Application of non-negative matrix factorization to multispectral FLIM data analysis

Existing methods of interpreting fluorescence lifetime imaging microscopy (FLIM) images are based on comparing the intensity and lifetime values at each pixel with those of known fluorophores. This method becomes unwieldy and subjective in many practical applications where there are several fluorescing species contributing to the bulk fluorescence signal, and even more so in the case of multispectral FLIM. Non-negative matrix factorization (NMF) is a multivariate data analysis technique aimed at extracting non-negative signatures of pure components and their non-negative abundances from an additive mixture of those components. In this paper, we present the application of NMF to multispectral time-domain FLIM data to obtain a new set of FLIM features (relative abundance of constituent fluorophores). These features are more intuitive and easier to interpret than the standard fluorescence intensity and lifetime values. The proposed approach, unlike several FLIM data analysis methods, is not limited by the number of constituent fluorescing species or their possibly complex decay dynamics. Moreover, the new set of FLIM features can be obtained by processing raw multispectral FLIM intensity data, thereby rendering time deconvolution unnecessary and resulting in lesser computational time and relaxed SNR requirements. The performance of the NMF method was validated on simulated and experimental multispectral time-domain FLIM data. The NMF features were also compared against the standard intensity and lifetime features, in terms of their ability to discriminate between different types of atherosclerotic plaques.OCIS codes: (170.1580) Chemometrics, (170.1610) Clinical applications, (300.2530) Fluorescence, laser-induced, (070.5010) Pattern recognition, (170.6920) Time-resolved imaging, (170.6935) Tissue characterization     

Enhanced neuroimaging genetics using multi-view non-negative matrix factorization with sparsity and prior knowledge

Neuroimaging genetics is a powerful approach to jointly explore genetic features with rich brain imaging phenotypes for neurodegenerative diseases. Conventional imaging genetics approaches based on canonical correlation analysis cannot accommodate multimodal inputs effectively and have limited interpretability. We propose a novel imaging genetics approach based on non-negative matrix factorization (NMF). By leveraging the parsimonious property known as topic modeling in multi-view NMF, we add sparsity constraints and prior information to identify a sparse set of biologically related features across modalities. Thus, our approach incorporates prior knowledge and improves multimodal integration capabilities and interpretability. We applied our algorithm to simulated and real imaging genetics datasets of Parkinson's disease (PD) for performance evaluation. Our algorithm could identify important associated features mapped to interpretable distinct topics more robustly than other methods. It revealed promising features of single-nucleotide polymorphisms and brain regions related to a subset of PD-related clinical scores in a few topics using a real imaging genetic dataset. The proposed imaging genetics approach can reveal novel associations between genetic and neuroimaging features to improve understanding of various neurodegenerative diseases.     

Adaptive analysis of fMRI data

This article introduces novel and fundamental improvements of fMRI data analysis. Central is a technique termed constrained canonical correlation analysis, which can be viewed as a natural extension and generalization of the popular general linear model method. The concept of spatial basis filters is presented and shown to be a very successful way of adaptively filtering the fMRI data. A general method for designing suitable hemodynamic response models is also proposed and incorporated into the constrained canonical correlation approach. Results that demonstrate how each of these parts significantly improves the detection of brain activity, with a computation time well within limits for practical use, are provided.     

A deep joint sparse non-negative matrix factorization framework for identifying the common and subject-specific functional units of tongue motion during speech

Intelligible speech is produced by creating varying internal local muscle groupings—i.e., functional units—that are generated in a systematic and coordinated manner. There are two major challenges in characterizing and analyzing functional units. First, due to the complex and convoluted nature of tongue structure and function, it is of great importance to develop a method that can accurately decode complex muscle coordination patterns during speech. Second, it is challenging to keep identified functional units across subjects comparable due to their substantial variability. In this work, to address these challenges, we develop a new deep learning framework to identify common and subject-specific functional units of tongue motion during speech. Our framework hinges on joint deep graph-regularized sparse non-negative matrix factorization (NMF) using motion quantities derived from displacements by tagged Magnetic Resonance Imaging. More specifically, we transform NMF with sparse and graph regularizations into modular architectures akin to deep neural networks by means of unfolding the Iterative Shrinkage-Thresholding Algorithm to learn interpretable building blocks and associated weighting map. We then apply spectral clustering to common and subject-specific weighting maps from which we jointly determine the common and subject-specific functional units. Experiments carried out with simulated datasets show that the proposed method achieved on par or better clustering performance over the comparison methods.Experiments carried out with in vivo tongue motion data show that the proposed method can determine the common and subject-specific functional units with increased interpretability and decreased size variability.     

A general statistical analysis for fMRI data.

We propose a method for the statistical analysis of fMRI data that seeks a compromise between efficiency, generality, validity, simplicity, and execution speed. The main differences between this analysis and previous ones are: a simple bias reduction and regularization for voxel-wise autoregressive model parameters; the combination of effects and their estimated standard deviations across different runs/sessions/subjects via a hierarchical random effects analysis using the EM algorithm; overcoming the problem of a small number of runs/session/subjects using a regularized variance ratio to increase the degrees of freedom.     

Nonadditive two-way ANOVA for event-related fMRI data analysis

A significant recent development in functional magnetic resonance imaging (fMRI) is the introduction of event-related fMRI, also known as time-resolved fMRI. Because the exact shape of the MR response in an event-related fMRI experiment is often not known, traditional methods developed for block design experiments, such as t test and correlation analysis, are not well-suited for extracting activated pixels from the event-related data. In this work, a statistical technique based on nonadditive two-way analysis of variance is developed for use in event-related studies. Theoretical and experimental work were carried out for establishing a statistical threshold to determine pixel activation. Experimental studies were performed to demonstrate the utility of this approach.     

Structure-seeking multilinear methods for the analysis of fMRI data

In comprehensive fMRI studies of brain function, the data structures often contain higher-order ways such as trial, task condition, subject, and group in addition to the intrinsic dimensions of time and space. While multivariate bilinear methods such as principal component analysis (PCA) have been used successfully for extracting information about spatial and temporal features in data from a single fMRI run, the need to unfold higher-order data sets into bilinear arrays has led to decompositions that are nonunique and to the loss of multiway linkages and interactions present in the data. These additional dimensions or ways can be retained in multilinear models to produce structures that are unique and which admit interpretations that are neurophysiologically meaningful. Multiway analysis of fMRI data from multiple runs of a bilateral finger-tapping paradigm was performed using the parallel factor (PARAFAC) model. A trilinear model was fitted to a data cube of dimensions voxels by time by run. Similarly, a quadrilinear model was fitted to a higher-way structure of dimensions voxels by time by trial by run. The spatial and temporal response components were extracted and validated by comparison to results from traditional SVD/PCA analyses based on scenarios of unfolding into lower-order bilinear structures.     

Using nonlinear models in fMRI data analysis: model selection and activation detection

There is an increasing interest in using physiologically plausible models in fMRI analysis. These models do raise new mathematical problems in terms of parameter estimation and interpretation of the measured data. In this paper, we show how to use physiological models to map and analyze brain activity from fMRI data. We describe a maximum likelihood parameter estimation algorithm and a statistical test that allow the following two actions: selecting the most statistically significant hemodynamic model for the measured data and deriving activation maps based on such model. Furthermore, as parameter estimation may leave much incertitude on the exact values of parameters, model identifiability characterization is a particular focus of our work. We applied these methods to different variations of the Balloon Model (Buxton, R.B., Wang, E.C., and Frank, L.R. 1998. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39: 855-864; Buxton, R.B., Uluda?, K., Dubowitz, D.J., and Liu, T.T. 2004. Modelling the hemodynamic response to brain activation. NeuroImage 23: 220-233; Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. 2000. Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12: 466-477) in a visual perception checkerboard experiment. Our model selection proved that hemodynamic models better explain the BOLD response than linear convolution, in particular because they are able to capture some features like poststimulus undershoot or nonlinear effects. On the other hand, nonlinear and linear models are comparable when signals get noisier, which explains that activation maps obtained in both frameworks are comparable. The tools we have developed prove that statistical inference methods used in the framework of the General Linear Model might be generalized to nonlinear models.     

Gender differences in brain activity evoked by muscle and cutaneous pain: a retrospective study of single-trial fMRI data

Gender greatly influences pain processing. Not only do females display greater pain sensitivity, many chronic pain conditions affect females more than males. Although gender-based differences in pain sensitivity may be related to cultural and social factors, animal studies also reveal gender differences in pain sensitivity, suggesting that physiological factors may contribute to differences in the processing of pain in males and females. It has been recently reported that noxious cutaneous heat stimuli evoke gender-based differences in activity in some brain regions. Given that most chronic pain conditions, including those with gender bias are of "deep" origin (e.g. arising in muscle, joints or viscera), we investigated whether gender differences also exist in the central processing of muscle pain. In 24 healthy adults we used functional magnetic resonance imaging (fMRI) to measure signal intensity changes during muscle and cutaneous pain induced by intramuscular and subcutaneous injections of hypertonic saline, respectively. In addition to activating the "pain neuromatrix", i.e. cingulate, insular, somatosensory and cerebellar cortices, both muscle pain and cutaneous pain evoked gender-based differences in the mid-cingulate cortex, dorsolateral prefrontal cortex, hippocampus and cerebellar cortex. These differences may reflect differences in emotional processing of noxious information in men and women and may underlie the gender bias that exists in many chronic pain conditions.     

Identifying group discriminative and age regressive sub-networks from DTI-based connectivity via a unified framework of non-negative matrix factorization and graph embedding

Diffusion tensor imaging (DTI) offers rich insights into the physical characteristics of white matter (WM) fiber tracts and their development in the brain, facilitating a network representation of brain’s traffic pathways. Such a network representation of brain connectivity has provided a novel means of investigating brain changes arising from pathology, development or aging. The high dimensionality of these connectivity networks necessitates the development of methods that identify the connectivity building blocks or sub-network components that characterize the underlying variation in the population. In addition, the projection of the subject networks into the basis set provides a low dimensional representation of it, that teases apart different sources of variation in the sample, facilitating variation-specific statistical analysis. We propose a unified framework of non-negative matrix factorization and graph embedding for learning sub-network patterns of connectivity by their projective non-negative decomposition into a reconstructive basis set, as well as, additional basis sets representing variational sources in the population like age and pathology. The proposed framework is applied to a study of diffusion-based connectivity in subjects with autism that shows localized sparse sub-networks which mostly capture the changes related to pathology and developmental variations.     

Real-time fMRI of temporolimbic regions detects amygdala activation during single-trial self-induced sadness

Temporolimbic circuits play a crucial role in the regulation of human emotion. A highly sensitive single-shot multiecho functional magnetic resonance imaging (fMRI) technique with gradient compensation of local magnetic field inhomogeneities and real-time data analysis were used to measure increases in amygdala activation during single 60-s trials of self-induced sadness. Six healthy male and female subjects performed a validated mood induction paradigm with randomized presentation of sad or neutral faces in 10 trials per scan. Subjects reported the intensity of experienced sadness after each trial. Immediate feedback of amygdala activation was given to the subjects during the ongoing scan to reinforce mood induction. Correspondence between increased intensity of predominantly left sided amygdala activation and self-rating of sadness was found in 78% of 120 sad trials, in contrast to only 14% of neutral trials. Amygdala activation was reproducible during repeated scanning sessions and displayed the strongest correlation with self-rating among all regions. These results suggest that amygdala activation may be closely associated with self-induced sadness. This novel real-time fMRI technology is applicable to a wide range of neuroscience studies, particularly those of the limbic system, and to neuropsychiatric conditions, such as depression, in which pathology of the amygdala has been implicated.     

Regional homogeneity approach to fMRI data analysis

Kendall's coefficient concordance (KCC) can measure the similarity of a number of time series. It has been used for purifying a given cluster in functional MRI (fMRI). In the present study, a new method was developed based on the regional homogeneity (ReHo), in which KCC was used to measure the similarity of the time series of a given voxel to those of its nearest neighbors in a voxel-wise way. Six healthy subjects performed left and right finger movement tasks in event-related design; five of them were additionally scanned in a rest condition. KCC was compared among the three conditions (left finger movement, right finger movement, and the rest). Results show that bilateral primary motor cortex (M1) had higher KCC in either left or right finger movement condition than in rest condition. Contrary to prediction and to activation pattern, KCC of ipsilateral M1 is significantly higher than contralateral M1 in unilateral finger movement conditions. These results support the previous electrophysiologic findings of increasing ipsilateral M1 excitation during unilateral movement. ReHo can consider as a complementary method to model-driven method, and it could help reveal the complexity of the human brain function. More work is needed to understand the neural mechanism underlying ReHo.     

Detection and detrending in fMRI data analysis

This article addresses the impact that colored noise, temporal filtering, and temporal detrending have on the fMRI analysis situation. Specifically, it is shown why the detection of event-related designs benefit more from pre-whitening than blocked designs in a colored noise structure. Both theoretical and empirical results are provided. Furthermore, a novel exploratory method for producing drift models that efficiently capture trends and drifts in the fMRI data is introduced. A comparison to currently employed detrending approaches is presented. It is shown that the novel exploratory model is able to remove a major part of the slowly varying drifts that are abundant in fMRI data. The value of such a model lies in its ability to remove drift components that otherwise would have contributed to a colored noise structure in the voxel time series.     

Identifying group discriminative and age regressive sub-networks from DTI-based connectivity via a unified framework of non-negative matrix factorization and graph embedding

Diffusion tensor imaging (DTI) offers rich insights into the physical characteristics of white matter (WM) fiber tracts and their development in the brain, facilitating a network representation of brain’s traffic pathways. Such a network representation of brain connectivity has provided a novel means of investigating brain changes arising from pathology, development or aging. The high dimensionality of these connectivity networks necessitates the development of methods that identify the connectivity building blocks or sub-network components that characterize the underlying variation in the population. In addition, the projection of the subject networks into the basis set provides a low dimensional representation of it, that teases apart different sources of variation in the sample, facilitating variation-specific statistical analysis. We propose a unified framework of non-negative matrix factorization and graph embedding for learning sub-network patterns of connectivity by their projective non-negative decomposition into a reconstructive basis set, as well as, additional basis sets representing variational sources in the population like age and pathology. The proposed framework is applied to a study of diffusion-based connectivity in subjects with autism that shows localized sparse sub-networks which mostly capture the changes related to pathology and developmental variations.     

Detection of buried objects in ground penetrating radar data using incremental nonnegative matrix factorization

Ground penetrating radar (GPR) is a popular tool for subsurface sensing and it is widely used for buried object detection. In this study, a new buried object detection method based on the modelling of A-scans by incremental nonnegative matrix factorization (INMF) is presented. The existing clutter in the GPR image is learned via nonnegative matrix factorization (NMF) and the resulting basis and encoding matrices are used in the initialization of the INMF method. Since clutter is learned by NMF in the initialization, the target is considered as an anomaly and a new A-scan containing target signal results in an increase in the error signal level permitting the detection of the target at this antenna location. The proposed method is applied to an original and noisy simulated dataset constructed by the electromagnetic simulation software gprMax as well as to a real dataset. The quantitative results based on receiver operating characteristic (ROC) curves and area under curves (AUC) obtained for the simulated dataset with different SNR levels show that there is an improvement around 5–7% in the detection rate.     

A unified framework for group independent component analysis for multi-subject fMRI data

Independent component analysis (ICA) is becoming increasingly popular for analyzing functional magnetic resonance imaging (fMRI) data. While ICA has been successfully applied to single-subject analysis, the extension of ICA to group inferences is not straightforward and remains an active topic of research. Current group ICA models, such as the GIFT [Calhoun, V.D., Adali, T., Pearlson, G.D., Pekar, J.J., 2001. A method for making group inferences from functional MRI data using independent component analysis. Hum. Brain Mapp. 14, 140–151.] and tensor PICA [Beckmann, C.F., Smith, S.M., 2005. Tensorial extensions of independent component analysis for multisubject FMRI analysis. Neuroimage 25, 294–311.], make different assumptions about the underlying structure of the group spatio-temporal processes and are thus estimated using algorithms tailored for the assumed structure, potentially leading to diverging results. To our knowledge, there are currently no methods for assessing the validity of different model structures in real fMRI data and selecting the most appropriate one among various choices. In this paper, we propose a unified framework for estimating and comparing group ICA models with varying spatio-temporal structures. We consider a class of group ICA models that can accommodate different group structures and include existing models, such as the GIFT and tensor PICA, as special cases. We propose a maximum likelihood (ML) approach with a modified Expectation–Maximization (EM) algorithm for the estimation of the proposed class of models. Likelihood ratio tests (LRT) are presented to compare between different group ICA models. The LRT can be used to perform model comparison and selection, to assess the goodness-of-fit of a model in a particular data set, and to test group differences in the fMRI signal time courses between subject subgroups. Simulation studies are conducted to evaluate the performance of the proposed method under varying structures of group spatio-temporal processes. We illustrate our group ICA method using data from an fMRI study that investigates changes in neural processing associated with the regular practice of Zen meditation.     

Correlator beware: correlation has limited selectivity for fMRI data analysis

Groups of time-courses created from fMRI data by the frequently used correlation analysis are often highly heterogeneous. This heterogeneity is due to the limited selectivity of correlation when trying to match brain time-courses to an externally imposed activation paradigm. Thus, this process unnecessarily generates many type I errors (false positives). Furthermore, as a consequence of the heterogeneity, time-courses identified and grouped by correlation may in fact describe different activations. After demonstrating this inadequacy, we give one particular approach to partition such a heterogeneous group into internally more homogeneous subgroups, using Kendall's coefficient of concordance W, and show its applicability and application to both simulated and in vivo data. Such group partition and "purification" will help subsequent inferential methods to deal more efficiently with false positives.     

Support vector machine learning-based fMRI data group analysis

To explore the multivariate nature of fMRI data and to consider the inter-subject brain response discrepancies, a multivariate and brain response model-free method is fundamentally required. Two such methods are presented in this paper by integrating a machine learning algorithm, the support vector machine (SVM), and the random effect model. Without any brain response modeling, SVM was used to extract a whole brain spatial discriminance map (SDM), representing the brain response difference between the contrasted experimental conditions. Population inference was then obtained through the random effect analysis (RFX) or permutation testing (PMU) on the individual subjects' SDMs. Applied to arterial spin labeling (ASL) perfusion fMRI data, SDM RFX yielded lower false-positive rates in the null hypothesis test and higher detection sensitivity for synthetic activations with varying cluster size and activation strengths, compared to the univariate general linear model (GLM)-based RFX. For a sensory-motor ASL fMRI study, both SDM RFX and SDM PMU yielded similar activation patterns to GLM RFX and GLM PMU, respectively, but with higher t values and cluster extensions at the same significance level. Capitalizing on the absence of temporal noise correlation in ASL data, this study also incorporated PMU in the individual-level GLM and SVM analyses accompanied by group-level analysis through RFX or group-level PMU. Providing inferences on the probability of being activated or deactivated at each voxel, these individual-level PMU-based group analysis methods can be used to threshold the analysis results of GLM RFX, SDM RFX or SDM PMU.     

A generalized regression model for region of interest analysis of fMRI data

In this study functional Magnetic Resonance Imaging (fMRI) was used to evaluate cortical motor network adaptation after a rehabilitation program for upper extremity motor function in chronic stroke patients. Patients and healthy controls were imaged when they attempted to perform shoulder-elbow and wrist-hand movements in a 1.5 T Siemens scanner. We perform fMRI analysis at both single- and group-subject levels. Activated voxel counts are calculated to quantify brain activation in regions of interest. We discuss several candidate regression models for making inference on the count data, and propose an application of a generalized negative-binomial model (GNBM) with structured dispersion in the study. The effects of inappropriate statistical models that ignore the nature of data are addressed through Monte Carlo simulations. Based on the GNBM, significant activation differences are observed in a number of cortical regions for stroke versus control and as a result of treatment; notably, these differences are not detected when the data are analyzed using a conventional linear regression model. Our findings provide an improved functional neuroimaging data analysis protocol, specifically for pixel/voxel counts.     

Structural analysis of fMRI data: a surface-based framework for multi-subject studies

We present a method for fMRI data group analysis that makes the link between two distinct frameworks: surface-based techniques, which process data in the domain defined by the surface of the cortex, and structural techniques, which use object-based representations of the data as opposed to voxel-based ones. This work is a natural surface-based extension of the volume-based structural approach presented in a previous paper. A multi-scale surface-based representation of individual activation maps is first computed for each subject. Then the inter-subject matching and the activation detection decision are performed jointly by optimization of a Markovian model. Finally, a significance measure is computed in a non-parametric way for the results, in order to assess their relevance and control the risk of type I error. The method is applied on simulated and real data and the results are compared to those produced by standard analyses. The surface-based structural analysis is shown to be particularly robust to inter-subject spatial variability and to produce relevant results with good specificity and sensitivity. We also demonstrate the advantages of the surface-based approach by comparing with the results of a 3D structural analysis.