A Mathematical Method to Calculate the Vertical Dimension for Fully
Edentulous Malaysians Patients
LAITH MAHMOUD ABDULHADI AL-SAMAWI, HANAA AL-ANI , HOMAM LAITH
Department of Prosthetic Dentistry,
Mahsa University,
Jalan SP 2, Bandar Saujana Putra, Selangor,
MALAYSIA
Abstract: - Recording of vertical dimension for patients who seek oral and occlusal rehabilitation is one of the
main steps of the treatment. Many methods were proposed for the profession yet none can be used solely to
determine the vertical dimension. Teaching and assessment of vertical dimensions for undergraduates should be
monitored by extra simple-use techniques. The aim of this study was to find a simple, reliable, fast method to
record and assess the vertical dimension by dental students and practitioners. Data were collected from 115
young volunteers from MAHSA University with natural healthy occlusion. Their age range was 18-25 years.
The distances from endocanthion to commissure of the mouth (IC-MC), nasion to gnathion at occlusion (NA-
GN occ), and at rest (NA-GN rest) were measured by 3 examiners. The records were correlated using the
Pearson correlation method at (ρ<.01, 2-tailed), and a linear regression model was calculated. In addition, the
ratios between the two measurements were calculated to find the Golden number. The results revealed the
presence of a significant linear relationship between the vertical dimension, measured from the nasion to
gnathion at occlusion and rest positions with IC-MC distance (r =0.90, and r =0.89 at ρ<.01 respectively). On
the other hand, regression analysis yielded two linear formulae that can be used to predict the vertical
dimension at occlusion and rest in edentulous patients. In conclusion, a new technique was presented to assess
the vertical dimension as a tailored method for Malaysian patients.
Key-Words: - Rest Vertical dimension, Vertical Dimension of Occlusion, New technique for vertical dimension
Recording
Received: April 21, 2022. Revised: January 14, 2023. Accepted: February 19, 2023. Published: April 3, 2023.
1 Introduction
The vertical dimension is the height of the lower
part of the face. Technically, it is the distance
between two selected anatomic or marked points,
one on a fixed and one on a movable member (one
on the tip of the nose and the other on the chin), [1].
For successful prosthodontic treatments and
rehabilitation, a precise determination of the vertical
dimension of occlusion (VDO) and vertical
dimension at rest (VDR) is considered one of the
most important steps, adding to that, its difficult
assessment during the construction of complete
denture, [2]. An increase or decrease in the vertical
dimension may cause problems in mastication,
speech, and temporomandibular joints as well as
rapid bone destruction of the jaws, [3].
Many methods based on craniofacial
measurements were suggested for the determination
of the VDO, such as direct measurements on the soft
tissues of the cranium and the face, [4], [5], [6], [7],
using old photographs, [4], radiographs
(Cephalometric methods) or photo-cephalometric
techniques, [8]. Although there are many methods to
determine the vertical dimension, the acceptability
of any method depends largely upon the skill,
experience, and judgment of the dentist. Therefore,
a need exists for a simple, reliable method to
determine accurately the vertical dimension to
facilitate dental restorations, [9]. The aim of this
study was to propose an easy method for recording
the vertical dimension of occlusion and at rest based
on simple mathematical analysis to help dental
students and dentists in their daily clinical practice.
2 Problem Formulation
The application of some equations cited in dental
literature on Malaysian samples was unsuccessful
due to a high discrepancy in recording VD.
Therefore, we conducted this research to find a
better model.
The hypothesis postulates that a high correlation
may exist between some facial measurements and
VD. This assumption is validated, then a linear
regression equation/s could be generated to predict
WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE
DOI: 10.37394/23208.2023.20.5
Laith Mahmoud Abdulhadi Al-Samawi,
Hanaa Al-Ani , Homam Laith
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the VD in a simple precise way during partial or
total oral and dental rehabilitation.
3 Material and Methods
The ethical committee of MAHSA University
College approved this research. The participants
were informed about the aim of the research and
they were asked to sign a written consent for
participation. Data were collected from 115 healthy
subjects, their age range varied between 18-25 years
(mean: 21.45±2.21). The inclusion criteria were the
presence of complete natural dentition, absence of
teeth attrition, and sign or symptoms of
temporomandibular joint dysfunction. Each subject
was asked to sit on a dental chair in an upright
position and under well-illuminated conditions
without headrest support. Three dentists examined
the subject’s health status and recorded the findings
on an examination record sheet that included
personal data in addition to the selected facial
measurements.
Before proceeding with recording, the assigned
facial references were marked by a black dot on a
small square paper Fig. 1 A, B.
Fig. 1 A, B: Making the facial references and
measuring the distances using a digital caliper
The vertical dimension of occlusion (VDO) was
recorded when the patient closed (bite) in maximum
intercuspation. While, the vertical dimension at rest
(VDR) was measured at the end of the swallowing
cycle, and the pronunciation of the (M) sound
without applying pressure to the soft tissues, [10].
Each record was repeated three times by each
examiner separately using two digits precision
calipers. The VDO and VDR were measured using
Nasion to Gnathion (NA-GN) distance as a
reference. In addition, the distance between the
inner canthus of the right eye to the mouth
commissure (IC- MC) was measured.
Data were analyzed using SPSS software version
17.0 (SPSS Inc., Chicago, IL, USA). Inter-examiner
reliability test for the readings of the three
examiners was performed to reveal their consistency
(ρ<.01, 2-tailed). Descriptive statistics tests were
used to disclose the features of the sample and the
normality of distribution. Parametric correlation and
linear regression analysis were used to reveal the
presence of statistical relation of VDO and VDR
with some facial measurements and to find the best
curve fit of the data. After formulae generation, the
accuracy percent of VDO prediction was calculated
at 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm
discrepancy.
4 Results
The inter-examiners' reliability in recording the
distances was highly significant for the records
gathered by the three investigators Table 1.
Table 1. Reliability results among 3 examiners
Correlation is significant at ρ<.01 level (2-tailed)
The features of the sample are shown in Table 2.
The data showed normal distribution.
Table 2. The features of the sample
IC; Endocanthion, MC; Mouth commissure, NA;
Nasion, GN; Gnathion, Rest; Physiologic rest
position, Occ; Occlusion
The relationships between the IC-MC and NA-
GN at occlusion and rest positions were linear and
significant (r = .90, r = .89, DF=115, ρ<.000,2-
tailed) respectively Table 3.
Variables
IC-MC
NA-GN occ
1st and 2nd
examiners
.985
.974
2nd and 3rd
examiners
.987
.984
1st and 3rd
examiners
.984
.978
No.
Min
Max
Mean
SD
Kurtosis
SE
Age
115
18
28
21.45
2.209
-.238
.447
IC-MC
115
55
79.7
65.85
4.603
.030
.447
NA-GN
Rest
115
95.3
127.3
112.1
6.973
-.609
.447
NA-GN
Occ
115
93
125.7
110.1
6.963
-.611
.474
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Table 3. The correlation between the IC-MC and
NA-GN during occlusion and at rest
The application of regression analysis for the
IC-MC and NA-GN during occlusion and rest
yielded 2 linear models that can be used to calculate
the VDR and VDO using the IC-MC distance as a
reference measurement on edentulous patients Table
4, Table 5.
Table 4. Regressions and Coefficients of
Correlations: IC-MC and NA-GNat rest
Cons; constant, Uns. Coef; unstandardized
coefficient, StdE; standard error, St.C; standard
coefficient, Sig; significance, Z-ord; zero order,Part;
partial
a- Dependent variable: NA-GN (rest) b-
Independent: IC-MC measurement, c- Constant =
23.79 d- Factor = 1.34
Table 5. Regressions and Coefficients of
Correlations: IC-MC and NA-GN at occlusion
Cons; constant, Unst. Coef; unstandardized
coefficient, StdE; standard error, St.C; standard
coefficient, Sig; significance, Z-ord; zero order,Part;
partial
a- Dependent variable: NA-GN (occlusion) b-
I n d e p e n d e n t : I C - M C m e a s u r e m e n t ,
c- Constant = 20.87 d- Factor = 1.36
To predict the VDR from IC-MC:
Y = 1.36 (X) + 20.87 (1)
Y is the NA-GN distance (at occlusion) and X is the
IC-MC distance in mm.
To calculate the VDR from IC-MC:
Y = 1.34 (X) + 23.79 (2)
Y is the NA-GN distance (at rest) and X is the IC-
MC distance in mm.
When the ratios between the mean records of NA-
GN and IC-MC at rest and occlusion were
calculated, two simple indices or Golden ratios
resulted.
Mean of (NA-GN rest) / Mean of (IC-MC) in mm=
1.68 (3)
Mean of (NA-GN occlusion) / Mean of (IC-MC) in
mm= 1.65 (4)
The mean difference between the measured actual
VDO (Nasion-Gnathion) and the predicted VDO
was ± . 25 mm. In addition, the mean difference
between the true VDR and the calculated VDR was
± .03mm. The results were not significant (DF: 114,
ρ= .913, and ρ= .277 respectively). The distribution
consistency of the predicted VDO records in
relation to the true records is shown in Table 6.
Table 6. The distribution of predicted results using
the newly generated formulae for VDO.
Reestablishing the correct vertical dimension in
edentulous patients is one of the important steps in
denture construction. Therefore, simplifying the
recording technique of VDO and VDR is a very
desirable achievement to reduce the time needed for
rehabilitation procedures as well as the undesirable
effects of incorrect VD measurements.
Teaching and practicing prosthetic rehabilitation
involves many clinical diagnostic and laboratory
procedures. For simplifying the pedagogic practice
and understanding the application of the clinical
steps in prosthodontics, the syllabus is usually
divided into consecutive steps preceded by lectures,
Facial records –VD
R-Coeff
Sig.2-t
N
IC-MC /NA-GN (occ)
.90**
.000
115
IC-MC /NA-GN (rest)
.89**
.000
115
Model
Unst. Coef
St.C
t
Sig.
Correlations
B
Std. E
Beta
Z-ord
Part
Part
Cons
23.794
4.383
5.429
.00
IC-
MC
1.340
.066
.885
20.189
.00
.885
.885
.885
Model
Unst.Coef
St.C
t
Sig.
Correlations
B
Std. E
Beta
Z-ord
Part
Part
Cons
20.869
4.179
4.994
.000
IC-
MC
1.355
.063
.896
21.397
.000
.896
.896
.896
Error range mm.
No. cases
Percent
0 – 1
31
27%
0 – 2
50
44.5%
0 – 3
70
61%
0- 4.5
106
92.2%
0 – 5
109
94.8%
> 5
6
5.2%
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briefings, and demonstrations on manikins or
patients to make students customize
with, understand and correctly apply the technique
in their daily clinical practice. However, because of
the VD’s inconsistent nature and the presence of
many opinions regarding the most suitable method
for recording, it is always considered a difficult step
to finish by the student or a new practitioner
confidently. Therefore, a new reliable, simple
recording and verification method dramatically
enhances the teaching and learning outcome as well
as the practice in oral rehabilitation and shortens
the clinical sessions.
Generally, there are many methods to determine
the vertical dimension of occlusion after the patient
is edentulous. All of these methods are not 100%
reliable. So, a combination of 2 or more methods is
advisable to achieve consistent results.
The anthropometric methods are still retaining a
privileged situation in recording especially
when experience is inadequate, and time is an
important task. The simplicity of applying this
technique increases its development by many
researchers, [4], [6], [14]. Some recording
techniques for VD were neglected or vanished but
still used for research purposes due to their
complexity and health safety such as radiographs
(Cephalometric methods) or Photo-cephalometric
methods, [8]. In this study, craniofacial biometric
references were selected and used in a pilot study to
calculate the vertical dimension at rest and
occlusion because facial measurements are quite
promising and unique simple devices are needed by
everyone, [11]. Therefore, by correlating some
vertical measurements, a simple and
applicable mathematics-based recording method
was revealed. This method was considered quite
promising since no complicated devices are needed
and unique to everyone, [11].
The proposed method showed 95% precision in
the recording. In addition, nearly 92% of the cases
were within an acceptable error range of
measurements on soft tissue (4%), [12] and 95%
were within the tolerable increase or decrease of VD
which is 3-5 mm. (Table. 6), [13]. Collecting and
analyzing clinical treatment over a prolonged time
provides an excellent in-depth solution for any
clinical problem as in this research, [15]. Therefore,
the next research work object proposes to focus on
the relation of the occlusal plane to facial
biometrical landmarks to find a simpler method of
recording the teeth levels and orientation.
5 Conclusion
Within the limits of this research, the following
results have been concluded:
A new reliable method to predict the vertical
dimension in edentulous patients was described. It
depends mainly on the presence of a high linear
correlation between the IC-MC and the NA-GN
measurements at occlusion and rest positions. Two
linear formulas were established.
NA-GN (at occlusion) = 20.87 + 1.36 x (IC-MC)
(1)
NA-GN (at rest) = 23.79 + 1.34 x (IC-MC) (2)
In addition, the Golden ratios between the means
of IC-MC and NA-GN records were calculated to
simplify the calculation of VD at rest and
occlusion. The golden ratios were evident
NA-GN (at rest) / IC-MC in mm = 1.68 (3)
NA-GN (at occlusion) / IC-MC in mm = 1.65 (4)
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
-Laith Al-Samawi, carried out the statistical
analysis, writing, and submission of the manuscript.
Moreover, Laith Al-Samawi was responsible for the
supervision of the procedures.
-Hana Al-Ani, was responsible for the supervision
of the experimental procedures, guidance, and
planning of the project.
-Humam Laith, was responsible for the patient
selection of the study, collection of data, and
submission to analysis.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflict of interest to declare
that is relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE
DOI: 10.37394/23208.2023.20.5
Laith Mahmoud Abdulhadi Al-Samawi,
Hanaa Al-Ani , Homam Laith
E-ISSN: 2224-2902
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Volume 20, 2023