101 White matter hyperintensity shape is associated with long-term dementia risk 5 5.8 SUPPLEMENTARY MATERIAL S.5.8.1. Definition of the WMH shape markers. WMH type Shape marker Description Formula Periventricular/ Confluent WMH Convexity (C) Convexity and Solidity show how concave or convex a shape is. A maximally convex shape has a convexity and solidity value of 1. Values decrease with a more concave, complex shape. C= Convex Hull Area Area Periventricular/ Confluent WMH Solidity (S) S= Volume Convex Hull Volume Periventricular/ Confluent WMH Concavity Index (CI) Concavity index—a measure of roughness—describes how dense, irregular or elongated and curved a lesion is. Higher CI values indicate a more complex WMH shape. CI C S = (2− ) +(1− ) 2 2 Periventricular/ Confluent WMH Deep WMH Fractal Dimension (FD) The Minkowski-Bouligand dimension (box counting dimension) is a measure of textural roughness. Higher FD values suggest a more complex WMH shape. ( ) FD n = lim log( ) log r r r →1 1 n = number of boxes r = box size Deep WMH Eccentricity (E) Eccentricity describes the deviation from a circle. The eccentricity of a circle is 1 and the eccentricity of a line is 0. E Minor Axis Major Axis = Major axis: largest diameter in 3D space. Minor axis: smallest diameter orthogonal to the major axis.
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