JPOR-279; No. of Pages 9 journal of prosthodontic research xxx (2015) xxx–xxx
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/jpor
Original article
Structural equation modeling for alteration of occlusal plane inclination Yuko Shigeta DDS, PhD*, Takumi Ogawa DDS, PhD, Yoshiharu Nakamura DDS, PhD, Eriko Ando DDS, PhD, Rio Hirabayashi DDS, PhD, Tomoko Ikawa DDS, PhD Department of Fixed Prosthodontics, School of Dental Medicine, Tsurumi University, Yokohama, Japan
article info
abstract
Article history:
Purpose: Occlusal plane inclination is important to maintain a normal opening closing/
Received 13 December 2013
biting function. However, there can be several causes that lead to alterations of the occlusal
Received in revised form
plane. The purpose of this study was to observe variations of occlusal plane inclination in
24 April 2015
adult patients, and to uncover the factors affecting changes in occlusal plane inclination
Accepted 1 May 2015
with aging.
Available online xxx
Methods: Subjects were 143 patients. A cephalometric image was taken of these patients. In
Keywords:
cephalometric analysis. To evaluate the possible causes that affect occlusal plane inclina-
Occlusal plane
tion, factor analysis was carried out, and each component was treated as factors, which
Cephalometric image
were then statistically applied to a structural equation model. Statistical analysis was
this study, our inquiry points were age, 3 variables on intra-oral findings, and 7 variables on
Camper-occlusal plane angle
carried out through the SPSS 20.0 (SPSS Inc., Chicago, USA).
Aging
Results: In all patients, Camper-occlusal plane angle (COA) ranged from 25.7 to 4.98
Missing teeth
(Mean SD: 6.4 5.36). In the 60 patients who had no missing teeth, COA ranged from 11.6 to 4.98 (Mean SD: 3.3 3.31). From the results of the structural analysis, it was suggested that the occlusal plane changes to counter-clockwise (on the right lateral cephalograms) with aging. Conclusion: In this study, variations of occlusal plane inclination in adult patients were observed, and the factors affecting changes in occlusal plane inclination with aging were investigated via factor analysis. From our results, it was suggested that the mandibular morphology change and loss of teeth with aging influence occlusal plane inclination. # 2015 Published by Elsevier Ireland on behalf of Japan Prosthodontic Society.
1.
Introduction
In 1978, Okane et al. [1] investigated the influence of occlusal plane inclination for biting force and biting force exertion
efficiency. When the occlusal plane was made parallel to Camper’s plane, during maximum clenching, biting force was greatest and the biting force exertion efficiency showed the best value. They concluded that anteroposterior inclination of the occlusal plane tends to affect the biting force, and the
* Corresponding author at: Department of Fixed Prosthodontics, School of Dental Medicine, Tsurumi University, 2-1-3 Tsurumi, Tsurumi-ku, Yokohama, Japan. Tel.: +81 45 580 8417; fax: +81 45 573 9599. E-mail address: [email protected] (Y. Shigeta). http://dx.doi.org/10.1016/j.jpor.2015.05.001 1883-1958/# 2015 Published by Elsevier Ireland on behalf of Japan Prosthodontic Society.
Please cite this article in press as: Shigeta Y, et al. Structural equation modeling for alteration of occlusal plane inclination. J Prosthodont Res (2015), http://dx.doi.org/10.1016/j.jpor.2015.05.001
JPOR-279; No. of Pages 9
2
journal of prosthodontic research xxx (2015) xxx–xxx
method with the Camper’s plane as a standard on the cranium seems to be the most reasonable for occlusal plane orientation. In 2007, Sato et al. [2] reported the relationship between the masticatory movement path and dentofacial morphology using lateral cephalograms and a jaw movement-recording system. They investigated the relationship between the occlusal plane inclination and the direction of the masticatory movement path, and concluded that there is a close association between each one. As mentioned above, occlusal plane inclination is important to maintain a normal opening closing/biting function. However, there can be several causes that lead to alterations of the occlusal plane. In 2000, Vukusˇie´ et al. [3] examined the change in occlusal plane inclination that takes place during craniofacial growth relative to various facio-cranial reference lines. Cephalometric images which were taken in 192 patients (from 10 to 18 years old) were analyzed. Namely, the alteration of occlusal plane inclination was investigated during growth, from mixeddentition to permanent dentition. They described that the anterior rotation (left profile) and a significant decrease of occlusal plane inclination were observed during growth. In 2010, Normand and Cavacami [4] evaluated cephalometric changes in patients with bilateral loss of lower first permanent molar teeth. They concluded that the bilateral loss of lower first permanent molars leads to counterclockwise rotation of the occlusal plane. From the results of these previous studies, it was revealed that occlusal plane inclination alters with growth or loss of teeth. As previously mentioned above, the occlusal plane has a close relation to oral function, and can vary due to several factors. Furthermore, due to the 8020 campaign by the Japan Dental Association from 1989 [5], the percentage of persons in all age groups having over 20 teeth has increased [6,7]. Subsequently, various kinds of prostheses, including fixed partial dentures, can be applied to these dentitions, and the unison with oral function has to be considered. Therefore, dentists have to consider the various changes in occlusal factors during prosthodontic treatment for dentulous patients in adults. However, the influence of aging and change of dentition status to the occlusal plane has not been revealed up to this point. The purpose of this study was to observe variations of occlusal plane inclination in adult patients, and to uncover the factors affecting changes in occlusal plane inclination with aging.
2.
Materials and methods
2.1.
Subjects
Subjects were 143 patients; 69 females and 74 males. Subjects were consecutively recruited from 2008 to 2012. The age of subjects ranged from 24 to 74 years old (Mean SD: 52 15.5). These patients visited our department (Tsurumi University Dental Hospital) to receive prosthodontic treatments for crown/missing teeth or obstructive sleep apnea. A cephalometric image was taken of these patients to observe the
condition of occlusion or upper airway. In this study, an inclusion criterion was adults over 20 years old without influence of growth factors. Exclusion criteria were as follows: 1. Jaw deformity, 2. Serious osteoarthritis, 3. Serious reversed occlusion, 4. Serious open-bite, 5. Undergoing Orthodontic treatment, 6. Patients without prosthesis for missing teeth in molars (the elongation of teeth causes the local disturbance of the occlusal plane due to un-treatment for missing teeth).
2.2.
Inquiry points and cephalometric analysis
In this study, our variables included age, number of missing teeth, number of restored teeth, and mandibular configuration as possible causes that affect the occlusal plane. The orientation of occlusal plane to the cranium and the mandible were evaluated. The cephalometric images were analyzed via image analyzing software Amira 3.1 (Mercury Computer Systems/ 3D viz. group, San Diego, CA). On the cephalometric images, 6 angles including 10 reference points were measured using the same software. In this study, our inquiry points were the following 11 variables: a. Age b. Intra-oral findings b-1. Number of missing molar teeth b-2. Number of missing and restored teeth in anterior teeth: Total number of missing teeth, and restored teeth with full-coverage crown in anterior teeth. b-3. Number of missing and restored teeth in molars: Total number of missing teeth, and restored teeth with onlay or full-coverage crown in molars. c. Cephalometric analysis c-1. Balkwill angle: the angle formed by the line of connection to the center of the condyle and the central incisor tip (Cd0 -L1) and occlusal plane (L1-MPC) c-2. Mandibular plane angle: the angle formed by Frankfort plane (Or-Po) and Mandibular plane (Me-iGo) c-3. Frankfort-occlusal plane angle (FOA): the angle formed by Frankfort plane (Or-Po) and occlusal plane (L1-MPC) c-4. Frankfort-Camper plane angle (FCA): the angle formed by Frankfort plane (Or-Po) and Camper plane (Sn0 -Po) c-5. Gonial angle (GoA): the angle formed by Mandibular plane (Me-iGo) and Ramus plane (Ar-pGo) c-6. Camper-occlusal plane angle (COA): the angle formed by Camper plane (Sn0 -Po) and occlusal plane (L1-MPC) c-7. Mandibular plane-occlusal plane angle (MOA): the angle formed by Mandibular plane (Me-iGo) and occlusal plane (L1-MPC) The details of the measure points mentioned above are explained in Fig. 1.
2.3.
Statistical analysis
Statistical analysis was carried out through the SPSS 20.0 (SPSS Inc., Chicago, USA).
Please cite this article in press as: Shigeta Y, et al. Structural equation modeling for alteration of occlusal plane inclination. J Prosthodont Res (2015), http://dx.doi.org/10.1016/j.jpor.2015.05.001
JPOR-279; No. of Pages 9 journal of prosthodontic research xxx (2015) xxx–xxx
3
Fig. 1 – Inquiry points on cephalometric image. Or: the most inferior point of the inferior margin of the orbit, Po: the most superior point of the ear-rod, Sn0 : the ala of nose inferior margin, Cd0 : the center of condyle, Ar: the posterior border of mandible rami, L1: the central incisor tip, Me: the most inferior point on the symphysis of the mandible, iGo: the point anterior to Go on the curvature of the angle of the mandible made by the tangent to the inferior border of the mandible, pGo: the point superior to Go on the curvature of the angle of the mandible made by the tangent to the posterior border of the mandible, MPC: the most posterior occlusal contact point on the second molar.
To evaluate the possible causes that affect occlusal plane inclination, factor analysis was carried out, and each component was treated as factors, which were then statistically applied to a structural equation model. The details of the above process in our statistical analysis were as follows:
(1) First, the mean and standard deviation in our 11 variables were calculated. The ceiling effect and the floor effect were then investigated. Appropriateness of the variables were thus proven from the results. (2) Next, factor analysis was carried out via the Principal Factor Method. This analysis was used to identify the underlying components that explain the correlations among a set of variables. A large number of variables were summarized with a smaller number of derived components, called factors (Determination by the appropriate number of component; 1, 2, 3, 4,. . .). Through the Promax rotation of the Principal Factor Method, the number of structure was hypothesized. The variable which has no adequate factor loading was removed. After that, we carried out the same analysis again. Each factor was entitled depending on the characteristics of the included variables. (3) Finally, the variables and factors, from the results of factor analysis, were statistically applied to a structural equation modeling, and goodness of fit in our model was verified.
This research was approved by the Ethics Committee at Tsurumi University (Approval number: 1030).
3.
Results
3.1.
Descriptive statistics in each variable
Table 1 shows the descriptive statistics in each variable.
3.2.
Distribution of missing molar teeth
Table 2 shows the distribution of missing molar teeth. Sixty of the 143 patients (42%) had no missing teeth. Approximately half of the eighty-three patients with missing teeth had from 1 to 3 missing teeth. Fig. 2 shows the relationship between age and number of missing molar teeth.
3.3. Occlusal plane inclination (Camper-occlusal plane angle: COA) In all patients, COA ranged from 25.7 to 4.98 (Mean SD: 6.4 5.36). In the 60 patients who had no missing teeth, COA ranged from 11.6 to 4.98 (Mean SD: 3.3 3.31). Fig. 3 shows the distribution of COA in the 60 patients who had no missing teeth.
Please cite this article in press as: Shigeta Y, et al. Structural equation modeling for alteration of occlusal plane inclination. J Prosthodont Res (2015), http://dx.doi.org/10.1016/j.jpor.2015.05.001
JPOR-279; No. of Pages 9
4
journal of prosthodontic research xxx (2015) xxx–xxx
Table 1 – Descriptive statistics for each variable. Variables
Minimum
Maximum
Average
Standard deviation
24 0 0 0 12.4 11.9 0.0 15.0 101.0 25.7 5.2
84 15 12 16 35.3 47.6 26.5 35.9 141.0 4.9 32.3
52.3 2.6 2.0 6.9 20.66 31.68 13.85 20.21 123.58 6.37 18.28
15.5 3.3 2.9 5.4 3.97 7.52 5.95 2.68 7.79 5.36 5.4
Age Number of missing molar teeth Number of missing and restored teeth in anterior teeth Number of missing and restored teeth in molars Balkwill angle Mandibular plane angle Frankfort-occlusal plane angle (FOA) Frankfort-Camper plane angle (FCA) Gonial angle (GoA) Camper-occlusal plane angle (COA) Mandibular plane-occlusal plane angle (MOA)
This descriptive statistics table shows the minimum value, maximum value, average and standard deviation for each variable included in the analysis.
Table 2 – Distribution of missing molar teeth. Number of missing teeth Number of patients
0
1
2
3
4
5
6
7
8
9
102
60
16
15
8
10
6
7
5
3
7
6
The subjects were classified by their number of missing teeth.
3.4.
Factor analysis
In order to reduce the number of components, it was necessary to calculate the eigenvalue for each factor, as it represents the variance explained by that factor. The initial eigenvalues, the percent of variance explained and cumulative percent are presented in Table 3. All factors with eigenvalues greater than 1 have to be included in the analysis; Factor 1: 4.61, Factor 2: 2.51, Factor 3: 1.47, and at the border, Factor 4: 0.918. Thus, 3 factors were extracted. Factor 1 explains 41.904% of total variance, and all 3 factors together explain 78.063% of total variance. The number of factors for selection can also be explained by scree plot, presented in Fig. 4. The alteration of eigenvalue shows the steep slowing after the first 3 components. Therefore, we carried out the factor analysis through the Promax rotation of Principal Factor Method when the 3 factor structure was hypothesized. From this result, one of the variables, Frankfort-Camper plane angle (FCA), which had no adequate factor loadings, was removed. After that, we carried out the same analysis again. The level of transformation of all factors to obtain a solution is described by the factor transformation matrix. This matrix is presented in Table 4. Table 5 shows the rotated component matrix (rotated factor matrix in factor analysis) which is a matrix of the factor loadings for each variable onto each factor. Factor loadings less than 0.4 are not displayed because it is defined that these loadings suppress during the calculation. The variables are presented in the order of size of corresponding factor loadings, and, to simplify the presentation, only loadings greater than that values are presented. The first factor was constructed with 3 variables; these variables implied the Balkwill angle and Occlusal angle for cranial standard plane. Thus, this factor indicates the
‘‘Occlusal plane.’’ The second factor was constructed with 4 variables; these variables implied the status of teeth and aging. Thus, this factor indicates the ‘‘Aging and missing teeth’’. The third factor was constructed with 3 variables; these variables implied the occlusal plane angle for mandible, Gonial angle and mandibular plane angle. Thus, this factor indicates the ‘‘Mandibular Configuration’’. From the results of the interfactor correlation matrix, there was significant negative correlation between the first (Occlusal plane) and the second (Aging and missing teeth) factors. Therefore, factor structure analysis was carried out based on the following hypothesis; Occlusal plane inclination and mandibular configuration change with aging. These 3 factors were statistically applied to a structural equation model, and goodness of fit in our model was verified. In each factor, the variables which had high percentage of variance explained were selected, and the base of the odds ratio on the path coefficient in these variables was set on 1. Fig. 5 shows the structural equation model. The goodness of fit of our model was Goodness-of-fit index (GFI) = 0.822, Comparative fit index (CFI) = 0.863 and Root mean square error of approximation (RMSEA) = 0.223. Therefore, the validity of our model was proved. Table 6 shows estimated value on our model. There was significant positive relationship between ‘‘Age and missing teeth’’ and ‘‘Occlusal plane’’ (0.73). Table 6 shows the parameter estimates between our variables (the observed variables and the latent variables). There was a significant relationship in all combinations. In the Discussion, the interpretation of each relation in Table 6 is described.
4.
Discussion
4.1. Occlusal plane inclination (Camper-occlusal plane angle (COA)) There were several reports that investigate the correlation between the cranio-facial reference plane and the occlusal plane. Gysi, Dalby [8] and Wilson [9] measured the occlusal plane as the line connected to the external auditory canal inferior margin and the ala of nose inferior margin. They reported that this line was parallel with the occlusal plane. On the other hand, Clapp and Tench [10] defined the occlusal
Please cite this article in press as: Shigeta Y, et al. Structural equation modeling for alteration of occlusal plane inclination. J Prosthodont Res (2015), http://dx.doi.org/10.1016/j.jpor.2015.05.001
JPOR-279; No. of Pages 9 journal of prosthodontic research xxx (2015) xxx–xxx
5
Fig. 2 – Relationship between age and number of missing molar teeth.
Fig. 3 – Distribution of COA in the 60 patients who had no missing teeth.
Table 3 – Total variance explained – initial eigenvalues. Component
1 2 3 4 5 6 7 8 9 10
Initial eigenvalues Total
% of variance
Cumulative %
4.609 2.508 1.469 .918 .649 .355 .258 .127 .089 .018
41.904 22.802 13.358 8.344 5.896 3.226 2.345 1.159 .806 .162
41.904 64.705 78.063 86.407 92.303 95.529 97.874 99.033 99.838 100.000
Extraction method: Principal Component Analysis. This table is intuitively labeled and reports the variance explained by each component, as well as the cumulative variance explained by all components.
plane as the line connected to the external auditory canal superior margin and the ala of nose inferior margin. They reported that this line was parallel with the occlusal plane. In this study, we focused on the Camper-occlusal plane angle (COA). In 1986, Sugaya et al. [11] investigated the correlation between the dento-facial referential planes using the facebow and 3-dimensional measurement system. One hundred
patients who had no missing teeth were recruited. They described that the mean Camper-occlusal plane angle was 3.1 3.58. In our study, the mean Camper-occlusal plane angle in patients with no missing teeth was 3.3 3.318. Our result corresponded with this previous study, which used a different measurement method. Therefore, the validity of our measurement method was proved.
4.2.
Structural equation model
4.2.1.
Occlusal plane (Factor 1)
In the FOA and COA, there was a significant negative relationship. In the Balkwill angle, there was a significant positive relationship. As you know, the Balkwill angle is defined by the Bonwill triangle and the occlusal plane. Therefore, there was no inconsistency, anatomically in the relation between the Balkwill angle and the occlusal plane angles (when the standard planes were in the cranial bone). This finding strengthens evidence of validity in our methods of measurement and structural equation model. From the structural equation modeling, it was suggested that the occlusal plane inclination changes to counterclockwise on the right lateral cephalometric image, and Balkwill angle increases with alteration of other latent variables. This phenomenon in the occlusal plane
Please cite this article in press as: Shigeta Y, et al. Structural equation modeling for alteration of occlusal plane inclination. J Prosthodont Res (2015), http://dx.doi.org/10.1016/j.jpor.2015.05.001
JPOR-279; No. of Pages 9
6
journal of prosthodontic research xxx (2015) xxx–xxx
Fig. 4 – Scree plot with eigenvalues. The scree plot graphically displays the information in Table 3; the components’ eigenvalues.
4.2.2. Table 4 – Component transformation matrix. 1
2
3
1.000 .519 .097
.519 1.000 .069
.097 .069 1.000
Component 1 2 3
Extraction method: Principal Component Analysis. Rotation method: Promax rotation. This table displays the correlations among the components prior to and after rotation.
Table 5 – Summary of factor analysis. Rotated factor loadings Factor 1 Balkwill angle FOA COA Number of missing and restored teeth in anterior teeth Number of missing and restored teeth in molars Age Number of missing teeth in molars MOA Gonial angle Mandibular plane angle
Factor 2
Factor 3
.955 .921 .902 .903
4.2.3. .862 .769 .705 .544 .405
.882 .882 .840
Extraction method: Principal Component Analysis. Rotation method: Promax rotation. This table shows rotated component matrix, and displays the loadings for each variable on each rotated component, clearly showing which variables make up each component.
corresponded with Normand’s report which investigated the alteration of occlusal plane inclination with the loss of molar teeth [4]. This is more logically explained with the path coefficient in Section 4.2.4.
Age and missing teeth (Factor 2)
In all variables, there was a significant positive relationship. The increase of the tooth loss and prosthesis with aging, are supported by the epidemiological survey. From the structural equation modeling, it was suggested that aging, increase of tooth loss and prosthodontic treatment may influence the occlusal plane and the mandibular morphology. In 2013, Uma et al. [12] investigated the effect of loss of dentition on the dimensions of mandible using lateral cephalogram. They reported that the Gonial angle was more obtuse in edentulous subjects. Consequently, they concluded that the mandible undergoes significant dimensional changes as a result of loss of teeth. From the findings of our study and the previous study, it was suggested that the increase of tooth loss, with aging, may contribute to anatomical morphology, including the occlusal plane inclination. This is more logically explained with the path coefficient in Section 4.2.4.
Mandibular configuration (Factor 3)
In all variables, there was a significant positive relationship. It was suggested that Mandibular plane angle increases with the increasing of Gonial angle. And it was considered that the increase of Gonial angle and the rotation of occlusal plane contribute to an increase of MOA. In 1995, Ishibashi et al. [13] investigated the osteoarthrotic changes in the condyle in relation to aging and the loss of dental occlusal contacts. They reported that the articular surface of the mandibular condyle morphologically showed severe degenerative changes with aging. These changes in condyle tended to occur from the side of the mandible with minimal areas of occlusal contact. Mathew et al. [14] evaluated the prevalence of radiographic changes in the condylar morphology and its association with age, clinical signs and symptoms of temporomandibular dysfunction and dentition status. They reported that the radiographic abnormalities in the mandibular condylar morphology increased with age. These findings were frequently observed in patients with
Please cite this article in press as: Shigeta Y, et al. Structural equation modeling for alteration of occlusal plane inclination. J Prosthodont Res (2015), http://dx.doi.org/10.1016/j.jpor.2015.05.001
JPOR-279; No. of Pages 9
7
journal of prosthodontic research xxx (2015) xxx–xxx
Fig. 5 – Structural analysis model. The structural equations are meant to represent causal relationships among the variables/ factors in the model.
Table 6 – Parameter estimates using maximum likelihood with Amos 5.0. Direct paths
Age and missing teeth Age and missing teeth Balkwill angle FOA COA Number of missing and restored teeth in anterior teeth Number of missing and restored teeth in molars Age Missing molar teeth MOA Gonial angle Mandibular plane angle
Parameter estimates
Occlusal plane Mandibular configuration Occlusal plane Occlusal plane Occlusal plane Age and missing teeth Age and missing teeth Age and missing teeth Age and missing teeth Mandibular configuration Mandibular configuration Mandibular configuration
Unstandardized
SE
0.58 0.15 1.00 2.16 1.74 1.00 2.07 3.79 1.46 1.00 1.88 2.47
0.103 0.075
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/jpor
Original article
Structural equation modeling for alteration of occlusal plane inclination Yuko Shigeta DDS, PhD*, Takumi Ogawa DDS, PhD, Yoshiharu Nakamura DDS, PhD, Eriko Ando DDS, PhD, Rio Hirabayashi DDS, PhD, Tomoko Ikawa DDS, PhD Department of Fixed Prosthodontics, School of Dental Medicine, Tsurumi University, Yokohama, Japan
article info
abstract
Article history:
Purpose: Occlusal plane inclination is important to maintain a normal opening closing/
Received 13 December 2013
biting function. However, there can be several causes that lead to alterations of the occlusal
Received in revised form
plane. The purpose of this study was to observe variations of occlusal plane inclination in
24 April 2015
adult patients, and to uncover the factors affecting changes in occlusal plane inclination
Accepted 1 May 2015
with aging.
Available online xxx
Methods: Subjects were 143 patients. A cephalometric image was taken of these patients. In
Keywords:
cephalometric analysis. To evaluate the possible causes that affect occlusal plane inclina-
Occlusal plane
tion, factor analysis was carried out, and each component was treated as factors, which
Cephalometric image
were then statistically applied to a structural equation model. Statistical analysis was
this study, our inquiry points were age, 3 variables on intra-oral findings, and 7 variables on
Camper-occlusal plane angle
carried out through the SPSS 20.0 (SPSS Inc., Chicago, USA).
Aging
Results: In all patients, Camper-occlusal plane angle (COA) ranged from 25.7 to 4.98
Missing teeth
(Mean SD: 6.4 5.36). In the 60 patients who had no missing teeth, COA ranged from 11.6 to 4.98 (Mean SD: 3.3 3.31). From the results of the structural analysis, it was suggested that the occlusal plane changes to counter-clockwise (on the right lateral cephalograms) with aging. Conclusion: In this study, variations of occlusal plane inclination in adult patients were observed, and the factors affecting changes in occlusal plane inclination with aging were investigated via factor analysis. From our results, it was suggested that the mandibular morphology change and loss of teeth with aging influence occlusal plane inclination. # 2015 Published by Elsevier Ireland on behalf of Japan Prosthodontic Society.
1.
Introduction
In 1978, Okane et al. [1] investigated the influence of occlusal plane inclination for biting force and biting force exertion
efficiency. When the occlusal plane was made parallel to Camper’s plane, during maximum clenching, biting force was greatest and the biting force exertion efficiency showed the best value. They concluded that anteroposterior inclination of the occlusal plane tends to affect the biting force, and the
* Corresponding author at: Department of Fixed Prosthodontics, School of Dental Medicine, Tsurumi University, 2-1-3 Tsurumi, Tsurumi-ku, Yokohama, Japan. Tel.: +81 45 580 8417; fax: +81 45 573 9599. E-mail address: [email protected] (Y. Shigeta). http://dx.doi.org/10.1016/j.jpor.2015.05.001 1883-1958/# 2015 Published by Elsevier Ireland on behalf of Japan Prosthodontic Society.
Please cite this article in press as: Shigeta Y, et al. Structural equation modeling for alteration of occlusal plane inclination. J Prosthodont Res (2015), http://dx.doi.org/10.1016/j.jpor.2015.05.001
JPOR-279; No. of Pages 9
2
journal of prosthodontic research xxx (2015) xxx–xxx
method with the Camper’s plane as a standard on the cranium seems to be the most reasonable for occlusal plane orientation. In 2007, Sato et al. [2] reported the relationship between the masticatory movement path and dentofacial morphology using lateral cephalograms and a jaw movement-recording system. They investigated the relationship between the occlusal plane inclination and the direction of the masticatory movement path, and concluded that there is a close association between each one. As mentioned above, occlusal plane inclination is important to maintain a normal opening closing/biting function. However, there can be several causes that lead to alterations of the occlusal plane. In 2000, Vukusˇie´ et al. [3] examined the change in occlusal plane inclination that takes place during craniofacial growth relative to various facio-cranial reference lines. Cephalometric images which were taken in 192 patients (from 10 to 18 years old) were analyzed. Namely, the alteration of occlusal plane inclination was investigated during growth, from mixeddentition to permanent dentition. They described that the anterior rotation (left profile) and a significant decrease of occlusal plane inclination were observed during growth. In 2010, Normand and Cavacami [4] evaluated cephalometric changes in patients with bilateral loss of lower first permanent molar teeth. They concluded that the bilateral loss of lower first permanent molars leads to counterclockwise rotation of the occlusal plane. From the results of these previous studies, it was revealed that occlusal plane inclination alters with growth or loss of teeth. As previously mentioned above, the occlusal plane has a close relation to oral function, and can vary due to several factors. Furthermore, due to the 8020 campaign by the Japan Dental Association from 1989 [5], the percentage of persons in all age groups having over 20 teeth has increased [6,7]. Subsequently, various kinds of prostheses, including fixed partial dentures, can be applied to these dentitions, and the unison with oral function has to be considered. Therefore, dentists have to consider the various changes in occlusal factors during prosthodontic treatment for dentulous patients in adults. However, the influence of aging and change of dentition status to the occlusal plane has not been revealed up to this point. The purpose of this study was to observe variations of occlusal plane inclination in adult patients, and to uncover the factors affecting changes in occlusal plane inclination with aging.
2.
Materials and methods
2.1.
Subjects
Subjects were 143 patients; 69 females and 74 males. Subjects were consecutively recruited from 2008 to 2012. The age of subjects ranged from 24 to 74 years old (Mean SD: 52 15.5). These patients visited our department (Tsurumi University Dental Hospital) to receive prosthodontic treatments for crown/missing teeth or obstructive sleep apnea. A cephalometric image was taken of these patients to observe the
condition of occlusion or upper airway. In this study, an inclusion criterion was adults over 20 years old without influence of growth factors. Exclusion criteria were as follows: 1. Jaw deformity, 2. Serious osteoarthritis, 3. Serious reversed occlusion, 4. Serious open-bite, 5. Undergoing Orthodontic treatment, 6. Patients without prosthesis for missing teeth in molars (the elongation of teeth causes the local disturbance of the occlusal plane due to un-treatment for missing teeth).
2.2.
Inquiry points and cephalometric analysis
In this study, our variables included age, number of missing teeth, number of restored teeth, and mandibular configuration as possible causes that affect the occlusal plane. The orientation of occlusal plane to the cranium and the mandible were evaluated. The cephalometric images were analyzed via image analyzing software Amira 3.1 (Mercury Computer Systems/ 3D viz. group, San Diego, CA). On the cephalometric images, 6 angles including 10 reference points were measured using the same software. In this study, our inquiry points were the following 11 variables: a. Age b. Intra-oral findings b-1. Number of missing molar teeth b-2. Number of missing and restored teeth in anterior teeth: Total number of missing teeth, and restored teeth with full-coverage crown in anterior teeth. b-3. Number of missing and restored teeth in molars: Total number of missing teeth, and restored teeth with onlay or full-coverage crown in molars. c. Cephalometric analysis c-1. Balkwill angle: the angle formed by the line of connection to the center of the condyle and the central incisor tip (Cd0 -L1) and occlusal plane (L1-MPC) c-2. Mandibular plane angle: the angle formed by Frankfort plane (Or-Po) and Mandibular plane (Me-iGo) c-3. Frankfort-occlusal plane angle (FOA): the angle formed by Frankfort plane (Or-Po) and occlusal plane (L1-MPC) c-4. Frankfort-Camper plane angle (FCA): the angle formed by Frankfort plane (Or-Po) and Camper plane (Sn0 -Po) c-5. Gonial angle (GoA): the angle formed by Mandibular plane (Me-iGo) and Ramus plane (Ar-pGo) c-6. Camper-occlusal plane angle (COA): the angle formed by Camper plane (Sn0 -Po) and occlusal plane (L1-MPC) c-7. Mandibular plane-occlusal plane angle (MOA): the angle formed by Mandibular plane (Me-iGo) and occlusal plane (L1-MPC) The details of the measure points mentioned above are explained in Fig. 1.
2.3.
Statistical analysis
Statistical analysis was carried out through the SPSS 20.0 (SPSS Inc., Chicago, USA).
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Fig. 1 – Inquiry points on cephalometric image. Or: the most inferior point of the inferior margin of the orbit, Po: the most superior point of the ear-rod, Sn0 : the ala of nose inferior margin, Cd0 : the center of condyle, Ar: the posterior border of mandible rami, L1: the central incisor tip, Me: the most inferior point on the symphysis of the mandible, iGo: the point anterior to Go on the curvature of the angle of the mandible made by the tangent to the inferior border of the mandible, pGo: the point superior to Go on the curvature of the angle of the mandible made by the tangent to the posterior border of the mandible, MPC: the most posterior occlusal contact point on the second molar.
To evaluate the possible causes that affect occlusal plane inclination, factor analysis was carried out, and each component was treated as factors, which were then statistically applied to a structural equation model. The details of the above process in our statistical analysis were as follows:
(1) First, the mean and standard deviation in our 11 variables were calculated. The ceiling effect and the floor effect were then investigated. Appropriateness of the variables were thus proven from the results. (2) Next, factor analysis was carried out via the Principal Factor Method. This analysis was used to identify the underlying components that explain the correlations among a set of variables. A large number of variables were summarized with a smaller number of derived components, called factors (Determination by the appropriate number of component; 1, 2, 3, 4,. . .). Through the Promax rotation of the Principal Factor Method, the number of structure was hypothesized. The variable which has no adequate factor loading was removed. After that, we carried out the same analysis again. Each factor was entitled depending on the characteristics of the included variables. (3) Finally, the variables and factors, from the results of factor analysis, were statistically applied to a structural equation modeling, and goodness of fit in our model was verified.
This research was approved by the Ethics Committee at Tsurumi University (Approval number: 1030).
3.
Results
3.1.
Descriptive statistics in each variable
Table 1 shows the descriptive statistics in each variable.
3.2.
Distribution of missing molar teeth
Table 2 shows the distribution of missing molar teeth. Sixty of the 143 patients (42%) had no missing teeth. Approximately half of the eighty-three patients with missing teeth had from 1 to 3 missing teeth. Fig. 2 shows the relationship between age and number of missing molar teeth.
3.3. Occlusal plane inclination (Camper-occlusal plane angle: COA) In all patients, COA ranged from 25.7 to 4.98 (Mean SD: 6.4 5.36). In the 60 patients who had no missing teeth, COA ranged from 11.6 to 4.98 (Mean SD: 3.3 3.31). Fig. 3 shows the distribution of COA in the 60 patients who had no missing teeth.
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Table 1 – Descriptive statistics for each variable. Variables
Minimum
Maximum
Average
Standard deviation
24 0 0 0 12.4 11.9 0.0 15.0 101.0 25.7 5.2
84 15 12 16 35.3 47.6 26.5 35.9 141.0 4.9 32.3
52.3 2.6 2.0 6.9 20.66 31.68 13.85 20.21 123.58 6.37 18.28
15.5 3.3 2.9 5.4 3.97 7.52 5.95 2.68 7.79 5.36 5.4
Age Number of missing molar teeth Number of missing and restored teeth in anterior teeth Number of missing and restored teeth in molars Balkwill angle Mandibular plane angle Frankfort-occlusal plane angle (FOA) Frankfort-Camper plane angle (FCA) Gonial angle (GoA) Camper-occlusal plane angle (COA) Mandibular plane-occlusal plane angle (MOA)
This descriptive statistics table shows the minimum value, maximum value, average and standard deviation for each variable included in the analysis.
Table 2 – Distribution of missing molar teeth. Number of missing teeth Number of patients
0
1
2
3
4
5
6
7
8
9
102
60
16
15
8
10
6
7
5
3
7
6
The subjects were classified by their number of missing teeth.
3.4.
Factor analysis
In order to reduce the number of components, it was necessary to calculate the eigenvalue for each factor, as it represents the variance explained by that factor. The initial eigenvalues, the percent of variance explained and cumulative percent are presented in Table 3. All factors with eigenvalues greater than 1 have to be included in the analysis; Factor 1: 4.61, Factor 2: 2.51, Factor 3: 1.47, and at the border, Factor 4: 0.918. Thus, 3 factors were extracted. Factor 1 explains 41.904% of total variance, and all 3 factors together explain 78.063% of total variance. The number of factors for selection can also be explained by scree plot, presented in Fig. 4. The alteration of eigenvalue shows the steep slowing after the first 3 components. Therefore, we carried out the factor analysis through the Promax rotation of Principal Factor Method when the 3 factor structure was hypothesized. From this result, one of the variables, Frankfort-Camper plane angle (FCA), which had no adequate factor loadings, was removed. After that, we carried out the same analysis again. The level of transformation of all factors to obtain a solution is described by the factor transformation matrix. This matrix is presented in Table 4. Table 5 shows the rotated component matrix (rotated factor matrix in factor analysis) which is a matrix of the factor loadings for each variable onto each factor. Factor loadings less than 0.4 are not displayed because it is defined that these loadings suppress during the calculation. The variables are presented in the order of size of corresponding factor loadings, and, to simplify the presentation, only loadings greater than that values are presented. The first factor was constructed with 3 variables; these variables implied the Balkwill angle and Occlusal angle for cranial standard plane. Thus, this factor indicates the
‘‘Occlusal plane.’’ The second factor was constructed with 4 variables; these variables implied the status of teeth and aging. Thus, this factor indicates the ‘‘Aging and missing teeth’’. The third factor was constructed with 3 variables; these variables implied the occlusal plane angle for mandible, Gonial angle and mandibular plane angle. Thus, this factor indicates the ‘‘Mandibular Configuration’’. From the results of the interfactor correlation matrix, there was significant negative correlation between the first (Occlusal plane) and the second (Aging and missing teeth) factors. Therefore, factor structure analysis was carried out based on the following hypothesis; Occlusal plane inclination and mandibular configuration change with aging. These 3 factors were statistically applied to a structural equation model, and goodness of fit in our model was verified. In each factor, the variables which had high percentage of variance explained were selected, and the base of the odds ratio on the path coefficient in these variables was set on 1. Fig. 5 shows the structural equation model. The goodness of fit of our model was Goodness-of-fit index (GFI) = 0.822, Comparative fit index (CFI) = 0.863 and Root mean square error of approximation (RMSEA) = 0.223. Therefore, the validity of our model was proved. Table 6 shows estimated value on our model. There was significant positive relationship between ‘‘Age and missing teeth’’ and ‘‘Occlusal plane’’ (0.73). Table 6 shows the parameter estimates between our variables (the observed variables and the latent variables). There was a significant relationship in all combinations. In the Discussion, the interpretation of each relation in Table 6 is described.
4.
Discussion
4.1. Occlusal plane inclination (Camper-occlusal plane angle (COA)) There were several reports that investigate the correlation between the cranio-facial reference plane and the occlusal plane. Gysi, Dalby [8] and Wilson [9] measured the occlusal plane as the line connected to the external auditory canal inferior margin and the ala of nose inferior margin. They reported that this line was parallel with the occlusal plane. On the other hand, Clapp and Tench [10] defined the occlusal
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Fig. 2 – Relationship between age and number of missing molar teeth.
Fig. 3 – Distribution of COA in the 60 patients who had no missing teeth.
Table 3 – Total variance explained – initial eigenvalues. Component
1 2 3 4 5 6 7 8 9 10
Initial eigenvalues Total
% of variance
Cumulative %
4.609 2.508 1.469 .918 .649 .355 .258 .127 .089 .018
41.904 22.802 13.358 8.344 5.896 3.226 2.345 1.159 .806 .162
41.904 64.705 78.063 86.407 92.303 95.529 97.874 99.033 99.838 100.000
Extraction method: Principal Component Analysis. This table is intuitively labeled and reports the variance explained by each component, as well as the cumulative variance explained by all components.
plane as the line connected to the external auditory canal superior margin and the ala of nose inferior margin. They reported that this line was parallel with the occlusal plane. In this study, we focused on the Camper-occlusal plane angle (COA). In 1986, Sugaya et al. [11] investigated the correlation between the dento-facial referential planes using the facebow and 3-dimensional measurement system. One hundred
patients who had no missing teeth were recruited. They described that the mean Camper-occlusal plane angle was 3.1 3.58. In our study, the mean Camper-occlusal plane angle in patients with no missing teeth was 3.3 3.318. Our result corresponded with this previous study, which used a different measurement method. Therefore, the validity of our measurement method was proved.
4.2.
Structural equation model
4.2.1.
Occlusal plane (Factor 1)
In the FOA and COA, there was a significant negative relationship. In the Balkwill angle, there was a significant positive relationship. As you know, the Balkwill angle is defined by the Bonwill triangle and the occlusal plane. Therefore, there was no inconsistency, anatomically in the relation between the Balkwill angle and the occlusal plane angles (when the standard planes were in the cranial bone). This finding strengthens evidence of validity in our methods of measurement and structural equation model. From the structural equation modeling, it was suggested that the occlusal plane inclination changes to counterclockwise on the right lateral cephalometric image, and Balkwill angle increases with alteration of other latent variables. This phenomenon in the occlusal plane
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Fig. 4 – Scree plot with eigenvalues. The scree plot graphically displays the information in Table 3; the components’ eigenvalues.
4.2.2. Table 4 – Component transformation matrix. 1
2
3
1.000 .519 .097
.519 1.000 .069
.097 .069 1.000
Component 1 2 3
Extraction method: Principal Component Analysis. Rotation method: Promax rotation. This table displays the correlations among the components prior to and after rotation.
Table 5 – Summary of factor analysis. Rotated factor loadings Factor 1 Balkwill angle FOA COA Number of missing and restored teeth in anterior teeth Number of missing and restored teeth in molars Age Number of missing teeth in molars MOA Gonial angle Mandibular plane angle
Factor 2
Factor 3
.955 .921 .902 .903
4.2.3. .862 .769 .705 .544 .405
.882 .882 .840
Extraction method: Principal Component Analysis. Rotation method: Promax rotation. This table shows rotated component matrix, and displays the loadings for each variable on each rotated component, clearly showing which variables make up each component.
corresponded with Normand’s report which investigated the alteration of occlusal plane inclination with the loss of molar teeth [4]. This is more logically explained with the path coefficient in Section 4.2.4.
Age and missing teeth (Factor 2)
In all variables, there was a significant positive relationship. The increase of the tooth loss and prosthesis with aging, are supported by the epidemiological survey. From the structural equation modeling, it was suggested that aging, increase of tooth loss and prosthodontic treatment may influence the occlusal plane and the mandibular morphology. In 2013, Uma et al. [12] investigated the effect of loss of dentition on the dimensions of mandible using lateral cephalogram. They reported that the Gonial angle was more obtuse in edentulous subjects. Consequently, they concluded that the mandible undergoes significant dimensional changes as a result of loss of teeth. From the findings of our study and the previous study, it was suggested that the increase of tooth loss, with aging, may contribute to anatomical morphology, including the occlusal plane inclination. This is more logically explained with the path coefficient in Section 4.2.4.
Mandibular configuration (Factor 3)
In all variables, there was a significant positive relationship. It was suggested that Mandibular plane angle increases with the increasing of Gonial angle. And it was considered that the increase of Gonial angle and the rotation of occlusal plane contribute to an increase of MOA. In 1995, Ishibashi et al. [13] investigated the osteoarthrotic changes in the condyle in relation to aging and the loss of dental occlusal contacts. They reported that the articular surface of the mandibular condyle morphologically showed severe degenerative changes with aging. These changes in condyle tended to occur from the side of the mandible with minimal areas of occlusal contact. Mathew et al. [14] evaluated the prevalence of radiographic changes in the condylar morphology and its association with age, clinical signs and symptoms of temporomandibular dysfunction and dentition status. They reported that the radiographic abnormalities in the mandibular condylar morphology increased with age. These findings were frequently observed in patients with
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journal of prosthodontic research xxx (2015) xxx–xxx
Fig. 5 – Structural analysis model. The structural equations are meant to represent causal relationships among the variables/ factors in the model.
Table 6 – Parameter estimates using maximum likelihood with Amos 5.0. Direct paths
Age and missing teeth Age and missing teeth Balkwill angle FOA COA Number of missing and restored teeth in anterior teeth Number of missing and restored teeth in molars Age Missing molar teeth MOA Gonial angle Mandibular plane angle
Parameter estimates
Occlusal plane Mandibular configuration Occlusal plane Occlusal plane Occlusal plane Age and missing teeth Age and missing teeth Age and missing teeth Age and missing teeth Mandibular configuration Mandibular configuration Mandibular configuration
Unstandardized
SE
0.58 0.15 1.00 2.16 1.74 1.00 2.07 3.79 1.46 1.00 1.88 2.47
0.103 0.075
