Curve of Spee is a naturally occurring phenomenon in the human dentition. This normal occlusal curvature is required for an efficient masticatory system. Exaggerated curve of Spee is frequently observed in dental malocclusions with deep overbites. Such excessive curve of Spee alters the muscle imbalance, ultimately leading to improper functional occlusion.
Orthodontists eventually deal with the curve of Spee in virtually every patient they treat. The purpose of this article to increase our knowledge regarding the development and its effect on dentition and its treatment in exaggerated cases.
Graf Von Spee
The curve of Spee was described by F. Graf von Spee in 1890. Spee was a German anatomist (1855–1937) who wrote an original article in 1890 and it has been recently represented in 1980.
He used skulls with abraded teeth to define the line of occlusion as the line on a cylinder tangent to the anterior border of the condyle, the occlusal surface of the second molar, and the incisal edges of the mandibular incisors.
Most of Spee's predictions were made from a view of skulls perpendicular to the midsagittal plane. He based his study using three propositions.
Proposition one: Spee indicated that from a profile view, the molar surfaces lie on the arc of a circle which, continued posteriorly, touches the anterior border of the condyle.
Proposition two: It is easy to demonstrate the curve in cases with marked attrition than in cases with well-preserved cusps.
Proposition three: When other points besides molars were included in measurements from the line of occlusion, they, along with the condyle, could be on a common arc.
Spee suggested that this geometric arrangement defined the most efficient pattern for maintaining maximum tooth contacts during chewing and considered it an important tenet in denture construction. This description became the basis for Monson's spherical theory on the ideal arrangement of teeth in the dental arch.
Curve of Spee – Today
Today, in orthodontics, the curve of Spee commonly refers to the arc of a curved plane that is tangent to the incisal edges and the buccal cusp tips of the mandibular dentition viewed in the sagittal plane.[5–8]
This anteroposterior curve, or curve of Spee, was defined as the anatomical curve established by the occlusal alignment of the teeth, as projected onto the median plane, beginning with the cusp tip of the mandibular canine and following the buccal cusp tips of the premolar and molar teeth, continuing through the anterior border of the mandibular ramus and ending at the anterior aspect of the mandibular condyle (Glossary of Prosthodontic terms 1994). The curvature of the arc would relate, on average, to part of a circle with a 4-inch radius.
More recently, it was suggested that the curve of Spee has a biomechanical function during food processing by increasing the crush/shear ratio between the posterior teeth and the efficiency of occlusal forces during mastication.
Viewed in the sagittal plane, occlusal curvature is a naturally occurring phenomenon in the human dentition. Found in the dentitions of other mammals and fossil humans, this curvature was termed the curve of Spee in 1890 when a German Anatomist, Ferdinand Graff Spee described it in humans.
The understanding of how the curve of Spee develops is limited in literature. Some suggest that its development probably results from a combination of factors including growth of orofacial structures, eruption of teeth, and development of the neuromuscular system. It has been suggested that the mandibular sagittal and vertical position relative to the cranium is related to the curve of Spee, which is present in various forms in mammals. In humans, an increased curve of Spee is often seen in brachycephalic facial patterns and associated with short mandibular bodies.
In a mechanical sense, the presence of a curve of Spee may make it possible for a dentition to resist the forces of occlusion during mastication.[15–21] Although several theories have been proposed to explain the presence of a curve of Spee in natural dentitions, its role during normal mandibular function has been questioned. It has been proposed that an imbalance between the anterior and the posterior components of occlusal force can cause the lower incisors to overerupt, the premolars to infraerupt, and the lower molars to be mesially inclined. According to Root and Fidler et al. when a skeletal open bite is not present, the curve of Spee in Class II malocclusions is deeper than in other malocclusions.
Andrews noted that the occlusal planes in 120 non-orthodontically treated and ostensibly normal occlusions varied from being generally flat to having a slight curve of Spee. This finding led him to believe that the presence of a curve of Spee could be associated with post-orthodontic treatment relapse. Andrews concluded, “even though not all of the orthodontic normals had flat planes of occlusion, I believe that a flat plane should be a treatment goal as a form of overtreatment.” A deep curve of Spee may make it almost impossible to achieve a Class I canine relationship, though it may also result in occlusal interferences that will manifest during mandibular function.
It is perhaps worthwhile noting that very little research has been undertaken to determine the most effective method of leveling and to evaluate the long-term stability of leveling the curve of Spee.
Curve of Spee – From Flat to Mild
It has been suggested that the deciduous dentition has a curve of Spee ranging from flat to mild, whereas the adult curve of Spee is more pronounced. The findings were supported by Ash. Its greatest increase occurs in the early mixed dentition as a result of permanent first molar and central incisor eruption; it maintains this depth until it increases to maximum depth with eruption of the permanent second molars and then remains relatively stable into late adolescence and early adulthood. These findings also support those of Carter and McNamara and Bishara et al. that once established in adolescence, the curve of Spee appears to be relatively stable.
Certain cephalometric and dental factors are associated with individual variations in the curve of Spee, but they do not predict its biologic variance unequivocally. It appears that craniofacial morphology is just of one of the many factors influencing its development.[31–33] The curve of Spee is only influenced to a minor extent by craniofacial morphology. The curve is greatly influenced by the horizontal position of the condyle and is weakly influenced by the vertical craniofacial dimension and by the position of the mandible with respect to the anterior cranial base.
Mew quotes that whenever the curve of Spee is increased, the margins of the tongue will be seen to overlay the lingual cusps of the mandibular premolar, and the greater the curve, the more likely it is to overlay both the lingual and buccal cusps, often with scalloping. This is because that the tongue adapts to dental and skeletal forms, but there is no evidence to suggest that tongue posture is one of the determining factors of arch form.
Andrews in describing the six characteristics of normal occlusion found that the curve of Spee in subjects with good occlusion ranged from flat to mild, noting that the best static intercuspation occurred when the occlusal plane was relatively flat. He proposed that flattening the occlusal plane should be a treatment goal in orthodontics. This concept, especially as applied to deep overbite patients, has been supported by others[37–42] and produces variable results with regard to maintaining a level after treatment.
Construction of Curve of Spee
Various authors have used various techniques to measure the depth of curve of Spee. The curve of Spee was universally likened to a part of a circle. In 1899, Bonwill proposed 4 inches (101.6 mm) for the dimension of his “mandibular triangle.” Later, Monson (1932) proposed 4 inches as the radius of this circle. However, Christensen (1959) reminds us that Wilson, in 1920, after measuring 300 mandibles, found only 6% of them in agreement with the 4-inch radius proposed by Bonwill. In fact, the mean radius of the curve, initially proposed by Spee himself, was much lower, 65–70 mm in adults. Similar values was obtained by Hitchcock (1983): 69.1 mm± and Orthlieb (1997): 83.5 mm.
However, there is little consensus in the literature concerning the measurement of the curve of the Spee. Baldridge used the perpendicular distances on both sides. Balridge and Garcia found the ratio to be more accurately expressed by the formulae: Y = 0.488x - 0.51 and Y = 0.657x + 1.34, respectively, where Y is the arch length differential in millimeters and x is the sum of right and left side maximum depths of the curve of Spee in millimeters.
Bishara et al. used the average of the sum of the perpendicular distances to each cusp tip. Sondhi et al. used the sum of the perpendiculars. Braun et al. and Braun and Schmidt used the sum of the maximum depth on both sides. Traditionally, these measurements are taken from study models or photographs with a divider or caliper and a coordinate measuring machine.
The curve of Spee can also be determined by using a simplified occlusal plane analyzer (SOPA). An SOPA is preset at 4 inches from the condylar axis. The SOPA works with Denar articulators. It is an excellent aid for establishing an ideal occlusal plane if all posterior teeth are to be restored.
Dawson (1989) described reconstruction of the curve of Spee with a flag technique (The Broadrick Occlusal Plane Analyzer) which incorporated the same radius for almost all patients. The flag technique was recently redescribed by Lynch and McConnell (2002).
As technology advanced, new measuring devices became available, e.g. 3-dimensional (3D) optical digitizers that accurately measure small changes. At present, 3D virtual models are available for clinicians, supplemented by dedicated software to perform the necessary measurements.
Leveling the curve of spee
A review of literature reveals that there is disagreement among the proponents of the various orthodontic techniques that are used to level deep curves of Spee.[1252–55] The discussion involves around which leveling technique produces the most effective overbite correction as well as the most stable long-term treatment outcomes. Clinicians who adhere to the Tweed philosophy of orthodontic treatment use continuous archwires that incorporate reverse curve of Spee to produce flat occlusal planes.
Accordingly, arch leveling occurs mostly by an extrusion of the lower premolar teeth in conjunction with a minimal intrusion of the mandibular incisor teeth. In contrast to the earlier approach, advocates of sectional arch orthodontic mechanics treat deep curve of Spee by intrusion of mandibular incisors while usually allowing the lower premolars to erupt into occlusion. These people believe that extruding posteriors will cause an increase in lower facial height. They further believe that in individuals with strong muscles of mastication, the orthodontically extruded buccal segments will tend to relapse after the orthodontic treatment, which will lead to recurrence of anterior deep bites.
But a study conducted by Carcara et al. with cases treated by Wick Alexander by his Alexander Discipline showed that curve of Spee could be leveled successfully and results were stable when continuous archwire mechanics were used. It must be kept in mind that not every straight wire appliance has the unique prescription that is part of the Alexander Discipline, namely the -5° torque in the mandibular incisor and the -6° distal tip built into the molar tubes. This unique appliance prescription may play a large role in allowing for an effective, and controlled, mandibular arch leveling. In addition, the mechanical principles of actively tying back a heat-treated curved archwire may contribute to the success of arch leveling.
Correction of Exaggerated Curve of Spee
Correction of exaggerated curve of Spee can be achieved by the following tooth movements:
- Extrusion of molars
- Intrusion of incisors
- Combination of both movements
Extrusion of posterior teeth
One millimeter of upper or lower molar extrusion effectively reduces the incisor overlap by 1.5–2.5 mm. A very common method is the use of continuous archwires. A close variation of this technique is to use mandibular reverse curve of Spee and/or maxillary exaggerated curve of Spee wires. Progressively increasing step bends in an archwire also levels the curve of Spee. Other common methods include the use of a bite plate, which allows the posterior teeth to erupt.
in patients with short lower facial height, excessive curve of Spee, and moderate-to-minimal incisor display.
stability is questionable in non-growing patients. Major disadvantages include excessive incisor display, increase in the interlabial gap, and worsening of gingival smile. Flaring of incisors is a common disadvantage with reverse curve wires. The primary drawback of using step bends in archwires to level curve of Spee is the change in cant of the occlusal plane toward a deeper bite.
Intrusion of incisors
Intrusion of upper and/or lower incisors is a desirable method to level curve of Spee in many adolescent and adult patients.[60–62] The four common methods to facilitate intrusion of the upper incisors are:
- Begg and Kesling
All four designs apply tipback bends at the molars to provide an intrusive force at the incisors. All of them recognize the need for a light and continuous force application.
is particularly indicated in patients with a large vertical dimension, excessive incision-stomion distance, and a large interlabial gap.
A major risk factor associated with orthodontic treatment is external apical root resorption.[67–71] Many clinicians seem to have a subjective opinion that incisor intrusion increases the risk of apical root resorption. Many recent clinical studies[72–78] have proven that the use of intrusion arches with average force provide a healthy biologic response with negligible root resorption.
Effects of Curve of Spee Leveling
A study conducted by Pandis et al. showed that Curve of spee (COS) is mainly flattened by proclining the mandibular incisors. For 1 mm of leveling, the mandibular incisors were proclined 4°, without increasing the arch width. But Afzal and Ahmed measured the pretreatment and postreatment plaster models and found that 1 mm of arch circumference necessary to level each 1 mm of COS was only an overestimation.
Bernstein et al. performed a long-term cephalometric study and found that leveling of COS with the continuous archwire technique takes place by a combination of premolar extrusion and, to a lesser extent, by incisor extrusion. It is very effective in leveling the COS in patients with Class II Division I deep bite malocclusions treated without extractions when the initial COS is 2–4 mm.
Comparison between rectangular and round archwires
AlQabandi et al. evaluated the effects of full continuous archwire, rectangular and round, in leveling and showed that in both groups, the lower incisors proclined with uncontrolled tipping, which can be probably attributed to the intrusive force introduced by the archwire being labial to the center of resistance of the lower incisors.
The curve of Spee may get altered physiologically with age or pathologically in situations resulting from rotation, tipping, and extrusion of teeth.
As the age advances, there is a significant change in the curve of Spee and decrease in posterior disclusion during mandibular protrusion. Hence, as patients grow older, clinicians should be aware that the occlusal adjustments with age have gradually altered the curve of Spee of youth toward a more favorable individual occlusal curvature. Thus, if the curve of Spee is not maintained in these dentitions during full mouth rehabilitation, it may lead to interferences along the mandibular movements which will jeopardize the health of the masticatory system.
The stability of leveling curve of Spee may be dependent on the specific nature of its correction. Additionally, various factors, such as growth and neuromuscular adaptation, may play a role in relapse. Simons and Joondeph, in a 10-year post-retention study, reported that proclination of lower incisors and a clockwise rotation of the occlusal plane during treatment were significant relapse factors. The stability of posterior extrusion is controversial. Variables such as the amount of growth and the patient's age during treatment, muscle strength, adaptation, and the original malocclusion have all been postulated as factors contributing to the long-term stability of correction of curve of Spee.
Burzin and Nanda specifically investigated the stability of incisor intrusion and found that maxillary incisor showed insignificant relapse.
According to Praeter et al., leveling the curve of Spee during orthodontic treatment seems to be very stable on a long-term basis.
In maxillary arch
Very few studies have examined the characteristics of the curve of Spee in the maxillary arch. A study conducted by Xu et al. showed that the curve was significantly flatter in maxillary arch than in mandibular arch.
A highly significant correlation is demonstrated between the forward inclination of the superficial masseter muscle and the forward tilt of molar teeth in the sagittal plane, conforming to the posterior end of the curve of Spee. The tilt of the curve of Spee increases the crush/shear ratio of the force produced on food between the posterior molars.[87–89]
Marshall et al. have shown in their study there are no significant differences in maximum depth of curve of Spee between either the right and left sides of the mandibular arch or the sexes.
The study was performed to gain a thorough knowledge of the curve of Spee from orthodontic aspect. The articles were searched in relation to orthodontic field from the year of 1970. But more importance was given to the articles in the 2000 group. Of the 186 articles reviewed, 106 articles were omitted as they did not match with the study purpose. The 90 articles used for this article are given as references. In the 2000 group, most of the articles were based on construction of Spee and leveling. We found that importance to its development or prevention was very less.
The understanding of curve of Spee in the field of orthodontics is very important as orthodontists deal with it in virtually every patient they treat. But, however, articles offering an in-depth understanding of its cause and development, and influencing factors are very few in the literature. It starts its journey from the deciduous dentition and travels taking variable forms influenced by various factors till the edentulous condition of an individual. Hence, clinicians should be aware that the occlusal adjustments with age gradually alter the curve of Spee of youth toward a more favorable individual occlusal curvature.
The correction of curve of Spee in a non-growing individual always poses a great problem to the orthodontists. Hence, in future, more studies should be aimed at predicting the right age for the correction of exaggerated curve of Spee. Studies should also be aimed at preventing the exaggerated curve of Spee in younger age group.
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Source of Support: Nil
Conflict of Interest: None declared.