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Posterior and anterior components of force during bite loading
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Journal of Biomechanics 40 (2007) 820–827 www.elsevier.com/locate/jbiomech www.JBiomech.com
Posterior and anterior components of force during bite loading A.D. Vardimona,, S. Beckmannb,1, N. Shpacka, O. Sarnea, T. Broshc a
Department of Orthodontics, The Maurice and Gabriela Goldschleger, School of Dental Medicine, Tel Aviv University, Tel Aviv, Israel b Private practice, Frambozenstraat 86, 2564 XN Den Haag, The Netherlands c Department of Oral Biology, The Maurice and Gabriela Goldschleger, School of Dental Medicine, Tel Aviv University, Tel Aviv, Israel Accepted 13 March 2006
Abstract Late anterior crowding of teeth has been associated with the anterior component of force (ACF) developed during biting. Possible physiologic mechanisms countering ACF, including the presence of a posterior component of force (PCF), are hypothesized. In this self-controlled study, 60 subjects aged 27.0573.9 years were examined for ACF and PCF that were calculated as the change in tightness of a mandibular dental contact points from non-biting to biting state. Both ACF and PCF were found to develop simultaneously. However, the PCF was 4–7 folds smaller than the ACF (po0.001). The ACF progressively declined by 10–20 folds (po0.001) from the posterior to anterior dentition. The lateral incisor–canine contact point had the greatest ACF decline (63–74%). ACF effect on the anterior dentition is counteracted by a protective mechanism consisted of PCF, progressive dissipation of ACF, and canine blockage. r 2006 Elsevier Ltd. All rights reserved. Keywords: Anterior component of force; Posterior component of force; Bite force; Contact point; Anterior crowding
1. Introduction The sagittal position of the dental arch in its skeletal capsule changes with aging even after cessation of growth (Rossouw et al., 1993; Bishara et al., 1998). Several causative factors have been suggested for this non-static arrangement (Little 1999; Huck et al., 2000; Richardson 2002). One of these factors is the physiological mesial drift that re-allocates the posterior dentition anteriorly (Moss and Picton, 1967; van Beek, 1979; Roux and Woda, 1994). This, in conjunction with mandibular third molar eruption, is considered a causative factor for late anterior crowding of mandibular incisors (Pirttiniemi et al., 1994; Richardson, 2002), although third molar involvement in anterior crowding is controversial (Norderval et al., 1975). Corresponding author. Tel.: +972 3 6407456; fax: +972 3 6409250.
E-mail address: [email protected] (A.D. Vardimon). In partial fulfillment of the requirements for the Master in Orthodontics degree. 1
0021-9290/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2006.03.009
Change in the labio/lingual muscular balance is a second factor that affects tooth position over time. Increase in incisor proclination may arise due to forces generated by a tongue thrust habit. In this instance these forces prevail over the opposing forces created by lips (Lapatki et al., 2002; Fujiki et al., 2004). Another factor that affects the dynamics of sagittal dental position is the anterior component of force (ACF) (Osborn, 1961; Southard et al., 1989, 1990). The ACF, a derivative of the vertically acting bite force, is a contributor to mesial drift of the posterior dentition and to late anterior crowding (Southard et al., 1990; Acar et al., 2002). The transseptal fibers reinforce its activity (Picton and Moss, 1973). Maximum bite force increases during the first 2 decades (Kamegai et al., 2005; Miyawaki et al., 2005) and decreases during 60 and 70+ years of age (Ikebe et al., 2005). Besides age, bite force magnitude is also directly dependent on number of natural teeth, i.e., increasing with number of teeth, craniofacial morphology, i.e., low in skeletal open bite (Sonnesen and Bakke,
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2005), and gender, i.e., low in females (Kamegai et al., 2005). However, conflicting results have been found in the latter two factors (Proffit and Fields, 1983; Proffit et al., 1983; Braun et al., 1996). There is evidence that the ACF is not the sole masticatory force component that affects tooth position. In rats, where distal drift is physiologically determined (King et al., 1995), mesial tooth drift occurs when the dental contact point (CP) is removed (Roux and Woda, 1994). Similar reaction was found in humans, where mesial drift is physiologically determined, second premolar extraction causes distal drift of the first premolar (Matteson et al., 1982). Furthermore, a decrease in tightness of CP4–52 and CP3–4 anterior to a mandibular first molar extraction site was found over time (Vardimon et al., 2003). The mesial displacement of a tooth distal to an extraction space can be explained by the ACF. The distal displacement of a tooth, that is located mesial to the extraction space, can be explained either by the absence of an ACF or by the presence of a posterior component of force (PCF). If such a force component is present then it may act as a balancing factor counteracting the ACF and its potential damage. However, the presence of a PCF was not yet investigated. The objectives of the present study was to investigate whether the PCF developed during bite force application (objective 1). The magnitude of PCF, when present, was determined and compared to the ACF (objective 2). Other mechanisms were examined that counteract the advert reaction of the ACF on the mandibular anterior dentition, when ACF dominated PCF (objective 3). Alternative hypotheses of the study were that PCF develops simultaneously with ACF during bite application; ACF is greater than PCF; and the dental arch provides means to overcome the imbalance state between ACF and PCF.
2. Materials and methods In this self-controlled study, 60 subjects were recruited based on age (27.0573.9 years), not under dental treatment, at least one mandibular quadrant without any interproximal spaces (o0.03 mm), and good periodontal health. Each subject gave their informal consent. An appropriate institutional review board protected their rights. The study design was based on previous findings which showed that CP tightness, located anterior to a loaded tooth, increases compared to the tightness during an unloaded state (Osborn, 1961; Southard et al., 1989, 1990; Fuhrmann et al., 2000). This increase is equal to 2 CP4-5 refers to the contact point between the first and second premolars. Tooth numbering is based on IDF nomenclature.
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the ACF. Therefore, when CP tightness located posterior to an applied bite force is increased compared to their level during an unloaded state, this increase would constitute the PCF. Measurements were taken with a bite fork (Fig. 1A) and a tightness of dental contact point (TDCP) device (Fig. 1B). CP tightness was measured with the TDCP device in N. The metal strip of the TDCP device was inserted between two adjacent teeth in an occlusogingival direction; and the amount of force required to separate these teeth was registered (Vardimon et al., 2003). Briefly, the TDCP device is comprised of a bowjig that includes a stainless-steel strip, and a handle that serves as a load cell with an internal binocular-shaped aluminum beam (Fig. 2) (Brosh et al., 2002). When force is applied to the metal strip (upon insertion in the contact point), the beam deflects and the strains that develop on the beam are measured by a full Wheatstone bridge. Since contact point tightness increased during (bite) loading, a 0.03 mm thick matrix strip was used, as opposed to a 0.05 mm thick strip in previous unloaded studies (Brosh et al., 2002; Vardimon et al., 2001, 2003). A custom-made stainless steel bite fork was designed to measure the bite load developed in N when biting on a unilateral mandibular tooth. The bite fork consisted of two prongs and a handle with a 901 offset bend to allow lingual intraoral placement (Fig. 1C). Plastic pads covered the biting areas of the prongs. The total bite opening during loading was 11.4 mm. Full-bridge strain gauges (J2A-09-S1425-35B, Vishay Measurements Group, Raleigh, NC) were bonded to one prong in full Wheatstone bridge adjacent to one plastic pad. Calibration of the TDCP device and bite fork was carried out using universal testing machine (Instron, High Wycombe, England). The bite fork and the TDCP were loaded 10 times each up to 1000 and 10 N, respectively for calibration. All calibration curves were linear (R2 ¼ 0:99, po0.001). Sensitivity (slope of the calibration curve) and repeatability (scatter between data sets) were high for both devices (0.24870.015 N/mS and 4.4870.084 mN/mS for the bite fork and TDCP devices, respectively). The signal-to-noise ratio is defined by the equation S/N ¼ 20 log10(Vs/Vn). Since the noises of the electrical units (e.g., strain gauges) are very low, only the fluctuations of the biting force were considered as characterizing the S/N ratio. This resulted in a high mean S/N ratio value (16.5 dB). The subject was seated in an upright position on a dental chair and simultaneous mandibular TDCPs and bite force measurements were registered by a Signal Conditioning Amplifier device (Vishay 2100, Vishay Measurements Group, Raleigh, NC). A baseline maximum bite force of the mandibular first premolar was determined for each subject. Subjects were instructed to maintain a constant bite force equaled to 75% of first premolar bite force, that was marked on the screen,
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Fig. 1. The measurement devices and schematic illustration of the clinical measurement procedure. (A) The bite fork. Dark arrow (red in online version) indicate the location of the strain gauges, light arrows (blue in online version) indicate the direction of the biting force. (B) Tightness of Dental Contact Point (TDCP) device. Light arrow indicates the direction of force determined by the device during measurement. (C) Intraorally, the bite fork was applied from lingual on a single mandibular tooth, and the TDCP device was applied from buccal.
Fig. 2. The TDCP device includes a bow-jig with a metal strip (0.03 mm) attached to a binocular beam with 4 strain gauges.
throughout the TDCP measuring procedure. This force level, applied to all loaded teeth, was selected to avoid fluctuation due to muscle fatigue, and was achieved practically by observing an assembly monitor displaying bite force values in real time. Measurements were taken in 2500 Hz and data averaged every 50 measurements resulting in data point for every 0.02 s. The duration of 7 CPs measurements during biting lasted up to 30 s. This included an adjustment lap of 5–10 s until the patient stabilized his biting at the required force level. A full one unit signal of a CP tightness measurement lasted approximately 2.5 s. For the study only the peak value of the signal (0.02 s) was considered as TDCP value.
The ACF and PCF magnitudes were examined in three protocols. First, TDCP base line values were recorded with no biting load. Then, measurement of ACF and PCF were conducted as they emerged from a loaded tooth and were transmitted to different CPs. Under the latter criteria, the subject was continuously biting on the second premolar, and ACF was measured at CPs anterior to the loading point (CP4–5, CP3–4) and PCF at CPs posterior to the loading point (CP5–6, CP6– 7) (Fig. 3A). The second protocol measured the ACF and PCF in the same CPs (CP4–5, CP5–6, CP6–7), i.e., between the mandibular first premolar and the second molar. ACF was measured when the subject was continuously biting on the mandibular second molar, and the PCF when biting on the mandibular first premolar (Fig. 3B). The third protocol, ACF transmission to the anterior dentition, was examined when biting on the second molar or second premolar and TDCP of all anterior CPs was measured (i.e., CP6–7, CP5–6. CP4–5, CP3–4, CP2– 3, CP1–2, CP1–1 for second molar and CP4–5, CP3–4, CP2–3, CP1–2, CP1–1 for second premolar) (Fig. 3C). The measurement error of the maximum bite force and of the TDCP for all contact points at no biting was calculated by the Dahlberg’s equation (Dahlberg, 1940) on 20 subjects: sffiffiffiffiffiffiffiffiffiffiffiffiffi Sðd i Þ2 D¼ , 2n
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compared with ANOVA with repeated measures with 2 within factors: biting location and CP location. ACF developed when biting on the second molar and second premolar was compared with paired t-test. The ACF dissipation was investigated with ANOVA with repeated measures. Descriptive statistics included mean and standard error of the mean. Statistical significant difference was considered for po0.05.
BF 5
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BF TDCP TDCP TDCP 4-5 3-4 5-6
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3. Results
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4
5
6
7 BF
BF TDCP TDCP TDCP TDCP TDCP TDCP 2-3 (C) 1-1 1-2 5-6 3-4 4-5
823
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Fig. 3. (A) First protocol, during biting on the mandibular second premolar ACF was measured at CP4–5, CP3–4 and PCF at CP5–6, CP6–7. (B) Second protocol, during bite on the mandibular first premolar a PCF was developed at CP4–5, CP5–6, CP6–7, subsequently while biting on the mandibular second molar an ACF developed at the same CPs. (C) Third protocol, biting on the second molar initiated an ACF at CP6–7, CP5–6. CP4–5, CP3–4, CP2–3, CP1–2, CP1–1, subsequently biting on the mandibular second premolar initiated an ACF at CP4–5, CP3–4, CP2–3, CP1–2, CP1–1.
where di is the difference between two repeated measures on the same subject and n is the number of subjects. Unloaded (baseline) and loaded TDCPs were compared using ANOVA with repeated measures including 2 within factors: loading condition and CP location. ACF and PCF of the first protocol (biting on second premolar) were compared using paired t-test. ACF and PCF of the second protocol (biting on first premolar for PCF vs. biting on second molar for ACF) were
Fig. 4 presents a characteristic plot obtained during simultaneous data acquisition of both bite force and TDCP while biting on the second premolar. The registered bite force (75% of the maximum bite force) was well maintained. The mean coefficient of variation of bite force during a trial, i.e., characterizing the fluctuation, was low (10%). The measurement error, according to Dahlberg’s equation, for the maximum bite force was 10.11 N, (6.2%), and for the TDCP 0.37 N (6.5%). That is, both measurement errors were within the acceptable range (o10%). The average bite force applied to all loaded teeth was 122.82712.29 N (75% of the maximum bite force at the mandibular first premolar). The intrasubject variation of the bite force when biting on the second premolar, and of the TDCP when measuring CP4–5 at different days, was 115.065 and 0.76, respectively. The inter-subject variation was 5432.353 and 6.986, respectively. These values show a good repeatability and reliability of both bite force and TDCP as the variation between subjects is much higher than the variation between different days of measurement for the same subject. 3.1. PCF A statistical interaction was found between baseline (unloaded) and loaded TDCPs (po0.001). When a bite load was applied to the second premolar (first protocol), the TDCP for all CPs measured increased significantly (po0.001). That is, simultaneously an ACF propagated anteriorly from CP4–5 (5.0372.23 N), and a PCF posteriorly from CP5–6 (0.7872.38 N) (Table 1, Fig. 5A). Of noted importance was that PCF measured at CP5–6 and CP6–7 increased significantly from baseline TDCP (p ¼ 0.014 and 0.022, respectively). 3.2. ACF vs. PCF In the second protocol, an ACF and a PCF alternately developed at the same CP. ACF was significantly (po0.001) greater than the PCF. For example, during second molar loading, an ACF of 2.6472.61 N developed at CP4–5. However, application
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CP4-5 BF
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400
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300 CP1-1
250
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-2
100 50
-4
0 -50
-6 0
2
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6
8
10 Time (s)
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Fig. 4. A characteristic plot obtained during simultaneous data acquisition of both bite force (gray line) and TDCP (black line) while biting on the second premolar at a continuous force of 75% of the maximal bite force (dashed line). Arrows indicate peak TDCP of measured CPs.
Table 1 Mean (7SD) ACF and PCF values for all experimental protocols and the related statistical p-values
Loaded tooth Force vector CP1–1 CP1–2 CP2–3 CP3–4 CP4–5 CP5–6 CP6–7 CP3–4 vs. CP6–7 CP4–5 vs. CP5–6
a
b
c
d
5 ACF (N) 0.4971.08 0.4871.01 1.2471.48 3.3472.14 5.0372.23
5 PCF (N)
7 ACF (N) 0.1571.00 0.0871.02 0.4271.19 1.6072.11 2.6472.61 3.2572.45 3.1072.10
4 PCF (N)
3.3472.14 5.0372.23
0.7872.38 0.6872.13 0.6872.13 0.7872.38
of an equal bite load to the first premolar resulted in a PCF of 0.6471.86 N at the same CP4–5 (Table 1, Fig. 5B). 3.3. ACF dissipation The ACF gradually dissipate towards the anterior dentition when a posterior tooth was loaded (Fig. 5C). When a bite load was applied to the second molar, the ACF adjacent to the loaded tooth at CP6–7 was 3.1072.10 N compared to 0.1571.00 N at CP1–1 (Table 1, Fig. 5C). This effect was also seen when the ACF commenced from the second premolar, with ACF of 5.0372.23 N at CP4–5 and 0.4971.08 N at CP1–1 (Table 1, Fig. 5C). The two mandibular incisors received an ACF lower than one half-Newton, regardless of whether the ACF initiated at the molar or second premolar (Fig. 5C). Dissipation of the ACF was significantly dependant on the location of the bite load. Thus, the ACF at CP3–
p (a vs. b)
p (c vs. d)
po0.001 po0.001 po0.001
0.6471.86 0.4771.92 1.0972.29
p (a vs. c)
p ¼ 0:061 p ¼ 0:007 po0.001 po0.001 po0.001
po0.001 po0.001
4 was 3.3472.14 and 1.6072.11 N when the bite load was applied to the second premolar and second molar, respectively. The greatest ACF dissipation was at the canine. This means that the difference between ACF on the distal and mesial CP of the same tooth was found in the canine (i.e., D of ACFCP3–4ACFCP2–3). Canine dissipation was 2.10 and 1.18 N after loading the second premolar or second molar, respectively (Fig. 5C— arrows).
4. Discussion 4.1. PCF The first alternative hypothesis that a PCF exists was validated. This is supported by the significant increase in TDCP from unloaded to loaded TDCP levels in teeth that received a PCF vector. A previous attempt to demonstrate this force vector failed because proximal
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6 5
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3.11
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1 0 CP4-5 CP5-6 Contact point
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7.0 6.97 5.6
5.79
5 4 3
4.28
Base line Biting on 4 Biting on 7
3.61 3.71 3.11
2 CP4-5
CP5-6 Contact point
Biting on 7
Biting on 5
(B) 6.00 5.00 ACF (N)
CP6-7
1.69
4.00 0.66 2.10
3.00
-0.14
1.02
2.00 0.76 1.00
-0.01 -0.07
1.18
One can argue that the fact that the distally directed PCF (CP5–6) was 6.5 times lower than the mesially directed ACF (CP4–5) may be because of the diversity in CPs and not solely as a characteristic of the two force components. However, when the same CP was measured as a result of the same bite load once as an ACF and once as a PCF, the same relationship was found of ACF significantly (4–5 fold) greater than PCF. These findings confirm the second alternative hypothesis. The simultaneous presence of both anterior and posterior vectors of force can be explained by the partition along the mesial and distal cusp slopes of the bite force. This is supported by variable directions of tooth migration found when altered cusp slopes were introduced experimentally in monkey teeth (Picton and Moss, 1980). The greater magnitude of the ACF may be related to the greater mesial inclination of the mandibular posterior teeth (Orthlieb, 1997), the natural presence of the curve of Spee (Shannon and Nanda, 2004), and the oblique fiber arrangement of the masseter muscle (Osborn, 1993).
0.33
4.3. ACF dissipation
0.00
(C)
This was well defined in the first protocol when a load was applied to the second premolar, and ACF and PCF developed concurrently on the mesial (CP4–5) and distal walls (CP5–6), respectively. PCF at low mean values demonstrated high values of standard deviations (Table 1). This could be due to the negative values in several PCF and ACF cases. Most likely, if the loaded tooth is sharply inclined anteriorly then the value of the PCF could be negative. However, in most instances, both ACF and PCF were positive. For this reason, all means of ACF and PCF were positive (Table 1). 4.2. ACF vs. PCF
8.89
7
825
CP1-1 CP1-2 CP2-3 CP3-4 CP4-5 CP5-6 CP6-7 Contact Point (CP)
Fig. 5. (A) First protocol—TDCP level at no bite (dashed line) and when biting on the second premolar (solid line). Increase in TDCP (loadedunloaded) at CPs anterior to the second premolar is related to ACF and at CPs posterior to the second premolar to PCF. (B) Second protocol—for the same CPs, TDCP level at no bite (dashed line) in comparison to TDCP when biting on the first premolar (solid line) and when biting on the second molar (unequaled dash line). The same CPs received PCF and ACF (TDCPloadedTDCPunloaded) when biting alternately on the first premolar and the second molar, respectively. (C) Third protocol—ACF dissipation when biting on the second molar (solid line) and on the second premolar (dashed line). The greatest dissipation gradient occurred between the distal and mesial CPs of the canine.
dental contact strength measurements were not taken during biting (Dorfer et al., 2000). Both ACF and PCF developed simultaneously to a single tooth bite load.
The potential side effect of the ACF, i.e., late anterior crowding, has been previously discussed (van Beek, 1979; Southard et al., 1990; Fuhrmann et al., 2000; Acar et al., 2002). It is possible that late anterior crowding develops during the second and third decades of life, is related to the maximum bite force that reaches its peak at this age. The PCF is the first component of the protective mechanism in reducing the ACF potential adverse effect. However, the presence of a PCF does not explain the dichotomy that the two horizontal force vectors delivered by the masticatory muscle system to the dentition are in an imbalance state. The data relevant to postero-anterior propagation of the ACF may provide a solution to the above-unexplained inequality. These findings show that regardless of
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where the ACF is initiated in the posterior region, its magnitude in the incisor region is significantly less. Quantitatively, it was found that the ACF at the incisor region was 10- and 20-folds lower than the posterior region when the ACF initiated at the second premolar and second molar, respectively. That is, the further the loaded tooth distally, the sharper the force dissipation process. Since most chewing behavior and maximum bite force capacity occur in the posterior region (Ferrario et al., 2004; Kohyama et al., 2004), the progressive dissipation of the ACF in a postero-anterior direction, may also play a role in dampening the possible detrimental effect that the full expression of this force might have on the dentition. In addition, the canine response to the ACF may be another possible physiologic rate-limiting factor. This tooth demonstrated the greatest difference in ACF from its distal to mesial contact points (i.e., dissipation). Examination of the amount of dissipation in the ACF for each tooth anterior to the loaded point, revealed that the canine provided the greatest such decline, regardless of where the ACF was initiated from (i.e., the second premolar or second molar). The significant impact that the canine has on ACF dissipation was further supported in a study on monkeys in which the caninelateral space was not affected by mesial drift when interproximal spaces were created along the whole dental arch (Moss and Picton, 1967). Taken together, the above factors, the existence of a PCF, ACF dissipation, and canine blockage, constitute a collective balancing effect to that of the ACF, which supports the third alternative hypothesis. In this manner a possible explanation for the quantitative disparity between ACF and PCF may be accounted for.
Acknowledgments The authors wish to thank Dr. Moshe Davidovitch, Department of Orthodontics, Ms. Rita Lazar, Scientific Editor, Ms. Ana Bahar, Department of Anatomy and Anthropology and Mrs. Ilana Gelernter, Department of Statistics.
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ARTICLE IN PRESS A.D. Vardimon et al. / Journal of Biomechanics 40 (2007) 820–827 Picton, D.C., Moss, J.P., 1973. The part played by the trans-septal fibre system in experimental approximal drift of the cheek teeth of monkeys (Macaca irus). Archives of Oral Biology 18, 669–680. Picton, D.C., Moss, J.P., 1980. The effect on approximal drift of altering the horizontal component of biting force in adult monkeys (Macaca irus). Archives of Oral Biology 25, 45–48. Pirttiniemi, P.M., Oikarinen, K.S., Raustia, A.M., 1994. The effect of removal of all third molars on the dental arches in the third decade of life. Cranio: The Journal of Craniomandibular Practice 12, 23–27. Proffit, W.R., Fields, H.W., 1983. Occlusal forces in normal- and longface children. Journal of Dental Research 62, 571–574. Proffit, W.R., Fields, H.W., Nixon, W.L., 1983. Occlusal forces in normal- and long-face adults. Journal of Dental Research 62, 566–570. Richardson, M.E., 2002. Late lower arch crowding: the aetiology reviewed. Dental Update 29, 234–238. Rossouw, P.E., Preston, C.B., Lombard, C.J., Truter, J.W., 1993. A longitudinal evaluation of the anterior border of the dentition. American Journal of Orthodontics and Dentofacial Orthopedics 104, 146–152. Roux, D., Woda, A., 1994. Biometric analysis of tooth migration after approximal contact removal in the rat. Archives of Oral Biology 39, 1023–1027.
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Shannon, K.R., Nanda, R.S., 2004. Changes in the curve of Spee with treatment and at 2 years posttreatment. American Journal of Orthodontics and Dentofacial Orthopedics 125, 589–596. Sonnesen, L., Bakke, M., 2005. Molar bite force in relation to occlusion, craniofacial dimensions, and head posture in preorthodontic children. European Journal of Orthodontics 27, 58–63. Southard, T.E., Behrents, R.G., Tolley, E.A., 1989. The anterior component of occlusal force Part 1. Measurement and distribution. American Journal of Orthodontics and Dentofacial Orthopedics 96, 493–500. Southard, T.E., Behrents, R.G., Tolley, E.A., 1990. The anterior component of occlusal force Part 2. Relationship with dental malalignment. American Journal of Orthodontics and Dentofacial Orthopedics 97, 41–44. van Beek, H., 1979. The transfer of mesial drift potential along the dental arch in Macaca irus: an experimental study of tooth migration rate related to the horizontal vectors of occlusal forces. European Journal of Orthodontics 1, 125–129. Vardimon, A.D., Matsaev, E., Lieberman, M., Brosh, T., 2001. Tightness of dental contact points in spaced and non-spaced permanent dentitions. European Journal of Orthodontics 23, 305–314. Vardimon, A.D., Tryman, Y., Brosh, T., 2003. Change over time in intra-arch contact point tightness. American Journal of Dentistry 16, 20A–24A.
Journal of Biomechanics 40 (2007) 820–827 www.elsevier.com/locate/jbiomech www.JBiomech.com
Posterior and anterior components of force during bite loading A.D. Vardimona,, S. Beckmannb,1, N. Shpacka, O. Sarnea, T. Broshc a
Department of Orthodontics, The Maurice and Gabriela Goldschleger, School of Dental Medicine, Tel Aviv University, Tel Aviv, Israel b Private practice, Frambozenstraat 86, 2564 XN Den Haag, The Netherlands c Department of Oral Biology, The Maurice and Gabriela Goldschleger, School of Dental Medicine, Tel Aviv University, Tel Aviv, Israel Accepted 13 March 2006
Abstract Late anterior crowding of teeth has been associated with the anterior component of force (ACF) developed during biting. Possible physiologic mechanisms countering ACF, including the presence of a posterior component of force (PCF), are hypothesized. In this self-controlled study, 60 subjects aged 27.0573.9 years were examined for ACF and PCF that were calculated as the change in tightness of a mandibular dental contact points from non-biting to biting state. Both ACF and PCF were found to develop simultaneously. However, the PCF was 4–7 folds smaller than the ACF (po0.001). The ACF progressively declined by 10–20 folds (po0.001) from the posterior to anterior dentition. The lateral incisor–canine contact point had the greatest ACF decline (63–74%). ACF effect on the anterior dentition is counteracted by a protective mechanism consisted of PCF, progressive dissipation of ACF, and canine blockage. r 2006 Elsevier Ltd. All rights reserved. Keywords: Anterior component of force; Posterior component of force; Bite force; Contact point; Anterior crowding
1. Introduction The sagittal position of the dental arch in its skeletal capsule changes with aging even after cessation of growth (Rossouw et al., 1993; Bishara et al., 1998). Several causative factors have been suggested for this non-static arrangement (Little 1999; Huck et al., 2000; Richardson 2002). One of these factors is the physiological mesial drift that re-allocates the posterior dentition anteriorly (Moss and Picton, 1967; van Beek, 1979; Roux and Woda, 1994). This, in conjunction with mandibular third molar eruption, is considered a causative factor for late anterior crowding of mandibular incisors (Pirttiniemi et al., 1994; Richardson, 2002), although third molar involvement in anterior crowding is controversial (Norderval et al., 1975). Corresponding author. Tel.: +972 3 6407456; fax: +972 3 6409250.
E-mail address: [email protected] (A.D. Vardimon). In partial fulfillment of the requirements for the Master in Orthodontics degree. 1
0021-9290/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2006.03.009
Change in the labio/lingual muscular balance is a second factor that affects tooth position over time. Increase in incisor proclination may arise due to forces generated by a tongue thrust habit. In this instance these forces prevail over the opposing forces created by lips (Lapatki et al., 2002; Fujiki et al., 2004). Another factor that affects the dynamics of sagittal dental position is the anterior component of force (ACF) (Osborn, 1961; Southard et al., 1989, 1990). The ACF, a derivative of the vertically acting bite force, is a contributor to mesial drift of the posterior dentition and to late anterior crowding (Southard et al., 1990; Acar et al., 2002). The transseptal fibers reinforce its activity (Picton and Moss, 1973). Maximum bite force increases during the first 2 decades (Kamegai et al., 2005; Miyawaki et al., 2005) and decreases during 60 and 70+ years of age (Ikebe et al., 2005). Besides age, bite force magnitude is also directly dependent on number of natural teeth, i.e., increasing with number of teeth, craniofacial morphology, i.e., low in skeletal open bite (Sonnesen and Bakke,
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2005), and gender, i.e., low in females (Kamegai et al., 2005). However, conflicting results have been found in the latter two factors (Proffit and Fields, 1983; Proffit et al., 1983; Braun et al., 1996). There is evidence that the ACF is not the sole masticatory force component that affects tooth position. In rats, where distal drift is physiologically determined (King et al., 1995), mesial tooth drift occurs when the dental contact point (CP) is removed (Roux and Woda, 1994). Similar reaction was found in humans, where mesial drift is physiologically determined, second premolar extraction causes distal drift of the first premolar (Matteson et al., 1982). Furthermore, a decrease in tightness of CP4–52 and CP3–4 anterior to a mandibular first molar extraction site was found over time (Vardimon et al., 2003). The mesial displacement of a tooth distal to an extraction space can be explained by the ACF. The distal displacement of a tooth, that is located mesial to the extraction space, can be explained either by the absence of an ACF or by the presence of a posterior component of force (PCF). If such a force component is present then it may act as a balancing factor counteracting the ACF and its potential damage. However, the presence of a PCF was not yet investigated. The objectives of the present study was to investigate whether the PCF developed during bite force application (objective 1). The magnitude of PCF, when present, was determined and compared to the ACF (objective 2). Other mechanisms were examined that counteract the advert reaction of the ACF on the mandibular anterior dentition, when ACF dominated PCF (objective 3). Alternative hypotheses of the study were that PCF develops simultaneously with ACF during bite application; ACF is greater than PCF; and the dental arch provides means to overcome the imbalance state between ACF and PCF.
2. Materials and methods In this self-controlled study, 60 subjects were recruited based on age (27.0573.9 years), not under dental treatment, at least one mandibular quadrant without any interproximal spaces (o0.03 mm), and good periodontal health. Each subject gave their informal consent. An appropriate institutional review board protected their rights. The study design was based on previous findings which showed that CP tightness, located anterior to a loaded tooth, increases compared to the tightness during an unloaded state (Osborn, 1961; Southard et al., 1989, 1990; Fuhrmann et al., 2000). This increase is equal to 2 CP4-5 refers to the contact point between the first and second premolars. Tooth numbering is based on IDF nomenclature.
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the ACF. Therefore, when CP tightness located posterior to an applied bite force is increased compared to their level during an unloaded state, this increase would constitute the PCF. Measurements were taken with a bite fork (Fig. 1A) and a tightness of dental contact point (TDCP) device (Fig. 1B). CP tightness was measured with the TDCP device in N. The metal strip of the TDCP device was inserted between two adjacent teeth in an occlusogingival direction; and the amount of force required to separate these teeth was registered (Vardimon et al., 2003). Briefly, the TDCP device is comprised of a bowjig that includes a stainless-steel strip, and a handle that serves as a load cell with an internal binocular-shaped aluminum beam (Fig. 2) (Brosh et al., 2002). When force is applied to the metal strip (upon insertion in the contact point), the beam deflects and the strains that develop on the beam are measured by a full Wheatstone bridge. Since contact point tightness increased during (bite) loading, a 0.03 mm thick matrix strip was used, as opposed to a 0.05 mm thick strip in previous unloaded studies (Brosh et al., 2002; Vardimon et al., 2001, 2003). A custom-made stainless steel bite fork was designed to measure the bite load developed in N when biting on a unilateral mandibular tooth. The bite fork consisted of two prongs and a handle with a 901 offset bend to allow lingual intraoral placement (Fig. 1C). Plastic pads covered the biting areas of the prongs. The total bite opening during loading was 11.4 mm. Full-bridge strain gauges (J2A-09-S1425-35B, Vishay Measurements Group, Raleigh, NC) were bonded to one prong in full Wheatstone bridge adjacent to one plastic pad. Calibration of the TDCP device and bite fork was carried out using universal testing machine (Instron, High Wycombe, England). The bite fork and the TDCP were loaded 10 times each up to 1000 and 10 N, respectively for calibration. All calibration curves were linear (R2 ¼ 0:99, po0.001). Sensitivity (slope of the calibration curve) and repeatability (scatter between data sets) were high for both devices (0.24870.015 N/mS and 4.4870.084 mN/mS for the bite fork and TDCP devices, respectively). The signal-to-noise ratio is defined by the equation S/N ¼ 20 log10(Vs/Vn). Since the noises of the electrical units (e.g., strain gauges) are very low, only the fluctuations of the biting force were considered as characterizing the S/N ratio. This resulted in a high mean S/N ratio value (16.5 dB). The subject was seated in an upright position on a dental chair and simultaneous mandibular TDCPs and bite force measurements were registered by a Signal Conditioning Amplifier device (Vishay 2100, Vishay Measurements Group, Raleigh, NC). A baseline maximum bite force of the mandibular first premolar was determined for each subject. Subjects were instructed to maintain a constant bite force equaled to 75% of first premolar bite force, that was marked on the screen,
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Fig. 1. The measurement devices and schematic illustration of the clinical measurement procedure. (A) The bite fork. Dark arrow (red in online version) indicate the location of the strain gauges, light arrows (blue in online version) indicate the direction of the biting force. (B) Tightness of Dental Contact Point (TDCP) device. Light arrow indicates the direction of force determined by the device during measurement. (C) Intraorally, the bite fork was applied from lingual on a single mandibular tooth, and the TDCP device was applied from buccal.
Fig. 2. The TDCP device includes a bow-jig with a metal strip (0.03 mm) attached to a binocular beam with 4 strain gauges.
throughout the TDCP measuring procedure. This force level, applied to all loaded teeth, was selected to avoid fluctuation due to muscle fatigue, and was achieved practically by observing an assembly monitor displaying bite force values in real time. Measurements were taken in 2500 Hz and data averaged every 50 measurements resulting in data point for every 0.02 s. The duration of 7 CPs measurements during biting lasted up to 30 s. This included an adjustment lap of 5–10 s until the patient stabilized his biting at the required force level. A full one unit signal of a CP tightness measurement lasted approximately 2.5 s. For the study only the peak value of the signal (0.02 s) was considered as TDCP value.
The ACF and PCF magnitudes were examined in three protocols. First, TDCP base line values were recorded with no biting load. Then, measurement of ACF and PCF were conducted as they emerged from a loaded tooth and were transmitted to different CPs. Under the latter criteria, the subject was continuously biting on the second premolar, and ACF was measured at CPs anterior to the loading point (CP4–5, CP3–4) and PCF at CPs posterior to the loading point (CP5–6, CP6– 7) (Fig. 3A). The second protocol measured the ACF and PCF in the same CPs (CP4–5, CP5–6, CP6–7), i.e., between the mandibular first premolar and the second molar. ACF was measured when the subject was continuously biting on the mandibular second molar, and the PCF when biting on the mandibular first premolar (Fig. 3B). The third protocol, ACF transmission to the anterior dentition, was examined when biting on the second molar or second premolar and TDCP of all anterior CPs was measured (i.e., CP6–7, CP5–6. CP4–5, CP3–4, CP2– 3, CP1–2, CP1–1 for second molar and CP4–5, CP3–4, CP2–3, CP1–2, CP1–1 for second premolar) (Fig. 3C). The measurement error of the maximum bite force and of the TDCP for all contact points at no biting was calculated by the Dahlberg’s equation (Dahlberg, 1940) on 20 subjects: sffiffiffiffiffiffiffiffiffiffiffiffiffi Sðd i Þ2 D¼ , 2n
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compared with ANOVA with repeated measures with 2 within factors: biting location and CP location. ACF developed when biting on the second molar and second premolar was compared with paired t-test. The ACF dissipation was investigated with ANOVA with repeated measures. Descriptive statistics included mean and standard error of the mean. Statistical significant difference was considered for po0.05.
BF 5
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3. Results
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Fig. 3. (A) First protocol, during biting on the mandibular second premolar ACF was measured at CP4–5, CP3–4 and PCF at CP5–6, CP6–7. (B) Second protocol, during bite on the mandibular first premolar a PCF was developed at CP4–5, CP5–6, CP6–7, subsequently while biting on the mandibular second molar an ACF developed at the same CPs. (C) Third protocol, biting on the second molar initiated an ACF at CP6–7, CP5–6. CP4–5, CP3–4, CP2–3, CP1–2, CP1–1, subsequently biting on the mandibular second premolar initiated an ACF at CP4–5, CP3–4, CP2–3, CP1–2, CP1–1.
where di is the difference between two repeated measures on the same subject and n is the number of subjects. Unloaded (baseline) and loaded TDCPs were compared using ANOVA with repeated measures including 2 within factors: loading condition and CP location. ACF and PCF of the first protocol (biting on second premolar) were compared using paired t-test. ACF and PCF of the second protocol (biting on first premolar for PCF vs. biting on second molar for ACF) were
Fig. 4 presents a characteristic plot obtained during simultaneous data acquisition of both bite force and TDCP while biting on the second premolar. The registered bite force (75% of the maximum bite force) was well maintained. The mean coefficient of variation of bite force during a trial, i.e., characterizing the fluctuation, was low (10%). The measurement error, according to Dahlberg’s equation, for the maximum bite force was 10.11 N, (6.2%), and for the TDCP 0.37 N (6.5%). That is, both measurement errors were within the acceptable range (o10%). The average bite force applied to all loaded teeth was 122.82712.29 N (75% of the maximum bite force at the mandibular first premolar). The intrasubject variation of the bite force when biting on the second premolar, and of the TDCP when measuring CP4–5 at different days, was 115.065 and 0.76, respectively. The inter-subject variation was 5432.353 and 6.986, respectively. These values show a good repeatability and reliability of both bite force and TDCP as the variation between subjects is much higher than the variation between different days of measurement for the same subject. 3.1. PCF A statistical interaction was found between baseline (unloaded) and loaded TDCPs (po0.001). When a bite load was applied to the second premolar (first protocol), the TDCP for all CPs measured increased significantly (po0.001). That is, simultaneously an ACF propagated anteriorly from CP4–5 (5.0372.23 N), and a PCF posteriorly from CP5–6 (0.7872.38 N) (Table 1, Fig. 5A). Of noted importance was that PCF measured at CP5–6 and CP6–7 increased significantly from baseline TDCP (p ¼ 0.014 and 0.022, respectively). 3.2. ACF vs. PCF In the second protocol, an ACF and a PCF alternately developed at the same CP. ACF was significantly (po0.001) greater than the PCF. For example, during second molar loading, an ACF of 2.6472.61 N developed at CP4–5. However, application
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-6 0
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Fig. 4. A characteristic plot obtained during simultaneous data acquisition of both bite force (gray line) and TDCP (black line) while biting on the second premolar at a continuous force of 75% of the maximal bite force (dashed line). Arrows indicate peak TDCP of measured CPs.
Table 1 Mean (7SD) ACF and PCF values for all experimental protocols and the related statistical p-values
Loaded tooth Force vector CP1–1 CP1–2 CP2–3 CP3–4 CP4–5 CP5–6 CP6–7 CP3–4 vs. CP6–7 CP4–5 vs. CP5–6
a
b
c
d
5 ACF (N) 0.4971.08 0.4871.01 1.2471.48 3.3472.14 5.0372.23
5 PCF (N)
7 ACF (N) 0.1571.00 0.0871.02 0.4271.19 1.6072.11 2.6472.61 3.2572.45 3.1072.10
4 PCF (N)
3.3472.14 5.0372.23
0.7872.38 0.6872.13 0.6872.13 0.7872.38
of an equal bite load to the first premolar resulted in a PCF of 0.6471.86 N at the same CP4–5 (Table 1, Fig. 5B). 3.3. ACF dissipation The ACF gradually dissipate towards the anterior dentition when a posterior tooth was loaded (Fig. 5C). When a bite load was applied to the second molar, the ACF adjacent to the loaded tooth at CP6–7 was 3.1072.10 N compared to 0.1571.00 N at CP1–1 (Table 1, Fig. 5C). This effect was also seen when the ACF commenced from the second premolar, with ACF of 5.0372.23 N at CP4–5 and 0.4971.08 N at CP1–1 (Table 1, Fig. 5C). The two mandibular incisors received an ACF lower than one half-Newton, regardless of whether the ACF initiated at the molar or second premolar (Fig. 5C). Dissipation of the ACF was significantly dependant on the location of the bite load. Thus, the ACF at CP3–
p (a vs. b)
p (c vs. d)
po0.001 po0.001 po0.001
0.6471.86 0.4771.92 1.0972.29
p (a vs. c)
p ¼ 0:061 p ¼ 0:007 po0.001 po0.001 po0.001
po0.001 po0.001
4 was 3.3472.14 and 1.6072.11 N when the bite load was applied to the second premolar and second molar, respectively. The greatest ACF dissipation was at the canine. This means that the difference between ACF on the distal and mesial CP of the same tooth was found in the canine (i.e., D of ACFCP3–4ACFCP2–3). Canine dissipation was 2.10 and 1.18 N after loading the second premolar or second molar, respectively (Fig. 5C— arrows).
4. Discussion 4.1. PCF The first alternative hypothesis that a PCF exists was validated. This is supported by the significant increase in TDCP from unloaded to loaded TDCP levels in teeth that received a PCF vector. A previous attempt to demonstrate this force vector failed because proximal
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CP6-7
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3.00
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2.00 0.76 1.00
-0.01 -0.07
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One can argue that the fact that the distally directed PCF (CP5–6) was 6.5 times lower than the mesially directed ACF (CP4–5) may be because of the diversity in CPs and not solely as a characteristic of the two force components. However, when the same CP was measured as a result of the same bite load once as an ACF and once as a PCF, the same relationship was found of ACF significantly (4–5 fold) greater than PCF. These findings confirm the second alternative hypothesis. The simultaneous presence of both anterior and posterior vectors of force can be explained by the partition along the mesial and distal cusp slopes of the bite force. This is supported by variable directions of tooth migration found when altered cusp slopes were introduced experimentally in monkey teeth (Picton and Moss, 1980). The greater magnitude of the ACF may be related to the greater mesial inclination of the mandibular posterior teeth (Orthlieb, 1997), the natural presence of the curve of Spee (Shannon and Nanda, 2004), and the oblique fiber arrangement of the masseter muscle (Osborn, 1993).
0.33
4.3. ACF dissipation
0.00
(C)
This was well defined in the first protocol when a load was applied to the second premolar, and ACF and PCF developed concurrently on the mesial (CP4–5) and distal walls (CP5–6), respectively. PCF at low mean values demonstrated high values of standard deviations (Table 1). This could be due to the negative values in several PCF and ACF cases. Most likely, if the loaded tooth is sharply inclined anteriorly then the value of the PCF could be negative. However, in most instances, both ACF and PCF were positive. For this reason, all means of ACF and PCF were positive (Table 1). 4.2. ACF vs. PCF
8.89
7
825
CP1-1 CP1-2 CP2-3 CP3-4 CP4-5 CP5-6 CP6-7 Contact Point (CP)
Fig. 5. (A) First protocol—TDCP level at no bite (dashed line) and when biting on the second premolar (solid line). Increase in TDCP (loadedunloaded) at CPs anterior to the second premolar is related to ACF and at CPs posterior to the second premolar to PCF. (B) Second protocol—for the same CPs, TDCP level at no bite (dashed line) in comparison to TDCP when biting on the first premolar (solid line) and when biting on the second molar (unequaled dash line). The same CPs received PCF and ACF (TDCPloadedTDCPunloaded) when biting alternately on the first premolar and the second molar, respectively. (C) Third protocol—ACF dissipation when biting on the second molar (solid line) and on the second premolar (dashed line). The greatest dissipation gradient occurred between the distal and mesial CPs of the canine.
dental contact strength measurements were not taken during biting (Dorfer et al., 2000). Both ACF and PCF developed simultaneously to a single tooth bite load.
The potential side effect of the ACF, i.e., late anterior crowding, has been previously discussed (van Beek, 1979; Southard et al., 1990; Fuhrmann et al., 2000; Acar et al., 2002). It is possible that late anterior crowding develops during the second and third decades of life, is related to the maximum bite force that reaches its peak at this age. The PCF is the first component of the protective mechanism in reducing the ACF potential adverse effect. However, the presence of a PCF does not explain the dichotomy that the two horizontal force vectors delivered by the masticatory muscle system to the dentition are in an imbalance state. The data relevant to postero-anterior propagation of the ACF may provide a solution to the above-unexplained inequality. These findings show that regardless of
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where the ACF is initiated in the posterior region, its magnitude in the incisor region is significantly less. Quantitatively, it was found that the ACF at the incisor region was 10- and 20-folds lower than the posterior region when the ACF initiated at the second premolar and second molar, respectively. That is, the further the loaded tooth distally, the sharper the force dissipation process. Since most chewing behavior and maximum bite force capacity occur in the posterior region (Ferrario et al., 2004; Kohyama et al., 2004), the progressive dissipation of the ACF in a postero-anterior direction, may also play a role in dampening the possible detrimental effect that the full expression of this force might have on the dentition. In addition, the canine response to the ACF may be another possible physiologic rate-limiting factor. This tooth demonstrated the greatest difference in ACF from its distal to mesial contact points (i.e., dissipation). Examination of the amount of dissipation in the ACF for each tooth anterior to the loaded point, revealed that the canine provided the greatest such decline, regardless of where the ACF was initiated from (i.e., the second premolar or second molar). The significant impact that the canine has on ACF dissipation was further supported in a study on monkeys in which the caninelateral space was not affected by mesial drift when interproximal spaces were created along the whole dental arch (Moss and Picton, 1967). Taken together, the above factors, the existence of a PCF, ACF dissipation, and canine blockage, constitute a collective balancing effect to that of the ACF, which supports the third alternative hypothesis. In this manner a possible explanation for the quantitative disparity between ACF and PCF may be accounted for.
Acknowledgments The authors wish to thank Dr. Moshe Davidovitch, Department of Orthodontics, Ms. Rita Lazar, Scientific Editor, Ms. Ana Bahar, Department of Anatomy and Anthropology and Mrs. Ilana Gelernter, Department of Statistics.
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