Osseous reaction to orthodontic tooth movement

Introduction

The tissue reaction to the application of orthodontic forces has classically been related to the pressure and tension of the periodontal ligament with changes of the collagen fibres and vascular alterations as the initial reaction from which the cells leading to resorption on the pressure side and apposition on the tension side (^{Reitan, 1957}; ^{Reitan, 1967}). The resorption has either been described as directly, occurring from the alveolar wall, or indirectly initiated from the bone marrow ^{(Reitan, 1967}; ^{Storey, 1973}; ^{Rygh, 1974)}. In the latter case the periodontal ligament is completely compressed and characterized by a local ischemia ^{(Rygh and Brudvik, 1995)}.

Orthodontists have when describing the tissue reaction used the word remodeling for the biological process init i ated by the application of orthodontic forces. Both this terminology and the fact that pressure has been related to resorption and tension to apposition is in conflict with the view of the reaction as perceived by the bone biologists.

Within bone biology remodeling comprises the reaction of a BMU - a basic multicellular unit - that in the sequence ARF (activation, resorption and formation) renews BSU's (basic structural units) that in cortical bone comprises Haversian systems and in the trabecular bone packets. The purpose of the remodeling is to renew old bone keeping the mean bone age low without changing the outer contour. The morphology is on the other hand changed by a modeling. The correct terminology for the change which the alveolus and the alveolar process is undergoing during an orthodontic tooth movement is therefore rather a modeling accompanied by a remodeling within the surrounding bone.

^{Wolff, already in 1892}, described the relationship between the mechanical loading and the organization of bone on both a macroscopic and microscopic level. The classical studies of bending of a long bone have clearly demonstrated that apposition took place where the curvature was increased and resorption where stretching occurred ^{(Lanyon and Rubin, 1985}; ^{Frost, 1986} ; ^{Frost, 1990} ; ^{Rubin and Lanyon, 1984)}. This is clear contrast the orthodontic perception of pressure leading to resorption ^{(Reitan, 1967)}.

Orthodontists have traditionally focused on force levels or eventually force per area root surface (i.e. stress) ^{(Nikolai, 1975)}. A biological reaction to loading is, on the other hand, generally related to the deformation generated and as such expressed in relation to strain. ^{Frost (1992)} defined 4 windows related the increasing strain values :

- the acute disuse window (< 50 microstrain) where the remodeling increases up to 5 times and no modeling takes place, thus leading to a net decrease in bone as seen around teeth that are not in occlusion ^{(Picton, 1969)} or in edentulous jaws where it may lead to atrophy ^{(Tallgren, 1970);}

- the adapted window (50-1 500 microstrain), where the BMU's equalize resorption and formation and no modeling is occurring. This strain would in most cases correspond to a normal function and no change in bone mass is occurring ;

- mild overuse window (1 500-3 000 microstrain) where lamellar drift occurs simultaneous with normal formation of BMU's and with no or little microdamage. In this window a slight increase in bone mass is taking place with low overload with the formation of lamellar bone and in the high end of this window with woven bone ;

- pathological overload window (> 3 000 microstrain) where microdamage occurs and the increase in BMU is part of the repair process. This leads to a negative balance and eventually a fracture (^{fig. 1}).

The values indicated by ^{Frost (1986)} and ^{Burr et al.(1989)} were developed on the basis of experiments in which roset strain gauges were applied below the periosteum on long bones. The bimodular reaction where extremely low and extremely high strain result in a negative balance was also valid in the case of trabecular bone as shown in a finite element analysis of the tissue reaction around dental implants loaded with a well-defined known force system ^{(Melsen et al., 1996}).

The biological reaction of alveolar bone to orthodontic tooth movement when studied around rat molars was not clearly differentiated in a so-called pressure and tension zone of the alveolus ^{(Verna et al., 1999a}; ^{Verna et al., 1999b}). When a well-known force was applied through the center of resistance of monkey premolars and molars, the activity expressed as relative extension of resorption and apposition was increased close to the teeth independent on the direction with respect to the applied force ^{(Melsen, 1999)}.

The obvious controversies related to the pressure tension theory were already discussed in ^{1965 by Epker and Frost}. These authors illustrated that the change in the shape of the alveolar circumference resulting from the stretching of the fibres across the periodontal ligament results in a decrease of the radius of the alveolar wall, i.e. a bending of the bone in the tension zone. Thus the apposition of the alveolar wall can be perceived as a reaction to the bending comparable to that of the long bones studied by the orthopedist.

Apart from the effect directly adjacent to the stimulus, it is generally recognized that the reaction to stimulus distributes regionally. In the case of a trauma of any kind, the reaction seems to include an acceleration of the regional tissue processes, a RAP (regional acceleratory phenomena), which leads to increased bone turnover ^{(Frost, 1990)}.

Whereas the tissue reaction of the periodontal ligament and the bone surface facing the periodontal ligament has been the subject of numerous studies, the reaction of the bone adjacent to the alveolus has not been thoroughly analyzed. Increased activity and increased density of the alveolar bone in the direction of the tooth movement indicate that the tissue reaction to orthodontic loading should be analyzed in terms of reaction to change strain values rather than seen in relation to the force applied to the tooth ^{(King et al., 1991} ; ^{Roberts, 1992}; ^{Melsen, 1999)}.

The purpose of the present paper is to present the data from a previous described animal experiment leading to the formulation of the following hypothesis: direct resorption could be perceived as a result of the lowering of the normal strain from the functioning PDL and as such as a start of remodeling, in the bone biological sense of the word. Indirect remodeling could be perceived a sterile inflammation attempting to remove ischemic bone under the hyalinized tissue. The presence of dense woven bone was observed at a distance from the alveolus in the direction of the tooth movement as a sign of a RAP. The apposition on the tension side could, according to the new hypothesis, be perceived as a result of the bending of the alveolar wall produced by the pull from the Sharpey fibres. The above suggested interpretation of tissue reaction would be shared with the bone biologists.

A second purpose with the present communication was to apply a finite element analysis to simulate the orthodontic loading regime in order to evaluate the stresses and strains generated in the periodontal tissues when different magnitudes of forces are applied. The findings were interpreted under the new paradigm regarding tissue reaction as a response to strains generated by orthodontic loading.

Material and methods (animal experiment)

The tissue reaction was studied in six Macaca fascicularis monkeys in which the first and the second molars had been extracted 3 month earlier and an appliance was inserted for approximation of the second premolar and the third molar. Three force levels, 100, 200, and 300 cN were applied for a period of 11 weeks. The forces were applied so that the resultant for would pass the center of resistance generating a translation (^{fig. 2}). After 11 weeks the monkeys were sacrificed under Ketalar^® anaesthesia by perfusion with neutral formalin. The alveolar process was subsequently excised, embedded in methyl methacrylate and prepared for the production of 15-20 parallel horizontal sections between the marginal bone level and the apex of the teeth cut with a diamond saw. The sections were then stained with fast green. For the histomorphometric analysis a grid consisting of 3 concentric outlines of the root intersected by six radii was placed on each section so that areas anticipated to be subject to differing stress/strain distributions were isolated (^{fig. 3}). The following parameters were evaluated :

- the fractional resorption surfaces (Sfract [f]) µm²/µm² : the extent of resorption lacunae as a fraction of the total trabecular bone surface ;

- the fractional formation surfaces (Sfract [f]) µm²/µm² : the extent of osteoid covered surfaces as a fraction of the trabecular surface ;

- the fractional resting surface was calculated as 100 % minus the fraction recorded as resorption or apposition. Bone density was additionally evaluated in the areas mesially and distally to the third molars and to the second premolars ^{(Gundersen et al., 1988}) (^{fig. 3} and ⁴ .

An a posteriori test was utilized in order to separate areas that differed with regard to parameters reflecting bone turnover.

Results

The type of tooth movement registered varied from translation to controlled tipping around a centre localized at varying distances above the apex of the teeth. The quantity of tooth movement varied between 0.21 and 0.9 mm per month measured at the bone margin. No relationship between force magnitude, the type of tooth movement, and the amount of displacement could be verified.

At the time of observation the alveolar wall in the direction of the tooth movement was undergoing resorption, while the alveolar surface opposite to the tooth movement was clearly appositional (^{fig. 3} and ⁵) Woven bone formation was seen of the alveolar bone ahead of the direction of the tooth movement. Relative to the control teeth the density in the direction of the tooth movement was increased. Independent of the magnitude of loading there was an increase in the density of the bone close to the alveolus (^{table I}).

All parameters measured in areas surrounding the loaded teeth deviated markedly from the corresponding variables from the unloaded control teeth. The loading also lead to a significant increase in the relative extension of resorption from 3-5 % observed in the specimens from the control teeth to 7-13 % of the total cancellous surfaces surrounding the loaded teeth. There was likewise an increase in the extension of appositional surfaces from 15-20 %, in the control to 35-49 % around the loaded teeth. When the activity of the bony surfaces were related to the anticipated stress/strain distribution, there was a clear separation between the different zones with respect to the relative extension of resorption and resting surfaces, whereas no separation could be done based on the extension of appositional surfaces ^{(Melsen, 1999)}.

Finite element analysis

A half-sided finite element (FE) model was made of a human incisor and its supporting structures. As a basis for this model a histological section of the root of a human incisor with the surrounding periodontal ligament (PDL) and the alveolar bone was used (^{fig. 6}). The image was digitized and tracings were made of the contours of the root, the alveolus and the outside of the bone. Using the built-in facilities of the FE program (COSMOS/M; Structural Research & Analysis Corp., Los Angeles, CA, USA), these contours were first swept 90° to create a quarter model. The volumes thus obtained were meshed with the automatic meshing option using 4-node tetraedrical elements. Elements were added manually on the buccal surface to get the correct shape of the mandible in the buccal/labial plane. Finally the quarter model was mirrored to obtain the half-sided model. To save calculation time, the crown of the incisor was not modeled. The total model consists of 55 586 elements and 10 601 nodes. Different views of the model are shown in ^{figure 6} .

The material properties of the root, the trabecular bone and the cortical bone were assumed to be both uniform and homogeneous. As it was the main purpose of this study to evaluate the strains in the alveolar bone, the choice of Young's modulus for the trabecular bone will have a considerable influence on the outcome of the calculations. For this reason, a lower limit of 100 MPa and an upper limit of 1 000 MPa were taken. Values for the Young's moduli and Poisson's ratios of the bone and root are given in ^{table II} .

Values for the Young's modulus of the PDL reported in the literature display an enormous range. With values as low as 0.01 MPa ^{(Bourauel et al., 1999}) all the way up to 6 900 MPa ^{(Tanne et al., 1991}), it spans more than 5 orders of magnitude. Due to its fibrous architecture, the PDL behaves fundamentally different in tension and compression. It can withstand tensile loading as the fibres are stretched, however its resistances against compressive loading is much less as the fibres are curled up and squeezed. For the present analyses, this phenomenon was taken into account by specifying a non-linear stress-strain relationship for the PDL (^{fig. 7}). At low strains the Young's modulus in tension is 0.044 MPa and this increases gradually up to 0.44 MPa up to 54 % strain. Beyond 54 % a low value of 0.01 MPa was assumed to denote failure of the ligament. In compression the initial Young's modulus is only 0.005 MPa and remains this low for a much broader strain range, yet for really high strains (> 80 %) it goes quickly up to 8.57 MPa. For the PDL a uniform Poisson's ratio of 0.49 is assumed. Due to this non-linear material behavior of the PDL, the FE analyses were non-linear as well. They were performed in force control mode, using the full Newton-Raphson method to achieve convergence. For the discretization of the actual time steps needed to gradually built-up the full loading scheme, the FE programs built-in auto-time step option was used.

As a loading case, a mesial-distally oriented force was applied at the top surface of the root. The magnitude of this force was taken at 40, 80, 120, 160 and 200 cN. Additional boundary conditions were applied to the nodes at the top surface of the root to ensure that the root was only allowed to move in the mesial-distal direction. In this way a pure translation of the incisor was simulated. Although the analyses provided stress and strain data for all the considered structures, we were particularly interested in the stresses and strains in the classical compression and tension regions of the alveolar bone.

Results

The strain and stress distributions on the classical compression and tension sides of the alveolar bone are not symmetrical. Strains and stress levels are, in absolute sense, much higher on the tension side (^{fig. 8}, ^8b , ^9a and ^9b) The strains and stresses are not uniformly distributed along the alveolar surface. Peak values on both the tension and compression side occur where the PDL is thinnest. The peak values of the bone strains on both the tension and the compression sides for increasing values of the applied orthodontic load are plotted in (^{fig. 10}). It shows that the range for the strains on the compression side is much smaller than on the tension side, where the peak values are about 5 times higher. Furthermore, this graphs shows that the range of both the compressive and the tensile strains is much narrower for the model with high stiffness trabecular bone. For the model with low stiffness trabecular bone it is almost seven times broader. Finally the shape change of the alveolar bone in the transverse plane is illustrated in ^{figure 11} . It shows how in relation to the unloaded situation, the largest deformations occur on the classical tension side. However, the largest changes in curvature of the alveolus do not occur on the tension side in the direction of the load (around 0°), but closer to the 45-90° segment.

Discussion

The strains generated in the tissues surrounding teeth loaded with well known forces through the center of resistance was estimated by means of an FE analysis and related to the bone turnover parameters found in the animal experiment.

At the time of observation all the teeth were being displaced by direct resorption but it was noteworthy that the bone in the direction of the tooth movement was exhibiting increased density and consisted of woven bone. According to ^{Frost (1986)}, any regional noxious stimulus of sufficient magnitude can evoke a RAP. The extension of the affected region and the intensity of the response vary directly with the nature and the magnitude of the stimulus. In the present study, the nature of the stimulus was a controlled orthodontic force and the magnitude had obviously been sufficient for the generation of this reaction. ^{Jee and Li (1990)} and ^{Burr et al. (1989)} also verified that the response to increased mechanical strain may be the formation of woven bone, if the strain is intense enough, thereby corroborating ^{Wolff (1892)}, who considered woven bone as a pathophysiological response to overloading and indication of healing.

A clear apposition of lamellar bone was present on the alveolar wall opposite the force direction but the activity of the bone opposite to the force direction at a distance from the tooth was significantly lower than that in the direction of the force.

According to the model described above (^{fig .1}), low strain values would result in a net loss of bone is occurring as a consequence of increased remodeling space. With increasing strain, the modeling is initiated and a positive balance is achieved. Where the strain curve is crossing the neutral line resorption and apposition are in balance and the newly formed bone consists of lamellar bone in contrast to the woven bone formed as a result of an even larger strain. Still higher strain will result in a negative balance since repair cannot keep up with the occurrence of micro fractures ^{(Burr et al., 1985}). The borderline between a noxa, i.e. a traumatic stimulus, and a mechanical stimulus resulting in an increased bone mass has not yet been established, but it is likely that the present model evokes strain values perceived as a trauma as well as strain values perceived as a mechanical usage provoking a structural adaptation to mechanical usage [SATMU] ^{(Frost, 1986)}.

The finite element analyses showed that the strain levels in the alveolar bone strongly depend on the assumed stiffness of the trabecular bone. For load cases as low as 40 cN tensile strains up to 320 microstrain were found. This is just above the critical MES level of inactivity (100-300 microstrain). For high modulus trabecular bone even the 200 cN loading case remains in the critical range (^{fig. 10}). On the compression side for both the low and high stiffness trabecular bone models, peak strains remain in or stay below this range. This non-symmetrical distribution of strains on either side of the root can be explained by the material behavior of the PDL, which has virtually no resistance against compression. Therefore, when a tooth is moved the PDL is predominantly loaded in tension.

Resorption of the alveolus in the direction of the force is a necessary precondition for the tooth movement to take place, and resorption of the alveolus wall was a consistent finding in all cases. The resorption of the alveolar wall may, according to ^{figure 1}, occur as a result of too low strain values under loading or as a result of high stain values. The tissue reaction to orthodontic loading is, however, initially characterized by a local ischaemia a hyalinization followed by an indirect or undermining resorption ^{(Brudvik and Rygh, 1993a} and ^b).

According to ^{Meikle et al.(1986)}, the first cells to react to the orthodontic forces are the pre-osteoblasts, the helper-osteoblasts, that through the synthesis of cytokines pass the necessary message for the differentiation of the resorption cells on. It is, however, also likely that the ischaemia generated in the periodontal ligament may lead to a local necrosis of the bony trabeculae beneath the hyalinized zone, where lining cells on the bone, in this case the alveolar surface, necessary for inter-cellular communication ^{(Melsen et al., 1998}) and thus the vitality of the bone has disappeared, and that the indirect resorption is an attempt to remove necrotic bone. The development of osteoclasts is thus not a reaction to the force but to the ischaemia of the tissue, a parallel phenomena to that of the PDL, where clasts are recruited for the removal of the hyalinized zone (^{Brudvik and Rygh, 1994} ; Brudvik and Rygh, 1993 ; ^{Meikle et al., 1986}). During the period of removal of the hyalinized tissues the teeth are not being displaced, but the forces are transferred to the bone in the direction of the tooth movement obviously resulting in a dramatic increase in density.

The discrimination of the areas according to stress/strain distribution could be done with respect to extent of resorption and resting surfaces but not with respect to appositional surfaces. This could be explained by relative duration of the individual events of the remodeling sequence ARF (activation, resorption, apposition) ^{(Eriksen, 1989)}. The duration of the resorption period is short in relation to that of apposition ^{(Jaworski, 1971)}. It is thus easier to differentiate the bone reaction on the basis of this parameter than in relation to the apposition. The extension of resting surfaces indirectly reflected the total activity, and it was also possible to distinguish between four subsets of data with respect to this parameter.

At the time of sacrifice apposition was observed in the region of tension. Analyzed in relation to the FEM this can be explained by an increase in the concavity of the alveolar wall, when the tooth is displaced as a consequence of the stretching of the periodontal ligament fibres that are oriented towards the center of the tooth. Evidence of apposition following bending of an alveolar wall was presented in 1961 by ^{Andrew and Bassett (1971)}. The direct resorption could based on the FEM occur as a response to the of the periodontal ligament fibres resulting in a loading below the limit for minimum effective strain (MES) ^{(Frost, 1990)} whereby the remodeling starts with a resorption. Whether the marked formation of woven bone is directly related to the present resorption of the alveolar wall cannot be clarified in this study, but it is important that the quantity of woven bone seen both in and around the alveolus that should have been healed completely almost 7 months after extraction will constitute an obstacle to the ongoing tooth movement since the dense bone with a high extension of osteoid will be resorbed less easily that trabecular bone with only few osteoid seams. This may increase the risk of root resorption. The effect of a loading large enough to generate hyalinization and an increased bone density in the direction of the tooth movement may thus increase the risk of root resorption both initially during the removal of the hyalinized tissue but also later, when the woven bone has to be passed.

Conclusion

The present paper is based on a series of experimentally produced tooth movements in monkeys and an FEM based on boundary conditions developed from a human model. It discusses the tissue reaction related to tooth movement more from a bone biological point of view than from that of the orthodontists. A new hypothesis regarding the initial tissue reaction is presented and an explanation of apparent controversy between orthopaedists that generates bone with compression and orthodontists that resorbs bone with compression is suggested. The direct resorption can be perceived as a activation of the remodeling and the undermining resorption as a repair to a trauma. The apposition can be taken as a reaction to a bending of the alveolar wall (^{fig. 11}).

The strain values found in the direction of the displacement were below the MES (^{fig. 8}, ^8b and ¹⁰) In the light of the mechanostat theory, this would release underload remodelling, thus explaining direct resorption in the so-called compression side (^{fig. 7}). On the other hand, the stretching of the PDL fibres on the opposite side generated a strain level corresponding to modelling, thus explaining new bone formation on the so-called tension side (^{fig. 3}).

The woven bone formation seen ahead of the alveolus in the direction of the displacement could be interpreted as an expression of a so-called RAP (^{fig. 3}). According to ^{Frost (1986)}, any regional noxious stimulus of sufficient magnitude can evoke a RAP. The extension of the affected region and the intensity of the response varies directly with the magnitude and the nature of the stimulus. The indirect resorption takes place in the PDL when ischaemia and hyalinization occurs. This is probably due to the disappearance of the lining cells necessary for the communication of the osteocytes. The hyalinized tissue of the PDL is removed by non-clast cells and the underlying bone is simultaneously resorbed by osteoclasts, as a repair response to the damaged tissues ( ^{fig. 3}, region 4).

In the studies reported the nature of the stimulus was a controlled orthodontic force. The strain developed, however, varied in magnitude both due to the difference in force and to biological variations related to root size and structure of the bone surrounding the teeth ^{(Melsen et al., 1996}). In that study the most conspicuous result was the increase in both activation level and density of the bone subjected to compression in the direction of tooth movement.

The study was supported by the Dannin Foundation, Denmark, and Aarhus University Research Foundation, Denmark.

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