:
Provided is an orthodontic splint and related methods, which use two or more bonding pads and a flexible connector beam that deflects in response to stress, effectively reducing the amount of stress felt by the adhesive. The connector beam has a non-uniform cross-section along its length, thereby shifting the maximum stress away from the ends of the beam and toward the mid-point of the beam. Further, the connector beam attached to each base along locations remote from the outer edge of the base. These splint configurations can decrease the likelihood of bond failure and improve fatigue performance by causing stress, and associated strain, encountered during treatment to be spread more evenly along the length of the beam.

Description:
FIELD 
       [0001]    The provided devices and methods are related to accessories used in orthodontic treatment. In particular, the provided devices and methods are related to splints used in orthodontic treatment. 
       BACKGROUND 
       [0002]    Orthodontics is a specialized profession in dentistry concerned with the precise application of forces to teeth, thereby guiding them into proper positions. Such treatment has many potential benefits, including improvement to bite function, maintenance of dental hygiene, and facial aesthetics. Fixed appliance therapy is one common type of orthodontic treatment which involves bonding tiny slotted appliances, called brackets, to the teeth. After bonding, a resilient arch-shaped wire (or “archwire”) is placed in the slots of the brackets to begin treatment. Although the archwire is initially deflected from its original shape when installed, the wire imparts gentle therapeutic forces over time, thereby progressively moving crooked teeth toward their proper locations in the mouth. 
         [0003]    The treating professional will sometimes use a device called an orthodontic splint to achieve a particular treatment result. The use of a splint, or “splinting,” involves joining together two or more teeth to immobilize them relative to each other. Because this effectively enlarges the root surface area engaged with the jawbone, this has the effect of providing greater anchorage by increasing the resistance to forces applied to the teeth. Achieving proper anchorage during treatment is generally important to resist reactive forces generated as a result of the activation of an orthodontic appliance, such as an archwire, and avoid undesirable tooth movement. Splinting can also be useful when treatment is confined to certain teeth segments (for example, in cuspid-to-cuspid, or “3×3” treatment, or bicuspid-to-bicuspid, or “5×5” treatment), where it can be useful to connect the first and second bicuspid teeth or first molar and second molar teeth. 
       SUMMARY 
       [0004]    A conventional banded orthodontic splint, shown attached to an orthodontic bracket in  FIG. 1 , can have a very low profile and provide a high level of patient comfort. This type of splint also has significant drawbacks. First, these splints can be highly rigid along directions coplanar with the underlying tooth surface, which tends to localize stresses on the splint. These splints are also limited in their ability to absorb energy from bite forces, thus causing this energy to be transmitted directly to the bonding joints. Second, the periodontal ligament extending around each tooth is, on average, around 0.15 to 0.20 millimeters thick. As a result, the teeth are naturally mobile and can move significantly relative to each another during treatment and especially during mastication. This relative movement of teeth imposes additional stress on both the bonding adhesive and splint, often resulting in either shear-peel type bond failure or fracture of the splint itself during treatment. This will often require re-fabrication and bonding of a new splint, which is a substantial nuisance to the treating professional. 
         [0005]    This problem can be somewhat alleviated by using a splint with two or more bonding pads and a flexible connector that deflects in response to the relative tooth movement, effectively reducing the amount of stress felt by the adhesive. It was found, however, that the use of a flexible connector alone does not sufficiently answer the problem. For example, stress can still concentrate near the ends of the connector, and such stress can induce either splint or adhesive failure. While the maximum stress can be reduced by increasing the length or reducing the cross-sectional area of the connector, this can have the effect of attenuating the mechanical coupling between the pads to the point where the functionality of the splint is compromised. Such adjustments can also adversely affect the overall profile of the splint, leading to decreased patient comfort. 
         [0006]    The provided orthodontic splints can overcome this dilemma by using a connector beam between two or more bases that is non-prismatic; in other words, the connector beam does not have uniform cross-section throughout its length. By tapering the cross-section from a relatively large cross-section near one base to a relatively smaller cross-section near the beam midpoint, it is possible to redistribute the stress field in the splint more uniformly. Redistributing stresses along the splint not only can decrease the likelihood of bond failure, but also improve fatigue performance since the stress (and associated strain) is spread more evenly along the length of the connector. A surprising enhancement in robustness can also be achieved by having the connector beam being joined to each base at a location remote from the outer edge of the base. 
         [0007]    In one aspect, an orthodontic splint is provided. The orthodontic splint comprises: a first base and second base, each base having a bonding surface for attachment to a respective tooth and an outer edge extending along at least a portion of the bonding surface as viewed from a direction generally perpendicular to the bonding surface; and a resilient, elongated connector beam having a cross-sectional dimension that generally increases with increasing proximity to the nearer of the first or second base, the connector beam attached to each base along locations remote from the outer edge of the base. 
         [0008]    In another aspect, an orthodontic splint is provided comprising: a first base and second base, each base having a bonding surface for attachment to a respective tooth surface and an outer edge extending along at least a portion of the bonding surface as viewed from a direction generally perpendicular to the bonding surface; and a resilient, elongated connector beam having a longitudinal midpoint and a cross-sectional dimension that generally decreases when approaching the midpoint from either the first or second base, the connector beam attached to each base in a position remote from the outer edge of the base. 
         [0009]    In still another aspect, an orthodontic splint is provided comprising: a first base and second base, each base having a bonding surface for attachment to a respective tooth surface and an outer edge extending along at least a portion of the bonding surface as viewed from a direction generally perpendicular to the bonding surface; and an elongated connector beam resiliently coupling the first and second bases to each other and having a cross-sectional dimension that generally increases with increasing proximity to the nearer of the first or second base, the connector beam extending outwardly away from each base at an angle ranging from 10 to 90 degrees relative to a tangent plane where the longitudinal axis of the connector beam intersects a respective outer surface of the base. 
         [0010]    In yet another aspect, a method of maintaining a fixed spatial relationship between a first and second tooth during orthodontic treatment is provided. The method comprises: coupling a first base to the first tooth; and coupling a second base to the second tooth, wherein the first and second bases are resiliently interconnected by an elongated connector beam with ends extending outwardly away from the tooth surface and a cross-sectional dimension that generally decreases toward the midpoint of the connector beam, whereby stress is delocalized along the length of the beam. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  is an occlusal lingual view of a conventional lingual orthodontic splint bonded to a test fixture, looking at its lingual side. 
           [0012]      FIG. 2  is an occlusal perspective view of a lingual orthodontic splint according to one embodiment, looking at the occlusal and lingual sides. 
           [0013]      FIG. 3  is a lingual view of the splint in  FIG. 2 , looking at its lingual side. 
           [0014]      FIG. 4  is a perspective view of a splint according to another embodiment bonded to adjacent bicuspid teeth, looking at the occlusal and lingual sides. 
           [0015]      FIG. 5  is a perspective view of the splint of  FIG. 4  bonded to adjacent bicuspid teeth, looking at its occlusal side. 
           [0016]      FIGS. 6(   a )-( g ) shows six three-dimensional solid models of splints provided as inputs for finite element analysis. 
           [0017]      FIG. 7  shows a finite element analysis of a splint according to still another embodiment, showing a simulated stress distribution from one angle. 
           [0018]      FIG. 8  shows a finite element analysis of the splint of  FIG. 7 , showing a simulated stress distribution from another angle. 
       
    
    
     DEFINITIONS 
       [0019]    As used herein: 
         [0020]    “Mesial” means in a direction toward the center of the patient&#39;s curved dental arch. 
         [0021]    “Distal” means in a direction away from the center of the patient&#39;s curved dental arch. 
         [0022]    “Occlusal” means in a direction toward the outer tips of the patient&#39;s teeth. 
         [0023]    “Gingival” means in a direction toward the patient&#39;s gums or gingiva. 
         [0024]    “Facial” means in a direction toward the patient&#39;s lips or cheeks. 
         [0025]    “Lingual” means in a direction toward the patient&#39;s tongue. 
       DETAILED DESCRIPTION 
       [0026]    Provided herein are splints for use in orthodontic treatment. In preferred embodiments, the splints provides anchorage as part of a system of appliances that are bonded to some or all of the central, lateral, cuspid, bicuspid, and molar teeth of a dental arch and cooperate with a suitable archwire for moving teeth to proper respective locations. The splints couple two or more teeth to each other and may have a configuration for attachment to either facial or lingual surfaces of the teeth, and can be adapted for use on either the upper or lower arches. While embodiments described herein are directed to lingual splints, it should be understood that similar features and benefits may also apply for labial splints with references to facial and lingual directions reversed. 
         [0027]    The provided splints may have a universal configuration reflecting normative tooth shapes in the patient population. Alternatively, the splints can be custom manufactured according to the shapes of a particular patient&#39;s teeth, and thus may have configurations that differ substantially from one patient to the next. Some of these possibilities are further explored in the sections below. While particular splint configurations and features are shown herein by way of illustration and example, however, these embodiments should not be construed as unduly limiting the scope of the invention. 
         [0028]    A lingual splint, according to one exemplary embodiment, is shown in  FIGS. 2-3  and broadly designated by the numeral  100 . The splint  100  has a mesial base  102  and a distal base  104 . Each of the bases  102 ,  104  has a bonding surface  106 ,  108  for attachment to a corresponding tooth. As shown in  FIG. 2 , the bases  102 ,  104  and respective bonding surfaces  106 ,  108  are customized to substantially match the lingual contours of the first and second bicuspid teeth of a patient. The bonding surfaces  106 ,  108  can have a surface structure that assists in providing mechanical retention with a suitable bonding adhesive. The surface structure can improve adhesion, for example, by forming a mechanical lock or chemical bond with a suitable adhesive disposed between the bonding surface  106 ,  108  and the tooth surface. The surface structure may include holes, grooves, particles, recesses, undercuts, a micro-etched surface, a chemical bond enhancement material, or any other structure, material or combination thereof. 
         [0029]    The bases  102 ,  104  can extend over a significant portion of its associated tooth surface to provide for adhesion over a larger surface area and a stronger overall bond. Although not shown here, one or both of the bases  102 ,  104  could even extend entirely around the tooth, resulting in a banded appliance. The bases  102 ,  104  also have respective outer surfaces  110 ,  112  opposite the bonding surfaces  106 ,  108  and facing the lingual direction. Preferably, the outer surfaces  110 ,  112  substantially match the contours of the underlying teeth surfaces, giving the splint  100  a low overall profile for enhanced patient comfort. 
         [0030]    Each of the bases  102 ,  104  also has a respective outer edge  114 ,  116  (shown in  FIG. 3 ) that extending along the periphery of the bonding surfaces  106 ,  108  as viewed from a direction generally perpendicular to the surfaces  106 ,  108 . As shown in the embodiment of  FIG. 3 , each outer edge  114 ,  116  fully surrounds its respective surface  106 ,  108 . 
         [0031]    An elongated connector beam  120  connects the mesial and distal bases  102 ,  104  to each other. The connector beam  120  has a mesial end  122  and a distal end  124  and a longitudinal midpoint  126 . In a preferred embodiment, the connector beam  120  is made from a flexible material that allows the splint  100  to visibly deflect, or “flex,” within its elastic limit in response to usual forces encountered during orthodontic treatment. Optionally, the connector beam  120  is also resilient along essentially its entire length, such that the beam  120  substantially returns to its original shape when relaxed. The connector beam  120  acts as a “shock absorber” that allows the mesial and distal bases  102 ,  104  to shift relative to each other during orthodontic treatment without inducing a significant degree of permanent deformation in either the bases  102 ,  104  or the connector beam  120 . This can be beneficial to the treating professional because it allows two (or more) teeth to be joined together to provide increased anchorage, while tolerating a small degree of relative movement that naturally occur between teeth as a result of chewing forces and treatment mechanics. 
         [0032]    The mesial and distal ends  122 ,  124  are joined to the respective outer surface  110 ,  112  of the bases  102 ,  104  along locations remote from (or away from) the outer edges  114 ,  116 . By spacing the joint between the connector beam  120  and each base  102 ,  104  to locations remote from the outer edge  114 ,  116 , the stress on the adhesive can be moved away from the edges of the bonding interface, where the bond between the tooth and the splint  100  is most vulnerable to shear-peel failure. As will be later shown in the Examples section, this aspect was found to significantly reduce the likelihood of shear-peel failure of the splint  100 . 
         [0033]    As further shown in  FIGS. 2-3 , the connector beam  120  has a generally rectangular cross-section as defined along reference planes perpendicular to the longitudinal axis of the connector beam  120 . In a preferred embodiment, the long axis of the rectangular cross-section is aligned along a generally occlusal-gingival direction. Optionally, the rectangular connector beam  120  is canted so that it lies approximately parallel with the underlying bonding surfaces  106 ,  108  in consideration with the inclination of the teeth to which the splint  100  is bonded. Such alignment can reduce facial-lingual height, thereby reducing the overall profile of the splint  100  and promoting patient comfort. 
         [0034]    Unlike the banded splint configuration shown in  FIG. 1 , the splint  100  has a cross-section whose size and shape vary along the longitudinal axis of the connector beam  120 . In the present instance, the connector beam  120  has a cross-sectional dimension that varies along two orthogonal axes. In  FIG. 2 , for example, the facial-lingual thickness of the connector beam  120  generally increases with increasing proximity to the nearest mesial or distal end  122 ,  124 , and generally decreases when approaching the midpoint  126  from either the first or second base  102 ,  104 . Stated another way, the cross-sectional dimension generally increases with increasing proximity to the nearer of the first or second base  102 ,  104 . This is also shown in  FIG. 3 , in which the splint has its largest gingival-occlusal dimension “A” toward the ends  122 ,  124  and its smallest gingival-occlusal dimension “B” toward the midpoint  126 . 
         [0035]    In some embodiments, the ratio between a cross-sectional dimension of the connector beam  120  at its widest point and the cross-sectional dimension at its narrowest point is at least 1, at least 1.25, at least 1.5, or at least 1.75. In some embodiments, the ratio between a cross-sectional dimension of the connector beam  120  at its widest point and the cross-sectional dimension at its narrowest point is at most 3, at most 2.5, at most 2, or at most 1.75. In some embodiments, the cross-sectional dimension itself at its narrowest point is at least 0.18 millimeters, at least 0.4 millimeters, or at least 0.5 millimeters. In some embodiments, the cross-sectional dimension at its narrowest point is at most 1.4 millimeters, at most 1.1 millimeters, or at most 0.8 millimeters. 
         [0036]    It can be advantageous for the facial-lingual dimension of the connector beam  120  to vary over a narrower range compared with the occlusal-gingival direction. In some embodiments, for example, the facial-lingual thickness of the connector beam  120  can be essentially uniform throughout its length while the occlusal-gingival thickness varies substantially along its length. Greater uniformity in thickness can allow the splint  100  to have a lower overall profile, a feature that could advantageously enhance patient comfort by reducing the extent to which the splint  100  impinges against the cheek of the patient. 
         [0037]    As further shown in  FIGS. 2-3 , an orthodontic bracket  128  is joined to the mesial base  102  of the splint  100 , providing options for engagement with an archwire, force module (such as a power chain or elastic), trans-palatal device or other ancillary orthodontic appliance. Optionally, the bracket  128  and splint  100  have a unitary construction and are manufactured as a unitary component. The bracket  128  has a slot for accommodating an archwire during the course of treatment. By fastening two or more teeth together, the splint  100  can provide enhanced anchorage when an archwire is activated in the slot of the bracket  128 . If desired, anchorage can be further improved by incorporating one or more additional bonding bases into the splint  100 , thereby leveraging the collective anchorage of three or more teeth. 
         [0038]    The shape of the connector beam  120  can impart significant and unexpected advantages to the splint  100 . First, by having a cross-sectional dimension that is enlarged near the ends  122 ,  124  and reduced near the midpoint  126 , the principal stresses on the splint  100  are delocalized, or distributed more evenly, along the length of the connector beam  120  as the teeth move relative to each other. This has the effect of lowering the principal stress at the ends  122 ,  124  where the adhesive/appliance and adhesive/tooth interface present weak boundary layers where debonding of the splint  100  can occur. Second, the distribution of stress over an extended portion of the connector beam  120  can provide superior fatigue resistance. As a result, the splint  100  can display dramatically improved robustness over previous splint configurations disclosed in the art. 
         [0039]    Optionally and as shown, the ends  122 ,  124  of the connector beam  120  extend outwardly from the bases  102 ,  104  along a direction approximately normal to planes  111 ,  113  tangent to the underlying outer surfaces  110 ,  112  (in  FIG. 3 , for example, the tangent planes  111 ,  113  are defined where the instantaneous longitudinal axis  123 ,  125  of the connector beam  120  intersects with each outer surface  110 ,  112 ). Referring to  FIG. 2 , the ends  122 ,  124  (as represented by the longitudinal axes  123 ,  125 ) extend outwardly at respective angles θ 1  and θ 2  relative to the tangent planes  111 ,  113 , where θ 1  is approximately 90 degrees and θ 2  is somewhat less than 90 degrees. 
         [0040]    Advantageously, this configuration can distribute principal stresses evenly along the cross-section of the connector beam  120  where each end  122 ,  124  is joined with its base  102 ,  104 , and reduce the likelihood of shear-peel failure at the joint connecting the connector beam  120  to the bases  102 ,  104 . Such a construction can also provide a minimal amount of facial-lingual separation between the connector beam  120  and the underlying bases  102 ,  104  to facilitate manufacturing of the splint  100 , for example, by microcasting. 
         [0041]    In some embodiments, each end of the connector portion extends outwardly away from each base  102 ,  104  at an angle θ of at least 10 degrees, at least 30 degrees, or at least 70 degrees, relative to a tangent plane  111 ,  113  where the longitudinal axis of the connector beam  120  intersects respective outer surface  110 ,  112 . In some embodiments, each end of the connector portion extends outwardly away from each base  102 ,  104  at an angle θ of up to 80 degrees, up to 85 degrees, or up to 90 degrees, relative to the tangent plane  111 ,  113  above. The connector beam  120  need not extend along a path that continually travels away from one base  102 ,  104  and toward the other. For example, the connector beam  120  could initially extend from base  102  in a direction away from the base  104 , then subsequently bend back toward base  104 . 
         [0042]      FIGS. 4-5  present views of a splint  100 ′ as it would appear when bonded to the lower first bicuspid  130  and second bicuspid  132  teeth of a patient. A connector beam  120 ′, having outer ends that extend outwardly away from the surface of each tooth  130 ,  132 , resiliently interconnects respective bases  102 ′,  104 ′. Optionally and as shown, the bases  102 ′,  104 ′ of the splint  100 ′ cover essentially all of the lingual surfaces of the teeth  130 ,  132 , providing an increased surface area for attachment and enhanced bond reliability. While the teeth  130 ,  132  are adjacent teeth as shown here, this need not be the case. In some embodiments, for example, the connector beam  120 ′ of the splint  100 ′ could extend over the lingual surfaces of one or more intermediate teeth without being directly bonded to them. Also, the splint  100 ′ can be bonded to three or more teeth in a consecutive manner if even greater anchorage is desired by the treating professional. 
       Finite Element Analysis 
       [0043]    To better understand the result of having the connector beam contacting respective bases of the splint at locations remote from (as opposed to adjacent to) the outer edge of the base, finite element analysis (FEA) was used to simulate the three-dimensional (3D) stress profiles of seven different splint configurations, shown in  FIGS. 6(   a )- 6 ( g ). The FEA was performed on 3D models of the splints using ANSYS brand simulation software (v. 13, available from ANSYS Inc., Canonsburg, Pa.). Each of the splint configurations included bases that were adhesively bonded to virtual first and second bicuspid teeth, and in some cases, the first molar tooth. In this model, the teeth were surrounded by periodontal ligaments, which connected each tooth to its surrounding bone. The adhesive pad connecting each base to its underlying tooth had a defined thickness of 0.127 millimeters. The thickness of the periodontal ligaments (“PDL”) was defined to be 0.15 millimeters for the bicuspid teeth and 0.20 millimeters for the first molar tooth. The thickness of the splint itself was defined as 0.508 millimeters, and the splint has a generally constant cross-sectional shape. 
         [0044]    The analysis also made certain assumptions concerning Young&#39;s Modulus and Poisson Ratio of the component materials represented in the simulations. These values are provided in Table 1 below. 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Young&#39;s Modulus and Poisson Ratio used in finite element analyses 
               
             
          
           
               
                   
                   
                 Young&#39;s 
                   
               
               
                   
                   
                 Modulus, MPa 
                 Poisson&#39;s Ratio 
               
               
                   
                   
               
             
          
           
               
                   
                 Adhesive 
                 1.17E+04 
                 0.21 
               
               
                   
                 Tooth 
                 1.96E+04 
                 0.3 
               
               
                   
                 Splint 
                 9.90E+04 
                 0.3 
               
               
                   
                   
               
             
          
         
       
     
         [0045]    The splints were then subjected to two different loading conditions to observe the resulting stress profiles: 1) a 178 N (40 lb.) occlusal force on the occlusal surface of the second bicuspid, and 2) an 89 N (20 lb.) occlusal force on the occlusal surface of the splint between the first and second bicuspids. The simulated force levels on the adhesive and PDL, and simulated principal stress imposed on splint, are shown for each splint configuration in Tables 2 and 3 below. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 FEA analysis of various splint configurations while 
               
               
                 applying a 178 N occlusal force to the second bicuspid 
               
             
          
           
               
                   
                   
                   
                 Force on 
                 Force on 
                 Max. 1P stress 
               
               
                 Splint 
                   
                   
                 adhesive, 
                 PDL, 
                 on splint, 
               
               
                 concept 
                 Description 
                 Tooth 
                 newtons 
                 newtons 
                 megapascals 
               
               
                   
               
             
          
           
               
                 A 
                 4-6 banded splint 
                 first bicuspid 
                 49.4 
                 49.8 
                 159 
               
               
                   
                   
                 second bicuspid 
                 115.2 
                 63.2 
               
               
                   
                   
                 first molar 
                 64.5 
                 64.5 
               
               
                 B 
                 4-5 banded splint 
                 first bicuspid 
                 60.9 
                 61.8 
                 159 
               
               
                   
                   
                 second bicuspid 
                 63.2 
                 116.1 
               
               
                   
                   
                 first molar 
                 — 
                 — 
               
               
                 C 
                 4-6 flexible splint, 
                 first bicuspid 
                 45.4 
                 45.8 
                 1320 
               
               
                   
                 0.51 × 0.64 mm 
                 second bicuspid 
                 102.3 
                 76.5 
               
               
                   
                 (0.020 × 0.025 in.) 
                 first molar 
                 55.6 
                 55.6 
               
               
                 D 
                 4-6 flexible splint, 
                 first bicuspid 
                 19.6 
                 19.6 
                 765 
               
               
                   
                 extended connection, 
                 second bicuspid 
                 36.9 
                 141.0 
               
               
                   
                 0.51 × 0.76 mm 
                 first molar 
                 17.3 
                 17.3 
               
               
                   
                 (0.020 × 0.030 in.) 
               
               
                 E 
                 4-6 flexible splint, 
                 first bicuspid 
                 12.0 
                 12.0 
                 552 
               
               
                   
                 offset connection, 
                 second bicuspid 
                 26.7 
                 154.4 
               
               
                   
                 0.51 × 0.76 mm 
                 first molar 
                 13.3 
                 13.3 
               
               
                   
                 (0.020 × 0.030 in.) 
               
               
                 F 
                 4-5 flexible splint, 
                 first bicuspid 
                 22.2 
                 22.7 
                 710 
               
               
                   
                 offset connection, 
                 second bicuspid 
                 24.5 
                 155.2 
               
               
                   
                 0.51 × 0.76 mm 
                 first molar 
                 — 
                 — 
               
               
                   
                 (0.020 × 0.030 in.) 
               
               
                 G 
                 4-5 flexible splint, 
                 first bicuspid 
                 8.4 
                 8.9 
                 358 
               
               
                   
                 non-prismatic 
                 second bicuspid 
                 10.7 
                 169.0 
               
               
                   
                   
                 first molar 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 FEA analysis of various splint configurations 
               
               
                 while applying an 89 N occlusal force to the splint 
               
               
                 between the first and second bicuspids 
               
             
          
           
               
                   
                   
                   
                 Force on 
                 Force on 
                 Max. 1P stress 
               
               
                 Splint 
                   
                   
                 adhesive, 
                 PDL, 
                 on splint, 
               
               
                 concept 
                 Description 
                 Tooth 
                 newtons 
                 newtons 
                 megapascals 
               
               
                   
               
             
          
           
               
                 A 
                 4-6 banded splint 
                 first bicuspid 
                 37.4 
                 37.8 
                 179 
               
               
                   
                   
                 second bicuspid 
                 26.7 
                 27.1 
               
               
                   
                   
                 first molar 
                 23.6 
                 23.6 
               
               
                 B 
                 4-5 banded splint 
                 first bicuspid 
                 43.6 
                 44.5 
                 228 
               
               
                   
                   
                 second bicuspid 
                 43.6 
                 44.5 
               
               
                   
                   
                 first molar 
                 — 
                 — 
               
               
                 C 
                 4-6 flexible splint, 
                 first bicuspid 
                 40.0 
                 40.5 
                 614 
               
               
                   
                 0.51 × 0.64 mm 
                 second bicuspid 
                 29.8 
                 30.2 
               
               
                   
                 (0.020 × 0.025 in.) 
                 first molar 
                 18.2 
                 18.2 
               
               
                 D 
                 4-6 flexible splint, 
                 first bicuspid 
                 44.5 
                 44.5 
                 676 
               
               
                   
                 extended connection, 
                 second bicuspid 
                 39.1 
                 39.1 
               
               
                   
                 0.51 × 0.76 mm 
                 first molar 
                 5.3 
                 5.3 
               
               
                   
                 (0.020 × 0.030 in.) 
               
               
                 E 
                 4-6 flexible splint, 
                 first bicuspid 
                 49.4 
                 50.3 
                 869 
               
               
                   
                 offset connection, 
                 second bicuspid 
                 34.7 
                 35.6 
               
               
                   
                 0.51 × 0.76 mm 
                 first molar 
                 3.1 
                 3.1 
               
               
                   
                 (0.020 × 0.030 in.) 
               
               
                 F 
                 4-5 flexible splint, 
                 first bicuspid 
                 44.0 
                 44.9 
                 462 
               
               
                   
                 offset connection, 
                 second bicuspid 
                 43.1 
                 44.0 
               
               
                   
                 0.51 × 0.76 mm 
                 first molar 
                 — 
                 — 
               
               
                   
                 (0.020 × 0.030 in.) 
               
               
                 G 
                 4-5 flexible splint, 
                 first bicuspid 
                 42.3 
                 43.6 
                 579 
               
               
                   
                 non-prismatic 
                 second bicuspid 
                 44.0 
                 45.4 
               
               
                   
                   
                 first molar 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
         [0046]    The FEA showed significant differences in force and stress levels amongst concepts A-G, particularly in response to occlusal forces to the second bicuspid as shown in Table 2. Referring to the results obtained for concepts A, B, and C in Table 2 above, the application of about 178 N (40 lbs.) of bite force to the second bicuspid generated a force on the adhesive ranging from about 11 to 115 N. As to concepts D and E, the inclusion of either a 0.51×0.76 mm or 0.51×0.76 mm connector beam reduced the force on the adhesive to less than 40 N (9 lbs.), with the majority of the force absorbed by the PDL. However, the stresses on the connector beams are still higher than those in concepts A and B. Concept G transmitted the lowest force to the adhesive of 10.7 N, while also showing decreased stress on the splint compared with other flexible splint concepts. Concept G also appeared to impart greater forces to the PDL, up to about 169 N. 
         [0047]      FIGS. 7 and 8  show the simulated stress profile obtained for a simulated splint  200  (similar to splint concept G above). As shown, the splint  200  has bonding bases  202 ,  204  and includes a connector beam  220 , with a cross-sectional area increasing toward its ends and decreasing toward its midpoint. In this concept, both the occlusal-gingival and facial-lingual components of the cross-sectional area vary along the longitudinal axis of the connector beam  220 .  FIGS. 7 and 8  show the distribution of the maximum principal stress from the ends of the connector beam toward the center of the connector beam  220 . Areas of relatively high stress are indicated by darker shading, while areas of relatively low stress are indicated by lighter shading. The simulation showed that the beam  220  has a geometry that allows stress to be spread over a significant length of the beam, rather than being concentrated at its ends. Optionally, the configuration of the splint  200  can be further modified such that that the locations subjected to the highest levels of stress are provided with an enlarged cross-section to strengthen the splint  200  in locations where failure is most likely to occur. 
       EXAMPLES 
       [0048]    Objects and advantages of the provided orthodontic splints are further illustrated by the following examples. 
         [0049]    As used herein, 
         [0050]    “SIL” refers to SIL brand silane primer, provided by 3M ESPE in St. Paul, Minn.; 
         [0051]    “Concise” refers to CONCISE brand orthodontic chemical cure adhesive (REF 196-002 &amp; 196-003), provided by 3M Unitek in Monrovia, Calif.; and 
         [0052]    “Rocatec Plus” refers to a ROCATEC brand Jr. blasting module using ROCATEC brand Plus media, both provided by 3M Company in St. Paul, Minn. 
       Splint Fabrication 
       [0053]    Splints were manufactured using a “lost-wax” investment casting procedure, similar to those described in U.S. Pat. No. 6,776,614 (Wiechmann, et al.). In brief, the procedure begins with obtaining a 3D model of the splint configuration, as shown for example in  FIG. 2 . The 3D model was then exported to a rapid prototyping machine (a 3D printer) that constructed, layer-by-layer, a resin model of the splint. After printing, the resin model is used as a core in an investment casting process, where the model is embedded in cement and then melted to afford a negative mold. The negative mold is used to cast the final splint from gold alloy, after which the splint is removed by quenching the mold in water. 
       Splint Bonding Procedure 
       [0054]    Each splint was bonded to two stainless steel rings having convex, knurled surfaces and positioned side-to-side. Each ring accommodated a respective base of the splint. The bonding surface of each base was sandblasted with Rocatec Plus (110 micrometer diameter silica, coated with aluminum oxide) according to manufacturer&#39;s instructions. A thin layer of SIL was then lightly brushed onto the sandblasted surfaces according to manufacturer&#39;s instructions. 
         [0055]    The splint was then bonded to the knurled rings using CONCISE in accordance with manufacturer instructions. 
       Fracture Test Procedure 
       [0056]    Debonding was conducted on each test specimen using a Q-TEST brand 5 Universal Test Machine (from MTS in Eden Prairie, Minn.) outfitted with a 1000 newton load cell. 
         [0057]    Once the splint to be tested has been bonded to the pair of knurled rings, the rings were mounted to a two-part fixture and subjected to a simple displacement test. In this test, the first part of the fixture is held in a fixed position, while the second part is translated upward by the Test Machine at a fixed crosshead speed of 2.54 millimeters/second (0.1 inches/second). Crosshead displacement and load were continuously recorded until splint failure occurred. Failure was defined as either debonding, fracture, or substantial permanent deformation of the splint. The maximum force, and displacement at the maximum force, were then recorded for the test run. 
         [0058]    Depending on the orientation of the rings in the fixture, the splint can be tested either in the facial-lingual direction or the occlusal-gingival direction. Facial-lingual fracture testing was conducted by orienting the rings such that the bonding surfaces of the splint were approximately parallel to the direction of the displacement. Occlusal-gingival testing was conducted by rotating the rings 90 degrees such that the bonding surfaces are approximately perpendicular to the direction of displacement. Since the splints were asymmetric when tested in the facial-lingual configuration, the orientation of the splint was flipped to provide an average measurement reflecting the results for both orientations. 
       Examples 1-2 and Comparative CE-1  
       [0059]    Facial-lingual fracture testing was performed on various splint samples according to the Fracture Test Procedure above. This test examines a failure mode in which one tooth shifts in along a facial-lingual direction relative to its neighbor. Examples 1 and Example 2 were fabricated based on the splint configuration shown in  FIGS. 6-7 . Examples 1 and 2 differed in that the former used a SOLIDSCAPE brand 3D printer (from Stratasys, Eden Prairie, Minn.), while the latter used a PERFACTORY brand 3D printer (from EnvisionTEC GmbH, Gladbeck, GERMANY). Comparative CE-1 used a band splint configuration shown in  FIG. 1  made using the SOLIDSCAPE brand printer. The results of these tests are shown in Table 4 below. As further noted below, some but not all splints debonded entirely from one of the rings during testing. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Maximum displacement and force in facial-lingual directions 
               
             
          
           
               
                   
                   
                 Average 
                   
                   
               
               
                   
                   
                 displacement 
                 Average load at 
               
               
                 Example/ 
                 No. of 
                 at failure 
                 failure 
               
               
                 Comparative 
                 samples 
                 (millimeters) 
                 (newtons) 
                 Notes 
               
               
                   
               
             
          
           
               
                 1 
                 5 
                 2.06 
                 71.2 
                 2 of 5 debonded 
               
               
                 2 
                 12 
                 2.41 
                 104 
                 3 of 12 debonded 
               
               
                 CE-1 
                 7 
                 0.117 
                 17.5 
               
               
                   
               
             
          
         
       
     
       Examples 3-4 and Comparative CE-2  
       [0060]    Occlusal-gingival fracture testing was performed in Examples 3-4 and CE-2. In these measurements, each splint was oriented in the fixture to simulate the failure mode caused by occlusal-gingival movement of one tooth relative to its neighbor. Like Examples 1 and 2 above, Examples 3 and 4 were prepared using a SOLIDSCAPE brand 3D printer and a PERFACTORY brand 3D printer, respectively. Fracture test results for Examples 3 and 4 are given in Table 5 below. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Maximum displacement and force in occlusal-gingival directions 
               
             
          
           
               
                   
                   
                 Average 
                   
                   
               
               
                   
                   
                 displacement 
                 Average load at 
               
               
                 Example/ 
                 No. of 
                 at failure  
                 failure 
               
               
                 Comparative 
                 samples 
                 (millimeters) 
                 (newtons) 
                 Notes 
               
               
                   
               
             
          
           
               
                 3 
                 5 
                 0.240 
                 105 
                   
               
               
                 4 
                 3 
                 2.14 
                 72.1 
                 1 of 3 debonded 
               
               
                 CE-2 
                 5 
                 1.60 
                 66.7 
                 1 of 5 debonded 
               
               
                   
               
             
          
         
       
     
       Examples 5-6 
       [0061]    Fatigue testing was then conducted on the splints of Examples 1 and 2, respectively, in an occlusal-gingival orientation. In these tests, all splints tested survived 500 cycles at a strain amplitude of ±0.30 mm. When the amplitude was subsequently increased to ±0.45 mm, all samples eventually failed. The average cycle life of each Example is shown in Table 6 below. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Fatigue test results 
               
             
          
           
               
                   
                 Example/ 
                   
                 Cycles at 
                 Cycles at 
               
               
                   
                 Comparative 
                 N 
                 ±0.30 millimeters 
                 ±0.45 millimeters 
               
               
                   
                   
               
             
          
           
               
                   
                 5 
                 3 
                 500* 
                 142 
               
               
                   
                 6 
                 10 
                 500* 
                 149 
               
               
                   
                   
               
               
                   
                 *without failure 
               
             
          
         
       
     
         [0062]    All of the patents and patent applications mentioned above are hereby expressly incorporated into the present disclosure. The foregoing invention has been described in some detail by way of illustration and example for purposes of clarity and understanding. However, various alternatives, modifications, and equivalents may be used and the above description should not be taken as limiting in the scope of the invention which is defined by the following claims and their equivalents.