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Morphological Study of the Intra-articular Space between the Head of the

Condyle and the Articular Eminence on 67 European Dry Skulls.

Master Thesis for obtaining the academic grade

Master of Science in Dental Sciences (MSc)

Submitted by

Dr Alain Méthot

Department of Interdisciplinary Dentistry and Technology

At the University of Continuing Education / Danube-University Krems

Advisor: Univ.-Prof. MR Dr Rudolf Slavicek

Krems, September 2011

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Introduction

The present study was done on 67 dried skulls from the Weissbach collection of

the Natural History Museum, Vienna. The objective of the present study was to

analyze the intra-articular space between the processus condylaris mandibulae

(condylar process) and the fossa mandibularis (articular fossa of the mandible) of

the temporal bone, and to correlate the intra-articular space with the supporting

teeth in occlusion.

A review of the literature on the intra-articular space showed some studies using

different technologies on living human subjects. Some studies are available in

French or English on the subject. In our revue of literature, no study has been

found on dry skulls.

In a study done by Hansson et al. (1977), they evaluated the thickness of the soft

tissue layers and articular disc of 48 right temporomandibular joints from Swedish

cadavers aged from 1 day to 93 years old without gross sign of arthrosis or

deviation in form. The specimens were examined histologically. The shrinkage of

these actual tissues seems to be less than 10% ( Hansson & Nordström). The

joint components were cut in 4 parts, lateral, latero-center, medio-center, and

medial. The total thickness of the soft tissue layers was measured in decalcified

sections. The middle and posterior parts of the articular disk were significally

thicker medio-centrally than laterally in the adults.

In a study done by Blaschke and Blaschke (1981) the condyle-temporal bone

spatial relationships were determined quantitatively in 50 asymptomatic TMJs (25

subjects) by making area measurements of the posterior and anterior portions of

the joint spaces on tomographic images. For both right and left sides, the

numerical expression of the joint relationship indicated that the condyle is

normally centered in the joint to a very high degree. Standard deviations around

the mean joint relationship values were large, however, which suggests that the

postero-anterior variation of condyle positions in asymptomatic TMJs is greater

than commonly thought. In addition, there was only mild correlation between

individual joint relationships on right and left sides.

A study by Christiansen et al. (1987) evaluated the condylar position and joint

space on 41 joints using computed tomography of the temporomandibular joint in

the axial plane with teeth in centric occlusion. Intra-articular joint spaces were

measured anterosuperiorly, superiorly, and posterosuperiorly (with the approach

of Pullinger and Hollender), and posteriorly by tracing a horizontal line from the

condylar surface to the anterior tympanic wall of the temporal bone. Those 4 joint

space measurements were done on 5 sagittal planes across the condyle.

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The superior, the posterosuperior, and the posterior joint spaces in the normal

joint were greater than the anterosuperior joint space. When the disk was

anterior to the condyle, the anterosuperior joint interval widened. When the disk

was medial, the superior joint space was significantly wider than normal.

Huddleston et al. (1999) studied the intra-articular distance within the TMJ during

Free and Loaded Closing Movements width on 10 subjects with two cathode ray

tubes. The opening and closing movement traces of the kinematic center were

reconstructed, and the average difference between the traces (the intra-articular

distance) was calculated. The average intra-articular distance was significantly

smaller during loaded closing than during free closing, whereas no significant

differences were found in the intra-articular distances between the loaded

situations of low and high manual loading and contralateral chewing. The

average intra-articular distance and its standard deviation were from 0.25mm to

0.45mm.

A study by Kinniburgh et al. (2000) determinates the relationships and osseous

morphology between temporomandibular joints in adolescents with normal and

anterior disc positions using MRI. Condylar position was calculated according to

the method of Pullinger and Hollender. There was a significant difference in joint

space and curvature of the eminence-loading surface between male and female

adolescents with normal disc position.

A study by Major et al. (2002) analyzed the association between osseous

temporomandibular joint (TMJ) characteristics and TMJ internal derangement

(disc position and deformation) with magnetic resonance imaging (MRI) in 335

TMJs in 175 subjects between the ages of 7.27 and 20.0 year. The authors

identified associations between disc displacement and reduced superior joint

space, increased posterior joint space, increased anterior joint space, and

reduced articular eminence convexity. This study demonstrates that TMJ internal

derangement is associated with functional osseous adaptation within the joint.

In a study done by Elias et al. (2006), they took measurements for lateral and

anterior capsule-condyle distances in the closed and open-mouth positions,

accomplished in longitudinal (coronal) and transverse (axial) ultrasonographic

scans and MRI on 19 patients from 18 to 45 years old (average age: 27.4 years;

16 females and 3 males) The average values for the lateral capsule-condyle

distance in the closed-mouth position were 1.4 mm in longitudinal scans and 1.6

mm in transverse scans. In the open-mouth position, for both longitudinal and

transverse scans, the average value was 1.2 mm. The average values for the

anterior capsule-condyle distance in the closed- and open-mouth positions were

respectively 2.3 mm and 1.1 mm.

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Hypothesis

Null hypothesis: The intra-articular space is not affected by the number of

posterior supporting teeth.

Definitions

Group of teeth: 3 groups of teeth have been created in relation with the number

of posterior occlusal contacts to support the occlusion:

4 teeth and less: means 4 posterior occlusal contacts or less.

5-7 teeth: means 5-7 posterior occlusal contacts

8 teeth and more: means 8 posterior occlusal contacts and more.

Virtual cut: Cuts made in the putties by the 3D software in 6 areas; 3 in protrusion

and 3 in mediotrusion at the lateral third, the center and the medial third.

Measurement: in each putty, 5 measurements were made at 10, 11, 12, 13, 14,

o‟clock for the right and left sides, 10 and 11 o‟clock being the posterior and

postero-superior intra-articular spaces and 13 and 14 o‟clock being the antero-

superior and anterior intra-articular spaces on both sides.

Intra-articular space: in our study, the term intra-articular space defines the space

between the processus condylaris and the fossa mandibularis. As our study was

done on dried skulls, this space includes also the space formerly occupied by the

articular disk and the cartilageous tissue covering the head of the condyle and

the eminentia on a living subject.

Putty: a mass of vinyl polysiloxane which was obtained by injection in the intra-

articular space.

This study has been done with 2 softwares; the first one named Catia and the

second one named Delcam.

Catia: This software treats 2D and 3D images in the same project.

Delcam : This software was used to make the cuts in the 3D putties. The X, Y

and Z axis measurements in both software (Catia & Delcam) do not correspond

to the X, Y and Z axis usually used in dentistry or orthopedics.

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2-D long axis of the putties: As the previous long axis as been drawn on a 2D

image, we had to locate it in the third dimension.

3-D long axis of the putties: For doing so, we drew a line at the base of the

putties (base line) and selected the highest point in the concavity made by the

imprint of the condyles in the putties (most concave part of the imprint done by

the condyle). Having done several tests to locate the long axis in the third

dimension, the most appropriate location of the long axis in the third dimension

was to select a point which would give us the best measurements possible, i.e. to

have the long axis located in 3-D, in the geometrical center of the condylar

process. The result of our preliminary analysis brought us to choose a point

located at 60% from the base line or, if you prefer, at 40% from the highest point

in the concavity made by the condyle imprint in the putties.

Methodology

The reference plane chosen is the Frankfurt horizontal plane

Our study intended to analyse the thickness of the intra-articular space in the

lateral, the middle and the medial thirds of the intra-articular space.

The sample of skulls having served in our study comes from the Natural

History Museum in Vienna (Figure 1).

Figure 1

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Thousands of skulls are stored in the anthropologic department. The skull

selection was done from the Weissbach collection (Figure 2). We had to find

skulls presenting dental arches articulating in a fairly good occlusion; it was

difficult to find very stable cases.

Figure 2

We had to select skulls with a solid and stable articulation. Once skulls

presenting a stable articulation were found we looked at the TMJ space to

see if there was enough space to inject an impression material in the intra

articular-space. The selected skulls were put on a table with the mandible in

occlusion (Figure 3).

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Figure 3

A team of 4 persons was needed to take the “impression” of the intra-articular

space and the occlusal bite registration;

The impression material allowed us to work on 10 skulls at the time. Both

regions were injected with vinyl polysiloxane hydrophilic impression material.

(IMPRINT from 3M Company)

Sequence followed for impression of the intra-articular spaces and the bite

registration:

Step 1:

• Each group of ten skulls was placed upside down on a table with the

mandible besides

• Mineral oil was placed on the head of the condyles and in the fossae

mandibularis

• 3 members of the team (named 1 to 3) were needed to hold the skulls and

the mandible in each of their hands

• The fourth member of the team injected the silicone in the fossae

mandibularis of the first skull

• Then the same person took the skull and the mandibule in his hands to

articulate the mandibule in a proper relationship with the maxilla via the

occluding teeth, and put a firm pressure on the occluding teeth only and

gave back the skull to the member 1 of the holding team. The person

number 1 was stabilizing the bite during the hardening of the material

• Then, the fourth member injected the silicone in the second skull with the

member 2 of the holding team.

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• This procedure was repeated for the following skulls. After the injection of

the material on the third skull, the impression material having hardened on

the first skull, the first skull was placed on a table (Figure 4) and a fourth

skull was taken by the member no 1 of the holding team and presented to

the fourth member of the team for injection of the impression material in

the intra-articular space (Figures 5 & 6). This procedure was repeated until

the impression material was injected in10 skulls.

Figure 4

Figure 5

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Figure 6

Step 2:

• When the material has hardened in the first group of 10 skulls, a bite

registration was taken leaving in place the impression material in the intra-

articular spaces previously injected (Figure 7).

• The bite registration material (IMPRINT 3M ) was placed on the occlusal

surfaces of the maxillary teeth.

• The fourth member of the team, after having injected the impression.

material applied the same amount of pressure on the teeth as he applied

for the impression of the intra-articular space.

• Then he gave back the skull to the member no 1 for stabilization during

the hardening of the impression material.

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Figure 7

Step 3:

We took out the intra-articular putty of each skull and we wrote on each

putty the skull number and the letter L for the left side and the letter R for

the right side (Figure 8 & 9). We left the occlusal registration bite in place

(Figure 10).

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Figure 8

Bite registration and the first set of putties in place.

Figure 9

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Figure 10

Step 4:

A second impression of the fossae mandibularis was taken by keeping the

bite registration in place on the teeth and using the same protocol as in step

1.

A picture of the occlusal bite registration and the first set of putties on both

right and left sides of each skull were taken on a trans-illuminating box to see

the occlusal contacts and the thickness of the putties (Figure 11).

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Figure 11: Pictures of the bite registration and of the first set of putties

Step 5:

Each skull was placed on a metallic stand and was hold in place by ear

rods which were inserted in the auditory meatus. A third rod helped to

stabilize the skull and was placed at the lower margin of the orbit Figure

12).

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Figure 12

The skull was then oriented perpendicularly to the floor to correspond to

the Frankfurt plane.

Photographs were then taken to see the putties in place in the fossae

mandibularis (Figure 13).

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Figure 13

Our study having to be done in Canada, the second set of putties were

sent to Canada.

Our first intention was to physically cut the putties and to measure the

slices obtained with an electronic micrometer (caliper).

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As our protocol was to analyze the thickness of the putties at the lateral,

central and medial part of the protrusive trajectory and of the mediotrusive

trajectory, we would have needed two separate sets of putties to use this

method.

As we had only one set of putties in Canada, it would not have been easily

feasible to do three cuts on the same putty on the protrusive trajectory and

then to do three cuts of this same putty on the mediotrusive trajectory

(Figure 14).

Figure 14

We analyzed the option of scanning the putties with a 3-D scanner and we

found the following advantages:

Due to the accuracy of the 3-D scanner, the results should be better than

trying to measure the thickness with a caliper, since the use of a caliper

could have easily compress the impression material

On 3-D software, it would be possible to draw lines (or vectors) more

easily than on the putties themselves, because it is possible to enlarge the

image on the software. So, the planes for the virtual cuts would be chosen

with greater accuracy

Last but not least, the putties could be kept intact and returned to Vienna

for further studies, if needed.

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So, for the above mentioned advantages, it was decided to scan

electronically the second set of the intra-articular putties and to use

2 software to produce the results.

It has to be understood that certain variance in the putty especially on the

surface of the fossae mandibularis will give certain variance in the

thickness of the putties in the present study (Figure 15).

Figure 15

A photograph of each skull with the second putty in place was taken with

the identification of the skull on the left side of the picture (Figure 16).

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Figure 16

The second set of putties shown on the picture was brought to Canada to

be scanned with a high precision scanner (Figure 17)

Called NextEngine 3D Scanner HD and the degree of precision is around

0.127 mm. See Appendix 1

Figure 17

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Step 6:

As our study was done in Canada and that the skulls stayed in Vienna, we

had to superpose the 3D image of the putties on a 2D photograph of the

skulls (which were taken by a member of the team when he was at the

Natural History Museum, in Vienna. The superposition of the 3D image

over the 2D image was achieved by a well trained operator used to use

the Catia software.

Each left and right 3D putties were scanned with NextEngine 3D Scanner

HD. After the 3D scanning, each putty was superposed on top of the

corresponding 2D picture of the fossa mandibularis of the temporal bone

of the dried skull. Great care has been taken to correlate the scanned

image of the 3D putties in the best orientation possible over the 2D

images. Our goal was to position the putties in the same spatial orientation

in the fossae mandibularis on the 2D picture as well as it would be on the

skull.

In the present example the putty on the right side of the dried skull 470

was selected to show how the measurements were done (Figure 18).

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Figure 18

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In our study we had to cope with the X, Y, Z, axis given by the Delcam

software, which orientation is given below:

X axis: vertical axis

Y axis: horizontal axis

Z axis: transversal axis

If we place the dried skull with the Frankfurt plane parallel to the floor we

will get a view like the underneath picture (Figure 19).

Figure 19

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Figure 20

Figure 21

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6 different sections were made along the 3D long axis of the imprint of the

mandibular condyle (the long axis going from the lateral pole to the medial

pole of each condyle.)

It has to be considered that the three axis (X, Y, Z) used in dentistry and

orthopedics are not the same three axis (X, Y, Z) in use in the Catia and

Delcam software Figure 20 & 21).

The center of the skull was determined by the intersection of the Y axis

line and the Z axis line passing at the posterior nasal spine of the palatine

bone (Figure 22).

Figure 22

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Figure 23

Once the 3-D scanned image was properly positioned on top of the 2-D

photograph of the fossae mandibularis, a line joining the lateral and the

medial poles of the putty was drawn (Figure 23 & 24). This line represents

the long axis of the imprint left in the putty by the condyle.

Then, to obtain a 3-D long axis of the condyle, we had to figure out how it

should be positioned three-dimensionally in the virtual putty. After many

trials, it was concluded that this 3-D long axis should be placed vertically

(X axis) at a distance of 40% from the most concave part of the putty

(Figure 25 & 26).

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Figure 24

Figure 25

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Figure 26

1- 3 virtual cuts following the protrusion trajectory of the condyle were

analyzed in 3 areas: the lateral, the center and the median part of

imprint of the condyle (Figure 27).

2- 3 virtual cuts were made at 90 degrees from the long axis of the 3-D

long axis of the condyle and the intersection point of X axis and the

protrusion trajectory to determine the mediotrusion trajectory (Figure

28).

For each of the 6 virtual cuts 5 measurement were taken at 10:00,

11:00, 12:00, 1:00 and 2:00 o‟clock. 12.00 o‟clock representing the X

(vertical) axis (perpendicular to the Frankfurt plane).

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Figure 27

Figure 28

The purpose of reproducing the 3D spatial position of the putties in the

dried skulls is to reproduce the real position of the putties to be able to

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compare with other studies and to better understand the intra articular

space in relation to supporting teeth in occlusion.

By using this methodology, the resulting analysis should be closer to

reality. The results should reflect the spaces in a real spatial position.

In some studies, cuts were made with no relation between the physical

putties (radiographs) and the skulls. In those studies the 12:00 cut was in

the middle of the head of the condyle.

In our study, the cuts were relatively well angulated through the putties.

The results gave a good lecture of the intra-articular spaces at those

areas.

Results

The mean values, standard deviations, minimum and maximums for the three

groups of supporting teeth on the left and right side are shown in the following six

tables:

Table 1 Results for Right Sides of skulls with 4 teeth or less.

4 teeth or less - Right Side - Mediotrusion - Center

Section N Mean St. Dev. Minimum Maximum

10h 37 2.829 0.918 0.574 4.973

11h 37 2.499 1.120 0.441 5.996

12h 37 2.853 1.133 0.466 4.809

13h 37 3.209 1.305 0.283 5.483

14h 37 2.838 1.345 0.000 6.284

4 teeth or less - Right Side - Mediotrusion - Lateral


10h 37 2.635 0.838 1.175 4.276

11h 37 3.129 1.157 0.777 5.316

12h 37 2.929 1.296 0.779 5.862

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13h 37 2.747 1.257 0.324 5.514

14h 37 2.658 1.348 0.531 6.543

4 teeth or less - Right Side - Mediotrusion - Median


10h 37 2.979 1.144 0.946 7.112

11h 37 2.356 0.953 0.809 4.516

12h 37 2.859 1.007 0.473 4.766

13h 37 3.335 1.283 0.000 5.697

14h 37 2.837 1.133 0.204 5.757

4 teeth or less - Right Side - Protrusion - Center


10h 37 2.877 0.899 0.574 4.528

11h 37 2.582 1.158 0.441 6.422

12h 37 2.853 1.133 0.466 4.804

13h 37 3.305 1.302 0.000 5.584

14h 37 2.750 1.149 0.000 5.082

4 teeth or less - Right Side - Protrusion - Lateral


10h 37 2.608 0.938 1.175 5.383

11h 37 3.063 1.105 0.574 5.386

12h 37 2.930 1.294 0.782 5.861

13h 37 2.961 1.271 0.519 5.856

14h 37 2.711 1.326 0.000 5.510

4 teeth or less - Right Side - Protrusion - Median


10h 37 2.812 1.038 0.946 6.226

11h 37 2.323 0.975 0.613 4.972

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12h 37 2.858 1.008 0.474 4.769

13h 37 3.292 1.224 0.000 5.618

14h 37 2.855 1.201 0.000 5.757

Table 2 Results for Left Sides of skulls with 4 teeth or less.

4 teeth or less - Left Side - Mediotrusion - Center


10h 37 2.669 0.948 1.035 4.380

11h 37 2.206 0.888 0.320 3.951

12h 37 2.870 1.280 0.457 5.312

13h 37 3.448 1.479 0.801 6.634

14h 37 2.913 1.348 0.183 6.640

4 teeth or less - Left Side - Mediotrusion - Lateral


10h 37 2.554 0.910 0.677 4.241

11h 37 2.882 1.132 0.931 5.096

12h 37 3.059 1.205 0.433 6.031

13h 37 2.999 1.350 0.655 6.807

14h 37 2.673 1.342 0.000 5.720

4 teeth or less - Left Side - Mediotrusion - Median


10h 37 3.337 1.503 1.065 7.263

11h 37 2.521 0.923 1.065 4.144

12h 37 3.167 1.322 0.973 6.227

13h 37 3.697 1.600 1.086 7.584

14h 37 3.056 1.332 0.486 6.721

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4 teeth or less - Left Side - Protrusion - Center


10h 37 2.727 0.992 1.215 4.554

11h 37 2.350 1.001 0.301 4.314

12h 37 2.870 1.279 0.457 5.311

13h 37 3.628 1.505 0.901 7.044

14h 37 3.047 1.419 0.308 6.927

4 teeth or less - Left Side - Protrusion - Lateral


10h 37 2.479 0.996 0.464 4.333

11h 37 2.714 1.125 0.632 5.341

12h 37 3.057 1.205 0.430 6.019

13h 37 3.320 1.408 0.747 7.105

14h 37 2.931 1.408 0.166 6.060

4 teeth or less - Left Side - Protrusion - Median


10h 37 3.002 1.311 1.006 6.573

11h 37 2.467 0.946 0.959 4.262

12h 37 3.168 1.322 0.973 6.226

13h 37 3.620 1.490 0.977 7.051

14h 37 3.085 1.404 0.534 6.671

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Table 3 Results for Right Sides of skulls with 5, 6 or 7 teeth.

5,6 or 7 teeth - Right Side - Mediotrusion - Center


10h 25 2.695 0.872 0.996 4.959

11h 25 2.460 0.863 0.804 4.770

12h 25 2.732 1.091 1.082 5.335

13h 25 2.622 1.557 0.000 5.733

14h 25 1.913 1.301 0.000 5.447

5,6 or 7 teeth - Right Side - Mediotrusion - Lateral


10h 25 2.784 0.997 0.601 4.289

11h 25 2.869 1.049 0.578 5.515

12h 25 2.587 1.092 0.988 4.900

13h 25 2.156 1.559 0.000 6.068

14h 25 2.060 1.333 0.000 5.953

5,6 or 7 teeth - Right Side - Mediotrusion - Median


10h 25 2.752 1.027 1.257 5.590

11h 25 2.188 0.752 0.276 3.891

12h 25 2.767 1.231 1.021 6.202

13h 25 2.898 1.630 0.212 5.698

14h 25 2.295 1.496 0.024 5.221

5,6 or 7 teeth - Right Side - Protrusion - Center


10h 25 2.945 1.035 0.839 5.118

11h 25 2.579 0.831 0.931 4.629

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12h 25 2.732 1.090 1.089 5.335

13h 25 2.737 1.496 0.539 5.733

14h 25 2.044 1.358 0.141 5.447

5,6 or 7 teeth - Right Side - Protrusion - Lateral


10h 25 2.848 0.976 0.507 4.627

11h 25 2.899 1.051 0.364 4.940

12h 25 2.587 1.091 0.990 4.899

13h 25 2.297 1.586 0.000 6.068

14h 25 1.977 1.424 0.000 5.953

5,6 or 7 teeth - Right Side - Protrusion - Median


10h 25 2.619 0.876 0.967 4.555

11h 25 2.220 0.768 0.080 3.864

12h 25 2.769 1.231 1.023 6.202

13h 25 2.766 1.598 0.000 5.698

14h 25 2.205 1.492 0.000 5.221

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Table 4 Results for Left Sides of skulls with 5, 6 or 7 teeth.

5,6 or 7 teeth - Left Side - Mediotrusion - Center


10h 25 2.319 0.868 0.000 4.212

11h 25 2.344 0.743 0.811 4.072

12h 25 2.687 0.841 1.137 4.832

13h 25 3.089 1.796 0.439 7.306

14h 25 2.324 1.324 0.420 5.642

5,6 or 7 teeth - Left Side - Mediotrusion - Lateral


10h 25 2.356 1.081 0.000 4.189

11h 25 2.526 0.973 0.611 4.254

12h 25 2.637 1.048 1.167 4.820

13h 25 2.443 1.468 0.509 6.043

14h 25 2.240 1.396 0.273 5.940

5,6 or 7 teeth - Left Side - Mediotrusion - Median


10h 25 2.453 0.899 0.688 5.370

11h 25 2.007 0.571 0.818 3.447

12h 25 2.745 0.985 0.881 5.731

13h 25 3.355 1.831 0.000 7.901

14h 25 2.647 1.564 0.233 6.419

5,6 or 7 teeth - Left Side - Protrusion - Center


10h 25 2.445 0.868 0.000 3.878

11h 25 2.479 0.859 0.904 4.906

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12h 25 2.687 0.842 1.139 4.832

13h 25 3.195 1.762 0.631 7.606

14h 25 2.420 1.377 0.531 6.091

5,6 or 7 teeth - Left Side - Protrusion - Lateral


10h 25 2.409 1.330 0.143 4.922

11h 25 2.471 0.976 0.522 4.178

12h 25 2.591 1.087 1.163 4.820

13h 25 2.641 1.588 0.572 7.146

14h 25 2.277 1.472 0.364 6.144

5,6 or 7 teeth - Left Side - Protrusion - Median


10h 25 2.536 0.941 1.199 5.229

11h 25 2.031 0.625 0.979 3.991

12h 25 2.745 0.985 0.883 5.734

13h 25 3.238 1.754 0.000 7.451

14h 25 2.654 1.563 0.000 6.265

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Table 5 Results for Right Sides of skulls with 8 teeth or more.

8 teeth or more - Right Side - Mediotrusion - Center


10h 5 2.856 0.790 1.610 3.646

11h 5 2.355 0.652 1.808 3.414

12h 5 2.567 0.973 1.800 4.120

13h 5 2.063 0.917 0.554 2.791

14h 5 1.373 0.544 0.569 1.868

8 teeth or more - Right Side - Mediotrusion - Lateral


10h 5 3.763 1.205 2.002 5.302

11h 5 3.462 1.016 2.072 4.761

12h 5 2.955 1.337 1.576 5.018

13h 5 1.634 0.723 0.445 2.260

14h 5 1.086 0.651 0.000 1.732

8 teeth or more - Right Side - Mediotrusion - Median


10h 5 2.956 0.709 1.837 3.512

11h 5 2.315 0.454 1.735 2.976

12h 5 2.515 0.884 1.728 3.974

13h 5 2.508 1.321 0.846 4.532

14h 5 1.811 0.525 1.163 2.345

8 teeth or more - Right Side - Protrusion - Center


10h 5 3.472 0.866 2.092 4.405

11h 5 2.589 0.923 1.906 4.094

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12h 5 2.567 0.972 1.800 4.119

13h 5 2.274 0.938 0.736 3.199

14h 5 1.469 0.510 0.755 2.016

8 teeth or more - Right Side - Protrusion - Lateral


10h 5 3.652 0.964 2.250 4.813

11h 5 3.581 1.019 2.075 4.797

12h 5 2.954 1.335 1.578 5.014

13h 5 1.782 0.756 0.511 2.427

14h 5 1.167 0.680 0.000 1.758

8 teeth or more - Right Side - Protrusion - Median


10h 5 2.793 0.620 2.158 3.631

11h 5 2.292 0.487 1.759 3.080

12h 5 2.514 0.885 1.728 3.974

13h 5 2.476 1.245 0.999 4.436

14h 5 1.885 0.530 1.265 2.483

38

Table 6 Results for Left Sides of skulls with 8 teeth or more.

8 teeth or more - Left Side - Mediotrusion - Center


10h 5 3.328 1.072 1.996 4.893

11h 5 3.446 1.007 2.435 5.142

12h 5 3.472 0.578 2.973 4.283

13h 5 2.703 0.648 1.752 3.344

14h 5 2.301 1.024 1.158 3.637

8 teeth or more - Left Side - Mediotrusion - Lateral


10h 5 3.079 0.660 2.528 4.171

11h 5 3.710 0.710 2.703 4.410

12h 5 2.947 1.520 1.411 5.302

13h 5 1.941 0.830 0.986 3.234

14h 5 1.953 0.666 1.403 3.090

8 teeth or more - Left Side - Mediotrusion - Median


10h 5 2.964 1.281 1.632 4.932

11h 5 2.523 0.359 2.132 2.969

12h 5 3.661 0.891 2.611 4.863

13h 5 3.764 0.813 2.545 4.693

14h 5 3.041 1.095 1.802 4.440

8 teeth or more - Left Side - Protrusion - Center


10h 5 3.693 0.855 2.755 5.073

11h 5 3.707 0.908 2.681 5.150

39

12h 5 3.473 0.577 2.973 4.282

13h 5 2.962 0.654 1.897 3.654

14h 5 2.460 1.027 1.280 3.788

8 teeth or more - Left Side - Protrusion - Lateral


10h 5 2.788 0.731 2.036 3.843

11h 5 3.736 1.243 2.472 5.403

12h 5 2.947 1.520 1.411 5.304

13h 5 2.142 0.784 1.181 3.314

14h 5 2.051 0.715 1.546 3.286

8 teeth or more - Left Side - Protrusion - Median


10h 5 2.907 1.317 1.252 4.830

11h 5 2.586 0.410 2.146 3.197

12h 5 3.663 0.892 2.612 4.867

13h 5 3.696 0.766 2.588 4.491

14h 5 3.099 0.968 2.104 4.289

40

The following figures are a graphic representation of the mean values for each

group of supporting teeth:

Figure 29 Illustration of distances (mm) for Right Side of skulls with 4 teeth or

less- Protrusion.

41


less- Mediotrusion.

42

Figure 31 Illustration of distances (mm) for Left Side of skulls with 4 teeth or

less- Protrusion.

43


less- Mediotrusion.

44

Figure 33 Illustration of distances (mm) for Right Side of skulls with 5, 6 or 7

teeth - Protrusion.

45

Figure 34 Illustration of distances (mm) for Right Side of skulls with 5, 6 or 7

teeth - Mediotrusion.

46

Figure 35 Illustration of distances (mm) for Left Side of skulls with 5, 6 or 7 teeth

- Protrusion.

47

Figure 36 Illustration of distances (mm) for Left Side of skulls with 5, 6 or 7 teeth

- Mediotrusion.

48


more - Protrusion.

49


more - Mediotrusion.

50


more - Protrusion.

51


more - Mediotrusion.

52

The mean values, standard deviations, minimum and maximum for the three

groups of supporting teeth for each side are shown in the following two tables:

Table 7 Results for Right Sides using all skulls.

Right Side - Mediotrusion - Lateral


10h 67 2.775 0.958 0.601 5.302

11h 67 3.057 1.106 0.578 5.515

12h 67 2.803 1.219 0.779 5.862

13h 67 2.443 1.382 0.000 6.068

14h 67 2.318 1.367 0.000 6.543

Right Side - Mediotrusion - Center


10h 67 2.781 0.882 0.574 4.973

11h 67 2.474 0.991 0.441 5.996

12h 67 2.786 1.095 0.466 5.335

13h 67 2.904 1.413 0.000 5.733

14h 67 2.383 1.377 0.000 6.284

Right Side - Mediotrusion - Median


10h 67 2.893 1.068 0.946 7.112

11h 67 2.290 0.848 0.276 4.516

12h 67 2.799 1.077 0.473 6.202

13h 67 3.110 1.429 0.000 5.698

14h 67 2.558 1.282 0.024 5.757

Right Side - Protrusion - Lateral


10h 67 2.776 0.979 0.507 5.383

53

11h 67 3.041 1.077 0.364 5.386

12h 67 2.804 1.218 0.782 5.861

13h 67 2.625 1.410 0.000 6.068

14h 67 2.322 1.398 0.000 5.953

Right Side - Protrusion - Center


10h 67 2.947 0.948 0.574 5.118

11h 67 2.581 1.017 0.441 6.422

12h 67 2.786 1.094 0.466 5.335

13h 67 3.016 1.382 0.000 5.733

14h 67 2.391 1.260 0.000 5.447

Right Side - Protrusion - Median


10h 67 2.739 0.948 0.946 6.226

11h 67 2.282 0.866 0.080 4.972

12h 67 2.799 1.078 0.474 6.202

13h 67 3.035 1.389 0.000 5.698

14h 67 2.540 1.320 0.000 5.757

54

Table 8 Results for Left Sides using all skulls.

Left Side - Mediotrusion - Lateral


10h 67 2.519 0.968 0.000 4.241

11h 67 2.811 1.081 0.611 5.096

12h 67 2.893 1.171 0.433 6.031

13h 67 2.713 1.392 0.509 6.807

14h 67 2.458 1.334 0.000 5.940

Left Side - Mediotrusion - Center


10h 67 2.588 0.952 0.000 4.893

11h 67 2.350 0.892 0.320 5.142

12h 67 2.847 1.100 0.457 5.312

13h 67 3.258 1.564 0.439 7.306

14h 67 2.647 1.334 0.183 6.640

Left Side - Mediotrusion - Median


10h 67 2.979 1.342 0.688 7.263

11h 67 2.329 0.809 0.818 4.144

12h 67 3.047 1.194 0.881 6.227

13h 67 3.575 1.639 0.000 7.901

14h 67 2.902 1.403 0.233 6.721

Left Side - Protrusion - Lateral


10h 67 2.476 1.107 0.143 4.922

11h 67 2.699 1.110 0.522 5.403

55

12h 67 2.875 1.188 0.430 6.019

13h 67 2.979 1.482 0.572 7.146

14h 67 2.621 1.423 0.166 6.144

Left Side - Protrusion - Center


10h 67 2.694 0.977 0.000 5.073

11h 67 2.499 0.994 0.301 5.150

12h 67 2.847 1.100 0.457 5.311

13h 67 3.417 1.565 0.631 7.606

14h 67 2.769 1.396 0.308 6.927

Left Side - Protrusion - Median


10h 67 2.821 1.189 1.006 6.573

11h 67 2.313 0.830 0.959 4.262

12h 67 3.047 1.194 0.883 6.226

13h 67 3.483 1.549 0.000 7.451

14h 67 2.925 1.437 0.000 6.671

56

The following figures illustrate the mean values for the three groups of supporting

teeth for each side:

Figure 41 Illustration of mean distances (mm) for Right Side - Protrusion.

57

Figure 42 Illustration of mean distances (mm) for Right Side - Mediotrusion.

58

Figure 43 Illustration of mean distances (mm) for Left Side - Protrusion.

59

Figure 44 Illustration of mean distances (mm) for Left Side - Mediotrusion.

60

The following table shows the mean values and the p-values between the

different groups of supporting teeth, for the lateral virtual cuts:

Table 9 Tests between number of teeth groups by Mediotrusion or protrusion

and Right or Left for Lateral results only.

Lateral

Mediotrusion Protrusion

Section = 10h Right Left Right Left

4 teeth or less 2.63 (b) 2.55 (a) 2.61 (a) 2.48 (a)

5, 6 or 7 teeth 2.78 (b) 2.36 (a) 2.85 (a) 2.41 (a)

8 teeth or more 3.76 (a) 3.08 (a) 3.65 (a) 2.79 (a)

p-value 0.0447 0.30 0.07 0.79



4 teeth or less 3.13 (a) 2.88 (a) 3.06 (a) 2.71 (a)

5, 6 or 7 teeth 2.87 (a) 2.53 (a) 2.90 (a) 2.47 (a)


p-value 0.47 0.07 0.43 0.06




5, 6 or 7 teeth 2.59 (a) 2.64 (a) 2.59 (a) 2.59 (a)


p-value 0.54 0.38 0.54 0.32

61




5, 6 or 7 teeth 2.16 (a) 2.44 (a) 2.30 (a) 2.64 (a)


p-value 0.10 0.13 0.07 0.09




5, 6 or 7 teeth 2.06 (ab) 2.24 (a) 1.98 (ab) 2.28 (a)

8 teeth or more 1.09 (b) 1.95 (a) 1.17 (b) 2.05 (a)

p-value 0.0242 0.31 0.0179 0.13

62


different groups of supporting teeth, for the central virtual cuts:

Table 10 Tests between number of teeth groups by Mediotrusion or protrusion

and Right or Left for Center results only.

Center



4 teeth or less 2.83 (a) 2.67 (a) 2.88 (a) 2.73 (b)

5, 6 or 7 teeth 2.69 (a) 2.32 (a) 2.95 (a) 2.45 (b)


p-value 0.83 0.07 0.43 0.0294



4 teeth or less 2.50 (a) 2.21 (b) 2.58 (a) 2.35 (b)

5, 6 or 7 teeth 2.46 (a) 2.34 (b) 2.58 (a) 2.48 (b)


p-value 0.95 0.0120 0.99 0.0141




5, 6 or 7 teeth 2.73 (a) 2.69 (a) 2.73 (a) 2.69 (b)


p-value 0.82 0.35 0.82 0.34

63




5, 6 or 7 teeth 2.62 (a) 3.09 (a) 2.74 (a) 3.19 (a)


p-value 0.11 0.49 0.13 0.46




5, 6 or 7 teeth 1.91 (ab) 2.32 (a) 2.04 (ab) 2.42 (a)


p-value 0.0064 0.20 0.0202 0.20

64


different groups of supporting teeth, for the medial virtual cuts:

Table 11 Tests between number of teeth groups by Mediotrusion or Protrusion

and Right or Left for Median results only.

Median



4 teeth or less 2,98 (a) 3,34 (a) 2,81 (a) 3,00 (a)

5, 6 or 7 teeth 2,75 (a) 2,45 (b) 2,62 (a) 2,54 (a)

8 teeth or more 2,96 (a) 2,96 (ab) 2,79 (a) 2,91 (a)

p-value 0.71 0.0368 0.73 0.32




5, 6 or 7 teeth 2,19 (a) 2,01 (b) 2,22 (a) 2,03 (a)

8 teeth or more 2,32 (a) 2,52 (a) 2,29 (a) 2,59 (a)

p-value 0.75 0.0397 0.90 0.09




5, 6 or 7 teeth 2,77 (a) 2,75 (a) 2,77 (a) 2,75 (a)


p-value 0.79 0.19 0.79 0.19

65




5, 6 or 7 teeth 2,90 (a) 3,36 (a) 2,77 (a) 3,24 (a)


p-value 0.31 0.70 0.22 0.61




5, 6 or 7 teeth 2,30 (a) 2,65 (a) 2,21 (a) 2,65 (a)


p-value 0.10 0.52 0.08 0.50

66

When we analyze the individual measurements of a single group of virtual cuts

(ex.: cuts on the protrusive vector, in the lateral third, for the right side), we found

very few results which present significative values between the groups of

supporting teeth. The only values that are significative are:

On the lateral cuts, there are significative differences on the

o 10 o‟clock cuts, mediotrusive vector, right side, between the group

< 4 teeth, the group 5-7 teeth and the group > 8 supporting teeth

(p-value: 0.0447), the mean value for the group > 8 supporting

contacts being larger than the two other groups

o 14 o‟clock cuts, protrusive vector, right side, between the group < 4

teeth and the group > 8 supporting teeth (p-value: 0.0179), the

mean value for the group < 4 supporting teeth being larger than the

group > 8 supporting teeth


< 4 teeth and the group > 8 supporting teeth (p-value: 0.0242), the



On the central cuts, there are significative differences on the

o 10 o‟clock cuts, protrusive vector, left side, between the group < 4

teeth, the group 5-7 teeth and the group > 8 supporting teeth (p-

value: 0.0294), the mean value for the group > 8 supporting


o 11 o‟clock cuts, protrusive vector, left side, between the group < 4

teeth, the group 5-7 teeth and the group > 8 supporting teeth (p-



o 11 o‟clock cuts, mediotrusive vector, left side, between the group <

4 teeth, the group 5-7 teeth and the group > 8 supporting teeth (p-



o 14 o‟clock cuts, protrusive vector, right side, between the group <

4 teeth and the group > 8 supporting teeth (p-value: 0.0202), the

67




< 4 teeth and the group > 8 supporting teeth (p-value: 0.0064), the



On the medial cuts, there are significative differences on the

o 11 o‟clock cuts, mediotrusive vector, left side,

Between the group < 4 supporting teeth and the group 5-7

teeth (p-value: 0.0397).

between the group 5-7 teeth and the group > 8 supporting

teeth (p-value: 0.0397).

o the mean value for the group < 4 supporting teeth being equal to

the group > 8 supporting teeth. Both groups present larger values

than the group 5-7 supporting teeth.

It is important to note that as the number of measurements is relatively low (67)

when we analyze an individual series of cuts (ex.: cuts on the protrusive vector,

in the lateral third, for the right side). So, it is more difficult to find statistical

significative differences because the power of the test is lowered. Thus, this was

rather normal to find less significative differences between individual cuts.

68

The following table shows the mean values and the p-values for the three virtual

cuts together (lateral, center and medial) on the protrusive vector and the

mediotrusive vectors:

Table 12 Tests between number of teeth groups by Mediotrusion or Protrusion

and Right or Left.



4 teeth or less 2.81 (a) 2.85 (ab) 2.77 (a) 2.74 (a)

5, 6 or 7 teeth 2.74 (a) 2.38 (b) 2.80 (a) 2.46 (a)


p-value 0.26 0.0046 0.12 0.0578




5, 6 or 7 teeth 2.51 (a) 2.29 (b) 2.57 (a) 2.33 (b)


p-value 0.56 0.0018 0.65 0.0012



4 teeth or less 2.88 (a) 3.03 (ab) 2.88 (a) 3.03 (ab)

5, 6 or 7 teeth 2.70 (a) 2.69 (b) 2.70 (a) 2.67 (b)


p-value 0.50 0.0441 0.50 0.0367

69




5, 6 or 7 teeth 2.56 (ab) 2.96 (a) 2.60 (ab) 3.02 (a)


p-value 0.0040 0.13 0.0021 0.0614




5, 6 or 7 teeth 2.09 (b) 2.40 (a) 2.08 (b) 2.45 (a)

8 teeth or more 1.42 (c) 2.43 (a) 1.51 (b) 2.54 (a)

p-value <0.0001 0.05 <0.0001 0.0204

When we group the lateral, central and medial virtual cuts and we analyze the

values for the protrusive and mediotrusive vectors for the right and left sides, we

found significative differences for the cuts, at:

10 o‟clock, mediotrusive vector, left side, between the group 5-7

supporting contacts and the group > 8 (p-value: 0.0046), the mean value

for the group > 8 supporting contacts being larger than the group 5-7

supporting teeth

11 o‟clock cuts,

o protrusive vector, left side, between the group < 4 teeth, the group

5-7 teeth and the group > 8 supporting teeth (p-value: 0.0012), the

70

mean value for the group > 8 supporting contacts being larger than

the two other groups

o mediotrusive vector, left side, between the group < 4 teeth, the

group 5-7 teeth and the group > 8 supporting teeth (p-value:

0.0018), the mean value for the group > 8 supporting contacts

being larger than the two other groups

12 o‟clock cuts,

o Protrusive vector, left side, between the group 5-7 supporting

contacts and the group > 8 (p-value: 0.0367), the mean value for

the group > 8 supporting contacts being larger than the group 5-7

supporting teeth

o Mediotrusive vector, left side, between the group 5-7 supporting


the group > 8 supporting contacts being larger than the group 5-7

supporting teeth

13 o‟clock cuts,

o Protrusive vector, right side, between the group 5-7 supporting


the group < 4 supporting contacts being larger than the group > 8

supporting teeth

o Mediotrusive vector, right side, between the group 5-7 supporting


the group < 4 supporting teeth being larger than the group > 8

supporting teeth

14 o‟clock cuts,

o Protrusive vector, right side, between the group < 4 teeth, the group

5-7 teeth and the group > 8 supporting teeth (p-value: < 0.0001),

the mean value for the group < 4 supporting teeth being larger than

the two other groups

o Mediotrusive vector, right side, between the group < 4 teeth, the

group 5-7 teeth and the group > 8 supporting teeth (p-value: <

0.0001), the mean value for the group < 4 supporting teeth being

larger than the group 5-7 supporting teeth which mean value is also

larger than the group > 8 supporting teeth

71

The following table shows the mean values and the p-values for:

for the lateral cuts (right and left, on the protrusive and mediotrusive

vectors)

for the center cuts (right and left, on the protrusive and mediotrusive

vectors)

for the medial cuts (right and left, on the protrusive and mediotrusive

vectors)

Table 13 Test results between number of teeth groups for Section at 10h.

Section = 10h Lateral**** Center***** Median******

4 teeth or less 2.57 (b) 2.78 (b) 3.03 (a)

5, 6 or 7 teeth 2.60 (b) 2.60 (b) 2.59 (b)

8 teeth or more 3.32 (a) 3.34 (a) 2.91 (a)

p-value 0.0064 0.0054 0.0107


4 teeth or less 2.95 (b) 2.41 (b) 2.42 (a)

5, 6 or 7 teeth 2.69 (b) 2.47 (b) 2.11 (b)

8 teeth or more 3.62 (a) 3.02 (a) 2.43 (a)

p-value 0.0017 0.0285 0.0141


4 teeth or less 2.99 (a) 2.86 (a) 3.01 (a)

5, 6 or 7 teeth 2.60 (b) 2.71 (a) 2.76 (a)

8 teeth or more 2.95 (a) 3.02 (a) 3.09 (a)

p-value 0.0354 0.39 0.18


4 teeth or less 3.01 (a) 3.40 (a) 3.49 (a)

5, 6 or 7 teeth 2.38 (b) 2.91 (ab) 3.06 (a)

72

8 teeth or more 1.87 (b) 2.50 (b) 3.11 (a)

p-value <0.0001 0.005 0.0832


4 teeth or less 2.74 (a) 2.89 (a) 2.96 (a)

5, 6 or 7 teeth 2.14 (b) 2.17 (b) 2.45 (b)

8 teeth or more 1.56 (c) 1.90 (b) 2.46 (b)

p-value <0.0001 <0.0001 0.0101

If we group both sides (right and left) plus the protrusive and mediotrusive

vectors and that we analyze the values on the lateral, center and medial vectors,

we find more significative differences:

For the lateral cuts:

o 10 o‟clock, between the group < 4 teeth, the group 5-7 teeth and

the group > 8 supporting teeth (p-value: 0.0064), the mean value

for the group > 8 supporting contacts being larger than the two

other groups




other groups

o 12 o‟clock, between the group 5-7 teeth and the group >8

supporting contacts (p-value: 0.0354), the mean value for the group

< 4 supporting teeth being almost equal to the group > 8 supporting

teeth. Both groups present larger values than the group 5-7

supporting teeth.

o 13 o‟clock, between the group < 4 contacts and the groups 5-7

contacts and > 8, (p-value: < 0.0001), the mean value for the group

< 4 supporting teeth being larger than the two other groups

o 14 o‟clock, between the 3 groups (p-value: < 0.0001), the mean

value for the group < 4 supporting teeth being larger than the group

5-7 teeth which mean value is also larger then the group > 8

supporting teeth

73

For the central cuts;




other groups




other groups

o 13 o‟clock, between the group < 4 teeth and the group > 8

supporting teeth (p-value: 0.005), the mean value for the group < 4

supporting teeth being larger than the group > 8 supporting teeth


the group > 8 supporting teeth (p-value: < 0.0001), the mean value

for the group < 4 supporting teeth being larger than the group > 8

supporting teeth

For the medial cuts:

o 10 o‟clock, between the groups < 4 supporting teeth, > 8 supporting

teeth and the group 5-7 supporting teeth (p-value: 0.0107), the

mean values of the groups < 4 supporting teeth and > 8 supporting

teeth being almost equal but larger than the group 5-7 teeth

o 11 o‟clock, between the groups < 4 supporting teeth, > 8 supporting

teeth and the group 5-7 supporting teeth (p-value: 0.0107), the

mean values of the groups < 4 supporting teeth and > 8 supporting

teeth being almost equal but larger than the group 5-7 teeth

o 14 o‟clock, the group < 4 supporting teeth and the group 5-7

supporting teeth, > 8 supporting teeth (p-value: 0.0101), the mean

value of the the group < 4 supporting teeth being larger than the

two other groups.

74

The following table shows the results, for all the skulls, of the lateral, central,

medial virtual cuts on the protrusive and mediotrusive vectors.

Table 14 Test results between number of teeth groups for Section at 10, 11, 12,

13, 14 o‟clock.

Section = 10h Right** Left***

4 teeth or less 2.79 (b) 2.79 (a)

5, 6 or 7 teeth 2.77 (b) 2.42 (b)

8 teeth or more 3.25 (a) 3.13 (a)

p-value 0.0382 0.0004


4 teeth or less 2.66 (a) 2.52 (b)

5, 6 or 7 teeth 2.54 (a) 2.31 (b)

8 teeth or more 2.77 (a) 3.28 (a)

p-value 0.39 <0.0001


4 teeth or less 2.88 (a) 3.03 (ab)

5, 6 or 7 teeth 2.70 (a) 2.68 (b)

8 teeth or more 2.68 (a) 3.36 (a)

p-value 0.25 0.0015


4 teeth or less 3.14 (a) 3.45 (a)

5, 6 or 7 teeth 2.58 (b) 2.99 (ab)

8 teeth or more 2.12 (b) 2.87 (b)

p-value <0.0001 0.0079


4 teeth or less 2.77 (a) 2.95 (a)

5, 6 or 7 teeth 2.08 (b) 2.43 (b)

75

8 teeth or more 1.47 (c) 2.48 (b)

p-value <0.0001 0.001

If we group all the cuts together (lateral, central, medial on the protrusive and

mediotrusive vectors) and that we analyse the data per side and by group of

teeth, we find the following significative values:

Right side:

10 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group

> 8 supporting teeth (p-value: 0.0382), the mean value for the group > 8

supporting teeth being larger than the two other groups


> 8 supporting teeth (p-value: < 0.0001), the mean value of the the group

< 4 supporting teeth being larger than the two other groups.


> 8 supporting teeth (p-value: < 0.0001), the mean value for the group < 4

supporting teeth being larger than the group 5-7 teeth which mean value

is also larger then the group > 8 supporting teeth

Left side:

10 o‟clock, between the group 5-7 teeth and the group > 8 supporting

teeth (p-value: 0.0004), the mean value for the group < 4 supporting teeth

being almost equal to the group > 8 supporting teeth. Both groups present

larger values than the group 5-7 supporting teeth.

11 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the

group > 8 supporting teeth (p-value: < 0.0001), the mean value for the

group > 8 supporting contacts being larger than the two other groups


teeth (p-value: 0.0015), the mean value for the group > 8 supporting teeth

being larger than the group 5-7 supporting teeth

13 o‟clock, between the group < 4 teeth and the group > 8 supporting

teeth (p-value: 0.0079), the mean value for the group < 4 supporting teeth

being larger than the group > 8 supporting teeth

76


> 8 supporting teeth (p-value: 0.001), the mean value of the the group < 4

supporting teeth being larger than the two other groups.

The following table shows the results, for all the skulls, both sides, of the lateral,

central, medial virtual cuts on the protrusive and mediotrusive vectors.

Table 15 Test results between number of teeth groups for Section at 10, 11, 12,

13, 14 o‟clock.

Section = 10h All*

4 teeth or less 2.79 (b)

5, 6 or 7 teeth 2.60 (b)

8 teeth or more 3.19 (a)

p-value 0.0001

Section = 11h All*

4 teeth or less 2.59 (b)

5, 6 or 7 teeth 2.42 (b)


p-value <0.0001

Section = 12h All*

4 teeth or less 2.96 (ab)

5, 6 or 7 teeth 2.69 (b)


p-value 0.0039

Section = 13h All*

4 teeth or less 3.30 (a)

5, 6 or 7 teeth 2.79 (b)

8 teeth or more 2.50 (b)

77

p-value <0.0001

Section = 14h All*

4 teeth or less 2.86 (a)

5, 6 or 7 teeth 2.25 (b)

8 teeth or more 1.97 (b)

p-value <0.0001

If we group all the right and left cuts together (lateral, central, medial on the

protrusive and mediotrusive vectors), and that we analyze the data by group of

supporting teeth, we find the following significative values:


> 8 supporting teeth (p-value: 0.0001), the mean value for the group > 8



> 8 supporting teeth (p-value: < 0.0001), the mean value for the group > 8



teeth (p-value: 0.0039), the mean value for the group > 8 supporting teeth

being larger than the group 5-7 supporting teeth


> 8 supporting teeth (p-value: < 0.0001), the mean value of the group < 4



> 8 supporting teeth (p-value: < 0.001), the mean value of the group < 4


78

Comparison with other studies

In a study from Kazumi Ikeda and Akira Kawamura show the following results

with Pullinger measurement protocol (Figure 45).

Figure 45

It is mentioned in that study that there are no quantitative standards for the

optimal position of the mandibular condyle in the glenoid fossa. Recently

developed limited cone-beam computed tomography (LCBCT) allows

measurement of this position with high accuracy. Methods: LCBCT was used to

assess 24 joints in 22 symptom-free subjects (10 male, 12 female; mean age, 18

years) who had no disc displacement as verified by magnetic resonance imaging.

Their joints had optimum function with the starting and end points of all functional

jaw movements coincident with maximum intercuspation.

Linear measurements of anterior space (AS), superior space (SS), and posterior

space (PS) were made to determine the position of the condyle for each joint.

Results: The mean AS, SS, and PS values were 1.3 mm (SD 6 0.2 mm), 2.5 mm

(SD 6 0.5 mm), and 2.1 mm (SD 6 0.3 mm), respectively (Figure 46). No

significant sex difference was noted in joint space distances. The results showed

less variability of condylar position in the fossa than previously reported in normal

subjects. Conclusions: These data from optimal joints might serve as norms for

the clinical assessment of condylar position obtained by LCBCT.

79

Figure 46

Ikeda Méthot (8 teeth and more)

10:00 = 2.10 mm 3.19 mm

12:00 = 2.50 mm 3.02mm

14:00 = 1.30 mm 1.97mm

We put the mean values of measurements of a few studies in a tabloid and the

results are quite similar. The results in red are the only ones that were made on

dried skulls.

Table 16

Studies 10 :00 12 :00 14 :00

Crhistiansen , Thompson 2.48 mm 2.26 mm 1.78 mm

Christiansen, Chan __ 2,25 mm 1.80 mm

Major 3.09 mm 2.65 mm 2.22 mm

80

Kinniburgh 3.62 mm 2.95 mm 1.92 mm

Ikeda 2.10 mm 2.50 mm 1.30 mm

Methot 3.19 mm 3.02 mm 1.97 mm

Discussion

We didn‟t found any study measuring the intra articular space on dried skulls.

We had many constraints doing this study;

First we didn‟t work directly on the skulls.

Second we scanned the imprint of the intra articular spaces; even if we worked

with high precision software and scanner the biggest error factor was in

positioning the 3D putties over the 2D pictures. In the repeatability test the

degree of repeatability gave certain credibility in the technique.

REPEATABILITY TEST

The repeatability test was performed by repeating three times on the same skulls

in order to evaluate the variability associated to the measure taking. The

statistical analyses associated to the repeatability test consist in presentation of

descriptive statistics allowing the evaluation of the measure taking variability.

The descriptive statistics presented are:

- Mean (in mm); In the repeatability study, this statistic is mainly used to calculate the coefficient of variation,

- Standard deviation (St. Dev.) (in mm); This statistic give a first estimate associated to the measure variability,

- Coefficient of variation (St. Dev. Divided by the Mean, does not have a unity of measure and is generally presented in %); This statistic is the most important to study the repeatability. Even though no statistical test associated to the coefficient of variation and no universally accepted value to indicate acceptable repeatability are available, in the present study, a coefficient of variation smaller than 5% or 10% will be considered as values to aim for.

81

- Minimum and maximum values (in mm); In addition to the direct information given by these statistics, they also allow an estimation of the variability by defining the range between the smallest and largest values of the three repetitions.

Tables 17 to 20 present the statistics for each measure. The statistics are

obtained for each skull, with three repetitions of the same measure. These tables

show that the vast majority of the measures present a coefficient of variation

smaller than 10% and almost all measures present a coefficient of variation

smaller than 20%. These results show that there is a non negligible variability

associated to the measure taking but this variability did not prevent the detection

of significant differences between the numbers of teeth groups. The measure

variability may however have reduced the number of significant differences

found, with a less variable measure, a larger number of significant differences

would probably have been found between the numbers of teeth groups.

Table 17 Descriptive statistics for the repeatability study for Mediotrusion on the

Right Side.

Right Side - Mediotrusion - Lateral - Skull #468

Section N Mean St. Dev. Coeff. of var. Minimum Maximum

10h 3 3.14 0.04 1.3% 3.10 3.18

11h 3 3.41 0.27 8.0% 3.24 3.72

12h 3 3.50 0.48 13.7% 3.15 4.05

13h 3 2.97 0.31 10.3% 2.68 3.29

14h 3 3.10 0.02 0.6% 3.08 3.12



10h 3 1.94 0.46 23.7% 1.66 2.47

11h 3 1.21 0.05 4.1% 1.16 1.25

12h 3 2.09 0.19 9.3% 1.87 2.22

13h 3 2.36 0.12 5.0% 2.27 2.49

14h 3 2.57 0.12 4.5% 2.44 2.64

Right Side - Mediotrusion - Center - Skull #468

82


10h 3 3.07 0.28 9.2% 2.74 3.28

11h 3 3.42 0.21 6.2% 3.23 3.65

12h 3 4.27 0.10 2.2% 4.19 4.37

13h 3 2.91 0.14 4.8% 2.81 3.07

14h 3 2.31 0.18 7.9% 2.10 2.43



10h 3 2.71 0.42 15.5% 2.39 3.19

11h 3 1.31 0.19 14.3% 1.20 1.53

12h 3 2.37 0.18 7.7% 2.21 2.57

13h 3 2.22 0.06 2.7% 2.15 2.26

14h 3 1.92 0.04 1.9% 1.89 1.96

Right Side - Mediotrusion - Median - Skull #468


10h 3 2.88 0.15 5.2% 2.77 3.06

11h 3 3.70 0.18 4.9% 3.52 3.88

12h 3 4.35 0.19 4.3% 4.14 4.47

13h 3 2.94 0.16 5.5% 2.83 3.13

14h 3 2.01 0.22 11.0% 1.85 2.26



10h 3 2.46 0.47 19.2% 2.06 2.98

11h 3 1.24 0.05 3.8% 1.20 1.29

12h 3 2.09 0.24 11.4% 1.93 2.36

13h 3 2.20 0.13 5.9% 2.11 2.35

14h 3 1.98 0.07 3.4% 1.91 2.05

83

Table 18 Descriptive statistics for the repeatability study for Protrusion on the

Right Side.

Right Side - Protrusion - Lateral - Skull #468


10h 3 3.26 0.07 2.1% 3.20 3.34

11h 3 3.61 0.30 8.4% 3.41 3.96

12h 3 3.50 0.48 13.7% 3.15 4.05

13h 3 2.96 0.23 7.8% 2.76 3.21

14h 3 3.32 0.03 0.9% 3.29 3.35



10h 3 2.40 0.51 21.3% 2.05 2.98

11h 3 1.30 0.08 6.2% 1.21 1.35

12h 3 2.09 0.20 9.4% 1.87 2.22

13h 3 1.95 0.14 7.1% 1.83 2.10

14h 3 2.35 0.10 4.0% 2.25 2.44

Right Side - Protrusion - Center - Skull #468


10h 3 2.96 0.14 4.6% 2.81 3.06

11h 3 3.54 0.24 6.7% 3.35 3.80

12h 3 4.26 0.09 2.2% 4.19 4.37

13h 3 2.88 0.17 5.9% 2.72 3.06

14h 3 2.71 0.22 8.1% 2.49 2.93



10h 3 2.92 0.51 17.6% 2.51 3.49

84

11h 3 1.31 0.14 10.8% 1.21 1.48

12h 3 2.37 0.18 7.7% 2.21 2.57

13h 3 2.20 0.04 1.6% 2.18 2.25

14h 3 2.19 0.07 3.0% 2.11 2.24

Right Side - Protrusion - Median - Skull #468


10h 3 2.98 0.20 6.7% 2.83 3.21

11h 3 3.74 0.16 4.3% 3.59 3.91

12h 3 4.36 0.19 4.4% 4.14 4.47

13h 3 3.07 0.25 8.0% 2.91 3.35

14h 3 1.92 0.13 6.7% 1.79 2.04



10h 3 2.03 0.31 15.5% 1.74 2.36

11h 3 1.19 0.03 2.3% 1.17 1.22

12h 3 2.08 0.24 11.4% 1.93 2.36

13h 3 2.50 0.16 6.2% 2.38 2.68

14h 3 1.90 0.04 1.9% 1.87 1.94

85

Table 19 Descriptive statistics for the repeatability study for Mediotrusion on the

Left Side.

Left Side - Mediotrusion - Lateral - Skull #468


10h 3 2.80 0.24 8.4% 2.53 2.96

11h 3 3.35 0.52 15.6% 2.83 3.88

12h 3 3.33 0.41 12.3% 2.89 3.70

13h 3 3.36 0.38 11.2% 3.00 3.75

14h 3 3.06 0.06 1.9% 3.00 3.12



10h 3 2.85 0.14 4.7% 2.73 3.00

11h 3 2.85 0.30 10.4% 2.57 3.16

12h 3 3.56 0.22 6.2% 3.38 3.80

13h 3 2.83 0.10 3.5% 2.73 2.93

14h 3 2.65 0.20 7.4% 2.48 2.86

Left Side - Mediotrusion - Center - Skull #468


10h 3 2.79 0.20 7.2% 2.60 3.00

11h 3 3.23 0.44 13.7% 2.75 3.62

12h 3 4.65 0.35 7.6% 4.45 5.06

13h 3 4.02 0.71 17.7% 3.47 4.83

14h 3 3.15 0.16 4.9% 3.02 3.32



10h 3 4.13 0.11 2.7% 4.00 4.22

11h 3 4.37 0.38 8.7% 3.97 4.72

86

12h 3 4.59 0.15 3.3% 4.43 4.73

13h 3 3.48 0.07 2.0% 3.42 3.55

14h 3 2.57 0.12 4.6% 2.45 2.69

Left Side - Mediotrusion - Median - Skull #468


10h 3 2.30 0.09 4.1% 2.19 2.35

11h 3 2.82 0.21 7.6% 2.63 3.05

12h 3 5.02 0.86 17.0% 4.04 5.55

13h 3 4.49 0.62 13.8% 4.02 5.19

14h 3 3.39 0.16 4.6% 3.21 3.49



10h 3 2.89 0.23 8.0% 2.69 3.14

11h 3 3.35 0.11 3.3% 3.24 3.46

12h 3 5.31 0.03 0.5% 5.30 5.34

13h 3 4.21 0.07 1.7% 4.17 4.30

14h 3 2.49 0.06 2.4% 2.44 2.55

87

Table 20 Descriptive statistics for the repeatability study for Protrusion on the

Left Side.

Left Side - Protrusion - Lateral - Skull #468


10h 3 2.87 0.22 7.7% 2.65 3.09

11h 3 3.01 0.58 19.1% 2.38 3.52

12h 3 3.33 0.41 12.3% 2.89 3.70

13h 3 3.65 0.43 11.8% 3.24 4.10

14h 3 3.26 0.08 2.5% 3.19 3.35



10h 3 2.32 0.07 3.2% 2.24 2.39

11h 3 2.42 0.23 9.4% 2.23 2.67

12h 3 3.55 0.22 6.1% 3.38 3.80

13h 3 3.43 0.10 3.0% 3.33 3.54

14h 3 2.83 0.11 3.9% 2.75 2.96

Left Side - Protrusion - Center - Skull #468


10h 3 3.12 0.10 3.3% 3.03 3.23

11h 3 3.41 0.47 13.8% 2.86 3.70

12h 3 4.65 0.35 7.6% 4.45 5.06

13h 3 4.10 0.70 17.1% 3.60 4.90

14h 3 3.21 0.14 4.3% 3.12 3.37



10h 3 3.89 0.31 7.9% 3.65 4.24

11h 3 4.15 0.12 3.0% 4.03 4.27

88

12h 3 4.59 0.15 3.3% 4.42 4.73

13h 3 4.14 0.04 0.9% 4.11 4.19

14h 3 2.42 0.00 0.2% 2.41 2.42

Left Side - Protrusion - Median - Skull #468


10h 3 2.28 0.11 4.7% 2.16 2.35

11h 3 2.88 0.28 9.6% 2.58 3.11

12h 3 5.02 0.86 17.0% 4.04 5.55

13h 3 4.65 0.58 12.5% 4.25 5.32

14h 3 3.49 0.23 6.5% 3.24 3.68



10h 3 3.18 0.36 11.3% 2.88 3.58

11h 3 3.63 0.07 1.8% 3.59 3.71

12h 3 5.31 0.03 0.5% 5.30 5.34

13h 3 4.41 0.12 2.8% 4.29 4.54

14h 3 2.64 0.02 0.8% 2.62 2.66

These tables show that the vast majority of the measures present a coefficient of

variation smaller than 10% and almost all measures present a coefficient of

variation smaller than 20%.

It have to be noted that in some studies like a study done by Hansson et al. on

Thickness of Soft Tissue Layer and Articular Disk in the Temporomandibular

Joint, the shrinkage of tissues on cadavers seems to be around 10%.

As it can be seen by the analysis of the data in the section “Results”, the more

we group the data, the more we find significative values.

Furthermore, the more we group the data, the p-values are greatly decreased.

To have significative values for individual groups of cuts (ex.: right side, lateral

cuts on the protrusive vector) we would have needed a larger number of skulls.

89

If we look at all the data, we can observe that there are significative differences

(p-values < 0.05) between the groups of supporting teeth, particularly between

the groups < 4 supporting teeth and the group > 8 supporting teeth.

Interestingly, the group > 8 supporting teeth presents more significative

differences on the cuts done at 10 o‟clock and 11 o‟clock and the mean values

are larger than the group < 4 supporting teeth. This suggests that the postero-

superior intra-articular space is larger for the group > 8 supporting teeth than for

the group < 4 supporting teeth. Also, the group of > 8 supporting teeth does not

show significative differences at 13 and 14 o‟clock and the mean values are

smaller than for the group < 4 supporting teeth which means that the antero-

superior intra-articular space is smaller for the group > 8 supporting teeth.

Also, the group < 4 supporting teeth presents more significative differences (p-

values < 0.05) on the cuts done at 13 o‟clock and 14 o‟clock, with mean values

larger than the group > 8 supporting teeth. This suggests that the antero-superior

intra-articular space is larger for the group < 4 supporting teeth than for the group

> 8 supporting teeth. Also, the group of < 4 supporting teeth does not show

significative differences at 10 and 11 o‟clock and the mean values are smaller

than for the group > 8 supporting teeth which means that the postero-superior

intra-articular space is smaller for the group < 4 supporting teeth.

To summarize, the intra-articular space seems to be larger postero-

superiorly and smaller antero-superiorly for the group > 8 supporting teeth.

Conversely, the intra-articular space seems to be smaller postero-

superiorly and larger antero-superiorly for the group < 4 supporting teeth.

It appears that the group > 8supporting teeth has the condyle positioned

more “anteriorly” in the so-called “glenoid fossae” than the group < 4

supporting teeth.

Conversely, the group < 4 supporting teeth has the condyle positioned

more postero-superiorly in the “glenoid fossae” than the group > 8

supporting teeth.

90

Figure 47 Right side; 4 teeth and less

Figure 48 Right side; 8 teeth and more

91

Figure 49 Left side; 4 teeth and less

Figure 50 Left side; 8 teeth and more

92

Conclusion

The null hypothesis is rejected.

The present study shows that there is a relationship between the number of

posterior teeth supporting the vertical dimension of occlusion and the intra-

articular space.

A further study including a larger number of skulls should be done to reinforce

this statement.

93

Appendix 1

Technical Specifications

94

Appendix 2

Report

Statistical analyses of thesis data.

Prepared for : Dr. Alain

Méthot

Claude Laberge

Experts-Conseils STATEX

August 3rd, 2011

95

TABLE OF CONTENTS

TABLE OF CONTENTS ................................................................................................................................... 95

INTRODUCTION .............................................................................................................................................. 96

DESCRIPTIVE RESULTS FOR ALL SKULLS ............................................................................................ 96

DESCRIPTIVE RESULTS BY NUMBER OF TEETH GROUPS .............................................................. 105

TESTS BETWEEN NUMBER OF TEETH GROUPS ................................................................................. 130

SUPPLEMENTARY TESTS BETWEEN NUMBER OF TEETH GROUPS ............................................ 133

REPEATABILITY TEST .................................................................................................................................. 80

96

INTRODUCTION

This report presents the statistical results for the data from Dr. Alain Méthot’s thesis.

DESCRIPTIVE RESULTS FOR ALL SKULLS

The statistical results presented for all skulls are:

1) A series of tables presenting Mean, standard deviation (St. Dev.), minimum and maximum in addition to the number of skulls used to calculate this statistics.;

2) Graphs of mean values to allow a more comprehensive visualisation of the results.

97

Table 1. Results for Right Sides using all skulls.

Right Side - Mediotrusion - Lateral


10h 67 2.775 0.958 0.601 5.302

11h 67 3.057 1.106 0.578 5.515

12h 67 2.803 1.219 0.779 5.862

13h 67 2.443 1.382 0.000 6.068

14h 67 2.318 1.367 0.000 6.543

Right Side - Mediotrusion - Center


10h 67 2.781 0.882 0.574 4.973

11h 67 2.474 0.991 0.441 5.996

12h 67 2.786 1.095 0.466 5.335

13h 67 2.904 1.413 0.000 5.733

14h 67 2.383 1.377 0.000 6.284

Right Side - Mediotrusion - Median


10h 67 2.893 1.068 0.946 7.112

11h 67 2.290 0.848 0.276 4.516

12h 67 2.799 1.077 0.473 6.202

13h 67 3.110 1.429 0.000 5.698

14h 67 2.558 1.282 0.024 5.757

Right Side - Protrusion - Lateral


10h 67 2.776 0.979 0.507 5.383

11h 67 3.041 1.077 0.364 5.386

98

12h 67 2.804 1.218 0.782 5.861

13h 67 2.625 1.410 0.000 6.068

14h 67 2.322 1.398 0.000 5.953

Right Side - Protrusion - Center


10h 67 2.947 0.948 0.574 5.118

11h 67 2.581 1.017 0.441 6.422

12h 67 2.786 1.094 0.466 5.335

13h 67 3.016 1.382 0.000 5.733

14h 67 2.391 1.260 0.000 5.447

Right Side - Protrusion - Median


10h 67 2.739 0.948 0.946 6.226

11h 67 2.282 0.866 0.080 4.972

12h 67 2.799 1.078 0.474 6.202

13h 67 3.035 1.389 0.000 5.698

14h 67 2.540 1.320 0.000 5.757

Table 2. Results for Left Sides using all skulls.

Left Side - Mediotrusion - Lateral


10h 67 2.519 0.968 0.000 4.241

11h 67 2.811 1.081 0.611 5.096

12h 67 2.893 1.171 0.433 6.031

13h 67 2.713 1.392 0.509 6.807

14h 67 2.458 1.334 0.000 5.940

Left Side - Mediotrusion - Center

99


10h 67 2.588 0.952 0.000 4.893

11h 67 2.350 0.892 0.320 5.142

12h 67 2.847 1.100 0.457 5.312

13h 67 3.258 1.564 0.439 7.306

14h 67 2.647 1.334 0.183 6.640

Left Side - Mediotrusion - Median


10h 67 2.979 1.342 0.688 7.263

11h 67 2.329 0.809 0.818 4.144

12h 67 3.047 1.194 0.881 6.227

13h 67 3.575 1.639 0.000 7.901

14h 67 2.902 1.403 0.233 6.721

Left Side - Protrusion - Lateral


10h 67 2.476 1.107 0.143 4.922

11h 67 2.699 1.110 0.522 5.403

12h 67 2.875 1.188 0.430 6.019

13h 67 2.979 1.482 0.572 7.146

14h 67 2.621 1.423 0.166 6.144

Left Side - Protrusion - Center


10h 67 2.694 0.977 0.000 5.073

11h 67 2.499 0.994 0.301 5.150

12h 67 2.847 1.100 0.457 5.311

13h 67 3.417 1.565 0.631 7.606

14h 67 2.769 1.396 0.308 6.927

100

Left Side - Protrusion - Median


10h 67 2.821 1.189 1.006 6.573

11h 67 2.313 0.830 0.959 4.262

12h 67 3.047 1.194 0.883 6.226

13h 67 3.483 1.549 0.000 7.451

14h 67 2.925 1.437 0.000 6.671

101

Figure 1. Illustration of mean distances (mm) for Right Side - Mediotrusion.

102

Figure 2. Illustration of mean distances (mm) for Right Side - Protrusion.

103

Figure 3. Illustration of mean distances (mm) for Left Side - Mediotrusion.

104

Figure 4. Illustration of mean distances (mm) for Left Side - Protrusion.

105

DESCRIPTIVE RESULTS BY NUMBER OF TEETH GROUPS

As for the preceding section for all skulls, the descriptive results by number of teeth groups are:

1) A series of tables presenting Mean, standard deviation (St. Dev.), minimum and maximum in addition to the number of skulls used to calculate this statistics.;

2) Graphs of mean values to allow a more comprehensive visualisation of the results.

Three number of teeth groups were defined as:

1) Skulls with 4 teeth or less; 2) Skulls with 5, 6 or 7 teeth; 3) Skulls with 8 teeth or more.

106

Table 3. Results for Left Sides of skulls with 4 teeth or less.

4 teeth or less - Left Side - Mediotrusion - Center


10h 37 2.669 0.948 1.035 4.380

11h 37 2.206 0.888 0.320 3.951

12h 37 2.870 1.280 0.457 5.312

13h 37 3.448 1.479 0.801 6.634

14h 37 2.913 1.348 0.183 6.640

4 teeth or less - Left Side - Mediotrusion - Lateral


10h 37 2.554 0.910 0.677 4.241

11h 37 2.882 1.132 0.931 5.096

12h 37 3.059 1.205 0.433 6.031

13h 37 2.999 1.350 0.655 6.807

14h 37 2.673 1.342 0.000 5.720

4 teeth or less - Left Side - Mediotrusion - Median


10h 37 3.337 1.503 1.065 7.263

11h 37 2.521 0.923 1.065 4.144

12h 37 3.167 1.322 0.973 6.227

13h 37 3.697 1.600 1.086 7.584

14h 37 3.056 1.332 0.486 6.721

4 teeth or less - Left Side - Protrusion - Center


10h 37 2.727 0.992 1.215 4.554

11h 37 2.350 1.001 0.301 4.314

107

12h 37 2.870 1.279 0.457 5.311

13h 37 3.628 1.505 0.901 7.044

14h 37 3.047 1.419 0.308 6.927

4 teeth or less - Left Side - Protrusion - Lateral


10h 37 2.479 0.996 0.464 4.333

11h 37 2.714 1.125 0.632 5.341

12h 37 3.057 1.205 0.430 6.019

13h 37 3.320 1.408 0.747 7.105

14h 37 2.931 1.408 0.166 6.060

4 teeth or less - Left Side - Protrusion - Median


10h 37 3.002 1.311 1.006 6.573

11h 37 2.467 0.946 0.959 4.262

12h 37 3.168 1.322 0.973 6.226

13h 37 3.620 1.490 0.977 7.051

14h 37 3.085 1.404 0.534 6.671

108

Table 4. Results for Right Sides of skulls with 4 teeth or less.

4 teeth or less - Right Side - Mediotrusion - Center


10h 37 2.829 0.918 0.574 4.973

11h 37 2.499 1.120 0.441 5.996

12h 37 2.853 1.133 0.466 4.809

13h 37 3.209 1.305 0.283 5.483

14h 37 2.838 1.345 0.000 6.284

4 teeth or less - Right Side - Mediotrusion - Lateral


10h 37 2.635 0.838 1.175 4.276

11h 37 3.129 1.157 0.777 5.316

12h 37 2.929 1.296 0.779 5.862

13h 37 2.747 1.257 0.324 5.514

14h 37 2.658 1.348 0.531 6.543

4 teeth or less - Right Side - Mediotrusion - Median


10h 37 2.979 1.144 0.946 7.112

11h 37 2.356 0.953 0.809 4.516

12h 37 2.859 1.007 0.473 4.766

13h 37 3.335 1.283 0.000 5.697

14h 37 2.837 1.133 0.204 5.757

4 teeth or less - Right Side - Protrusion - Center


10h 37 2.877 0.899 0.574 4.528

11h 37 2.582 1.158 0.441 6.422

109

12h 37 2.853 1.133 0.466 4.804

13h 37 3.305 1.302 0.000 5.584

14h 37 2.750 1.149 0.000 5.082

4 teeth or less - Right Side - Protrusion - Lateral


10h 37 2.608 0.938 1.175 5.383

11h 37 3.063 1.105 0.574 5.386

12h 37 2.930 1.294 0.782 5.861

13h 37 2.961 1.271 0.519 5.856

14h 37 2.711 1.326 0.000 5.510

4 teeth or less - Right Side - Protrusion - Median


10h 37 2.812 1.038 0.946 6.226

11h 37 2.323 0.975 0.613 4.972

12h 37 2.858 1.008 0.474 4.769

13h 37 3.292 1.224 0.000 5.618

14h 37 2.855 1.201 0.000 5.757

110

Table 5. Results for Left Sides of skulls with 5, 6 or 7 teeth.

5,6 or 7 teeth - Left Side - Mediotrusion - Center


10h 25 2.319 0.868 0.000 4.212

11h 25 2.344 0.743 0.811 4.072

12h 25 2.687 0.841 1.137 4.832

13h 25 3.089 1.796 0.439 7.306

14h 25 2.324 1.324 0.420 5.642

5,6 or 7 teeth - Left Side - Mediotrusion - Lateral


10h 25 2.356 1.081 0.000 4.189

11h 25 2.526 0.973 0.611 4.254

12h 25 2.637 1.048 1.167 4.820

13h 25 2.443 1.468 0.509 6.043

14h 25 2.240 1.396 0.273 5.940

5,6 or 7 teeth - Left Side - Mediotrusion - Median


10h 25 2.453 0.899 0.688 5.370

11h 25 2.007 0.571 0.818 3.447

12h 25 2.745 0.985 0.881 5.731

13h 25 3.355 1.831 0.000 7.901

14h 25 2.647 1.564 0.233 6.419

5,6 or 7 teeth - Left Side - Protrusion - Center


10h 25 2.445 0.868 0.000 3.878

11h 25 2.479 0.859 0.904 4.906

111

12h 25 2.687 0.842 1.139 4.832

13h 25 3.195 1.762 0.631 7.606

14h 25 2.420 1.377 0.531 6.091

5,6 or 7 teeth - Left Side - Protrusion - Lateral


10h 25 2.409 1.330 0.143 4.922

11h 25 2.471 0.976 0.522 4.178

12h 25 2.591 1.087 1.163 4.820

13h 25 2.641 1.588 0.572 7.146

14h 25 2.277 1.472 0.364 6.144

5,6 or 7 teeth - Left Side - Protrusion - Median


10h 25 2.536 0.941 1.199 5.229

11h 25 2.031 0.625 0.979 3.991

12h 25 2.745 0.985 0.883 5.734

13h 25 3.238 1.754 0.000 7.451

14h 25 2.654 1.563 0.000 6.265

112

Table 6. Results for Right Sides of skulls with 5, 6 or 7 teeth.

5,6 or 7 teeth - Right Side - Mediotrusion - Center


10h 25 2.695 0.872 0.996 4.959

11h 25 2.460 0.863 0.804 4.770

12h 25 2.732 1.091 1.082 5.335

13h 25 2.622 1.557 0.000 5.733

14h 25 1.913 1.301 0.000 5.447

5,6 or 7 teeth - Right Side - Mediotrusion - Lateral


10h 25 2.784 0.997 0.601 4.289

11h 25 2.869 1.049 0.578 5.515

12h 25 2.587 1.092 0.988 4.900

13h 25 2.156 1.559 0.000 6.068

14h 25 2.060 1.333 0.000 5.953

5,6 or 7 teeth - Right Side - Mediotrusion - Median


10h 25 2.752 1.027 1.257 5.590

11h 25 2.188 0.752 0.276 3.891

12h 25 2.767 1.231 1.021 6.202

13h 25 2.898 1.630 0.212 5.698

14h 25 2.295 1.496 0.024 5.221

5,6 or 7 teeth - Right Side - Protrusion - Center


10h 25 2.945 1.035 0.839 5.118

11h 25 2.579 0.831 0.931 4.629

113

12h 25 2.732 1.090 1.089 5.335

13h 25 2.737 1.496 0.539 5.733

14h 25 2.044 1.358 0.141 5.447

5,6 or 7 teeth - Right Side - Protrusion - Lateral


10h 25 2.848 0.976 0.507 4.627

11h 25 2.899 1.051 0.364 4.940

12h 25 2.587 1.091 0.990 4.899

13h 25 2.297 1.586 0.000 6.068

14h 25 1.977 1.424 0.000 5.953

5,6 or 7 teeth - Right Side - Protrusion - Median


10h 25 2.619 0.876 0.967 4.555

11h 25 2.220 0.768 0.080 3.864

12h 25 2.769 1.231 1.023 6.202

13h 25 2.766 1.598 0.000 5.698

14h 25 2.205 1.492 0.000 5.221

Table 7. Results for Left Sides of skulls with 8 teeth or more.

8 teeth or more - Left Side - Mediotrusion - Center


10h 5 3.328 1.072 1.996 4.893

11h 5 3.446 1.007 2.435 5.142

12h 5 3.472 0.578 2.973 4.283

13h 5 2.703 0.648 1.752 3.344

14h 5 2.301 1.024 1.158 3.637

8 teeth or more - Left Side - Mediotrusion - Lateral

114


10h 5 3.079 0.660 2.528 4.171

11h 5 3.710 0.710 2.703 4.410

12h 5 2.947 1.520 1.411 5.302

13h 5 1.941 0.830 0.986 3.234

14h 5 1.953 0.666 1.403 3.090

8 teeth or more - Left Side - Mediotrusion - Median


10h 5 2.964 1.281 1.632 4.932

11h 5 2.523 0.359 2.132 2.969

12h 5 3.661 0.891 2.611 4.863

13h 5 3.764 0.813 2.545 4.693

14h 5 3.041 1.095 1.802 4.440

8 teeth or more - Left Side - Protrusion - Center


10h 5 3.693 0.855 2.755 5.073

11h 5 3.707 0.908 2.681 5.150

12h 5 3.473 0.577 2.973 4.282

13h 5 2.962 0.654 1.897 3.654

14h 5 2.460 1.027 1.280 3.788

8 teeth or more - Left Side - Protrusion - Lateral


10h 5 2.788 0.731 2.036 3.843

11h 5 3.736 1.243 2.472 5.403

12h 5 2.947 1.520 1.411 5.304

13h 5 2.142 0.784 1.181 3.314

14h 5 2.051 0.715 1.546 3.286

115

8 teeth or more - Left Side - Protrusion - Median


10h 5 2.907 1.317 1.252 4.830

11h 5 2.586 0.410 2.146 3.197

12h 5 3.663 0.892 2.612 4.867

13h 5 3.696 0.766 2.588 4.491

14h 5 3.099 0.968 2.104 4.289

116

Table 8. Results for Right Sides of skulls with 8 teeth or more.

8 teeth or more - Right Side - Mediotrusion - Center


10h 5 2.856 0.790 1.610 3.646

11h 5 2.355 0.652 1.808 3.414

12h 5 2.567 0.973 1.800 4.120

13h 5 2.063 0.917 0.554 2.791

14h 5 1.373 0.544 0.569 1.868

8 teeth or more - Right Side - Mediotrusion - Lateral


10h 5 3.763 1.205 2.002 5.302

11h 5 3.462 1.016 2.072 4.761

12h 5 2.955 1.337 1.576 5.018

13h 5 1.634 0.723 0.445 2.260

14h 5 1.086 0.651 0.000 1.732

8 teeth or more - Right Side - Mediotrusion - Median


10h 5 2.956 0.709 1.837 3.512

11h 5 2.315 0.454 1.735 2.976

12h 5 2.515 0.884 1.728 3.974

13h 5 2.508 1.321 0.846 4.532

14h 5 1.811 0.525 1.163 2.345

8 teeth or more - Right Side - Protrusion - Center


10h 5 3.472 0.866 2.092 4.405

11h 5 2.589 0.923 1.906 4.094

117

12h 5 2.567 0.972 1.800 4.119

13h 5 2.274 0.938 0.736 3.199

14h 5 1.469 0.510 0.755 2.016

8 teeth or more - Right Side - Protrusion - Lateral


10h 5 3.652 0.964 2.250 4.813

11h 5 3.581 1.019 2.075 4.797

12h 5 2.954 1.335 1.578 5.014

13h 5 1.782 0.756 0.511 2.427

14h 5 1.167 0.680 0.000 1.758

8 teeth or more - Right Side - Protrusion - Median


10h 5 2.793 0.620 2.158 3.631

11h 5 2.292 0.487 1.759 3.080

12h 5 2.514 0.885 1.728 3.974

13h 5 2.476 1.245 0.999 4.436

14h 5 1.885 0.530 1.265 2.483

118

Figure 5. Illustration of distances (mm) for Right Side of skulls with 4 teeth or less-

Mediotrusion.

119

Figure 6. Illustration of distances (mm) for Right Side of skulls with 4 teeth or less- Protrusion.

120

Figure 7. Illustration of distances (mm) for Left Side of skulls with 4 teeth or less- Mediotrusion.

121

Figure 8. Illustration of distances (mm) for Left Side of skulls with 4 teeth or less- Protrusion.

122

Figure 9. Illustration of distances (mm) for Right Side of skulls with 5,6 or 7 teeth -

Mediotrusion.

123

Figure 10. Illustration of distances (mm) for Right Side of skulls with 5,6 or 7 teeth - Protrusion.

124

Figure 11. Illustration of distances (mm) for Left Side of skulls with 5,6 or 7 teeth -

Mediotrusion.

125

Figure 12. Illustration of distances (mm) for Left Side of skulls with 5,6 or 7 teeth - Protrusion.

126

Figure 13. Illustration of distances (mm) for Right Side of skulls with 8 teeth or more -

Mediotrusion.

127

Figure 14. Illustration of distances (mm) for Right Side of skulls with 8 teeth or more -

Protrusion.

128

Figure 15. Illustration of distances (mm) for Left Side of skulls with 8 teeth or more -

Mediotrusion.

129

Figure 16. Illustration of distances (mm) for Left Side of skulls with 8 teeth or more - Protrusion.

130

TESTS BETWEEN NUMBER OF TEETH GROUPS

Tests for mean differences between number of teeth groups are performed by section (10h,

11h, 12h, 13h and 14h). The tests are also performed using different groupings of the studied

factors. Hence, tables with test results contain 6 columns :

*In column „All‟ : Means are compared using all results for Right and Left, Mediotrusion and protrusion, Lateral, Median and Center.

** In column „Right‟ : Means are compared for Right Side using all results for Mediotrusion and protrusion, Lateral, Median and Center.

*** In column „Left‟ : Means are compared for Left Side using all results for Mediotrusion and protrusion, Lateral, Median and Center.

**** In column „Lateral‟ Means are compared for „Lateral‟ using all results for Right and Left, Mediotrusion and protrusion.

***** In column „Center‟ Means are compared for 'Center' using all results for Right and Left, Mediotrusion and protrusion.

****** In column „Median‟ Means are compared for 'Median' using all results for Right and Left, Mediotrusion and protrusion.

The test used to compare means between number of teeth groups is the F-Test from an Analysis

of Variance (ANOVA). This analysis test if at least two of the means are significantly different; a

significant conclusion (at least two means are different) can be drawn if the p-value (last line in

the tables) is smaller than 0.05. When the ANOVA conclude to a significant difference, a Duncan

multiple comparison test is performed to determine which means are significantly different.

The conclusions of Duncan multiple comparison tests are presented with the help of letters

which group means that are not significantly different. Hence, two means associated to the

same letter are not significantly different. For example, in Table 9, column ‘All’ : Group of 8

teeth or more has a mean significantly higher than the other two groups, however, groups of 4

teeth or less and 5, 6 or 7 teeth do not present significantly different means, since these groups

are both associated to the letter (b). Similarly, in Table 11 and column ‘All’: Group of 8 teeth or

more has a mean significantly higher than group 5, 6 or 7 teeth, but groups 4 teeth or less and 5,

6 or 7 teeth are not significantly different, since they both have letter (b) in common; similarly,

groups 4 teeth or less and 8 teeth or more are not significantly different, since they both have

letter (a) in common.

131

Table 9. Test results between number of teeth groups for Section at 10h.

Section = 10h All* Right** Left*** Lateral**** Center***** Median******

4 teeth or less 2.79 (b) 2.79 (b) 2.79 (a) 2.57 (b) 2.78 (b) 3.03 (a)

5, 6 or 7 teeth 2.60 (b) 2.77 (b) 2.42 (b) 2.60 (b) 2.60 (b) 2.59 (b)

8 teeth or more 3.19 (a) 3.25 (a) 3.13 (a) 3.32 (a) 3.34 (a) 2.91 (a)

p-value 0.0001 0.0382 0.0004 0.0064 0.0054 0.0107



4 teeth or less 2.59 (b) 2.66 (a) 2.52 (b) 2.95 (b) 2.41 (b) 2.42 (a)

5, 6 or 7 teeth 2.42 (b) 2.54 (a) 2.31 (b) 2.69 (b) 2.47 (b) 2.11 (b)


p-value <0.0001 0.39 <0.0001 0.0017 0.0285 0.0141



4 teeth or less 2.96 (ab) 2.88 (a) 3.03 (ab) 2.99 (a) 2.86 (a) 3.01 (a)

5, 6 or 7 teeth 2.69 (b) 2.70 (a) 2.68 (b) 2.60 (b) 2.71 (a) 2.76 (a)


p-value 0.0039 0.25 0.0015 0.0354 0.39 0.18



4 teeth or less 3.30 (a) 3.14 (a) 3.45 (a) 3.01 (a) 3.40 (a) 3.49 (a)

5, 6 or 7 teeth 2.79 (b) 2.58 (b) 2.99 (ab) 2.38 (b) 2.91 (ab) 3.06 (a)

132

8 teeth or more 2.50 (b) 2.12 (b) 2.87 (b) 1.87 (b) 2.50 (b) 3.11 (a)

p-value <0.0001 <0.0001 0.0079 <0.0001 0.005 0.0832



4 teeth or less 2.86 (a) 2.77 (a) 2.95 (a) 2.74 (a) 2.89 (a) 2.96 (a)

5, 6 or 7 teeth 2.25 (b) 2.08 (b) 2.43 (b) 2.14 (b) 2.17 (b) 2.45 (b)

8 teeth or more 1.97 (b) 1.47 (c) 2.48 (b) 1.56 (c) 1.90 (b) 2.46 (b)

p-value <0.0001 <0.0001 0.001 <0.0001 <0.0001 0.0101

133

SUPPLEMENTARY TESTS BETWEEN NUMBER OF TEETH GROUPS

A supplementary series of tests between number of teeth groups is presented in this section.

These supplementary tests are also performed by section (10h, 11h, 12h, 13h and 14h).

However, the groupings by Side, Protrusion or Mediotrusion and by lateral, median or center

are different.

Table 14. Tests between number of teeth groups by Mediotrusion or Protrusion and Right or

Left.



4 teeth or less 2.81 (a) 2.85 (ab) 2.77 (a) 2.74 (a)

5, 6 or 7 teeth 2.74 (a) 2.38 (b) 2.80 (a) 2.46 (a)


p-value 0.26 0.0046 0.12 0.0578




5, 6 or 7 teeth 2.51 (a) 2.29 (b) 2.57 (a) 2.33 (b)


p-value 0.56 0.0018 0.65 0.0012



4 teeth or less 2.88 (a) 3.03 (ab) 2.88 (a) 3.03 (ab)

5, 6 or 7 teeth 2.70 (a) 2.69 (b) 2.70 (a) 2.67 (b)

134


p-value 0.50 0.0441 0.50 0.0367




5, 6 or 7 teeth 2.56 (ab) 2.96 (a) 2.60 (ab) 3.02 (a)


p-value 0.0040 0.13 0.0021 0.0614




5, 6 or 7 teeth 2.09 (b) 2.40 (a) 2.08 (b) 2.45 (a)

8 teeth or more 1.42 (c) 2.43 (a) 1.51 (b) 2.54 (a)

p-value <0.0001 0.05 <0.0001 0.0204

Table 15. Tests between number of teeth groups by Mediotrusion or Protrusion and Right or

Left for Median results only.

Median




5, 6 or 7 teeth 2,75 (a) 2,45 (b) 2,62 (a) 2,54 (a)

8 teeth or more 2,96 (a) 2,96 (ab) 2,79 (a) 2,91 (a)

p-value 0.71 0.0368 0.73 0.32

135




5, 6 or 7 teeth 2,19 (a) 2,01 (b) 2,22 (a) 2,03 (a)


p-value 0.75 0.0397 0.90 0.09




5, 6 or 7 teeth 2,77 (a) 2,75 (a) 2,77 (a) 2,75 (a)


p-value 0.79 0.19 0.79 0.19




5, 6 or 7 teeth 2,90 (a) 3,36 (a) 2,77 (a) 3,24 (a)


p-value 0.31 0.70 0.22 0.61




5, 6 or 7 teeth 2,30 (a) 2,65 (a) 2,21 (a) 2,65 (a)

136


p-value 0.10 0.52 0.08 0.50

137

Table 16. Tests between number of teeth groups by Mediotrusion or protrusion and Right or

Left for Lateral results only.

Lateral



4 teeth or less 2.63 (b) 2.55 (a) 2.61 (a) 2.48 (a)

5, 6 or 7 teeth 2.78 (b) 2.36 (a) 2.85 (a) 2.41 (a)


p-value 0.0447 0.30 0.07 0.79




5, 6 or 7 teeth 2.87 (a) 2.53 (a) 2.90 (a) 2.47 (a)


p-value 0.47 0.07 0.43 0.06




5, 6 or 7 teeth 2.59 (a) 2.64 (a) 2.59 (a) 2.59 (a)


p-value 0.54 0.38 0.54 0.32




138

5, 6 or 7 teeth 2.16 (a) 2.44 (a) 2.30 (a) 2.64 (a)


p-value 0.10 0.13 0.07 0.09




5, 6 or 7 teeth 2.06 (ab) 2.24 (a) 1.98 (ab) 2.28 (a)


p-value 0.0242 0.31 0.0179 0.13

139

Table 17. Tests between number of teeth groups by Mediotrusion or protrusion and Right or

Left for Center results only.

Center



4 teeth or less 2.83 (a) 2.67 (a) 2.88 (a) 2.73 (b)

5, 6 or 7 teeth 2.69 (a) 2.32 (a) 2.95 (a) 2.45 (b)


p-value 0.83 0.07 0.43 0.0294




5, 6 or 7 teeth 2.46 (a) 2.34 (b) 2.58 (a) 2.48 (b)


p-value 0.95 0.0120 0.99 0.0141




5, 6 or 7 teeth 2.73 (a) 2.69 (a) 2.73 (a) 2.69 (b)


p-value 0.82 0.35 0.82 0.34




140

5, 6 or 7 teeth 2.62 (a) 3.09 (a) 2.74 (a) 3.19 (a)


p-value 0.11 0.49 0.13 0.46




5, 6 or 7 teeth 1.91 (ab) 2.32 (a) 2.04 (ab) 2.42 (a)


p-value 0.0064 0.20 0.0202 0.20

It is important to note that the fact that the number of observation decreases when more

restricted groups are considered (for example: Right, protrusion, Lateral has less measures than

Right with other factors grouped) result in increasing difficulties to find statistically significant

differences (i.e. smaller power for the test). Consequently, it is normal to find a smaller number

of significant results in tables 15 through 17.

141

REPEATABILITY TEST

The repeatability test was performed by repeating three times on the same skulls in order to

evaluate the variability associated to the measure taking. The statistical analyses associated to

the repeatability test consist in presentation of descriptive statistics allowing the evaluation of

the measure taking variability.

The descriptive statistics presented are:

- Mean (in mm); In the repeatability study, this statistic is mainly used to calculate the coefficient of variation,

- Standard deviation (St. Dev.) (in mm); This statistic give a first estimate associated to the measure variability,

- Coefficient of variation (St. Dev. Divided by the Mean, does not have a unity of measure and is generally presented in %); This statistic is the most important to study the repeatability. Even though no statistical test associated to the coefficient of variation and no universally accepted value to indicate acceptable repeatability are available, in the present study, a coefficient of variation smaller than 5% or 10% will be considered as values to aim for.

- Minimum and maximum values (in mm); In addition to the direct information given by these statistics, they also allow an estimation of the variability by defining the range between the smallest and largest values of the three repetitions.

Tables 18 to 21 present the statistics for each measure. The statistics are obtained for each skull,

with three repetitions of the same measure. These tables show that the vast majority of the

measures present a coefficient of variation smaller than 10% and almost all measures present a

coefficient of variation smaller than 20%. These results show that there is a non negligible

variability associated to the measure taking but this variability did not prevent the detection of

significant differences between the number of teeth groups. The measure variability may

however have reduced the number of significant differences found, with a less variable

measure, a larger number of significant differences would probably have been found between

the number of teeth groups.

142

Table 18. Descriptive statistics for the repeatability study for Mediotrusion on the Right Side.



10h 3 3.14 0.04 1.3% 3.10 3.18

11h 3 3.41 0.27 8.0% 3.24 3.72

12h 3 3.50 0.48 13.7% 3.15 4.05

13h 3 2.97 0.31 10.3% 2.68 3.29

14h 3 3.10 0.02 0.6% 3.08 3.12



10h 3 1.94 0.46 23.7% 1.66 2.47

11h 3 1.21 0.05 4.1% 1.16 1.25

12h 3 2.09 0.19 9.3% 1.87 2.22

13h 3 2.36 0.12 5.0% 2.27 2.49

14h 3 2.57 0.12 4.5% 2.44 2.64



10h 3 3.07 0.28 9.2% 2.74 3.28

11h 3 3.42 0.21 6.2% 3.23 3.65

12h 3 4.27 0.10 2.2% 4.19 4.37

13h 3 2.91 0.14 4.8% 2.81 3.07

14h 3 2.31 0.18 7.9% 2.10 2.43



10h 3 2.71 0.42 15.5% 2.39 3.19

11h 3 1.31 0.19 14.3% 1.20 1.53

12h 3 2.37 0.18 7.7% 2.21 2.57

143

13h 3 2.22 0.06 2.7% 2.15 2.26

14h 3 1.92 0.04 1.9% 1.89 1.96



10h 3 2.88 0.15 5.2% 2.77 3.06

11h 3 3.70 0.18 4.9% 3.52 3.88

12h 3 4.35 0.19 4.3% 4.14 4.47

13h 3 2.94 0.16 5.5% 2.83 3.13

14h 3 2.01 0.22 11.0% 1.85 2.26



10h 3 2.46 0.47 19.2% 2.06 2.98

11h 3 1.24 0.05 3.8% 1.20 1.29

12h 3 2.09 0.24 11.4% 1.93 2.36

13h 3 2.20 0.13 5.9% 2.11 2.35

14h 3 1.98 0.07 3.4% 1.91 2.05

144

Table 19. Descriptive statistics for the repeatability study for Protrusion on the Right Side.



10h 3 3.26 0.07 2.1% 3.20 3.34

11h 3 3.61 0.30 8.4% 3.41 3.96

12h 3 3.50 0.48 13.7% 3.15 4.05

13h 3 2.96 0.23 7.8% 2.76 3.21

14h 3 3.32 0.03 0.9% 3.29 3.35



10h 3 2.40 0.51 21.3% 2.05 2.98

11h 3 1.30 0.08 6.2% 1.21 1.35

12h 3 2.09 0.20 9.4% 1.87 2.22

13h 3 1.95 0.14 7.1% 1.83 2.10

14h 3 2.35 0.10 4.0% 2.25 2.44



10h 3 2.96 0.14 4.6% 2.81 3.06

11h 3 3.54 0.24 6.7% 3.35 3.80

12h 3 4.26 0.09 2.2% 4.19 4.37

13h 3 2.88 0.17 5.9% 2.72 3.06

14h 3 2.71 0.22 8.1% 2.49 2.93



10h 3 2.92 0.51 17.6% 2.51 3.49

11h 3 1.31 0.14 10.8% 1.21 1.48

12h 3 2.37 0.18 7.7% 2.21 2.57

145

13h 3 2.20 0.04 1.6% 2.18 2.25

14h 3 2.19 0.07 3.0% 2.11 2.24



10h 3 2.98 0.20 6.7% 2.83 3.21

11h 3 3.74 0.16 4.3% 3.59 3.91

12h 3 4.36 0.19 4.4% 4.14 4.47

13h 3 3.07 0.25 8.0% 2.91 3.35

14h 3 1.92 0.13 6.7% 1.79 2.04



10h 3 2.03 0.31 15.5% 1.74 2.36

11h 3 1.19 0.03 2.3% 1.17 1.22

12h 3 2.08 0.24 11.4% 1.93 2.36

13h 3 2.50 0.16 6.2% 2.38 2.68

14h 3 1.90 0.04 1.9% 1.87 1.94

146

Table 20. Descriptive statistics for the repeatability study for Mediotrusion on the Left Side.



10h 3 2.80 0.24 8.4% 2.53 2.96

11h 3 3.35 0.52 15.6% 2.83 3.88

12h 3 3.33 0.41 12.3% 2.89 3.70

13h 3 3.36 0.38 11.2% 3.00 3.75

14h 3 3.06 0.06 1.9% 3.00 3.12



10h 3 2.85 0.14 4.7% 2.73 3.00

11h 3 2.85 0.30 10.4% 2.57 3.16

12h 3 3.56 0.22 6.2% 3.38 3.80

13h 3 2.83 0.10 3.5% 2.73 2.93

14h 3 2.65 0.20 7.4% 2.48 2.86



10h 3 2.79 0.20 7.2% 2.60 3.00

11h 3 3.23 0.44 13.7% 2.75 3.62

12h 3 4.65 0.35 7.6% 4.45 5.06

13h 3 4.02 0.71 17.7% 3.47 4.83

14h 3 3.15 0.16 4.9% 3.02 3.32



10h 3 4.13 0.11 2.7% 4.00 4.22

11h 3 4.37 0.38 8.7% 3.97 4.72

12h 3 4.59 0.15 3.3% 4.43 4.73

147

13h 3 3.48 0.07 2.0% 3.42 3.55

14h 3 2.57 0.12 4.6% 2.45 2.69



10h 3 2.30 0.09 4.1% 2.19 2.35

11h 3 2.82 0.21 7.6% 2.63 3.05

12h 3 5.02 0.86 17.0% 4.04 5.55

13h 3 4.49 0.62 13.8% 4.02 5.19

14h 3 3.39 0.16 4.6% 3.21 3.49



10h 3 2.89 0.23 8.0% 2.69 3.14

11h 3 3.35 0.11 3.3% 3.24 3.46

12h 3 5.31 0.03 0.5% 5.30 5.34

13h 3 4.21 0.07 1.7% 4.17 4.30

14h 3 2.49 0.06 2.4% 2.44 2.55

148

Table 21. Descriptive statistics for the repeatability study for Protrusion on the Left Side.



10h 3 2.87 0.22 7.7% 2.65 3.09

11h 3 3.01 0.58 19.1% 2.38 3.52

12h 3 3.33 0.41 12.3% 2.89 3.70

13h 3 3.65 0.43 11.8% 3.24 4.10

14h 3 3.26 0.08 2.5% 3.19 3.35



10h 3 2.32 0.07 3.2% 2.24 2.39

11h 3 2.42 0.23 9.4% 2.23 2.67

12h 3 3.55 0.22 6.1% 3.38 3.80

13h 3 3.43 0.10 3.0% 3.33 3.54

14h 3 2.83 0.11 3.9% 2.75 2.96



10h 3 3.12 0.10 3.3% 3.03 3.23

11h 3 3.41 0.47 13.8% 2.86 3.70

12h 3 4.65 0.35 7.6% 4.45 5.06

13h 3 4.10 0.70 17.1% 3.60 4.90

14h 3 3.21 0.14 4.3% 3.12 3.37



10h 3 3.89 0.31 7.9% 3.65 4.24

11h 3 4.15 0.12 3.0% 4.03 4.27

12h 3 4.59 0.15 3.3% 4.42 4.73

149

13h 3 4.14 0.04 0.9% 4.11 4.19

14h 3 2.42 0.00 0.2% 2.41 2.42



10h 3 2.28 0.11 4.7% 2.16 2.35

11h 3 2.88 0.28 9.6% 2.58 3.11

12h 3 5.02 0.86 17.0% 4.04 5.55

13h 3 4.65 0.58 12.5% 4.25 5.32

14h 3 3.49 0.23 6.5% 3.24 3.68



10h 3 3.18 0.36 11.3% 2.88 3.58

11h 3 3.63 0.07 1.8% 3.59 3.71

12h 3 5.31 0.03 0.5% 5.30 5.34

13h 3 4.41 0.12 2.8% 4.29 4.54

14h 3 2.64 0.02 0.8% 2.62 2.66

150

Appendix 3

Pictures of skulls with the putties in the fossae mandibularis

Pictures of the bite & putties on trans-illuminating box

Please see the 2 files on the CD-Rom enclosed

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