Brain morphometric features predict medication response in youth with bipolar disorder: a prospective randomized clinical trial.

BACKGROUND: Identification of treatment-specific predictors of drug therapies for bipolar disorder (BD) is important because only about half of individuals respond to any specific medication. However, medication response in pediatric BD is variable and not well predicted by clinical characteristics. METHODS: A total of 121 youth with early course BD (acute manic/mixed episode) were prospectively recruited and randomized to 6 weeks of double-blind treatment with quetiapine (n = 71) or lithium (n = 50). Participants completed structural magnetic resonance imaging (MRI) at baseline before treatment and 1 week after treatment initiation, and brain morphometric features were extracted for each individual based on MRI scans. Positive antimanic treatment response at week 6 was defined as an over 50% reduction of Young Mania Rating Scale scores from baseline. Two-stage deep learning prediction model was established to distinguish responders and non-responders based on different feature sets. RESULTS: Pre-treatment morphometry and morphometric changes occurring during the first week can both independently predict treatment outcome of quetiapine and lithium with balanced accuracy over 75% (all p < 0.05). Combining brain morphometry at baseline and week 1 allows prediction with the highest balanced accuracy (quetiapine: 83.2% and lithium: 83.5%). Predictions in the quetiapine and lithium group were found to be driven by different morphometric patterns. CONCLUSIONS: These findings demonstrate that pre-treatment morphometric measures and acute brain morphometric changes can serve as medication response predictors in pediatric BD. Brain morphometric features may provide promising biomarkers for developing biologically-informed treatment outcome prediction and patient stratification tools for BD treatment development.

Magnetization transfer imaging alterations and its diagnostic value in antipsychotic-naïve first-episode schizophrenia.

Magnetization transfer imaging (MTI) may provide more sensitivity and mechanistic understanding of neuropathological changes associated with schizophrenia than volumetric MRI. This study aims to identify brain magnetization transfer ratio (MTR) changes in antipsychotic-naïve first-episode schizophrenia (FES), and to correlate MTR findings with clinical symptom severity. A total of 143 individuals with antipsychotic-naïve FES and 147 healthy controls (HCs) were included and underwent 3.0 T brain MTI between August 2005 and July 2014. Voxelwise analysis was performed to test for MTR differences with family-wise error corrections. Relationships of these differences to symptom severity were assessed using partial correlations. Exploratory analyses using a support vector machine (SVM) classifier were conducted to discriminate FES from HCs using MTR maps. Model performance was examined using a 10-fold stratified cross-validation. Compared with HCs, individuals with FES exhibited higher MTR values in left thalamus, precuneus, cuneus, and paracentral lobule, that were positively correlated with schizophrenia symptom severity [precuneus (r = 0.34, P = 0.0004), cuneus (r = 0.33, P = 0.0006) and paracentral lobule (r = 0.37, P = 0.001)]. Whole-brain MTR maps identified individuals with FES with overall accuracy 75.5% (219 of 290 individuals) based on SVM approach. In antipsychotic-naïve FES, clinically relevant biophysical abnormalities detected by MTI mainly in the left parieto-occipital regions are informative about local brain pathology, and have potential as diagnostic markers.

Unsupervised brain imaging 3D anomaly detection and segmentation with transformers.

Pathological brain appearances may be so heterogeneous as to be intelligible only as anomalies, defined by their deviation from normality rather than any specific set of pathological features. Amongst the hardest tasks in medical imaging, detecting such anomalies requires models of the normal brain that combine compactness with the expressivity of the complex, long-range interactions that characterise its structural organisation. These are requirements transformers have arguably greater potential to satisfy than other current candidate architectures, but their application has been inhibited by their demands on data and computational resources. Here we combine the latent representation of vector quantised variational autoencoders with an ensemble of autoregressive transformers to enable unsupervised anomaly detection and segmentation defined by deviation from healthy brain imaging data, achievable at low computational cost, within relative modest data regimes. We compare our method to current state-of-the-art approaches across a series of experiments with 2D and 3D data involving synthetic and real pathological lesions. On real lesions, we train our models on 15,000 radiologically normal participants from UK Biobank and evaluate performance on four different brain MR datasets with small vessel disease, demyelinating lesions, and tumours. We demonstrate superior anomaly detection performance both image-wise and pixel/voxel-wise, achievable without post-processing. These results draw attention to the potential of transformers in this most challenging of imaging tasks.

Graph Convolutional Networks Reveal Network-Level Functional Dysconnectivity in Schizophrenia.

BACKGROUND AND HYPOTHESIS: Schizophrenia is increasingly understood as a disorder of brain dysconnectivity. Recently, graph-based approaches such as graph convolutional network (GCN) have been leveraged to explore complex pairwise similarities in imaging features among brain regions, which can reveal abstract and complex relationships within brain networks. STUDY DESIGN: We used GCN to investigate topological abnormalities of functional brain networks in schizophrenia. Resting-state functional magnetic resonance imaging data were acquired from 505 individuals with schizophrenia and 907 controls across 6 sites. Whole-brain functional connectivity matrix was extracted for each individual. We examined the performance of GCN relative to support vector machine (SVM), extracted the most salient regions contributing to both classification models, investigated the topological profiles of identified salient regions, and explored correlation between nodal topological properties of each salient region and severity of symptom. STUDY RESULTS: GCN enabled nominally higher classification accuracy (85.8%) compared with SVM (80.9%). Based on the saliency map, the most discriminative brain regions were located in a distributed network including striatal areas (ie, putamen, pallidum, and caudate) and the amygdala. Significant differences in the nodal efficiency of bilateral putamen and pallidum between patients and controls and its correlations with negative symptoms were detected in post hoc analysis. CONCLUSIONS: The present study demonstrates that GCN allows classification of schizophrenia at the individual level with high accuracy, indicating a promising direction for detection of individual patients with schizophrenia. Functional topological deficits of striatal areas may represent a focal neural deficit of negative symptomatology in schizophrenia.

Using graph convolutional network to characterize individuals with major depressive disorder across multiple imaging sites.

BACKGROUND: Establishing objective and quantitative neuroimaging biomarkers at individual level can assist in early and accurate diagnosis of major depressive disorder (MDD). However, most previous studies using machine learning to identify MDD were based on small sample size and did not account for the brain connectome that is associated with the pathophysiology of MDD. Here, we addressed these limitations by applying graph convolutional network (GCN) in a large multi-site MDD dataset. METHODS: Resting-state functional MRI scans of 1586 participants (821 MDD vs. 765 controls) across 16 sites of Rest-meta-MDD consortium were collected. GCN model was trained with individual whole-brain functional network to identify MDD patients from controls, characterize the most salient regions contributing to classification, and explore the relationship between topological characteristics of salient regions and clinical measures. FINDINGS: GCN achieved an accuracy of 81·5% (95%CI: 80·5-82·5%, AUC: 0·865), which was higher than other common machine learning classifiers. The most salient regions contributing to classification were primarily identified within the default mode, fronto-parietal, and cingulo-opercular networks. Nodal topologies of the left inferior parietal lobule and left dorsolateral prefrontal cortex were associated with depressive severity and illness duration, respectively. INTERPRETATION: These findings based on a large, multi-site dataset support the feasibility and effectiveness of GCN in characterizing MDD, and also illustrate the potential utility of GCN for enhancing understanding of the neurobiology of MDD by detecting clinically-relevant disruption in functional network topology. FUNDING: This study was supported by the National Natural Science Foundation of China (Grant Nos. 81621003, 82027808, 81820108018).

Using deep learning to classify pediatric posttraumatic stress disorder at the individual level.

BACKGROUND: Children exposed to natural disasters are vulnerable to developing posttraumatic stress disorder (PTSD). Previous studies using resting-state functional neuroimaging have revealed alterations in graph-based brain topological network metrics in pediatric PTSD patients relative to healthy controls (HC). Here we aimed to apply deep learning (DL) models to neuroimaging markers of classification which may be of assistance in diagnosis of pediatric PTSD. METHODS: We studied 33 pediatric PTSD and 53 matched HC. Functional connectivity between 90 brain regions from the automated anatomical labeling atlas was established using partial correlation coefficients, and the whole-brain functional connectome was constructed by applying a threshold to the resultant 90 * 90 partial correlation matrix. Graph theory analysis was used to examine the topological properties of the functional connectome. A DL algorithm then used this measure to classify pediatric PTSD vs HC. RESULTS: Graphic topological measures using DL provide a potentially clinically useful classifier for differentiating pediatric PTSD and HC (overall accuracy 71.2%). Frontoparietal areas (central executive network), cingulate cortex, and amygdala contributed the most to the DL model's performance. CONCLUSIONS: Graphic topological measures based on fMRI data could contribute to imaging models of clinical utility in distinguishing pediatric PTSD from HC. DL model may be a useful tool in the identification of brain mechanisms PTSD participants.

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.

Inferring the heritability of large-scale functional networks with a multivariate ACE modeling approach.

Recent evidence suggests that the human functional connectome is stable at different timescales and is unique. These characteristics posit the functional connectome not only as an individual marker but also as a powerful discriminatory measure characterized by high intersubject variability. Among distinct sources of intersubject variability, the long-term sources include functional patterns that emerge from genetic factors. Here, we sought to investigate the contribution of additive genetic factors to the variability of functional networks by determining the heritability of the connectivity strength in a multivariate fashion. First, we reproduced and extended the connectome fingerprinting analysis to the identification of twin pairs. Then, we estimated the heritability of functional networks by a multivariate ACE modeling approach with bootstrapping. Twin pairs were identified above chance level using connectome fingerprinting, with monozygotic twin identification accuracy equal to 57.2% on average for whole-brain connectome. Additionally, we found that a visual (0.37), the medial frontal (0.31), and the motor (0.30) functional networks were the most influenced by additive genetic factors. Our findings suggest that genetic factors not only partially determine intersubject variability of the functional connectome, such that twins can be identified using connectome fingerprinting, but also differentially influence connectivity strength in large-scale functional networks.

Disrupted brain gray matter networks in drug-naïve participants with essential tremor.

PURPOSE: To use structural magnetic resonance imaging and graph theory approaches to investigate the topological organization of the brain morphological network based on gray matter in essential tremor, and its potential relation to disease severity. METHODS: In this prospective study conducted from November 2018 to November 2019, 36 participants with essential tremor and 37 matched healthy controls underwent magnetic resonance imaging. Brain networks based on the morphological similarity of gray matter across regions were analyzed using graph theory. Nonparametric permutation testing was used to assess group differences in topological metrics. Support vector machine was applied to the gray matter morphological matrices to classify participants with essential tremor vs. healthy controls. RESULTS: Compared with healthy controls, participants with essential tremor showed increased global efficiency (p < 0.01) and decreased path length (p < 0.01); abnormal nodal properties in frontal, parietal, and cerebellar lobes; and disconnectivity in cerebello-thalamo-cortical network. The abnormal brain nodal centralities (left superior cerebellum gyrus; right caudate nucleus) correlated with clinical measures, both motor (Fahn-Tolosa-Marìn tremor rating, p = 0.017, r = - 0.41) and nonmotor (Hamilton depression scale, p = 0.040, r = - 0.36; Hamilton anxiety scale, p = 0.008, r = - 0.436). Gray matter morphological matrices classified individuals with high accuracy of 80.0%. CONCLUSION: Participants with essential tremor showed randomization in global properties and dysconnectivity in the cerebello-thalamo-cortical network. Participants with essential tremor could be distinguished from healthy controls by gray matter morphological matrices.

Brain age prediction: A comparison between machine learning models using region- and voxel-based morphometric data.

Brain morphology varies across the ageing trajectory and the prediction of a person's age using brain features can aid the detection of abnormalities in the ageing process. Existing studies on such "brain age prediction" vary widely in terms of their methods and type of data, so at present the most accurate and generalisable methodological approach is unclear. Therefore, we used the UK Biobank data set (N = 10,824, age range 47-73) to compare the performance of the machine learning models support vector regression, relevance vector regression and Gaussian process regression on whole-brain region-based or voxel-based structural magnetic resonance imaging data with or without dimensionality reduction through principal component analysis. Performance was assessed in the validation set through cross-validation as well as an independent test set. The models achieved mean absolute errors between 3.7 and 4.7 years, with those trained on voxel-level data with principal component analysis performing best. Overall, we observed little difference in performance between models trained on the same data type, indicating that the type of input data had greater impact on performance than model choice. All code is provided online in the hope that this will aid future research.

Disruption of gray matter morphological networks in patients with paroxysmal kinesigenic dyskinesia.

This study explores the topological properties of brain gray matter (GM) networks in patients with paroxysmal kinesigenic dyskinesia (PKD) and asks whether GM network features have potential diagnostic value. We used 3D T1-weighted magnetic resonance imaging and graph theoretical approaches to investigate the topological organization of GM morphological networks in 87 PKD patients and 115 age- and sex-matched healthy controls. We applied a support vector machine to GM morphological network matrices to classify PKD patients versus healthy controls. Compared with the HC group, the GM morphological networks of PKD patients showed significant abnormalities at the global level, including an increase in characteristic path length (Lp) and decreases in local efficiency (Eloc ), clustering coefficient (Cp), normalized clustering coefficient (γ), and small-worldness (σ). The decrease in Cp was significantly correlated with disease duration and age of onset. The GM morphological networks of PKD patients also showed significant changes in nodal topological characteristics, mainly in the basal ganglia-thalamus circuitry, default-mode network and central executive network. Finally, we used the GM morphological network matrices to classify individuals as PKD patients versus healthy controls, achieving 87.8% accuracy. Overall, this study demonstrated disruption of GM morphological networks in PKD, which might extend our understanding of the pathophysiology of PKD; further, GM morphological network matrices might have the potential to serve as network neuroimaging biomarkers for the diagnosis of PKD.

Brain-Age Prediction Using Shallow Machine Learning: Predictive Analytics Competition 2019.

As we age, our brain structure changes and our cognitive capabilities decline. Although brain aging is universal, rates of brain aging differ markedly, which can be associated with pathological mechanism of psychiatric and neurological diseases. Predictive models have been applied to neuroimaging data to learn patterns associated with this variability and develop a neuroimaging biomarker of the brain condition. Aiming to stimulate the development of more accurate brain-age predictors, the Predictive Analytics Competition (PAC) 2019 provided a challenge that included a dataset of 2,640 participants. Here, we present our approach which placed between the top 10 of the challenge. We developed an ensemble of shallow machine learning methods (e.g., Support Vector Regression and Decision Tree-based regressors) that combined voxel-based and surface-based morphometric data. We used normalized brain volume maps (i.e., gray matter, white matter, or both) and features of cortical regions and anatomical structures, like cortical thickness, volume, and mean curvature. In order to fine-tune the hyperparameters of the machine learning methods, we combined the use of genetic algorithms and grid search. Our ensemble had a mean absolute error of 3.7597 years on the competition, showing the potential that shallow methods still have in predicting brain-age.

An automated machine learning approach to predict brain age from cortical anatomical measures.

The use of machine learning (ML) algorithms has significantly increased in neuroscience. However, from the vast extent of possible ML algorithms, which one is the optimal model to predict the target variable? What are the hyperparameters for such a model? Given the plethora of possible answers to these questions, in the last years, automated ML (autoML) has been gaining attention. Here, we apply an autoML library called Tree-based Pipeline Optimisation Tool (TPOT) which uses a tree-based representation of ML pipelines and conducts a genetic programming-based approach to find the model and its hyperparameters that more closely predicts the subject's true age. To explore autoML and evaluate its efficacy within neuroimaging data sets, we chose a problem that has been the focus of previous extensive study: brain age prediction. Without any prior knowledge, TPOT was able to scan through the model space and create pipelines that outperformed the state-of-the-art accuracy for Freesurfer-based models using only thickness and volume information for anatomical structure. In particular, we compared the performance of TPOT (mean absolute error [MAE]: 4.612 ± .124 years) and a relevance vector regression (MAE 5.474 ± .140 years). TPOT also suggested interesting combinations of models that do not match the current most used models for brain prediction but generalise well to unseen data. AutoML showed promising results as a data-driven approach to find optimal models for neuroimaging applications.

Using Machine Learning and Structural Neuroimaging to Detect First Episode Psychosis: Reconsidering the Evidence.

Despite the high level of interest in the use of machine learning (ML) and neuroimaging to detect psychosis at the individual level, the reliability of the findings is unclear due to potential methodological issues that may have inflated the existing literature. This study aimed to elucidate the extent to which the application of ML to neuroanatomical data allows detection of first episode psychosis (FEP), while putting in place methodological precautions to avoid overoptimistic results. We tested both traditional ML and an emerging approach known as deep learning (DL) using 3 feature sets of interest: (1) surface-based regional volumes and cortical thickness, (2) voxel-based gray matter volume (GMV) and (3) voxel-based cortical thickness (VBCT). To assess the reliability of the findings, we repeated all analyses in 5 independent datasets, totaling 956 participants (514 FEP and 444 within-site matched controls). The performance was assessed via nested cross-validation (CV) and cross-site CV. Accuracies ranged from 50% to 70% for surfaced-based features; from 50% to 63% for GMV; and from 51% to 68% for VBCT. The best accuracies (70%) were achieved when DL was applied to surface-based features; however, these models generalized poorly to other sites. Findings from this study suggest that, when methodological precautions are adopted to avoid overoptimistic results, detection of individuals in the early stages of psychosis is more challenging than originally thought. In light of this, we argue that the current evidence for the diagnostic value of ML and structural neuroimaging should be reconsidered toward a more cautious interpretation.

Detecting schizophrenia at the level of the individual: relative diagnostic value of whole-brain images, connectome-wide functional connectivity and graph-based metrics.

BACKGROUND: Previous studies using resting-state functional neuroimaging have revealed alterations in whole-brain images, connectome-wide functional connectivity and graph-based metrics in groups of patients with schizophrenia relative to groups of healthy controls. However, it is unclear which of these measures best captures the neural correlates of this disorder at the level of the individual patient. METHODS: Here we investigated the relative diagnostic value of these measures. A total of 295 patients with schizophrenia and 452 healthy controls were investigated using resting-state functional Magnetic Resonance Imaging at five research centres. Connectome-wide functional networks were constructed by thresholding correlation matrices of 90 brain regions, and their topological properties were analyzed using graph theory-based methods. Single-subject classification was performed using three machine learning (ML) approaches associated with varying degrees of complexity and abstraction, namely logistic regression, support vector machine and deep learning technology. RESULTS: Connectome-wide functional connectivity allowed single-subject classification of patients and controls with higher accuracy (average: 81%) than both whole-brain images (average: 53%) and graph-based metrics (average: 69%). Classification based on connectome-wide functional connectivity was driven by a distributed bilateral network including the thalamus and temporal regions. CONCLUSION: These results were replicated across the three employed ML approaches. Connectome-wide functional connectivity permits differentiation of patients with schizophrenia from healthy controls at single-subject level with greater accuracy; this pattern of results is consistent with the 'dysconnectivity hypothesis' of schizophrenia, which states that the neural basis of the disorder is best understood in terms of system-level functional connectivity alterations.

Integrating machining learning and multimodal neuroimaging to detect schizophrenia at the level of the individual.

Schizophrenia is a severe psychiatric disorder associated with both structural and functional brain abnormalities. In the past few years, there has been growing interest in the application of machine learning techniques to neuroimaging data for the diagnostic and prognostic assessment of this disorder. However, the vast majority of studies published so far have used either structural or functional neuroimaging data, without accounting for the multimodal nature of the disorder. Structural MRI and resting-state functional MRI data were acquired from a total of 295 patients with schizophrenia and 452 healthy controls at five research centers. We extracted features from the data including gray matter volume, white matter volume, amplitude of low-frequency fluctuation, regional homogeneity and two connectome-wide based metrics: structural covariance matrices and functional connectivity matrices. A support vector machine classifier was trained on each dataset separately to distinguish the subjects at individual level using each of the single feature as well as their combination, and 10-fold cross-validation was used to assess the performance of the model. Functional data allow higher accuracy of classification than structural data (mean 82.75% vs. 75.84%). Within each modality, the combination of images and matrices improves performance, resulting in mean accuracies of 81.63% for structural data and 87.59% for functional data. The use of all combined structural and functional measures allows the highest accuracy of classification (90.83%). We conclude that combining multimodal measures within a single model is a promising direction for developing biologically informed diagnostic tools in schizophrenia.

Brazilian montane rainforest expansion induced by Heinrich Stadial 1 event.

The origin of modern disjunct plant distributions in the Brazilian Highlands with strong floristic affinities to distant montane rainforests of isolated mountaintops in the northeast and northern Amazonia and the Guyana Shield remains unknown. We tested the hypothesis that these unexplained biogeographical patterns reflect former ecosystem rearrangements sustained by widespread plant migrations possibly due to climatic patterns that are very dissimilar from present-day conditions. To address this issue, we mapped the presence of the montane arboreal taxa Araucaria, Podocarpus, Drimys, Hedyosmum, Ilex, Myrsine, Symplocos, and Weinmannia, and cool-adapted plants in the families Myrtaceae, Ericaceae, and Arecaceae (palms) in 29 palynological records during Heinrich Stadial 1 Event, encompassing a latitudinal range of 30°S to 0°S. In addition, Principal Component Analysis and Species Distribution Modelling were used to represent past and modern habitat suitability for Podocarpus and Araucaria. The data reveals two long-distance patterns of plant migration connecting south/southeast to northeastern Brazil and Amazonia with a third short route extending from one of them. Their paleofloristic compositions suggest a climatic scenario of abundant rainfall and relative lower continental surface temperatures, possibly intensified by the effects of polar air incursions forming cold fronts into the Brazilian Highlands. Although these taxa are sensitive to changes in temperature, the combined pollen and speleothems proxy data indicate that this montane rainforest expansion during Heinrich Stadial 1 Event was triggered mainly by a less seasonal rainfall regime from the subtropics to the equatorial region.

Using deep autoencoders to identify abnormal brain structural patterns in neuropsychiatric disorders: A large-scale multi-sample study.

Machine learning is becoming an increasingly popular approach for investigating spatially distributed and subtle neuroanatomical alterations in brain-based disorders. However, some machine learning models have been criticized for requiring a large number of cases in each experimental group, and for resembling a "black box" that provides little or no insight into the nature of the data. In this article, we propose an alternative conceptual and practical approach for investigating brain-based disorders which aim to overcome these limitations. We used an artificial neural network known as "deep autoencoder" to create a normative model using structural magnetic resonance imaging data from 1,113 healthy people. We then used this model to estimate total and regional neuroanatomical deviation in individual patients with schizophrenia and autism spectrum disorder using two independent data sets (n = 263). We report that the model was able to generate different values of total neuroanatomical deviation for each disease under investigation relative to their control group (p < .005). Furthermore, the model revealed distinct patterns of neuroanatomical deviations for the two diseases, consistent with the existing neuroimaging literature. We conclude that the deep autoencoder provides a flexible and promising framework for assessing total and regional neuroanatomical deviations in neuropsychiatric populations.

Default Mode Network Maturation and Environmental Adversities During Childhood.

Default mode network (DMN) plays a central role in cognition and brain disorders. It has been shown that adverse environmental conditions impact neurodevelopment, but how these conditions impact in DMN maturation is still poorly understood. This article reviews representative neuroimaging functional studies addressing the interactions between DMN development and environmental factors, focusing on early life adversities, a critical period for brain changes. Studies focused on this period of life offer a special challenge: to disentangle the neurodevelopmental connectivity changes from those related to environmental conditions. We first summarized the literature on DMN maturation, providing an overview of both typical and atypical development patterns in childhood and early adolescence. Afterward, we focused on DMN changes associated with chronic exposure to environmental adversities during childhood. This summary suggests that changes in DMN development could be a potential allostatic neural feature associated with an embodiment of environmental circumstances. Finally, we discuss about some key methodological issues that should be considered in paradigms addressing environmental adversities and open questions for future investigations.