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The cerebral cortex displays a bewildering diversity of shapes and sizes across and within species. Despite this diversity, we present a universal multi-scale description of primate cortices. We show that all cortical shapes can be described as a set of nested folds of different sizes. As neighbouring folds are gradually merged, the cortices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps with over 70 other mammalian species. Our results indicate that all cerebral cortices are approximations of the same archetypal fractal shape with a fractal dimension of d f = 2.5. Importantly, this new understanding enables a more precise quantification of brain morphology as a function of scale. To demonstrate the importance of this new understanding, we show a scale-dependent effect of ageing on brain morphology. We observe a more than fourfold increase in effect size (from two standard deviations to eight standard deviations) at a spatial scale of approximately 2 mm compared to standard morphological analyses. Our new understanding may, therefore, generate superior biomarkers for a range of conditions in the future. Many of the brain’s essential functions – from decision-making to movement – take place in its outer layer known as the cerebral cortex. The shape of the cerebral cortex varies significantly between species. For instance, in humans, it is folded in to grooves and ridges, whereas in other animals, including mice, it is completely smooth. The structure of the cortex can also differ within a species, and be altered by aging and certain diseases. This vast variation can make it difficult it to characterize and compare the structure of the cortex between different species, ages and diseases. To address this, Wang et al. developed a new mathematical model for describing the shape of the cortex. The model uses a method known as coarse graining to erase, or ‘melt away’, any cortical folds or structures smaller than a given threshold size. As this threshold increases, the cortex becomes progressively smoother. The relationship between surface areas and threshold sizes indicates the fractal dimension – that is, how fragmented the cortex is across different scales. Wang et al. applied their model to the brain scans of eleven primates, including humans, and found the fractal dimension of the cortex was almost exactly 2.5 for all eleven species . This suggests that the cortices of the different primates follow a single fractal shape, which means the folds of each cortex have a similar branching pattern. Although there were distinctions between the species, they were mainly due to the different ranges of fold sizes in each cortex. The model revealed that the broader the range of fold sizes, the more folded the brain – but the fractal pattern remains the same. The brain melting method created by Wang et al. provides a new way to characterise cortical shape. Besides revealing a hitherto hidden regularity of nature, they hope that in the future their new method will be useful in assessing brain changes during human development and ageing, and in diseases like Alzheimer’s and epilepsy.

•Strengths and challenges of longitudinal non-human primate MRI are described.•Statistical power calculation of longitudinal and cross-sectional designs are provided.•The impact of template choice on grey matter estimation is demonstrated.•Recommendations for designing and analysing such studies are provided. Longitudinal non-human primate neuroimaging has the potential to greatly enhance our understanding of primate brain structure and function. Here we describe its specific strengths, compared to both cross-sectional non-human primate neuroimaging and longitudinal human neuroimaging, but also its associated challenges. We elaborate on factors guiding the use of different analytical tools, subject-specific versus age-specific templates for analyses, and issues related to statistical power.

The cerebral cortex displays a bewildering diversity of shapes and sizes across and within species. Despite this diversity, we present a universal multi-scale description of primate cortices. We show that all cortical shapes can be described as a set of nested folds of different sizes. As neighbouring folds are gradually merged, the cortices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps with over 70 other mammalian species. Our results indicate that all cerebral cortices are approximations of the same archetypal fractal shape with a fractal dimension of d f = 2.5. Importantly, this new understanding enables a more precise quantification of brain morphology as a function of scale. To demonstrate the importance of this new understanding, we show a scale-dependent effect of ageing on brain morphology. We observe a more than fourfold increase in effect size (from two standard deviations to eight standard deviations) at a spatial scale of approximately 2 mm compared to standard morphological analyses. Our new understanding may, therefore, generate superior biomarkers for a range of conditions in the future. Many of the brain’s essential functions – from decision-making to movement – take place in its outer layer known as the cerebral cortex. The shape of the cerebral cortex varies significantly between species. For instance, in humans, it is folded in to grooves and ridges, whereas in other animals, including mice, it is completely smooth. The structure of the cortex can also differ within a species, and be altered by aging and certain diseases. This vast variation can make it difficult it to characterize and compare the structure of the cortex between different species, ages and diseases. To address this, Wang et al. developed a new mathematical model for describing the shape of the cortex. The model uses a method known as coarse graining to erase, or ‘melt away’, any cortical folds or structures smaller than a given threshold size. As this threshold increases, the cortex becomes progressively smoother. The relationship between surface areas and threshold sizes indicates the fractal dimension – that is, how fragmented the cortex is across different scales. Wang et al. applied their model to the brain scans of eleven primates, including humans, and found the fractal dimension of the cortex was almost exactly 2.5 for all eleven species . This suggests that the cortices of the different primates follow a single fractal shape, which means the folds of each cortex have a similar branching pattern. Although there were distinctions between the species, they were mainly due to the different ranges of fold sizes in each cortex. The model revealed that the broader the range of fold sizes, the more folded the brain – but the fractal pattern remains the same. The brain melting method created by Wang et al. provides a new way to characterise cortical shape. Besides revealing a hitherto hidden regularity of nature, they hope that in the future their new method will be useful in assessing brain changes during human development and ageing, and in diseases like Alzheimer’s and epilepsy.

The cerebral cortex displays a bewildering diversity of shapes and sizes across and within species. Despite this diversity, we present a universal multi-scale description of primate cortices. We show that all cortical shapes can be described as a set of nested folds of different sizes. As neighbouring folds are gradually merged, the cortices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps with over 70 other mammalian species. Our results indicate that all cerebral cortices are approximations of the same archetypal fractal shape with a fractal dimension of \\(d_f=2.5\\). Importantly, this new understanding enables a more precise quantification of brain morphology as a function of scale. To demonstrate the importance of this new understanding, we show a scale-dependent effect of ageing on brain morphology. We observe a more than four-fold increase in effect size (from 2 standard deviations to 8 standard deviations) at a spatial scale of approximately 2 mm compared to standard morphological analyses. Our new understanding may therefore generate superior biomarkers for a range of conditions in the future.

and AimsPatients with Crohn's disease (CD) are often prescribed opioids chronically to manage pain associated with their disease. However, little evidence exists to support this practice. Here, we examine newly diagnosed patients with CD with and without chronic opioid use (COU) and sought to identify predictors and consequences of COU.MethodsA nationally representative administrative health care claims that data set identified newly diagnosed patients with CD. Their data were examined during the periods 6 months before and 2 years after diagnosis. Multivariable logistic regression was used to assess predictors of COU at diagnosis.ResultsThe final study cohort consisted of 47,164 patients with CD. Of them, 3.8% were identified with new COU. Chronic opioid users were more likely women, older, and likely who had more surgeries, endoscopies, admissions, and medication usage compared with other patients. Features detected before CD diagnosis that correlated with COU after diagnosis included previous opioid use (odds ratio [OR] = 6.6), chronic pain (OR = 1.36), arthritis (OR = 1.95), and mental disorders (OR = 1.58). Interestingly, emergency department visits before CD Dx increased the risk of COU (OR = 1.11), whereas endoscopy reduced COU risk (OR = 0.88).ConclusionsThis study presents a nationally representative assessment of COU in newly diagnosed patients with CD. The results may be used to determine the impact of COU in this population and to alert clinicians to those patients with CD at high risk of COU. Chronic opioids are consistently associated with indicators of more severe disease; however, additional research is needed to determine whether COU drives disease severity or vice versa.

We describe a correspondence between Turaev surfaces of link diagrams on \\(S^2\\subset S^3\\) and special Heegaard diagrams for \\(S^3\\) adapted to links.