Abstract
Rectangular stainless steel (SS) archwires were coupled with four SS bracket designs: Mini Diamond Twin, which was a conventional twin bracket; VersaT, which had bumps along the slot floor and rounded slot walls; Shoulder, which had bosses outside the tie-wings to lift the ligation off the archwire; and Synergy, which had bosses between the outer and inner tie-wings, bumps along the slot floor, and rounded slot walls. For all designs, the values of resistance to sliding (RS) were measured at five normal forces and 32 second-order angulations in the dry and wet (saliva) states. RS values at these same angles and states were also measured for the following: Mini Diamond Twin brackets ligated with rings and SS ligature wires; VersaT brackets ligated with rings; Shoulder brackets ligated with rings in a figure-8 and a figure-O around the tie-wings; and Synergy brackets ligated with rings around the outer tie-wings and around the inner tie-wings. In both states, the coefficients of friction were similar for the Mini Diamond Twin, VersaT, and Synergy brackets; the values for the Shoulder brackets were slightly greater than for the other three designs. In the passive configuration, the features of the Shoulder and Synergy brackets reduced RS when the rings were not in contact with the archwires. In the active configuration, the binding behavioral patterns of the brackets were not influenced by ligation methods. Thus, these different ligation types and methods only affected the classical frictional component of RS in the passive configuration.
INTRODUCTION
Recently, methods of reducing the resistance to sliding (RS) of stainless steel (SS) archwire-bracket couples have focused on bracket design and ligation technique. Previous studies have established that, when clearance exists between the archwire and the bracket's slot walls (the passive configuration), only classical friction (FR) contributes to RS.1–3 The value of FR is equal to the normal force (FN) applied by the ligation multiplied by the kinetic coefficient of friction (μk-FR) of the orthodontic couple.4 Because FN and μk-FR differ for different ligation types (ie, elastomeric O-rings, SS ligature wires) and methods (ie, “figure-O,” “figure-8,” number of twists), previous measurements of FR for similar SS archwire-bracket couples have varied considerably.5–12 Although some studies concluded that couples ligated with O-rings had greater FR values than those tied with SS ligature wires,5,6,8,10,11 others have disagreed.7 Apparently, the methods that were used to tie the SS ligature wires caused the FR values to vary.13 The ligation method also affected the FR values of the elastomeric O-rings; O-rings ligated in a figure-8 exhibited greater FR values than those placed in a figure-O around the tie-wings.10,11 Dowling et al and Matassa attributed the differences in FR values to the shapes that the O-rings formed as they passed over the archwires and under the brackets' tie-wings when placed in a figure-O.12,14
When clearance no longer exists (the active configuration), elastic binding (BI) additionally contributes to RS.1–3 The second-order angulation at which the archwire first contacted the bracket's slot walls is defined as the critical contact angle for binding (θc).3,15 At low angles (θ) relative to θc (in other words, small relative angulations [θr = θ − θc ≈ 0]), the BI contribution to RS is small.2,3,16 As θr increases, the BI component overwhelms FR, and the overall effects of the ligation type and method decrease.17
In the present study, the RS values of two SS bracket designs with bosses that prevent contact between the ligation and the archwire were compared with those of two SS bracket designs without these bosses. The placement of the ligation over the bosses was hypothesized to reduce the FR component of RS but not the BI component. To test this hypothesis, the manufacturers' suggested ligation methods were used to restrain the archwires in the brackets using O-rings. Additionally, SS ligatures were used to tie the archwires into the SS brackets without bosses, bumps, or rounded slot walls. The outcomes show that the bosses did reduce or eliminate the FR component of RS. The BI component, however, increased at a constant rate with angulation regardless of the different ligation types and methods that were used.
MATERIALS AND METHODS
Materials—dimensions and morphologies
All brackets were made of SS and had a prescription of 0° angulation and −7° torque. The Mini Diamond Twin bracket (Figure 1, top row; Table 1), which was the control bracket, was a conventional bracket. The VersaT bracket (Figure 1, bottom row; Table 1) served as a secondary control bracket with the addition of bumps in the slot floor and rounded slot walls. The Shoulder bracket (Figure 2, top row; Table 1) had a small boss on the outside of each tie-wing that lifted the ligation off the archwire. The Synergy bracket (Figure 2, bottom row; Table 1) could be considered a “triple” bracket. When the ligation was placed around the inner tie-wing, the bosses prevented the ligation from contacting the archwire. Like the VersaT bracket, the Synergy bracket also had bumps in the slot floor and rounded slot walls. The brackets were coupled with SS archwires (Table 1) and then were ligated with either elastomeric O-rings or SS ligature wires (Table 1).
From a top view, scanning electron micrographs of the Mini Diamond Twin brackets (top row) and of the VersaT brackets (bottom row). In the left column, only the bracket is shown. Middle column: the archwire was ligated into the bracket using an elastomeric O-ring. Right column: the archwire was tied into the bracket with a SS ligature wire, which was twisted until taut and then untwisted a quarter turn. For the VersaT brackets, the bumps along the slot floor are not obvious, but the rounded slot walls are
From a top view, scanning electron micrographs of the Mini Diamond Twin brackets (top row) and of the VersaT brackets (bottom row). In the left column, only the bracket is shown. Middle column: the archwire was ligated into the bracket using an elastomeric O-ring. Right column: the archwire was tied into the bracket with a SS ligature wire, which was twisted until taut and then untwisted a quarter turn. For the VersaT brackets, the bumps along the slot floor are not obvious, but the rounded slot walls are
From a side view, scanning electron micrographs of the brackets with bosses. For the Shoulder brackets (top row), note the bosses outside of the tie-wings. Left column: only the bracket is shown; middle column: the O-ring was placed in a figure-8 around the four tie-wings; right column: the O-ring was placed in a figure-O around the four tie-wings. For the Synergy brackets (bottom row), note the inner tie-wings (which formed the “triple” bracket); the bumps along the slot floor and the rounded slot walls are not obvious. Left column: only the bracket is shown; middle column: the O-ring was placed around the outer tie-wings; right column: the O-ring was placed around the inner tie-wings such that it sat on the bosses between the inner and outer tie-wings.
From a side view, scanning electron micrographs of the brackets with bosses. For the Shoulder brackets (top row), note the bosses outside of the tie-wings. Left column: only the bracket is shown; middle column: the O-ring was placed in a figure-8 around the four tie-wings; right column: the O-ring was placed in a figure-O around the four tie-wings. For the Synergy brackets (bottom row), note the inner tie-wings (which formed the “triple” bracket); the bumps along the slot floor and the rounded slot walls are not obvious. Left column: only the bracket is shown; middle column: the O-ring was placed around the outer tie-wings; right column: the O-ring was placed around the inner tie-wings such that it sat on the bosses between the inner and outer tie-wings.
For each archwire, the occlusogingival SIZE dimension was measured.3 For each Mini Diamond or Shoulder bracket, the occlusogingival SLOTtrue and the mesiodistal WIDTHtrue dimensions were measured.3 For each Synergy and VersaT bracket, the SLOTtrue dimension at the narrowest regions of the opposing bumps of the slot walls, the SLOTapparent dimension at the widest regions of the opposing bumps, the WIDTHtrue dimension between the adjacent bumps, and the mesiodistal WIDTHapparent dimension were measured (unpublished data).
Using a scanning electron microscope (JEOL JSM-6300, JEOL America, Peabody, Mass) at 15 keV in the secondary electron mode, the bracket morphologies were evaluated in the as-received condition and after ligation. The ligated archwire-bracket couples were carbon-coated prior to viewing.
Frictional testing
The RS values were measured using a frictional testing apparatus that was mounted to the transverse beam on a mechanical testing machine (Instron Model TTCM, Instron Corp, Canton, Mass).16 For the brackets tested at known FN values, a constant FN was applied using a machined SS tube, which was fitted with a SS ligature wire, and maintained by a feedback loop. All O-rings were stretched over the tie-wings using a blunt probe. The archwire-bracket couples were serially translated two mm in 12 seconds at 34°C at these second-order angulations (θ values): 0°, −12°, −10°, −8°, −6°, −5°, −4.5°, −4°, −3.5°, −3°, −2.5°, −2°, −1.5°, −1°, −0.5°, 0°, 0°, 0.5°, 1°, 1.5°, 2°, 2.5°, 3°, 3.5°, 4°, 4.5°, 5°, 6°, 8°, 10°, 12°, and 0°. To prevent any interaction between the test bracket and the simulated adjacent brackets,16 the interbracket distances were maintained at 18 mm. For the wet state, a peristaltic pump dripped saliva at a flow rate of 3 cm3/min; the saliva's viscosity was certified to be between 1.3 and 2.0 milliPascal-seconds (mP-sec) at 34°C (Brookfield Model LVTDV-II CP viscometer, Brookfield Engineering Laboratories Inc, Stoughton, Mass).18
Couples evaluated
For the Mini Diamond Twin brackets, the data for the RS values at normal forces (FN) of 200, 300, 400, 500, and 600 cN (1 cN = 1.02 g) were restated.19 Two of the Mini Diamond Twin brackets, ligated with O-rings or SS ligature wires (Figure 1; top row, middle and right columns, respectively), were tested in the dry and wet states. All the O-rings were used as received, without prestretching.20 The SS ligature wires were first twisted until they were taut against the archwire and then untwisted a quarter turn.13,21
For the VersaT brackets, the RS values of four brackets in each state were measured at 500, 600, 700, and 800 cN, using one bracket at each FN value. Data obtained with a FN value of 300 cN were also included (unpublished data). In each state, two additional VersaT brackets were tested with O-rings ligated around the tie-wings (Figure 1, bottom row, middle column).
For the Shoulder bracket, one bracket was tested in each state at each of five FN values: 300, 500, 600, 700, and 800 cN. Additionally, four brackets were ligated with O-rings in a figure-8 (Figure 2, top row, middle column) and in a figure-O around the tie-wings (Figure 2, top row, right column). Two brackets were tested in each of the dry and wet states.
For the Synergy bracket, the RS values were either evaluated or included (unpublished data) at the same FN values as the VersaT brackets. Two brackets in each state were studied with the O-rings ligated around the outer tie-wings (Figure 2, bottom row, middle column) and around the inner tie-wings (Figure 2, bottom row, right column).
Data analysis and statistics
For the brackets with straight slot walls, the theoretical critical contact angle (θc) was calculated using the SIZE, SLOTtrue, and WIDTHtrue values.15 For the brackets with the rounded slot walls, a model was used in which the changes from SLOTtrue and WIDTHtrue to SLOTapparent and WIDTHapparent were considered, and the theoretical θc value was determined (unpublished data). Using the theoretical θc value, linear regression lines22 were fitted to the passive and active regions, whose intersection was at the experimental θc.3,16
When RS = FR, the FR value may be determined by averaging FR or calculating the y-axis intercept (b) of the linear regression line.16 When RS = FR + BI, the FR component can be subtracted from the RS value.16 The isolated BI component was plotted against the relative angulation (θr = θ − θc, where θc was the experimental value).16
RESULTS
For all bracket designs, the theoretical θc values that were calculated from the average dimensions of each bracket design and those of the archwires were within 0.7° of the experimental θc value (Table 2). For all bracket designs in which the O-rings contacted the archwire, except the VersaT brackets, the RS value (= FR) in the passive configuration was greater in the wet than in the dry state (Figures 3, 5, and 6, left side of each plot in the middle column; Figure 4, left side of each plot in the right column; Table 3). For the Mini Diamond Twin brackets ligated with SS ligature wires, the Shoulder brackets ligated with O-rings in a figure-O, and the Synergy brackets ligated with O-rings around the inner tie-wing, the FR values in both states were negligible (Figures 3, 5, and 6, left side of each plot in the right column; Table 3). For all the brackets tested, the intercepts (b values) were within 19 cN of the average FR values (cf. Tables 3 and 4). The values of RS (= FR) in the passive configuration generally were independent of θ, as shown by the low P values of the linear regression lines even when the number of data points (n) was great (Table 4).22
For the Mini Diamond Twin brackets, plots of RS (= FR + BI) as a function of θ in the dry (top row) and wet (bottom row) states. Left column: constant normal forces of 200, 300, 400, 500, and 600 cN (1 cN = 1.02 g) were applied to the archwires using SS ligature wires; middle column: O-rings were placed around the tie-wings (see Figure 1, top row, middle column); right column: the archwires were tied into the brackets with SS ligature wires (see Figure 1, top row, right column)
For the Mini Diamond Twin brackets, plots of RS (= FR + BI) as a function of θ in the dry (top row) and wet (bottom row) states. Left column: constant normal forces of 200, 300, 400, 500, and 600 cN (1 cN = 1.02 g) were applied to the archwires using SS ligature wires; middle column: O-rings were placed around the tie-wings (see Figure 1, top row, middle column); right column: the archwires were tied into the brackets with SS ligature wires (see Figure 1, top row, right column)
For the Shoulder brackets, plots of RS (= FR + BI) as a function of θ in the dry (top row) and wet (bottom row) states. Left column: constant normal forces of 300, 500, 600, 700, and 800 cN were applied; middle column: O-rings were placed in a figure-8 around the tie-wings (see Figure 2, top row, middle column); right column: O-rings were placed in a figure-O around the tie-wings (see Figure 2, top row, right column).
For the Shoulder brackets, plots of RS (= FR + BI) as a function of θ in the dry (top row) and wet (bottom row) states. Left column: constant normal forces of 300, 500, 600, 700, and 800 cN were applied; middle column: O-rings were placed in a figure-8 around the tie-wings (see Figure 2, top row, middle column); right column: O-rings were placed in a figure-O around the tie-wings (see Figure 2, top row, right column).
For the Synergy brackets, plots of RS (= FR + BI) as a function of θ in the dry (top row) and wet (bottom row) states. Left column: constant normal forces of 300, 500, 600, 700, and 800 cN were applied; middle column: O-rings were placed around the outer tie-wings (see Figure 2, bottom row, middle column); right column: O-rings were placed around the inner tie-wings such that the O-rings were over the bosses between the inner and outer tie-wings (see Figure 2, bottom row, right column)
For the Synergy brackets, plots of RS (= FR + BI) as a function of θ in the dry (top row) and wet (bottom row) states. Left column: constant normal forces of 300, 500, 600, 700, and 800 cN were applied; middle column: O-rings were placed around the outer tie-wings (see Figure 2, bottom row, middle column); right column: O-rings were placed around the inner tie-wings such that the O-rings were over the bosses between the inner and outer tie-wings (see Figure 2, bottom row, right column)
For the VersaT brackets, plots of RS (= FR + BI) as a function of θ in the dry (top row) and wet (bottom row) states. Left column: constant normal forces of 300, 500, 600, 700, and 800 cN were applied; right column: O-rings were placed around the tie-wings (see Figure 1, bottom row, middle column).
For the VersaT brackets, plots of RS (= FR + BI) as a function of θ in the dry (top row) and wet (bottom row) states. Left column: constant normal forces of 300, 500, 600, 700, and 800 cN were applied; right column: O-rings were placed around the tie-wings (see Figure 1, bottom row, middle column).
Average RS Values and Kinetic Coefficients of Friction (μk-FR) in Dry and Wet States for the Passive Configuration
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Linear Regression Analyses of RS vs Angulation in the Dry and Wet States for the Passive Configuration
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In the active configuration, the RS values increased as θ increased (Figures 3–6, right side of each plot). In both states, the slopes (m values) of the regression lines were similar for the Mini Diamond Twin and Shoulder brackets regardless of ligation method (Table 5). The m values of the VersaT and Synergy brackets were also similar regardless of ligation method, but were greater than those of the Mini Diamond Twin and Shoulder brackets.
DISCUSSION
The control brackets (Figure 1)
For a specific archwire-bracket-ligature combination, the slope of an average FR against FN regression (not shown) equaled the kinetic coefficient of friction (μk-FR).4 For SS couples, the μk-FR values in the dry state are generally lower than those in the wet state (Table 3).23 The addition of bumps to the VersaT brackets did not reduce FR or μk-FR value, but the rounded slot walls did increase the value of the experimental θc substantially beyond that of the Mini Diamond Twin brackets (Table 2) (unpublished data).
With the μk-FR value of the Mini Diamond Twin brackets (Table 3),19 the FR value of the O-rings corresponded to FN values of 1100 cN in the dry state and 1000 cN in the wet state (Figure 7), but whether those high values were attributable to a greater μk-FR value (because of the elastomeric material) or a greater FN value than in SS ligatures is not presently known. For the VersaT brackets ligated with O-rings, FR corresponded to FN = 1150 cN in the dry state, but to FN = 800 cN in the wet state (Figure 7). Frank and Nikolai found no difference between O-rings and SS ligature wires that applied FN = 220 cN to the archwire.17 Edwards et al found similar FR values between O-rings and tied SS archwires that applied an estimated FN = 675 cN to the archwire.10 The variation of FN values can be attributed to the different brands of O-rings used, which have various material properties,12 and to the different bracket designs, which affect the force applied by the O-rings.12,14
In the passive configuration for all four bracket designs, linear regression analyses for FR (= RS) as a function of θ in the dry (top row) and wet (bottom row) states. For each plot, the hatched region shows the range in which the linear regression lines for the known normal forces are situated, ranging from the least normal force ( ) to the greatest normal force (
). (See Tables 3 and 4 for details.) For the Mini Diamond Twin brackets, regression lines are shown for the O-ring ligation (▪) and the SS wire ligation (
). For the VersaT brackets, regression lines are shown for the O-ring ligation (▪). For the Shoulder brackets, regression lines are shown for the O-ring ligation in a figure-8 (▪) and a figure-O (
) around the tie-wings. For the Synergy brackets, regression lines are shown for the O-ring ligation around the outer tie-wings (▪) and around the inner tie-wings (
)
In the passive configuration for all four bracket designs, linear regression analyses for FR (= RS) as a function of θ in the dry (top row) and wet (bottom row) states. For each plot, the hatched region shows the range in which the linear regression lines for the known normal forces are situated, ranging from the least normal force ( ) to the greatest normal force (
). (See Tables 3 and 4 for details.) For the Mini Diamond Twin brackets, regression lines are shown for the O-ring ligation (▪) and the SS wire ligation (
). For the VersaT brackets, regression lines are shown for the O-ring ligation (▪). For the Shoulder brackets, regression lines are shown for the O-ring ligation in a figure-8 (▪) and a figure-O (
) around the tie-wings. For the Synergy brackets, regression lines are shown for the O-ring ligation around the outer tie-wings (▪) and around the inner tie-wings (
)
For the Mini Diamond Twin brackets that were tied with SS ligature wires, the FR values were negligible (Figure 7; Table 3). These low values were attributed to a decrease in FN caused by loosening each ligature by a quarter turn.7,13,21 When the SS ligature wires are slack, conventional SS archwire-bracket couples act like self-ligating brackets with passive slides.19 Note that, for self-ligating brackets, a passive slide or clip does not apply a force to an archwire, whereas an active clip does apply a force to an archwire.19 This is not to be confused with the passive (or active) configurations, which terms refer to the clearance (or lack thereof) of an archwire within a bracket.1–3
In the active configuration, the BI component depended upon the angle (θ) between the bracket and the archwire. For each bracket design, plots of BI against θr = θ − θc (Figure 8) showed that there was little difference among the regression lines of the known normal forces, those of the O-rings, and those of the tied SS ligature wires; these regression lines were highly significant (P < 0.001) (Table 5). For the VersaT brackets, the rates of BI (which were equivalent to m values; Table 5) were greater than those of the Mini Diamond Twin brackets. As discussed in a previous study, this greater rate of BI was attributed to the shape of the slot walls (unpublished data). Although the archwire was tangential to the rounded slot walls where the wire entered and exited the VersaT bracket, the archwire bent where the wire contacted the curve between the two bumps (Figure 1, bottom row), leading to a greater bend of the archwire within the bracket slot than the measured θ and a greater BI than expected.
In the active configuration for all four bracket designs, linear regression analyses for BI (= RS − FR) as a function of θr (= θ − θc) in the dry (top row) and wet (bottom row) states. For all four designs, regression lines are shown for various normal forces (light colored lines). For the Mini Diamond Twin brackets, regression lines are shown for the O-ring ligation (dark colored lines) and the SS wire ligation (medium colored lines). For the VersaT brackets, regression lines are shown for the O-ring ligation (dark colored lines). For the Shoulder brackets, regression lines are shown for the O-ring ligation in a figure-8 (dark colored lines) and a figure-O (medium colored lines) around the tie-wings. For the Synergy brackets, regression lines are shown for the O-ring ligation around the outer tie-wings (dark colored lines) and around the inner tie-wings (medium colored lines). Note the profound uniformity among bracket designs.
In the active configuration for all four bracket designs, linear regression analyses for BI (= RS − FR) as a function of θr (= θ − θc) in the dry (top row) and wet (bottom row) states. For all four designs, regression lines are shown for various normal forces (light colored lines). For the Mini Diamond Twin brackets, regression lines are shown for the O-ring ligation (dark colored lines) and the SS wire ligation (medium colored lines). For the VersaT brackets, regression lines are shown for the O-ring ligation (dark colored lines). For the Shoulder brackets, regression lines are shown for the O-ring ligation in a figure-8 (dark colored lines) and a figure-O (medium colored lines) around the tie-wings. For the Synergy brackets, regression lines are shown for the O-ring ligation around the outer tie-wings (dark colored lines) and around the inner tie-wings (medium colored lines). Note the profound uniformity among bracket designs.
Effects of bosses on brackets with straight walls (Figures 1 and 2, top rows)
In the passive configuration for both states, the values of μk-FR were greater for the Shoulder brackets than for the Mini Diamond Twin brackets (Table 3). For the brackets ligated with O-rings in a figure-8, the FR values for both states were between the FR values for FN values of 300 and 500 cN (Figure 7); the FN values for the dry and wet states that were calculated using the μk-FR values (Table 3), however, were 250 and 300 cN, respectively. These FR values were much less than those estimated for O-rings with the archwires and Mini Diamond brackets. Although contact between the ligatures and the archwires did occur at the center of each figure-8, the bosses outside the tie-wings prevented the ligatures from contacting the archwires at those locations, which led to a lower FN being applied to the archwire than for the Mini Diamond Twin brackets. For the Shoulder brackets that were ligated with O-rings in a figure-O, the negligible FR values further confirmed that the bosses did displace the ligature from the archwire (Figure 7; Table 3). Ogata et al observed greater FR values at zero mm deflection (which was equivalent to 0°) than presented in this study, but their FR values for the bracket designs without bosses were still three to four times those of the Shoulder brackets.24
Effects of bosses on brackets with bumps in the slot floors and walls (Figures 1 and 2, bottom rows)
In the passive configuration for the Synergy brackets, the values of μk-FR for both states were similar to those of the VersaT brackets (Table 3). As noted previously (unpublished data), the bumps along the slot floor did not reduce the FR values of the Synergy or VersaT brackets as compared with the Mini Diamond Twin brackets. For the Synergy brackets ligated with O-rings around the outer tie-wings, the FR values for the dry and wet states were comparable to FN values of 800 and 650 cN, respectively (Figure 7). When the Synergy brackets were ligated with O-rings around the inner tie-wings, FR was negligible (Figure 7; Table 3), as was also observed by Ogata et al.24 The bosses between the outer and inner tie-wings therefore prevented the ligature from applying any substantial FN to the archwire.
In the active configuration, the rates of BI for the Synergy brackets were similar to those of the VersaT brackets, and thus greater than those for the Mini Diamond Twin brackets (Table 5). This trend was expected because the slot shapes of the Synergy and VersaT brackets were similar.
CONCLUSIONS
When clearance existed for the SS archwire-bracket couples, the coefficients of friction of all brackets ranged from 0.13 to 0.21 in the dry state and from 0.16 to 0.22 in the wet state, confirming that the bumps in the slot do not reduce friction. When the brackets without bosses were ligated with O-rings, the equivalent normal force was approximately 1000 cN (1020 g). Placing the elastomeric O-rings over bosses, whether outside the tie-wings (ie, the Shoulder brackets) or between the outer tie-wings and the inner tie-wing (ie, the Synergy brackets), reduced or eliminated the FR as compared with brackets without bosses. For the conventional SS twin brackets, ligation with loosely tied SS ligature wires also eliminated FR.
When clearance no longer existed, the shape of the rounded slot walls increased the rate of BI relative to the conventional SS twin brackets. For a given bracket design, however, the ligation type and method did not alter the rate of BI.
With regard to the overall RS ( = FR + BI), the effects of the ligation type and method depended on the second-order angulation of the archwire relative to the bracket. When the angulation was just greater than the critical contact angle for binding, the frictional component was greater than the binding component; thus, the ligation continued to affect the RS. When the angulation greatly exceeded the critical contact angle for binding, the binding component overwhelmed the frictional component, and the effects of ligation type and method were minimal.
REFERENCES
Author notes
Corresponding author: Robert P. Kusy, BS, MS, PhD, DRC Building 210H, CB#7455, University of North Carolina, Chapel Hill, NC 27599 ([email protected])