133 Distinct brain MRI phenotypes and their association with long-term dementia risk 6 6.8 SUPPLEMENTARY MATERIAL Table S.6.8.1. Definition of the WMH shape markers. Shape marker WMH type Description Formula Solidity (S) Periventricular/Confluent WMH Solidity and Convexity 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. A convex hull is the smallest convex envelop of a shape. S= Volume Convex Hull Volume Convexity (C) Periventricular/Confluent WMH C= Convex Hull Area Area Concavity Index (CI) Periventricular/Confluent WMH 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 Fractal Dimension (FD) Periventricular/Confluent and deep WMH 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 Eccentricity (E) Deep WMH Eccentricity describes the deviation from a circle. The eccentricity of a circle is 0 and the eccentricity of a line is 1. E Major Axis Minor Axis = Major axis: largest diameter in 3D space. Minor axis: smallest diameter orthogonal to the major axis. Lower convexity and solidity and a higher concavity index and fractal dimension indicate a more irregularly shaped WMH. A higher eccentricity corresponds to a more elongated lesion, while a lower eccentricity corresponds to a rounder lesion. Averages were calculated per participant for each shape marker. A more irregular shape of a WMH type was defined by taking the separate markers and their directionality into account to assess the main shape. This was only done for interpretation and description of the findings.
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