Darvann, Tron Andre

Ersbøll, Bjarne Kjær

Frangi, Alejandro F.

Hermann, Nuno V.

Kreiborg, Sven

Larsen, Per

Morriss-Kay, Gillian

Oubel, Estanislao

Perlyn, Chad A.

Ólafsdóttir, Hildur

This paper presents the automatic assessment of differences between Wild-Type mice and Crouzon mice based on high-resolution 3D Micro CT data. One factor used for the diagnosis of Crouzon syndrome in humans is the cephalic index, which is the skull width/length ratio. This index has traditionally been computed by time-consuming manual measurements that prevent large-scale populational studies. In this study, an automatic method to estimate cephalic index for this mouse model of Crouzon syndrome is presented. The method is based on constructing a craniofacial atlas of Wild-type mice and then registering each mouse to the atlas using affine transformations. The skull length and width are then measured on the atlas and propagated to all subjects to obtain automatic measurements of the cephalic index. The registration accuracy was estimated by RMS landmark errors. Even though the accuracy of landmark matching is limited using only affine transformations, the errors were considered acceptable. The automatic estimation of the cephalic index was in full agreement with the gold standard measurements. Discriminant analysis of the three scaling parameters resulted in a good classification of the mouse groups

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Automatic Assessment of Global CraniofacialDifferences between Crouzon mice andWild-Type mice in terms of the Cephalic IndexHildur O´lafsdo´ttir1, Estanislao Oubel2, Alejandro F. Frangi2, Tron Darvann3,Nuno V. Hermann3,4, Sven Kreiborg3,4,5, Per Larsen1, Bjarne K. Ersbøll1,Chad A. Perlyn6, and Gillian Morriss-Kay71 Informatics and Mathematical Modelling, Technical University of Denmark,ho@imm.dtu.dk2 Computational Imaging Lab, Department of Technology - D.326, Pompeu FabraUniversity, Barcelona3 3D-Laboratory, School of Dentistry, University of Copenhagen; CopenhagenUniversity Hospital4 Department of Pediatric Dentistry and Clinical Genetics, School of Dentistry,Faculty of Health Sciences, University of Copenhagen5 Department of Clinical Genetics, The Juliane Marie Centre, CopenhagenUniversity Hospital, Copenhagen, Denmark6 Division of Plastic Surgery, Washington University School of Medicine7 Department of Physiology, Anatomy and Genetics, Oxford University, Oxford, UKAbstract. This paper presents the automatic assessment of differencesbetween Wild-Type mice and Crouzon mice based on high-resolution 3DMicro CT data. One factor used for the diagnosis of Crouzon syndromein humans is the cephalic index, which is the skull width/length ratio.This index has traditionally been computed by time-consuming man-ual measurements that prevent large-scale populational studies. In thisstudy, an automatic method to estimate cephalic index for this mousemodel of Crouzon syndrome is presented. The method is based on con-structing a craniofacial atlas of Wild-type mice and then registering eachmouse to the atlas using affine transformations. The skull length andwidth are then measured on the atlas and propagated to all subjects toobtain automatic measurements of the cephalic index. The registrationaccuracy was estimated by RMS landmark errors. Even though the accu-racy of landmark matching is limited using only affine transformations,the errors were considered acceptable. The automatic estimation of thecephalic index was in full agreement with the gold standard measure-ments. Discriminant analysis of the three scaling parameters resulted ina good classification of the mouse groups.1 IntroductionCrouzon syndrome was first described nearly a century ago when calvarial defor-mities, facial anomalies, and abnormal protrusion of the eyeball were reported ina mother and her son [1]. Later, the condition was characterized as a constellationof premature fusion of the cranial sutures (craniosynostosis), orbital deformity,maxillary hypoplasia, beaked nose, overcrowding of teeth, and high arched orcleft palate. Identification of heterozygous mutations in the gene encoding fi-broblast growth factor receptor type 2 (FGFR2) have been found responsible forCrouzon syndrome [2]. Recently a mouse model was created to study one ofthese mutations (FGFR2Cys342Tyr)[3].The severity of Crouzon syndrome is of various stages and often it is difficultto estimate. One of the factors measured when diagnosing children with Crouzonsyndrome is the cephalic index (CI). Currently, this is obtained by manual mea-surements of the skull. A step towards automating the diagnosis of children withCrouzon syndrome and quantifying the severity of the syndrome is presentedhere. In [4] it was shown that manual measurements of skull parameters on themouse model were in correspondence with those obtained in humans. Further,they gave discrimination between Crouzon and Wild-type (WT) mice. This pa-per extends this work by presenting an automatic method for quantifying thedifferences in CI between mouse groups. This was achieved by constructing acraniofacial WT mouse atlas from 3D Micro CT data and then acquiring CIs byregistering each subject to the atlas by an affine transformation. The consistencywith manual measurements from [4] were then investigated. Additionally, a sta-tistical analysis of the anisotropic scaling parameters was performed in order tofurther examine the differences between the two groups.In addition to the automatisation of the diagnosis of Crouzon syndrome, itis anticipated that this study will contribute to our understanding of how pre-mature fusion of sutures and synchrondroses affects craniofacial morphogenesis.The outline of the paper is the following. In the next section, data acquisitionand methodology will be discussed. Section 3 presents the experimental resultsin terms of registration accuracy, consistency with manual measurements of CIand statistical analysis of group differences. Section 4 provides a discussion ofthe results and conclusions.2 Methods and Materials2.1 DataProduction of the FGFR2C342Y/+ and FGFR2C342Y/C342Y mutant mouse (Crou-zon mouse) has been previously described [3]. All procedures were carried out inagreement with the United Kingdom Animals (Scientific Procedures) Act, guide-lines of the Home Office, and regulations of the University of Oxford. Mutantmice of breeding age were determined by phenotype.For three-dimensional (3D) CT scanning, 10 WT and 10 FGFR2C342Y/+specimens at six weeks of age (42 days) were sacrificed using Schedule I meth-ods and fixed in 95% ethanol. They were sealed in conical tubes and shippedto the Micro CT imaging facility at the University of Utah. Images of the skullwere obtained at approximately 46µm × 46µm × 46µm resolution using a Gen-eral Electric Medical Systems EVS-RS9 Micro CT scanner. Figure 1 shows anexample of the mice and imaging data appearance.(a) (b) (c)Fig. 1. (a) Photo of a Crouzon mouse (left) and a WT mouse (right). Skulls Extractedfrom CT images of (b) a Crouzon mouse, (c) WT mouse.2.2 Cephalic indexThe cephalic index is defined as CI = (W/L) · 100, where W is the skull width(the distance between the left- and rightmost lateral points (euryon) on theskull) and L is the skull length (the distance from nasale to to most distantpoint on occipital bone). This index contributes to quantify the severity of theCrouzon syndrome. For humans, a CI over 80 is connected to brachycephaly,seen in children with premature fusion of the coronal sutures bilaterally. This isone of the indicators for Crouzon syndrome.2.3 Image registrationAn image registration algorithm aims at optimising a similarity metric withrespect to a transformation of a given type. In this study, Sum of Squared Dif-ferences (SSD) and Cross Correlation (CC) and Normalised Mutual Information(NMI) were tested as similarity metrics. In short, NMI outperformed the othertwo and was therefore used in the remaining experiments. The type of trans-formations used here was selected with the application in mind. Since the aimof the study was to investigate the CI, affine transformations with anisotropicscaling parameters were applied (i.e. nine degrees of freedom). For this study, theimplementation of an affine registration algorithm by Rueckert8 [5] was adopted.8 http://www.doc.ic.ac.uk/∼dr/software/2.4 PreprocessingPrior to registration of the images, a few steps needed to be made. In order toinitialise the registration close to the region of capture for NMI, four landmarkswere used to align all mice with respect to their mid-sagittal planes (MSP). Sec-ondly, the neck part was removed from all 20 cases since heads were removed atdifferent positions prior to scanning. Additionally, the mice had different jaw po-sitions, which could give problems in the registration due to a possible change intopology (closed vs. open mouth). The shape differences of the mandible (lowerjaw) are not of interest in this study since they are considered a secondary conse-quence of the syndrome. Therefore, the mandible was manually segmented andmasked out. The same applied to the hyoid bone. Furthermore, in order to speedup registrations and removing bias due to different orientations in background,a region of interest (ROI) was defined automatically in the images. The skullwas segmented by thresholding and subsequently a sequence of dilations anderosions were carried out resulting in a ROI nicely body-fitted around the skull.2.5 Atlas ConstructionThe craniofacial atlas was generated from the set of WT mice. Although the setincludes few subjects (10 cases) the biological variation is small since they all hadthe same DNA and it was therefore considered reasonable to build an atlas fromthis set. The atlas was generated as follows. A reference subject was chosen fromthe set to represent the initial atlas. The remaining subjects were registered tothe atlas using the affine transformation (9 degrees of freedom). In each iterationa new atlas was generated by averaging the transformed images, including only“active voxels” (i.e. voxels which had not been masked out). The procedure wasrepeated until the Mean Squared Error (MSE) between two successive atlasesdropped below a given limit. In order to remove bias towards the choice of areference subject, the atlas was transformed into its affine natural coordinateswith a procedure similar to the one described in [6]. In our case, the naturalcoordinate system was defined in terms of an affine transformation, since wewere to discriminate between the mouse groups in terms of scaling parameters.In this way, the atlas had aspect ratio and gross shape corresponding to theaverage of the population used in its construction as opposed to be biased to themouse used as starting point for atlas building. The average scalings from all theregistrations were calculated, and the inverses of these scalings were applied tothe atlas to transform it into the affine natural coordinate system. After atlasconstruction, relabelling was carried out, i.e. mandible, hyoid bone and neck weresegmented and masked out of the atlas in order to assure proper masks in thesubsequent registration experiments. The resulting atlas is shown in Figure 2.(a) (b) (c) (d)Fig. 2. (a) Axial, (b) sagittal and (c) coronal views of the craniofacial WT mouse atlas.(d) 3D surface view of the atlas.3 Experimental Results3.1 Evaluation of Registration AccuracyTo give a qualitative impression of the registration accuracy, Figures 3 showsthe difference images for registration of a Crouzon mouse to the atlas. For thequantitative evaluation of the registration accuracy, the average of two sets ofmanually annotated landmarks, set by two independent observers were used as agold standard (GS). Landmarks were obtained in the atlas domain by propagat-ing the GS landmarks from each subject to the atlas by using the transformationsobtained by the registration. Landmark registration errors were calculated as theEuclidean distances of each of the transformed landmarks to the correspondingGS landmark on the atlas (point to point errors). From those, RMS errors werecalculated. Table 1 presents the registration errors. An examination of the errorsfor Crouzon cases in terms of Euclidean distances of each landmark (point topoint error) is presented in Figure 4.Table 1. Registration errors in mm: Errors between an observer and GS and errorsbetween the automatic method and the GS.Errors [mm] RMS SD Med Max MinOBS - GS, WT 0.1845 0.0490 0.1827 0.2937 0.1318Automatic - GS, WT 0.5435 0.07089 0.542 0.7081 0.4548OBS - GS, Crouzon 0.1741 0.0269 0.1728 0.2175 0.1400Automatic - GS, Crouzon 1.1370 0.1754 1.1761 1.4223 0.87133.2 Consistency with previous resultsIn a previous study of the same dataset, manual measurements of seven skullparameters were performed [4]. Two of those were the skull width and length(a) (b) (c)Fig. 3. Difference images before (above) and after (below) registration of a Crouzonmouse to the atlas in (a) axial, (b) saggital and (c) coronal view.1 2 3 4 5 6 7 8 9 10 111213 141516 1718 192021 2223 24252600.511.522.533.54Landmark error [mm]Landmark number1 2 3 4 5 6 7 8 9 10 111213 141516 1718 192021 2223 24252600.511.522.533.54Landmark number(a) (b)Fig. 4. Errors for Crouzon mice. (a): Automatic vs. GS. (b): Observer vs. GS.from which the CI was derived. These measurements were used as a GS. Toautomatically estimate the CI, landmarks defining the skull width and lengthwere manually placed on the atlas. Subsequently, these were propagated to allsubjects using the inverse of the transformations obtained previously by theregistration. Figure 5 shows the CI plotted for the automatic approach and theGS for both groups of mice. Further, the figure shows a Bland-Altman plot for theCrouzon mice to further evaluate the the accuracy of the automatic method withrespect to the GS and to include an examination of inter-observer variability. Inaddition to the plots shown in Figure 5 a paired t-test was applied to comparethe automatic method to the GS. The test stated that the difference betweenthe two methods was statistically insignificant in terms of the CI.0 2 4 6 8 10 12 14 16 18 203840424446485052545658Mouse numberCI [%]Automatic normalGS normalAutomatic CrouzonGS Crouzon0.5 0.51 0.52 0.53 0.54 0.55−0.04−0.03−0.02−0.0100.010.020.030.040.05(CImethod+CIGS)/N [%]CImethod−CIGS [%]Automatic vs. GSOBS I vs. GSOBS II vs. GS+ 2SD− 2SD Bias(a) (b)Fig. 5. (a) CI estimated by the automatic method compared to the GS, plotted forWT mice and Crouzon mice. (b) Bland-Altman plots for CI measured on Crouzonmice. The plot shows the bias with respect to the GS for three different approaches,the automatic method and the manual measurements from the two observers.3.3 Statistical analysis of group differencesThe differences between the two groups were analysed in terms of the scalingparameters, sx, sy and sz required for each registration. For this purpose, aFisher Linear Discriminant analysis was applied. Figure 6 shows a plot of thethree scaling parameters with the Fisher discriminator plane included.4 Discussion and ConclusionsThe difference images shown in Figure 3 indicate that an affine registration is ableto compensate for the gross craniofacial shape changes between a Crouzon mouseand the WT mouse atlas. The registration errors in Table 1 were not expectedto outperform the observer error since differences between individual skulls cannever be modelled completely by an affine transformation. Keeping that in mindwe consider the registration errors for the WT mice acceptable. The errors forCrouzon cases are quite high. Judged from the left plot in Figure 4, the errorsare highly dependent on landmark positions. Some landmarks have considerably0.90.9510.90.95111.051.11.151.21.25sysxs zWTCrouzonFig. 6. Scaling parameters: sx, sy and sz for registration of WT mice and Crouzonmice to atlas. Fisher linear discriminator is shown.higher error than others. Due to the fact that an affine transformation is used, itis to be expected that some landmarks are more difficult to match than others.An inspection of the landmark positions revealed that the most problematiclandmarks were placed at the skull sutures. The Crouzon syndrome has provento cause early suture patency and the skull growth is known to be hinderedand very complex at these regions. It is therefore not surprising that additionalnonrigid warps are assumably required to match landmarks in this region and todescribe in more detail the Crouzon phenotype. However, it is noted that mostof the errors lie around 0.5 mm, which is close to the errors from the observer-GSplot to the right. In general the landmark errors are considered acceptable for themain topic of this paper, i.e. building a global morphometric tool to automatethe discrimination of different groups of mice in terms of the CI and scalingparameters. From Figure 5, one can observe that the differences between themanual and automatic methods and the GS for estimating CI are very similar.This was confirmed by the paired t-test. This result suggests that it is possibleto quantify the CI without actually measuring it manually. The plot in Figure6 demonstrates that the skulls of WT mice and Crouzon mice differ in terms ofscaling parameters of the registration. This especially applies to the z-direction,which is correlated to the difference in skull length. The Fisher discriminatorconfirms this, by a perfect classification between the two groups.In summary, an automatic assessment of differences in Crouzon and Wild-Type mice in terms of the cephalic index and scaling parameters has been pre-sented. Good consistency with manual measurements was obtained and it isconcluded that automatic assessment of the cephalic index to quantify severityof Crouzon syndrome can replace manual measurements.References1. Crouzon, O.: De l’acrocephalosyndactylie. Bull Soc. Med. Paris 35 (1912) 13102. Reardon, W., Winter, R.M., Rutland, P., Pulleyn, L.J., Jones, B.M., Malcolm, S.:Mutations in the fibroblast growth factor receptor 2 gene cause Crouzon syndrome.Nat Genet 8 (1994) 98–1033. Eswarakumar, V.P., Horowitz, M.C., Locklin, R., Morriss-Kay, G.M., Lonai, P.: Again-of-function mutation of fgfr2c demonstrates the roles of this receptor variantin osteogenesis. Proc Natl Acad Sci, U.S.A. 101 (2004) 12555–604. Perlyn, C.A., DeLeon, V.B., Babbs, C., Govier, D., Burell, L., Darvann, T., Krei-borg, S., Morriss-Kay, G.: The craniofacial phenotype of the Crouzon mouse: Anal-ysis of a model for syndromic craniosynostosis using 3D MicroCT. Cleft PalateCraniofac. J (2006, in press)5. Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., Leach, M.O., Hawkes, D.J.:Nonrigid registration using free-form deformations: application to breast MR im-ages. Medical Imaging, IEEE Trans. on 18(8) (1999) 712–7216. Frangi, A.F., Rueckert, D., Schnabel, J.A., Niessen, W.J.: Automatic constructionof multiple-object three-dimensional statistical shape models: Application to cardiacmodeling. IEEE Transactions on Medical Imaging 21(9) (2002) 1151–1166

Automatic Assessment of Global Craniofacial Differences between Crouzon mice and Wild-type mice in terms of the Cephalic Index

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Automatic Assessment of Global Craniofacial Differences between Crouzon mice and Wild-type mice in terms of the Cephalic Index

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