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Recent advancements in medicine have confirmed that brain disorders often comprise multiple subtypes of mechanisms, developmental trajectories, or severity levels. Such heterogeneity is often associated with demographic aspects (e.g., sex) or disease-related contributors (e.g., genetics). Thus, the predictive power of machine learning models used for symptom prediction varies across subjects based on such factors. To model this heterogeneity, one can assign each training sample a factor-dependent weight, which modulates the subject's contribution to the overall objective loss function. To this end, we propose to model the subject weights as a linear combination of the eigenbases of a spectral population graph that captures the similarity of factors across subjects. In doing so, the learned weights smoothly vary across the graph, highlighting sub-cohorts with high and low predictability. Our proposed sample weighting scheme is evaluated on two tasks. First, we predict initiation of heavy alcohol drinking in young adulthood from imaging and neuropsychological measures from the National Consortium on Alcohol and NeuroDevelopment in Adolescence (NCANDA). Next, we detect Dementia vs. Mild Cognitive Impairment (MCI) using imaging and demographic measurements in subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Compared to existing sample weighting schemes, our sample weights improve interpretability and highlight sub-cohorts with distinct characteristics and varying model accuracy.

Deep learning can help uncover patterns in resting-state functional Magnetic Resonance Imaging (rs-fMRI) associated with psychiatric disorders and personal traits. Yet the problem of interpreting deep learning findings is rarely more evident than in fMRI analyses, as the data is sensitive to scanning effects and inherently difficult to visualize. We propose a simple approach to mitigate these challenges grounded on sparsification and self-supervision. Instead of extracting post-hoc feature attributions to uncover functional connections that are important to the target task, we identify a small subset of highly informative connections during training and occlude the rest. To this end, we jointly train a (1) sparse input mask, (2) variational autoencoder (VAE), and (3) downstream classifier in an end-to-end fashion. While we need a portion of labeled samples to train the classifier, we optimize the sparse mask and VAE with unlabeled data from additional acquisition sites, retaining only the input features that generalize well. We evaluate our method - Sparsely Reconstructed Graphs (SpaRG) - on the public ABIDE dataset for the task of sex classification, training with labeled cases from 18 sites and adapting the model to two additional out-of-distribution sites with a portion of unlabeled samples. For a relatively coarse parcellation (64 regions), SpaRG utilizes only 1% of the original connections while improving the classification accuracy across domains. Our code can be found at github.com/yanismiraoui/SpaRG.

Many longitudinal neuroimaging studies aim to improve the understanding of brain aging and diseases by studying the dynamic interactions between brain function and cognition. Doing so requires accurate encoding of their multidimensional relationship while accounting for individual variability over time. For this purpose, we propose an unsupervised learning model (called \underline{\textbf{Co}}ntrastive Learning-based \underline{\textbf{Gra}}ph Generalized \underline{\textbf{Ca}}nonical Correlation Analysis (CoGraCa)) that encodes their relationship via Graph Attention Networks and generalized Canonical Correlational Analysis. To create brain-cognition fingerprints reflecting unique neural and cognitive phenotype of each person, the model also relies on individualized and multimodal contrastive learning. We apply CoGraCa to longitudinal dataset of healthy individuals consisting of resting-state functional MRI and cognitive measures acquired at multiple visits for each participant. The generated fingerprints effectively capture significant individual differences and outperform current single-modal and CCA-based multimodal models in identifying sex and age. More importantly, our encoding provides interpretable interactions between those two modalities.

Deep learning models generating structural brain MRIs have the potential to significantly accelerate discovery of neuroscience studies. However, their use has been limited in part by the way their quality is evaluated. Most evaluations of generative models focus on metrics originally designed for natural images (such as structural similarity index and Frechet inception distance). As we show in a comparison of 6 state-of-the-art generative models trained and tested on over 3000 MRIs, these metrics are sensitive to the experimental setup and inadequately assess how well brain MRIs capture macrostructural properties of brain regions (i.e., anatomical plausibility). This shortcoming of the metrics results in inconclusive findings even when qualitative differences between the outputs of models are evident. We therefore propose a framework for evaluating models generating brain MRIs, which requires uniform processing of the real MRIs, standardizing the implementation of the models, and automatically segmenting the MRIs generated by the models. The segmentations are used for quantifying the plausibility of anatomy displayed in the MRIs. To ensure meaningful quantification, it is crucial that the segmentations are highly reliable. Our framework rigorously checks this reliability, a step often overlooked by prior work. Only 3 of the 6 generative models produced MRIs, of which at least 95% had highly reliable segmentations. More importantly, the assessment of each model by our framework is in line with qualitative assessments, reinforcing the validity of our approach., Comment: Accepted MICCAI 20224

The number of samples in structural brain MRI studies is often too small to properly train deep learning models. Generative models show promise in addressing this issue by effectively learning the data distribution and generating high-fidelity MRI. However, they struggle to produce diverse, high-quality data outside the distribution defined by the training data. One way to address the issue is using causal models developed for 3D volume counterfactuals. However, accurately modeling causality in high-dimensional spaces is a challenge so that these models generally generate 3D brain MRIS of lower quality. To address these challenges, we propose a two-stage method that constructs a Structural Causal Model (SCM) within the latent space. In the first stage, we employ a VQ-VAE to learn a compact embedding of the MRI volume. Subsequently, we integrate our causal model into this latent space and execute a three-step counterfactual procedure using a closed-form Generalized Linear Model (GLM). Our experiments conducted on real-world high-resolution MRI data (1mm) demonstrate that our method can generate high-quality 3D MRI counterfactuals.

Logical anomalies (LA) refer to data violating underlying logical constraints e.g., the quantity, arrangement, or composition of components within an image. Detecting accurately such anomalies requires models to reason about various component types through segmentation. However, curation of pixel-level annotations for semantic segmentation is both time-consuming and expensive. Although there are some prior few-shot or unsupervised co-part segmentation algorithms, they often fail on images with industrial object. These images have components with similar textures and shapes, and a precise differentiation proves challenging. In this study, we introduce a novel component segmentation model for LA detection that leverages a few labeled samples and unlabeled images sharing logical constraints. To ensure consistent segmentation across unlabeled images, we employ a histogram matching loss in conjunction with an entropy loss. As segmentation predictions play a crucial role, we propose to enhance both local and global sample validity detection by capturing key aspects from visual semantics via three memory banks: class histograms, component composition embeddings and patch-level representations. For effective LA detection, we propose an adaptive scaling strategy to standardize anomaly scores from different memory banks in inference. Extensive experiments on the public benchmark MVTec LOCO AD reveal our method achieves 98.1% AUROC in LA detection vs. 89.6% from competing methods., Comment: Accepted in AAAI2024

Generative AI models hold great potential in creating synthetic brain MRIs that advance neuroimaging studies by, for example, enriching data diversity. However, the mainstay of AI research only focuses on optimizing the visual quality (such as signal-to-noise ratio) of the synthetic MRIs while lacking insights into their relevance to neuroscience. To gain these insights with respect to T1-weighted MRIs, we first propose a new generative model, BrainSynth, to synthesize metadata-conditioned (e.g., age- and sex-specific) MRIs that achieve state-of-the-art visual quality. We then extend our evaluation with a novel procedure to quantify anatomical plausibility, i.e., how well the synthetic MRIs capture macrostructural properties of brain regions, and how accurately they encode the effects of age and sex. Results indicate that more than half of the brain regions in our synthetic MRIs are anatomically accurate, i.e., with a small effect size between real and synthetic MRIs. Moreover, the anatomical plausibility varies across cortical regions according to their geometric complexity. As is, our synthetic MRIs can significantly improve the training of a Convolutional Neural Network to identify accelerated aging effects in an independent study. These results highlight the opportunities of using generative AI to aid neuroimaging research and point to areas for further improvement.

Interpretability is a key issue when applying deep learning models to longitudinal brain MRIs. One way to address this issue is by visualizing the high-dimensional latent spaces generated by deep learning via self-organizing maps (SOM). SOM separates the latent space into clusters and then maps the cluster centers to a discrete (typically 2D) grid preserving the high-dimensional relationship between clusters. However, learning SOM in a high-dimensional latent space tends to be unstable, especially in a self-supervision setting. Furthermore, the learned SOM grid does not necessarily capture clinically interesting information, such as brain age. To resolve these issues, we propose the first self-supervised SOM approach that derives a high-dimensional, interpretable representation stratified by brain age solely based on longitudinal brain MRIs (i.e., without demographic or cognitive information). Called Longitudinally-consistent Self-Organized Representation learning (LSOR), the method is stable during training as it relies on soft clustering (vs. the hard cluster assignments used by existing SOM). Furthermore, our approach generates a latent space stratified according to brain age by aligning trajectories inferred from longitudinal MRIs to the reference vector associated with the corresponding SOM cluster. When applied to longitudinal MRIs of the Alzheimer's Disease Neuroimaging Initiative (ADNI, N=632), LSOR generates an interpretable latent space and achieves comparable or higher accuracy than the state-of-the-art representations with respect to the downstream tasks of classification (static vs. progressive mild cognitive impairment) and regression (determining ADAS-Cog score of all subjects). The code is available at https://github.com/ouyangjiahong/longitudinal-som-single-modality.

Publicly available data sets of structural MRIs might not contain specific measurements of brain Regions of Interests (ROIs) that are important for training machine learning models. For example, the curvature scores computed by Freesurfer are not released by the Adolescent Brain Cognitive Development (ABCD) Study. One can address this issue by simply reapplying Freesurfer to the data set. However, this approach is generally computationally and labor intensive (e.g., requiring quality control). An alternative is to impute the missing measurements via a deep learning approach. However, the state-of-the-art is designed to estimate randomly missing values rather than entire measurements. We therefore propose to re-frame the imputation problem as a prediction task on another (public) data set that contains the missing measurements and shares some ROI measurements with the data sets of interest. A deep learning model is then trained to predict the missing measurements from the shared ones and afterwards is applied to the other data sets. Our proposed algorithm models the dependencies between ROI measurements via a graph neural network (GNN) and accounts for demographic differences in brain measurements (e.g. sex) by feeding the graph encoding into a parallel architecture. The architecture simultaneously optimizes a graph decoder to impute values and a classifier in predicting demographic factors. We test the approach, called Demographic Aware Graph-based Imputation (DAGI), on imputing those missing Freesurfer measurements of ABCD (N=3760) by training the predictor on those publicly released by the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA, N=540)..., Comment: Accepted at the 6th workshop on PRedictive Intelligence in Medicine (PRIME 2023) - MICCAI 2023

One of the hallmark symptoms of Parkinson's Disease (PD) is the progressive loss of postural reflexes, which eventually leads to gait difficulties and balance problems. Identifying disruptions in brain function associated with gait impairment could be crucial in better understanding PD motor progression, thus advancing the development of more effective and personalized therapeutics. In this work, we present an explainable, geometric, weighted-graph attention neural network (xGW-GAT) to identify functional networks predictive of the progression of gait difficulties in individuals with PD. xGW-GAT predicts the multi-class gait impairment on the MDS Unified PD Rating Scale (MDS-UPDRS). Our computational- and data-efficient model represents functional connectomes as symmetric positive definite (SPD) matrices on a Riemannian manifold to explicitly encode pairwise interactions of entire connectomes, based on which we learn an attention mask yielding individual- and group-level explainability. Applied to our resting-state functional MRI (rs-fMRI) dataset of individuals with PD, xGW-GAT identifies functional connectivity patterns associated with gait impairment in PD and offers interpretable explanations of functional subnetworks associated with motor impairment. Our model successfully outperforms several existing methods while simultaneously revealing clinically-relevant connectivity patterns. The source code is available at https://github.com/favour-nerrise/xGW-GAT ., Comment: Accepted by the 26th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2023). MICCAI Student-Author Registration (STAR) Award. 11 pages, 2 figures, 1 table, appendix. Source Code: https://github.com/favour-nerrise/xGW-GAT

As acquiring MRIs is expensive, neuroscience studies struggle to attain a sufficient number of them for properly training deep learning models. This challenge could be reduced by MRI synthesis, for which Generative Adversarial Networks (GANs) are popular. GANs, however, are commonly unstable and struggle with creating diverse and high-quality data. A more stable alternative is Diffusion Probabilistic Models (DPMs) with a fine-grained training strategy. To overcome their need for extensive computational resources, we propose a conditional DPM (cDPM) with a memory-efficient process that generates realistic-looking brain MRIs. To this end, we train a 2D cDPM to generate an MRI subvolume conditioned on another subset of slices from the same MRI. By generating slices using arbitrary combinations between condition and target slices, the model only requires limited computational resources to learn interdependencies between slices even if they are spatially far apart. After having learned these dependencies via an attention network, a new anatomy-consistent 3D brain MRI is generated by repeatedly applying the cDPM. Our experiments demonstrate that our method can generate high-quality 3D MRIs that share a similar distribution to real MRIs while still diversifying the training set. The code is available at https://github.com/xiaoiker/mask3DMRI_diffusion and also will be released as part of MONAI, at https://github.com/Project-MONAI/GenerativeModels.

The white-matter (micro-)structural architecture of the brain promotes synchrony among neuronal populations, giving rise to richly patterned functional connections. A fundamental problem for systems neuroscience is determining the best way to relate structural and functional networks quantified by diffusion tensor imaging and resting-state functional MRI. As one of the state-of-the-art approaches for network analysis, graph convolutional networks (GCN) have been separately used to analyze functional and structural networks, but have not been applied to explore inter-network relationships. In this work, we propose to couple the two networks of an individual by adding inter-network edges between corresponding brain regions, so that the joint structure-function graph can be directly analyzed by a single GCN. The weights of inter-network edges are learnable, reflecting non-uniform structure-function coupling strength across the brain. We apply our Joint-GCN to predict age and sex of 662 participants from the public dataset of the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA) based on their functional and micro-structural white-matter networks. Our results support that the proposed Joint-GCN outperforms existing multi-modal graph learning approaches for analyzing structural and functional networks.

For the first time, we propose using a multiple instance learning based convolution-free transformer model, called Multiple Instance Neuroimage Transformer (MINiT), for the classification of T1weighted (T1w) MRIs. We first present several variants of transformer models adopted for neuroimages. These models extract non-overlapping 3D blocks from the input volume and perform multi-headed self-attention on a sequence of their linear projections. MINiT, on the other hand, treats each of the non-overlapping 3D blocks of the input MRI as its own instance, splitting it further into non-overlapping 3D patches, on which multi-headed self-attention is computed. As a proof-of-concept, we evaluate the efficacy of our model by training it to identify sex from T1w-MRIs of two public datasets: Adolescent Brain Cognitive Development (ABCD) and the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA). The learned attention maps highlight voxels contributing to identifying sex differences in brain morphometry. The code is available at https://github.com/singlaayush/MINIT.

A fundamental approach in neuroscience research is to test hypotheses based on neuropsychological and behavioral measures, i.e., whether certain factors (e.g., related to life events) are associated with an outcome (e.g., depression). In recent years, deep learning has become a potential alternative approach for conducting such analyses by predicting an outcome from a collection of factors and identifying the most "informative" ones driving the prediction. However, this approach has had limited impact as its findings are not linked to statistical significance of factors supporting hypotheses. In this article, we proposed a flexible and scalable approach based on the concept of permutation testing that integrates hypothesis testing into the data-driven deep learning analysis. We apply our approach to the yearly self-reported assessments of 621 adolescent participants of the National Consortium of Alcohol and Neurodevelopment in Adolescence (NCANDA) to predict negative valence, a symptom of major depressive disorder according to the NIMH Research Domain Criteria (RDoC). Our method successfully identifies categories of risk factors that further explain the symptom., Comment: Accepted at the 5th workshop on PRedictive Intelligence in Medicine (PRIME 2022) - MICCAI 2022

Translating machine learning algorithms into clinical applications requires addressing challenges related to interpretability, such as accounting for the effect of confounding variables (or metadata). Confounding variables affect the relationship between input training data and target outputs. When we train a model on such data, confounding variables will bias the distribution of the learned features. A recent promising solution, MetaData Normalization (MDN), estimates the linear relationship between the metadata and each feature based on a non-trainable closed-form solution. However, this estimation is confined by the sample size of a mini-batch and thereby may cause the approach to be unstable during training. In this paper, we extend the MDN method by applying a Penalty approach (referred to as PDMN). We cast the problem into a bi-level nested optimization problem. We then approximate this optimization problem using a penalty method so that the linear parameters within the MDN layer are trainable and learned on all samples. This enables PMDN to be plugged into any architectures, even those unfit to run batch-level operations, such as transformers and recurrent models. We show improvement in model accuracy and greater independence from confounders using PMDN over MDN in a synthetic experiment and a multi-label, multi-site dataset of magnetic resonance images (MRIs).

Parkinson's disease (PD) is a neurological disorder that has a variety of observable motor-related symptoms such as slow movement, tremor, muscular rigidity, and impaired posture. PD is typically diagnosed by evaluating the severity of motor impairments according to scoring systems such as the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS). Automated severity prediction using video recordings of individuals provides a promising route for non-intrusive monitoring of motor impairments. However, the limited size of PD gait data hinders model ability and clinical potential. Because of this clinical data scarcity and inspired by the recent advances in self-supervised large-scale language models like GPT-3, we use human motion forecasting as an effective self-supervised pre-training task for the estimation of motor impairment severity. We introduce GaitForeMer, Gait Forecasting and impairment estimation transforMer, which is first pre-trained on public datasets to forecast gait movements and then applied to clinical data to predict MDS-UPDRS gait impairment severity. Our method outperforms previous approaches that rely solely on clinical data by a large margin, achieving an F1 score of 0.76, precision of 0.79, and recall of 0.75. Using GaitForeMer, we show how public human movement data repositories can assist clinical use cases through learning universal motion representations. The code is available at https://github.com/markendo/GaitForeMer ., Comment: Accepted as a conference paper at MICCAI (Medical Image Computing and Computer Assisted Intervention) 2022

Starting from childhood, the human brain restructures and rewires throughout life. Characterizing such complex brain development requires effective analysis of longitudinal and multi-modal neuroimaging data. Here, we propose such an analysis approach named Longitudinal Correlation Analysis (LCA). LCA couples the data of two modalities by first reducing the input from each modality to a latent representation based on autoencoders. A self-supervised strategy then relates the two latent spaces by jointly disentangling two directions, one in each space, such that the longitudinal changes in latent representations along those directions are maximally correlated between modalities. We applied LCA to analyze the longitudinal T1-weighted and diffusion-weighted MRIs of 679 youths from the National Consortium on Alcohol and Neurodevelopment in Adolescence. Unlike existing approaches that focus on either cross-sectional or single-modal modeling, LCA successfully unraveled coupled macrostructural and microstructural brain development from morphological and diffusivity features extracted from the data. A retesting of LCA on raw 3D image volumes of those subjects successfully replicated the findings from the feature-based analysis. Lastly, the developmental effects revealed by LCA were inline with the current understanding of maturational patterns of the adolescent brain.

Batch Normalization (BN) and its variants have delivered tremendous success in combating the covariate shift induced by the training step of deep learning methods. While these techniques normalize feature distributions by standardizing with batch statistics, they do not correct the influence on features from extraneous variables or multiple distributions. Such extra variables, referred to as metadata here, may create bias or confounding effects (e.g., race when classifying gender from face images). We introduce the Metadata Normalization (MDN) layer, a new batch-level operation which can be used end-to-end within the training framework, to correct the influence of metadata on feature distributions. MDN adopts a regression analysis technique traditionally used for preprocessing to remove (regress out) the metadata effects on model features during training. We utilize a metric based on distance correlation to quantify the distribution bias from the metadata and demonstrate that our method successfully removes metadata effects on four diverse settings: one synthetic, one 2D image, one video, and one 3D medical image dataset., Comment: Accepted to CVPR 2021. Project page: https://mml.stanford.edu/MDN/

Longitudinal MRIs are often used to capture the gradual deterioration of brain structure and function caused by aging or neurological diseases. Analyzing this data via machine learning generally requires a large number of ground-truth labels, which are often missing or expensive to obtain. Reducing the need for labels, we propose a self-supervised strategy for representation learning named Longitudinal Neighborhood Embedding (LNE). Motivated by concepts in contrastive learning, LNE explicitly models the similarity between trajectory vectors across different subjects. We do so by building a graph in each training iteration defining neighborhoods in the latent space so that the progression direction of a subject follows the direction of its neighbors. This results in a smooth trajectory field that captures the global morphological change of the brain while maintaining the local continuity. We apply LNE to longitudinal T1w MRIs of two neuroimaging studies: a dataset composed of 274 healthy subjects, and Alzheimer's Disease Neuroimaging Initiative (ADNI, N=632). The visualization of the smooth trajectory vector field and superior performance on downstream tasks demonstrate the strength of the proposed method over existing self-supervised methods in extracting information associated with normal aging and in revealing the impact of neurodegenerative disorders. The code is available at \url{https://github.com/ouyangjiahong/longitudinal-neighbourhood-embedding.git}., Comment: Provisional Accepted by Medical Image Computing and Computer Assisted Intervention (MICCAI) 2021

Multi-modal MRIs are widely used in neuroimaging applications since different MR sequences provide complementary information about brain structures. Recent works have suggested that multi-modal deep learning analysis can benefit from explicitly disentangling anatomical (shape) and modality (appearance) information into separate image presentations. In this work, we challenge mainstream strategies by showing that they do not naturally lead to representation disentanglement both in theory and in practice. To address this issue, we propose a margin loss that regularizes the similarity in relationships of the representations across subjects and modalities. To enable robust training, we further use a conditional convolution to design a single model for encoding images of all modalities. Lastly, we propose a fusion function to combine the disentangled anatomical representations as a set of modality-invariant features for downstream tasks. We evaluate the proposed method on three multi-modal neuroimaging datasets. Experiments show that our proposed method can achieve superior disentangled representations compared to existing disentanglement strategies. Results also indicate that the fused anatomical representation has potential in the downstream task of zero-dose PET reconstruction and brain tumor segmentation. The code is available at \url{https://github.com/ouyangjiahong/representation-disentanglement}., Comment: Accepted by Information Processing in Medical Imaging (IPMI) 2021

Interpretability is a critical factor in applying complex deep learning models to advance the understanding of brain disorders in neuroimaging studies. To interpret the decision process of a trained classifier, existing techniques typically rely on saliency maps to quantify the voxel-wise or feature-level importance for classification through partial derivatives. Despite providing some level of localization, these maps are not human-understandable from the neuroscience perspective as they do not inform the specific meaning of the alteration linked to the brain disorder. Inspired by the image-to-image translation scheme, we propose to train simulator networks that can warp a given image to inject or remove patterns of the disease. These networks are trained such that the classifier produces consistently increased or decreased prediction logits for the simulated images. Moreover, we propose to couple all the simulators into a unified model based on conditional convolution. We applied our approach to interpreting classifiers trained on a synthetic dataset and two neuroimaging datasets to visualize the effect of the Alzheimer's disease and alcohol use disorder. Compared to the saliency maps generated by baseline approaches, our simulations and visualizations based on the Jacobian determinants of the warping field reveal meaningful and understandable patterns related to the diseases.

Parkinson's disease (PD) is a progressive neurological disorder primarily affecting motor function resulting in tremor at rest, rigidity, bradykinesia, and postural instability. The physical severity of PD impairments can be quantified through the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS), a widely used clinical rating scale. Accurate and quantitative assessment of disease progression is critical to developing a treatment that slows or stops further advancement of the disease. Prior work has mainly focused on dopamine transport neuroimaging for diagnosis or costly and intrusive wearables evaluating motor impairments. For the first time, we propose a computer vision-based model that observes non-intrusive video recordings of individuals, extracts their 3D body skeletons, tracks them through time, and classifies the movements according to the MDS-UPDRS gait scores. Experimental results show that our proposed method performs significantly better than chance and competing methods with an F1-score of 0.83 and a balanced accuracy of 81%. This is the first benchmark for classifying PD patients based on MDS-UPDRS gait severity and could be an objective biomarker for disease severity. Our work demonstrates how computer-assisted technologies can be used to non-intrusively monitor patients and their motor impairments. The code is available at https://github.com/mlu355/PD-Motor-Severity-Estimation., Comment: Accepted as a conference paper at MICCAI (Medical Image Computing and Computer Assisted Intervention), Lima, Peru, October 2020. 11 pages, LaTeX

Machine learning analysis of longitudinal neuroimaging data is typically based on supervised learning, which requires a large number of ground-truth labels to be informative. As ground-truth labels are often missing or expensive to obtain in neuroscience, we avoid them in our analysis by combing factor disentanglement with self-supervised learning to identify changes and consistencies across the multiple MRIs acquired of each individual over time. Specifically, we propose a new definition of disentanglement by formulating a multivariate mapping between factors (e.g., brain age) associated with an MRI and a latent image representation. Then, factors that evolve across acquisitions of longitudinal sequences are disentangled from that mapping by self-supervised learning in such a way that changes in a single factor induce change along one direction in the representation space. We implement this model, named Longitudinal Self-Supervised Learning (LSSL), via a standard autoencoding structure with a cosine loss to disentangle brain age from the image representation. We apply LSSL to two longitudinal neuroimaging studies to highlight its strength in extracting the brain-age information from MRI and revealing informative characteristics associated with neurodegenerative and neuropsychological disorders. Moreover, the representations learned by LSSL facilitate supervised classification by recording faster convergence and higher (or similar) prediction accuracy compared to several other representation learning techniques.

Many neurological diseases are characterized by gradual deterioration of brain structure and function. Large longitudinal MRI datasets have revealed such deterioration, in part, by applying machine and deep learning to predict diagnosis. A popular approach is to apply Convolutional Neural Networks (CNN) to extract informative features from each visit of the longitudinal MRI and then use those features to classify each visit via Recurrent Neural Networks (RNNs). Such modeling neglects the progressive nature of the disease, which may result in clinically implausible classifications across visits. To avoid this issue, we propose to combine features across visits by coupling feature extraction with a novel longitudinal pooling layer and enforce consistency of the classification across visits in line with disease progression. We evaluate the proposed method on the longitudinal structural MRIs from three neuroimaging datasets: Alzheimer's Disease Neuroimaging Initiative (ADNI, N=404), a dataset composed of 274 normal controls and 329 patients with Alcohol Use Disorder (AUD), and 255 youths from the National Consortium on Alcohol and NeuroDevelopment in Adolescence (NCANDA). In all three experiments our method is superior to other widely used approaches for longitudinal classification thus making a unique contribution towards more accurate tracking of the impact of conditions on the brain. The code is available at https://github.com/ouyangjiahong/longitudinal-pooling., Comment: Accepted by Journal of Biomedical and Health Informatics (JBHI)

The Blood-Oxygen-Level-Dependent (BOLD) signal of resting-state fMRI (rs-fMRI) records the temporal dynamics of intrinsic functional networks in the brain. However, existing deep learning methods applied to rs-fMRI either neglect the functional dependency between different brain regions in a network or discard the information in the temporal dynamics of brain activity. To overcome those shortcomings, we propose to formulate functional connectivity networks within the context of spatio-temporal graphs. We train a spatio-temporal graph convolutional network (ST-GCN) on short sub-sequences of the BOLD time series to model the non-stationary nature of functional connectivity. Simultaneously, the model learns the importance of graph edges within ST-GCN to gain insight into the functional connectivities contributing to the prediction. In analyzing the rs-fMRI of the Human Connectome Project (HCP, N=1,091) and the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA, N=773), ST-GCN is significantly more accurate than common approaches in predicting gender and age based on BOLD signals. Furthermore, the brain regions and functional connections significantly contributing to the predictions of our model are important markers according to the neuroscience literature.

Presence of bias (in datasets or tasks) is inarguably one of the most critical challenges in machine learning applications that has alluded to pivotal debates in recent years. Such challenges range from spurious associations between variables in medical studies to the bias of race in gender or face recognition systems. Controlling for all types of biases in the dataset curation stage is cumbersome and sometimes impossible. The alternative is to use the available data and build models incorporating fair representation learning. In this paper, we propose such a model based on adversarial training with two competing objectives to learn features that have (1) maximum discriminative power with respect to the task and (2) minimal statistical mean dependence with the protected (bias) variable(s). Our approach does so by incorporating a new adversarial loss function that encourages a vanished correlation between the bias and the learned features. We apply our method to synthetic data, medical images (containing task bias), and a dataset for gender classification (containing dataset bias). Our results show that the learned features by our method not only result in superior prediction performance but also are unbiased. The code is available at https://github.com/QingyuZhao/BR-Net/., Comment: WACV 2021

With recent advances in deep learning, neuroimaging studies increasingly rely on convolutional networks (ConvNets) to predict diagnosis based on MR images. To gain a better understanding of how a disease impacts the brain, the studies visualize the salience maps of the ConvNet highlighting voxels within the brain majorly contributing to the prediction. However, these salience maps are generally confounded, i.e., some salient regions are more predictive of confounding variables (such as age) than the diagnosis. To avoid such misinterpretation, we propose in this paper an approach that aims to visualize confounder-free saliency maps that only highlight voxels predictive of the diagnosis. The approach incorporates univariate statistical tests to identify confounding effects within the intermediate features learned by ConvNet. The influence from the subset of confounded features is then removed by a novel partial back-propagation procedure. We use this two-step approach to visualize confounder-free saliency maps extracted from synthetic and two real datasets. These experiments reveal the potential of our visualization in producing unbiased model-interpretation.

While unsupervised variational autoencoders (VAE) have become a powerful tool in neuroimage analysis, their application to supervised learning is under-explored. We aim to close this gap by proposing a unified probabilistic model for learning the latent space of imaging data and performing supervised regression. Based on recent advances in learning disentangled representations, the novel generative process explicitly models the conditional distribution of latent representations with respect to the regression target variable. Performing a variational inference procedure on this model leads to joint regularization between the VAE and a neural-network regressor. In predicting the age of 245 subjects from their structural Magnetic Resonance (MR) images, our model is more accurate than state-of-the-art methods when applied to either region-of-interest (ROI) measurements or raw 3D volume images. More importantly, unlike simple feed-forward neural-networks, disentanglement of age in latent representations allows for intuitive interpretation of the structural developmental patterns of the human brain.

Variation Autoencoder (VAE) has become a powerful tool in modeling the non-linear generative process of data from a low-dimensional latent space. Recently, several studies have proposed to use VAE for unsupervised clustering by using mixture models to capture the multi-modal structure of latent representations. This strategy, however, is ineffective when there are outlier data samples whose latent representations are meaningless, yet contaminating the estimation of key major clusters in the latent space. This exact problem arises in the context of resting-state fMRI (rs-fMRI) analysis, where clustering major functional connectivity patterns is often hindered by heavy noise of rs-fMRI and many minor clusters (rare connectivity patterns) of no interest to analysis. In this paper we propose a novel generative process, in which we use a Gaussian-mixture to model a few major clusters in the data, and use a non-informative uniform distribution to capture the remaining data. We embed this truncated Gaussian-Mixture model in a Variational AutoEncoder framework to obtain a general joint clustering and outlier detection approach, called tGM-VAE. We demonstrated the applicability of tGM-VAE on the MNIST dataset and further validated it in the context of rs-fMRI connectivity analysis.

As shown in computer vision, the power of deep learning lies in automatically learning relevant and powerful features for any perdition task, which is made possible through end-to-end architectures. However, deep learning approaches applied for classifying medical images do not adhere to this architecture as they rely on several pre- and post-processing steps. This shortcoming can be explained by the relatively small number of available labeled subjects, the high dimensionality of neuroimaging data, and difficulties in interpreting the results of deep learning methods. In this paper, we propose a simple 3D Convolutional Neural Networks and exploit its model parameters to tailor the end-to-end architecture for the diagnosis of Alzheimer's disease (AD). Our model can diagnose AD with an accuracy of 94.1\% on the popular ADNI dataset using only MRI data, which outperforms the previous state-of-the-art. Based on the learned model, we identify the disease biomarkers, the results of which were in accordance with the literature. We further transfer the learned model to diagnose mild cognitive impairment (MCI), the prodromal stage of AD, which yield better results compared to other methods.

Segmentation is a fundamental task for extracting semantically meaningful regions from an image. The goal of segmentation algorithms is to accurately assign object labels to each image location. However, image-noise, shortcomings of algorithms, and image ambiguities cause uncertainty in label assignment. Estimating the uncertainty in label assignment is important in multiple application domains, such as segmenting tumors from medical images for radiation treatment planning. One way to estimate these uncertainties is through the computation of posteriors of Bayesian models, which is computationally prohibitive for many practical applications. On the other hand, most computationally efficient methods fail to estimate label uncertainty. We therefore propose in this paper the Active Mean Fields (AMF) approach, a technique based on Bayesian modeling that uses a mean-field approximation to efficiently compute a segmentation and its corresponding uncertainty. Based on a variational formulation, the resulting convex model combines any label-likelihood measure with a prior on the length of the segmentation boundary. A specific implementation of that model is the Chan-Vese segmentation model (CV), in which the binary segmentation task is defined by a Gaussian likelihood and a prior regularizing the length of the segmentation boundary. Furthermore, the Euler-Lagrange equations derived from the AMF model are equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image denoising. Solutions to the AMF model can thus be implemented by directly utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We qualitatively assess the approach on synthetic data as well as on real natural and medical images. For a quantitative evaluation, we apply our approach to the icgbench dataset.

We introduce the moduli space of spectral curves of constant mean curvature (\cmc\hspace{-5pt}) cylinders of finite type in the round unit 3-sphere. The subset of spectral curves of mean-convex Alexandrov embedded cylinders is explicitly determined using a combination of integrable systems and geometric analysis techniques. We prove that these cylinders are surfaces of revolution. As a consequence all mean-convex Alexandrov embedded {\sc{cmc}} tori in the 3-sphere are surfaces of revolution., Comment: This is a revised version of arXiv:0712.0108

In $\mathbb{S}^2 \times \mathbb{R}$ there is a two-parameter family of properly embedded minimal annuli foliated by circles. In this paper we show that this family contains all properly embedded minimal annuli. We use the description of minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$ by periodic harmonic maps $G : \mathbb{C} \to \mathbb{S}^2$ of finite type. Due to the algebraic geometric correspondence of Hitchin [14], these harmonic maps are parametrized by hyperelliptic algebraic curves together with Abelian differentials with prescribed poles. We deform annuli by deforming spectral data in the corresponding moduli space. Along this deformation we control the flux and we preserve embeddedness. The center of the theory concerns the study of singularities of the flow. In particular we open and close nodes of singular spectral curves. This approach applies also to mean convex Alexandrov embedded cmc annuli in $\mathbb{S}^3$ [12]., Comment: 47 pages. v2: minor corrections in response to a referee remark

We study minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$ of finite type by relating them to harmonic maps $\mathbb{C} \to \mathbb{S}^2$ of finite type. We rephrase an iteration by Pinkall-Sterling in terms of polynomial Killing fields. We discuss spectral curves, spectral data and the geometry of the isospectral set. We consider polynomial Killing fields with zeroes and the corresponding singular spectral curves, bubbletons and simple factors. We investigate the differentiable structure on the isospectral set of any finite type minimal annulus. We apply the theory to a 2-parameter family of embedded minimal annuli foliated by horizontal circles., Comment: 30 pages. v2: Normalizations and minor typos fixed. Accepted for publication in Illinois J. Math

This article presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a proper distance, called Weighted Spectral Distance (WESD), for quantifying shape dissimilarity. The definition of WESD is derived through analysing the heat-trace. This analysis provides the proposed distance an intuitive meaning and mathematically links it to the intrinsic geometry of objects. We analyse the resulting distance definition, present and prove its important theoretical properties. Some of these properties include: i) WESD is defined over the entire sequence of eigenvalues yet it is guaranteed to converge, ii) it is a pseudometric, iii) it is accurately approximated with a finite number of eigenvalues, and iv) it can be mapped to the [0,1) interval. Lastly, experiments conducted on synthetic and real objects are presented. These experiments highlight the practical benefits of WESD for applications in vision and medical image analysis.

We show that one-sided Alexandrov embedded constant mean curvature cylinders of finite type in the 3-sphere are surfaces of revolution. This confirms a conjecture by Pinkall and Sterling that the only embedded constant mean curvature tori in the 3-sphere are rotational., Comment: Expanded and revised

The generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mean curvature surface which has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is embedded if the Delaunay surface is unduloidal.

We prove that a primitive harmonic map is equivariant if and only if it admits a holomorphic potential of degree one. We investigate when the equivariant harmonic map is periodic, and as an application discuss constant mean curvature cylinders with screw motion symmetries.

In this note we consider the relationship between the dressing action and the holonomy representation in the context of constant mean curvature surfaces. We characterize dressing elements that preserve the topology of a surface and discuss dressing by simple factors as a means of adding bubbles to a class of non finite type cylinders., Comment: 36 pages, 1 figure

We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus $g \geq 1$, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends., Comment: 14 pages, 10 figures

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms $\R^3$, $\bbS^3 $ and $\bbH^3$. Additionally, we compute the extended frame for any associated family of Delaunay surfaces., Comment: 18 pages, revised version

We use the DPW method to obtain the associate family of Delaunay surfaces and derive a formula for the neck size of the surface in terms of the entries of the holomorphic potential., Comment: 9 pages