Lost in Space: Orthodontic Space Analysis. Part 1

The diagnostic dilemma

A common problem in the clinical practice of orthodontics is the lack of an objective and easy-to-use method by which to quantify crowding during routine orthodontic diagnosis. In assessing crowding, two features require measurement: mesio-distal tooth width and arch length. Although it is possible, given the time, to accurately measure mesio-distal tooth widths, the determination of arch length is considerably more difficult, as it is both complex and highly variable.²

To further complicate matters, diagnosis and treatment planning require not only a consideration of spacing and crowding, but skeletal and soft tissue factors, as well as potential facial growth. This mass of diagnostic information becomes highly individualized in the sense that it not only reflects patient characteristics, such as facial appearance, but also the instinct and experience of the clinician and their preferred treatment modalities. The value attributed to various aspects of diagnosis therefore depends to a degree on the operator, and it may be argued that, at some point, there is a departure from science into art when making diagnostic decisions. In an interesting paper, Hicks et al discussed the potential pitfalls of relying on numerical data as well as instinct in the diagnostic process.³ Numerical data can be misleading as it may be inappropriately applied in individual cases and is potentially flawed if based on poor research. Instinct draws on past experiences and individual bias, which can also be misleading. Furthermore, specific appliances may have a ‘treatment philosophy’ that carries its own interpretation of the significance of crowding. Some experienced clinicians may question the value of numerical diagnostic data, such as might be gained from a cephalometric analysis or space analysis. However, it is widely accepted and generally taught that numerical diagnostic data is nonetheless helpful in directing, particularly the inexperienced clinician, towards an appropriate treatment plan.⁴ For instance, although crowding as dento-alveolar disproportion is easily recognized when it is due to tooth irregularity, impactions or displacements, it is often less well recognized when it presents as proclination of teeth, or as an increased overbite. A simple estimation of crowding in millimetres is therefore a widely accepted starting point in the diagnostic process, which may then be modified by additional skeletal, soft tissue and dental factors.

It would therefore seem that an everyday challenge for the orthodontist is to process a large amount of diagnostic information, some of which may be conflicting, and then to crystallize this into a decision regarding a definitive treatment plan, including whether extractions are indicated.⁵ This places a heavy burden on the operator because, if treatment entails the loss of healthy teeth, it may be the first time the patient has had active dental treatment and it is likely to be a negative experience. Since extractions are usually bilateral to preserve the centrelines, in most cases more space is obtained than is actually required. In a number of patients there is a borderline need for extractions, and this presents the clinician with a ‘double-edged sword’. This is because extractions may lead to difficulties with complete space closure, while a non-extraction approach may in some cases necessitate significant arch expansion, leading to a potential risk of increased instability and periodontal complications such as bone dehiscences.

Poor diagnosis not only leads to difficulty in case management, but may compromise facial appearance and the integrity of the dento-alveolar complex.⁶ Experienced clinicians also recognize the possibility that a seemingly appropriate diagnosis at the commencement of treatment can subsequently be negated by natural underlying changes in arch dimension,⁷ and inappropriate treatment may increase the likelihood of relapse. These uncertain aspects of orthodontic treatment planning therefore have the potential to become medico-legal problems.

Despite significant advances in orthodontic science and technology, there are few tools available at the present time to assist the clinician in quantifying crowding. As a result, most specialists depend on a potentially unreliable visual assessment. To quote Jones and Richmond:⁸

Furthermore, in a study looking at the consistency of orthodontic decisions relative to diagnostic records, Han et al concluded that: ‘in the majority of cases, study models alone provided adequate information for treatment planning, and incremental addition of information from other types of diagnostic records made small differences’.⁹

Although a survey of UK orthodontists revealed the vast majority supported the need for a method of space analysis to be taught during postgraduate training, very few subsequently used this in clinical practice, instead relying purely on ‘eyeballing’.¹⁰ A review of the current literature suggests that research into space analysis or methods of estimating crowding has, for the last 20 years at least, failed to capture the imagination of our specialty, as there are very few recently published articles on the topic.

What other factors need to be considered during space estimation?

In addition to either eyeballing the mesio-distal widths of the teeth relative to the arch length, or formally measuring it, the other factors that need to be considered when estimating space requirements may include:

How good are we at eyeballing space requirements and planning whether to extract?

In an effort to try to answer the question as to how good orthodontists are in estimating crowding, one study invited 62 orthodontists from both primary and secondary care, and with varying levels of experience, to quantify crowding and the need for extractions in eight lower study models (Figure 2).²

Each model had differing degrees of crowding, having been constructed and measured digitally (Figures 3 and 4) at Bristol Dental School.^2,10 Although rulers, dividers and brass wire were provided, all of the participants chose to eyeball when estimating the crowding.

Table 1 indicates the mean, mode, minimum and maximum estimates of crowding in millimetres for each of the eight lower models. Where the actual amount of crowding was low, most orthodontists estimated it as such, eg typodont 1. However, as the true crowding increased so did the variance in the estimates. For example, in typodont 8 (Figure 5), although the most frequent estimates were close to 8 mm (true value 7.45 mm), they varied from 5 mm to 20 mm.

It is important to note how the assessments of crowding translated into extraction decisions. In the case of each clinician, for typodonts 1–3, the decision was made not to extract. Although model 4 had virtually no crowding (0.1 mm), six clinicians considered this a possible extraction case. By contrast, and more reassuringly, all 62 clinicians considered the most crowded model, with 7.45 mm of crowding, to be an extraction case. Of further interest is the fact that eight clinicians prescribed extractions for model 5, which only had 2.48 mm of crowding. For model 3, with 1.27 mm of crowding, estimates of crowding ranged from 0 mm to 5 mm. Model 6, with slightly over 4 mm of crowding, seemed to produce a wide range of opinion. Of the 28 clinicians who made a definite decision to extract, 24 had overestimated the crowding, with 11 of these having assessed the crowding to be in excess of 7 mm. Where there was a tendency to overestimate crowding, an extraction decision was more likely.

When estimating crowding, it is those estimates where there is some uncertainty as to whether a case does or does not require extractions, ie the borderline case, that is perhaps of greatest clinical significance. Nine months after the original assessments, 11 of the 62 orthodontists were asked to reassess models 4, 5 and 6, which were considered the ‘borderline’ cases. For each model, again, the decision was either non-extraction, borderline, or extraction. Of the 33 repeat estimations, only five were the same. In the case of model 6 (4.19 mm of crowding), estimates of crowding ranged from 4 mm to 12 mm, again revealing the tendency in most instances to overestimate crowding. Only three clinicians made the same decision to extract on the repeat questionnaire; four changed from a borderline decision to a definite extraction decision, two changed from extractions to borderline, one changed from non-extraction to borderline and, interestingly, one clinician changed their opinion from borderline to non-extraction, despite estimating 12 mm of crowding on the repeat occasion. Defending an extraction or non-extraction decision in a subsequent legal challenge could in itself therefore prove challenging in the face of such variability.

Arch form

The term ‘arch form’ refers to the two-dimensional shape of the arch. The fundamental difficulty in its assessment is that every patient has a unique arch form and arch length is directly related to it. The individual arch form is unlikely to consistently follow any particular identifiable shape that can be accurately described or assessed geometrically. It is also possible that an arch will be asymmetric and may therefore vary in length on each side. In orthodontics, arch form is usually considered to be represented by a curve described by the mesial and distal contact points of the teeth. Although a succession of such contact points may represent a logical indication of arch form, they are frequently difficult to identify and locate, as well as being subject to individual variations in tooth morphology. A range of arch forms has been proposed over the years, not only for the purpose of general description, but also in an attempt to devise a mathematical formula for calculating arch length.

Based on previous work by Bonwill,¹⁴ Hawley suggested that the basis of an ideal arch could be constructed on a modified equilateral triangle.¹⁵ According to Angle,¹⁶ the ideal arch took the form of a parabola and later still, in 1917, Williams,¹⁷ like Hawley, considered the anterior teeth to follow the arc of a circle. These early theories on arch form had their opponents and both Stanton¹⁸ and Izard¹⁹ subsequently developed more complex shapes based on ellipses and parabolas. Further mathematical constructions included a catenary curve by McConnail and Scher,²⁰ a trifocal ellipse proposed by Brader²¹ and later, more complex arch forms based on a fourth polynomial.^22,23

If ‘arch form’ is to be considered in three-dimensions and taken as a function of a series of (at least some) potentially indeterminate contact points, it will be represented by two highly variable superimposed ‘curves’, namely the arch shape and the curve of Spee.

The curve of Spee

Earlier, the various factors that are important in space estimation were listed, and of these, one of the most significant is the impact of the curve of Spee. It is unlikely that the curve of Spee in any patient will be a smooth curve that could be quantified geometrically. Burstone, in his biomechanical rationale for orthodontic therapy, drew attention to three general shapes of the curve of Spee dictated by the position of the deepest point.²⁴ This is because, although the deepest point of the curve is commonly in the mid-arch region, it may also be more mesial or more distal to this. Several methods of assessing the curve of Spee require the operator to assess the deepest point of the curve, but this again is subject to ‘eyeballing’.

From a practical viewpoint the curve of Spee has significant implications in terms of space analysis since additional arch perimeter is required if it is to be flattened. It is clearly important to quantify this component of a space analysis, as it could influence the decision regarding the extraction of teeth. Baldridge sectioned and then levelled the teeth on 30 well-aligned lower arch models that were reported to have significant curves of Spee and, as a result, reported how the mean arch length was found to increase by 3.54 mm.²⁵ In the two cases with the deepest curves of Spee, an additional 5.2 mm of space was required to facilitate arch levelling. Therefore, a failure to consider the space implications of a significant curve of Spee could make a seemingly mildly crowded arch, with say 2–4 mm of incisor crowding, difficult to manage, or lead to excessive incisor proclination. Many clinicians assess crowding clinically by observing the lower arch from above, which may fail to appreciate the curve of Spee (Figure 6). Any attempts to evaluate the space implications of the curve may be best made by observing the lower study model laterally.

Garcia demonstrated how the projection of selected points along an arch onto a flat plate makes it possible to measure the space needed for levelling the curve of Spee (Figure 7).²⁶ Easily identifiable points were used to divide the arch into segments that could be measured directly.

Various other attempts have been made to assess the space implications of flattening the curve of Spee. Indeed, Baldridge pointed out that, although orthodontists recognized that levelling the curve of Spee led to an increase in arch length,²⁵ few references can be located that attempt to quantify this relationship. A common manifestation of increasing arch length is certainly potentially unstable proclination of the incisor teeth. By means of a flat template, cut away in the canine area, and resting posteriorly on the molar cusps and anteriorly on the incisor edges, Andrews used a simple formula to predict the effect of the curve of Spee on this labial movement.¹² Taking a measurement from the flat template to the cusp tip in the deepest part of the curve of Spee, a ratio of 3:1 was said to exist between the depth of curve and the inclination of the incisors that would result from levelling. The example quoted is a 15-degree increase in the inclination of the incisors to level a 5 mm curve of Spee.