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.

Extreme deviations from the normative model reveal cortical heterogeneity and associations with negative symptom severity in first-episode psychosis from the OPTiMiSE and GAP studies.

There is currently no quantifiable method to predict long-term clinical outcomes in patients presenting with a first episode of psychosis. A major barrier to developing useful markers for this is biological heterogeneity, where many different pathological mechanisms may underly the same set of symptoms in different individuals. Normative modelling has been used to quantify this heterogeneity in established psychotic disorders by identifying regions of the cortex which are thinner than expected based on a normative healthy population range. These brain atypicalities are measured at the individual level and therefore potentially useful in a clinical setting. However, it is still unclear whether alterations in individual brain structure can be detected at the time of the first psychotic episode, and whether they are associated with subsequent clinical outcomes. We applied normative modelling of cortical thickness to a sample of first-episode psychosis patients, with the aim of quantifying heterogeneity and to use any pattern of cortical atypicality to predict symptoms and response to antipsychotic medication at timepoints from baseline up to 95 weeks (median follow-ups = 4). T1-weighted brain magnetic resonance images from the GAP and OPTiMiSE samples were processed with Freesurfer V6.0.0 yielding 148 cortical thickness features. An existing normative model of cortical thickness (n = 37,126) was adapted to integrate data from each clinical site and account for effects of gender and site. Our test sample consisted of control participants (n = 149, mean age = 26, SD = 6.7) and patient data (n = 295, mean age = 26, SD = 6.7), this sample was used for estimating deviations from the normative model and subsequent statistical analysis. For each individual, the 148 cortical thickness features were mapped to centiles of the normative distribution and converted to z-scores reflecting the distance from the population mean. Individual cortical thickness metrics of +/- 2.6 standard deviations from the mean were considered extreme deviations from the norm. We found that no more than 6.4% of psychosis patients had extreme deviations in a single brain region (regional overlap) demonstrating a high degree of heterogeneity. Mann-Whitney U tests were run on z-scores for each region and significantly lower z-scores were observed in FEP patients in the frontal, temporal, parietal and occipital lobes. Finally, linear mixed-effects modelling showed that negative deviations in cortical thickness in parietal and temporal regions at baseline are related to more severe negative symptoms over the medium-term. This study shows that even at the early stage of symptom onset normative modelling provides a framework to identify individualised cortical markers which can be used for early personalised intervention and stratification.

Revealing the impact of psychiatric comorbidities on treatment outcome in early psychosis using counterfactual model explanation.

Introduction: Psychiatric comorbidities have a significant impact on the course of illness in patients with schizophrenia spectrum disorders. To accurately predict outcomes for individual patients using computerized prognostic models, it is essential to consider these comorbidities and their influence. Methods: In our study, we utilized a multi-modal deep learning architecture to forecast symptomatic remission, focusing on a multicenter sample of patients with first-episode psychosis from the OPTiMiSE study. Additionally, we introduced a counterfactual model explanation technique to examine how scores on the Mini International Neuropsychiatric Interview (MINI) affected the likelihood of remission, both at the group level and for individual patients. Results: Our findings at the group level revealed that most comorbidities had a negative association with remission. Among them, current and recurrent depressive disorders consistently exerted the greatest negative impact on the probability of remission across patients. However, we made an interesting observation: current suicidality within the past month and substance abuse within the past 12 months were associated with an increased chance of remission in patients. We found a high degree of variability among patients at the individual level. Through hierarchical clustering analysis, we identified two subgroups: one in which comorbidities had a relatively limited effect on remission (approximately 45% of patients), and another in which comorbidities more strongly influenced remission. By incorporating comorbidities into individualized prognostic prediction models, we determined which specific comorbidities had the greatest impact on remission at both the group level and for individual patients. Discussion: These results highlight the importance of identifying and including relevant comorbidities in prediction models, providing valuable insights for improving the treatment and prognosis of patients with psychotic disorders. Furthermore, they open avenues for further research into the efficacy of treating these comorbidities to enhance overall patient outcomes.

Predictive Clinical Neuroscience Portal (PCNportal): instant online access to research-grade normative models for clinical neuroscientists.

Background: The neurobiology of mental disorders remains poorly understood despite substantial scientific efforts, due to large clinical heterogeneity and to a lack of tools suitable to map individual variability. Normative modeling is one recently successful framework that can address these problems by comparing individuals to a reference population. The methodological underpinnings of normative modelling are, however, relatively complex and computationally expensive. Our research group has developed the python-based normative modelling package Predictive Clinical Neuroscience toolkit (PCNtoolkit) which provides access to many validated algorithms for normative modelling. PCNtoolkit has since proven to be a strong foundation for large scale normative modelling, but still requires significant computation power, time and technical expertise to develop. Methods: To address these problems, we introduce PCNportal. PCNportal is an online platform integrated with PCNtoolkit that offers access to pre-trained research-grade normative models estimated on tens of thousands of participants, without the need for computation power or programming abilities. PCNportal is an easy-to-use web interface that is highly scalable to large user bases as necessary. Finally, we demonstrate how the resulting normalized deviation scores can be used in a clinical application through a schizophrenia classification task applied to cortical thickness and volumetric data from the longitudinal Northwestern University Schizophrenia Data and Software Tool (NUSDAST) dataset. Results: At each longitudinal timepoint, the transferred normative models achieved a mean[std. dev.] explained variance of 9.4[8.8]%, 9.2[9.2]%, 5.6[7.4]% respectively in the control group and 4.7[5.5]%, 6.0[6.2]%, 4.2[6.9]% in the schizophrenia group. Diagnostic classifiers achieved AUC of 0.78, 0.76 and 0.71 respectively. Conclusions: This replicates the utility of normative models for diagnostic classification of schizophrenia and showcases the use of PCNportal for clinical neuroimaging. By facilitating and speeding up research with high-quality normative models, this work contributes to research in inter-individual variability, clinical heterogeneity and precision medicine.

A stable and replicable neural signature of lifespan adversity in the adult brain.

Environmental adversities constitute potent risk factors for psychiatric disorders. Evidence suggests the brain adapts to adversity, possibly in an adversity-type and region-specific manner. However, the long-term effects of adversity on brain structure and the association of individual neurobiological heterogeneity with behavior have yet to be elucidated. Here we estimated normative models of structural brain development based on a lifespan adversity profile in a longitudinal at-risk cohort aged 25 years (n = 169). This revealed widespread morphometric changes in the brain, with partially adversity-specific features. This pattern was replicated at the age of 33 years (n = 114) and in an independent sample at 22 years (n = 115). At the individual level, greater volume contractions relative to the model were predictive of future anxiety. We show a stable neurobiological signature of adversity that persists into adulthood and emphasize the importance of considering individual-level rather than group-level predictions to explain emerging psychopathology.

Regional, circuit and network heterogeneity of brain abnormalities in psychiatric disorders.

The substantial individual heterogeneity that characterizes people with mental illness is often ignored by classical case-control research, which relies on group mean comparisons. Here we present a comprehensive, multiscale characterization of the heterogeneity of gray matter volume (GMV) differences in 1,294 cases diagnosed with one of six conditions (attention-deficit/hyperactivity disorder, autism spectrum disorder, bipolar disorder, depression, obsessive-compulsive disorder and schizophrenia) and 1,465 matched controls. Normative models indicated that person-specific deviations from population expectations for regional GMV were highly heterogeneous, affecting the same area in <7% of people with the same diagnosis. However, these deviations were embedded within common functional circuits and networks in up to 56% of cases. The salience-ventral attention system was implicated transdiagnostically, with other systems selectively involved in depression, bipolar disorder, schizophrenia and attention-deficit/hyperactivity disorder. Phenotypic differences between cases assigned the same diagnosis may thus arise from the heterogeneous localization of specific regional deviations, whereas phenotypic similarities may be attributable to the dysfunction of common functional circuits and networks.

Revealing Individual Neuroanatomical Heterogeneity in Alzheimer Disease Using Neuroanatomical Normative Modeling.

BACKGROUND AND OBJECTIVES: Alzheimer disease (AD) is highly heterogeneous, with marked individual differences in clinical presentation and neurobiology. To explore this, we used neuroanatomical normative modeling to index regional patterns of variability in cortical thickness. We aimed to characterize individual differences and outliers in cortical thickness in patients with AD, people with mild cognitive impairment (MCI), and controls. Furthermore, we assessed the relationships between cortical thickness heterogeneity and cognitive function, ß-amyloid, phosphorylated-tau, and ApoE genotype. Finally, we examined whether cortical thickness heterogeneity was predictive of conversion from MCI to AD. METHODS: Cortical thickness measurements across 148 brain regions were obtained from T1-weighted MRI scans from 62 sites of the Alzheimer's Disease Neuroimaging Initiative. AD was determined by clinical and neuropsychological examination with no comorbidities present. Participants with MCI had reported memory complaints, and controls were cognitively normal. A neuroanatomical normative model indexed cortical thickness distributions using a separate healthy reference data set (n = 33,072), which used hierarchical Bayesian regression to predict cortical thickness per region using age and sex, while adjusting for site noise. Z-scores per region were calculated, resulting in a Z-score brain map per participant. Regions with Z-scores <-1.96 were classified as outliers. RESULTS: Patients with AD (n = 206) had a median of 12 outlier regions (out of a possible 148), with the highest proportion of outliers (47%) in the parahippocampal gyrus. For 62 regions, over 90% of these patients had cortical thicknesses within the normal range. Patients with AD had more outlier regions than people with MCI (n = 662) or controls (n = 159) (F(2, 1,022) = 95.39, p = 2.0 × 10-16). They were also more dissimilar to each other than people with MCI or controls (F(2, 1,024) = 209.42, p = 2.2 × 10-16). A greater number of outlier regions were associated with worse cognitive function, CSF protein concentrations, and an increased risk of converting from MCI to AD within 3 years (hazard ratio 1.028, 95% CI 1.016-1.039, p = 1.8 × 10-16). DISCUSSION: Individualized normative maps of cortical thickness highlight the heterogeneous effect of AD on the brain. Regional outlier estimates have the potential to be a marker of disease and could be used to track an individual's disease progression or treatment response in clinical trials.

Age-related brain deviations and aggression.

BACKGROUND: Disruptive behavior disorders (DBD) are heterogeneous at the clinical and the biological level. Therefore, the aims were to dissect the heterogeneous neurodevelopmental deviations of the affective brain circuitry and provide an integration of these differences across modalities. METHODS: We combined two novel approaches. First, normative modeling to map deviations from the typical age-related pattern at the level of the individual of (i) activity during emotion matching and (ii) of anatomical images derived from DBD cases (n = 77) and controls (n = 52) aged 8-18 years from the EU-funded Aggressotype and MATRICS consortia. Second, linked independent component analysis to integrate subject-specific deviations from both modalities. RESULTS: While cases exhibited on average a higher activity than would be expected for their age during face processing in regions such as the amygdala when compared to controls these positive deviations were widespread at the individual level. A multimodal integration of all functional and anatomical deviations explained 23% of the variance in the clinical DBD phenotype. Most notably, the top marker, encompassing the default mode network (DMN) and subcortical regions such as the amygdala and the striatum, was related to aggression across the whole sample. CONCLUSIONS: Overall increased age-related deviations in the amygdala in DBD suggest a maturational delay, which has to be further validated in future studies. Further, the integration of individual deviation patterns from multiple imaging modalities allowed to dissect some of the heterogeneity of DBD and identified the DMN, the striatum and the amygdala as neural signatures that were associated with aggression.

Closing the life-cycle of normative modeling using federated hierarchical Bayesian regression.

Clinical neuroimaging data availability has grown substantially in the last decade, providing the potential for studying heterogeneity in clinical cohorts on a previously unprecedented scale. Normative modeling is an emerging statistical tool for dissecting heterogeneity in complex brain disorders. However, its application remains technically challenging due to medical data privacy issues and difficulties in dealing with nuisance variation, such as the variability in the image acquisition process. Here, we approach the problem of estimating a reference normative model across a massive population using a massive multi-center neuroimaging dataset. To this end, we introduce a federated probabilistic framework using hierarchical Bayesian regression (HBR) to complete the life-cycle of normative modeling. The proposed model provides the possibilities to learn, update, and adapt the model parameters on decentralized neuroimaging data. Our experimental results confirm the superiority of HBR in deriving more accurate normative ranges on large multi-site neuroimaging datasets compared to the current standard methods. In addition, our approach provides the possibility to recalibrate and reuse the learned model on local datasets and even on datasets with very small sample sizes. The proposed method will facilitate applications of normative modeling as a medical tool for screening the biological deviations in individuals affected by complex illnesses such as mental disorders.

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.

The normative modeling framework for computational psychiatry.

Normative modeling is an emerging and innovative framework for mapping individual differences at the level of a single subject or observation in relation to a reference model. It involves charting centiles of variation across a population in terms of mappings between biology and behavior, which can then be used to make statistical inferences at the level of the individual. The fields of computational psychiatry and clinical neuroscience have been slow to transition away from patient versus 'healthy' control analytic approaches, probably owing to a lack of tools designed to properly model biological heterogeneity of mental disorders. Normative modeling provides a solution to address this issue and moves analysis away from case-control comparisons that rely on potentially noisy clinical labels. Here we define a standardized protocol to guide users through, from start to finish, normative modeling analysis using the Predictive Clinical Neuroscience toolkit (PCNtoolkit). We describe the input data selection process, provide intuition behind the various modeling choices and conclude by demonstrating several examples of downstream analyses that the normative model may facilitate, such as stratification of high-risk individuals, subtyping and behavioral predictive modeling. The protocol takes ~1-3 h to complete.

Charting brain growth and aging at high spatial precision.

Defining reference models for population variation, and the ability to study individual deviations is essential for understanding inter-individual variability and its relation to the onset and progression of medical conditions. In this work, we assembled a reference cohort of neuroimaging data from 82 sites (N=58,836; ages 2-100) and used normative modeling to characterize lifespan trajectories of cortical thickness and subcortical volume. Models are validated against a manually quality checked subset (N=24,354) and we provide an interface for transferring to new data sources. We showcase the clinical value by applying the models to a transdiagnostic psychiatric sample (N=1985), showing they can be used to quantify variability underlying multiple disorders whilst also refining case-control inferences. These models will be augmented with additional samples and imaging modalities as they become available. This provides a common reference platform to bind results from different studies and ultimately paves the way for personalized clinical decision-making.

Individualized prediction of three- and six-year outcomes of psychosis in a longitudinal multicenter study: a machine learning approach.

Schizophrenia and related disorders have heterogeneous outcomes. Individualized prediction of long-term outcomes may be helpful in improving treatment decisions. Utilizing extensive baseline data of 523 patients with a psychotic disorder and variable illness duration, we predicted symptomatic and global outcomes at 3-year and 6-year follow-ups. We classified outcomes as (1) symptomatic: in remission or not in remission, and (2) global outcome, using the Global Assessment of Functioning (GAF) scale, divided into good (GAF ≥ 65) and poor (GAF < 65). Aiming for a robust and interpretable prediction model, we employed a linear support vector machine and recursive feature elimination within a nested cross-validation design to obtain a lean set of predictors. Generalization to out-of-study samples was estimated using leave-one-site-out cross-validation. Prediction accuracies were above chance and ranged from 62.2% to 64.7% (symptomatic outcome), and 63.5-67.6% (global outcome). Leave-one-site-out cross-validation demonstrated the robustness of our models, with a minor drop in predictive accuracies of 2.3% on average. Important predictors included GAF scores, psychotic symptoms, quality of life, antipsychotics use, psychosocial needs, and depressive symptoms. These robust, albeit modestly accurate, long-term prognostic predictions based on lean predictor sets indicate the potential of machine learning models complementing clinical judgment and decision-making. Future model development may benefit from studies scoping patient's and clinicians' needs in prognostication.

Replicating extensive brain structural heterogeneity in individuals with schizophrenia and bipolar disorder.

Identifying brain processes involved in the risk and development of mental disorders is a major aim. We recently reported substantial interindividual heterogeneity in brain structural aberrations among patients with schizophrenia and bipolar disorder. Estimating the normative range of voxel-based morphometry (VBM) data among healthy individuals using a Gaussian process regression (GPR) enables us to map individual deviations from the healthy range in unseen datasets. Here, we aim to replicate our previous results in two independent samples of patients with schizophrenia (n1 = 94; n2 = 105), bipolar disorder (n1 = 116; n2 = 61), and healthy individuals (n1 = 400; n2 = 312). In line with previous findings with exception of the cerebellum our results revealed robust group level differences between patients and healthy individuals, yet only a small proportion of patients with schizophrenia or bipolar disorder exhibited extreme negative deviations from normality in the same brain regions. These direct replications support that group level-differences in brain structure disguise considerable individual differences in brain aberrations, with important implications for the interpretation and generalization of group-level brain imaging findings to the individual with a mental disorder.

Fractionating autism based on neuroanatomical normative modeling.

Autism is a complex neurodevelopmental condition with substantial phenotypic, biological, and etiologic heterogeneity. It remains a challenge to identify biomarkers to stratify autism into replicable cognitive or biological subtypes. Here, we aim to introduce a novel methodological framework for parsing neuroanatomical subtypes within a large cohort of individuals with autism. We used cortical thickness (CT) in a large and well-characterized sample of 316 participants with autism (88 female, age mean: 17.2 ± 5.7) and 206 with neurotypical development (79 female, age mean: 17.5 ± 6.1) aged 6-31 years across six sites from the EU-AIMS multi-center Longitudinal European Autism Project. Five biologically based putative subtypes were derived using normative modeling of CT and spectral clustering. Three of these clusters showed relatively widespread decreased CT and two showed relatively increased CT. These subtypes showed morphometric differences from one another, providing a potential explanation for inconsistent case-control findings in autism, and loaded differentially and more strongly onto symptoms and polygenic risk, indicating a dilution of clinical effects across heterogeneous cohorts. Our results provide an important step towards parsing the heterogeneous neurobiology of autism.

From pattern classification to stratification: towards conceptualizing the heterogeneity of Autism Spectrum Disorder.

Pattern classification and stratification approaches have increasingly been used in research on Autism Spectrum Disorder (ASD) over the last ten years with the goal of translation towards clinical applicability. Here, we present an extensive scoping literature review on those two approaches. We screened a total of 635 studies, of which 57 pattern classification and 19 stratification studies were included. We observed large variance across pattern classification studies in terms of predictive performance from about 60% to 98% accuracy, which is among other factors likely linked to sampling bias, different validation procedures across studies, the heterogeneity of ASD and differences in data quality. Stratification studies were less prevalent with only two studies reporting replications and just a few showing external validation. While some identified strata based on cognition and intelligence reappear across studies, biology as a stratification marker is clearly underexplored. In summary, mapping biological differences at the level of the individual with ASD is a major challenge for the field now. Conceptualizing those mappings and individual trajectories that lead to the diagnosis of ASD, will become a major challenge in the near future.

Correction: Conceptualizing mental disorders as deviations from normative functioning.

A correction to this paper has been published and can be accessed via a link at the top of the paper.

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.

Group-level spatio-temporal pattern recovery in MEG decoding using multi-task joint feature learning.

BACKGROUND: The use of machine learning models to discriminate between patterns of neural activity has become in recent years a standard analysis approach in neuroimaging studies. Whenever these models are linear, the estimated parameters can be visualized in the form of brain maps which can aid in understanding how brain activity in space and time underlies a cognitive function. However, the recovered brain maps often suffer from lack of interpretability, especially in group analysis of multi-subject data. NEW METHOD: To facilitate the application of brain decoding in group-level analysis, we present an application of multi-task joint feature learning for group-level multivariate pattern recovery in single-trial magnetoencephalography (MEG) decoding. The proposed method allows for recovering sparse yet consistent patterns across different subjects, and therefore enhances the interpretability of the decoding model. RESULTS: Our experimental results demonstrate that the mutli-task joint feature learning framework is capable of recovering more meaningful patterns of varying spatio-temporally distributed brain activity across individuals while still maintaining excellent generalization performance. COMPARISON WITH EXISTING METHODS: We compare the performance of the multi-task joint feature learning in terms of generalization, reproducibility, and quality of pattern recovery against traditional single-subject and pooling approaches on both simulated and real MEG datasets. CONCLUSIONS: These results can facilitate the usage of brain decoding for the characterization of fine-level distinctive patterns in group-level inference. Considering the importance of group-level analysis, the proposed approach can provide a methodological shift towards more interpretable brain decoding models.

Interpretability of Multivariate Brain Maps in Linear Brain Decoding: Definition, and Heuristic Quantification in Multivariate Analysis of MEG Time-Locked Effects.

Brain decoding is a popular multivariate approach for hypothesis testing in neuroimaging. Linear classifiers are widely employed in the brain decoding paradigm to discriminate among experimental conditions. Then, the derived linear weights are visualized in the form of multivariate brain maps to further study spatio-temporal patterns of underlying neural activities. It is well known that the brain maps derived from weights of linear classifiers are hard to interpret because of high correlations between predictors, low signal to noise ratios, and the high dimensionality of neuroimaging data. Therefore, improving the interpretability of brain decoding approaches is of primary interest in many neuroimaging studies. Despite extensive studies of this type, at present, there is no formal definition for interpretability of multivariate brain maps. As a consequence, there is no quantitative measure for evaluating the interpretability of different brain decoding methods. In this paper, first, we present a theoretical definition of interpretability in brain decoding; we show that the interpretability of multivariate brain maps can be decomposed into their reproducibility and representativeness. Second, as an application of the proposed definition, we exemplify a heuristic for approximating the interpretability in multivariate analysis of evoked magnetoencephalography (MEG) responses. Third, we propose to combine the approximated interpretability and the generalization performance of the brain decoding into a new multi-objective criterion for model selection. Our results, for the simulated and real MEG data, show that optimizing the hyper-parameters of the regularized linear classifier based on the proposed criterion results in more informative multivariate brain maps. More importantly, the presented definition provides the theoretical background for quantitative evaluation of interpretability, and hence, facilitates the development of more effective brain decoding algorithms in the future.