The curve of Spee in Stone Age man

H. Perry Hitchcock, D.M.D., M.S.D.* San Antonio, Texas

The purpose of this research was to test Spee’s predictions on a sample of skulls with well-worn occlusions. Thirty-nine Shell Mound Indian skulls with marked attrition of the teeth were x-rayed in the Margolis cephalostat Following Spee’s suggested landmarks, three curves were obtained which included the condyle. A fourth curve was investigated-not using the condyle but based from three landmarks of the occlusal surface. All curves, radii, and centers were generated by a computer using the landmarks digitized from each skull’s film. When only the molars and the condyle were used, the length of the radius and the location of the center came closest to Spee s predictions. In most of the sample, however, Spee’s inclusion of the incisor along that arc could not be verified. Prosthodontic experiments which might give clues to finishing curves for orthodontic patients are suggested.

Key words: Profile, condyle, lachryma, radius, attrition

T he availability of an English translation of Graf von Spee’s original work led to the testing of some of his premises on a group of Stone Age skulls.‘, :X -1

Most of Spee’s predictions were made from a view of skulls perpendicular to the midsagittal plane. Cephalometric radiographs permit a study of the oc- clusion in this position. The items investigated in this particular study are based on three propositions, de- scribed by Spee, as follows:

Proposition I. Spee indicated that, from a profile view, the molar surfaces lie on the arc of a circle which, continued posteriorly, touches the anterior bor- der of the condyle. Considering both sides, a cylinder is described. The central axis of that cylinder is located somewhere on the horizontal midorbital plane posterior to the ‘ ‘crista lacrimalis posterior” (Fig. 1, a). ’

Proposition 2. This is more of a proviso, or condi- tion, to make investigation easier. Spee suggested that it was easier to demonstrate the curve in cases with marked attrition than in cases with well-preserved cusps.

Proposition 3. When other points besides molars were included in measurements from the line of occlu- sion, they, along with the condyle, could be on a com- mon arc. “. . . In most cases such a center could be obtained approximately. In some cases with decided abrasion all points were located exactly on the same circle. “I (See Spee’s Fig. 4 in Fig. 1.)

Presented at the Clinical Dental Science Symposium, San Antonio, Texas, May 5, 1983, and to members and alumni of the Orthodontic Department, Zahnarztliches Institut der Universitat Zurich, May 18, 1983. Professor and Chairman, Department of Orthodontics, University of Texas at San Antonio Dental School.

248

Fig. 1. la and Ib, Illustrations from same skull; la in exact profile view; 7b from somewhat anterior view. 2, Dentition of adult with well-preserved crown cusps. 3, Mandible of child. 4, Series of points of human, worn occlusal surface accurately located in relative position to each other and to anterior surface of mandibular condyle (k). Two preparations a, b. (From Spee et al.: J. Am. Dent. Assoc. 100:672, 1980.)

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Curve of Spee in Stone Age man 249

Fig. 2. Palate and mandible of Shell Mound Indian, showing marked occlusal and interproximal wear. (From Barton: Dent. Radiogr. Photogr. 2951-56, 1956.)

Turner* used two groups of teeth on models of pa- tients to derive the curve of Spee and its radius. Group A included the tip of the lower canine and the distal cusp of the second molar. Group B used the tip of the lower canine and the distobuccal cusp of the lirst molar. The average radius for Group A was 222 mm. That for Group B was 247 mm. The condyle was not used in any of Turner’s groups of points. This is mentioned here in relation to the current sample’s Group IV points (those not including the condyle).

MATERIALS AND METHOD

The above propositions form the basis for three groups of points used in the current investigation. Thirty-nine Shell Mound Indian skulls from the Ten- nessee river banks showed marked attrition and oblit- eration of cusps (Fig. 2). 3, 4 The skulls met the second proviso suggested by Spee concerning the worn cases.

Each of the skulls was x-rayed in a Margolis cephalostat (Fig. 3) .5

1. Nasion was accurately marked with a small piece of 0.018 inch wire fastened with modeling clay.

2. Orbitale was accurately marked on the lower rim of the left orbit with a small piece of 0.018 inch wire.

3. Porion was selected 3 mm. above the center of the ear rod.

4. The anterior border of the condyle was deter- mined as a tangent to the condyle parallel to the anterior limit of the mandibular canal within the ascending ramus.

5. A distal interocclusal point was established where the occlusal surface of upper third molars met the distal surface of lower third molars in occlusion or where the distal surface of the lower second molars occluded with the upper second molars.

Fig. 3. Cephalometric x-ray image of a Shell Mound Indian skull.

6. The mesial interocclusal point was established where the mesial portion of the maxillary first molar met the mesial portion of the mandibular tirst molar. In the cases in which third molars were not in occlusion, the mesial interocclusal point was where the second deciduous molars or the second premolars met in oc- clusion.

7. The tip of the lower incisor was established as close as possible halfway between the labioincisal line angle and the linguoincisal line angle.

These seven points were entered into a computer by digitizing the points on the individual skull films. The X axis was the Frankfort horizontal plane, and the Y axis was perpendicular to the Frankfort through nasion.

8. An eighth point, which will be called lachryma, was established internally by the computer halfway be- tween nasion and orbitale.

The means and standard deviations for the eight points are shown (Fig. 4) on graph paper. For clarity the squares measure one centimeter.

250 Hitchcock

14r I Y

13 - I

NAClnN

6

I 2 3 4 5 6 7 6 9 IO II 12 I3 I4 I5 I6 I7 I6

Fig. 4. Eight points used in the study, with their standard deviations. The X axis is the Frankfort plane, and the Y axis is perpendicular to it through nasion.

(2) DISTAL lN7EROCCLUSAL 131 MESIAL INTEROccLuSAL

C, AT X - 12.0 f 7.2 Y + IT.0 f 11.4

: 69. I t 12.3 Y

Fig. 5. Curve generated by molar points and anterior point on the condyle. The center of this circle is the closest to that desig- nated by Graf Spee.

The point lachryma, established halfway between nasion and orbitale, was the closest that could be esti- mated for Spee’s designation for the position of the axis of cylinder curvature-‘ ‘. . . at the level of the hori- zontal midorbital plane, posteriorly from the crista lac- rimalis posterior. “l This had to be determined by the computer, because in almost all cases the lacrimal bones of the skulls had been lost over a period of 4,000 or 5,000 years.

According to Spee ‘s proposition 1, the anterior border of the condyle, the distal interocclusal mark, and the mesial interocclusal mark make up a Group I set of three points which can be used to construct a circle (Fig. 5). Spee had indicated that such a circle would have its center somewhere along the horizontal midorbital plane, posterior from the posterior crista lacrimalis.

In line with Spee’s proposition 3, the anterior bor- der of the condyle, the distal interocclusal mark, and the tip of the lower incisor form a Group II set of three points from which a circle was constructed (Fig. 6).

Still in keeping with Spee ‘s proposition 3, a Group III set of three points consists of the condyle, the mesial interocclusal landmark, and the tip of the lower incisor.

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(2) DISTAL INTEKOCCL (3) TIP LDWR INCISOR

C2 AT: X - 3.3 t 6.0 Y 24.0 t 10.3

Curve of Spee in Stone Age man 251

Fig. 6. Curve generated by anterior condyle point, distal molar point, and incisal point.

The profile of a cylinder (circle) was drawn with the use of these points (Fig. 7).

The Group IV collection of points used to generate a circle does not include the condyle and was not con- sidered separately by Spee. However, they involve some of the points which most dentists today think of as comprising the “curve of Spee. ” For illustration, one such set of points had already been located: (1) distal interocclusal point, (2) mesial interocclusal point, and (3) tip of the lower incisor. These formed the Group IV set of points (Fig. 8).

RESULTS

The results of using the Group I set-(l) anterior border of the condyle, (2) distal interocclusal mark, and (3) mesial interocclusal mark-are shown in Fig. 5. The center labeled C, in the diagram turned out to be 7.7 mm. away from the average position of lachryma. The average radius of the circle generated by these three points is 69.1 mm. -+ 12.3, The lower incisal edge will be included in some cases on the plus stan- dard deviation side of the radius. The average length of the radius at 69.1 mm. is included in the radius that Spee mentions toward the end of his article as being 6.5 to 7.0 cm.

Fig. 6 shows the results of using the Group II set: (1) the tip of the lower incisor, (2) a distal interocclusal point, and (3) the anterior surface of the condyle. The center C4 for this group of points has an average radius of 80 mm. and a standard deviation of 10. The point Cz

Fig. 7. Curve generated by anterior condyle point, mesial molar point, and incisal point.

Fig. 8. Curve generated by distal molar point, mesial molar point, and incisal point, without condyle.

is situated 10.5 mm. away from the average lachryma position.

Fig. 7 shows the results of using the Group III set of points: (1) the tip of the lower incisor, (2) the mesial interocclusal landmark, and (3) the condyle. The cen- ter C, has an average radius of 98.9 mm., located 32.7 mm. away from lachryma.

252 Hitchcock

Fig. 8 shows that when the condyle is excluded from the construction of the curve, the variability in- creases markedly. The center of the Group IV set is situated inside a very large rectangle representing the standard deviation. C,, on the average, is 225.2 mm. away from the teeth and 158.4 mm. away from lachryma .

DISCUSSION

The Group I points-condyle, distal interocclusal, and mesial interocclusal-generate the radius which is the closest in length and position to what Spee origi- nally proposed. The length of the radius is at the upper limit of his range of 6.5 to 7.0 cm. In most of the sample, however, the incisor would not be included along the arc generated from that axis. Nowhere in his article does he give the number of skulls that he inves- tigated by this method or the standard deviation. A close examination of his Fig. 1, b shows the arc cutting through the tip of the upper incisor. Presumably, if seen through the tip of the upper incisor, the arc would be contacting the tip of the lower incisor. However, he does not say so in the text of his original article. Spee does say, however: “Their number was not very large because only beautifully preserved and completely de- veloped jaws could be used . . . since good jaws of different races yielded the same findings just described they have a general significance. ”

Later in his paper, in a section called “specific findings in different dentitions,” Spee uses a set of arbitrary points on the occlusal surface and says that “ . . . in most cases . . . a center could be obtained approximately. In some cases with decided abrasion all points were located exactly on the same circle.” This particular current study of skulls with abraded mas- ticatory surfaces does not confirm this when Group II or Group III sets of points are used.

If the condyle is not included in the curve generated only the surfaces or the interocclusal contacts of the teeth are used (Fig. 8). The lengths and positions of the radii exhibit such large deviations that the mean cannot be applied as a standard. Turner,2 as mentioned earlier, did not use the condyle in his studies. The average radius of the Group IV points, at 225.2 mm., falls between Turner’s radii of 222 mm. and 247 mm., which he obtained by using two different sets of occlusal landmarks but without the condyle.

The curve established by a pattern of occlusal landmarks described by Spee has been referred to by some as a “fable. ” Quite probably this attitude is jus- tified if the construction of the curve is limited only to the teeth. With the advent of cephalometrics, the profile

view of the condyle is exposed for easier documenta- tion. As a nonprosthodontist, I can see a series of quite interesting prosthodontic experiments whereby the same patient with the same edentulous models would have dentures constructed along the path generated by the Group I landmarks. The condyle landmark being available from the cephalometric x-ray image, the PO-- sition of the molars could be determined from a center that would be approximately 70 mm. removed from the anterior border of the condyle and 7.5 mm. away from a point halfway between nasion and orbitale. A second set of dentures could be made on duplicate models using Group II landmarks: the condyle, which is known, and the second molars and incisors set at points determined by a radius of approximately 80 mm., with the center of rotation somewhere in the vicinity of 10.5 mm. away from the lachryma point. A denture could also be made using the curve generated by Group III contacts, where the condyle is available and the lower incisor and first mesial interocclusal landmark are used.

A series of experiments with those dentures. de- termining chewing ability, speech, stability and com- fort, and electromyographic recordings, might even give clues as to the amount of curve to be used in finishing up orthodontic cases.

The Group I and Group II points include second and third molars and probably would not yield pertinent information for adolescents. The Group III informa- tion, derived from incisor, first molar, and condyle, might have some application in early and late mixed- dentition cases. Often the orthodontist places the pa- tient in retention before the second molars are fully erupted. Therefore, the curve of the Group III points might be helpful for incorporation into finishing appliances in young adolescents.

The maxillary teeth and the mandibular teeth con- tinue to meet in a downward convex curve and an up- ward concave curve. Whether the ultimate position of this curve will have more or less variability than that described by Spee would make very little, if any, dif- ference in the nomenclature. Such a curved meeting place of upper and lower teeth, viewed from the lateral aspect, will probably always be referred to as the “curve of Spee. ”

REFERENCES I. Spee, F., Biedenbach, M. A., Hotz, M., and Hitchcock, H. P.:

The gliding path of the mandible along the skull, J. Am. Dent. Assoc. loo: 670-675, 1980.

2. Turner, D. S.: A method of classifying overbite and curve of Spee and their correlation with dental classifications of malocclusion, unpublished thesis, University of Texas at Houston Dental Branch, 1973.

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3. Barton, E. I.: Alabamian paleopathology and anomalies, Dent. Radiogr. Photogr. 29: 51-56, 1956.

4. Webb, Wm., DeJarnette, D. L., et al.: An archeological survey of the Pickwick Basin in the adjacent portions of the states of Alabama, Mississippi and Tennessee, Smithsonian Inst. Bureau Am. Ethnol. Bull. 129: 1-2, 1942.

5. Hitchcock, H. P.: Facial variations in Shell Mound Indians, un- published thesis, University of Alabama, 1958.

Curve oj’Spee in Stone Age man 253

Reprint requests to: Dr. H. Perry Hitchcock Department of Orthodontics University of Texas at San Antonio Dental School 2703 Floyd Curl Dr. San Antonio, Texas 78229