Quantitative assessment of gestational sac shape: the gestational sac shape score

Abstract

Objective: To develop a quantitative method for characterizing gestational sac shape.

Methods: Twenty first-trimester gestational sacs in normal pregnancies were studied with three-dimensional (3D) ultrasonography. The 3D coordinates of surface-point sets were obtained for each sac using 30-, 15- and six-slice sampling. Cubic spline interpolation was used with the 15- and six-slice surface-point samples to generate coordinates for those 30-slice surface points not measured. Interpolated and measured values, the latter from the 30-slice sample, were compared and the percent error calculated. Cubic spline interpolation was used to determine the coordinates of a standard surface-point sample (3660) for each sac in each slice sample. These coordinate data were used to give each sac a standard configuration by moving its center of gravity to the origin, aligning its inertial axes along the coordinate axes and converting its volume to 1.0 mL. In this form, a volume shape descriptor could be generated for each sac that was then transformed into a vector containing only shape information. The 20 shape vectors of each slice sample were subjected to principal components analysis, and principal component scores (PCSs) calculated. The first four PCSs were used to define a gestational sac shape score (GSSS-30, GSSS-15 or GSSS-6) for each sac in a given slice sample. The characteristics of each set of GSSSs were determined and those for the GSSS-15 and GSSS-6 were compared with the GSSS-30 characteristics.

Results: Cubic spline interpolations were very accurate in most cases, with means close to 0%, and approximately 95% of the errors being less than 10%. GSSS-30 accounted for 67.6% of the shape variance, had a mean of zero and an SD of 1.1, was normally distributed and was not related to menstrual age (R=-0.16, P=0.51). GSSS-15 and GSSS-6 had essentially the same characteristics. No significant differences between individual GSSS-30 values and those for GSSS-15 or GSSS-6 were found, indicating the absence of a slice sample effect.

Conclusion: Using sophisticated mathematical methods, the gestational sac shape, initially represented by the 3D coordinates of 3660 surface points, was converted to a single number, the GSSS. This score had the appropriate properties for quantitatively characterizing normal, first-trimester gestational sac shapes. As it can be obtained from as few as six slices, it should be useful in many clinical situations. This novel approach has the potential for providing quantitative shape information about a variety of biological shapes and how they change over time.

Figure 1

Gestational sac contouring, illustrating the steps used to obtain sac contours. (a) The sac-sectioning axis is chosen (arrowheads). (b) A section made at right angle to the sectioning axis in (a). (c) The small white dots outline the sac contour of the sac surface. (d) The data obtained by contouring are in the form of a three-dimensional image of the sac or the x, y and z coordinates of surface points.

Figure 2

Gestational sac slice sampling, depicting the three slice samples used in this investigation. Slices of each gestational sac are generated at 6-degree intervals using VOCAL and their contours determined manually (30-slice set). To obtain a 15-slice set, every other contour is selected (slices at 12-degree intervals). If every fifth slice is selected (six-slice set), the slice interval is 30 degrees.

Figure 3

Location of voxels inside or outside of the gestational sac, showing the procedure for identifying the position of voxels. The nearest surface triangle (A) to a voxel (B or C) is identified (size of voxels magnified for illustration). From the center of the triangle, the normal unit vector (N), perpendicular to the sac surface, and vectors to the centers of the voxels are determined. The voxel vectors are projected onto the unit vector N and their dot products calculated. Dot product values are positive if the voxels are outside the sac and negative if they are inside the sac.

Figure 4

Standardization of gestational sac location and orientation, illustrating the procedures used to eliminate the effects of location and orientation on coordinate data. (a) The locations of the center of gravity (C) and the inertial axes (U, V and W) of a gestational sac are determined with respect to the external coordinate system. (b) The sac center of gravity is then moved to the origin (O) of this coordinate system and its inertial axes aligned with the X, Y and Z axes.

Figure 5

Volume shape descriptor, illustrating the box (left side) into which each standardized gestational sac is placed, their centers of gravity coinciding. The box is subdivided into cubes, some completely inside or outside the sac and some partially inside/outside the sac (right side). The locations of the cubes with respect to the sac are determined only by sac shape.

Figure 6

The procedure used to calculate cube scores. Cubes are composed of voxels that are assigned a score of 0 (upper left corner) or 1 (lower right corner), depending on whether they are outside or inside the sac. Cube scores are averages of their voxel scores. If all voxels are outside the sac (A, B) the cube scores are 0. If all voxels are inside the sac (H, I), the cube scores are 1.0. If some voxels are inside and some are outside (C, D, E, F, G), the cube scores are between 0 and 1.0. Such cube scores indicate the location of the sac surface and are determined only by shape.