A spatio-temporal reference model of the aging brain

Alzheimer's disease heterogeneity revealed by neuroanatomical normative modeling

INTRODUCTION

Overlooking the heterogeneity in Alzheimer's disease (AD) may lead to diagnostic delays and failures. Neuroanatomical normative modeling captures individual brain variation and may inform our understanding of individual differences in AD-related atrophy.

METHODS

We applied neuroanatomical normative modeling to magnetic resonance imaging from a real-world clinical cohort with confirmed AD (n = 86). Regional cortical thickness was compared to a healthy reference cohort (n = 33,072) and the number of outlying regions was summed (total outlier count) and mapped at individual- and group-levels.

RESULTS

The superior temporal sulcus contained the highest proportion of outliers (60%). Elsewhere, overlap between patient atrophy patterns was low. Mean total outlier count was higher in patients who were non-amnestic, at more advanced disease stages, and without depressive symptoms. Amyloid burden was negatively associated with outlier count.

DISCUSSION

Brain atrophy in AD is highly heterogeneous and neuroanatomical normative modeling can be used to explore anatomo-clinical correlations in individual patients.

Brain structure ages-A new biomarker for multi-disease classification

Age is an important variable to describe the expected brain's anatomy status across the normal aging trajectory. The deviation from that normative aging trajectory may provide some insights into neurological diseases. In neuroimaging, predicted brain age is widely used to analyze different diseases. However, using only the brain age gap information (i.e., the difference between the chronological age and the estimated age) can be not enough informative for disease classification problems. In this paper, we propose to extend the notion of global brain age by estimating brain structure ages using structural magnetic resonance imaging. To this end, an ensemble of deep learning models is first used to estimate a 3D aging map (i.e., voxel-wise age estimation). Then, a 3D segmentation mask is used to obtain the final brain structure ages. This biomarker can be used in several situations. First, it enables to accurately estimate the brain age for the purpose of anomaly detection at the population level. In this situation, our approach outperforms several state-of-the-art methods. Second, brain structure ages can be used to compute the deviation from the normal aging process of each brain structure. This feature can be used in a multi-disease classification task for an accurate differential diagnosis at the subject level. Finally, the brain structure age deviations of individuals can be visualized, providing some insights about brain abnormality and helping clinicians in real medical contexts.

Applications of generative adversarial networks in neuroimaging and clinical neuroscience

Generative adversarial networks (GANs) are one powerful type of deep learning models that have been successfully utilized in numerous fields. They belong to the broader family of generative methods, which learn to generate realistic data with a probabilistic model by learning distributions from real samples. In the clinical context, GANs have shown enhanced capabilities in capturing spatially complex, nonlinear, and potentially subtle disease effects compared to traditional generative methods. This review critically appraises the existing literature on the applications of GANs in imaging studies of various neurological conditions, including Alzheimer's disease, brain tumors, brain aging, and multiple sclerosis. We provide an intuitive explanation of various GAN methods for each application and further discuss the main challenges, open questions, and promising future directions of leveraging GANs in neuroimaging. We aim to bridge the gap between advanced deep learning methods and neurology research by highlighting how GANs can be leveraged to support clinical decision making and contribute to a better understanding of the structural and functional patterns of brain diseases.

Fast three-dimensional image generation for healthy brain aging using diffeomorphic registration

Predicting brain aging can help in the early detection and prognosis of neurodegenerative diseases. Longitudinal cohorts of healthy subjects scanned through magnetic resonance imaging (MRI) have been essential to understand the structural brain changes due to aging. However, these cohorts suffer from missing data due to logistic issues in the recruitment of subjects. This paper proposes a methodology for filling up missing data in longitudinal cohorts with anatomically plausible images that capture the subject-specific aging process. The proposed methodology is developed within the framework of diffeomorphic registration. First, two novel modules are introduced within Synthmorph, a fast, state-of-the-art deep learning-based diffeomorphic registration method, to simulate the aging process between the first and last available MRI scan for each subject in three-dimensional (3D). The use of image registration also makes the generated images plausible by construction. Second, we used six image similarity measurements to rearrange the generated images to the specific age range. Finally, we estimated the age of every generated image by using the assumption of linear brain decay in healthy subjects. The methodology was evaluated on 2662 T1-weighted MRI scans from 796 healthy participants from 3 different longitudinal cohorts: Alzheimer's Disease Neuroimaging Initiative, Open Access Series of Imaging Studies-3, and Group of Neuropsychological Studies of the Canary Islands (GENIC). In total, we generated 7548 images to simulate the access of a scan per subject every 6 months in these cohorts. We evaluated the quality of the synthetic images using six quantitative measurements and a qualitative assessment by an experienced neuroradiologist with state-of-the-art results. The assumption of linear brain decay was accurate in these cohorts (R2  ∈ [.924, .940]). The experimental results show that the proposed methodology can produce anatomically plausible aging predictions that can be used to enhance longitudinal datasets. Compared to deep learning-based generative methods, diffeomorphic registration is more likely to preserve the anatomy of the different structures of the brain, which makes it more appropriate for its use in clinical applications. The proposed methodology is able to efficiently simulate anatomically plausible 3D MRI scans of brain aging of healthy subjects from two images scanned at two different time points.

Traumatic stress load and stressor reactivity score associated with accelerated gray matter maturation in youths indexed by normative models

Understanding how traumatic stress affects typical brain development during adolescence is critical to elucidate underlying mechanisms related to both maladaptive functioning and resilience after traumatic exposures. The current study aimed to map deviations from normative ranges of brain gray matter for youths with traumatic exposures. For each cortical and subcortical gray matter region, normative percentiles of variations were established using structural MRI from typically developing youths without any traumatic exposure (n = 245; age range = 8-23) from the Philadelphia Neurodevelopmental Cohort (PNC). The remaining PNC participants with neuroimaging data (n = 1129) were classified as either within the normative range (5-95%), delayed (>95%) or accelerated (<5%) maturational ranges for each region using the normative model. An averaged quantile regression index was calculated across all regions. Mediation models revealed that high traumatic stress load was positively associated with poorer cognitive functioning and greater psychopathology, and these associations were mediated by accelerated gray matter maturation. Furthermore, higher stressor reactivity scores, which represent a less resilient response under traumatic stress, were positively correlated with greater acceleration of gray matter maturation (r = 0.224, 95% CI = [0.17, 0.28], p < 0.001), suggesting that more accelerated maturation was linked to greater stressor response regardless of traumatic stress load. We conclude that traumatic stress is a source of deviation from normative brain development associated with poorer cognitive functioning and more psychopathology in the long run.

Normative Modeling using Multimodal Variational Autoencoders to Identify Abnormal Brain Volume Deviations in Alzheimer's Disease

Normative modelling is a method for understanding the underlying heterogeneity within brain disorders like Alzheimer Disease (AD), by quantifying how each patient deviates from the expected normative pattern that has been learned from a healthy control distribution. Existing deep learning based normative models have been applied on only single modality Magnetic Resonance Imaging (MRI) neuroimaging data. However, these do not take into account the complementary information offered by multimodal M RI, which is essential for understanding a multifactorial disease like AD. To address this limitation, we propose a multi-modal variational autoencoder (mmVAE) based normative modelling framework that can capture the joint distribution between different modalities to identify abnormal brain volume deviations due to AD. Our multi-modal framework takes as input Freesurfer processed brain region volumes from T1-weighted (cortical and subcortical) and T2-weighed (hippocampal) scans of cognitively normal participants to learn the morphological characteristics of the healthy brain. The estimated normative model is then applied on AD patients to quantify the deviation in brain volumes and identify abnormal brain pattern deviations due to the progressive stages of AD. We compared our proposed mmVAE with a baseline unimodal VAE having a single encoder and decoder and the two modalities concatenated as unimodal input. Our experimental results show that deviation maps generated by mmVAE are more sensitive to disease staging within AD, have a better correlation with patient cognition and result in higher number of brain regions with statistically significant deviations compared to the unimodal baseline model.

Equitable modelling of brain imaging by counterfactual augmentation with morphologically constrained 3D deep generative models

We describe CounterSynth, a conditional generative model of diffeomorphic deformations that induce label-driven, biologically plausible changes in volumetric brain images. The model is intended to synthesise counterfactual training data augmentations for downstream discriminative modelling tasks where fidelity is limited by data imbalance, distributional instability, confounding, or underspecification, and exhibits inequitable performance across distinct subpopulations. Focusing on demographic attributes, we evaluate the quality of synthesised counterfactuals with voxel-based morphometry, classification and regression of the conditioning attributes, and the Fréchet inception distance. Examining downstream discriminative performance in the context of engineered demographic imbalance and confounding, we use UK Biobank and OASIS magnetic resonance imaging data to benchmark CounterSynth augmentation against current solutions to these problems. We achieve state-of-the-art improvements, both in overall fidelity and equity. The source code for CounterSynth is available at https://github.com/guilherme-pombo/CounterSynth.

Accommodating site variation in neuroimaging data using normative and hierarchical Bayesian models

The potential of normative modeling to make individualized predictions from neuroimaging data has enabled inferences that go beyond the case-control approach. However, site effects are often confounded with variables of interest in a complex manner and can bias estimates of normative models, which has impeded the application of normative models to large multi-site neuroimaging data sets. In this study, we suggest accommodating for these site effects by including them as random effects in a hierarchical Bayesian model. We compared the performance of a linear and a non-linear hierarchical Bayesian model in modeling the effect of age on cortical thickness. We used data of 570 healthy individuals from the ABIDE (autism brain imaging data exchange) data set in our experiments. In addition, we used data from individuals with autism to test whether our models are able to retain clinically useful information while removing site effects. We compared the proposed single stage hierarchical Bayesian method to several harmonization techniques commonly used to deal with additive and multiplicative site effects using a two stage regression, including regressing out site and harmonizing for site with ComBat, both with and without explicitly preserving variance caused by age and sex as biological variation of interest, and with a non-linear version of ComBat. In addition, we made predictions from raw data, in which site has not been accommodated for. The proposed hierarchical Bayesian method showed the best predictive performance according to multiple metrics. Beyond that, the resulting z-scores showed little to no residual site effects, yet still retained clinically useful information. In contrast, performance was particularly poor for the regression model and the ComBat model in which age and sex were not explicitly modeled. In all two stage harmonization models, predictions were poorly scaled, suffering from a loss of more than 90% of the original variance. Our results show the value of hierarchical Bayesian regression methods for accommodating site variation in neuroimaging data, which provides an alternative to harmonization techniques. While the approach we propose may have broad utility, our approach is particularly well suited to normative modeling where the primary interest is in accurate modeling of inter-subject variation and statistical quantification of deviations from a reference model.

Accommodating site variation in neuroimaging data using normative and hierarchical Bayesian models

The potential of normative modeling to make individualized predictions from neuroimaging data has enabled inferences that go beyond the case-control approach. However, site effects are often confounded with variables of interest in a complex manner and can bias estimates of normative models, which has impeded the application of normative models to large multi-site neuroimaging data sets. In this study, we suggest accommodating for these site effects by including them as random effects in a hierarchical Bayesian model. We compared the performance of a linear and a non-linear hierarchical Bayesian model in modeling the effect of age on cortical thickness. We used data of 570 healthy individuals from the ABIDE (autism brain imaging data exchange) data set in our experiments. In addition, we used data from individuals with autism to test whether our models are able to retain clinically useful information while removing site effects. We compared the proposed single stage hierarchical Bayesian method to several harmonization techniques commonly used to deal with additive and multiplicative site effects using a two stage regression, including regressing out site and harmonizing for site with ComBat, both with and without explicitly preserving variance caused by age and sex as biological variation of interest, and with a non-linear version of ComBat. In addition, we made predictions from raw data, in which site has not been accommodated for. The proposed hierarchical Bayesian method showed the best predictive performance according to multiple metrics. Beyond that, the resulting z-scores showed little to no residual site effects, yet still retained clinically useful information. In contrast, performance was particularly poor for the regression model and the ComBat model in which age and sex were not explicitly modeled. In all two stage harmonization models, predictions were poorly scaled, suffering from a loss of more than 90% of the original variance. Our results show the value of hierarchical Bayesian regression methods for accommodating site variation in neuroimaging data, which provides an alternative to harmonization techniques. While the approach we propose may have broad utility, our approach is particularly well suited to normative modeling where the primary interest is in accurate modeling of inter-subject variation and statistical quantification of deviations from a reference model.

Invertible Modeling of Bidirectional Relationships in Neuroimaging With Normalizing Flows: Application to Brain Aging

Many machine learning tasks in neuroimaging aim at modeling complex relationships between a brain's morphology as seen in structural MR images and clinical scores and variables of interest. A frequently modeled process is healthy brain aging for which many image-based brain age estimation or age-conditioned brain morphology template generation approaches exist. While age estimation is a regression task, template generation is related to generative modeling. Both tasks can be seen as inverse directions of the same relationship between brain morphology and age. However, this view is rarely exploited and most existing approaches train separate models for each direction. In this paper, we propose a novel bidirectional approach that unifies score regression and generative morphology modeling and we use it to build a bidirectional brain aging model. We achieve this by defining an invertible normalizing flow architecture that learns a probability distribution of 3D brain morphology conditioned on age. The use of full 3D brain data is achieved by deriving a manifold-constrained formulation that models morphology variations within a low-dimensional subspace of diffeomorphic transformations. This modeling idea is evaluated on a database of MR scans of more than 5000 subjects. The evaluation results show that our bidirectional brain aging model (1) accurately estimates brain age, (2) is able to visually explain its decisions through attribution maps and counterfactuals, (3) generates realistic age-specific brain morphology templates, (4) supports the analysis of morphological variations, and (5) can be utilized for subject-specific brain aging simulation.

A diffeomorphic aging model for adult human brain from cross-sectional data

Normative aging trends of the brain can serve as an important reference in the assessment of neurological structural disorders. Such models are typically developed from longitudinal brain image data—follow-up data of the same subject over different time points. In practice, obtaining such longitudinal data is difficult. We propose a method to develop an aging model for a given population, in the absence of longitudinal data, by using images from different subjects at different time points, the so-called cross-sectional data. We define an aging model as a diffeomorphic deformation on a structural template derived from the data and propose a method that develops topology preserving aging model close to natural aging. The proposed model is successfully validated on two public cross-sectional datasets which provide templates constructed from different sets of subjects at different age points.

Establishing a Baseline for Human Cortical Folding Morphological Variables: A Multisite Study

Differences in the way human cerebral cortices fold have been correlated to health, disease, development, and aging. However, to obtain a deeper understanding of the mechanisms that generate such differences, it is useful to derive one's morphometric variables from the first principles. This study explores one such set of variables that arise naturally from a model for universal self-similar cortical folding that was validated on comparative neuroanatomical data. We aim to establish a baseline for these variables across the human lifespan using a heterogeneous compilation of cross-sectional datasets as the first step to extending the model to incorporate the time evolution of brain morphology. We extracted the morphological features from structural MRI of 3,650 subjects: 3,095 healthy controls (CTL) and 555 patients with Alzheimer's Disease (AD) from 9 datasets, which were harmonized with a straightforward procedure to reduce the uncertainty due to heterogeneous acquisition and processing. The unprecedented possibility of analyzing such a large number of subjects in this framework allowed us to compare CTL and AD subjects' lifespan trajectories, testing if AD is a form of accelerated aging at the brain structural level. After validating this baseline from development to aging, we estimate the variables' uncertainties and show that Alzheimer's Disease is similar to premature aging when measuring global and local degeneration. This new methodology may allow future studies to explore the structural transition between healthy and pathological aging and may be essential to generate data for the cortical folding process simulations.

LEARNING TO SYNTHESIZE CORTICAL MORPHOLOGICAL CHANGES USING GRAPH CONDITIONAL VARIATIONAL AUTOENCODER

Changes in brain morphology, such as cortical thinning are of great value for understanding the trajectory of brain aging and various neurodegenerative diseases. In this work, we employed a generative neural network variational autoencoder (VAE) that is conditional on age and is able to generate cortical thickness maps at various ages given an input cortical thickness map. To take into account the mesh topology in the model, we proposed a loss function based on weighted adjacency to integrate the surface topography defined as edge connections with the cortical thickness mapped as vertices. Compared to traditional conditional VAE that did not use the surface topological information, our method better predicted "future" cortical thickness maps, especially when the age gap became wider. Our model has the potential to predict the distinctive temporospatial pattern of individual cortical morphology in relation to aging and neurodegenerative diseases.

Beyond the average patient: how neuroimaging models can address heterogeneity in dementia

Dementia is a highly heterogeneous condition, with pronounced individual differences in age of onset, clinical presentation, progression rates and neuropathological hallmarks, even within a specific diagnostic group. However, the most common statistical designs used in dementia research studies and clinical trials overlook this heterogeneity, instead relying on comparisons of group average differences (e.g. patient versus control or treatment versus placebo), implicitly assuming within-group homogeneity. This one-size-fits-all approach potentially limits our understanding of dementia aetiology, hindering the identification of effective treatments. Neuroimaging has enabled the characterization of the average neuroanatomical substrates of dementias; however, the increasing availability of large open neuroimaging datasets provides the opportunity to examine patterns of neuroanatomical variability in individual patients. In this update, we outline the causes and consequences of heterogeneity in dementia and discuss recent research that aims to tackle heterogeneity directly, rather than assuming that dementia affects everyone in the same way. We introduce spatial normative modelling as an emerging data-driven technique, which can be applied to dementia data to model neuroanatomical variation, capturing individualized neurobiological 'fingerprints'. Such methods have the potential to detect clinically relevant subtypes, track an individual's disease progression or evaluate treatment responses, with the goal of moving towards precision medicine for dementia.

Differences Between MR Brain Region Segmentation Methods: Impact on Single-Subject Analysis

For the segmentation of magnetic resonance brain images into anatomical regions, numerous fully automated methods have been proposed and compared to reference segmentations obtained manually. However, systematic differences might exist between the resulting segmentations, depending on the segmentation method and underlying brain atlas. This potentially results in sensitivity differences to disease and can further complicate the comparison of individual patients to normative data. In this study, we aim to answer two research questions: 1) to what extent are methods interchangeable, as long as the same method is being used for computing normative volume distributions and patient-specific volumes? and 2) can different methods be used for computing normative volume distributions and assessing patient-specific volumes? To answer these questions, we compared volumes of six brain regions calculated by five state-of-the-art segmentation methods: Erasmus MC (EMC), FreeSurfer (FS), geodesic information flows (GIF), multi-atlas label propagation with expectation–maximization (MALP-EM), and model-based brain segmentation (MBS). We applied the methods on 988 non-demented (ND) subjects and computed the correlation (PCC-v) and absolute agreement (ICC-v) on the volumes. For most regions, the PCC-v was good (>0.75), indicating that volume differences between methods in ND subjects are mainly due to systematic differences. The ICC-v was generally lower, especially for the smaller regions, indicating that it is essential that the same method is used to generate normative and patient data. To evaluate the impact on single-subject analysis, we also applied the methods to 42 patients with Alzheimer’s disease (AD). In the case where the normative distributions and the patient-specific volumes were calculated by the same method, the patient’s distance to the normative distribution was assessed with the z-score. We determined the diagnostic value of this z-score, which showed to be consistent across methods. The absolute agreement on the AD patients’ z-scores was high for regions of thalamus and putamen. This is encouraging as it indicates that the studied methods are interchangeable for these regions. For regions such as the hippocampus, amygdala, caudate nucleus and accumbens, and globus pallidus, not all method combinations showed a high ICC-z. Whether two methods are indeed interchangeable should be confirmed for the specific application and dataset of interest.

Degenerative adversarial neuroimage nets for brain scan simulations: Application in ageing and dementia

•

We implemented a new deep learning framework capable of synthesising realistic and accurate 4D brain MRI in ageing and Alzheimer’s disease.

•

We proposed a sequence of memory-efficient techniques designed to improve model stability, reduce artefacts, and improve individualization.

•

Synthesised T1w MRI scans contain only minor structural differences with real data, and have minimal noise/texture artefacts.

•

Synthesised MRI scans were diagnostically indistinguishable from real scans.

•

Synthetic MRI can be used for: i) data augmentation, ii) model validation and iii) understanding biological/disease mechanisms in the brain.

Accurate and realistic simulation of high-dimensional medical images has become an important research area relevant to many AI-enabled healthcare applications. However, current state-of-the-art approaches lack the ability to produce satisfactory high-resolution and accurate subject-specific images. In this work, we present a deep learning framework, namely 4D-Degenerative Adversarial NeuroImage Net (4D-DANI-Net), to generate high-resolution, longitudinal MRI scans that mimic subject-specific neurodegeneration in ageing and dementia. 4D-DANI-Net is a modular framework based on adversarial training and a set of novel spatiotemporal, biologically-informed constraints. To ensure efficient training and overcome memory limitations affecting such high-dimensional problems, we rely on three key technological advances: i) a new 3D training consistency mechanism called Profile Weight Functions (PWFs), ii) a 3D super-resolution module and iii) a transfer learning strategy to fine-tune the system for a given individual. To evaluate our approach, we trained the framework on 9852 T1-weighted MRI scans from 876 participants in the Alzheimer’s Disease Neuroimaging Initiative dataset and held out a separate test set of 1283 MRI scans from 170 participants for quantitative and qualitative assessment of the personalised time series of synthetic images. We performed three evaluations: i) image quality assessment; ii) quantifying the accuracy of regional brain volumes over and above benchmark models; and iii) quantifying visual perception of the synthetic images by medical experts. Overall, both quantitative and qualitative results show that 4D-DANI-Net produces realistic, low-artefact, personalised time series of synthetic T1 MRI that outperforms benchmark models.

Using normative modelling to detect disease progression in mild cognitive impairment and Alzheimer's disease in a cross-sectional multi-cohort study

Normative modelling is an emerging method for quantifying how individuals deviate from the healthy populational pattern. Several machine learning models have been implemented to develop normative models to investigate brain disorders, including regression, support vector machines and Gaussian process models. With the advance of deep learning technology, the use of deep neural networks has also been proposed. In this study, we assessed normative models based on deep autoencoders using structural neuroimaging data from patients with Alzheimer's disease (n = 206) and mild cognitive impairment (n = 354). We first trained the autoencoder on an independent dataset (UK Biobank dataset) with 11,034 healthy controls. Then, we estimated how each patient deviated from this norm and established which brain regions were associated to this deviation. Finally, we compared the performance of our normative model against traditional classifiers. As expected, we found that patients exhibited deviations according to the severity of their clinical condition. The model identified medial temporal regions, including the hippocampus, and the ventricular system as critical regions for the calculation of the deviation score. Overall, the normative model had comparable cross-cohort generalizability to traditional classifiers. To promote open science, we are making all scripts and the trained models available to the wider research community.

Learning to synthesise the ageing brain without longitudinal data

How will my face look when I get older? Or, for a more challenging question: How will my brain look when I get older? To answer this question one must devise (and learn from data) a multivariate auto-regressive function which given an image and a desired target age generates an output image. While collecting data for faces may be easier, collecting longitudinal brain data is not trivial. We propose a deep learning-based method that learns to simulate subject-specific brain ageing trajectories without relying on longitudinal data. Our method synthesises images conditioned on two factors: age (a continuous variable), and status of Alzheimer's Disease (AD, an ordinal variable). With an adversarial formulation we learn the joint distribution of brain appearance, age and AD status, and define reconstruction losses to address the challenging problem of preserving subject identity. We compare with several benchmarks using two widely used datasets. We evaluate the quality and realism of synthesised images using ground-truth longitudinal data and a pre-trained age predictor. We show that, despite the use of cross-sectional data, our model learns patterns of gray matter atrophy in the middle temporal gyrus in patients with AD. To demonstrate generalisation ability, we train on one dataset and evaluate predictions on the other. In conclusion, our model shows an ability to separate age, disease influence and anatomy using only 2D cross-sectional data that should be useful in large studies into neurodegenerative disease, that aim to combine several data sources. To facilitate such future studies by the community at large our code is made available at https://github.com/xiat0616/BrainAgeing.

Individual deviations from normative models of brain structure in a large cross-sectional schizophrenia cohort

The heterogeneity of schizophrenia has defied efforts to derive reproducible and definitive anatomical maps of structural brain changes associated with the disorder. We aimed to map deviations from normative ranges of brain structure for individual patients and evaluate whether the loci of individual deviations recapitulated group-average brain maps of schizophrenia pathology. For each of 48 white matter tracts and 68 cortical regions, normative percentiles of variation in fractional anisotropy (FA) and cortical thickness (CT) were established using diffusion-weighted and structural MRI from healthy adults (n = 195). Individuals with schizophrenia (n = 322) were classified as either within the normative range for healthy individuals of the same age and sex (5-95% percentiles), infra-normal (<5% percentile) or supra-normal (>95% percentile). Repeating this classification for each tract and region yielded a deviation map for each individual. Compared to the healthy comparison group, the schizophrenia group showed widespread reductions in FA and CT, involving virtually all white matter tracts and cortical regions. Paradoxically, however, no more than 15-20% of patients deviated from the normative range for any single tract or region. Furthermore, 79% of patients showed infra-normal deviations for at least one locus (healthy individuals: 59 ± 2%, p < 0.001). Thus, while infra-normal deviations were common among patients, their anatomical loci were highly inconsistent between individuals. Higher polygenic risk for schizophrenia associated with a greater number of regions with infra-normal deviations in CT (r = -0.17, p = 0.006). We conclude that anatomical loci of schizophrenia-related changes are highly heterogeneous across individuals to the extent that group-consensus pathological maps are not representative of most individual patients. Normative modeling can aid in parsing schizophrenia heterogeneity and guiding personalized interventions.

Measuring heterogeneity in normative models as the effective number of deviation patterns

Normative modeling is an increasingly popular method for characterizing the ways in which clinical cohorts deviate from a reference population, with respect to one or more biological features. In this paper, we extend the normative modeling framework with an approach for measuring the amount of heterogeneity in a cohort. This heterogeneity measure is based on the Representational Rényi Heterogeneity method, which generalizes diversity measurement paradigms used across multiple scientific disciplines. We propose that heterogeneity in the normative modeling setting can be measured as the effective number of deviation patterns; that is, the effective number of coherent patterns by which a sample of data differ from a distribution of normative variation. We show that lower effective number of deviation patterns is associated with the presence of systematic differences from a (non-degenerate) normative distribution. This finding is shown to be consistent across (A) application of a Gaussian process model to synthetic and real-world neuroimaging data, and (B) application of a variational autoencoder to well-understood database of handwritten images.

Surface Registration with Eigenvalues and Eigenvectors

This paper presents a novel surface registration technique using the spectrum of the shapes, which can facilitate accurate localization and visualization of non-isometric deformations of the surfaces. In order to register two surfaces, we map both eigenvalues and eigenvectors of the Laplace-Beltrami of the shapes through optimizing an energy function. The function is defined by the integration of a smoothness term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efficiency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. In our technique, the variation of the shape is expressed using a scale function defined at each vertex. Consequently, the total energy function to align the two given surfaces can be defined using the linear interpolation of the scale function derivatives. Through the optimization of the energy function, the scale function can be solved and the alignment is achieved. After the alignment, the eigenvectors can be employed to calculate the point-to-point correspondence of the surfaces. Therefore, the proposed method can accurately define the displacement of the vertices. We evaluate our method by conducting experiments on synthetic and real data using hippocampus, heart, and hand models. We also compare our method with non-rigid Iterative Closest Point (ICP) and a similar spectrum-based methods. These experiments demonstrate the advantages and accuracy of our method.

Brain Age Prediction of Children Using Routine Brain MR Images via Deep Learning

Predicting brain age of children accurately and quantitatively can give help in brain development analysis and brain disease diagnosis. Traditional methods to estimate brain age based on 3D magnetic resonance (MR), T1 weighted imaging (T1WI), and diffusion tensor imaging (DTI) need complex preprocessing and extra scanning time, decreasing clinical practice, especially in children. This research aims at proposing an end-to-end AI system based on deep learning to predict the brain age based on routine brain MR imaging. We spent over 5 years enrolling 220 stacked 2D routine clinical brain MR T1-weighted images of healthy children aged 0 to 5 years old and randomly divided those images into training data including 176 subjects and test data including 44 subjects. Data augmentation technology, which includes scaling, image rotation, translation, and gamma correction, was employed to extend the training data. A 10-layer 3D convolutional neural network (CNN) was designed for predicting the brain age of children and it achieved reliable and accurate results on test data with a mean absolute deviation (MAE) of 67.6 days, a root mean squared error (RMSE) of 96.1 days, a mean relative error (MRE) of 8.2%, a correlation coefficient (R) of 0.985, and a coefficient of determination (R 2) of 0.971. Specially, the performance on predicting the age of children under 2 years old with a MAE of 28.9 days, a RMSE of 37.0 days, a MRE of 7.8%, a R of 0.983, and a R 2 of 0.967 is much better than that over 2 with a MAE of 110.0 days, a RMSE of 133.5 days, a MRE of 8.2%, a R of 0.883, and a R 2 of 0.780.

Medical Informatics Platform (MIP): A Pilot Study Across Clinical Italian Cohorts

Introduction: With the shift of research focus to personalized medicine in Alzheimer's Dementia (AD), there is an urgent need for tools that are capable of quantifying a patient's risk using diagnostic biomarkers. The Medical Informatics Platform (MIP) is a distributed e-infrastructure federating large amounts of data coupled with machine-learning (ML) algorithms and statistical models to define the biological signature of the disease. The present study assessed (i) the accuracy of two ML algorithms, i.e., supervised Gradient Boosting (GB) and semi-unsupervised 3C strategy (Categorize, Cluster, Classify-CCC) implemented in the MIP and (ii) their contribution over the standard diagnostic workup. Methods: We examined individuals coming from the MIP installed across 3 Italian memory clinics, including subjects with Normal Cognition (CN, n = 432), Mild Cognitive Impairment (MCI, n = 456), and AD (n = 451). The GB classifier was applied to best discriminate the three diagnostic classes in 1,339 subjects, and the CCC strategy was used to refine the classical disease categories. Four dementia experts provided their diagnostic confidence (DC) of MCI conversion on an independent cohort of 38 patients. DC was based on clinical, neuropsychological, CSF, and structural MRI information and again with addition of the outcome from the MIP tools. Results: The GB algorithm provided a classification accuracy of 85% in a nested 10-fold cross-validation for CN vs. MCI vs. AD discrimination. Accuracy increased to 95% in the holdout validation, with the omission of each Italian clinical cohort out in turn. CCC identified five homogeneous clusters of subjects and 36 biomarkers that represented the disease fingerprint. In the DC assessment, CCC defined six clusters in the MCI population used to train the algorithm and 29 biomarkers to improve patients staging. GB and CCC showed a significant impact, evaluated as +5.99% of increment on physicians' DC. The influence of MIP on DC was rated from "slight" to "significant" in 80% of the cases. Discussion: GB provided fair results in classification of CN, MCI, and AD. CCC identified homogeneous and promising classes of subjects via its semi-unsupervised approach. We measured the effect of the MIP on the physician's DC. Our results pave the way for the establishment of a new paradigm for ML discrimination of patients who will or will not convert to AD, a clinical priority for neurology.

The definition and measurement of heterogeneity

Heterogeneity is an important concept in psychiatric research and science more broadly. It negatively impacts effect size estimates under case-control paradigms, and it exposes important flaws in our existing categorical nosology. Yet, our field has no precise definition of heterogeneity proper. We tend to quantify heterogeneity by measuring associated correlates such as entropy or variance: practices which are akin to accepting the radius of a sphere as a measure of its volume. Under a definition of heterogeneity as the degree to which a system deviates from perfect conformity, this paper argues that its proper measure roughly corresponds to the size of a system's event/sample space, and has units known as numbers equivalent. We arrive at this conclusion through focused review of more than 100 years of (re)discoveries of indices by ecologists, economists, statistical physicists, and others. In parallel, we review psychiatric approaches for quantifying heterogeneity, including but not limited to studies of symptom heterogeneity, microbiome biodiversity, cluster-counting, and time-series analyses. We argue that using numbers equivalent heterogeneity measures could improve the interpretability and synthesis of psychiatric research on heterogeneity. However, significant limitations must be overcome for these measures-largely developed for economic and ecological research-to be useful in modern translational psychiatric science.

Objectives, design and main findings until 2020 from the Rotterdam Study

The Rotterdam Study is an ongoing prospective cohort study that started in 1990 in the city of Rotterdam, The Netherlands. The study aims to unravel etiology, preclinical course, natural history and potential targets for intervention for chronic diseases in mid-life and late-life. The study focuses on cardiovascular, endocrine, hepatic, neurological, ophthalmic, psychiatric, dermatological, otolaryngological, locomotor, and respiratory diseases. As of 2008, 14,926 subjects aged 45 years or over comprise the Rotterdam Study cohort. Since 2016, the cohort is being expanded by persons aged 40 years and over. The findings of the Rotterdam Study have been presented in over 1700 research articles and reports. This article provides an update on the rationale and design of the study. It also presents a summary of the major findings from the preceding 3 years and outlines developments for the coming period.

A Spatio-Temporal Ageing Atlas of the Proximal Femur

Osteoporosis is an age-associated disease characterised by low bone mineral density (BMD) and micro-architectural deterioration leading to enhanced fracture risk. Conventional dual-energy X-ray absorptiometry (DXA) analysis has facilitated our understanding of BMD reduction in specific regions of interest (ROIs) within the femur, but cannot resolve spatial BMD patterns nor reflect age-related changes in bone microarchitecture due to its inherent averaging of pixel BMD values into large ROIs. To address these limitations and develop a comprehensive model of involutional bone loss, this paper presents a fully automatic pipeline to build a spatio-temporal atlas of ageing bone in the proximal femur. A new technique, termed DXA region free analysis (DXA RFA), is proposed to eliminate morphological variation between DXA scans by warping each image into a reference template. To construct the atlas, we use unprocessed DXA data from Caucasian women aged 20-97 years participating in three cohort studies in Western Europe ( ,000). A novel calibration procedure, termed quantile matching regression, is proposed to integrate data from different DXA manufacturers. Pixel-wise BMD evolution with ageing was modelled using smooth quantile curves. This technique enables characterisation of spatially-complex BMD change patterns with ageing, visualised using heat-maps. Furthermore, quantile curves plotted at different pixel coordinates showed consistently different rates of bone loss at different regions within the femoral neck. Given the close relationship between spatio-temporal bone loss and osteoporotic fracture, improved understanding of the bone ageing process could lead to enhanced prognostic, preventive and therapeutic strategies for the disease.

Analysing brain networks in population neuroscience: a case for the Bayesian philosophy

Network connectivity fingerprints are among today's best choices to obtain a faithful sampling of an individual's brain and cognition. Widely available MRI scanners can provide rich information tapping into network recruitment and reconfiguration that now scales to hundreds and thousands of humans. Here, we contemplate the advantages of analysing such connectome profiles using Bayesian strategies. These analysis techniques afford full probability estimates of the studied network coupling phenomena, provide analytical machinery to separate epistemological uncertainty and biological variability in a coherent manner, usher us towards avenues to go beyond binary statements on existence versus non-existence of an effect, and afford credibility estimates around all model parameters at play which thus enable single-subject predictions with rigorous uncertainty intervals. We illustrate the brittle boundary between healthy and diseased brain circuits by autism spectrum disorder as a recurring theme where, we argue, network-based approaches in neuroscience will require careful probabilistic answers. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

Age Prediction Based on Brain MRI Image: A Survey

Human age prediction is an interesting and applicable issue in different fields. It can be based on various criteria such as face image, DNA methylation, chest plate radiographs, knee radiographs, dental images and etc. Most of the age prediction researches have mainly been based on images. Since the image processing and Machine Learning (ML) techniques have grown up, the investigations were led to use them in age prediction problem. The implementations would be used in different fields, especially in medical applications. Brain Age Estimation (BAE) has attracted more attention in recent years and it would be so helpful in early diagnosis of some neurodegenerative diseases such as Alzheimer, Parkinson, Huntington, etc. BAE is performed on Magnetic Resonance Imaging (MRI) images to compute the brain ages. Studies based on brain MRI shows that there is a relation between accelerated aging and accelerated brain atrophy. This refers to the effects of neurodegenerative diseases on brain structure while making the whole of it older. This paper reviews and summarizes the main approaches for age prediction based on brain MRI images including preprocessing methods, useful tools used in different research works and the estimation algorithms. We categorize the BAE methods based on two factors, first the way of processing MRI images, which includes pixel-based, surface-based, or voxel-based methods and second, the generation of ML algorithms that includes traditional or Deep Learning (DL) methods. The modern techniques as DL methods help MRI based age prediction to get results that are more accurate. In recent years, more precise and statistical ML approaches have been utilized with the help of related tools for simplifying computations and getting accurate results. Pros and cons of each research and the challenges in each work are expressed and some guidelines and deliberations for future research are suggested.

Conceptualizing mental disorders as deviations from normative functioning

Normative models are a class of emerging statistical techniques useful for understanding the heterogeneous biology underlying psychiatric disorders at the level of the individual participant. Analogous to normative growth charts used in paediatric medicine for plotting child development in terms of height or weight as a function of age, normative models chart variation in clinical cohorts in terms of mappings between quantitative biological measures and clinically relevant variables. An emerging body of literature has demonstrated that such techniques are excellent tools for parsing the heterogeneity in clinical cohorts by providing statistical inferences at the level of the individual participant with respect to the normative range. Here, we provide a unifying review of the theory and application of normative modelling for understanding the biological and clinical heterogeneity underlying mental disorders. We first provide a statistically grounded yet non-technical overview of the conceptual underpinnings of normative modelling and propose a conceptual framework to link the many different methodological approaches that have been proposed for this purpose. We survey the literature employing these techniques, focusing principally on applications of normative modelling to quantitative neuroimaging-based biomarkers in psychiatry and, finally, we provide methodological considerations and recommendations to guide future applications of these techniques. We show that normative modelling provides a means by which the importance of modelling individual differences can be brought from theory to concrete data analysis procedures for understanding heterogeneous mental disorders and ultimately a promising route towards precision medicine in psychiatry.

Groupwise image registration based on a total correlation dissimilarity measure for quantitative MRI and dynamic imaging data

The most widespread technique used to register sets of medical images consists of selecting one image as fixed reference, to which all remaining images are successively registered. This pairwise scheme requires one optimization procedure per pair of images to register. Pairwise mutual information is a common dissimilarity measure applied to a large variety of datasets. Alternative methods, called groupwise registrations, have been presented to register two or more images in a single optimization procedure, without the need of a reference image. Given the success of mutual information in pairwise registration, we adapt one of its multivariate versions, called total correlation, in a groupwise context. We justify the choice of total correlation among other multivariate versions of mutual information, and provide full implementation details. The resulting total correlation measure is remarkably close to measures previously proposed by Huizinga et al. based on principal component analysis. Our experiments, performed on five quantitative imaging datasets and on a dynamic CT imaging dataset, show that total correlation yields registration results that are comparable to Huizinga's methods. Total correlation has the advantage of being theoretically justified, while the measures of Huizinga et al. were designed empirically. Additionally, total correlation offers an alternative to pairwise mutual information on quantitative imaging datasets.