DOI: 10.1051/odfen/2011104 J Dentofacial Anom Orthod 2011;14:105 RODF / EDP Sciences

A new method of using cephalometric measurements in orthodontics (part 2) or how standard deviations can be the practitioner’s false friends

Rene´ BONNEFONT, Jean-François ERNOULT, Olivier SOREL C.R.A.N.I.O.M, January 2012

ABSTRACT It is generally agreed that cephalometric analyses of the Americans Ricketts, Steiner, and Tweed are of questionable utility. The C.R.A.N.I.O.M group has formulated a new method of using cephalometric measurements that it believes will be moderately helpful to orthodontists in making their diagnoses. We analyzed 83 young adults in Class I who had had no orthodontic treatment. The most interesting new formulation of our plan was to examine the extremes of the variables that we considered in this population. These figures constituted limits that differed widely from each other: there was more than a 30 gap between the measurement of the incisor inclined furthest buccally and the one inclined most lingually (or palatally). Accordingly, for these lower anterior teeth inclinations to Downs’s mandibular plane ranging from 78 to 114 were acceptable. And for the maxillary incisors inclinations to the Frankfort plane varying from 97.5 to 130.1 are considered to be in a standard range. The need to reposition incisors in order to conform to what we can now see as an abusively rigid normal accordingly occurs much less frequently. For this reason, orthodontists will find far fewer indications for the extraction of bicuspid teeth than they would in rigidly adhering to the standards imposed by the Ricketts, Steiner, and Tweed cephalometric analyses. We believe that measurements of skeletal, osseous structures merely differentiate between various typologies and do not describe forms that constitute anomalies. The C.R.A.N.I.O.M group affirms that cephalometrics occupies a position in the array of orthodontic diagnostic tools that comes after the assessment of esthetic, periodontal status, and muscular equilibrium.

Conflict of interest: none Received: 09-2009. Address for correspondence: Accepted: 06-2010. R. BONNEFONT, 149 rue Perronet, 92200 Neuilly-sur-Seine. Rene´[email protected] 1

Article available at http://www.jdao-journal.org or http://dx.doi.org/10.1051/odfen/2011104 RENE´ BONNEFONT, JEANFRANÇOIS ERNOULT, OLIVIER SOREL

KEYWORDS

Cephalometrics Averages Standard deviation Extreme values Incisal inclination Facial and mandibular forms Cephalometric repositioning of incisors.

In the last issue we announced that Professor Julien PHILIPPE had written a commentary on our . At the beginning, we had jointly prepared a text that was to serve as an introduction to this article before we knew that it would appear in two parts. We think that this is not an inappropriate time to print it as originally planned. Rene´ Bonnefont

So here it is, after a little delay...

A PREFACE TO THE CRANIOM ARTICLE ON CEPHALOMETRICS

As the reader knows, our CRANIOM asserted that they hadn’t made him group sent a copy of its analysis to Pr. change his mind about the inadvisa- Julien PHILIPPE before its publication. bility of using cephalometric measure- ments as a component of the We are pleased to incorporate into diagnostic process. this introduction to our article the comments he was kind enough to Obviously, he has every right to send us in reply. take this stand and we respect it. Julien PHILIPPE has deftly discerned What Dr. Philippe’s position does do the three principal points of our new is to provoke CRANIOM to ask itself method that he describes in his text, this question: has our group gone too which we cite below. There are, far in its use of cephalometrics? however, other benefits of our plan We do not think so, primarily like, for example, the aid it offers because we have employed cephalo- orthodontists in making a differential metric measurements with thoughtful diagnosis of maxillary and mandibular moderation. osseous antero-posterior anomalies. For example, the utilization of limits After having pointed out these demarcated by the extreme values of interesting improvements, this very the parameters we studied in our distinguished orthodontist then sample opens up a vast range of

2 Bonnefont R, Ernoult JF, Sorel O. A new method of using cephalometric measurements in orthodontics (part 2) A NEW METHOD OF USING CEPHALOMETRICMEASUREMENTS IN ORTHODONTICS (PART 2)

situations that would permit us, marks? This recognition has led among other things, to accept without CRANIOM to replace angle ANB much change the initial position of our with another cleverly chosen mea- patients’ incisor teeth. surement. Accordingly, in our analysis a man- 2. The restoration of the ‘‘line of sight dibular incisor inclination, under cer- plane’’ as a physiological way to tain conditions, anywhere from 78 to position the head. This orientation 114 is acceptable. allows the evaluator to take the variability of the SN and Frankfort We leave it to all our readers to form planes into account; it also makes their own opinions about this ques- clear how variable Pellerin’s 1984 tion. orientation based on the organs of And to do this, of course, they will equilibrium, the semi-circular canals have to allow themselves enough of the inner ear, is. time to test it in all of its aspects. This position is one that the clinical Rene´ Bonnefont examination dictates. 3. Their utilization of the extreme values of a normal population is an Julien PHILIPPE’S Commentary original idea that improves on by earlier methods by encompassing In sending me the CRANIOM article, all the variations of reference lines Rene´ Bonnefont knew that in my view and structures being observed to- no cephalometric analysis can supply gether, without insisting that varia- useful therapeutic indications and, tions come only from the observed therefore, I would not be interested in structures. This is objective and the first two lines of their essay. We unbiased. know that the classic American ana- In addition, this type of measure- lyses presuppose that the patient’s ment rescues the practitioner from the reference lines are well oriented, in ridiculous obsession with the so-called harmony with those of their theoretical ‘‘ideal’’ average that conflicted with model. Accordingly, any variations the scientific biological view that any from the model of the patient’s mea- value lying within two standard devia- surements would derive from the tions of either side of the average, that structure being measured, while in is 95.5% of all values, is normal. Let reality they might just as well result us not forget that the world admires from a deviation in the reference line the champions and stars, who are that can vary every bit as much as the anything but average. structure being evaluated. To sum up, let me state that this Having made this point, I wish to method of analysis seems to me to acknowledge that the CRANIOM ana- represent an important improvement lysis constitutes progress for many over the classical American analyses, reasons, which include: without in any way modifying my 1. The recognition that point N is fundamental opinion that cephalo- variable. Admittedly, but what metric measurements do not consti- about all the other reference land- tute diagnostic data.

J Dentofacial Anom Orthod 2011;14:105 3 RENE´ BONNEFONT, JEANFRANÇOIS ERNOULT, OLIVIER SOREL

What this new method does offer And to emphasize the point, let me the profession is a good descriptive quote once more, as so many others tool, with all the worst errors of the have done, the timeworn but still classic analyses stripped away. eminently sage counsel of my tea- But CRANIOM is quite right, in fine, cher, L. MULLER, ‘‘Cephalometrics is a to make subjugate the therapeutic good servant, but a bad master.’’ notions to clinical realities. Julien Philippe

INTRODUCTION TO PART 2

We shall now present our method are introducing here: of using, first, the extreme values of 1 – What are and how do we our sample and, second, the averages employ extreme values? and standard deviations. 2 – What are and how do we These two different utilizations employ standard deviations? define the new cephalometric that we

HOW AND WHEN TO USE EXTREME VALUES?

Answer: extreme values are used, had completed their growth period. essentially, to analyze the inclina- At this stage of the article, it is time tion of upper and lower incisor for us to report how we accumulated teeth. the ensemble of our data. In obtaining this series of values For one thing our CRANIOM analysis from our sample we used only mea- is the first and only one to present the surements taken from individuals who extreme values of every variable. How- ever, our sample contained only indivi- duals whose average age was 20. And, clearly, for completeness, we ought to be able to present useful measurements from every stage of orthodontic treatment as well as from different stages of the growth period. To accomplish this, we were forced to extrapolate our data using other well-known and well-recognized stu- dies as guides. We chose: 1– The Michigan growth atlas, 2– The report of the 1995 SFODF convention in Rennes.

Figure 38

4 Bonnefont R, Ernoult JF, Sorel O. A new method of using cephalometric measurements in orthodontics (part 2) A NEW METHOD OF USING CEPHALOMETRICMEASUREMENTS IN ORTHODONTICS (PART 2)

Figure 39 a Figure 39 b 1 – An examination of the measure- ments contained in the Riolo, Moyers, MacNamara, and Hun- ter Atlas of Craniofacial Growth – the facial growth rhythms of (Ann Arbor, Michigan, 1974) (fig. French adolescents as recorded 38). by the SFODF Rennes conven- tion of 1995 (fig. 40 a to c), Observations of the inclinations focusing especially on the rhythm of incisors in 16 year-olds: of mandibular growth as indi- – upper incisors to the Frankfort cated by the segment, or dis- plane = 111 (fig. 39 a). tance from point S to menton, – lower incisors to the mandibular point Pogonion. plane = 95 (fig. 39 b) – and the same segments, or The average and standard devia- distances, defining the tion values of our sample are more rhythms of mandibular growth or less the same as those of the of subjects in the Michigan study Michigan Atlas. (revue d’ODF, vol. 19, n IV, October 1985 (fig. 41). 2 – Comparison of growth rhythms Taking into account the Atlas having We compared: followed its subjects from the age of 6

Figures 40 a to c

J Dentofacial Anom Orthod 2011;14:105 5 RENE´ BONNEFONT, JEANFRANÇOIS ERNOULT, OLIVIER SOREL

Figure 41

to 16 and the Rennes study only from Lower incisors 9 to 16, we can conclude that the The inclinations of the mandibular correlation between the two curves is incisors ranged from 78 (fig. 42 a) significantly similar enough to allow us to 114 (fig. 42 b) which is a gap of to use the Atlas data for subjects 36. 9 years of age and older. Clearly these figures are very, very Whatever differences existed be- far from the 90 Tweed prescribed and tween the two groups were insignif- also quite distant from the formula- icant. Later we shall discuss this in tions of others. grater detail. But we can say now, that this Our values can constitute perfectly procedure in no way differs from what acceptable limits because we found we do in our offices every day when them in normal subjects who had had we employ the values presented by no orthodontic treatment. North American analyzes like the What is also striking to the naked Ricketts, Steiner, and Tweed to eval- eye are the two osseous and uate our French patients. mandibular forms in the two subjects As we have already said, a general whose cephalograms are depicted overview of the tracings we made of below. our sample greatly surprised us by the – The head plate on the left, fig. 42 a, wide disparity they demonstrated be- shows an individual whose growth tween minimal and maximal values. was primarily vertical, dolichofacial, And this, let us repeat, is an or hyperdivergent, observation made on a group of – The head plate on the right, fig. 42 b, subjects who had never been trea- shows an individual whose growth ted orthodontically but were all in was primarily horizontal, brachyfa- Class I occlusion. cial, or hypodivergent.

6 Bonnefont R, Ernoult JF, Sorel O. A new method of using cephalometric measurements in orthodontics (part 2) A NEW METHOD OF USING CEPHALOMETRICMEASUREMENTS IN ORTHODONTICS (PART 2)

These two figures are copies of the figures 2 and 3 that appeared in Part 1 of this article published in, vol. 14 n 4 this journal 2010.

Figure 42 a Figure 42 b The most upright at 78 . The most buccally inclined at 11.

We have already seen that we can We can note here the difference immediately notice the differences between the situation of individuals between skeletal structures by placing whose values are at either end of the two tracings (1 and 2), as we have limits of our values with the situation done below, side by side (fig. 44 and depicted by an average value and 45). standard deviations: Moreover, in our sample the calcu- If we utilize the classical reference lation of the correlation coefficient of the average plus or minus two showed a significant relationship be- standard deviations we arrive at limits tween facial type and lower incisor of 82 and 108; inclination values inclination: rather more narrowly divergent than those of the extreme values, 78 to 114. We can safely say, then, that standard deviations are false friends of orthodontists. In order to incorporate these differ- ent readings of averages and standard deviations in a single sketch we installed them on an average a tracing of an average cephalogram (fig. 43) that would portray the neighboring skeletal structures in an ‘‘average’’ form and, obviously, without any specific osseous feature, which would be the case with extreme values. Figure 43

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Figure 44 Figure 45 The most lingual lower incisor angulation. The most buccal lower incisor angulation.

– the more the lower incisor is What is most striking at first glance inclined lingually the more the facial is the difference in the skeletal type, type will tend toward the vertical; the relative antero-posterior protrusion – the more the lower incisor is of these two subjects: inclined lingually the more the facial – the one on the left (fig. 46) repre- type will tend toward the horizontal. sents skeletal Class II type, where Extreme inclinations of upper in- the upper incisor has had to lead cisors extensively toward the palate in The inclinations of upper incisors to order to maintain contact with the the Frankfort plane varied from 97.5 lower incisor, in other words there (fig. 46) to 130.1 (fig. 47), which is, has been a considerable compen- accordingly, a gap of 32.6. sation characterized by a strong palatal inclination of the maxillary incisal teeth; – the one on the right (fig. 47) represents a highly pronounced skeletal Class III type, where the upper incisor has had to tilt buccally in a pronounced fashion in order to keep in contact with the lower incisor, in other words, this is also an instance of extensive dental compensation, this time buccally. We have already pointed out that these two subjects in our sample whose incisor teeth demonstrated the most extreme inclinations had Figure 46 found these positions altogether ac- The most palatally inclined maxillary incisor at 97.5. ceptable and never thought of having

8 Bonnefont R, Ernoult JF, Sorel O. A new method of using cephalometric measurements in orthodontics (part 2) A NEW METHOD OF USING CEPHALOMETRICMEASUREMENTS IN ORTHODONTICS (PART 2)

In this situation, which is quite infrequent, the question must, then, be asked, what value must be given to the inclination of the incisor antagonist to an extreme value incisor in the other jaw. We believe that is useful to analyze the inclinations of the incisor teeth that, on a tracing, are antagonist to incisors representing extreme values. Analysis of the degrees of inclina- tion of incisors antagonist to ex- treme value incisors on tracings of Figure 47 subjects with the most extreme The most buccally inclined maxillary incisor at 130 . values of our sample • Maximal values them ‘‘corrected,’’ which would lead – If the lower incisor = 114 the an observer to think that there was inclination of the upper incisor = nothing unpleasing in the appearance 115.1 (fig 48). of these two incisor inclinations de- – If the upper incisor = 130.1 the spite the gap of 32.6 that separated inclination of the lower incisor = 90 them. (fig. 49). An inspection of the net difference • Minimal values between the skeletal structures of the – If the lower incisor = 78 the four subjects presenting extreme va- inclination of the upper incisor = lues is of especial interest. 117.2 (fig 50). It indicates that we cannot as- – If the upper incisor = 97.5 the sociate the extreme inclinations of inclination of the lower incisor = upper and lower incisors on the 97.0 (fig. 51). same tracing because they exist in patients whose facial forms and skeletal protrusions are not com- parable. For example, if we wanted to compensate for a Class III type skele- tal protrusion by changing the inclina- tion of incisor teeth, it is not possible to associate the lowest mandibular incisor inclination, 78, with highest upper incisor angulation, 130. It is, therefore, not possible to join them artificially, on the tracing of the same subject. That would constitute a representation of a cephalogram that could not exist. Figure 48

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Figure 49 Figure 50

We believe it is necessary to take this inclination of the incisor antago- nist to incisor of the high reference value in the case of a real subject from our sample that we have just pre- sented. Thus, for example: – the subject whose mandibular in- cisor had the low inclination value of 78 had a maxillary incisor inclined at 117.2. – the subject whose mandibular in- cisor was angulated at the high value of 114 had an upper incisor Figure 51 inclined at 115.1. Without going into detail about the methodology of the Ricketts, Steiner, who had never had orthodontic treat- and Tweed analyses, we should re- ment did not, as the extreme value member that, for example, the outer cases did, portray situations not ac- limits of these appraisals were based ceptable cephalometrically. on variable averages that differed from It would be logical to conclude that analysis to analysis. subjects with inclinations values lo- But we cannot utilize the extreme cated well between within the limits values from any of them because they on either extreme would be consid- were not published. ered normal. We feel that we must emphasize But we cannot add that these initial that the standard deviations of the incisor readings are equally normal Class I cases in our sample of subjects clinically because they are the result

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of the influence of the growth of this cephalometrically to be in a subject in a general sense and of the pathological condition. muscular equilibrium in a specific There should be a discussion to sense. elucidate this point: it is clear that And we all know the essential role this appreciation is uniquely cepha- that the muscular system plays in the lometric. It does not touch on other inclination of teeth. essential notions like the position of roots within bone, the period- Thus cephalometrics can play a role ontal status, muscular equilibrium, in the decision of whether or not to or overall esthetics. accept the initial position of the lower incisor. Let us add that the practitioner using this framework is not obliged to accept We also clearly understand that this original incisor inclination even if it falls is also the case of other analyses with within our described limits. the major difference concerning incisor inclination: we take into account ex- Practitioners may want to modify treme inclinations as reference limits. incisor position to achieve stability by placing it more comfortably within In our new cephalometric method the dental corridor that respects well we propose the following rule for the known rules of muscular balance even management of incisor teeth: if that initial position falls within our We must: described extreme limits. – accept as cephalometrically nor- And, happily, we have observed that mal the inclination of the incisors we can achieve stability for incisors by of the patient being examined moving them therapeutically. If this when the value falls between the were not axiomatic, orthodontic treat- extreme limits, which are: ment without relapse would not be – between 78 and 114 for lower possible. incisors, and But we should remember that the – between 97.5 and 130 for upper initial position of the incisor was a incisors; point of the best balance, so keeping it – and decide to adjust the incisor at the same angulation is the surest inclinations when, initially, they way to maintain stability. fall outside these extreme limits and, therefore, can be considered

HOW AND WHEN TO USE AVERAGS AND STANDARD DEVIATIONS?

Answer: averages and standard subjects’ conformance to categories deviations are used only to define defined in advance. and classify different shapes of We do not, at this point, introduce skeletal structures. They are never the concept of normality as is so often employed to assess the positions of done in descriptions. The subjects of teeth our study are neither normal nor What seems to us a reasonable abnormal. procedure is essentially to classify

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For example, to classify individuals • Shape of the mandible according to size they are said to be Similarly, this will be described as big, average, or small, which is noth- vertical (fig. 55), average (fig. 56), or ing more than an observation. horizontal (fig. 57). In statistics, we know that a biolo- Classification of horizontal skele- gical norm utilizes on the average, tal structures or basal bone discre- more or less, two standard deviations pancies to define observed limits. The variable measured here is the We have preferred in our work to one CRANIOM selected, that is the use only one standard deviation as a segment A’B’ (or A’’B’’), defined by base for our classification. the orthogonal projections of points A In effect, if we had selected two and B on the Frankfort plane (fig. 58). standard deviations, only 5% of the In this framework, three skeletal subjects would have been classified categories can b postulated: outside the average category, which – type III (fig. 59), would have deprived this typology of – type I (fig. 61), any interest. – type II (fig. 60). We shall now enumerate the differ- • Observations ent categories we retained without An analysis of the ensemble of giving any figures. these cephalograms clearly shows All the figures, averages and stan- how the teeth and the skeletal struc- dard deviations, are reproduced in the tures are independent of each other. synthetic record we assembled. But we knew already that this study Classification of the vertical ske- would clearly show that. letal structures In this spirit, Ballard in 1951 had • Facial form introduced the concept of skeletal This will be described in three protrusions in order to distinguish forms, vertical (fig. 52), average (fig. between dental classes and skeletal 53), or horizontal (fig. 54). classes.

Figure 52 Figure 53

12 Bonnefont R, Ernoult JF, Sorel O. A new method of using cephalometric measurements in orthodontics (part 2) A NEW METHOD OF USING CEPHALOMETRICMEASUREMENTS IN ORTHODONTICS (PART 2)

Figure 54 Figure 55

Figure 56 Figure 57

Figure 58 Figure 59

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Figure 60 Figure 61

Figures 62 a and b

Today, it seems to us that we can designate dental discrepancies and clarify the concept more explicitly by type to designate skeletal discrepan- using the following terms: class, to cies.

CONCLUSION

We have divided this last chapter – Our reference sample was com- into two parts. posed of 83 young French adults, • In the first section we shall re- all of whom had Class I dental view the important differences occlusions but had never had ortho- between our cephalometric ana- dontic treatment; so by definition all lysis and all the others. the measurements we made on

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their cephalograms were accepta- the average figures proposed in all the ble. We collected our records at the North American cephalometric ana- faculties of of Rennes and lyses, concepts that we now consider Nancy. We began our analysis to be outdated. by dividing them into two different But, nevertheless, we have not groups controlled by statistically forgotten the benefits that these compatible means and then joined American pioneers bestowed on the them to form a homogenous profession. group. We defended the Steiner analysis – We used the measurements of ardently from the dais of the S.FO.D.F. skeletal structures only to classify convention of 1966 and did the same them into different types that did for Ricketts in the 1970 session of not constitute anomalies. Actualite´ s OdontoStomatologiques. In order to focus on discrepancies between basal bone structures we We have based our position on the eliminated variables using point critical analyses of these predeces- Nasion because this landmark sors. biases every measurement contain- The four extreme inclinations of ing it. incisor teeth in our sample constitute –Onthe other hand, for the teeth, LIMITS that are broad enough to quite we selected from the records the often permit orthodontists to accept extreme values of the inclinations the initial incisor inclinations of their of the upper and lower incisor own patients. teeth. We were quite astonished at the large gap that separated the And, as a result, orthodontists may extreme values at either end of the now less frequently have to resort to spectrum: the extraction of bicuspid teeth in – 32.6 for the upper incisors, the order to place incisors in some arbi- most buccal inclination having been trary preconceived position. 130.6 and the most palatal 97.5; • In the second part, we present – and 34 for the lower incisors, the a general reflection containing most buccal inclination having been related perspectives. 114 and the most lingual 78. We conducted this study using so- The measurements describing the called conventional two-dimensional extreme inclinations of the incisor cephalogram. But we are convinced teeth are sufficiently large to accom- that it would have been even more modate any type of movement ortho- instructive if we had been able to dontists might determine to apply to evaluate a sample of 83, or more, them. subjects with three-dimensional ce- Each extreme tooth value corre- phalometrics (fig. 62). sponds to a well-defined skeletal We are indebted to Professor form; they are not interchangeable. Jean CASTEIGT for suggesting the The reader can easily see that the innovative idea of attempting to as- diverse inclinations deemed accepta- sess in its full volume, not as a flat ble in our analysis diverge greatly from plane.

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The principal benefit derived from a not have been sufficiently well Three Dimensional analysis is that it thought out... gives endows the picture with the That is why we have devised the reality of the true size of skeletal new concept that we have just pre- structures, a picture that is important sented for your inspection. in evaluating the cortical bone invest- And we shall be delighted to give ing lower incisor teeth labially. serious attention to any suggestions Independent of the values of the you would be kind enough to make extreme limits, it is this thickness of about it. lower anterior labial bone that deter- We are quite ready to employ other mines whether mandibular incisor methods on the condition that they teeth can be moved labially. provide useful information for devising But the periodontal examination of treatment strategies, which, alas, is this region is more critical than the not really true of the North American cephalometric. analyses that are still far too often We hope to be able to replicate this utilized in orthodontic offices. study with Three Dimensional data in We count ourselves members of the near future. the group that believes all those Before we conclude this article responsible for teaching orthodon- we are eager to make the stance tics and for disseminating informa- that our CRANIOM group takes on tion about cephalometrics should the position that orthodontists unite to reflect on whether or not should consider cephalometric oc- we should maintain the status quo. cupies in the management of their And if this group of thinkers . decides to select a new analysis it Like most of our colleagues, we does not matter whose brainchild it believe that clinical assessments in is so long as it fulfills the require- general deserve first place in our ments we have discussed in our attentions, including in this panoply presentation. periodontal exams, a variety of func- N.B. tional studies, and esthetic evalua- While we do not, of course, endorse tions. any specific soft ware company, we However, we believe that it would are persuaded that in the year 2011 be a great mistake to reject totally the cephalometrics has to be fully digi- contributions that cephalometrics can tized. make. And the distinctive way we Among the many programs now employ head X-rays is ours alone. available, we do note that one version, As we said earlier, we have rejected distributed by a French computer the North American analyses that company specializing in dental infor- gave us our introduction to cephalo- mation technology, has a number of metrics. advantages. But we are determined not to be This soft ware program, distributed bound by earlier approaches that may by a company based in Valence

16 Bonnefont R, Ernoult JF, Sorel O. A new method of using cephalometric measurements in orthodontics (part 2) A NEW METHOD OF USING CEPHALOMETRICMEASUREMENTS IN ORTHODONTICS (PART 2)

(Droˆ me) offers precise measurements repositioning together with automatic with zero risk of calculation error and digitized superimpositions of all types presents a reasoned and reasonable for photographs, cephalograms, and interpretation. It also offers a helpful digitized tracing of the kind we used in management incisor positioning and this article.

ACKNOWLEDGEMENTS

We want to extend our warm this journal for his intelligent and ex- thanks to Professor Claude Charron perience based advice and to Baltazard who calculated all the aspects of the da Sylva, the information technologist statistics employed in our study with who managed, with a great deal of his attention and competence that are competence and always congenial the hallmarks of all his activities. availability, the integration of our CRA- We also offer our appreciative thanks NIOM documentation into Odrade ce- to Yves Barat, a former editor-in-chief of phalometric soft ware program.

WORKS TO CONSULT

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18 Bonnefont R, Ernoult JF, Sorel O. A new method of using cephalometric measurements in orthodontics (part 2)