A Comparative Cephalometric Study of the Cranial Base in Craniofacial Anomalies: Part I: Tensor Analysis Barry H. Grayson, D.D.S. Nei WeintrausB, M.D. Freep L. BookstEin, PH.D. JoseEPH G. McCartHYy, M.D. The method of mean tensor analysis was used to study the cranial base in six craniofacial anomalies: Crouzon's disease, Apert's syn- drome, Pfeiffer's syndrome, craniofacial microsomia (CFM), Treacher Collins (TC) syndrome, and frontonasal dysplasia (FND). The form was represented by five landmarks: the nasion (N), basion (Ba), sella (S), frontomaxilionasal suture (FMN), and sphenoethmoidal registration point (SE), and the deformities were computed as mean deformations from age- and sex-matched normal mean forms. The cranial base in CFM is normal in shape. The other five syndromes manifest four dis- tinct patterns of shape variation. Only in TC and Pfeiffer's syndrome is the cranial-base angle distinctive. In Apert's and Crouzon's syn- dromes, point SE is displaced anteriorly upon a cranial base, small in size but otherwise normal in shape. In TC syndrome and FND, point SE is displaced posteriorly toward the sella. The role of the cranial base in the de- represent the primary site of the pathol- velopment of craniofacial anomalies is not ogy in craniofacial synostosis syndromes well understood. However, it has been (Moss, 1959; Kreiborg and Pruzansky, speculated that cranial base abnormalities 1971; Ousterhout and Melsen, 1982). Widening of the ethmoid portion (pre- sphenoidal portion) of the anterior cranial Dr. Grayson is Associate Professor of Orthodon- base has been observed in orbital hyper- tics at New York University College of Dentistry and telorism, and abnormalities in the cranial Associate Professor of Surgery (Orthodontics) at the base often accompany Treacher Collins New York University Medical Center, Institute of (TC) syndrome (Rogers, 1964). Reconstructive Plastic Surgery, New York University School of Medicine, 560 First Avenue, New York, New The bulk of information reported in the York 10016. Dr. Weintraub is Clinical Instructor in literature on cranial base morphology in Surgery, New York University Medical Center, 550 patients with major craniofacial anomalies First Avenue, New York, New York 10016. Dr. has been derived from measurements of Bookstein is a Research Scientist at the Center for dry skulls from affected individuals or from Human Growth and Development at the University of Michigan, Ann Arbor, Michigan 48109. Dr. conventional cephalometric measure- McCarthy is Director of the Variety Club Center for ments on small samples of patients (Dahl Craniofacial Rehabilitation, Institute of Reconstruc- et al, 1975; Herring et al, 1979; Bjork, tive Plastic Surgery at New York University Medical 1972; Sperber, 1981). Center, 560 First Avenue, New York, New York 10016. In our study, the cephalometrics of the Preparation of this manuscript was supported by cranial base were documented in each of N.LH. Grant DE-03568 to Joseph G. McCarthy, M.D. six groups of children with craniofacial The computer program for tensor computations anomalies: Crouzon's disease, Apert's syn- was developed under N.LH. Grants DE-05410 to F. L. Bookstein and DE-03610 to R. E. Moyers. drome, Pfeiffer's syndrome, craniofacial Mr. Allan Kolber supervised all aspects of the data microsomia (CFM), TC syndrome, and management. ' e frontonasal dysplasia (FND). Age- and sex- 75 76 Cleft Palate Journal, April 1985, Vol. 22 No. 2 matched normal children from the Uni- TABLE 1. Distribution of Sample by Syndrome. versity of Michigan reference population Crouzon's disease 24 (Riolo et al, 1974) served as the controls. Apert's syndrome 11 The typical pattern of difference from Pfeiffer's syndrome 4 normal for each group studied was com- Craniofacial microsomia (CFM) 78 puted and evaluated. Treacher Collins syndrome (TC) 9 Frontonasal dysplasia (FND) 31 N = 157 MATERIALS AND METHODS Figure 1 illustrates the five cranial base landmarks used in this study. The nasion the University of Michigan sample, ages (N) is conventionally defined as the most ranged from 6 to 15 years. The five syn- posterior point on the frontonasal suture dromal cases aged 5 years or less were on the curve at the bridge of the nose. It matched to the University of Michigan is actually seen on the dry skull to be at an means for 6 year olds; all cases aged 15 or intersection of three sutures. The basion older were matched with the University of (Ba) is the most inferior posterior point on Michigan means for 15 year olds. Because the anterior margin of the foramen mag- growth of the cranial base is essentially num. The sella (S8) is the center of the pi- complete by age 14, little error is intro- tuitary fossa of the sphenoid bone and is duced in this step. This population pro- reliably found by a trained technician. vided age- and sex-specific normal mean Frontomaxillonasal suture (FMN) is the forms of the cranial base for comparison junction of the frontal, maxillary, and na- with the study population. sal bones. It is the overlapping image of a laterally symmetric pair of intersections of MEAsUREMENT DESIGN:; DEFORMATION three sutures. Sphenoethmoidal registra- or NoRMAL MEAN INTO STUDY tion point (SE) is the intersection of the PorPULATION MEAN sphenoidal plane with the averaged greater sphenoid wings. The location of this "point" Each cranial base in the study popula- expresses the position of two structures, tion may be viewed as a deformation of . not one. 2 the age- and sex-matched normal mean The locations of the five landmarks were cranial base. The findings of the study in- recorded from the lateral cephalograms of clude the distances, angles, and ratios that 157 individuals, all of whom had one of differ most across the comparison (Book- the six craniofacial anomalies (Table 1). stein, 1983a). To facilitate the visualization From the archives at the Center for Hu- of cranial base deformations in the study man Growth and Development, Ann Ar- population, the landmarks were linked to- bor, Michigan, the same landmarks for 83 gether in sets forming convenient trian- subjects from the University of Michigan gles. From the five landmarks it is possible University School Study were averaged in to define a total of ten triangles for anal- a consistent coordinate system (S-N). In ysis. For six of the ten triangles, the area proved too small for the study of defor- mation to be usefully employed. The four remaining triangles, which are relatively useful for analysis, are diagrammed in Figure 2. TENSOR ANALYSIS Ba The most effective way to describe the FIGURE 1 The cranial base landmarks used in ‘ deformation between a single pair of tri- this study: (N) nasion, (Ba) basion, (S) sella turcica, (FMN) frontomaxillonasal suture, (SE) sphenoeth- angles (Bookstein, 1982a, 1982b, 1983) moidal registration point. begins by considering its effect on length Grayson et al, CRANIAL BASE IN CRANIOFACIAL ANOMALIES "77 FIGURE 3 Changes in shape between two tri- angles may be studied in terms of length measure- ments made in all directions. Lines passing through a single point in the "reference" triangle ABC are compared in length to the corresponding (homolo- gous) lines found in the "deformed" triangle A'B'C'. greater than 1.0 represent increase of length or stretch; dilatations less than 1.0 represent reduction of length or shrink. Circle to Ellipse: The Principal Cross In Figure 3 the dilatations are implied as ratios of corresponding lengths be- tween the triangles. In obtaining these ra- AP tios one may avoid the necessity for divi- Ba sion by beginning with lines of constant length, i.e., diameters of a circle. In the FIGURE 2 Cephalometric landmarks linked to- deformation of a circle (Fig. 4A) one can gether in sets forming triangles. Deformation of the then read the dilatation function directly. cranial base in the study population may be visual- ized in terms of change in distances, angles, and ra- In Figure 4, the curve on the right, which tios in the landmark triangles. The quantitative com- is the distortion of the circle on the left, is parison of these triangles was made between the an ellipse. There are two facts about el- normal and the study populations. lipses which tell all one needs to know about smooth shape change. An ellipse has two axes: one is the longest diameter of the in all directions. Figure 3 depicts these ef- form and the other is the shortest. These fects, using lines through one point in the axes, which are at an angle of 90° to each normal triangle ABC and through its cor- other, are also the axes of symmetry of the responding location in a deformed trian- ellipse. Because the diameters of the el- gle, its counterpart A'B'C'. lipse in Figure 4B represent the dilata- In the context of the study of deform- tions of the shape change depicted, these ity, the triangle on the left will be a "ref- simple properties can be restated as as- erence triangle", the typical or mean shape pects of the shape change. for the normative population. The trian- Any shape change between triangles has gle on the right will be a "study triangle" a direction of greatest rate of change of representing the same landmarks in a pa- length and a direction of least rate of tient. change of length. These directions are at Each line drawn has a dilatation. A dil- an angle of 90° both before and after atation is a ratio of lengths: the length of transformation. the line on the right divided by corre- Without measuring the shapes of the sponding length on the left, that is, de- triangles, one can measure the change in formed versus normal.