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A method for structural mandibular superimpositioning
A method for structural mandibular superimpositioning d. M. H. Dibbets Groningen, The Netherlands
Structural mandibular superimpositioning on stable natural references has gained wide acceptance in the orthodontic literature. However, accurate instructions that provide a simple step-by-step procedure are not readily available. Considering the specific method described here and assuming stability of the natural reference structures, a reliable procedure for marking two artificial references (simulating "implants") on mandibles in a longitudinal series of cephalograms appears to be possible. In essence, the method is based on the construction of a template, drawn on a small auxiliary tracing sheet, which contains only information relevant for structural mandibular superimpositioning plus error checks. This template is subsequently superimposed on the radiographs in a longitudinal series by the structural method, which permits the transference of two fiducial points. These fiducial points consequently replace the images of metallic implants and thus facilitate local superimpositioning of mandibles. It is a convenient method for longitudinal growth research as well as for any two successive records in the clinical situation. (AMJ ORTHOD DENTOFACORTHOP 1990;97:66-73.)
L o c a l superimpositioning on mandibular structures has found wide acceptance since Bj/Srk's publications. Because the use of implants is not routinely indicated for clinical purposes, Bj6rk) in 1969, suggested certain stable structures within the mandible as acceptable substitutes. Bj6rk had observed that the mandibular canal, the molar crypts, the endosteal surfaces of the mandible in the symphyseal area, and the periosteal surfaces at pogonion appeared to be remodeled at a comparatively slow rate, thereby making these structures reasonable substitutes for the metallic implant. This observation formed the basis for the method to be described here. Although much has been published on the reliability of head film measurements, 27 only a few studies on the applicability of what has come to be known as the "mandibular structural method" are available. A detailed listing of stable structures was given by Bj6rk and Skieller? Solow and Siersbaek-Nielsen 9 superimposed radiographs directly and reported as method error that "the mandible could usually be assessed within ± 3 ° by the structure-based method . . . . " Buschang and associates ~° studied errors inherent in the method of superimpositioning and concluded that " . . . mandibular superimposition is less reliable than cranial base superimposition, a l t h o u g h . . , the methodology is reFrom the Department of Orthodontics, School of Dentistry, University of Groningen. 8/1/10369
66
liable." On the other hand, Ari-Viro and Wisth" disputed the reliability of the method. Recently, Cook and Gravely 12 studied tracing errors for mandibular structures and concluded that error levels of horizontal measurements were less than those of the vertical ones. Baumrind et al. 2'3 and Isaacson et al? 3 developed procedures by which fiducial points were transferred from tracing to tracing after establishment of best fit. These fiducial points facilitated repeated superimpositioning later on. This procedure was elegantly modified for manual applications by Moorrees et al? 4 However, all these methods depend on the superimpositioning of tracings on which the reference structures have been previously marked. In our experience, this superimposition of mandibular tracings is laborious and the results are unsatisfactory. Therefore, it was decided to modify the known methods and to develop a new and improved procedure for locating fiducial points on head film tracings. The resulting method is quick because, in a series, the natural reference structures have to be marked only once. It is reliable because these reference structures are taken from one selected best cephalogram. It is convenient because the template is small and therefore is manipulated easily. Finally, it provides two built-in safeguards against errors. First, the method is described, beginning with the procedure for construction of a template on a separate tracing sheet. The template then has to be superimposed on the stable mandibular reference structures of the successive radiographs in a longitudinal series, with addition to the
Volume 97 Number I
Structural mandibular superimpositioning
o ~
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.
t
Articulare'--___.-
5~4 -.
',,
Canal
"-
"
Crypts
Gonial angle Fig. 1. TemPlate on auxiliary tracing sheet, !0 x 15 cm maximum, drawn from best radiograph of longitudinal series (i.e., 1954). The natural reference structures of symphysis, middle of the opaque lower demarcation of the canal, and bottom of the crypts are drawn. Pogonion is added for horizontal reference; the gonial angle for vertical help. Articulate, labeled for the year of photograph (1954), is going to serve as a "double check" before transference of fiducial points. The broken line indicates the contours of the 1954 mandible a/ldis depicted only as an illustration of the total structure. This template is constructed in step 3 of the procedure.
template of the landmark articulare, which is going to serve as a safeguard against errors. Next, two holes are drilled in this template, permitting the reproducible transference of two fiducial points. These fiduciai points are subsequently transferred with lead pencil after a second SUl~erimpositioning o f the template on stable structures and a "security check" for the position of articulare. Since the method proved reliable in actual practice, an indication of the precision of the procedure is obtained by quadrupl!ng of the template on one random series of t~,eive radiogrfipfis. MATERIAL AND METHOD
Any longitudinal series of two or more cephalograms may/:onstitute the material for the method to be described. For illustration of the procedural steps, a series o f 12 radiographs from the Groningen elementary school study was selected randomly. In t.his study, standardized cephalograms were taken at yearly intervals of children from the elementary schools in Groningen. Descript.ion of the method
The pi'ocedure consists of seven successive steps. Step 1. Conventional tracings are made. All usual structures may be drawn except for the natural structural mandibular references: the inner contour of the 6Tmphysis, the molar copts, the (pre)molar apices, and the canal. This series of x-ray films, complete with tracings, is .stacked chronologically. Step 2. The best x-ray film from this series is selected according !o the following quality criteria: • Best contrast. In ad(!ition, the crypts must be
sharply projected and the opaque contours of the mandibular canal or parts of it must be clearly visible. • Best symmetry. Rotation or canting of the head is minimal; mandibular contours, molar crypts, teeth, and canals are maximally overprojected. The symphysis should show a sharp inner contour. • Teeth in occlusion, with no dual bite. From this selected best film, the natural reference structures are copied. Step 3. On a small (10 x 15 cm maximum) auxiliary tracing sheet overlaying the selected best film, the following natural reference structures are marked to serve as a template (Fig. 1): • The middle of the opaque demarcation of the lower border from the mandibular canal. • The middle of the opaque semicircular demarcation of the molar crypts. • The semicircular demarcation of the apices of erupted molars. • The outer contour of the symphysis, from menton to pogonion. • The inner contour of the symphysis on the sharp demarcation between white (bone) and black (interior), ventrally following the inner contour as high (cranially) as possible. These structures have been reported as relativelY stable throughout growth.~'8 As a safeguard against errors, two additional references are marked: articulare and the contour (averaged for left and right) of the gonial angle. These references must be labeled for the year of the radiograph. This security procedure is completed in steps 4 and 5.
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Dibbets
Am. J. Orthod. Dentofizc. Orthop. Janua O. 1 9 9 0
I I
I
",76
"'--__-~'"
% % % % % % %
,,
54- "51 ~
Fig. 2. Template marked for articulare and gonial contour of youngest (1951) and oldest (1976) cephalograms of longitudinal series. This provides an indication of the extreme values. Intermediate gonial contours and landmarks articulare will occupy positions between these extremes. The mandibular canal may be extended on later photographs, or crypts may be added. It is advised that all available structural information be concentrated on the template. This represents step 4 of the procedure.
.76 .62 61",60 59" 58
5~,"~5653 7 6 ~ l J
Fig. 3. The template has been structurally superimposed on all successive cephalograms of one series. Articulare is always transferred to the template, the gonial contour only when helpful (in this case, 1958). The numbers indicate the years in which the radiographs were taken: 1951, 1952, 1953, 1954, 1956, 1957, 1958, 1959, 1960, 1961, 1962, and 1976. The oblique cluster labeled 51 to 76 represents the twelve landmarks articulare. This represents step 5 of the procedure.
Step 4. Articulare and the gonial contour of the newest and oldest cephalograms available are marked on the template. For this purpose, the template is superimposed on the radiographs by the structural method, with best fit established on the symphyseal inner contour, the canal, and the crypts. First, the best fit is established on the inner contour of the symphysis and the template is held gently with a finger at the symphysis so as to create a fulcrum around Which the template may bE rotated. Throflgh rotation, the best fit of the mandibular structures in the corpus is located: the middle of the lower opaque demarcation of the canal and crypts. Then the symphysis is readjusted, and subse-
quently the best fit for canal and crypt is established. After establishment of the best fit, articulare and the gonial contour are marked on the template, with a reference to their date (as 1951 and 1976 in our illustrations, Fig. 2). Step 5. The security procedure is completed by structural superimpositioning of the template on the whole series of cephalograms (plus overall tracings). Articulare is always marked on the template and labeled for the date of the photograph, and the gonial angle is marked only when helpful (too many lines may become confusing). The result is depicted in Fig. 3. These references will later be used as a "security check."
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Structural mandibular superimpositioning
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.62 61",60 59" 58
57",5653 76~58~54
51,'~
~-
~--
Fig. 4. Two 0.5 mm holes are drilled through tracing sheet, 50 mm apart and representing Iocat!on of fiducial points (step 6). When the template is readjusted onto the radiographs and tracings, the location of these hoIes permits easy transference of fiducial points by marking with a lead pencil (step 7).
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Fig. 5. Approximation of precision of method. The procedure, up to step 5 and Fig. 3, was repeated four times on one randomly selected longitudinal series of 12 yearly cephalograms. The 12 scatter plots, of four landmarks articulare each, are indicative of the dispersion resulting from error. The scale is in millimeters.
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70
90%
Dibbers
= 1,1 m m
Am. J.
~
1
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Fig. 6. The twelve scatter plots from Fig. 5, of four landmarks articulare each, superimposed on their geometric centers. The 90th percentile is indicated by a 1.1 mm circle.
Step 6. The next step in the procedure is the drilling of two 0.5 mm holes in the template, 50 mm apart in the "corpus" of the mandible, as shown in Fig. 4. Their position is not critical, but we prefer to keep them inside the mandibular contour (see Discussion). This arbitrary distance of 50 mm is easily obtained by means of a simple Plexiglas or acrylic plastic jig and a 0.5 mm drill in a small holder. After these preparations, the template is ready for transference of fiducial points. Step 7. The position of the fiducial points is established by structural superimposition of the template on the series of radiographs (plus overall tracing) for a second time. As a safeguard against errors, it isadvisable in this second procedure not to "peek" at the position of the previously marked articulare. Only after the best fit on symphysis, molar crypts and canal has been found is articulare used as a check. Differences Of more than 1 mm between the actual and the previously located articulare should be regarded as an indication that more trials are necessary (see Results and Discussion). After a satisfactory fit has been found, the two fiducial points are transferred onto the original overall tracing by means of a pencil mark through the t.wo holes in the template. These two dots consequently indicate structurally determined "stable references" for this particular lower jaw. Indication of precision To assess the precision of the method, the procedure for constructing the template was repeated four times in one randomly selecl(ed longitudinal series of 12 radiographs. This included four independent determinations of articulare on each of 12 individual radiographs. There had been an interval of severa ! days between
Orthod. Dentofac. Orthop. January 1990
construction of the templates. This represented the procedure up to and including step 5 (Fig. 3). Since the PrOcedure essentially consists of a rotation around the inner symphyseal contour, the error will be maximal at the most distant landmark. Thus the position of articulare on the template can be expected to display the largest error--in any event, larger than the error in the subsequent marking of fiducial points. The four templates resulting from the four repeated procedures, each with 12 landmarks "articulare" (as i n Fig. 3), were digitized and superimposed by computer. This superimpositioning was performed through minimizing of the distances of the corresponding yearly time-point landmarks articulare by means of"least squares" procedures for finding the best fit between the four separate scatters of twelve landmarks. The dispersion of the four positions of articulare for each radiograph was studied after the results were plotted. To minimize the bias of a marked deviation in any one year under study, the positions of articulare in the year to be plotted were not used in the computing of the least squares. Consequently, the twelve plots, each representing a yearly scatter of four landmarks articulare, had to be produced in twelve separate computer runs. A further illustration of the total dispersion was obtained by depiction of 4 x 12 = 48 single determinations of articulare. This was performed by computation of the center of each yearly scatter (of four landmarks articulare) and by subsequent superimpositioning of the twelve scatters on their centers. Finally, precision was assessed b y comparison of angular measurements. The angular values from articulare-pogonion and a tangent to the lower border of the mandible were computed. The lower-border tangent was drawn arbitrarily to the mandible on the template in each of the four trials. Consequently the computations for the angular values articulare-pogonion to the lowerborder tangent differed systematically for each o f the four templates. Therefore the resulting four sets of twelve angular measurements could not be compared directly. To estimate the standard deviation of residual, a two-way analysis of variance (i.e., angular measurement with the systematic factors of "trial" and "year of photograph") was applied. The standard deviation of residual may be considered as measurement error. RESULTS When the procedure is followed up to step 7 for all radiographs in one series, the mandibles will be marked with two fiducial points. The distance between these points is fixed, while their position represents the stability of natural reference structures. These two fiducial points subsequentlY may serve as reference landmarks for local superimpositioning by computer or by handl
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Structural mandibular superimpositionhzg
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~-~76 ,,62~ 61",,60 ~ 59" 58
s-?,56sa Pg
~51
~76
M P ~
Fig. 7. A tangent to the lower border, NIP, and a line connecting articulare-pogonion, define angle a. The tangent MP is drawn arbitrarily by hand to the lower border' on the template, and therefore the position relative to articulare-pogonion will differ from template to template. Consequently, the angular values of ~ in each of the four trials shown in TabIe I will differ systematically. In the illustration the construction of ~ for 1976 and 1951 is depicted (method error).
Table I. Two-way analysis of variance of angle articulare-pogonion to an arbitrary tangent to lower border (in degrees)
I 1 11 1952 I 1
2 3 4 Age
0.9 0.4 0.9 0.4 6.8
1.2 0.6 1.3 0.9 7.9
I 1954 I 1.6 1.1 1.0 1.0 8.7
1.8 1.4 1.2 1.8 9.9
I 3.6 2.8 3.1 3.7 12.4
I 4.5 4.3 4.2 4.0 13.5
I 4.9 4.4 4.6 4.2 13.9
i 1960 ( 1961 ( 1 62 6.9 6.4 6.7 6.4 14.8
8.1 7.5 8.3 8.0 15.9
8.9 9.2 9.1 9.1 16.8
10.2 9.5 9.9 10.0 17.8
1976 11.7 11.3 11.8 11.7 31.7
p < 0.001; standard deviation of residual = 0.23 °.
A first approximation of the precision of the method was obtained as shown graphically in Fig. 5. The scale is in millimeters, one square outline being 4 × 4 ram. The maximum distance between points in the scatters ranges from 0.7 to 1.4 mm and is, on the average, 1.0 ram. The best results are obtained for 1951 and 1976, with a measurement of 0.7 mm. The largest variation (or 1.4 mm) is displayed for 1956 and 1961. In Fig. 6 the maximum distance between two points is 1.4 ram, and this apparently resulted from the radiographs of 1956 and 1961. (See Fig. 5.) The 90th percentile encloses a scatter of 1.1 ram. Even more elucidative of the precision of the method is Table I, which lists the computations for the angle between articulare-pogonion and a tangent to the lower border (Fig. 7). The standard deviation of residual from a two-way analysis of variance was 0.23 ° and may be considered method error.
DISCUSSION A method for constructing fiducial points on tracings from longitudinal series of cephalograms is pre-
sented. In research experience, the method has been applied on nearly 2000 x-ray films. It is surprisingly fast and simple and gives good, reproducible results. The construction of the template and the subsequent location of the fiducial points in the demonstrated series of 12 cephalograms required less than t/z hour. The method is fast because, among other things, the natural reference structures are copied only o n c e - - o n the template. In addition, the selection of a "best" cephalogram improved accuracy considerably. The chronologic position of this "best" cephalogram had no influence. Since the work has to be done in a darkened room, it is advisable to use two stacks for the x-ray films, alternately going from oldest to newest and vice versa. In essence, the procedure consists of the use of one small auxiliary tracing sheet on which a template is drawn, representing the mandibular natural reference structures. This template is subsequently superimposed on the radiographs in a longitudinal series by the structural method, precisely described in step 4. Marking of the middle of the opaque demarcation of the canal or a molar crypt on the template has proved to be of greater
"/2
Dibbets
benefit than marking of the internal or external lining, since the thickness of the opaque demarcation may vary from record to record. Smaller projection errors resuiting from poor positioning in the head holder are in this way averaged out and eliminated. The lower border of the canal was preferred because it is projected without overlapping apices. Some experimentation will demonstrate that even seemingly meaningless white spots in the mandibular interior may fall on the previously marked middle of the opaque demarcation of the mandibular canal on the template. Only with the aid of the template does this otherwise useless information on an imperfectly projected canal become useful. In addition, the template prevents confusion over which structure is correct. It is important to note that the template has to be superimposed on the natural reference structures o f the radiographs directly and not on previously marked structures on tracings.
Ventrally, the vertical position of the symphysis is reasonably well defined to allow accurate superimpositioning. Horizontally, the position of pogonion may be helpful since the literature reports no gross remodeling in this a r e a Y 5 Furthermore, the horizontal position was specified by the cranially followed ventral inner contour of the symphysis. In those exceptional cases in which, during development, a discrepancy becomes evident between symphysis and mandibular canal, the canal is to be given the benefit of the doubt. This implies a caudal remodeling of the symphysis, which is not in conflict with the literature. 8 Dorsally, the gonial contour is acceptable as a vertical reference, since remodeling in this area may be expected to follow a logical pattern. No alternating deposition and resorption patterns are known to occur in this region, s Thus, marking of the gonial contour prevents the erroneous registration of mandibles remodeled alternately upward and downward. Crypts, as a rule, initially may undergo caudal remodeling but, once crown formation is completed, no caudal drift has ever been noted. After some experience with structural mandibular superimpositioning, the original semicircular demarcation of the crypt may be found, even after eruption, and may subsequently serve as an additional safeguard against a wrongly detected rotational pattern. A second and most reliable safeguard against errors is created by duplication and verification of the position of articulare. Strictly speaking, the template from Fig. 1 contained sufficient information for structural superimpositioning and transference of fiducial points. Gross errors would thereby be eliminated through the position of the gonial contour. However, the marking of articulare during the first round and the verification in the second serve as precautions against subtle errors and force the operator to proceed methodically.
Am. J.
Orthod. Dentofac. Orthop. January 1990
After the template is superimposed by the structural method on the mandibles of the longitudinal series of cephalograms, the fiducial points are transferred onto the radiographs or radiographic tracings. Neither the use of auxiliary tracing sheets z6 nor the marking of fiducial points for the mandible is n e w . 2"t3"14 However, neither has been applied in the combination presented or has acted as a safeguard. The literature further indicates that geometrically constructed landmarks may be used with confidence and are not statistically different from the landmarks directly identified on bony contours. 7 To provide some insight into the precision of the method, the procedure was repeated four times in one random longitudinal series of 12 x-ray films. This included four independent trials, separated in time, of twelve individual determinations of articulare. In view of the relatively well-defined position of the symphyseal inner contour, articulare was the most appropriate landmark for the study of reliability and was expected to show maximal deviation. The 90th percentile of the scatter of all 48 (4 × 12) separately determined positions of articulate, which is 1.1 mm, may indicate this method's precision in locating this landmark. The scatters were easily produced by standard computer programs with least squares routines and an on-line plotter. Since articulare apparently may be located with a precision close to 1 mm, it follows that discrepancies that are too far outside this range should not be accepted in the "security check." Another quantification of precision was obtained by computation of the angle between articulare-pogonion and an arbitrarily drawn tangent to the lower border of the mandible on each of the four templates, as depicted in Fig. 7. In this way, twelve angles could be computed from each template after the addition of only one arbitrarily drawn tangent. (The outcome was not made better by repeated establishment of the angle between the two fiducial points and the lower border. Any two fiducial points would yield only one angle relative to one arbitrarily chosen lower-border tangent on one template.) This tangent made the four sets of twelve angles differ systematically. To estimate the precision of the method, a two-way analysis of variance was therefore applied to the angular measurements with systematic factors of "trial" (which stands for each of the four templates) and "year of radiograph." The residual standard deviation of 0.23 ° may be considered method error and fell within the range of normal tracing errors for meticulously repeated measurements on x-ray films. Since articulare was expected to display the largest error, the subsequent marking of the fiducial points with the template may be considered reliable. 7 Surprisingly, the 1954 radiograph, from which the
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template was made, did not produce the best results. A p p a r e n t l y "best radiograph" and "best fit" are separate entities. T h e location o f the fiducial points inside the m a n dibular contour is not critical, just practical. Outside the m a n d i b u l a r area, t h e s e p o i n t s tend to interfere with other head structures or even run the risk o f falling outside the tracing sheet in the case o f an o d d l y positioned film. T h e construction o f two fiducial points in the m a n dible, 50 m m apart, has the advantage o f permitting easy and quick m e a s u r e m e n t s as well as superimpositioning. This holds true for d i r e c t - m e a s u r e m e n t techniques as well as for indirect techniques that require digitation o f the landmarks. It is a reliable m e t h o d for longitudinal growth research as well as for two succ e s s i v e records in the clinical situation. I wish to express my gratitude to Mrs. Gerda Wouwenaar for her fast and skillful secretarial assistance. L. Th. van der Weele discussed the text and provided statistical advice, Drs. J. H. B. Verbeek and R. de Bruin programmed the leastsquares superimpositionings, Erik van Ommen made the drawings, and Dr. J. T. Wilmink assisted in the final preparation of the text.
REFERENCES I. Bjrrk A. Prediction of mandibular growth rotation. AMJ OR'HtOD 1969;55:585-99. 2. Baumrind S, Frantz RC~ The reliability of head film measurements. AM J ORTHOD1971 ;60: I l 1-22. 3. Baumrind S, Miller DM. Computer-aided head film analysis: the University of California San Francisco method. AM J ORTHOD 1980;78:41-65. 4. Buschang PM, Tanguay I R, Demirjian A. Cephalometric reliability: a full anova model for the estimation of true and error variance. Angle Orthod 1987;57:168-75.
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5. Ghafari J, Engel FE, Laster LL. Cephalometfic superimposition on the cranial base: a review and comparison of four methods. AM J OR'roODDErCroFAcOR'mOP 1987;91:403-13. 6. Houston WJB. The analysis of errors in orthodontic measurements. AM J OR'i'HOD1983;83:382-90. 7. Savage AW, Showfety KJ, Yancey J. Repeated measures analysis of geometrically constructed and directly determined cephalometric points. AM J OR'ntODDEN'rOFACOR'n~OP1987;91:295-9. 8. Bjrrk A, Skieller V. Normal and abnormal growth of the mandible: a synthesis of longitudinal cephalometric implant studies over a period of 25 years. Eur J Orthod 1983;5:1-46. 9. Solow B, Siersbaek-Nielsen S. Growth changes in head posture related to craniofacial development. AM J ORTnOD1986;89:13240. 10. Buschang PH, LaPalme L, Tanguay R, Demirjian A. The technical reliability of superimposition on cranial base and mandibular structures. Eur J Orthod 1986;8:152-6. 11. Ari-Viro A, Wisth PJ. An evaluation of the method of structural growth prediction. Eur J Orthod 1983;5:199-207. 12. Cook PA, Gravely JF. Tracing error with Bj6rk's mandibular structures. Angle Orthod 1988;58:169-78. 13. Isaacson ILl, Zapfel RJ, Worms FW, Bevis RR, Speidel TM. Some effects of mandibular growth on the dental occlusion and profile. Angle Orthod 1977;47:97-106. 14. Moorrees CFA, Kent RL, Efstratiadis SS, Reed RB. Components of landmark movements during facial growth. In: Beek J, ed, Proceedings of International Studyweek. Noordwijkerhout: Nederlandse Vereniging Orthodontische Studie, 1985:55-70. 15. Enlow DH. Handbook of facial growth. 2nd ed. Philadelphia: WB Saunders, 1982. 16. EkstrSm C. Facial growth rate and its relation to somatic maturation in healthy children. Swed Dent J 1982;11(suppl.):l-99. Reprint requests to:
Dr. J. M. H. Dibbets Department of Orthodontics School of Dentistry A. Deusinglaan 1 9713 AV Groningen, The Netherlands
Structural mandibular superimpositioning on stable natural references has gained wide acceptance in the orthodontic literature. However, accurate instructions that provide a simple step-by-step procedure are not readily available. Considering the specific method described here and assuming stability of the natural reference structures, a reliable procedure for marking two artificial references (simulating "implants") on mandibles in a longitudinal series of cephalograms appears to be possible. In essence, the method is based on the construction of a template, drawn on a small auxiliary tracing sheet, which contains only information relevant for structural mandibular superimpositioning plus error checks. This template is subsequently superimposed on the radiographs in a longitudinal series by the structural method, which permits the transference of two fiducial points. These fiducial points consequently replace the images of metallic implants and thus facilitate local superimpositioning of mandibles. It is a convenient method for longitudinal growth research as well as for any two successive records in the clinical situation. (AMJ ORTHOD DENTOFACORTHOP 1990;97:66-73.)
L o c a l superimpositioning on mandibular structures has found wide acceptance since Bj/Srk's publications. Because the use of implants is not routinely indicated for clinical purposes, Bj6rk) in 1969, suggested certain stable structures within the mandible as acceptable substitutes. Bj6rk had observed that the mandibular canal, the molar crypts, the endosteal surfaces of the mandible in the symphyseal area, and the periosteal surfaces at pogonion appeared to be remodeled at a comparatively slow rate, thereby making these structures reasonable substitutes for the metallic implant. This observation formed the basis for the method to be described here. Although much has been published on the reliability of head film measurements, 27 only a few studies on the applicability of what has come to be known as the "mandibular structural method" are available. A detailed listing of stable structures was given by Bj6rk and Skieller? Solow and Siersbaek-Nielsen 9 superimposed radiographs directly and reported as method error that "the mandible could usually be assessed within ± 3 ° by the structure-based method . . . . " Buschang and associates ~° studied errors inherent in the method of superimpositioning and concluded that " . . . mandibular superimposition is less reliable than cranial base superimposition, a l t h o u g h . . , the methodology is reFrom the Department of Orthodontics, School of Dentistry, University of Groningen. 8/1/10369
66
liable." On the other hand, Ari-Viro and Wisth" disputed the reliability of the method. Recently, Cook and Gravely 12 studied tracing errors for mandibular structures and concluded that error levels of horizontal measurements were less than those of the vertical ones. Baumrind et al. 2'3 and Isaacson et al? 3 developed procedures by which fiducial points were transferred from tracing to tracing after establishment of best fit. These fiducial points facilitated repeated superimpositioning later on. This procedure was elegantly modified for manual applications by Moorrees et al? 4 However, all these methods depend on the superimpositioning of tracings on which the reference structures have been previously marked. In our experience, this superimposition of mandibular tracings is laborious and the results are unsatisfactory. Therefore, it was decided to modify the known methods and to develop a new and improved procedure for locating fiducial points on head film tracings. The resulting method is quick because, in a series, the natural reference structures have to be marked only once. It is reliable because these reference structures are taken from one selected best cephalogram. It is convenient because the template is small and therefore is manipulated easily. Finally, it provides two built-in safeguards against errors. First, the method is described, beginning with the procedure for construction of a template on a separate tracing sheet. The template then has to be superimposed on the stable mandibular reference structures of the successive radiographs in a longitudinal series, with addition to the
Volume 97 Number I
Structural mandibular superimpositioning
o ~
67
.
t
Articulare'--___.-
5~4 -.
',,
Canal
"-
"
Crypts
Gonial angle Fig. 1. TemPlate on auxiliary tracing sheet, !0 x 15 cm maximum, drawn from best radiograph of longitudinal series (i.e., 1954). The natural reference structures of symphysis, middle of the opaque lower demarcation of the canal, and bottom of the crypts are drawn. Pogonion is added for horizontal reference; the gonial angle for vertical help. Articulate, labeled for the year of photograph (1954), is going to serve as a "double check" before transference of fiducial points. The broken line indicates the contours of the 1954 mandible a/ldis depicted only as an illustration of the total structure. This template is constructed in step 3 of the procedure.
template of the landmark articulare, which is going to serve as a safeguard against errors. Next, two holes are drilled in this template, permitting the reproducible transference of two fiducial points. These fiduciai points are subsequently transferred with lead pencil after a second SUl~erimpositioning o f the template on stable structures and a "security check" for the position of articulare. Since the method proved reliable in actual practice, an indication of the precision of the procedure is obtained by quadrupl!ng of the template on one random series of t~,eive radiogrfipfis. MATERIAL AND METHOD
Any longitudinal series of two or more cephalograms may/:onstitute the material for the method to be described. For illustration of the procedural steps, a series o f 12 radiographs from the Groningen elementary school study was selected randomly. In t.his study, standardized cephalograms were taken at yearly intervals of children from the elementary schools in Groningen. Descript.ion of the method
The pi'ocedure consists of seven successive steps. Step 1. Conventional tracings are made. All usual structures may be drawn except for the natural structural mandibular references: the inner contour of the 6Tmphysis, the molar copts, the (pre)molar apices, and the canal. This series of x-ray films, complete with tracings, is .stacked chronologically. Step 2. The best x-ray film from this series is selected according !o the following quality criteria: • Best contrast. In ad(!ition, the crypts must be
sharply projected and the opaque contours of the mandibular canal or parts of it must be clearly visible. • Best symmetry. Rotation or canting of the head is minimal; mandibular contours, molar crypts, teeth, and canals are maximally overprojected. The symphysis should show a sharp inner contour. • Teeth in occlusion, with no dual bite. From this selected best film, the natural reference structures are copied. Step 3. On a small (10 x 15 cm maximum) auxiliary tracing sheet overlaying the selected best film, the following natural reference structures are marked to serve as a template (Fig. 1): • The middle of the opaque demarcation of the lower border from the mandibular canal. • The middle of the opaque semicircular demarcation of the molar crypts. • The semicircular demarcation of the apices of erupted molars. • The outer contour of the symphysis, from menton to pogonion. • The inner contour of the symphysis on the sharp demarcation between white (bone) and black (interior), ventrally following the inner contour as high (cranially) as possible. These structures have been reported as relativelY stable throughout growth.~'8 As a safeguard against errors, two additional references are marked: articulare and the contour (averaged for left and right) of the gonial angle. These references must be labeled for the year of the radiograph. This security procedure is completed in steps 4 and 5.
68
Dibbets
Am. J. Orthod. Dentofizc. Orthop. Janua O. 1 9 9 0
I I
I
",76
"'--__-~'"
% % % % % % %
,,
54- "51 ~
Fig. 2. Template marked for articulare and gonial contour of youngest (1951) and oldest (1976) cephalograms of longitudinal series. This provides an indication of the extreme values. Intermediate gonial contours and landmarks articulare will occupy positions between these extremes. The mandibular canal may be extended on later photographs, or crypts may be added. It is advised that all available structural information be concentrated on the template. This represents step 4 of the procedure.
.76 .62 61",60 59" 58
5~,"~5653 7 6 ~ l J
Fig. 3. The template has been structurally superimposed on all successive cephalograms of one series. Articulare is always transferred to the template, the gonial contour only when helpful (in this case, 1958). The numbers indicate the years in which the radiographs were taken: 1951, 1952, 1953, 1954, 1956, 1957, 1958, 1959, 1960, 1961, 1962, and 1976. The oblique cluster labeled 51 to 76 represents the twelve landmarks articulare. This represents step 5 of the procedure.
Step 4. Articulare and the gonial contour of the newest and oldest cephalograms available are marked on the template. For this purpose, the template is superimposed on the radiographs by the structural method, with best fit established on the symphyseal inner contour, the canal, and the crypts. First, the best fit is established on the inner contour of the symphysis and the template is held gently with a finger at the symphysis so as to create a fulcrum around Which the template may bE rotated. Throflgh rotation, the best fit of the mandibular structures in the corpus is located: the middle of the lower opaque demarcation of the canal and crypts. Then the symphysis is readjusted, and subse-
quently the best fit for canal and crypt is established. After establishment of the best fit, articulare and the gonial contour are marked on the template, with a reference to their date (as 1951 and 1976 in our illustrations, Fig. 2). Step 5. The security procedure is completed by structural superimpositioning of the template on the whole series of cephalograms (plus overall tracings). Articulare is always marked on the template and labeled for the date of the photograph, and the gonial angle is marked only when helpful (too many lines may become confusing). The result is depicted in Fig. 3. These references will later be used as a "security check."
Volume 97 Number I
Structural mandibular superimpositioning
.76
.62 61",60 59" 58
57",5653 76~58~54
51,'~
~-
~--
Fig. 4. Two 0.5 mm holes are drilled through tracing sheet, 50 mm apart and representing Iocat!on of fiducial points (step 6). When the template is readjusted onto the radiographs and tracings, the location of these hoIes permits easy transference of fiducial points by marking with a lead pencil (step 7).
,I I
I I 1951
r 19'52
I
I
I 19153
I
oo Oo
,
1954
I
1956
•I
f
I
I
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ibJ57
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I
o" I
1959
1958
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l
I
I
i .
|
1960
Oo
6o
19
,
61
!
7
I
1962
i
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I
1
1976
Fig. 5. Approximation of precision of method. The procedure, up to step 5 and Fig. 3, was repeated four times on one randomly selected longitudinal series of 12 yearly cephalograms. The 12 scatter plots, of four landmarks articulare each, are indicative of the dispersion resulting from error. The scale is in millimeters.
69
70
90%
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= 1,1 m m
Am. J.
~
1
mm
4
Fig. 6. The twelve scatter plots from Fig. 5, of four landmarks articulare each, superimposed on their geometric centers. The 90th percentile is indicated by a 1.1 mm circle.
Step 6. The next step in the procedure is the drilling of two 0.5 mm holes in the template, 50 mm apart in the "corpus" of the mandible, as shown in Fig. 4. Their position is not critical, but we prefer to keep them inside the mandibular contour (see Discussion). This arbitrary distance of 50 mm is easily obtained by means of a simple Plexiglas or acrylic plastic jig and a 0.5 mm drill in a small holder. After these preparations, the template is ready for transference of fiducial points. Step 7. The position of the fiducial points is established by structural superimposition of the template on the series of radiographs (plus overall tracing) for a second time. As a safeguard against errors, it isadvisable in this second procedure not to "peek" at the position of the previously marked articulare. Only after the best fit on symphysis, molar crypts and canal has been found is articulare used as a check. Differences Of more than 1 mm between the actual and the previously located articulare should be regarded as an indication that more trials are necessary (see Results and Discussion). After a satisfactory fit has been found, the two fiducial points are transferred onto the original overall tracing by means of a pencil mark through the t.wo holes in the template. These two dots consequently indicate structurally determined "stable references" for this particular lower jaw. Indication of precision To assess the precision of the method, the procedure for constructing the template was repeated four times in one randomly selecl(ed longitudinal series of 12 radiographs. This included four independent determinations of articulare on each of 12 individual radiographs. There had been an interval of severa ! days between
Orthod. Dentofac. Orthop. January 1990
construction of the templates. This represented the procedure up to and including step 5 (Fig. 3). Since the PrOcedure essentially consists of a rotation around the inner symphyseal contour, the error will be maximal at the most distant landmark. Thus the position of articulare on the template can be expected to display the largest error--in any event, larger than the error in the subsequent marking of fiducial points. The four templates resulting from the four repeated procedures, each with 12 landmarks "articulare" (as i n Fig. 3), were digitized and superimposed by computer. This superimpositioning was performed through minimizing of the distances of the corresponding yearly time-point landmarks articulare by means of"least squares" procedures for finding the best fit between the four separate scatters of twelve landmarks. The dispersion of the four positions of articulare for each radiograph was studied after the results were plotted. To minimize the bias of a marked deviation in any one year under study, the positions of articulare in the year to be plotted were not used in the computing of the least squares. Consequently, the twelve plots, each representing a yearly scatter of four landmarks articulare, had to be produced in twelve separate computer runs. A further illustration of the total dispersion was obtained by depiction of 4 x 12 = 48 single determinations of articulare. This was performed by computation of the center of each yearly scatter (of four landmarks articulare) and by subsequent superimpositioning of the twelve scatters on their centers. Finally, precision was assessed b y comparison of angular measurements. The angular values from articulare-pogonion and a tangent to the lower border of the mandible were computed. The lower-border tangent was drawn arbitrarily to the mandible on the template in each of the four trials. Consequently the computations for the angular values articulare-pogonion to the lowerborder tangent differed systematically for each o f the four templates. Therefore the resulting four sets of twelve angular measurements could not be compared directly. To estimate the standard deviation of residual, a two-way analysis of variance (i.e., angular measurement with the systematic factors of "trial" and "year of photograph") was applied. The standard deviation of residual may be considered as measurement error. RESULTS When the procedure is followed up to step 7 for all radiographs in one series, the mandibles will be marked with two fiducial points. The distance between these points is fixed, while their position represents the stability of natural reference structures. These two fiducial points subsequentlY may serve as reference landmarks for local superimpositioning by computer or by handl
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Structural mandibular superimpositionhzg
71
~-~76 ,,62~ 61",,60 ~ 59" 58
s-?,56sa Pg
~51
~76
M P ~
Fig. 7. A tangent to the lower border, NIP, and a line connecting articulare-pogonion, define angle a. The tangent MP is drawn arbitrarily by hand to the lower border' on the template, and therefore the position relative to articulare-pogonion will differ from template to template. Consequently, the angular values of ~ in each of the four trials shown in TabIe I will differ systematically. In the illustration the construction of ~ for 1976 and 1951 is depicted (method error).
Table I. Two-way analysis of variance of angle articulare-pogonion to an arbitrary tangent to lower border (in degrees)
I 1 11 1952 I 1
2 3 4 Age
0.9 0.4 0.9 0.4 6.8
1.2 0.6 1.3 0.9 7.9
I 1954 I 1.6 1.1 1.0 1.0 8.7
1.8 1.4 1.2 1.8 9.9
I 3.6 2.8 3.1 3.7 12.4
I 4.5 4.3 4.2 4.0 13.5
I 4.9 4.4 4.6 4.2 13.9
i 1960 ( 1961 ( 1 62 6.9 6.4 6.7 6.4 14.8
8.1 7.5 8.3 8.0 15.9
8.9 9.2 9.1 9.1 16.8
10.2 9.5 9.9 10.0 17.8
1976 11.7 11.3 11.8 11.7 31.7
p < 0.001; standard deviation of residual = 0.23 °.
A first approximation of the precision of the method was obtained as shown graphically in Fig. 5. The scale is in millimeters, one square outline being 4 × 4 ram. The maximum distance between points in the scatters ranges from 0.7 to 1.4 mm and is, on the average, 1.0 ram. The best results are obtained for 1951 and 1976, with a measurement of 0.7 mm. The largest variation (or 1.4 mm) is displayed for 1956 and 1961. In Fig. 6 the maximum distance between two points is 1.4 ram, and this apparently resulted from the radiographs of 1956 and 1961. (See Fig. 5.) The 90th percentile encloses a scatter of 1.1 ram. Even more elucidative of the precision of the method is Table I, which lists the computations for the angle between articulare-pogonion and a tangent to the lower border (Fig. 7). The standard deviation of residual from a two-way analysis of variance was 0.23 ° and may be considered method error.
DISCUSSION A method for constructing fiducial points on tracings from longitudinal series of cephalograms is pre-
sented. In research experience, the method has been applied on nearly 2000 x-ray films. It is surprisingly fast and simple and gives good, reproducible results. The construction of the template and the subsequent location of the fiducial points in the demonstrated series of 12 cephalograms required less than t/z hour. The method is fast because, among other things, the natural reference structures are copied only o n c e - - o n the template. In addition, the selection of a "best" cephalogram improved accuracy considerably. The chronologic position of this "best" cephalogram had no influence. Since the work has to be done in a darkened room, it is advisable to use two stacks for the x-ray films, alternately going from oldest to newest and vice versa. In essence, the procedure consists of the use of one small auxiliary tracing sheet on which a template is drawn, representing the mandibular natural reference structures. This template is subsequently superimposed on the radiographs in a longitudinal series by the structural method, precisely described in step 4. Marking of the middle of the opaque demarcation of the canal or a molar crypt on the template has proved to be of greater
"/2
Dibbets
benefit than marking of the internal or external lining, since the thickness of the opaque demarcation may vary from record to record. Smaller projection errors resuiting from poor positioning in the head holder are in this way averaged out and eliminated. The lower border of the canal was preferred because it is projected without overlapping apices. Some experimentation will demonstrate that even seemingly meaningless white spots in the mandibular interior may fall on the previously marked middle of the opaque demarcation of the mandibular canal on the template. Only with the aid of the template does this otherwise useless information on an imperfectly projected canal become useful. In addition, the template prevents confusion over which structure is correct. It is important to note that the template has to be superimposed on the natural reference structures o f the radiographs directly and not on previously marked structures on tracings.
Ventrally, the vertical position of the symphysis is reasonably well defined to allow accurate superimpositioning. Horizontally, the position of pogonion may be helpful since the literature reports no gross remodeling in this a r e a Y 5 Furthermore, the horizontal position was specified by the cranially followed ventral inner contour of the symphysis. In those exceptional cases in which, during development, a discrepancy becomes evident between symphysis and mandibular canal, the canal is to be given the benefit of the doubt. This implies a caudal remodeling of the symphysis, which is not in conflict with the literature. 8 Dorsally, the gonial contour is acceptable as a vertical reference, since remodeling in this area may be expected to follow a logical pattern. No alternating deposition and resorption patterns are known to occur in this region, s Thus, marking of the gonial contour prevents the erroneous registration of mandibles remodeled alternately upward and downward. Crypts, as a rule, initially may undergo caudal remodeling but, once crown formation is completed, no caudal drift has ever been noted. After some experience with structural mandibular superimpositioning, the original semicircular demarcation of the crypt may be found, even after eruption, and may subsequently serve as an additional safeguard against a wrongly detected rotational pattern. A second and most reliable safeguard against errors is created by duplication and verification of the position of articulare. Strictly speaking, the template from Fig. 1 contained sufficient information for structural superimpositioning and transference of fiducial points. Gross errors would thereby be eliminated through the position of the gonial contour. However, the marking of articulare during the first round and the verification in the second serve as precautions against subtle errors and force the operator to proceed methodically.
Am. J.
Orthod. Dentofac. Orthop. January 1990
After the template is superimposed by the structural method on the mandibles of the longitudinal series of cephalograms, the fiducial points are transferred onto the radiographs or radiographic tracings. Neither the use of auxiliary tracing sheets z6 nor the marking of fiducial points for the mandible is n e w . 2"t3"14 However, neither has been applied in the combination presented or has acted as a safeguard. The literature further indicates that geometrically constructed landmarks may be used with confidence and are not statistically different from the landmarks directly identified on bony contours. 7 To provide some insight into the precision of the method, the procedure was repeated four times in one random longitudinal series of 12 x-ray films. This included four independent trials, separated in time, of twelve individual determinations of articulare. In view of the relatively well-defined position of the symphyseal inner contour, articulare was the most appropriate landmark for the study of reliability and was expected to show maximal deviation. The 90th percentile of the scatter of all 48 (4 × 12) separately determined positions of articulate, which is 1.1 mm, may indicate this method's precision in locating this landmark. The scatters were easily produced by standard computer programs with least squares routines and an on-line plotter. Since articulare apparently may be located with a precision close to 1 mm, it follows that discrepancies that are too far outside this range should not be accepted in the "security check." Another quantification of precision was obtained by computation of the angle between articulare-pogonion and an arbitrarily drawn tangent to the lower border of the mandible on each of the four templates, as depicted in Fig. 7. In this way, twelve angles could be computed from each template after the addition of only one arbitrarily drawn tangent. (The outcome was not made better by repeated establishment of the angle between the two fiducial points and the lower border. Any two fiducial points would yield only one angle relative to one arbitrarily chosen lower-border tangent on one template.) This tangent made the four sets of twelve angles differ systematically. To estimate the precision of the method, a two-way analysis of variance was therefore applied to the angular measurements with systematic factors of "trial" (which stands for each of the four templates) and "year of radiograph." The residual standard deviation of 0.23 ° may be considered method error and fell within the range of normal tracing errors for meticulously repeated measurements on x-ray films. Since articulare was expected to display the largest error, the subsequent marking of the fiducial points with the template may be considered reliable. 7 Surprisingly, the 1954 radiograph, from which the
Volume 97 Number 1
template was made, did not produce the best results. A p p a r e n t l y "best radiograph" and "best fit" are separate entities. T h e location o f the fiducial points inside the m a n dibular contour is not critical, just practical. Outside the m a n d i b u l a r area, t h e s e p o i n t s tend to interfere with other head structures or even run the risk o f falling outside the tracing sheet in the case o f an o d d l y positioned film. T h e construction o f two fiducial points in the m a n dible, 50 m m apart, has the advantage o f permitting easy and quick m e a s u r e m e n t s as well as superimpositioning. This holds true for d i r e c t - m e a s u r e m e n t techniques as well as for indirect techniques that require digitation o f the landmarks. It is a reliable m e t h o d for longitudinal growth research as well as for two succ e s s i v e records in the clinical situation. I wish to express my gratitude to Mrs. Gerda Wouwenaar for her fast and skillful secretarial assistance. L. Th. van der Weele discussed the text and provided statistical advice, Drs. J. H. B. Verbeek and R. de Bruin programmed the leastsquares superimpositionings, Erik van Ommen made the drawings, and Dr. J. T. Wilmink assisted in the final preparation of the text.
REFERENCES I. Bjrrk A. Prediction of mandibular growth rotation. AMJ OR'HtOD 1969;55:585-99. 2. Baumrind S, Frantz RC~ The reliability of head film measurements. AM J ORTHOD1971 ;60: I l 1-22. 3. Baumrind S, Miller DM. Computer-aided head film analysis: the University of California San Francisco method. AM J ORTHOD 1980;78:41-65. 4. Buschang PM, Tanguay I R, Demirjian A. Cephalometric reliability: a full anova model for the estimation of true and error variance. Angle Orthod 1987;57:168-75.
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5. Ghafari J, Engel FE, Laster LL. Cephalometfic superimposition on the cranial base: a review and comparison of four methods. AM J OR'roODDErCroFAcOR'mOP 1987;91:403-13. 6. Houston WJB. The analysis of errors in orthodontic measurements. AM J OR'i'HOD1983;83:382-90. 7. Savage AW, Showfety KJ, Yancey J. Repeated measures analysis of geometrically constructed and directly determined cephalometric points. AM J OR'ntODDEN'rOFACOR'n~OP1987;91:295-9. 8. Bjrrk A, Skieller V. Normal and abnormal growth of the mandible: a synthesis of longitudinal cephalometric implant studies over a period of 25 years. Eur J Orthod 1983;5:1-46. 9. Solow B, Siersbaek-Nielsen S. Growth changes in head posture related to craniofacial development. AM J ORTnOD1986;89:13240. 10. Buschang PH, LaPalme L, Tanguay R, Demirjian A. The technical reliability of superimposition on cranial base and mandibular structures. Eur J Orthod 1986;8:152-6. 11. Ari-Viro A, Wisth PJ. An evaluation of the method of structural growth prediction. Eur J Orthod 1983;5:199-207. 12. Cook PA, Gravely JF. Tracing error with Bj6rk's mandibular structures. Angle Orthod 1988;58:169-78. 13. Isaacson ILl, Zapfel RJ, Worms FW, Bevis RR, Speidel TM. Some effects of mandibular growth on the dental occlusion and profile. Angle Orthod 1977;47:97-106. 14. Moorrees CFA, Kent RL, Efstratiadis SS, Reed RB. Components of landmark movements during facial growth. In: Beek J, ed, Proceedings of International Studyweek. Noordwijkerhout: Nederlandse Vereniging Orthodontische Studie, 1985:55-70. 15. Enlow DH. Handbook of facial growth. 2nd ed. Philadelphia: WB Saunders, 1982. 16. EkstrSm C. Facial growth rate and its relation to somatic maturation in healthy children. Swed Dent J 1982;11(suppl.):l-99. Reprint requests to:
Dr. J. M. H. Dibbets Department of Orthodontics School of Dentistry A. Deusinglaan 1 9713 AV Groningen, The Netherlands