Assessing the outcome of orthognathic surgery by three ... · surgery. produced following orthognathic soft Previousstudieshavereportedon and tissue changes between pre-surgery studies

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Assessing the outcome of orthognathic surgery bythree-dimensional soft tissue analysisVittert, L; Khambay, Balvinder; Katina, S; Ayoub, A; Bowman, A.W

DOI:10.1016/j.ijom.2018.05.024

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Citation for published version (Harvard):Vittert, L, Khambay, B, Katina, S, Ayoub, A & Bowman, AW 2018, 'Assessing the outcome of orthognathicsurgery by three-dimensional soft tissue analysis', International Journal of Oral and Maxillofacial Surgery.https://doi.org/10.1016/j.ijom.2018.05.024

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YIJOM-3967; No of Pages 9

Research Paper

Orthognathic Surgery

Int. J. Oral Maxillofac. Surg. 2018; xxx: xxx–xxxhttps://doi.org/10.1016/j.ijom.2018.05.024, available online at https://www.sciencedirect.com

Assessing the outcome oforthognathic surgery by three-dimensional soft tissue analysisL. Vittert, S. Katina, A. Ayoub, B. Khambay, A.W. Bowman: Assessing the outcome oforthognathic surgery by three-dimensional soft tissue analysis. Int. J. Oral Maxillofac.Surg. 2018; xxx: xxx–xxx. ã 2018 The Author(s). Published by Elsevier Ltd on behalfof International Association of Oral and Maxillofacial Surgeons. This is an openaccess article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Please cite this article in press as: Vittert L, et al. Assessing the outcome of orthognathic

analysis, Int J Oral Maxillofac Surg (2018), https://doi.org/10.1016/j.ijom.2018.05.024

0901-5027/000001+09 ã 2018 The Author(s). Published by Elsevier Ltd on behalf of International Associ

open access article under the CC BY li

L. Vittert1, S. Katina2, A. Ayoub3,B. Khambay4, A. W. Bowman1

1School of Mathematics and Statistics, TheUniversity of Glasgow, Glasgow, UK; 2Instituteof Mathematics and Statistics, MasarykUniversity, Brno, Czech Republic; 3GlasgowDental Hospital and School, The University ofGlasgow, Glasgow, UK; 4School of Dentistry,University of Birmingham, Birmingham, UK

Abstract. Studies of orthognathic surgery often focus on pre-surgical versus post-surgical changes in facial shape. In contrast, this study provides an innovativecomparison between post-surgical and control shape. Forty orthognathic surgerypatients were included, who underwent three different types of surgical correction:Le Fort I maxillary advancement, bilateral sagittal split mandibular advancement,and bimaxillary advancement surgery. Control facial images were captured fromvolunteers from local communities in Glasgow, with patterns of age, sex, and ethnicbackground that matched those of the surgical patients. Facial models were fittedand Procrustes registration and principal components analysis used to allowquantitative analysis, including the comparison of group mean shape and meanasymmetry. The primary characteristic of the difference in shape was found to beresidual mandibular prognathism in the group of female patients who underwent LeFort I maxillary advancement. Individual cases were assessed against this type ofshape difference, using a quantitative scale to aid clinical audit. Analysis of thecombined surgical groups provided strong evidence that surgery reduces asymmetryin some parts of the face such as the upper lip region. No evidence was found thatmean asymmetry in post-surgical patients is greater than that in controls.

Key words: orthognathic surgery; facial shape;comparison with controls; asymmetry.

Accepted for publication

One of the main objectives of orthognathicsurgery is to normalize the patient’s dento-facial morphology by bringing them withinthe range of normal facial shape. Quantita-tive evaluation of the outcome of orthog-nathic surgery is therefore essential, withcharacterizationof thenormal facial shapeacrucial component in achieving this.

Methods of assessing facial changeshave predominantly been based on two-dimensional radiographs in the form oflateral cephalograms. Registration ofpre- and post-surgical radiographs allowsboth bone and soft tissue changes to bequantified1. More recently this has beenexpanded into three dimensions with the

introduction of cone beam computed to-mography (CBCT), which allows imagingof both the hard and soft tissue structures2.However the use of CBCT is limited byboth cost and radiation exposure concerns.At present in the United Kingdom, themost suitable reported outcome measureis based on the static inter-occlusal dental

surgery by three-dimensional soft tissue

ation of Oral and Maxillofacial Surgeons. This is an

cense (http://creativecommons.org/licenses/by/4.0/).


http://creativecommons.org/licenses/by/4.0/



http://creativecommons.org/licenses/by/4.0/

2 Vittert et al.


relationship3. This is reported as an im-provement in peer assessment rating(PAR) score4–6.Currently there are no standardized out-

come measures to assess the soft tissuechanges produced following orthognathicsurgery. Previous studies have reported onsoft tissue changes between pre-surgeryand post-surgery facial shapes. Very fewstudies have reported on the outcome ofsurgery in comparison to a ‘normal’ ref-erence group7. This distinction is impor-tant, as the elective surgical procedure,driven predominantly by aesthetics,should result in a ‘peer-acceptable’ facialsoft tissue appearance. In one study, laser-scanned images of 80 adult subjects withno known facial disharmony wereobtained, in order to produce an averagethree-dimensional (3D) facial template forthe comparison of facial disproportion8.However, an average shape does not cap-ture the variation that exists in a normalpopulation. The primary aim of the studyreported here was to compare groups ofpost-surgical patients with a sample ofcontrols.Systematic analysis requires structured

information to be derived from raw facialsurface images, to allow clear anatomicalinterpretation. Landmarks are a traditionaland very useful starting point, but repre-sentations of the full facial surface providemuch richer mechanisms for studying theshapes, and shape changes, of interest.There are several approaches to construct-ing surface representations, with a major-ity of these employing landmarks as astarting point. A common approachemploys a surface template that is de-formed, or warped, so that landmark po-sitions on the template match exactlythose on the surface of interest. This ap-proach has been used to develop a densepoint correspondence model, where stan-dardized non-landmark locations on theimage of interest are identified as theclosest points to the corresponding posi-tions on the warped template9. A furtherdevelopment of this approach was madeby adding information on local surfacecurvature to guide deformation of thetemplate and increase the quality of thematch between the two surfaces in geo-metrical terms10. A different approach,applied to human faces, uses a Rieman-nian framework to produce a coordinatesystem that allows both deformation andcomparison using a single elastic metric11.A Darcyan curvilinear coordinate system,based on the geodesic distance functionfrom a fixed reference point, allows thefacial surface to be represented as anindexed collection of level curves. In the

Please cite this article in press as: Vittert L

analysis, Int J Oral Maxillofac Surg (2018)

study reported here, a new method isemployed12. This uses surface curvatureinformation to augment manually identi-fied anatomical landmarks with anatomi-cal curves and extend these into a fullsurface representation. The hierarchicalnature of this process is illustrated graphi-cally in Fig. 1.The aim of this study was to perform a

systematic analysis of images from post-surgical orthognathic patients in order toassess outcomes. The principal focus wason the comparison of postoperative facialappearance with the facial shape of con-trols. This was first conducted at the grouplevel, to explore evidence of any system-atic differences in outcome amongpatients undergoing orthognathic surgery.It was also applied at the individual levelto assess the post-surgical shape of partic-ular patients.

Materials and methods

Image capture

The 3D facial images of 40 patients due toundergo orthognathic surgery were cap-tured at the University of Glasgow DentalSchool using a stereophotogrammetriccamera system (Di3D; Dimensional Imag-ing Ltd, Glasgow, UK) and a captureprotocol developed by the Face3D project,funded by the Wellcome Trust (see fund-ing acknowledgements).

Orthognathic group

All patients were diagnosed and had sur-gery planned using a comprehensive clin-ical and radiographic assessmentperformed by the multidisciplinary team.Patients were subdivided into three groupsaccording to the surgical correction per-formed: Le Fort I maxillary advancement(n = 20), bilateral sagittal split mandibularadvancement (n = 8), and bimaxillary ad-vancement surgery (n = 12). The verticalmaxillary position did not require correc-tion. None of the patients exhibited facialasymmetry that warranted surgical correc-tion. All orthognathic patients were cap-tured shortly before surgery and at 1 yearpost-surgery.

Control group

In order to obtain information on facialshape in the population at large, 169 con-trol facial images were also captured fromvolunteers from local communities inGlasgow. Subjects were asked to providebasic demographic information, includingage, sex, ethnic background, and any con-

, et al. Assessing the outcome of orthognathic

, https://doi.org/10.1016/j.ijom.2018.05.024

cerns or history of craniofacial anomalies,surgery, or trauma. This was used to createa control database with sufficient homo-geneity to provide a focused comparisonwith the characteristics of the patients whohad orthognathic surgery. Specifically, thefollowing inclusion criteria were applied:(1) all parents and grandparents of WhiteBritish, White Scottish, or White Irishorigin (note that White Scottish is not asubset of White British); (2) no history ofcleft lip/palate in the individual or a first-degree relative; (3) no history of facialaccidents, facial surgery, or interest inseeking facial surgery; (4) age <53 years,to match the age range of the orthognathicpatients.In selecting control subjects, it was

possible that some would exhibit facialdysmorphology that trained medical per-sonnel might advise merits orthognathiccorrection. However, inclusion criteria 2and 3 made the probability of severe clin-ical dysmorphology low, and the presenceof a small number of cases of mild dys-morphology would not substantially affectresults in a control group of this size.Retaining any such marginal cases alsowould have the merit of properly reflectingthe facial variation present in the popula-tion at large.Figure 2 and Table 1 show the patterns

of sex and age for the 40 orthognathicpatients and 169 control subjects includedin the analysis. Although the number oforthognathic cases was much smaller thanthe number of controls, the age distribu-tion in the two groups was very similar.

Landmarking

All images were manually annotated with23 standard anatomical landmarks, as in-dicated in the left hand image of Fig. 1,using Landmark IDAV software13. Sets ofanatomical curves were then produced,using the anatomical landmarks as startingpoints. These curves are illustrated in thesecond image of Fig. 1. Full surfacemeshes were then constructed12, as illus-trated in the remaining images of Fig. 1.

Statistical analysis

The first step in exploring differencesbetween the post-surgical and controlpopulations was to register the imagesthrough generalized Procrustes superim-position on the discretized mesh (shown inthe third and fourth images of Fig. 1) withlocation, orientation, and scale effects re-moved. The Procrustes mean shapes couldthen be viewed, split by type of surgeryand sex, as displayed in Fig. 3. Of course,



3D soft tissue analysis in orthognathic surgery 3


Please cite this article in press as: Vittert L, et al. Assessing the outcome of orthognathic

analysis, Int J Oral Maxillofac Surg (2018), https://doi.org/10.1016/j.ijom.2018.05.024

Fig. 1. The process of construction of a facial surface model. The images from left to right show the 23 anatomical landmarks (two at the ears notvisible), anatomical curves, and a full facial mesh in discretized and rendered forms.

Fig. 2. Histograms of the ages of orthognathic and control patients.

these means cannot usefully be interpretedwithout considering the associated varia-tion. Principal components analysis (PCA)is a statistical method designed for data-sets where many variables are measuredon each subject14. PCA creates a smallernumber of new variables, referred to asprincipal components (PCs), which areable to express the bulk of the variationin the data. Each successive PC is con-structed as a linear combination of theoriginal variables, with the aim of captur-



4 Vittert et al.


Table 1. Sample sizes by sex and type of surgery, in the control and orthognathic surgerygroups.

Male Female Total

OrthognathicMaxilla, Le Fort 4 16 20Mandible, BSSO 4 4 8Bimaxillary, combined 5 7 12

All orthognathic 13 27 40Controls 83 86 169

BSSO, bilateral sagittal split osteotomy.

ing as much variation in the data as possi-ble. The proportion of variability capturedby each PC diminishes successively. In thepresent study, the first 10 PCs were foundto capture 84% of the total variability inthe data. Analysis of this small number ofPCs therefore provides a very effectivemeans of studying the patterns in the data,as an alternative to analysing the muchlarger number of individual variables re-



Fig. 3. Mean shape of control subjects (blue) a

quired to define each mesh. Each PC isassociated with a particular type of shapechange, which can be represented andinterpreted graphically.Evidence of differences in mean shape

was assessed through a two-sampleHotelling T2 test, applied to the PC scores.In order to protect against inappropriatedistributional assumptions, these testswere implemented in permutation form



nd post-surgical patients (magenta) for each type

(500 permutations). A more detailed anal-ysis of individual PCs was also performedthrough t-tests. PCs are constructed not toidentify differences between groups butthe shape changes that successively cap-ture as much variability as possible. Thefirst few components therefore correspondto the dominant general sources of vari-ability in facial shape, while lower com-ponents are more likely to carry theinformation on group differences.With several groups to be compared to

controls, a single global assessment of theevidence for change in mean shape acrossall groups was conducted simultaneously.However, as different surgical groups maydisplay different departures from theshape of controls, separate analyses basedon the comparison of each group againstcontrols were applied to maximize theopportunity for these differences to beexpressed.


of surgery and each sex.




An assessment of facial asymmetry be-fore and after orthognathic surgery wasalso carried out. The resulting asymmetryscores represent the square-root of thesummed squared distances between eachlocation on the surface representation andits partner in the reflected, relabelled, andProcrustes-matched version. Several dif-ferent approaches to this have beenproposed15–17, and some allow the con-struction of a decomposition associatedwith individual features, when these areavailable18. For analysis, use of a furthersquare-root transformation of the scores isrecommended, as this transforms thescores to a scale of measurement wherethe variability is approximately normallydistributed18. This additional square-roottransformation was applied in the presentstudy. Asymmetry scores were also com-puted for individual features, namely thelower face, the nose, and the upper andlower lips. Paired t-tests were used toassess the evidence for differences inpre-surgical and post-surgical mean asym-metry scores, within each surgical group.In order to protect against the effects of

multiple testing, Bonferroni adjustments(equivalent to multiplying the P-values bythe number of tests carried out) were usedwhen interpreting the results.All calculations were conducted in the

statistical computing environment R (RFoundation for Statistical Computing,Vienna, Austria)19.

Results

Differences in mean shape

Overall evidence for systematic differ-ences was assessed through Hotelling T2

tests, as shown in Table 2. The evidence ofdifferences in mean values between post-surgical and control groups was found tobe unconvincing for male subjects butstrong for female subjects, driven largelyby the group of patients who underwent LeFort I maxillary advancement. This wasthe category with the largest number oforthognathic cases (n = 16) and hence thestrongest potential to identify differences.



Table 2. Differences in the means of the post-orthognathic and control populations, basedon 10 components: P-values from the Hotell-ing T2 test.

Male Female

Maxilla, Le Fort I 0.105 0.002Mandible, BSSO 0.066 0.058Bimaxillary, combined 0.153 0.050All 0.060 0.001

BSSO, bilateral sagittal split osteotomy.

The evidence is further borne out inFig. 4, where the ranges of successivescores reflect the decreasing amounts ofvariability captured. The box plots foreach PC are coloured to show the strengthof the two-sample t-statistic. Strong dif-ferences between controls and post-orthognathic cases were found in the thirdand seventh PCs, with P-values of 0.001and 0.026, respectively. Bonferroni cor-rection for multiple testing led to a refer-ence of 0.05/10 = 0.005, which highlightsthe third PC as the source of shape differ-ences between the female patients whohad undergone maxillary Le Fort I osteot-omy and the control cases.The shape change associated with the

third PC is displayed in Fig. 4, using the‘extreme’ shapes associated with 3 stan-dard deviations from the overall mean.Positive scores in this PC correspond toprotrusion of the entire midface, an effectthat is mirrored by the mean shape differ-ences in the top right-hand images ofFig. 3. This therefore suggests that a moreharmonious result might be achieved forfemale patients undergoing Le Fort I max-illary advancement if mandibular setbacksurgery is performed at the same time.

Assessment of individual patients

While it is of interest to identify system-atic differences in shape between the post-surgical and control groups, it is also ofconsiderable clinical interest to assess in-dividual patients against the patternsexhibited in the control group. This isillustrated in Fig. 5. The middle row ofimages characterizes the variation in thecontrol group associated with the third PC.(This is the PC associated with a system-atic difference in shape between the post-surgical and control populations.) Thecentral shape shows the control mean,while the others display the shapes asso-ciated with �1, �2, and �3 standarddeviations away from this mean, alongthe third PC. The images for �2 standarddeviations show the limits between whichapproximately 95% of the variation inshape lies. This can be considered to de-fine a ‘normal range’ for control shape inthis PC. The images for �3 standarddeviations indicate much more unusualcontrol shapes.This gives a very helpful scale against

which individual post-surgical patientscan be assessed. The shapes of two indi-vidual patients are shown above and belowthe control patterns. The two images foreach patient correspond to the pre- andpost-surgical shapes, and the post-surgicalshape is placed on the scale at the position



corresponding to the score on the third PC(now expressed in control standard devia-tions). For patients 1 and 2, the positionsfor the post-surgical shapes were 0.793and 2.121, respectively. The pre-surgicalshapes clearly reflect the inconsistencywith control shape that prompted surgicalintervention. For patient 1, the post-surgi-cal shape was quite consistent with thecontrols, as it was found to lie within thenormal range (�2 standard deviations) ofthe observed control variation. For patient2, the outcome was a little unusual in thepositive PC direction, with greater mid-face prominence than would normally beexpected in controls. These two examplesillustrate how surgical outcomes can help-fully be assessed in a quantitative manner.

Asymmetry

The asymmetry scores for controls togeth-er with pre-surgical and post-surgicalorthognathic cases are illustrated inFig. 6. The first column of plots inFig. 6 compares pre-surgical and post-surgical asymmetry with that of controls.The remaining columns disaggregate theorthognathic cases into the different sur-gical groups, but the numbers involvedhere are too small to provide evidenceof differences. The analysis is thereforeconcentrated on the combined surgicalgroups. The data are also combined acrossthe sexes. Although male and femaleshape may be systematically different,there is no evidence of differential asym-metry.The rows of Fig. 6 refer to asymmetry

measurements from different parts of theface. The top two rows show scores fromthe whole face, constructed from anatom-ical curves (first row) and the full facialmesh (second row). The marked similarityhere indicates that the facial curves areeffective in capturing asymmetry, withlittle information added by the more de-tailed mesh. The four lower rows constructmesh asymmetry measurements from par-ticular features: the lower face, nose, andupper and lower lips. (Note that the smal-ler spatial extent of these regions leads tocloser Procrustes matching and hence toscores that are intrinsically slightly lower.)In the first column of plots, which dis-

play global asymmetry, colour is used toindicate the strength of evidence for dif-ferences in means. The pre-surgicalgroups are coloured by the value of thet-statistic for a pair-wise comparison withpost-surgical measurements. (Boxplots donot display the links between the pre-surgical and post-surgical pairs, but theyare a useful means of displaying the over-



6 Vittert et al.


Fig. 4. Shape change associated with the third principal component for female control subjects and maxilla Le Fort I post-surgical cases. Top: boxplots of principal component scores, where the colour of the box plot indicates the size of the t-statistic. Bottom: suitably magnified shapescorresponding to the extremes (3 standard deviations) from a negative score (blue) to a maximal (positive) score (magenta).

all patterns of the scores.) Strong evidencewas found for a reduction in asymmetry inthe upper lips (P-value = 0.003), but onlymarginal evidence for the nose (P-val-ue = 0.011), with the evidence expressedin this latter value considerably dimin-ished by the Bonferroni correction factorof a multiple of 6 for the number of testsinvolved. The post-surgical groups arecoloured by the value of the t-statisticfor a two-sample comparison of post-sur-gical cases with the controls. No convinc-ing evidence was found here that post-surgical asymmetry was greater in com-parison to controls. (The smallest P-valueis 0.042 for the upper lips.)

Discussion

The most significant finding of this studyis the residual mandibular prognathismthat was detected in the group of patients



who had undergone Le Fort I osteotomyfor the correction of maxillary retrognath-ism. These cases had the facial character-istics of a class III skeletal relationship dueto the combined maxillary hypoplasia andmandibular prognathism. The decisionwas taken to limit the correction to LeFort maxillary osteotomy only, in order tominimize the magnitude of surgical inter-vention and eliminate the potential mor-bidities associated with the mandibularsagittal split osteotomy, which includespermanent numbness of the lower lip sec-ondary to damage to the inferior alveolarnerve. It was also predicted and agreedwith the patients that maxillary advance-ment only would achieve the desired im-provement in facial appearance.The rationale of this study was to guide

orthognathic surgery towards a 3D softtissue facial shape that lies within therange of the relevant control population,



with similar age, sex, and ethnic charac-teristics. The availability of 3D images ofthe soft tissue of the face provides theclinician with the opportunity to analyse,predict, and compare the outcomes inrelation to a relevant control group. Theresults of this study suggest that there aresignificant differences in mean facial ap-pearance between some post-surgicalorthognathic patient groups and the cor-responding control group. The resultspresented in this study give a clear indi-cation of the benefits of auditing, andpotentially improving, the outcome ofsurgery, using population-based data asan informative reference. It has beenshown that although populations of whitedescent have strong similarities, they alsodisplay distinct morphological differen-ces8. It is therefore important that mor-phological norms are specificallyconstructed for each population, in order





Fig. 5. The middle row of images shows the shape change associated with the third principal component for female controls. The central imageshows the control mean, while the others illustrate the shapes associated with �1, �2, and �3 standard deviations of the control variation. Theupper and lower rows show the pre-surgical (boxed) and post-surgical (red dashed line) shapes of two individual female patients undergoingmaxilla Le Fort I surgery.

to establish effective normative data toguide orthognathic surgical correction.Maxillary hypoplasia is usually managed

with a Le Fort I maxillary advancement,while the need for simultaneous mandibularsurgery depends on the magnitude of themaxillomandibular discrepancies. In classIII skeletal relationships, the bilateral sag-ittal split osteotomy is indicated if clinicalassessment leads to a diagnosis of mandib-ular prognathism that requires treatment,and/or the measured discrepancy betweenthe maxilla and the mandible is more than10 mm. In most of these cases, mandibularsetback surgery reduces the magnitude ofthe required Le Fort I maxillary advance-ment, which impacts positively on the long-term stability20,21. In some subgroups ofclass III skeletal relationship, the mandibleis in the correct position in relation to thenose and the upper mid third of the face. Inthese cases, a simultaneous advancementgenioplasty is performed if mandibular set-back surgery is to be carried out to deal withthe marked occlusal discrepancy. Thiscould be avoided in the pre-surgical



orthodontic phase; partial dental decom-pensation should be considered to reducethe occlusal discrepancy and determine themagnitude of the required maxillary surgi-cal movement. Following this protocol mayeliminate the need for a simultaneous man-dibular procedure.Another important aspect that influ-

ences the decision-making process regard-ing the need for a simultaneousmandibular surgical procedure is thepatient’s perception of their facial appear-ance and the desired improvements fol-lowing surgery. In class III skeletalrelationships mainly due to predominantmaxillary deficiency, patients are focusedon their paranasal hollowing, increasedsclera show above the lower eyelids, theflattened upper lip, lack of upper lip full-ness, and the increased nasolabial angle.Most of these perceived facial dys-morphologies will be readily addressedwith a Le Fort I advancement osteotomy.The clinical features of any accompanyingmandibular prognathism are generallymild and are thought to be acceptable to



both the patient and the surgical teamfollowing computerized 3D predictionplanning. This result is not surprising, asthe aim of treatment is to restore facialharmony, which is not absolute but withina range of levels of acceptability.When evaluating surgical outcomes,

there is particular interest in asymmetry.All faces are asymmetric to some degree,but pronounced asymmetry is a feature towhich the human visual system is stronglysensitive. With orthognathic patients, sur-gery is not conducted principally to reduceasymmetry, but these patients are morelikely to exhibit asymmetry than othersand so a post-surgical reduction in asym-metry is of interest. There is also thepossibility that surgery may inadvertentlyincrease asymmetry22. The quantificationand evaluation of asymmetry is thereforevaluable. It is reassuring that some evi-dence was found of a reduction in asym-metry between pre-surgical and post-surgical facial shape, while no evidencewas found of increased post-surgicalasymmetry in comparison to controls.



8 Vittert et al.


Fig. 6. Asymmetry scores for controls together with pre-surgical and post-surgical orthognathic cases. The surgical groups are distinguished by L(Le Fort I maxillary advancement), BO (mandible bilateral sagittal split osteotomy), and Bi (bimaxillary combined surgery). In the first column ofplots, the colour of the pre-surgical box plot indicates the size of the t-statistic for a paired comparison of means with the post-surgical group, whilethe colour of the post-surgical box plot indicates the size of the t-statistic for a two-sample comparison of means with the control group.

The results reported here are based onmodest numbers of patients from a singlesurgical centre. The issues of sample sizebecome more acute when the data are splitby sex or by surgical group. However, thestudy has demonstrated the value of 3Dsoft tissue analysis and given a valuableinsight into orthognathic surgical out-comes.

Funding

This research was supported by a Well-come Trust grant (WT086901MA) to theFace3D research consortium.



Competing interests

None.

Ethical approval

This study was approved by the West ofScotland Ethics Committee 5 (reference10/S1001/19) for orthognathic patientsand the Ethics Committee of the Collegeof Science and Engineering, University ofGlasgow, for controls.

Patient consent

Not required.



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Address:Adrian BowmanSchool of Mathematics and StatisticsThe University of GlasgowGlasgow G12 8QQUKE-mail: [email protected]








































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