On force and tooth movement

On force and tooth movement iL H. Hixon, T. 0. Aaoen,* J. Arango,* R. A. Clark,* R. Klosterman,* S. S. Miller,* and W. M. Odom* Portlannd,

Ore.

.

A

n earlier study of force and rate of orthodontic tooth movement provided enough data to challenge the clinical usefulness of the theories of optimal force and differential force.2 Unfortunately, certain artifacts (namely, tipping tooth movement) which confounded the optimal force theory were also present in our previous data. The problem was primarily mechanical in nature in that heavy arch wires (0.022 by 0.025 inch) were not sufficiently rigid to prevent measurable tipping of tooth movement when the applied forces exceed 100 grams. Consequently, the present investigation was undertaken to produce bodily canine movement so as to provide a better understanding of the relationship between force and the rate of tooth movement. Tipping tooth movement introduces several variables which mask study of the relationship between force and rate of tooth movement. Besides the initial compression of the periodontal ligament (PDL), the most obvious variable is the unequal distribution of the load along the root. The high load at the alveolar crest, which decreases to zero at the axis of rotation, is also capable of deforming the wall of the socket. The magnitude of such bone bending may also -be sufficient to influence interpretation of the data utilized for studying tooth move. ment.3-g This is obviously of some importance for an understanding of initial mechanical response of the PDL and bone. It may also have implications for an understanding of the clinically more important long-term metabolic changes induced in the supporting tissues. t While bodily tooth movement helps clarify the picture by reducing much of the initial tissue deformation, it does not permit one to assume that the applied

476

*Summary of Oregon Dental

theses submitted Sohoo1.l

tDeformation “tooth bending” our study.10

of

for

certificate

a tooth under load has been is too small to be of either

in

orthodontics

at

the

University

measured, but the magnitude of clinical or theoretical significance

of this to

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pressure is equally distributed over every square millimeter of the root. One need only recall the porosity of the alveolar socket and the fact that the compression and the stretching of the PDL cannot be a constant around the curved surfaces of the tooth and socket, especially on the buccal and lingual aspects of the tooth. Nevertheless, elimination of some of the variables introduced by tipping tooth movement should provide a better clinical description of cellular response to force. Research

protocol

The subjects for this study were six children, 12 to 15 years of age, who required removal of four first premolars and distal retraction of the canines for correction of their malocclusions. Canine, second premolar, and first molar bands were transferred from the patients to plaster models (by means of an impression) to permit soldering of 0.045 inch tubes to the buccal and lingual surfaces of the posterior segments (parallel to the occlusal plane and to each other), soldering of the premolar and molar bands to each other, and placement of 0.045 inch wires through the tubes to then be soldered to the canines (Fig. 1). Four such units were cemented in each patient for two weeks and left before activation. While dividing the elastic traction equally between the buccal and lingual arches solved the problem of rotation (Fig. l), we were unable to eliminate tipping of all teeth. Of the twenty-four quadrants under study, a total of nineteen teeth (nine maxillary canines, seven mandibular canines, and three mandibular molars) met the rather rigid criteria established for bodily tooth movement. After we discovered that tipping sometimes occurred despite two 0.045 inch arches, a simulated system was used to measure the deflection of these wires (Figs. 2 and 3). This was done with the aid of a traveling microscope which could detect deflection of less than 3 microns from the rest position. The standard error of the measurement (S.E. meas.) was 0.017 mm. The mechanical couple produced by placing one force at the crown and the other at the apex is probably more severe than that produced in patients because the PDL and the alveolar bone, even at the crest, ,offer some resistance to de-

Fig.

1,

Appliance

employed

for

bodily

tooth

movement.

478

Hixon

Fig. 2. Laboratory

Amer.

et al.

mock-up

of

appliance

to

study

arch

deflection,

static,

J. Orthodont. May 1970

and

dynamic

friction.

Fig. 3.

Portrayal of how deflection generated by the equal and opposing resistance of the periodontal ligament than occurs in the oral cavity (where in the mouth, there is tipping of both band was soldered to the molar band

of

arch wire was measured when a couple was forces. The force at the apex substitutes for the and bone and probably creates a stronger couple the arch bends as shown by the dotted line). Also, the canine and the molar even though the premolar in this experiment.

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formation. It was rather surprising to note a deflection of 1.5 mm. with opposing 1,000 Gm. forces and a 20 mm. span between the buccal tubes and the canines.12 Fig. 4 portrays the range of deflection at this distance for two 0.045 inch arches and for forces between 0 and 1,400 Gm. By way of comparison with the usual clinical situation, the deflection with a 7 mm. span is included for both the 0.045 inch appliance and an edgewise arch. The deflection of an 0.0215 by 0.028 inch wire with a 7 mm. span between the brackets is especially worth noting. With this steel arch, which is “heavy” by clinical standards, there was a 1.0 mm. deflection (which permits tipping) when 200 Gm. forces were applied. While these findings illustrate one reason that only two thirds of the canines and one fourth of the mandibular molar units moved bodily, they also indicate that retraction, even with conventional (0.014 to 0.022 inch) arches, probably consists of initial tipping movements as the arch bends, followed by a certain amount of uprighting as the activating force exhausts itself before reactivation. With the Begg technique there is but one large “tipping” and one “uprighting” movement, as compared to a series of such movements with conventional arches. While describing the mechanical system employed in this study, consideration must be given to how much of the applied force was delivered to the teeth. This involved study of the loss of force through friction as well as through decay of the elastics in saliva. The apparatus illustrated in Fig. 2 was also used to measure the maximum friction encountered in this study. After the addition of equal weights (from 50 to 1,400 Gm.) to the threads pulling at the occlusal

DEFLECTION OF WIRE (mm.1 Fig. 4. Deflection of two “arch The deflection of the two 0.045 rectangular arch and a 7 mm.

as portrayed in Fig. 3, with differing force wires,” inch arches with a 20 mm. span is less than with the span.

loads. heavy

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STATIC PRICTIOU :$ - .007j

v-i

Fig. 5. The per

cent

static of applied

friction force.

and

kinetic

friction

of

0.045

inch

appliances

are

presented

as

surface and the apex, additional small increments were then added to the thread pulling at the occlusal level until the wires moved through the parallel tubes in the center support. The additional weight necessary to cause movement of the tooth is plotted in Fig. 5 as a per cent of applied forces to the couple.” The static friction varied from 10 per cent of the applied force at 50 Cm. to 20 per cent at 1,400 Gm. (S.E. meas. of 0.44 per cent). When this apparatus was employed in the patient, however, it was subject to a variety of oral forces, especially from mastication, which produced other motions and permitted the wire to slide through the tube more easily. An estimate of this dynamic (or kinetic) friction was obtained by repeating the above procedure but vibrating the apparatus with an electrical (60 cycle) vibrator. After computation of the linear regression of the equation describing the results, the slope was so minute (0.0005) that dynamic or kinetic friction was accepted as 5 per cent of the applied force, irrespective of the forces of magnitude. The force delivered by the elastics which activated the appliance was *The deviation rate regression for all thirty-six

of the equations points.

static were

friction in the not significantly

600 Gm. different,

range was tested, but since sepaa single linear model was adopted

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Per

cent

of

elastic

force

lost

in

481

vivo

Fig. 6. Per cent of elastic force lost under tension in vivo.

measured each time they were applied and again when they were removed (three times a week). When it was noted that the force decayed more than 15 per cent during the 2- and 3-day intervals, a rather detailed investigation of elastic force decay (while under tension) was undertaken, utilizing an Instron tensile testing instrument.13 The primary finding, as shown in Fig. 6, was a rapid initial loss of force (13 per cent in 3 hours) followed by a slow loss of 3 per cent before elastics were changed. Although all elastics were latex, the loss was greater for the lighter (2 ounce) than the heavier (6 ounce) elastics. However, the rate of decay after the first 3 hours (slope of the lines in Fig. 5) was not different.* Because of this factor, because the elastics were used in combinations, and because the elastics were occasionally nicked from mastication, we decided to utilize the average of the forces that the elastics delivered at the time they were removed (three times a week) as the single figure which best represented *From the regression model used, it was possible to test the effects of differing media (water, air, saliva, and the differences in saliva), the weight of the elastic, the initial force, the force at 3 hours, the force at 72 hours, and the interaction of these factors.13 After the effects of the media were removed, the slope of the lines did not change and a comparison of end-point values (after adjusting initial values) gave F,,, = 0.21.

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force applied to the teeth. The average of these forces for the 8-week period underestimates the average force delivered, but it nearly offsets the loss of applied force attributable to kinetic friction (5 per cent). Further adjustment was not deemed meaningful, since the reliability of measurements in calibrating the elastics (S.E. meas. = 4 per cent) is larger than the unaccountable residual from the effects of friction and elastic decay. It can be said with considerable confidence, however, that the oscillations of the forces acting on the teeth during the S-week period rarely exceeded 10 per cent of the figures given as the “mean” force applied to the teeth. To provide fixed landmarks against which to measure tooth movement, tantalum implants were placed in the maxilla and the mandible after the method of Bj6rk.14-16 Open-mouth head films were then secured with the head holder rotated 25 degrees toward the film, so that the posterior segment of each film was approximately parallel to the filnl.2 Measurements of tooth movement were secured by first scribing a vertical line through an anatomic landmark on the crown and at the apex of the image of the tooth in the initial film and repeating this procedure in the final film. By superimposing on the metallic implants, measurements between the scribed lines (on initial and final films) then depicted tooth movement through the bone (S.E. meas. = 0.2 mm.). Measurements of relative tooth movement (space closure) were secured from alginate impressions collected three times a week for the 8-week period (S.E. meas. = 0.08). As indicated earlier, only two thirds of the canines and one fourth of the available molars met t,he criteria established for bodily movement. The requirements were (1) clear initial and final x-rays (25 degree head films) of the crown and the apex of the tooth under study, (2) the three implants coincided with each other within 0.2 mm.@ when the initial and final tooth movement films were superimposed, (3) the scribed lines through the teeth before and after tooth movement were within 0.2 mm. of parallel, and (4) space closure as measured on the film and the casts agreed within 0.5 mm. Because of the wide variation in canine root area,2’ 17-26it was hoped that a clinically useful technique (correlation coefficient r = 0.8 or better) could be devised to estimate the surface area of the roots from their radiographic image. H By knowing the average force per square millimeter of root area, one might better describe the cellular response to force and study anchorage in greater detail. To this end, another attempt was made to estimate root area from radiographs. This time tracings of the images of roots of mandibular teeth were made from cephalometric films of a group of adults scheduled for extractions. After extraction the roots of teeth were painted with a rubber-base impression material, and the area of the impression measured with a photogenerative cell in the same manner described previously.2 Since the correlations were lower than those obtained from intraoral radiographs of roots obtained with a *With sagittal in the slightest

conventional cephalometric techniques, most landmarks are either in the midplane or are bilateral landmarks from which the midpoint behaves as if it were midsagittal plane. Since implants are in non-midline planes, they reflect even the change in head position between films.

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Table I. Root areas for selected mandibular Tooth Canine First premolar Second premolar First molar

483

teeth

N

Mean. (112m.p)

18 58 52 11

302 220 234 525

S. D. (mm.“) 50 31 26 76

c. r. (per cent) 16 14 11 15

16 inch cone, this effort was not pursued. Table I, which presents the data on root area, again emphasizes large variability (C. V. = 15 per cent) between persons. Even within this small sample, one canine had but 190 mm.2 root area and another had 345 mm.2 The clinical significance of this variability lies in the fact that a given appliance force may exert twice as much pressure per square millimeter of root area for one patient as for another. Findings

When the total bodily movement of the mandibular canines (Fig. 7) and maxillary canines (Fig. 8) is plotted against the force applied to the teeth, the first and most obvious observation is the wide variation in response between individuals.* Within a given person there is an observable tendency for the higher forces to move teeth farther in 8 weeks than can be done with lighter forces.2s This is reflected by the dotted line which connects the right and left canine movement for the same person. In all but one pair of maxillary canines (Patient 3, Fig. 8), the higher force produced a greater movement than the lighter force. A comparison of Figs. 7 and 8 also suggests that maxillary canines move somewhat more rapidly than their mandibular counterparts. Far more important to an understanding of the tissue response to force is the time series analysis shown in Fig. 9. Before these are noted, a little more background on how data were collected will be helpful in interpreting the results. Whenever one of the molars (in one case, a canine) moved less than 0.2 mm. in relation to the metallic implants during the 8-week period of study, space closure was attributed to movement of the other tooth.2g The space closures as measured on the casts (which were taken 3 times a week) were then plotted against time.t Space closure of less than 0.20 mm. was considered *Because criteria quantity discussed

two canines from one patient (B) from a previous for bodily tooth movement, these data are included of information available. The minor deviation from in another footnote.

study2 essentially met the to supplement the meager the established criteria is

tAlthough a more conservative protocol would define the limits of measurement error as ? 2 S. E. meas. of the radiograph (or ?r 0.40 mm.), the coincidence of the information derived from the casts with their small S. E. meas. of 0.08 mm. and the radiograph made 0.20 mm. “seem” a reasonable estimate to use at the present state of the art. The inclusion of data from a previous study to augment our knowledge (Patient B) includes one “blip” of 0.25 mm. movement the first day. This undoubtedly reflects initial mechanical tipping. Otherwise, the data appear to reflect the metabolic response to tooth movement. Additional details are found in an article by Hixon and associates2 which appeared last year.

484

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5 .

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4 .

/ *-------- P

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200

300

I

L

I

I

.

,

,

1

400

500

600

700

800

900

1000

1100

Force

(grams)

*I+0 days

Fig. 7. Bodily movement of maxillary canines (average for 8 weeks meters per week). Whenever data from both the right and left sides were available, the results were identified with a dashed line.

B // /

i 1’

1’ 4’ T 5*' I,

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expressed as milliof the same patient

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II 500

I,. 600 (grams)

11 700

1 I, BOO 900

1 1,.I I moo 1100

*40 days

Fig. 8. Bodily movement of mandibular canines (average for 8 weeks meters per week). Whenever data from both the right and left sides were available, the results were identified with a dashed line.

of

expressed as millithe same patient

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3Ol*m%

Mood.- 6

6061~.

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64.3~~~.

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DAYS Fig. 9. Rate of

measurement

curves

for canine error which

retraction. includes

The gray some tipping

zone of 0.20 mm. represents an estimate and the initial “blip” noted in Patient

B.

as within the zone which included measurement error, that is, movement of the “stable” tooth, tipping of either or both teeth, as well as comparison of the PDL and possible deformation of the bone. To return to the results portrayed in Fig. 9, one can note, aside from minor tipping the first day, that the mandibular canine movement for one patient (B) exceeded the measurement error in 14 days, while for another patient (No. 2) no movement was detected (0.20 mm.) by the end of the 56-day experiment. For both, the applied force was in the 300 Gm. range. Other force values initiated bodily tooth movement at intermediate times, irrespective of whether the force was greater or less than 300 Gm. The slopes of the lines are too short and too variable to permit a meaningful generalization about the rate of movement after it has been initiated. One might again note that in data obtained on both the right and left sides of the same patient (Patients B and 2), the higher forces initiated a metabolic response slightly sooner and at a more rapid rate. The data collected which relate to anchorage and differential force are also nebulous and are presented more as a guide to future investigators than to argue a theoretical concept. Fig. 10 displays the usable data regarding the mesial crown movement of the mandibular molars and premolars in relation to the distal bodily movement of the corresponding canine.3o The three molars which moved bodily are those of Patient 2 (at 132 and 354 Cm.) and Patient 3 (at 328 Cm.), while all others manifest measurable (more than 0.2 mm.)

486

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DIFFERENCE IN CUSPID AND MOLAR MOVEMENT Movement (id 1.0 Patient

Forc.(@ns)

2

132

3

328

2

354

4

bo

5

213

5

214

3

650

1

1037

CuSPlD

MOLAR

2.0

1.0

3.0

c

Fig. 10. Distal movement of the canine is portrayed mesial movement of the molar and premolar of right. The length of the bars represents millimeters

on the the same of crown

left of the quadrant movement

vertical line is portrayed in 8 weeks.

and on

the the

mesial tipping of the molar and premolar. Since bodily movement of the canines was involved in all cases, only these three provide any data which relate to differential force. The difference between the two sides in Patient 2 and the difference between Patients 2 and 3 at the 300 Cm. level certainly are not in agreement with the concept of differential force. As one would expect from the manner of measuring, those molars which tipped generally showed greater space closure than the three which moved bodily. Discussion

As in the previous study, a major conclusion is that the large variation between patients precludes formulation of simple theories regarding force and anchorage. Perhaps this is why the more experienced practitioners tend to “eyeball” forces rather than become deeply entangled in theory. To begin with, the flexion of most arch wires is such that they are incapable of preventing some tipping. Thus, there is a high probability that initial canine retraction is a tipping movement and the resulting deformation of the alveolar crestal bone (especially on the distal aspect of the canine with forces in excess of 100 Gm.) introduces great variation in the physical load per unit of area in different parts of the root. Even when this is controlled, one must remember the 2 :1 ratio in root area which introduces a large source

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of variation in load per unit of root area. As yet, the variation cannot be determined from radiographs with sufficient accuracy (r = 0.8 or better) to warrant adjustment of data. When tipping is eliminated and bodily tooth movement ensues, there appear to be two distinct stages of tooth movement. One is the small initial mechanical compression of the PDL. This is followed in a couple of weeks by bone resorption and tooth movement which reflects the metabolic shifts that undoubtedly involve changes of the DNA, RNA, and enzyme “dynamic equilibrium ’ ’ of the connective tissue cells. This is the bodily translation of canines which forms the pattern of tooth movement seen in the right side of Fig. 7. The variation in initiation as well as the rate of movement is well known to all clinicians. These data indicate that the major source of variation is probably not the magnitude of force but variation in metabolic response. For e.xample, Patient B (from the previous study) continued to show rapid tooth movement (and good cooperation) so that all treatment was completed and appliances were removed 13 months after the study began. Another slightly older patient (not included in this study) showed less than 3 mm. of space closure (combined molar and canine movement) in the same 13 months with the same 300 Cm. force and good cooperation. Besides the variation in local metabolism, most of us are aware of the changes in rates of general metabolism with age. Another variable involved in tooth movement related to age is concerned with the rate of facial growth. In the adult (or the near adult), when facial growth is essentially complete, the canine must be translated horizontally through bone. In younger children with an increasing facial height, the canine is erupting and may be moved “diagonally” through developing bone. In addition to active deposition and resorption, there is an “occlusal and distal” translation relative to the mandible or maxilla. The data presented here regarding differential force and anchorage are limited but tend to confirm the earlier conclusion that there is no evidence to support the theory of differential force. The fact that molars that did not tip moved less than those that did tends to argue for the use of tip-back bends or angulated brackets to minimize anchorage loss. Such mechanics overcome mechanical weakness of the arch and tend to equalize the distribution of force throughout the molar root and perhaps minimize mesial movement. Conclusions

1. The mechanical flexion inherent in all arch wires permits considerable tipping tooth movement. This impedes collection of valid (as distinct from reliable) data that might be useful in constructing clinically useful theories of orthodontic tooth movement. 2. Other important observations of this study were the large differences between patients with regard to root area, time of beginning tooth movement, and rate of tooth movement. The magnitude of the variation in each of these factors (none of which can be controlled by the orthodontist) are far more important than differences in magnitude of force (above 100 Cm.). That the

488

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J. Orthodont. May 1970

higher forces produce more rapid movement than lighter ones is generally valid within an individual patient, although the contribution of this difference is small in relation to the metabolic variation between patients. 3. It appears meaningful to distinguish at least two phases of tooth movement : (1) an initial mechanical displacement of tissues and (2) a delayed metabolic response of the connective tissues. The first stage probably includes measurable deformation of alveolar bone as well as compression of the PDL when the applied forces exceed 100 Gm. The variation in the physiologic or biochemical response of the tooth-supporting apparatus is large. Clinically measurable response was detected in 2 weeks for some persons, while none could be found in 8 weeks for other patients. The authors wish consolation provided Dental School.

to express their by D. B. Mahler

appreciation and F. M.

for the Sorenson

invaluable help, of the University

advice, ant1 of Oregon

REFERENCES

1. Hixon, E. H. : Graduate education and the training of orthodontists, AM. J. ORTHOIXINTICS 49: 521, 1963. 2. Hixon, E. H., Atikian, H., Callow, G. E., McDonald, IL W., and Tacy, R. J.: Optimal force, differential force, and anchorage, AM. J. ORTHODONTICS 55: 437-457, 1969. 3. Muhlemann, H., and Zander, H. A.: The mechanics of tooth mobility, II, J. Periodont. 25: 127, 1954. 4. Muhlemann, H.: Tooth mobility: A review, J. Periodont. 38: 114-686, 1967. 5. Pieton, D. C. A: On the role played by the socket in tooth support, Arch. Oral. Biol. 10: 945, 1965. 6. Picton, D. C. A., and Davis, W. I. R.: Dimensional changes in the periodontal membrane of monkeys, Arch. Oral. Biol. 12: 1635, 1967. 7. Parfitt, G. J.: The physical analysis of the tooth-supporting structures. In The Mechanisms of Tooth Support, Bristol, 1967, John Wright & Sons, Ltd., p. 154. 8. Miller, S.: Rotational axes in human incisor teeth, M. S. thesis, University of Oregon Dental School, 1966. 9. Baumrind, 5.: A reconsideration of the propriety of the “pressure-tension” hypothesis, AM. J. ORTHODONTICS 55: 12, 1969. 10. Korber, K. H., and Korber, E.: Patterns of physiological movement in tooth support. In The Mechanisms of Tooth Support, Bristol, 1967, John Wright & Sons, Ltd., p. 148. 11. Miller, S. S.: Bodily retraction of cuspids, Certificate thesis, University of Oregon Dental School, 1969. 12. Odom, W. M.: The effect of the oral environment on the rate of elastic decay, Certificate thesis, University of Oregon Dental School, 1969. 13. BjSrk, A.: Facial growth in man studied with the aid of metallic implants, Acta odont. scandinav. 13: 9, 1955. 14. Bjiirk, A. : Variation in the growth pattern of the human mandible : Longitudinal roentgenographic study by the implant method, J. D. Res. 42: 400, 1963. 15. Bjiirk, A.: The use of metallic implants in the study of facial growth in children: Method and application, Am. J. Phys. Anthrop. 29: 2, 1968. 16. Jepsen, A.: Root surface measurement and a method for x-ray determination of root surface area, Acta odont. scandinav. 21: 35, 1963. 17. Tylman, 5. D.: Theory and practice of crown and bridge prosthodontics, ed. 2, St. Louis, 1947, The C. V. Mosby Company. 18. Brown, R.: A method of measurement of root area, J. Canad. Dent. A. 16: 136, 1950. 19. Kay, S., Forscher, B. K., and Sackett, L. M.: Tooth root length-volume relationships, an

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22. 23.

24. 25. 26. 27. 28. 29.

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aid to periodontal prognosis. I. Anterior Teeth, Oral Surg., Oral Med. & Oral Path. 7: 735, 1954. Phillips, J. R.: Apical root resorption under orthodontic therapy, Angle Orthodontist 25: 1, 1955. Boyd, J. L., Watt, D. M., MacGregor, A. R., Geddes, M., and Cockburn, A.: A preliminary investigation of the support of partial dentures and its relationship to vertical loads, D. Practitioner 9: 2, 1958. Freeman, D. C.: Root surface area related to anchorage in the Begg technique, Master’s thesis, University of Tennessee, Memphis, 1965. Comparative odontometry of the Moss, M. L., Chase, P. S., and Howes, R. I., Jr.: permanent post-canine dentition of American whites and Negroes, Am. 5. Phys. Anthrop. 27: 125, 1967. Emmanuelli, J. R.: A study of the effective and total root surface area of extracted mandibular human teeth (Abst.), AM. J. ORTHODOWICS 56: 437, 1969. Taylor, R. M. S.: Variation in form of human teeth. II. An anthropologic and forensic study of maxillary canines, J. D. l&s. 48: 173, 1969. Clark, R. A.: Root surface area, Certificate thesis, University of Oregon Dental School, 1969. Arango, Jorge: Rate of cuspid movement as related to force, Certificate thesis, University of Oregon Dental School, 1969. Klosterman, Robert: Patterns of tooth movement, Certificate thesis, University of Oregon Dental School, 1969. Aasen, Tore 0.: A study of rate of molar movement as related to force, Certificate thesis, University of Oregon Dental School, 1969. 611

S.W.

Campzls

Dr.