INTRODUCTION

In literature, different opinions can be found about the force level that results in optimal mechanical conditions within the periodontal ligament for orthodontic tooth movement. It is assumed that an optimal force system is important for an adequate biological response in the periodontal ligament.1 It also has been suggested for a long time that the optimal force is related to the surface area of the root.2–4

In the past 70 years, the concept of optimal force has changed considerably. Schwarz5 proposed the classic concept of the optimal force. He defined optimal continuous force as “the force leading to a change in tissue pressure that approximated the capillary vessels' blood pressure, thus preventing their occlusion in the compressed periodontal ligament.” According to Schwarz5, forces well below the optimal level cause no reaction in the periodontal ligament. Forces exceeding the optimal level would lead to areas of tissue necrosis, preventing frontal bone resorption. Tooth movement would thus be delayed until undermining resorption had eliminated the necrotic tissue obstacle.

Schwarz's5 definition was slightly modified by Oppenheim,6 who advocated the use of the lightest force capable of bringing about tooth movement, and by Reitan,7 who demonstrated cell-free compressed areas within the pressure site even in cases where light forces were applied and also advocated the use of very light forces.

The current concept of optimal force is based on the hypothesis that a force of a certain magnitude and temporal characteristics (continuous vs intermittent, constant vs declining, etc ) would be capable of producing a maximum rate of tooth movement without tissue damage and with maximum patient comfort. The optimal force for tooth movement may differ for each tooth and for each individual patient.8

The magnitude of force has received significant attention in orthodontics without considering that it is important only because it is related to other characteristics of the force system and surface area of the periodontal ligament over which it is dissipated. The forces, which are applied to the crowns of the teeth, are distributed over the entire supporting structure and so are the stresses and strains. From a cellular point of view, distribution of stress (force per unit area), distortion of the periodontal ligament (shear stress, strain), and bone deformation (strain) are critical factors, and the remodeling response is directly related to stress and strain levels within the periodontium.910 The orthodontic force as an extrinsic mechanical stimulus thus evokes a biologic cellular response that aims to restore equilibrium by remodeling of the periodontal supporting tissues.11–13 Because it is very difficult to measure stresses and strains within the periodontal ligament of loaded teeth directly, only measuring the forces that are applied directly to teeth with known root surface areas can provide an estimate of these parameters.

A thorough systematic review of the available literature on this topic could be a basis for the application of appropriate forces in clinical orthodontics. But such a review on this topic has never been published. Nowadays, a meta-analysis of the literature, ie, a mathematical analysis of summary results across a group of studies with common underlying characteristics, appears to be the preferred choice. In contrast to traditional narrative literature reviews, a meta-analysis allows covering a large number of studies. It focuses on the size of treatment effect, not just whether results are statistically significant.

Therefore, the present study was planned as a meta-analysis aiming at a description of the relation between orthodontic force and the rate of subsequent tooth movement and, more specifically, at the assessment of an optimal force or force range for clinical use in orthodontics.

MATERIALS AND METHODS

RESULTS

After applying the exclusion criteria, 17 of 161 articles on animal studies and 12 of 305 articles on human studies remained. The general results of these studies are summarized in Tables 1 through 3.

TABLE 1.  List of Included Animal Studies (Cat, Dog, Monkey)

View Fullscreen

The main properties of articles included in this analysis are as follows: The articles on animal experiments (Tables 1 and 2) show a wide range of species such as cat (n = 2), beagle dog (n = 5), monkey (n = 2), rat (n = 7), rabbit (n = 1), and guinea pig (n = 2).

TABLE 2.  List of Included Animal Studies (Rat, Rabbit, Guinea Pig)*

View Fullscreen

In the two studies on cat maxillary canines, tipping forces ranging from 40 to 500 cN were used.1415 The five studies in dogs used bodily movement of mandibular second premolars (M. Von Böhl et al and J. C. Maltha et al, personal communication).16–18 The forces used in these studies ranged from 10 to 1200 cN. One of the studies gave detailed information on tooth movement only for some of the experimental animals; the other four have a rather uniform experimental setup. One of the studies on monkeys is on maxillary premolar movement using tipping forces of 10–300 cN;19 the other study is on incisors, using a bodily force of 50 cN.20 From the seven studies on rats, five studied the effect of forces ranging from 20 to 60 cN on the maxillary first molar.21–26 The other two studies dealt with the maxillary and mandibular incisors, respectively, using forces from 10 to 150 cN.2122 Six of these seven studies on rats used tipping forces, and one study used an intrusive force. Only one study on rabbits was included in which tipping forces of 25–150 cN were used on maxillary incisors.21 The two studies on guinea pigs were both on maxillary incisors, using tipping forces from 10 to 150 cN.2128 These large variations in species, applied force, experimental setup, and type of tooth movement made it impossible to perform the review as a meta-analysis of the relation between force magnitude and rate of tooth movement on the basis of animal experiments.

The number of human studies included in this review (n = 12) dealing with the relation between force magnitude and rate of tooth movement is rather limited (Table 3). Eight studies dealt with canine retraction.2329–34 A wide range of initial forces (18–1500 cN) were used in these studies; also, the regimen of reactivation and other parameters, such as the type of movement, showed a wide variation. Three articles reported on premolar tipping using forces from 50 to 200 cN,35–37 and two articles reported on molar tipping using forces from 100 to 500 cN.3238 The number and the homogeneity of the included human studies were too limited to enable a meta-analysis.

TABLE 3.  List of Included Studies on Humans*

View Fullscreen

DISCUSSION

Interest in characterizing the nature of the relation between the magnitudes of applied force and the rate of orthodontic tooth movement and the extent of anchorage loss began in the 1950s. The use of “light” forces once became popular on the basis of the classic studies of Storey and Smith2 and Reitan7 in the 1950s and 1960s, respectively. The assumption was that a so-called differential movement of teeth, at first proposed by Begg,13 could be generally achieved. Moreover, it was generally thought that light forces are more efficient and more “biologic” and, hence, less painful. Although the “light force concept” sounds attractive, the term is used freely and arbitrarily. There is neither universal consensus nor sound scientific evidence regarding specific numeric values of force magnitude. The concept of light force is application-dependent: a force that is considered too high for a certain application may be ideal for another,8 but few studies ever gave substantial evidence for this concept.

In the last two decades, a growing interest became manifest for the view that orthodontic tooth movement should be considered as the result of biological reactions to externally applied mechanical stimuli. One of the central questions raised was whether higher stresses and strains result in greater biologic activity and thus in a faster rate of tooth movement or whether an optimal force or force range would exist to stimulate this process. This question led to the classic article of Quinn and Yoshikawa4 in which they proposed four possible models for the relation between force magnitude and the rate of orthodontic tooth movement.

Searching the orthodontic literature revealed that no publications are available that elucidate the fundamental clinical question about the optimal force. On evaluating all the retrieved literature, two periods can be distinguished. Earlier studies (1950–1980) dealt more with the efficiency of orthodontic tooth movement than do later studies. Great efforts were taken to investigate the optimal force that could produce a maximum rate of tooth movement and the advantages of light forces compared with heavy forces. The differential force theory as proposed by Begg13 was also a topic of interest. All these studies, however, did not lead to a general conclusion. In later years (1981–2001), the studies mainly focused on topics as histological or cell biological changes, or changes in blood flow velocity during different stages of tooth movement, and on the side effects of orthodontic treatment such as root resorption and drug effects on tooth movement. Only few studies further investigated the efficiency of orthodontic tooth movement; also, these studies did not lead to a general conclusion.

We aimed at performing a meta-analysis of the existing literature. This, however, appeared to be impossible. Four main problems were encountered throughout the literature.

The first difficulty is the inability to precisely calculate the distribution of stresses and strains at the level of the periodontal ligament. Most literature pertaining to the relation between the magnitudes of applied force and rate of tooth movement is based on measurements of the magnitude of the applied force and the rate of tooth movement. But the forces applied to the teeth per se are not the critical factors leading to the biologic reactions. The fundamental considerations are the local stresses and strains that are experienced by the cells within the supporting tissues.111215 Direct measurement of these parameters is almost impossible, and current literature could not provide a reliable biomechanical model from which they can be derived.

The second problem is that many of the experiments cited failed to control the type of tooth movement. In most experiments, tipping tooth movement has been performed, which means that an uneven distribution of stresses and strains is invoked within the periodontal ligament. The clinical result is that the crown and root of a tooth move at different rates or even in different directions. The center of rotation, which determines the rate of crown and root movement, is difficult to determine and very likely to change during the tipping movement.16 Therefore, a well-defined and reproducible tipping tooth movement is almost impossible. A related problem is that measurements of tooth displacement generally are performed at the crowns rather than at the center of resistance, leading to an overestimation of the effect of the applied force. Therefore, experimental studies with tipping movement are difficult to interpret, and their results are very hard to compare with other experiments.

The third consideration that contributes to confusion on the relationship between force and rate of tooth movement is that orthodontic tooth movement can be divided into several phases that were categorized by Burstone17 as initial phase, lag phase, and postlag phase. Later studies on beagle dogs proposed four phases: initial phase, phase of arrest, phase of start, and linear phase.18 Structural changes in bony and periodontal tissues during the different phases of tooth movement lead to changes in their biomechanical characteristics and thus to changes in local stresses and strains within the periodontium and to modulations in the biological response. In many studies, tooth movement was evaluated over a relatively short period of time, leading to data pertaining only to the first two phases of the process and not to the postlag or linear phase in which true orthodontic tooth movement is considered to take place.

Finally, a large interindividual variation is recognized in both human research and animal experiments. Even with standardized, constant, and equal forces, the rate of orthodontic tooth movement may vary substantially among and even within individuals (M. Von Böhl et al and J. C. Maltha et al, personal communication).17–19 On the other hand, with substantially different forces, rates of tooth movement may be almost the same among or within individuals.182021 These individual differences in tooth movement characteristics are possibly related to individual variation in the structure of and cellular activity within the periodontal ligament and alveolar bone22 or to localized differences in the expression of factors such as cytokines and growth factors.23

After more than half a century of research on orthodontic tooth movement, it is disappointing to conclude that the answer to the question of the optimal force is still far away. The four main problems outlined above largely explain why the current confusion exists. So a rationale for future work should take these problems into consideration. But the stress/strain distribution in the periodontal ligament, PDL, is a point of major concern. No empirical or experimental evidence has ever been reported to verify the concept of tooth translation. This concept assumes a homogeneous distribution of stress/strain in the PDL. Because the center of rotation is in continuous repositioning in vivo, the biomechanical concept of translation can only exist instantaneously and cannot be sustained over time by any existing appliance system. Clinical tooth movement is accompanied by a constantly changing spectrum of stress/strain in the PDL that ranges from compression to tension.24

As a starting point to estimate the optimal force, mathematical modeling could be performed by evaluating all individual data on tooth movement that can be retrieved from literature. A nonlinear regression analysis of these data may provide an equation to describe the characteristics of the relation between force magnitude and the rate of tooth movement. In this way, the power of the analysis is increased because small sample size and a large interindividual variation is a general shortcoming in almost every single study. Care should be taken in categorizing data according to different force systems, ie, tipping vs bodily tooth movement and continuous vs intermittent application of force. Such a model may identify a range of optimal force and the maximal velocity of tooth movement produced.

Because experimental or clinical techniques are usually limited in applying known complex force systems, biomechanical modeling has become a necessity. From a biomechanical point of view, stress and/or strain in the periodontal ligament play an important role in tooth movement. The finite element method (FEM) is a useful technique for stress analysis in biological systems, where local stress and/or strain cannot be measured directly in a nondestructive manner. As such, it offers a possibility for accurate modeling of the tooth-periodontium system with its complicated 3-dimensional geometry. Different material models, ie, a viscoelastic material model or a poroelastic model, have been proposed for analyzing the mechanical properties of the PDL.25–28 Such models must be validated by biological data from well-controlled experimental or clinical studies that go beyond the early phases of orthodontic tooth movement, thus providing data on linear phases as well. Ultimately, a computer stimulation model might be constructed to reflect the local tissues' reactions in terms of stress and strain and to predict tooth movement in relation to orthodontic forces.

CONCLUSIONS

Because it is not possible to perform a meta-analysis of the relation between force magnitude and rate of tooth movement from current literature, no evidence-based force level could be recommended for the optimal efficiency in clinical orthodontics. But promising alternative approaches are suggested as mathematical modeling on retrieved data from literature, biomechanical modeling by FEM for stress/strain analysis, and well-controlled clinical studies or animal experiments with standardized setup. These combined efforts might lead to a better understanding ofhow the efficiency of orthodontic treatment can be improved in the future.