  Quantification of brain morphology has become an important cornerstone in
understanding brain structure. Measures of cortical morphology such as
thickness and surface area are frequently used to compare groups of subjects or
characterise longitudinal changes. However, such measures are often treated as
independent from each other.
  A recently described scaling law, derived from a statistical physics model of
cortical folding, demonstrates that there is a tight covariance between three
commonly used cortical morphology measures: cortical thickness, total surface
area, and exposed surface area.
  We show that assuming the independence of cortical morphology measures can
hide features and potentially lead to misinterpretations. Using the scaling
law, we account for the covariance between cortical morphology measures and
derive novel independent measures of cortical morphology. By applying these new
measures, we show that new information can be gained; in our example we show
that distinct morphological alterations underlie healthy ageing compared to
temporal lobe epilepsy, even on the coarse level of a whole hemisphere.
  We thus provide a conceptual framework for characterising cortical morphology
in a statistically valid and interpretable manner, based on theoretical
reasoning about the shape of the cortex.
