Summary

The mechanism of orthodontic teeth movement is not entirely explained. The principal reac­tion on tissues at the cellular and molecular level is initiated by the force applied to the tooth crown and transferred in turn upon the periodontal ligament (PDL). It seems, therefore, that the PDL and particularly its properties play a key role in bone remodelling. One of the more commonly used methods, which is capable of analysis of a wide range of orthodontic move­ments or distribution of stress and strain within teeth and periodontium, is the finite element method (FEM). Aiming to achieve the FEM model as close as possible to in vivo conditions, it is necessary to account for accurate material properties. The aim of the present study is to compare particular studies and descriptions of material characteristics of the PDL. The analysis of available articles shows how imperfect modern descriptions of PDL material properties available today are, which in the precise method could allow the analysis of the occurrences within the in vivo processes in a non-destructive manner. The complicated ana­tomy and physiology of PDL, which incur significant parameter changes with age and disease susceptibility, make the accurate description of this material so difficult. The available study results show that those characteristics should be precise and complicated, which undoubtedly impedes the calculation processes but generates reliable results.

Key words:FEM • material properties • PDL • bone remodelling • orthodontic forces

Introduction

The forces that are applied to the tooth are in turn transferred to periodontal tissues – which include the periodontal ligament (PDL) and the alveolar bone. The positional change of individual teeth is based on those fundamental mechanisms of bone tissue remodelling – resorption and apposition. The mechanism of teeth mo­vement however is not entirely explained. The principal reaction on both tissues at the cellular and molecular level is initiated by the force applied to the tooth crown and transferred in turn upon the PDL. It seems, there­fore, that the periodontal ligament and particularly its properties play a key role in bone remodelling [3]. From the anatomical point of view, PDL is a structure which consists of collagen fibres (53-47%), blood vessels and ne­rve endings (1-2%) that are embedded in an amorphous mucopolysaccharide matrix [9]. It is impossible to evalu­ate experimentally, in vivo, the distribution of stress and strain exerted within the tooth and periodontium during active orthodontic treatment. Therefore, one can find in the literature cases involving the evaluation of tho­se parameters in vitro. For this purpose, various types of measuring methods, for example laser holography [2], optoelectronical set-ups [12], photoelastic models [18] or electronic speckle pattern interferometry (ESPI) [7] are utilized. One of the more commonly used methods, which is capable of analysis of a wide range of orthodontic mo­vements or distribution of stress and strain within teeth and periodontium, is the finite element method (FEM). Aiming to achieve the FEM model as close as possible to in vivo conditions, and only such a model allows the col­lection of reliable results, it is necessary to account for accurate material properties. However, by reviewing the available literature we can find examples of different me­asuring methods or different materials, thus making the specification of ideal characteristics extremely difficult.

The aim of the present study is to compare particular studies and descriptions of material characteristics of the PDL which are used in articles that analyse teeth positio­nal movements induced by orthodontic forces.

Articles were identified by searches of the following data­bases: EMBASE, MEDLINE, PubMed, Scopus. The following search terms were used: “finite element analysis”, “finite element method”, “mechanical properties”, “elasticity”, “nonlinear elasticity”, “orthodontic tooth movement”, “pe­riodontal ligament (PDL)”.

A comparison of material properties is shown in table 1. One of the describing properties of PDL is Poisson’s ratio, whose value ranged in individual studies from 0.3 to 0.49 MPa (table 1). The studies conducted in the 1990s recognised PDL as a linear, isotropic and elastic mate­rial [6,10,15,19,21,27,29,30]. Worth noting is the fact that even today there are articles published which use such characteristics [5,8]. Cattaneo et al. however, using very precise data concerning PDL anatomy, gained from com­puted microtomography, proved that PDL is anisotropic tissue with strong nonlinear characteristics. Moreover, the studies of Cattaneo et al. showed that the material properties of PDL have a strong influence on the transfer of orthodontic forces. Vollmer et al., Provadis, Poppe et al., and Pietrzak et al. also came to similar conclusions in their studies [23,24,25,31].

Table 1. Material properties of periodontal ligament (PDL)

Discussion

Bone remodelling engages a complicated net of interactions between cells from the osteoblast line, hormones, and lo­cally produced cytokine and growth factors [20]. It is not difficult to agree with the impression that orthopaedic and orthodontic concepts concerning bone remodelling have a lot in common. Both require the understanding of bone biology and in particular the relation between mechanical stress and strain and various types of cells. Orthodontic teeth movements however seem to be a slightly more complicated process, which requires remodelling not only within alveolar bone but also within the PDL.

The significant differences in the description of the material characteristics of PDL are probably caused by many factors. Undoubtedly there are various measuring methods used, for example compression, extension, pressure or ultrasound. In each of these methods, the differences are noticeable depending on value, time, direction of the applied force or the frequency in the ultrasound method. Furthermore, also extremely significant seems to be the material studied. As the above-mentioned literature review revealed, studies conducted evaluate not only human PDL but also those of animals such as rats [11,17] or pigs [33]. The animal mate­rial does not exactly reflect the properties of human tissue because of differing anatomy and metabolism. Furthermore, the differences also concerned those between human teeth types – premolar [8,14,21], molar [13], incisor [10,27], and canine [5,16] or full dentition [4]. Also important to consider seems to be the individual factors of each instance – the root of each tooth has a slightly different length and shape, which influences the PDL magnitude. The next significant factor is the humidity of the material because different results are gained when the material properties are determined using dry samples or physiologically wet samples.

Despite many publications concerning the analysis of ortho­dontic teeth movement within the alveolar bone being pre­sent, it is difficult to resist the conclusion that the material properties of the PDL are the Achilles’ heel of these studies. The articles published in prestigious journals over the last 30 years very often give completely different properties and are sometimes simply excluded. In many articles there is a lack of detailed description regarding how the analysed material was harvested, prepared or loaded. Insufficient description of the methodology sometimes prevents identification of whether the material properties were gained from original studies or taken from other sources, which may indicate identical features in different studies.

Conclusions

The analysis of available articles shows how imperfect modern descriptions of PDL material properties available today are, which in the precise method could allow the analysis of the occurrences within the in vivo processes in a non-destructive manner. The complicated anatomy and physiology of PDL, which incur significant parameter changes with age and disease susceptibility, make the accu­rate description of this material so difficult. If the authors analyse the processes occurring in the whole cranium or craniofacial complex, the modelling of this complicated structure, namely PDL, may be even ignored [1,21,26,28,32]. However, if we want to analyse the movement of a sin­gle tooth within the alveolar bone in both patients with a healthy periodontium and periodontally compromised ones, precise modelling of the PDL with an account of all of its features is necessary. The available study results show that those characteristics should be precise and complica­ted, which undoubtedly impedes the calculation processes but generates reliable data.

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The author has no potential conflicts of interest to declare.

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