Analyzing the Developing Brain by Quantifying Curvature Measures

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Analyzing the Developing Brain by Quantifying
Curvature Measures

• Rudolph Pienaar1,2, Bruce Fischl1, Nikos Makris2,
  P Ellen Grant1
• 1 MGH/MIT/HMS Athinoula A. Martinos Center for
  Biomedical Imaging 2 MGH Center for
  Morphometric Analysis

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Curvature Information at Each Vertex of
Reconstructed Surface

• Reconstructed surfaces were analyzed with
  curvature functions
• Max curvature, k1
• Min curvature, k2
• Sharpness, S (k1 k2)2
• Gaussian, K k1k2

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Curvature Evolution Across Different Functions
S
k1
k2
K
S

• S ? k1 ? k2 ? K
• k1 cylindrical folding of major gyri and sulci
• k2 undulations along major gyri and sulci
• The sharpest folding (S red) occurs at sulcal
  depths (k1 red) and gyral peaks (k1 green).
• Gaussian (K) is close to 0 at all ages despite
  increases in folding -- indicating that the brain
  can be flattened with few tears or folds (these
  tend to occur in depth of sulci or peaks of gyri).

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Histogram and Centroids
k1
k2
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Histogram and Centroids
k1
k2
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Dynamic Filtering and Surface Energy

• Brain curves at different scales.
• Measure folding at gyral scale.
• 1/A?(k22 k12)dA

K