Relative percentage values for compression considering volume (Rel. % of Volume) and Biological Response Units (Rel. %BRU) during application of incisive or molar bite force in individual teeth.

<p>With the exception of second molars, a general pattern of compression in coronal tissues and tension in apical tissues predominated. Considering the relative percentage of volume under compression in canines and premolars only, exceptions (#) were seen in 7 out of 24 instances. Further refinement by evaluation of BRU reduced exceptions to 5 out of 24 (&). 4 of these exceptions (&a) in BRU were within 4 percentage points of the 50% value marking consistency with the general rule, and 3 of these were in right sided apical tissues during right molar biting, likely representing localized asymmetrical effects of molar bite force.</p

Percentage distribution of coronal and apical soft tissue follicle volume according to hydrostatic stress.

<p>Data for apical and coronal soft tissue caps, pooled separately from canines and premolars, under incisive or right molar bite force application are shown. For almost all bite force and hydrostatic stress conditions, greater volumes were devoted to compression (solid lines) in coronal follicle tissues, and to tension (dashed lines) in apical follicle tissues.</p

Percentage distribution of apical soft tissue follicle volume according to the range of hydrostatic stress.

<p>Data for apical soft tissue caps from each unerupted tooth is shown. Generally greater volumes had tensile (dashed lines) as opposed to compressive (solid lines) hydrostatic stress across most hydrostatic stress ranges. Exceptions to this pattern were seen, however, in the right first premolar and right second molar during incisive bite force application, as well as in the two first premolars and the right second premolar and molar, during right molar force application.</p

Dental follicle compression (red) and tension (green) during incisor or right molar bite force.

<p>The surface of dental follicles is seen from coronal or apical perspectives, while left (L) and right (R) sides are indicated. The upper surfaces of dental follicles for unerupted canines, first premolars and second premolars appeared subject to greater compression during both incisor and right molar loading, as compared with the lower surfaces of the same teeth which were in general subject to greater tension. This general pattern did not, however, appear to apply in the case of the unerupted second molars.</p

Percentage distribution of coronal soft tissue follicle volume according to the range of hydrostatic stress.

<p>Data for coronal soft tissue caps from each unerupted tooth is shown. For canines and premolars known to undergo active eruption at this stage of development, generally greater volumes had compressive (solid lines) as opposed to tensile (dashed lines) hydrostatic stress across most hydrostatic stress ranges. Tension, however, appeared more prominent in second molars which do not erupt at this stage of development. Further exceptions were in the left canine during incisive and molar bite force application, as well as in the right first premolar during right molar loading.</p

The number of finite elements, volumes, as well as the physical properties assigned to each tissue type in the finite element model used in this study.

<p>Young’s modulus and Poisson’s ratio for each tissue modelled was taken from the literature including for enamel, dentine, cancellous bone <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058803#pone.0058803-Field2" target="_blank">[53]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058803#pone.0058803-Field4" target="_blank">[63]</a>, Condylar Elastic Support <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058803#pone.0058803-Tanaka1" target="_blank">[66]</a>, and dental pulp <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058803#pone.0058803-Williams1" target="_blank">[65]</a>. Cortical bone and lamina dura were assumed to have the identical properties <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058803#pone.0058803-Field2" target="_blank">[53]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058803#pone.0058803-Field4" target="_blank">[63]</a>, as were the periodontal ligament and dental follicle <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058803#pone.0058803-Ichim2" target="_blank">[64]</a>.</p

Diagram illustrating the significance of ‘Biological Response Units’ as defined in this paper.

<p>The interface between bone and dental follicle soft tissue is critical for tooth eruption, as it is only at this surface that bone is either deposited by osteoblasts as fresh osteoid, or alternatively resorbed by osteoclasts. Finite elements in soft tissue follicle are illustrated under differing levels of either tension or compression, marked with increasing intensities of green or red colour respectively. Soluble factors driving either bone formation (green arrows) or bone resorption (red arrows) are indicated as produced by cells residing in volumes described by the finite elements shown, such that where ‘green arrows’ predominate, bone deposition would occur, with bone resorption occurring where there is a preponderance of ‘red arrows’ marking resorptive factors. Cell responses to most stimuli are dose dependent, while a necessary assumption in this work is that there is a linear relationship between compression or tension quantitated in terms of hydrostatic stress in the current paper, and the amount of bone resorptive or formative soluble factor produced by cells. Finite elements vary greatly in volume, so that the number of cells and hence total quantity of bone resorptive or stimulatory soluble factors must vary in direct proportion to finite element volume. To allow for variability in finite element volume and permit meaningful quantitation of the biological impact of compression and tension across finite elements, we have multiplied the volume by hydrostatic stress within individual finite elements, and thus defined a new measure we term the ‘Biological Response Unit’.</p

Colour plot diagrams showing patterns of equivalent strain.

<p>Four vertical sections of the mandible are shown, through each of the unerupted teeth during incisor loading (left side images) and right molar loading (right side images). Right (R) and left (L) joints are indicated respectively, while colour scales for incisor and molar loading images are shown separately. Irrespective of the pattern of loading applied, equivalent strain was maximal in soft tissues of the periodontal ligaments (red arrows) and dental follicles (green arrows), with generally lower levels of strain seen in hard tissues.</p

Relative percentage values for compression considering volume (Rel. % of Volume) and Biological Response Units (Rel. %BRU) during application of incisive or molar bite force in pooled incisors and premolars.

<p>Compression in coronal tissues and tension in apical tissues predominated considering both volume and BRU separately, in both bite force conditions studied.</p

Diagrams illustrating the finite element model constructed in this study.

<p>Illustrated are the boundary conditions, as well as the muscle attachments on the lateral left and medial right surfaces of the mandible, while left (L) and right (R) joints are indicated respectively. Hard tissues modelled included cortical bone, cancellous bone, enamel and dentine. Two solid blocks with the properties of cortical bone were modelled in replacement of the base of skull. Soft tissues included dental follicle, periodontal ligaments and dental pulps, while articular disk material with the physical properties of cartilage were modelled between the mandible and articulating cortical bone blocks. The lateral surface of the mandible had only temporalis and masseter muscle attachments, while attachments for the digastric, temporalis, lateral pterygoid and medial pterygoid muscles were modelled on the medial surface. The direction of muscle force is indicated with blue arrows. The articulating cortical bone blocks were assumed fastened at the corners indicated with black arrows, while in the case of incisor biting, single fixed points were assumed at all four incisor edges (red arrows), with muscle traction generating strain within the constructed model was applied. Right molar bite force was also modelled by fixing 6 points on the outer and upper surfaces of the right first molar as indicated (green arrows), and applying muscle traction.</p