A Virtual Investigation of the Change in Arch Length from Leveling a Curve of Spee: A Pilot Study

doi:10.21203/rs.3.rs-2126690/v1

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A Virtual Investigation of the Change in Arch Length from Leveling a Curve of Spee: A Pilot Study

https://doi.org/10.21203/rs.3.rs-2126690/v1

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Background

Leveling a Curve of Spee (COS) is often a primary treatment intention in orthodontic and oral rehabilitation cases. It is a prevalent belief that additional arch length or “space” is always required to level a COS to avoid undesirable incisor proclination. The objective of the study was to evaluate changes in arch length from virtually leveling a COS and compare these virtual changes to estimated changes using several published formulas.

Methods

Sixteen pretreatment digital mandibular casts were randomly selected and imported to and evaluated using uDesign® software. COS of 1 mm (n = 4), 2mm (n = 6), 3mm (n = 4), and 4mm (n = 2) were identified. The AP distance from a midpoint between the central incisors perpendicular to a tangent contacting the distal surfaces of the second molars (D1) was calculated. Each arch was virtually leveled and the AP distance from the incisor midpoint to the second molar tangent (D2) was recalculated. The difference (+ or -) between D1 and D2 was multiplied by 2 to calculate total arch length changes. Virtual arch length changes were compared to changes calculated using several published formulas.

Results

Virtually calculated arch length changes for leveling were: 1mm COS (mean 0.43mm, SD +/-0.06, range 0.84mm; 2mm COS (mean 0.63mm, SD +/- 0.91, range 3.0 mm); 3mm COS (mean 1.43mm, SD +/- 0.15, range 2.02mm); and 4mm COS (mean 1.85mm, SD +/- 5.04, range 2.17mm). The mean difference between the virtual assessments and across all formula-based assessments was + 1.53mm with a range of 6.7 mm.

Conclusions

A virtual simulation of leveling demonstrated variation in arch length changes among COS of similar depth. Considerable differences were found in arch length changes between virtually leveled COS and changes estimated using published formulas.

Clinical Relevance

Virtual simulation of leveling a COS can give reliable information for both orthodontic and oral rehabilitation treatment planning.

Curve of Spee

Arch Length

Leveling Dental Arch

An exaggerated Curve of Spee (COS) is frequently observed in dental malocclusions with deep overbites. Such excessive COS can create muscle imbalance, ultimately leading to an improper functional occlusion [1, 2]. A deep COS may also result in occlusal interferences that manifest during mandibular function as well as tissue trauma associated with palatal impingement [1–3].

Leveling a COS is generally a primary objective in orthodontic treatment [4, 5] and for some prosthodontic treatment protocols [6]. It is a prevalent belief in orthodontics that additional arch length or “space” is always required to level a COS to avoid incisor proclination. Excessive incisor proclination may be undesirable due to the tendency towards causing a class II posterior occlusion, maxillary incisor spacing, and mandibular incisor gingival recession. There is some disagreement among proponents of various orthodontic techniques as to a mechanical approach most suitable for leveling an exaggerated COS [5, 7–9]. Woods proposed that an increase in arch length while leveling a COS is more a product of the mechanics utilized and not necessarily the curve itself [10]. A comprehensive understanding of the effects of leveling a COS is essential since a COS is present in a majority of patients requiring orthodontic treatment. However, published research relating to the COS is limited and typically inconclusive.

In addition to orthodontic concerns, an excessive COS and associated deep bite is a challenging factor in prosthodontic cases. Studies have shown the significance of managing the COS for oral rehabilitation to avoid interferences during mandibular movements which may jeopardize the health of the stomatognathic system [2, 6].

Previous studies have measured manually the COS in dental casts [1, 2, 4]. With the advent of intraoral scanning and digital models, this new technology shows potential for more precise and reliable evaluations. 3D virtual levelling of a COS may provide an effective tool to anticipate changes in arch dimensions prior to initiating orthodontic treatment. In addition, the technology provides a method to simulate orthodontic treatment by virtually moving teeth and jaws. According to a previous study, 3D virtual setups are as accurate as manual setups [11]. Specific tasks also include performing a Bolton Analysis and predicting a need for interproximal reduction or extractions [12]. Additional benefits include the ease of acquiring, preserving, and sharing casts.

The purpose of this pilot study was to evaluate virtual leveling of various COS in pretreatment mandibular dental casts utilizing an orthodontic software and to calculate the changes in arch length. These measurements were compared to calculations on the same casts using formulas published by Garcia, Baldridge, Germane, and Andrews. To the best of our knowledge, this is the first study to virtually level the COS using a digital orthodontic software and to measure related arch length changes.

This study was approved by the Medical University of South Carolina IRB ethics board as an Exempt study (Pro00103976). Sixteen pretreatment digital mandibular casts previously acquired by intraoral scanning with an iTero Element® (Align Technology, Inc., 410 North Scottsdale Road, Suite 1300, Tempe, Arizona, 85281) and saved in the MUSC Orthodontic Clinic were randomly selected for having an observable COS. Inclusion criterion included: complete permanent dentition including 2nd molars, minimal crowding or spacing (< 3mm), and a COS ≥ to 1mm. Exclusion criteria consisted of: missing, severely abraded, fractured, or decayed teeth. The digital casts were imported to and evaluated using uDesign® treatment planning software (uLab Systems Inc.,7005 Appling Farms Parkway, Suite 103, Memphis, TN 38133).

COS of 1 mm (n = 4), 2mm (n = 6), 3mm (n = 4), and 4mm (n = 2) were identified by measuring perpendicular from a line extending from the incisors to the distobuccal cusp of the second molar, to a buccal cusp of a tooth at the greatest depth of the curve. Both right and left sides of the arch were measured and averaged if different (Fig. 1).

From an occlusal perspective of the original models, the AP distance from a midpoint between the central incisors to the distal surfaces of the second molars was measured (Fig. 2A-D)

Using the Pythagorean Theorem (A² + B² = C²), a calculation was made to determine the anteroposterior (AP) distance from the incisor midpoint to a tangent to the distal of the second molars of the unleveled cast (D1) (Fig. 3).

A single trained operator (VB) leveled the COS of each cast via virtual tooth movement to a flat occlusal plane by buccal tipping of lingually inclined and distal tipping of mesially inclined posterior teeth, extruding infraerupted premolars and molars, correcting over angulated premolars and molars, and intruding overerupted incisors. The AP position and inclination of the incisors, however, was maintained. Minor spacing, crowding, or rotations of a limited number of teeth were maintained to avoid introducing confounding variables to the arch length calculations. The spaces and interferences tool provided in the uLabs software ensured that no spacing or crowding was created during this process. The software’s grid and plane tools were utilized to constantly check and ensure that all teeth were properly planed out to achieve a level arch. Six of the sixteen casts were chosen at random, leveled again virtually, and remeasured to evaluate intra-rater reliability.

After each arch was virtually leveled, the AP distance from the incisor midpoint to the second molar tangent (D2) was recalculated. The difference (+ or -) between D1 and D2 was multiplied by 2 to reflect the total arch length change taking into account both right and left side changes. The virtually determined arch length changes from leveling the COS were compared to amounts calculated using several formulas historically proposed in the literature.

Virtually calculated arch length changes for leveling required a mean of 0.43mm (SD+/-0.06; range of 0.84mm) for 1mm COS, 0.63mm (SD +/- 0.91; range of 3 mm) for 2mm COS, 1.43mm (SD +/- 0.15; range of 2.02mm) for 3mm COS, and 1.85mm (SD +/- 5,04; range 2.17) for 4mm COS. The mean difference between the virtual assessments and across all formula-based assessments was + 1.53mm with a range of 6.7 mm. (Table 1)

Table 1

Estimated Arch length required to level COS
COS Depth (mm)	Virtual Increase in Arch Length (mm)	Garcia Formula	Baldridge Formula	Germane Formula	Germane Formula	Andrews Estimation
	ULabs Calculation	Y = 0.657x + 1.34	Yc = .51 + .488X	Catenary	Bonwill-Howley	Chart
4	0.96	3.968	4.414	1.630	1.870	3.0
3.5	-1.21	3.640	3.926	1.275	1.465	2.5
3	0.46	3.311	3.348	0.920	1.060	2
3	2.48	3.311	3.348	0.920	1.060	2
3	1.84	3.311	3.348	0.920	1.060	2
3	0.92	3.311	3.348	0.920	1.060	2
2	-0.69	2.654	2.462	0.410	0.470	1
2	0.70	2.654	2.462	0.410	0.470	1
2	2.33	2.654	2.462	0.410	0.470	1
2	0.19	2.654	2.462	0.410	0.470	1
2	1.18	2.654	2.462	0.410	0.470	1
2	0.05	2.654	2.462	0.410	0.470	1
1	-0.08	1.997	1.486	0.100	0.110	0
1	0.76	1.997	1.486	0.100	0.110	0
1	0.72	1.997	1.486	0.100	0.110	0
1	0.30	1.997	1.486	0.100	0.110	0

Table 1: Data derived from virtual leveling and formula-based leveling estimate for 16 patients arranged in order of decreasing depth of COS. Space required to level virtually (column A), and formula-based estimates (columns B, C, D, E, F).

Findings from the intra-rater data demonstrated the reliability of the measurements by a mean error of .216mm. The six cases had a mean difference between the recalculated measurements and the original measurements of 0.216mm with a range of 0.111 to 0.453 millimeters (Table 2).

Table 2

Intra-rater reliability test
Cast	COS Depth (mm)	Arch Length Change 1 (mm)	Arch Length Change 2 (mm)	Difference 1 versus 2 (mm)
1	1	+ 0.72	+ 0.83	0.11
2	2	+ 1.18	+ 1.31	0.13
3	2	+ 0.05	− 0.12	0.17
4	2	+ 2.33	+ 2.52	0.18
5	3	+ 0.46	+ 0.91	0.45
6	3	+ 0.92	+ 0.67	0.25

Table 2: Intra-rater reliability data illustrating the consistency of repeated calculations of six cases. Five of the six cases had measurements < 0.25mm, while one case showed a difference of 0.45mm.

As a result of the rapid development in digital dentistry, the ability to do a 3D virtual setup has provided a revolutionary tool for dentistry. The purpose of this pilot study was to investigate, using a digital software program, the effect that leveling a COS has on arch length, and also compare these findings to calculated values using proposed formulas from the literature. The results show that leveling COS of similar depths can have noticeably different effects on the arch length. This variability can make a substantial difference in treatment decisions, especially in cases of moderate crowding where extraction decisions are borderline, and when full mouth rehabilitation is required.

It is a prevalent thought in orthodontics that leveling of the COS must be offset by a change in the buccolingual or anterior boundaries of the arch form, assuming no interdental space and a fixed posterior boundary [1, 4, 5]. Throughout the literature many authors have attempted to establish a relationship between the depth of the COS and the arch length required, i.e., “space”, to level this curve. Baldridge and Garcia both attempted to establish a linear relationship between the depth of the COS and the space required to level it [13, 14].

Some years later, Germane expanded on this concept and developed a relationship between the COS and the depth required to level it based on arch form and modeled it as a cylinder [15]. His argument was that by using a linear regression to describe the data it forces the relationship to be linear, but the true underlying relationship between the two variables may not be linear. Andrews also developed a reference table for the additional arch length required to level the COS [5]. However, shortcomings of these studies are they attempt to develop an all-inclusive equation or ratio ignoring the countless variables which are confounding to such a dynamic 3-D structure as the mandibular arch.

For COS of 4mm, the calculated effect on arch length from leveling (1.85mm; SD +/- 5,04; range 2.17) was determined to be much less than the expected values predicted from the equations provided by Garcia, Baldridge, and Andrews. For COS of 3mm, the amount of space required for virtually leveling had a mean of 1.43mm (SD +/- 0.15; range of 2.02mm). These values had a reasonable agreement with the calculated values by Germane and Andrews, but is much less than the expected space required based on the equations of Garcia and Baldridge. For COS of 2mm, the mean amount of space required from virtually leveling was 0.63mm (SD +/- 0.91; range of 3 mm). Again, these values share relative agreement with Germane and Andrews but is far less than the expected amount of space required based on the equations given by Garcia and Baldridge. COS of 1mm in depth required a mean of 0.43mm (SD+/- 0.06; range of 0.84mm) of space to level virtually. This calculation is much less than the amount of space expected by Garcia and Baldridge but is also more than what was expected by Germane and Andrews.

One of the shortcomings of deducing arch length changes associated with leveling a three-dimensionally shaped COS from a simple equation is that it does not account for the influence of inclination or angulation of teeth which may contribute to additional space requirements for leveling. In many malocclusions, a significant contributor to the COS is excessive lingual inclination of posterior teeth with supraerupted second molars and infraerupted premolars and first molars. Correction of this inclination through torqueing the crowns of the mandibular posterior teeth buccally and subsequently intruding or extruding the respective teeth does not require space. This can easily be demonstrated in virtual set ups utilizing a digital software program (Fig. 4A-E).

Similarly, excessive mesial angulation of posterior teeth can be characteristic of a COS. However, if the tooth crowns are rotated distally concurrently with leveling of the arch with posterior tooth eruption, no to minimal space is required (Fig. 5A-D). Woods investigated this and found that if the lower molars are angulated mesially, tooth uprighting will be necessary, but minimal space may be required for a deep curve to be leveled [10].

Some situations allow leveling a COS by distal and vertical eruption of the posterior teeth with intermaxillary elastics if some space is required to level the arch and to avoid incisor proclination. An orthognathic surgical case demonstrates this concept (Fig. 6A-C).

Specific to this concept, a COS due only to a height difference between anterior and posterior teeth with the posterior teeth having upright angulation can be leveled without any need for space by posterior eruption and/or incisor intrusion (Fig. 7).

The results of this pilot study suggest the amount of space required to level a COS is patient specific. A universal simple equation cannot accurately predict arch length requirements for leveling a COS due to the complex 3-dimensional aspects of tooth alignment. Findings suggest a misconception that “space” is always required, or substantially less space than suspected is needed, to level a COS. A more extensive study is warranted to further investigate merits of virtual leveling a COS, as well as the impact of other tooth and arch form parameters such as crowding, spacing, rotations, angulations, and inclinations on arch length.

The study indicates that a virtual simulation may be a more effective way to determine arch length changes associated with leveling a COS. Adverse changes in arch length often experienced by orthodontists, particularly incisor proclination, are more likely a result of particular treatment mechanics utilized. Virtual treatment planning may allow more emphasis to be focused on effective biomechanics to achieve desired outcomes.

This pilot study of virtual leveling a selection of various COS demonstrated:

Arch length changes from leveling a COS is patient specific with considerable variation among COS of similar depths.
Additional arch length or ‘space” is not necessarily required to level all COS.
Considerable differences were found between several published equation-based methods of estimating space requirements to level a COS and measurements based on virtual simulation.

Ethical Approval:

This study was approved by the Medical University of South Carolina Internal Review Board (IRB) ethics board as an Exempt study (Pro00103976).

Competing Interests:

Authors attest to no financial or personal conflicts of interest.

Authors' Contributions:

VB was a major contributor to the research design and data collection, TT was a major contributor to the research design and in writing the final manuscript, IA was a major contributor to data interpretation and manuscript review, LR contributed to review of the research design and manuscript, JM provided statistical analysis and data interpretation, and manuscript review.

Funding:

Not Applicable

Availability of Data and Materials:

Datasets can be accessed on the MUSC site for theses and dissertations;

https://medica-musc.researchcommons.org/theses/

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A Virtual Investigation of the Change in Arch Length from Leveling a Curve of Spee: A Pilot Study

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