Independent components of human brain morphology

Abstract

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.

Independent morphological variables correlate with Aging, Mild Cognitive Impairment, and Alzheimer’s Disease

“…In addition, brain gyrification variables S and I are mathematically derived from K, but they are independent. Changes on K do not imply changes in S and I, as previously described (22). Therefore, corroborating the primary hypothesis in this study, our results suggest that K is a sensitive variable for differentiating AD patients, MCI patients, and normal aging subjects, with complex biological and theoretical backgrounds compared to other previously established structural biomarkers such as Cortical Thickness.…”

“…In addition, brain gyrification variables S and I are mathematically derived from K, but they are independent. Changes on K do not imply changes in S and I, as previously described (22).…”

“…Besides, AD presents a higher unfolding rate for the four lobes. In (22), it is proposed that including S and I would improve our knowledge about brain morphology and our capability of removing aging effects. In our sample, AD visually mimics aging in K, S, and I.…”

“…A follow-up study by Wang et al, 2016 (20) described the universal law of gyrification for the human brain across gender, age, and pathology, with further confirmation that the universal law is also respected in smaller fractions of the cortex by applying the at four lobes (Frontal, Occipital, Parietal, and Temporal Lobes)(21). In Wang et al 2021 (22), by taking the logarithmic variables log 10 A T , log 10 A E and log 10 T 2 as the base space, it was proposed a new set of independent variables to described brain morphology derived from perpendicular planes of log 10 k: K (Equation 1), representing the axonal tension, S (Equation 2), that encapsulates brain shape, and I (Equation 3), representing brain volume. Combined, those three variables could help distinguish pathological events similar to age effects, such as AD.…”

Multivariate white matter alterations are associated with epilepsy duration

“…Third, univariate analyses do not account for the natural covariance between tracts in individuals (Cox et al, 2016;Wahl et al, 2010;Westlye et al, 2010), nor spatial colocalisation of tract segments. Accounting for this covariation is important because if multiple tracts are affected by the same process then a univariate approach does not correct for this in the statistical analysis, and can lead to erroneous conclusions (Wang et al, 2020). Furthermore, if different tracts are affected in different patients then the overall effect for each individual tract will be less than if using a multivariate approach which accounts for this (Taylor et al, 2020).…”