Shape Analysis of Pediatric Thoracic Vertebrae using Generalized Procrustes
Analysis
Evan Bisirri, James Peters B.S., Sriram Balasubramanian Ph.D.
School of Biomedical Engineering, Science & Health Systems, Drexel University, Philadelphia, PA
BACKGROUND
• Spine morphology changes rapidly between birth and skeletal maturity.
• Age-dependent changes in normative thoracic vertebral morphology are not well
understood.
• While size-variations in the vertebra related to thoracic level and gender are
expected and have been documented [1], there are no studies evaluating the
changes in vertebral shape with age.
• Generalized Procrustes Analysis (GPA) has been previously used to quantify
changes in rib cage shape in normative adults and children [2,3].
• There is a need to study age and gender dependent thoracic vertebral shape
change in the pediatric population.
• To standardize the vertebral point cloud orientations and simplify ‘landmark’
identification, the vertebrae were translated and rotated to the position of the
template by using an iterative closest point algorithm.
• 31 landmark points were consistently identified on each vertebra (Figure 3) using a
custom MATLAB script.
• For visualization, the landmarks can be connected to create a wireframe (Figure 4).
OBJECTIVE
•
To quantify shape change as a function of age for the thoracic vertebrae of
male and female subjects between ages 1 and 18 years.
• Hypothesis:
• The shape change of the vertebra will vary with thoracic level.
METHODS
Vertebrae Reconstruction
•
•
Retrospective chest CT scans of 55 skeletally normal females and 45 skeletally
normal males were obtained from the Children’s Hospital of Philadelphia.
The chest CT scans were reconstructed using MIMICS v16 software
(Materialise, Belgium), to create 3-dimensional surface models of each
vertebra (Figure 1).
Axial View
Coronal View
Sagittal View
3D
Reconstruction
Figure 1. MIMICS interface 1 year old vertebra reconstruction
•
The surface models were exported to 3-matic v8 (Materialise, Belgium) and
refined in preparation for ‘landmark’ point identification.
Landmark point (colors: grey,
blue, red, green, and yellow)
Figure 2. Point cloud
Figure 3. Landmark points
•
•
A template vertebra was created in 3-matic by smoothing a normal vertebra
to eliminate any surface irregularities.
STL files of the template and all vertebrae were imported to MATLAB r2011b
(The MathWorks, Inc., Natick, MA) for viewing, centering, scaling, rotating,
and analysis of the point clouds (Figure 2).
The template vertebra was centered at (0, 0, 0) by its centroid, and rotated so
the superior face of the vertebral body was orthogonal to the z-axis, the left
transverse process extended in the negative x-direction, and the spinous
process extended in the negative y-direction.
• Raw data of landmark point coordinates for each level of thoracic vertebra and
gender correlated with age (Figure 6). (2232 of these graphs were generated)
Figure 6. (left) thoracic level-6 landmark-25 female y-position vs age
(right) thoracic level-6 landmark-25 male y-position vs age
Figure 4. Wireframe
• The landmark point sets of all vertebrae were saved, each in a 31 x 3 matrix (31
rows for the number of landmark points, and 3 columns for the x, y, z coordinates).
Generalized Procrustes Analysis [4]
• A custom MATLAB script was written to perform the following GPA operations
separately for each thoracic level and gender.
• A mean shape was generated by taking the mean x, y, z coordinates for each of the
31 landmarks for all vertebrae.
• To center the landmark point cloud centroids at (0, 0, 0), the mean shape
coordinates for each landmark were subtracted from the landmark point
coordinates.
• The following operations were used in the Generalized Procrustes Analysis:
• The landmark point sets were scaled to the same size.
• The landmark point sets were rotated to the position of another landmark point set
by applying an individual rotational matrix to each point set.
• To obtain the rotational matrix, a covariance matrix was created by multiplying the
transpose of the first landmark matrix by the landmark matrix of the shape to be
rotated.
• A single variable decomposition was performed on this value to obtain the
rotational matrix which was multiplied with the landmark matrix of the object
being rotated to complete the rotation.
• An average shape model was calculated.
• Error was calculated in preparation for a residual sum of squares.
• Figure 5 illustrates the format in which these operations were applied.
• The 2-dimensional equations created from the raw
data were combined to produce a 3-dimensional
model of vectors pointing in the direction of
increasing age (Figure 7).
• This model was used as the main mode of analysis.
Figure 7. 3-dimensional vector model of shape change
with age (Level 6 female) (blue=youngest, purple=midrange, red=oldest, black points=mean shape). Landmark
points have been connected as a reference.
CONCLUSIONS
• The vertebral body expands axially in the upper half of the thoracic spine with age,
while it expands axially, laterally, posteriorly, and anteriorly in the lower half with age.
• The pedicles move medially and enlarge as the spinous process extends towards the
posterior inferiorly with age.
• The facets move anteriorly as does the posterior of the spinal column with age.
• The transverse processes above thoracic level 8 move superiorly with age, while at
lower levels move little, or in some cases drift inferiorly.
• Shape changes between male and female vertebra were minimal.
• GPA-based shape models can be used to generate subject-specific computational
models by morphing the landmark points to a specific subject.
• Future work will include statistical analyses of differences between male and female
vertebral shape changes, and a larger data set with longitudinal subject measurements.
REFERENCES
Landmark Identification
•
RESULTS
[1] Peters, J. et al., 2014, Gender and Age Dependent Changes in Pediatric Thoracic Spine
Dimensions, ORS Annual Meeting
[2] Gayzik, F. S., et al. 2008 Quantification of age-related shape change of the human rib
cage through geometric morphometrics, Journal of Biomechanics, vol. 41, pp. 15451554
[3] Weaver AA, Schoell SL, Stitzel JD. (2014). Morphometric analysis of variation in the ribs
with age and sex. Journal of Anatomy, Aug;225(2):246-61
[4] Rohlf, F., Slice, D., 1990, Extensions of the Procrustes Method for the Optimal
Superimposition of Landmarks, Systematic Zoology, Vol. 39, No. 1, pp. 40-59
Figure 5. Generalized Procrustes Analysis