Geometric morphometric analysis of shape outlines of the normal and abnormal fetal skull using three-dimensional sonographic multiplanar display




Geometric morphometric analysis has been used to quantify differences in biological shapes. Cranial irregularities are described in anomalous fetuses but are qualitative and ill-defined. Our goal was to apply geometric morphometric statistical analysis using three-dimensional (3D) multiplanar display to quantify shape differences in normal and abnormal fetal skulls.


This was a retrospective pilot study of mid-trimester patients undergoing ultrasonography. 3D multiplanar display using spatial rotation was used to identify landmarks in coronal and transverse planes to establish a consistent fetal facial profile. Outline coordinates of the brow were determined by blinded examiners using computer software. Elliptical Fourier analysis (EFA) was used to obtain sets of functional coefficients. An atypicality index (AI) was determined from retained principal component (PC) scores. An AI > 95th percentile of the expected distribution defined outliers.


Outlines were successfully identified in 38 patients (six abnormal). Using the AI, there were three outliers, all from abnormal fetuses (trisomy 18, trisomy 21, and campomelic dysplasia). Two fetuses with trisomy 21 and one with an unbalanced translocation had normal atypicality indices.


3D multiplanar display and geometric morphometric analysis enable quantification of fetal skull shape. An abnormal skull shape was identified in two of four aneuploid fetuses and no normal ones. Geometric morphometric analysis represents a promising new quantitative modality which, when applied with 3D sonographic multiplanar display, may be used to more objectively analyze fetal malformation. Larger prospective trials are needed to refine the technique and improve reproducibility. Copyright © 2006 ISUOG. Published by John Wiley & Sons, Ltd.


Prenatal diagnosis of congenital anomalies, especially in fetuses with aneuploidy, relies largely on subjective impression, even of the experienced sonographer. A flat nasal bone, echogenic bowel and cranial irregularities such as frontal bossing are described in anomalous fetuses but are qualitative and ill-defined. These impressions are based partly on decades-old literature describing unique but subjective morphologic changes in skull and facial shape in fetuses with Down syndrome1. In 1966 Hall described, but did not define, his observation that 90% of Down syndrome newborns had ‘flat facies’2. More recently, others have tried to quantify abnormalities in aneuploid infants and children by using anthropometric indices of the craniofacial region3. Craniofacial manifestations are among the few features common to most individuals with trisomy 21, and the characteristic face of these individuals is a result primarily of maldevelopment of the craniofacial skeleton4. An abnormal skull shape may frequently reflect underlying brain insult or maldevelopment5.

Geometric morphometric analysis has been used to quantify differences in biologic shapes6–11. Although it has a long history in the anthropological literature, its application to medical imaging is relatively recent. Advances in imaging using morphometric and/or landmark geometric analysis include applications in neuroradiologic analysis of neurologic and psychiatric disorders11–13.

Three-dimensional (3D) ultrasonography has increasing applicability in prenatal diagnosis. Most work in this area either has focused on the rendered image or uses 3D technology to achieve volumetric calculations14. The use of spatial rotation in the multiplanar display modality of 3D imaging allows consistent orientation of images to achieve reproducible and quantitative evaluation of similar structures.

Our goal was to apply geometric morphometric statistical analysis using 3D ultrasound multiplanar display to attempt to quantify shape differences in the normal and abnormal fetal skull.


The study was approved by the Institutional Review Board of the North Shore Long Island Jewish Health System. This was a retrospective pilot study of patients undergoing routine mid-trimester ultrasound scans. Coronal images were obtained and volumes that had been stored in the course of these anatomical surveys in 85 patients during the study period were reviewed retrospectively. Initial sonographic images were obtained by a group of experienced obstetrical sonographers and maternal fetal medicine specialists. 3D multiplanar display with the use of spatial rotation was used to identify landmarks in the coronal (midline between the orbits at the nasal bridge) and transverse (midline at the level of the anterior orbit) planes in order to establish a reproducible, consistent facial profile in the mid-saggital plane (Figure 1a). The outline of the fetal brow was thus created and evaluated in the multiplanar display and reviewed by a single examiner, a maternal fetal medicine specialist.

Figure 1.

(a) Three-dimensional multiplanar imaging is perfomed to identify landmarks in the coronal (midline between the orbits at the nasal bridge) and transverse (midline at the level of the anterior orbit) planes in order to establish the mid-sagittal plane required for geometric morphometric analysis; (b) placement of two landmarks on the fetal head—one at the bridge of the nose and one at the apex of the skull—using digitizing software.

Profiles in 38 of the 85 cases reviewed in our database were found to have subjectively sufficient rotation and clarity to be suitable for retrospective analysis. Six fetuses were abnormal, three with trisomy 21, one with trisomy 18, one with an unbalanced translocation, and one with campomelic dysplasia. In no case was more than one image per patient used in statistical calculations. A still image was selected and sent for mathematical analysis of shape variation, which was performed by two of the authors (V. J. M. and D. K.), blinded to the patient's name and diagnosis.

Digitizing software (TPSDIG—SUNY Stony Brook, NY, USA) was used to create the outline of the fetal skull in the mid-saggital image using a manual procedure. One of the analysts placed two landmarks on the fetal head—one at the bridge of the nose and one at the apex of the skull—by clicking on the image at the appropriate location (Figure 1b). Next the file containing the coordinates was analyzed and updated to create a ‘fan’ by first determining a center point with an x-coordinate equal to the x-coordinate of point 1 and the y-coordinate of point 2. The coordinates for a series of lines were then generated with the first line starting from the center point and going through the landmark at the bridge of the nose. The remaining lines started at the center point and were at a 6-degree rotation from the previous point in a counterclockwise direction until a line was generated that was at a 90-degree angle from the initial line (Figure 2). Once the coordinates of this ‘fan’ had been created, the digitizing software was reloaded and the analyst manually placed points along the outline of the skull where it crossed the equidistant lines of the fan (Figure 3). The coordinates of the first eight points of each outline were then used for further analysis. The eighth point represented the top of the curve.

Figure 2.

The same scan as in Figure 1, showing the creation of a ‘fan’ to achieve consistency in digitizing the outline from patient to patient.

Figure 3.

The same scan as in Figures 1 and 2, showing the points used after removing all of the lines. The first eight points were used in the analysis.

Prior to analysis, the points for each curve were rotated so that the first and last points were on the horizontal axis (Figure 4). The area between the curve and the x-axis was then normalized to 1 so that the size and the orientation of the curve were consistent. The coordinates of the normalized curve were then used as input into the elliptical Fourier analysis (EFA) algorithm using NTSYSpc (Exeter Software, Setauket, NY, USA) software. For each image, EFA was performed to obtain a set of functional coefficients using NTSYSpc (Exeter Software) software. EFA is a curve-fitting technique that is used to create a smooth curve to a series of individual points with x and y coordinates15, 16. The curve fitting involves determining coefficients that can determine any x and y coordinate in terms of a third variable ‘t’. The coefficients were then used as variables in a principal component analysis, which is a multivariate procedure that can reduce the number of variables in a multivariate analysis by creating a series of linear combinations (principal components) of the original variables17. For each patient an atypicality index (AI) was determined from the retained principal component (PC) scores. An AI can be used to assess how far an individual result based on multivariate data is away from the average result18. Outliers were defined as an AI > 95th percentile of the expected distribution.

Figure 4.

Graphs showing an example of coordinates for a curve from a single image before and after adjusting for the size and orientation. Original units are in pixels.

To assess reproducibility, each of 10 images was analyzed twice and the square root of the atypicality index determined. The intraclass correlation coefficient was 0.70, indicating that the ratio of the population variance to the sum of the population variance plus measurement error was 70%. Statistical analysis was by the Mann–Whitney test.


Outlines were successfully identified in 38 patients; six of the fetuses were abnormal. EFA showed that three harmonics consisting of 12 variables fitted the outline well (Figure 5). The first three PCs were retained. Using the AI, there were three outliers (using the Chi-square test with three degrees of freedom), all abnormal (trisomy 18, trisomy 21, and one fetus with campomelic dysplasia (Figure 6)). Two trisomy 21 and one case with an unbalanced translocation had normal atypicality indices. Figures 7 and 8 illustrate a comparison between the data for the three outliers and those for the three most average examples.

Figure 5.

Graphs showing smooth fitting of a single specimen (after orientation and size normalization) using elliptical Fourier analysis with 1 (H1) and 3 (H3) harmonics; 3 harmonics provided a reasonable fit. equation image, outline; equation image, H1; equation image, H3.

Figure 6.

The atypicality index (AI); AI > 7.815 (95th percentile of Chi-squared with three degrees of freedom) was considered an outlier. All outliers were of abnormal fetuses. ○, unaffected fetuses; ▵, Down syndrome; equation image, trisomy 18; equation image, campomelic dysplasia; ▴, translocation.

Figure 7.

(a) Visualization of the three most average curves; equation image, AI = 0.234; equation image, AI = 0.321; equation image, AI = 0.417. (b) Visualization of the three outliers; equation image, AI = 10.082 (trisomy 18); equation image, AI = 12.619 (campomelic dysplasia); equation image, AI = 15.384 (Down syndrome). Curves are observed data points after orientation and size normalization but before elliptical Fourier analysis.

Figure 8.

Ultrasound images of the fetuses that gave rise to (a) the three most average curves and (b) the three outliers.

There was a significant difference in the AI between affected and unaffected groups (P < 0.0225)


Sonographic phenotyping of the aneuploid fetus has become an essential part of the mid-trimester targeted ultrasound scan19. Nonetheless, many of the markers analyzed rely on a qualitative impression. The ability to quantify shapes and to statistically evaluate the difference in shape between unaffected and affected pregnancies offers significant advantages. Traditionally, assessment of shape differences has been based on ad-hoc collections of distances and angles, or is largely subjective.

Geometric morphometrics offers a more rigorous approach to analyzing shape differences in which all of the necessary variation in shape can be evaluated based on a series of points represented as coordinate values (for example (x,y) or (x,y,z)). When a series of discrete landmarks are being evaluated (e.g. chin, eyes, nose, etc.) landmark morphometric techniques can be used4. However, when landmarks are not available, such as when the edge of a curve is to be analyzed, an alternative approach is used, namely outline methods. Outline methods use one or more functions to describe a series of points represented by coordinates (e.g. (x,y) or (x,y,z)). The functions used to describe each specimen are of the same form. However, the coefficients associated with the function will vary for each specimen. For example, in this study two functions were fitted for each curve. The coefficients in the function each represent a variable that can be used in further multivariate statistical analysis. As a result, these coefficients can be determined for a series of unaffected pregnancies and a series of affected pregnancies and the means, standard deviations, correlations, etc. can be analyzed to determine whether there are significant differences between the two groups. In smaller data sets traditional multivariate statistics can also be used to assess outliers, as was done in this study.

Others have studied shape differences in the aneuploid individual. Farkas et al.3 studied nine indices in the craniofacial region in 125 individuals with trisomy 21 using quantitative indices on physical examination. They found abnormal measurements in up to 30%. In 1976 Lestrel and Roche1 described the use of Fourier analysis to demonstrate significant differences in cranial shape in radiographs of newborns with trisomy 21. Of course, in obtaining skull X-rays, the head must be placed in a consistent imaging plane for each newborn. The advent of 3D ultrasonography and multiplanar display enables a similar consistency of planes in fetal imaging.

In both animals and humans, Richtsmeier and coworkers7–10 have used quantitative morphometric analysis to identify quantitative measures of craniofacial malformation. The phenotype of Ts65Dn mice is parallel to humans with trisomy 2110. Her group as well has used this quantitative methodology to study craniofacial growth in children with Crouzon and Apert syndromes9. To date, however, all of these studies have analyzed individuals after birth using either physical examination or radiologic studies. To our knowledge there have been no previous reports on the use of quantitative morphometrics in sonographic analysis of the fetus.

Not all imaging was acceptable for analysis. A poor two-dimensional image results in a poor and unacceptable 3D image. For the most accurate application of this technology, care must be taken to obtain the best coronal views possible. The accurate placement of the initial two points is critical, as all subsequent measurements are derived from this placement.

3D multiplanar display and geometric morphometric statistical analysis may be used to enable quantification of the shape of the fetal skull. An abnormal skull shape was identified in two of four cases of aneuploidy and in no normal fetuses. This may be owing to an overlap in the shape of the normal and abnormal skull, or to the variety of anomalies seen. Although our results may indicate a lack of sensitivity in this technique, they would still be at least comparable with those of all of the minor markers used today in prenatal ultrasonography. The intraclass correlation coefficient in our study was 0.70. This indicates that more standardization in methodology is required, or the outline procedure may need to be performed twice for each image in order to achieve more reliability in the results.


The goal of the present pilot study was to evaluate the feasibility of this technique in principle. At present, reproducibility would not meet the standards required for clinical application.

The fact that some abnormal fetuses have normal AIs may reflect the wide range of variability in features even in the abnormal fetus. In addition, there may be better anatomical landmarks or outline methods to identify abnormal fetal shape, and these are probably disorder-specific. For example, in some skeletal anomalies such as Apert syndrome, widening of the frontal suture may result in only soft tissue being present at the fetal brow, affecting the ability to use this technique. Large prospective trials are necessary to evaluate the precise anatomic area and identifiable landmarks best suited for maximum sensitivity in identifying trisomies. Further refinement of the technique is needed.

Although this approach requires complex mathematics, improvements in clinical evaluation may include improved detection and counseling, and may lead to the development of more precise risk estimates for the identification of the abnormal fetus. Geometric morphometric analysis represents a promising new quantitative modality which, when applied with the use of 3D sonographic multiplanar display, may be used to more objectively analyze fetal malformation.