The Veterinary Journal 198 (2013) 590–598

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Finite element analysis of equine incisor teeth. Part 2: Investigation of stresses and strain energy densities in the periodontal ligament and surrounding bone during tooth movement P. Schrock a,b,⇑, M. Lüpke a, H. Seifert a, C. Staszyk c a b c

Institute for General Radiology and Medical Physics, University of Veterinary Medicine Hannover, Bischofsholer Damm 15, D-30173 Hannover, Germany Institute of Anatomy, University of Veterinary Medicine Hannover, Bischofsholer Damm 15, D-30173 Hannover, Germany Institute of Veterinary-Anatomy, -Histology and -Embryology, Faculty of Veterinary Medicine, Justus-Liebig-University Giessen, Frankfurter Str. 98, D-35392 Giessen, Germany1

a r t i c l e

i n f o

Article history:

Keywords: Equine dentistry EOTRH Finite element analysis Incisors Periodontal ligament

a b s t r a c t This study investigated the hypothetical contribution of biomechanical loading to the onset of equine odontoclastic tooth resorption and hypercementosis (EOTRH) and to elucidate the physiological agerelated positional changes of the equine incisors. Based on high resolution micro-computed tomography (lCT) datasets, 3-dimensional models of entire incisor arcades and the canine teeth were constructed representing a young and an old incisor dentition. Special attention was paid to constructing an anatomically correct model of the periodontal ligament (PDL). Using previously determined Young’s moduli for the equine incisor PDL, finite element (FE) analysis was performed. Resulting strains, stresses and strain energy densities (SEDs), as well as the resulting regions of tension and compression within the PDL and the surrounding bone were investigated during occlusion. The results showed a distinct distribution pattern of high stresses and corresponding SEDs in the PDL and bone. Due to the tooth movement, peaks of SEDs were obtained in the PDL as well as in the bone on the labial and palatal/lingual sides of the alveolar crest. At the root, highest SEDs were detected in the PDL on the palatal/lingual side slightly occlusal of the root tip. This distribution pattern of high SEDs within the PDL coincides with the position of initial resorptive lesions in EOTRH affected teeth. The position of high SEDs in the bone can explain the typical age-related alteration of shape and angulation of equine incisors. Ó 2013 Elsevier Ltd. All rights reserved.

Introduction Equine teeth are adapted to forage containing high levels of silica and subject to permanent dental wear inducing an age-related shortening. Due to the prolonged eruption, the clinical (erupted) crown maintains an almost constant length, the reserve crown (intra-alveolar part) however gradually shortens (Staszyk et al., 2006b). The intra-alveolar part of the tooth (reserve crown and root) serves as the attaching area of the periodontal ligament (PDL) which is known to be the most important tissue for the attenuation and conduction of masticatory forces (Staszyk and Gasse, 2005). Consequently, a shortening of the intra-alveolar parts of the tooth leads to a decrease in the PDL’s attachment area, which causes an increase in the strains, stresses and strain energy ⇑ Corresponding author at: Institute for General Radiology and Medical Physics, University of Veterinary Medicine Hannover, Bischofsholer Damm 15, D-30173 Hannover, Germany. Tel.: +49 511 856 7295. E-mail address: [email protected] (P. Schrock). 1 Formerly Institute of Anatomy, University of Veterinary Medicine Hannover, Bischofsholer Damm 15, D-30173 Hannover, Germany. 1090-0233/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tvjl.2013.10.010

densities (SEDs) in the remaining PDL. It is hypothesized that high stresses and SEDs cause local trauma such as fibre rupture and micronecrosis that may establish a suitable environment for microbiological settlement (Bender and Bender, 2003; Cordes et al., 2012a). A reduction in the angle formed by the upper and lower incisors is accompanied by shortening of the incisor teeth (Habermehl, 1981; McMullan, 1983; Muylle, 2011). In young horses viewed in profile the upper and lower incisors stand almost in a straight line. Due to advanced wear, the cross-sectional shape of the dental crowns change and the angle formed by the incisors becomes increasingly acute in old horses (Muylle, 2011). The shortening of the incisor teeth, as well as the changing tooth position and angulation, affect the mechanical behaviour and load distribution of the PDL in older horses. While the kinematics of the temporomandibular joint and the mandibular motion (Collinson, 1994; Baker and Easley, 2000; Bonin et al., 2006, 2007) and masticatory forces in equine cheek teeth (Staszyk et al., 2006a; Huthmann et al., 2009) are quite well understood, little is known about the masticatory forces in equine

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incisor teeth (Wallraff, 1942; Ritter, 1953), or the kinematics of incisor occlusion. Interestingly, a disease recently termed equine odontoclastic tooth resorption and hypercementosis (EOTRH) affecting the incisor and canine teeth of aged horses has been clinically recognized (Staszyk et al., 2008). This painful disorder causes variable periodontitis with resorptive and proliferative alterations, initially starting in distinct areas along the lingual/palatal aspects of the incisors. The aetiology of this disorder is still unknown but it is considered to be a multifactorial disease and mechanical stresses in the PDL are assumed to represent an initiating factor (Staszyk et al., 2008). We hypothesize that distinct areas of the incisor PDL are subjected to local biomechanical overload causing focal periodontal disorders, which either become repaired, or alternatively initiate a cascade of cellular processes leading to EOTRH. Thus, we assume that a focal periodontal disorder is necessary for the onset of EOTRH. In the first part of this study, we used the recently determined age-related and load-dependent Young’s moduli of the PDL to simulate a physiological masticatory action (Schrock et al., 2013). The aim of this second part of our work was to investigate the resulting tooth movements and induced regions of high stresses, leading to high strains in the incisor’s PDL. The SEDs in the PDL as well as in the surrounding bones were also examined. We aimed to draw conclusions on the age-related alterations of stressed regions in the PDL and in the jaw bones. Materials and methods Finite element (FE) analyses: Construction of 3-dimensional (3-D) models The rostral aspects of upper and lower jaws of two horses (6 and 22 years old) were obtained. Using the same procedure as described in Part 1 (Schrock et al., 2013), cross-sectional images were generated by a micro-computed tomography (lCT) system (XTremeCT, Scanco Medical). Subsequently, 3-D models were constructed creating the tooth and the supporting bones uniformly and homogenously (Kawarizadeh et al., 2003) whilst paying great attention to constructing the PDL in a detailed and realistic manner. Surface and tetrahedral volume meshes were generated out of the 3-D models as described by Lüpke et al. (2010) (Fig. 1). After net quality optimization, the meshes were transferred to the computer program COMSOL Multiphysics (version 4.3a, COMSOL) and the net quality was controlled as described in Schrock et al. (2013).

Table 1 Young’s moduli and Poisson’s ratios used for the finite element simulations. Young’s modulus (MPa)

Poisson’s ratio

Tooth

20,000

0.3

Bone PDL

20,000 1–8

0.3 0.45

Kawarizadeh et al. (2003), Cattaneo et al. (2005), Ziegler et al. (2005) Abé et al. (1996), Vollmer et al. (2000) Kawarizadeh et al. (2003), Schrock et al. (2013)

PDL, periodontal ligament; MPa, megapascals.

Determination of material parameters The Young’s modulus and the Poisson’s ratio, values describing the material properties of tooth and bone, were taken from published values (Table 1) and were assumed to have linear elastic behaviour for the purposes of this study. As no literature exists on the Young’s modulus of equine incisor’s PDL, data were determined specifically by intrusive displacement experiments using 5 mm thick slice samples and FE calculations (Schrock et al., 2013). As an approach to the visco-elastic, non-linear behaviour of the PDL, the load-dependent, slice sample specific Young’s modulus was used for the FE simulations of the corresponding teeth in the entire incisor arcades. Validation The experimentally determined intrusions of the slice samples were used to validate the complex 3-D models of the entire incisor arcades (Schrock et al., 2013). Therefore, the measured intrusions of the slice samples were compared with the calculated total displacements of the corresponding entire tooth. To simulate the intrusive displacement experiments the loading direction of the entire tooth was selected according to the loading direction of the slice samples. The resulting loading direction on the entire tooth was therefore along the longitudinal axis of its alveolus in an apical direction (‘loading direction a)’) (Fig. 2.1). For each material used in the FE calculations, the boundary conditions had to be defined as either free (i.e. movable) or fixed (i.e. not movable). In this calculation the teeth and the PDL were defined as free, enabling displacements similar to the intrusive experiments. A fixation of the entire bone was chosen as a necessary physical requirement, as the embedding of the slice samples disabled any movement of the bone in the intrusive experiments. The appropriate loading levels for the entire tooth are dependent on the ratio of the attaching areas between PDL and tooth, and between PDL and bone. As these attaching areas of the slice sample (5 mm thick) are only a fraction of the areas compared to the entire teeth (PDL attachment area of the young horse’s root on a length of about 5.5 cm and of the old horse’s root of about 3 cm length) the loading levels were selected in the same ratio as the slice sample’s PDL and tooth’s PDL

Fig. 1. 3-D tetrahedral volume meshes of the rostral aspects of an upper (A and B) and lower (C and D) jaw of a 6 year old horse (A and C) and a 22 year old horse (B and D). PDL is marked in blue.

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Fig. 2. Direction of the tooth loading: (1) Loading direction a) along the longitudinal axis of the alveolus in apical direction and (2) loading direction b) perpendicular to the occlusal surface. (Y, incisor of Triadan 202 and entire upper jaw of a 6 year old horse; O, incisor of Triadan 202 and entire upper jaw of a 22 year old horse; blue area is the PDL; blue line shows the longitudinal axis of the tooth; red arrow is the loading direction).

Fig. 3. Ratio of the connecting areas between the PDL and tooth, and PDL and bone in slice samples (1) and corresponding entire jaws (2) of a 6 year old horse (Y) and a 22 year old horse (O). PDL is marked in blue. Slice samples are about 5 mm thick. The young tooth root (Y2) has a length of about 5.5 cm, the old tooth root (O2) is about 3 cm. The applied force level on the entire young tooth was about 11 greater than on the slice sample, and for the old tooth about 6 greater. (Fig. 3). For loading direction a), the appropriate entire tooth load and the corresponding experimentally determined load-dependent Young’s modulus (Schrock et al., 2013) were selected based on a slice sample load of 20 N (Table 2). Simulation The main loading direction of the equine incisors during a physiological prehending movement (e.g. prehending grass while grazing) is perpendicular to the occlusal surface. Therefore, the loading direction on the entire tooth (‘loading direction b)’) (Fig. 2.2) was selected perpendicular to the occlusal surface. In these calculations the fixation of the bone was restricted to the caudal cut-surface of the bone. This enabled a more realistic simulation set-up, as a movement within the bone was possible. The aim of these simulations was to determine tooth movements, resulting in regions of high normal stresses in the PDL in an axial direction, thus initiating SEDs in the PDL as well as in the surrounding bones in the young and old horse. Based on recent studies on masticatory forces in equine cheek teeth (Staszyk et al., 2006a; Huthmann et al., 2009) and earlier work on incisor teeth (Wallraff, 1942; Ritter, 1953), loading levels of 50–200 N for an entire incisor tooth were

chosen as within a plausible range for physiologically occurring masticatory forces in horses‘ incisors. The selection of the corresponding PDL’s Young’s modulus was similar to the determination of the loading levels for loading direction a), based on the ratios of the attachment areas of the PDL. For a loading level of 200 N on each entire tooth, the corresponding load of the appropriate slice sample was also calculated based on the ratios of the PDL’s attachment areas. Subsequently, the matching Young’s modulus was assigned (Table 2).

Results Construction of 3-D models Highly detailed 3-D models of entire rostral aspects of upper and lower jaws of a young (6 years) and an old (22 years) horse were constructed (Fig. 1). The volume meshes for the FE analysis consisted of between 475,000 and 582,000 tetrahedrons. The

P. Schrock et al. / The Veterinary Journal 198 (2013) 590–598 Table 2 Average ratio of the connecting areas between periodontal ligament (PDL) and tooth and between PDL and bone, in the slice samples and entire jaws, corresponding loads to the reference loads, and appropriate Young’s moduli for loading directions a) and b). Slice sample number/entire jaw Average ratio of the PDL’s connecting areas (slice sample:entire tooth) Loading direction a) Reference load on the slice sample (N) Corresponding load on the entire tooth (N) Appropriate PDL’s Young’s moduli (MPa)a Loading direction b) Reference load on the entire tooth (N) Corresponding load on the slice samples (N) Appropriate PDL’s Young’s moduli (MPa)a

03/OU

05/OL

22/YU

23/YL

1:6.5

1:5

1:11

1:11

20

20

20

20

130

100

220

220

1.54

2.30

2.13

1.54

200

200

200

200

30

40

20

20

1.77

3.15

2.13

1.54

OU, old upper jaw; OL, old lower jaw; YU, young upper jaw; YL, young lower jaw. a Determination of the Young’s modulus (Schrock et al., 2013).

Table 3 Experimentally determined intrusions of the slice samples (at a load of 20 N) and calculated displacements of the entire teeth (at corresponding loads). Slice sample number/entire jaw

03/OU

05/OL

22/YU

23/YL

Intrusions of the slice samples (lm)a Displacements of the entire teeth (lm)

70 70–80

63 60–70

38.5 20–30

74.3 20–30

OU, old upper jaw; OL, old lower jaw; YU, young upper jaw; YL, young lower jaw. a Determination of the intrusions (Schrock et al., 2013).

evaluation of the mesh-quality tests showed that only 0.02–0.18% of the tetrahedrons were suboptimal (mesh quality q < 0.1) and their position was exactly determined when analysing the FE solutions. Validation The 3-D-models of the entire incisor arcades were proven to be valid as the experimentally determined intrusions of the slice

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samples and the calculated displacements of the teeth in the entire jaws were very similar in the old horse, and the variations in the young horse were within a plausible range (Table 3).

Simulation Two principal directions of the tooth movements were observed in all jaws, namely (1) an intrusive movement in an apical direction, along the longitudinal axis of the tooth into its alveolus, and (2) a tilting movement in a labial direction (Fig. 4). Due to the tilting movement of the teeth, a specific distribution pattern of the normal stresses in an axial direction within the PDL was obtained. Regions with high stresses occurred near the alveolar crest and in the apical region. Compressive stresses were predominant on the labial side of the alveolar crest and on the palatal/lingual side of the root tip, whereas tensile stresses prevailed on the palatal/lingual side near the alveolar crest (Fig. 5). The size of the regions of stresses as well as the total amount of the stresses within the PDL increased slightly in the lower jaws compared to the corresponding upper jaws, and increased markedly in the old jaw compared to the young jaw. The distribution pattern of regions with high strain energy densities in the PDL was analogous to the accumulations of the compressive and tensile stresses. High SEDs could be observed around the alveolar crest, especially on the labial and palatal/lingual side, and apical, slightly occlusal, from the root tip on the palatal/lingual side of the PDL. The size of the regions of the SEDs increased slightly in the lower jaws compared to the corresponding upper jaws, and markedly in the old horse’s PDL compared to that of the young horse (Fig. 6). In the mandibular and the maxillary jaws, bone regions with high SEDs were detected predominantly on the labial side of the jaws along the alveolar crest (Fig. 7). Smaller regions with lower SEDs occurred on the palatal/lingual side along the alveolar crest. The distribution patterns of the calculated SEDs were similar in the old and the young horses. However, the amount of the calculated SEDs as well as the size of the regions where SEDs occurred decreased in the old horse compared to the young horse. Regions of high SEDs were also detected around the canine teeth and in the PDL as well as in the surrounding bone, especially on the labial and palatal/lingual side of the teeth (Fig. 7). The size of

Fig. 4. Tooth movement at loading direction b). Outlined 3-D-model of a 6 year old horse’s upper jaw. Green tooth is the incisor without movement; red tooth is an exaggerated representation of the tooth movement; black arrows indicate the intrusion in apical direction (1) and tilting movement towards labial (2), and the red arrows show the loading direction perpendicular to the occlusal surface of the tooth.

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Fig. 5. Normal stresses in axial direction occurring in periodontal ligament (PDL) at loading direction b) (perpendicular to the occlusal surface of the tooth). Finite element results of the PDL of a 6 year old horse (A and B) and a 22 year old horse (C and D). View on labial side (1) and palatal/lingual side (2) of the PDL. Compressive stresses are demonstrated by negative scale values (green to blue) and tensile stresses by positive scale values (yellow to red). The size of the regions of occurring stresses increased slightly in the lower jaw PDL (B and D) compared to the corresponding upper jaw PDL (A and C), and markedly in the old jaw compared to the young one.

these regions and the amount of the SEDs increased in the old horse compared to the young horse.

Discussion The predictive ability of FE calculations is highly dependent on the quality of the applied material parameters and on the level of detail of the 3-D models (Wakabayashi et al., 2008). Our models combine a very high net quality with a reasonable and feasible computer calculation time. For this study, the teeth were considered as homogeneous and isotropic materials even though they are composed of different hard substances. Because of the solid structure and the considerably higher Young’s modulus of the teeth compared to the soft tissue of the PDL (Kawarizadeh et al., 2003), this simplification has no significant influence on calculated strains and stresses occurring in the PDL (Bourauel et al., 1999). This fact also applies to the modelling of the bone that was designed homogenously and isotropically (Andersen et al., 1991). Special attention was paid to modelling the PDL as this is the most important tissue for attenuation and conduction of masticatory forces (Staszyk and Gasse, 2005), predominantly by applying tension on its collagen fibres (Pini et al., 2004; Cattaneo et al., 2005). The PDL was constructed homogenously, as other studies have shown that a realistic construction (i.e. separation of collagen-fibre bundles and gel-like extracellular ground substance) is not necessary to obtain realistic FE calculations of stresses and strains within the PDL (Toms and Eberhardt, 2003). However, the thickness of the PDL was constructed manually and based on the

actual dental anatomy of the species used, as the width of the periodontal space is important for an accurate prediction of calculated stresses (Toms and Eberhardt, 2003; Ona and Wakabayashi, 2006; Men et al., 2010). The PDL’s Young’s modulus was determined in the first part of our study by intrusive displacement experiments (Schrock et al., 2013). The PDL reacts hyperelastically to tension due to the collagen fibre architecture (Cattaneo et al., 2005). In compression, however, a viscous and pseudo-elastic behaviour is seen with damping effects due to interactions between the porous matrix and unbound fluid (Bergomi et al., 2010). Yet, this compressive behaviour could not be analyzed in our study as the visco-elastic behaviour mainly exists in vital tissues. Furthermore, our intrusive experiments (Schrock et al., 2013) were only focused on the tensile behaviour of the PDL. By assuming the Young‘s moduli of the PDL to be linear-elastic instead of visco-elastic a considerable simplification was performed. However, it has been shown that such a simplification does not affect the quality but the quantity of results from FE-simulations. Compressive stresses are overrated, whereas tensile stresses as well as accompanying strains are underrated (Cattaneo et al., 2005). Therefore, interpretation of the absolute quantities of the stress amounts as well as occurrence of compressive stresses should be conducted with caution. Nevertheless, identification of highly stressed areas and areas of high SEDs within the PDL as well as in the surrounding bone is not influenced by the simplifications. The reliability of our FE simulations was confirmed by the consistency of the results of the previously performed intrusive displacement experiments (Schrock et al., 2013), and the similarity

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Fig. 6. Strain energy density (SED) occurring in PDL at loading direction b) (perpendicular to the occlusal surface of the tooth). FE results of the PDL of a 6 year old horse (A and B) and a 22 year old horse (C and D). View on labial side (1) and palatal/lingual side (2) of the PDL. High SEDs are marked in yellow and red, blue represents low SEDs. The size of the regions of occurring SEDs increased slightly in the lower jaw PDL (B and D) compared to the corresponding upper jaw PDL (A and C), and markedly in the old horse PDL compared to the young horse PDL.

of the experimentally determined intrusions and the calculated displacements in the old horse. The differences in experimental data and calculated results in the young horse’s incisors can be explained by the different root shapes. Whereas the incisors of old horses have a straight and conical root, the roots of a young horse’s incisors are curved, often presenting an additional twist around their own axis. So a loading direction along the tooth‘s longitudinal axis (in accordance with the loading direction of the slice samples) could easily be defined in the old horse. In the young horse, however, the principal direction of the tooth’s movement was not only an intrusive displacement along the tooth’s long axis, but performed an additional tilting movement in a labial direction (Fig. 4). As a result, the intrusion was hampered and the calculated values of the entire tooth movement smaller than those that had been experimentally determined. The simulation of a physiological jaw movement, such as prehending grass, was performed with loading levels up to 200 N. These values were considered plausible and were adopted from previous masticatory force measurements and calculations (Staszyk et al., 2006a; Huthmann et al., 2009). To detect the presence of highly stressed areas in the PDL, the stresses in an axial direction and the strain energy densities were calculated. As the Young’s modulus was exactly determined only in the tooth’s axial direction, the interpretation of the SEDs and stresses occurring in other directions had to be considered with caution. Such simplification would not however influence the general conclusions concerning localization of occurring stresses and SEDs. The SED, defined as elastic strain energy per volume, is known to be a parameter which is related to cell reactions (e.g. cell

movements) (Vermolen and Gefen, 2012) and bone remodelling, induced by strain effects through biomechanical activation of distinct cellular processes (Carter et al., 1987; Huiskes et al., 1987; Huiskes, 2000). As cell reactions of tendons, such as the production of prostaglandin (PGE2), have been reported to result from strains following a mechanical stimulus (Almekinders et al., 1993; Devkota et al., 2007), an SED dependent tissue response within the PDL can be expected (Carter et al., 1987). Our simulations showed a specific distribution pattern of occurring stresses and SEDs within the PDL (Figs. 5 and 6). Highly stressed areas were present around the alveolar crest and slightly occlusal of the root tip. In old horses, the same areas of the PDL showed high stresses and SEDs, but the size increased. The accumulations of stresses and SEDs around the alveolar crest are in line with previous studies reporting that high stresses and SEDs in this region cause mechanical distress (gingival and sub-gingival), contributing to the development of gingivitis and periodontal pockets, and creating an excellent milieu for microbial growth (Simon et al., 2009). These pathological findings are often reported prior to periodontal diseases (Simon et al., 2009; Dixon, 2011). Furthermore, high stresses within the PDL have been reported to lead to local overstressing, fibre rupture and tissue necrosis (Brudvik and Rygh, 1993; Cordes et al., 2012a), encouraging the invasion of microorganisms by haematogenous spread and causing suitable conditions for their settlement (Bender and Bender, 2003). Our findings of strain accumulations slightly occlusal to the root tip might indicate the region is predisposed to focal periodontal disorders. The higher incidence of periodontal diseases in old horses (Crabill and Schumacher, 1998; Cordes et al., 2012b) with short

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Fig. 7. Strain energy densities (SED) occurring in the upper (A and C) and lower jaw (B and D) of a 6 year old horse (A and B) and a 22 year old horse (C and D). View on labial side (1) and palatal/lingual side (2) of the rostral aspect of the jaws. The dimension of occurring SEDs around the alveolar crest decreased but the region of SEDs at the canine teeth increased in the old horse compared to the young horse.

teeth and a small anchorage area of the PDL, is reflected in our simulations, which show larger areas of higher strains and stresses in the old incisors compared to the young incisors. Thus, the absolute values of the calculated strains and stresses have to be considered with caution. It is generally expected that the higher the energy the higher the probability of pathologically relevant cell reactions (Carter et al., 1987; Huiskes et al., 1987; Huiskes, 2000), and yet an SED threshold causing pathological changes remains unidentified (Huiskes, 2000). The aetiology of EOTRH affecting incisor and canine teeth of aged horses is still unknown, but is considered to be multifactorial with mechanical stresses as an initiating factor (Staszyk et al., 2008), possibly with bacteriological involvement in some cases (Sykora et al., 2013). Histological findings show a typical spatial pattern of periodontal inflammation and odontoclastic tooth resorption with most affected areas at the palatal/lingual side, slightly occlusal to the root tip (Staszyk et al., 2008). Other studies have shown periodontal inflammation at the sub-gingival level (Klugh, 2004) and initial lesions in the middle of the reserve crown (Baratt, 2007) later progressing in an apical direction. Remarkably, the areas presenting high stresses and strains observed in our study are similar to the areas with initial histological findings in EOTRH affected teeth. High stresses and SEDs along the alveolar crest can be assumed to be predisposing for gingival lesions causing a suitable environment for the invasion of microorganisms. On the other hand, highly stressed areas on the palatal/lingual side slightly occlusal to the root tip can possibly lead to tissue necrosis in these areas causing activation of clastic cells and again create a suitable environment for microbes.

It is known that root resorption is induced by local periodontal trauma, starting in the periphery of necrotic PDL areas, and most often caused by over-compression (Brudvik and Rygh, 1993). These conditions might create suitable entrances (gingival lesions) and environments (necrotic areas) for microorganisms and promote the development of EOTRH. This aetiological proposal is in accordance with a recent study suggesting different Treponema spp. are involved in some cases of EOTRH (Sykora et al., 2013). The occurrence of EOTRH in equine canine teeth seems to contradict the assumption that biomechanical stresses play a major role in the aetiology of this disease, as equine canine teeth do not occlude during mastication. However, FE simulations with forces acting on incisors showed a remarkable transfer of strain energies along the jaw bone caudally causing stress accumulations in the alveolar bone and PDL of the canine teeth (Fig. 7). Although the occurring SEDs are noticeably smaller than those occurring in the incisor teeth, these data provide further evidence of a combined biomechanical and microbiological cause of EOTRH. In our simulations, stressed regions were also detected in the surrounding jaw bones. It is generally known that bone is subject to constant remodelling, driven by tooth movements (Bourauel et al., 1999; Sarrafpour et al., 2013), dynamic loads (Turner, 1998) and fatigue loads, which can potentially ‘accumulate’ (Jepsen and Davy, 1997), leading to an activation of osteoblasts and osteoclasts on external loading (i.e. the SED) (Carter et al., 1987; Huiskes, 2000). Bone mass is adjusted in response to strength or energy considerations (Carter et al., 1987). The general reaction of bone to compressive stresses is loss of material (Polson and Zander, 1983), whereas the reaction to tensile stresses is deposition of

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bone. In our simulations, compressive stresses were predominant on the labial side of the jaw bone along the alveolar crest, the areas of which are congruent with highly stressed areas within the PDL and fading areas in the jaw bone of old horses. Tensile stresses predominantly occurred on the palatal/lingual parts of the alveolar crest, reflected by the massive trabecular bone structure in the palatal/lingual part of the jaw bones as seen on lCT images of old horses. The age-related changes in the incisor position and the flattening of the incisor angle (Habermehl, 1981; McMullan, 1983; Muylle, 2011) can therefore be explained by accumulated skeletal reactions to the biomechanical stimuli initiated by mastication. Conclusions Using FE analysis, the forces occurring in the periodontal structures of equine incisors have been examined and increase our understanding of age-related alterations in the incisor position and the aetiology of diseases such as EOTRH that affect aged horses. The localization of stress and strain accumulations could be detected within the PDL and the jaw bones. However, statements regarding absolute stress and strain values can only be assessed with future studies, given that the kinematics of incisor occlusion and the masticatory forces that occur during the complex equine chewing cycle will be elucidated, and the non-linear elastic behaviour of the PDL clarified. Conflict of interest statement None of the authors has any financial or personal relationships which could inappropriately influence or bias the content of this paper. Acknowledgement The authors wish to thank Mrs. F. Sherwood-Brock for proofreading the manuscript. References Abé, H., Hayashi, K., Sato, M., 1996. Data Book on Mechanical Properties of Living Cells, Tissues and Organs. Springer, New York. Almekinders, L.C., Banes, A.J., Ballenger, C.A., 1993. Effects of repetitive motion on human fibroblasts. Medicine and Science in Sports and Exercises 25, 603–607. Andersen, K.L., Mortensen, H.T., Pedersen, E.H., Melsen, B., 1991. Determination of stress levels and profiles in the periodontal ligament by means of an improved three-dimensional finite element model for various types of orthodontic and natural force systems. Journal of Biomedical Engineering 13, 293–303. Baker, G.J., Easley, J., 2000. Equine Dentistry. WB Saunders Co., New York. Baratt, R.M., 2007. Equine incisor resorptive lesions. In: Proceedings of the 21st Annual Veterinary Dental Forum, Minneapolis, USA. Bender, I.B., Bender, A.B., 2003. Diabetes mellitus and the dental pulp. Journal of Endodontics 29, 383–389. Bergomi, M., Cugnoni, J., Botsis, J., Belser, U.C., Anselm Wiskott, H.W., 2010. The role of the fluid phase in the viscous response of bovine periodontal ligament. Journal of Biomechanics 43, 1146–1152. Bonin, S.J., Clayton, H.M., Lanovaz, J.L., Johnson, T.J., 2006. Kinematics of the equine temporomandibular joint. American Journal of Veterinary Research 67, 423– 428. Bonin, S.J., Clayton, H.M., Lanovaz, J.L., Johnson, T.J., 2007. Comparison of mandibular motion in horses chewing hay and pellets. Equine Veterinary Journal 39, 258–262. Bourauel, C., Freudenreich, D., Vollmer, D., Kobe, D., Drescher, D., Jäger, A., 1999. Simulation of orthodontic tooth movements: A comparison of numerical models. Journal of Orofacial Orthopedics 60, 136–151. Brudvik, P., Rygh, P., 1993. Non-clast cells start orthodontic root resorption in the periphery of hyalinized zones. European Journal of Orthodontics 15, 467–480. Carter, D.R., Fyhrie, D.P., Whalen, R.T., 1987. Trabecular bone density and loading history: Regulation of connective tissue biology by mechanical energy. Journal of Biomechanics 20, 785–794. Cattaneo, P.M., Dalstra, M., Melsen, B., 2005. The finite element method: A tool to study orthodontic tooth movement. Journal of Dental Research 84, 428–433.

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Collinson, M., 1994. Food processing and digestibility in horses (Equus caballus). Doctoral Thesis, Clayton, Monash University. Cordes, V., Lüpke, M., Gardemin, M., Seifert, H., Staszyk, C., 2012a. Periodontal biomechanics: Finite element simulations of closing stroke and power stroke in equine cheek teeth. BMC Veterinary Research 8, 60. Cordes, V., Gardemin, M., Lüpke, M., Seifert, H., Borchers, L., Staszyk, C., 2012b. Finite element analysis in 3-D models of equine cheek teeth. The Veterinary Journal 193, 391–396. Crabill, M.R., Schumacher, J., 1998. Pathophysiology of acquired dental diseases of the horse. Veterinary Clinics of North America: Equine Practice 14, 291–307. Devkota, A.C., Tsuzaki, M., Almekinders, L.C., Banes, A.J., Weinhold, P.S., 2007. Distributing a fixed amount of cyclic loading to tendon explants over longer periods induces greater cellular and mechanical responses. Journal of Orthopedic Surgery and Research 25, 1078–1086. Dixon, P.M., 2011. Periodontal disease research and treatment – UK experiences. Focus on Dentistry, Albuquerque, 18–20 September 2011, pp. 153–159. Habermehl, K.H., 1981. How accurate is age determination in horses. Berliner und Münchener Tierärztliche Wochenschrift 94, 167–171. Huiskes, R., 2000. If bone is the answer, then what is the question? Journal of Anatomy 197, 145–156. Huiskes, R., Weinans, H., Grootenboer, H.J., Dalstra, M., Fudala, B., Slooff, T.J., 1987. Adaptive bone-remodeling theory applied to prosthetic-design analysis. Journal of Biomechanics 20, 1135–1150. Huthmann, S., Staszyk, C., Jacob, H.G., Rohn, K., Gasse, H., 2009. Biomechanical evaluation of the equine masticatory action: Calculation of the masticatory forces occurring on the cheek tooth battery. Journal of Biomechanics 42, 67–70. Jepsen, K.J., Davy, D.T., 1997. Comparison of damage accumulation measures in human cortical bone. Journal of Biomechanics 30, 891–894. Kawarizadeh, A., Bourauel, C., Jäger, A., 2003. Experimental and numerical determination of initial tooth mobility and material properties of the periodontal ligament in rat molar specimens. European Journal of Orthodontics 25, 569–578. Klugh, D.O., 2004. Incisor and canine periodontal disease. In: 18th Annual Veterinary Dental Forum, Proceedings, pp. 166–169. Lüpke, M., Gardemin, M., Kopke, S., Seifert, H., Staszyk, C., 2010. Finite element analysis of the equine periodontal ligament under masticatory loading. Veterinary Medicine Austria – Wiener Tierärztliche Monatsschrift 97, 101–106. McMullan, W.C., 1983. Dental criteria for estimating age in the horse. Equine Practice 5, 36–43. Men, Q.L., Chen, X.M., Xu, C., Ren, S.P., Peng, Y., 2010. Relationship between tissular structure and strength of fresh bull periodontal ligament. Sichuan Da Xue Xue Bao Yi Xue Ban 41, 299–302. Muylle, S., 2011. Aging. In: Easley, J., Dixon, J.P., Schumacher, J. (Eds.), Equine Dentistry. Elsevier Saunders, London, pp. 85–96. Ona, M., Wakabayashi, N., 2006. Influence of alveolar support on stress in periodontal structures. Journal of Dental Research 85, 1087–1091. Pini, M., Zysset, P., Botsis, J., Contro, R., 2004. Tensile and compressive behaviour of the bovine periodontal ligament. Journal of Biomechanics 37, 111–119. Polson, A.M., Zander, H.A., 1983. Effect of periodontal trauma upon intrabony pockets. Journal of Periodontology 54, 586–591. Ritter, G., 1953. Kaukraft und Kaudruck des Pferdes. Doctoral Thesis, Fachbereich Veterinärmedizin, Freie Universität Berlin. Sarrafpour, B., Swain, M., Li, Q., Zoellner, H., 2013. Tooth eruption results from bone remodelling driven by bite forces sensed by soft tissue dental follicles: A finite element analysis. PLoS ONE 8, e58803. Schrock, P., Lüpke, M., Seifert, H., Borchers, L., Staszyk, C., 2013. Finite element analysis of equine incisor teeth. Part 1: Determination of the material parameters of the periodontal ligament. The Veterinary Journal 198, 583–589. Simon, T., Herold, I., Schlemper, H., 2009. Praxisleitfaden Zahn- und Kiefererkrankungen des Pferdes. Parey Verlag, Stuttgart. Staszyk, C., Bienert, A., Kreutzer, R., Wohlsein, P., Simhofer, H., 2008. Equine odontoclastic tooth resorption and hypercementosis. The Veterinary Journal 178, 372–379. Staszyk, C., Gasse, H., 2005. Distinct fibro-vascular arrangements in the periodontal ligament of the horse. Archives of Oral Biology 50, 439–447. Staszyk, C., Lehmann, F., Bienert, A., Ludwig, K., Gasse, H., 2006a. Measurement of masticatory forces in the horses. Pferdeheilkunde 22, 12–16. Staszyk, C., Wulff, W., Jacob, H.G., Gasse, H., 2006b. Collagen fiber architecture of the periodontal ligament in equine cheek teeth. Journal of Veterinary Dentistry 23, 143–147. Sykora, S., Pieber, K., Simhofer, H., Hackl, V., Brodesser, D., Brandt, S., 2013. Isolation of Treponema and Tannerella spp. from equine odontoclastic tooth resorption and hypercementosis related periodontal disease. Equine Veterinary Journal. http://dx.doi.org/10.1111/evj.12115. Toms, S.R., Eberhardt, A.W., 2003. A nonlinear finite element analysis of the periodontal ligament under orthodontic tooth loading. American Journal of Orthodontics and Dentofacial Orthopedics 123, 657–665. Turner, C.H., 1998. Three rules for bone adaptation to mechanical stimuli. Bone 23, 399–407. Vermolen, F.J., Gefen, A., 2012. A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies. Biomechanics and Modeling in Mechanobiology 11, 183–195.

598

P. Schrock et al. / The Veterinary Journal 198 (2013) 590–598

Vollmer, D., Haase, A., Bourauel, C., 2000. Semi-automatic generation of finite element meshes for dental preparations. Biomedizinische Technik (Berlin) 45, 62–69. Wakabayashi, N., Ona, M., Suzuki, T., Igarashi, Y., 2008. Nonlinear finite element analyses: Advances and challenges in dental applications. Journal of Dentistry 36, 463–471.

Wallraff, W., 1942. Untersuchungen über die Kaukraft des Pferdes. Doctoral Thesis, Friedrich-Wilhelm-University, Berlin. Ziegler, A., Keilig, L., Kawarizadeh, A., Jäger, A., Bourauel, C., 2005. Numerical simulation of the biomechanical behaviour of multi-rooted teeth. European Journal of Orthodontics 27, 333–339.