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Orthodontics d

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

aDepartment of Orthodontics, The Maurice and Gabriela Goldschleger, School of Dental Medicine, Tel Aviv University, Tel Aviv, IsraelbPrivate practice, Frambozenstraat 86, 2564 XN Den Haag, The Netherlands

cDepartment 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 skeletalcapsule changes with aging even after cessation ofgrowth (Rossouw et al., 1993; Bishara et al., 1998).Several causative factors have been suggested for thisnon-static arrangement (Little 1999; Huck et al., 2000;Richardson 2002). One of these factors is the physiolo-gical mesial drift that re-allocates the posterior dentitionanteriorly (Moss and Picton, 1967; van Beek, 1979;Roux and Woda, 1994). This, in conjunction withmandibular third molar eruption, is considered acausative factor for late anterior crowding of mandib-ular incisors (Pirttiniemi et al., 1994; Richardson, 2002),although third molar involvement in anterior crowdingis controversial (Norderval et al., 1975).

e front matter r 2006 Elsevier Ltd. All rights reserved.

iomech.2006.03.009

ing author. Tel.: +972 3 6407456; fax: +972 3 6409250.

ess: andyva@post.tau.ac.il (A.D. Vardimon).

fulfillment of the requirements for the Master in

egree.

Change in the labio/lingual muscular balance is asecond factor that affects tooth position over time.Increase in incisor proclination may arise due to forcesgenerated by a tongue thrust habit. In this instance theseforces prevail over the opposing forces created by lips(Lapatki et al., 2002; Fujiki et al., 2004).

Another factor that affects the dynamics of sagittaldental position is the anterior component of force(ACF) (Osborn, 1961; Southard et al., 1989, 1990). TheACF, a derivative of the vertically acting bite force, is acontributor to mesial drift of the posterior dentition andto late anterior crowding (Southard et al., 1990; Acar etal., 2002). The transseptal fibers reinforce its activity(Picton and Moss, 1973).

Maximum bite force increases during the first 2decades (Kamegai et al., 2005; Miyawaki et al., 2005)and decreases during 60 and 70+ years of age (Ikebe etal., 2005). Besides age, bite force magnitude is alsodirectly dependent on number of natural teeth, i.e.,increasing with number of teeth, craniofacial morphol-ogy, i.e., low in skeletal open bite (Sonnesen and Bakke,

ARTICLE IN PRESSA.D. Vardimon et al. / Journal of Biomechanics 40 (2007) 820–827 821

2005), and gender, i.e., low in females (Kamegai et al.,2005). However, conflicting results have been found inthe latter two factors (Proffit and Fields, 1983; Proffitet al., 1983; Braun et al., 1996).

There is evidence that the ACF is not the solemasticatory force component that affects tooth position.In rats, where distal drift is physiologically determined(King et al., 1995), mesial tooth drift occurs when thedental contact point (CP) is removed (Roux and Woda,1994). Similar reaction was found in humans, wheremesial drift is physiologically determined, second pre-molar extraction causes distal drift of the first premolar(Matteson et al., 1982). Furthermore, a decrease intightness of CP4–52 and CP3–4 anterior to a mandibularfirst molar extraction site was found over time(Vardimon et al., 2003).

The mesial displacement of a tooth distal to anextraction space can be explained by the ACF. Thedistal displacement of a tooth, that is located mesial tothe extraction space, can be explained either by theabsence of an ACF or by the presence of a posteriorcomponent of force (PCF). If such a force component ispresent then it may act as a balancing factor counter-acting the ACF and its potential damage. However, thepresence of a PCF was not yet investigated.

The objectives of the present study was to investigatewhether the PCF developed during bite force applica-tion (objective 1). The magnitude of PCF, when present,was determined and compared to the ACF (objective 2).Other mechanisms were examined that counteract theadvert reaction of the ACF on the mandibular anteriordentition, when ACF dominated PCF (objective 3).

Alternative hypotheses of the study were that PCFdevelops simultaneously with ACF during bite applica-tion; ACF is greater than PCF; and the dental archprovides means to overcome the imbalance statebetween ACF and PCF.

2. Materials and methods

In this self-controlled study, 60 subjects were recruitedbased on age (27.0573.9 years), not under dentaltreatment, at least one mandibular quadrant withoutany interproximal spaces (o0.03mm), and good period-ontal health. Each subject gave their informal consent.An appropriate institutional review board protectedtheir rights.

The study design was based on previous findingswhich showed that CP tightness, located anterior to aloaded tooth, increases compared to the tightness duringan unloaded state (Osborn, 1961; Southard et al., 1989,1990; Fuhrmann et al., 2000). This increase is equal to

2CP4-5 refers to the contact point between the first and second

premolars. Tooth numbering is based on IDF nomenclature.

the ACF. Therefore, when CP tightness located poster-ior to an applied bite force is increased compared totheir level during an unloaded state, this increase wouldconstitute 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 TDCPdevice in N. The metal strip of the TDCP device wasinserted between two adjacent teeth in an occluso-gingival direction; and the amount of force required toseparate these teeth was registered (Vardimon et al.,2003). Briefly, the TDCP device is comprised of a bow-jig that includes a stainless-steel strip, and a handle thatserves as a load cell with an internal binocular-shapedaluminum beam (Fig. 2) (Brosh et al., 2002). When forceis applied to the metal strip (upon insertion in thecontact point), the beam deflects and the strains thatdevelop on the beam are measured by a full Wheatstonebridge. Since contact point tightness increased during(bite) loading, a 0.03mm thick matrix strip was used, asopposed to a 0.05mm thick strip in previous unloadedstudies (Brosh et al., 2002; Vardimon et al., 2001, 2003).

A custom-made stainless steel bite fork was designedto measure the bite load developed in N when biting ona unilateral mandibular tooth. The bite fork consisted oftwo prongs and a handle with a 901 offset bend to allowlingual intraoral placement (Fig. 1C). Plastic padscovered the biting areas of the prongs. The total biteopening during loading was 11.4mm. Full-bridge straingauges (J2A-09-S1425-35B, Vishay MeasurementsGroup, Raleigh, NC) were bonded to one prong in fullWheatstone bridge adjacent to one plastic pad. Calibra-tion of the TDCP device and bite fork was carried outusing universal testing machine (Instron, High Wy-combe, England). The bite fork and the TDCP wereloaded 10 times each up to 1000 and 10N, respectivelyfor calibration. All calibration curves were linear(R2 ¼ 0:99, po0.001). Sensitivity (slope of the calibra-tion curve) and repeatability (scatter between data sets)were high for both devices (0.24870.015N/mS and4.4870.084mN/mS for the bite fork and TDCP devices,respectively). The signal-to-noise ratio is defined by theequation S/N ¼ 20 log10(Vs/Vn). Since the noises of theelectrical units (e.g., strain gauges) are very low, only thefluctuations of the biting force were considered ascharacterizing the S/N ratio. This resulted in a highmean S/N ratio value (16.5 dB).

The subject was seated in an upright position on adental chair and simultaneous mandibular TDCPs andbite force measurements were registered by a SignalConditioning Amplifier device (Vishay 2100, VishayMeasurements Group, Raleigh, NC). A baseline max-imum bite force of the mandibular first premolar wasdetermined for each subject. Subjects were instructed tomaintain a constant bite force equaled to 75% of firstpremolar bite force, that was marked on the screen,

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Fig. 2. The TDCP device includes a bow-jig with a metal strip

(0.03mm) attached to a binocular beam with 4 strain gauges.

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.

A.D. Vardimon et al. / Journal of Biomechanics 40 (2007) 820–827822

throughout the TDCP measuring procedure. This forcelevel, applied to all loaded teeth, was selected to avoidfluctuation due to muscle fatigue, and was achievedpractically by observing an assembly monitor displayingbite force values in real time.

Measurements were taken in 2500Hz and dataaveraged every 50 measurements resulting in data pointfor every 0.02 s. The duration of 7 CPs measurementsduring biting lasted up to 30 s. This included anadjustment lap of 5–10 s until the patient stabilized hisbiting at the required force level. A full one unit signal ofa 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 inthree protocols. First, TDCP base line values wererecorded with no biting load. Then, measurement ofACF and PCF were conducted as they emerged from aloaded tooth and were transmitted to different CPs.Under the latter criteria, the subject was continuouslybiting on the second premolar, and ACF was measuredat CPs anterior to the loading point (CP4–5, CP3–4) andPCF at CPs posterior to the loading point (CP5–6, CP6–7) (Fig. 3A).

The second protocol measured the ACF and PCF inthe same CPs (CP4–5, CP5–6, CP6–7), i.e., between themandibular first premolar and the second molar. ACFwas measured when the subject was continuously bitingon the mandibular second molar, and the PCF whenbiting on the mandibular first premolar (Fig. 3B).

The third protocol, ACF transmission to the anteriordentition, was examined when biting on the secondmolar or second premolar and TDCP of all anterior CPswas 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 forceand of the TDCP for all contact points at no biting wascalculated by the Dahlberg’s equation (Dahlberg, 1940)on 20 subjects:

D ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiSðd iÞ

2

2n

s,

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PCFACF

1

TDCP TDCP TDCP TDCP3-4 5-6

1 4 5 6 7

BF

BF

75

2

1

TDCP4-5

TDCP5-6

1 3

3

4 5 6 7

BF

BF BF

BF

ACFPCF

TDCP6-7

74

ACF

1

TDCP TDCP TDCP TDCP TDCP TDCP TDCP1-1 1-2 2-3 4-5 6-7

1 3 4 5 6 7

BF

BF

75

BF

BF

ACF

4-5 6-7

5-63-4

(A)

(B)

(C)

2

2

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.

A.D. Vardimon et al. / Journal of Biomechanics 40 (2007) 820–827 823

where di is the difference between two repeated measureson the same subject and n is the number of subjects.

Unloaded (baseline) and loaded TDCPs were com-pared using ANOVA with repeated measures including2 within factors: loading condition and CP location.ACF and PCF of the first protocol (biting on secondpremolar) were compared using paired t-test. ACF andPCF of the second protocol (biting on first premolar forPCF vs. biting on second molar for ACF) were

compared with ANOVA with repeated measures with2 within factors: biting location and CP location. ACFdeveloped when biting on the second molar and secondpremolar was compared with paired t-test. The ACFdissipation was investigated with ANOVA with repeatedmeasures. Descriptive statistics included mean andstandard error of the mean. Statistical significantdifference was considered for po0.05.

3. Results

Fig. 4 presents a characteristic plot obtained duringsimultaneous data acquisition of both bite force andTDCP while biting on the second premolar. Theregistered bite force (75% of the maximum bite force)was well maintained. The mean coefficient of variationof bite force during a trial, i.e., characterizing thefluctuation, was low (10%).

The measurement error, according to Dahlberg’sequation, for the maximum bite force was 10.11N,(6.2%), and for the TDCP 0.37N (6.5%). That is, bothmeasurement errors were within the acceptable range(o10%). The average bite force applied to all loadedteeth was 122.82712.29N (75% of the maximum biteforce at the mandibular first premolar). The intra-subject variation of the bite force when biting on thesecond premolar, and of the TDCP when measuringCP4–5 at different days, was 115.065 and 0.76,respectively. The inter-subject variation was 5432.353and 6.986, respectively. These values show a goodrepeatability and reliability of both bite force and TDCPas the variation between subjects is much higher thanthe variation between different days of measurement forthe same subject.

3.1. PCF

A statistical interaction was found between baseline(unloaded) and loaded TDCPs (po0.001). When a biteload was applied to the second premolar (first protocol),the TDCP for all CPs measured increased significantly(po0.001). That is, simultaneously an ACF propa-gated anteriorly from CP4–5 (5.0372.23N), and aPCF posteriorly from CP5–6 (0.7872.38N) (Table 1,Fig. 5A). Of noted importance was that PCF measuredat CP5–6 and CP6–7 increased significantly frombaseline TDCP (p ¼ 0.014 and 0.022, respectively).

3.2. ACF vs. PCF

In the second protocol, an ACF and a PCFalternately developed at the same CP. ACF wassignificantly (po0.001) greater than the PCF. Forexample, during second molar loading, an ACF of2.6472.61N developed at CP4–5. However, application

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0

50

150

300

0 2 4 6 8 10 12 16 20

Bite

forc

e (N

)

-6

-4

-2

0

2

4

6

8

TD

CP

(N

)

BF TDCP

75% of maximum bite force

Time (s)

CP1-1 CP1-2

CP2-3

CP3-4

CP4-5

-50

100

200

250

350

400

450

500

14 18

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

a b c d p (a vs. b) p (c vs. d) p (a vs. c)

Loaded tooth 5 5 7 4

Force vector ACF (N) PCF (N) ACF (N) PCF (N)

CP1–1 0.4971.08 0.1571.00 p ¼ 0:061CP1–2 0.4871.01 0.0871.02 p ¼ 0:007CP2–3 1.2471.48 0.4271.19 po0.001

CP3–4 3.3472.14 1.6072.11 po0.001

CP4–5 5.0372.23 2.6472.61 0.6471.86 po0.001 po0.001

CP5–6 0.7872.38 3.2572.45 0.4771.92 po0.001

CP6–7 0.6872.13 3.1072.10 1.0972.29 po0.001

CP3–4 vs. CP6–7 3.3472.14 0.6872.13 po0.001

CP4–5 vs. CP5–6 5.0372.23 0.7872.38 po0.001

A.D. Vardimon et al. / Journal of Biomechanics 40 (2007) 820–827824

of an equal bite load to the first premolar resultedin a PCF of 0.6471.86N at the same CP4–5 (Table 1,Fig. 5B).

3.3. ACF dissipation

The ACF gradually dissipate towards the anteriordentition when a posterior tooth was loaded (Fig. 5C).When a bite load was applied to the second molar, theACF adjacent to the loaded tooth at CP6–7 was3.1072.10N compared to 0.1571.00N at CP1–1(Table 1, Fig. 5C). This effect was also seen when theACF commenced from the second premolar, with ACFof 5.0372.23N at CP4–5 and 0.4971.08N at CP1–1(Table 1, Fig. 5C). The two mandibular incisors receivedan ACF lower than one half-Newton, regardless ofwhether the ACF initiated at the molar or secondpremolar (Fig. 5C).

Dissipation of the ACF was significantly dependanton the location of the bite load. Thus, the ACF at CP3–

4 was 3.3472.14 and 1.6072.11N when the bite loadwas applied to the second premolar and second molar,respectively. The greatest ACF dissipation was at thecanine. This means that the difference between ACF onthe distal and mesial CP of the same tooth was found inthe canine (i.e., D of ACFCP3–4�ACFCP2–3). Caninedissipation was 2.10 and 1.18N after loading the secondpremolar or second molar, respectively (Fig. 5C—arrows).

4. Discussion

4.1. PCF

The first alternative hypothesis that a PCF exists wasvalidated. This is supported by the significant increase inTDCP from unloaded to loaded TDCP levels in teeththat received a PCF vector. A previous attempt todemonstrate this force vector failed because proximal

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0

1

2

3

4

5

6

7

8

9

CP4-5

TD

CP

(N

)

Base lineBiting on 5

6.47

5.98

3.713.11

5.794.91

8.14

2.65

2

3

4

5

6

7

8

9

Contact point

TD

CP

(N

)

Base lineBiting on 4Biting on 7

8.89

4.28

5.79

6.97

5.6

7.0

3.61

3.713.11

0.00

1.00

2.00

3.00

4.00

5.00

6.00

CP1-1 CP2-3 CP4-5

AC

F (

N)

Biting on 7 Biting on 5

1.69

0.76

2.10

0.33

1.18

1.02

0.66-0.14

-0.07

Contact Point (CP)

CP1-2 CP3-4 CP5-6 CP6-7

CP4-5 CP5-6 CP6-7

Contact pointCP3-4 CP5-6 CP6-7

-0.01

(A)

(B)

(C)

Fig. 5. (A) First protocol—TDCP level at no bite (dashed line) and

when biting on the second premolar (solid line). Increase in TDCP

(loaded�unloaded) 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 (TDCPloaded�TDCPunloaded) 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.

A.D. Vardimon et al. / Journal of Biomechanics 40 (2007) 820–827 825

dental contact strength measurements were not takenduring biting (Dorfer et al., 2000). Both ACF and PCFdeveloped simultaneously to a single tooth bite load.

This was well defined in the first protocol when a loadwas applied to the second premolar, and ACF and PCFdeveloped concurrently on the mesial (CP4–5) and distalwalls (CP5–6), respectively.

PCF at low mean values demonstrated high values ofstandard deviations (Table 1). This could be due to thenegative values in several PCF and ACF cases. Mostlikely, if the loaded tooth is sharply inclined anteriorlythen 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 werepositive (Table 1).

4.2. ACF vs. PCF

One can argue that the fact that the distally directedPCF (CP5–6) was 6.5 times lower than the mesiallydirected ACF (CP4–5) may be because of the diversity inCPs and not solely as a characteristic of the two forcecomponents. However, when the same CP was measuredas a result of the same bite load once as an ACF andonce as a PCF, the same relationship was found of ACFsignificantly (4–5 fold) greater than PCF. These findingsconfirm the second alternative hypothesis.

The simultaneous presence of both anterior andposterior vectors of force can be explained by thepartition along the mesial and distal cusp slopes of thebite force. This is supported by variable directions oftooth migration found when altered cusp slopes wereintroduced experimentally in monkey teeth (Picton andMoss, 1980).

The greater magnitude of the ACF may be related tothe greater mesial inclination of the mandibular poster-ior teeth (Orthlieb, 1997), the natural presence of thecurve of Spee (Shannon and Nanda, 2004), and theoblique fiber arrangement of the masseter muscle(Osborn, 1993).

4.3. ACF dissipation

The potential side effect of the ACF, i.e., late anteriorcrowding, has been previously discussed (van Beek,1979; Southard et al., 1990; Fuhrmann et al., 2000; Acaret al., 2002). It is possible that late anterior crowdingdevelops during the second and third decades of life, isrelated to the maximum bite force that reaches its peakat this age.

The PCF is the first component of the protectivemechanism in reducing the ACF potential adverseeffect. However, the presence of a PCF does not explainthe dichotomy that the two horizontal force vectorsdelivered by the masticatory muscle system to thedentition are in an imbalance state.

The data relevant to postero-anterior propagation ofthe ACF may provide a solution to the above-unex-plained inequality. These findings show that regardless of

ARTICLE IN PRESSA.D. Vardimon et al. / Journal of Biomechanics 40 (2007) 820–827826

where the ACF is initiated in the posterior region, itsmagnitude in the incisor region is significantly less.Quantitatively, it was found that the ACF at the incisorregion was 10- and 20-folds lower than the posteriorregion when the ACF initiated at the second premolarand second molar, respectively. That is, the further theloaded tooth distally, the sharper the force dissipationprocess. Since most chewing behavior and maximum biteforce capacity occur in the posterior region (Ferrario etal., 2004; Kohyama et al., 2004), the progressivedissipation of the ACF in a postero-anterior direction,may also play a role in dampening the possibledetrimental effect that the full expression of this forcemight have on the dentition.

In addition, the canine response to the ACF may beanother possible physiologic rate-limiting factor. Thistooth demonstrated the greatest difference in ACF fromits distal to mesial contact points (i.e., dissipation).Examination of the amount of dissipation in the ACFfor each tooth anterior to the loaded point, revealed thatthe canine provided the greatest such decline, regardlessof where the ACF was initiated from (i.e., the secondpremolar or second molar). The significant impact thatthe canine has on ACF dissipation was furthersupported in a study on monkeys in which the canine-lateral space was not affected by mesial drift wheninterproximal spaces were created along the wholedental arch (Moss and Picton, 1967).

Taken together, the above factors, the existence of aPCF, ACF dissipation, and canine blockage, constitutea collective balancing effect to that of the ACF, whichsupports the third alternative hypothesis. In this mannera possible explanation for the quantitative disparitybetween ACF and PCF may be accounted for.

Acknowledgments

The authors wish to thank Dr. Moshe Davidovitch,Department of Orthodontics, Ms. Rita Lazar, ScientificEditor, Ms. Ana Bahar, Department of Anatomy andAnthropology and Mrs. Ilana Gelernter, Department ofStatistics.

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