The folding of the cortex in mammalian brains across species has recently been shown to follow a universal scaling law that can be derived from a simple physics model. However, it was yet to be determined whether this law also applies to the morphological diversity of different individuals in a single species, in particular with respect to factors, such as age, sex, and disease. To this end, we derived and investigated the cortical morphology from magnetic resonance images (MRIs) of over 1,000 healthy human subjects from three independent public databases. Our results show that all three MRI datasets follow the scaling law obtained from the comparative neuroanatomical data, which strengthens the case for the existence of a common mechanism for cortical folding. Additionally, for comparable age groups, both male and female brains scale in exactly the same way, despite systematic differences in size and folding. Furthermore, age introduces a systematic shift in the offset of the scaling law. In the model, this shift can be interpreted as changes in the mechanical forces acting on the cortex. We also applied this analysis to a dataset derived from comparable cohorts of Alzheimer's disease patients and healthy subjects of similar age. We show a systematically lower offset and a possible change in the exponent for Alzheimer's disease subjects compared with the control cohort. Finally, we discuss implications of the changes in offset and exponent in the data and relate it to existing literature. We, thus, provide a possible mechanistic link between previously independent observations. brain morphogenesis | cortical gyrification | folding | aging | Alzheimer's disease T he expansion of the cerebral cortex is the most obvious feature of mammalian brain evolution and generally accompanied by increasing degrees of folding of the cortical surface. The mechanisms that drive gyrification have been a matter of intense research interest lately (1-4), with a number of proposals being put forward to explain it. Most such studies have focused on human cortices, using detailed MRI data to postulate folding as driven by the [possibly differential (5) or multilayered (6)] expansion of the cortical surface. In contrast, we have recently proposed a model (7), in which folding is a consequence of the dynamics of surface expansion and self-avoidance coupled with a negative tension term. This model was partly inspired by the axonal tension hypothesis by Van Essen (8) and the statistical physics of membranes (9). By assuming that healthy adult mammalian cortices have a shape that minimizes an effective free energy term that takes into account these effects, this model predicts a power law relation between cortical average thickness T, exposed area A e , and total area A t , namely[1]The only free parameter is k, or offset, a dimensionless coefficient that is presumed to be related to both the axonal tension and the pressure of cerebral spinal fluid (CSF) (supplemental text in ref. 7). In geometric terms, the variables T, A t , and A e ass...

Different cortical regions vary systematically in their morphology. Here we investigate if the scaling law of cortical morphology, which was previously demonstrated across both human subjects and mammalian species, still holds within a single cortex across different brain regions. By topologically correcting for regional curvature, we could analyse how different morphological parameters co-vary within single cortices. We show in over 1500 healthy individuals that, despite their morphological diversity, regions of the same cortex obey the same universal scaling law, and age morphologically at similar rates. In Alzheimer’s disease, we observe a premature ageing in the morphological parameters that was nevertheless consistent with the scaling law. The premature ageing effect was most dramatic in the temporal lobe. Thus, while morphology can vary substantially across cortical regions, subjects, and species, it always does so in accordance with a common scaling law, suggesting that the underlying processes driving cortical gyrification are universal.

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.

No abstract

Lithium is a major treatment for bipolar disorder and the likelihood of a favourable response may be determined by its distribution in the brain. Lithium can be directly detected by magnetic resonance (MR), but previous 7Li MR spectroscopy studies have demonstrated that this is challenging compared to conventional 1H MR imaging due to the MR properties of the lithium nucleus and its low concentration in brain tissue, as dictated by therapeutic dose. We have tested and implemented a highly efficient balanced steady state free precession 7Li-MRI method to address these challenges and enable MRI of brain lithium in a short duration scan. We report a 3D 7Li-MRI acquisition with 25 mm isotropic resolution in an eight minute scan that demonstrates heterogeneity in lithium concentration within the brain in subjects with bipolar disorder. This represents the direct imaging of a pharmaceutical agent in its target organ and notably expands the repertoire of techniques available to investigate the effects of lithium in man.