Dynamic contrast-enhanced ultrasound (DCEUS) is an imaging modality for assessing microvascular perfusion and dispersion kinetics. However, the presence of speckle noise may hamper the quantitative analysis of the contrast kinetics. Common speckle denoising techniques based on low-rank approximations typically model the speckle noise as white Gaussian noise (WGN) after the log transformation and apply matrix-based algorithms. We address the high dimensionality of the 4D DCEUS data and apply low-rank tensor decomposition techniques to denoise speckles. Although there are many tensor decompositions that can describe low rankness, we limit our research to multilinear rank and tubal rank. We introduce a gradient-based extension of the multilinear singular value decomposition to model low multilinear rankness, assuming that the log-transformed speckle noise follows a Fisher-tippet distribution. In addition, we apply an algorithm based on tensor singular value decomposition to model low tubal rankness, assuming that the log-transformed speckle noise is WGN with sparse outliers. The effectiveness of the methods is evaluated through simulations and phantom studies. Additionally, the tensor-based algorithms’ real-world performance is assessed using DCEUS prostate recordings. Comparative analyses with existing DCEUS denoising literature are conducted, and the algorithms’ capabilities are showcased in the context of prostate cancer classification. The addition of Fisher-tippet distribution did not improve the results of tr-MLSVD in the in vivo case. However, most cancer markers are better distinguishable when using a tensor denoising technique than state-of-the-art approaches.

Objective: To investigate whether local lesions created by stereo-electroencephalography (SEEG)–guided radiofrequency thermocoagulation (RFTC) affect distant brain connectivity and excitability in patients with focal, drug-resistant epilepsy (DRE). Methods: Ten patients with focal DRE underwent SEEG implantation and subsequently 1 Hz bipolar repetitive electrical stimulation (RES) for 30 s before and after RFTC. Root mean square (RMS) of cortico-cortical evoked potentials (CCEPs) was calculated for 15 ms to 300 ms post-stimulation with baseline correction. Contact pairs were categorized as both coagulated, hybrid, or both non-coagulated. The data were divided into nine categories based on the stimulating and recording contact pair combinations. RMS of CCEPs was compared before and after (<12 h) RFTC using a two-sample t test (Hochberg corrected, p < 0.05) for each patient. Boost score, indicating power increase during seizures before RFTC relative to baseline, was analyzed in 4 s windows with 1 s overlap during seizure duration. Results: RFTC altered connectivity across all categories. Of interest, decreases and increases in RMS were observed in connections between non-coagulated contacts distant from coagulation site (range: 1.09–85 mm, median = 17.7 mm, interquartile range [IQR] 10.1–32.3). Contact pairs involved in significantly altered non-coagulated connections showed a higher boost score correlation in the theta, beta, and gamma bands, as well as a stronger maximum correlation with coagulated sites in the delta band than contacts for which connectivity did not change after RFTC. Significance: This study highlights how local lesions alter distant brain connectivity, providing insights for future research on epilepsy network changes and seizure outcomes following RFTC.

This paper proposes a scalable method for identifying interactions in higher-order networks from observations of nodal processes. Finding such dependencies is important in many disciplines, including neuroscience, social influence modeling, and beyond. However, current approaches are either limited to extracting pairwise dependencies or struggle with scalability, as estimating higher-order dependencies becomes computationally prohibitive. To overcome these challenges, we introduce a tensorbased graph Volterra model that leverages low-rank decomposition techniques to estimate higher-order interactions efficiently. Our approach not only reduces computational and storage complexity but also acts as an implicit regularizer, improving network estimation in ill-posed settings. We validate our method through simulations and real data experiments, demonstrating competitive performance and enhanced scalability compared to existing techniques.

Objective: Alzheimer's disease (AD) is a slowly progressive neurodegenerative disorder with insidious onset. Accurate prediction of the disease progression has received increasing attention. Cognitive scores that reflect patients' cognitive status have become important criteria for predicting AD. Most existing methods consider the relationship between neuroimages and cognitive scores to improve prediction results. However, the inherent structure information in interrelated cognitive scores is rarely considered. Method: In this article, we propose a relation-aware tensor completion multitask learning method (RATC-MTL), in which the cognitive scores are represented as a third-order tensor to preserve the global structure information in clinical scores. We combine both tensor completion and linear regression into a unified framework, which allows us to capture both inter and intra modes correlations in cognitive tensor with a low-rank constraint, as well as incorporate the relationship between biological features and cognitive status by imposing a regression model on multiple cognitive scores. Result: Compared to the single-task and state-of-the-art multi-task algorithms, our proposed method obtains the best results for predicting cognitive scores in terms of four commonly used metrics. Furthermore, the overall performance of our method in classifying AD progress is also the best. Conclusion: Our results demonstrate the effectiveness of the proposed framework in fully exploring the global structure information in cognitive scores. Significance: This study introduces a novel concept of leveraging tensor completion to assist in disease diagnoses, potentially offering a solution to the issue of data scarcity encountered in prolonged monitoring scenarios.

Analysis of functional neuroimaging data aims to unveil spatial and temporal patterns of interest. Existing analysis methods fall into two categories: fully data-driven approaches and those reliant on prior information, e.g. the stimulus time course. While using the stimulus signal directly can help identify the activated brain areas, it is known that the relationship between stimuli and the brain's response exhibits nonlinear and time-varying characteristics. As such, relying completely on the stimulus signal to describe the brain's temporal response leads to a restricted interpretation of the brain function. In this paper, we present a new technique called Evoked Component Analysis (ECA), which leverages prior information up to a defined extent. This is achieved by including the general linear model (GLM) design matrix as a regulatory term and estimating the factor matrices in both space and time through an alternating minimization approach. We apply ECA to 2D and swept-3D functional ultrasound (fUS) experiments conducted with mice. When decomposing 2D fUS data, we employ GLM regularization at various intensities to emphasize the role of prior information. Furthermore, we show that incorporating multiple hemodynamic response functions within the design matrix can provide valuable insights into region-specific characteristics of evoked activity. Finally, we use ECA to analyze swept-3D fUS data recorded from five mice engaged in two distinct visual tasks. Swept-3D fUS images the 3D brain sequentially using a moving probe, resulting in different slice acquisition time instants. We show that ECA can estimate factor matrices with a fine resolution at each slice acquisition time instant and yield higher t-statistics compared to GLM and correlation analysis for all subjects.

Identifying overlapping communities from data is crucial for grasping the complex structure and dynamics of networks, amongst others in fields such as computational neuroscience. Research using fMRI has demonstrated that brain regions can change their functional network membership over time using temporal independent component analysis (tICA). However, reproducibility of such overlapping communities remains a challenge. Recently, several alternative approaches have been proposed to identify such overlapping communities. While results are promising, less is known about the model and assumptions that underlie these approaches. This paper shows that the bilinear model, combined with the assumption of quasi-stationary and uncorrelated sources, underlies novel methods for identifying overlapping brain networks. Furthermore, we propose a new algorithm, and through simulations, we investigate the robustness of our algorithm and several existing methods to solve the problem in noisy conditions with few available data samples. We conclude that quasi-stationary blind source separation-based techniques can have a promising advantage over tICA in terms of identifiability of overlapping communities and thus have the potential to contribute towards greater reproducibility of results.

Functional ultrasound (fUS) is an emerging neuroimaging modality that records changes in local blood dynamics. While it is known that the brain can respond variably to the same stimuli presented at different time instants, the extent to which fUS detects this variability based on the measured hemodynamics remains an open question. In this work, we characterize trial variability using fUS by estimating activation coefficients per trial using region-specific hemodynamic response functions. Our visual fUS experiments conducted on a mouse consistently reveal an increase of trial variability from the lateral geniculate nucleus to the visual cortex across different brain slices. These results are in parallel with prior findings in neuronal studies, suggesting a link between fluctuations of the evoked fUS response and true neural variability.

Recent developments in wearable devices have made accurate and efficient seizure detection more important than ever. A challenge in seizure detection is that patient-specific models typically outperform patient-independent models. However, in a wearable device one typically starts with a patient-independent model, until such patient-specific data is available. To avoid having to construct a new classifier with this data, as required in conventional kernel machines, we propose a transfer learning approach with a tensor kernel machine. This method learns the primal weights in a compressed form using the canonical polyadic decomposition, making it possible to efficiently update the weights of the patient-independent model with patient-specific data. The results show that this patient fine-tuned model reaches as high a performance as a patient-specific SVM model with a model size that is twice as small as the patient-specific model and ten times as small as the patient-independent model.

Functional ultrasound (fUS) is a neuroimaging modality that indirectly measures local neuronal activity by imaging cerebral blood volume fluctuations. However, accurately estimating neuronal activity from fUS measurements remains an open challenge. Hemodynamic changes are often modeled as the output of a system characterized by the hemodynamic response function (HRF), with neuronal activations as input. In this work, we propose a model for fUS measurements that assumes that hemodynamic activity has a low-rank spatial characterization. Starting from the tensor block term decomposition, we propose a method to estimate the spatial signatures, the HRF and the neuronal activation signals. This method is entirely data-driven and can be applied to entire fUS datasets. After an investigation using simulations, application to task experiment data of a mouse verified that activity that is spatially low rank and temporally correlated with the stimulus can be extracted in expected regions, which opens up the way to application on resting state data.

Objective: The severity of atrial fibrillation (AF) can be assessed from intra-operative epicardial measurements (high-resolution electrograms), using metrics such as conduction block (CB) and continuous conduction delay and block (cCDCB). These features capture differences in conduction velocity and wavefront propagation, but ignore complementary properties such as the morphology of the action potentials. In this work, we focus on such complementary properties, and derive features to detect variations in the atrial potential waveforms. Methods: We show that the spatial variation of atrial potential morphology during a single beat may be described by changes in the singular values of the epicardial measurement matrix. The method is non-parametric and requires little preprocessing. A corresponding singular value map points at areas subject to fractionation and block. Further, we developed an experiment where we simultaneously measure electrograms (EGMs) and a multi-lead ECG. Results: The captured data showed that the normalized singular values of the heartbeats during AF are higher than during SR, and that this difference is more pronounced for the (non-invasive) ECG data than for the EGM data, if the electrodes are positioned at favorable locations. Conclusion: Overall, the singular value-based features are a useful indicator to detect and evaluate AF. Significance: The proposed method might be beneficial for identifying electropathological regions in the tissue without estimating the local activation time.

Speckle noise is commonly assumed to be multiplicative. Non-local speckle denoising algorithms stack the correlated data patches into a tensor and take the logarithm such that the noise becomes additive. The log-transformed speckle noise is commonly assumed to be white Gaussian noise. The denoising is done through the low-rank approximation techniques applied to the non-local data patches. However, the log-transformed speckle noise can be better approximated as white Gaussian noise with sparse outliers. In this paper, we model the log-transformed speckle noise with this assumption and assess the importance of the noise model under various SNRs. In addition, we propose a weighting scheme for the tensor-based low-rank convex denoising method that utilizes the known ranks. The performance of the proposed algorithm is benchmarked against truncated multilinear singular value decomposition, higher-order orthogonal iteration, and robust tensor decomposition methods that use the sum of the nuclear norm and the tubal nuclear norm. Robust tensor decomposition methods that use the tubal nuclear norm perform better in low SNR scenarios. For high SNR scenarios, the proposed algorithm is found to perform better.

The pursuit of sensitive and dependable biomarkers capable of capturing the neural processes associated with cognition is a prominent area of interest. Event-related potentials (ERPs) hold significant promise for assessing cognitive dysfunction in various neurological disorders. However, existing data analysis techniques often underutilize the available data and may benefit from potential enhancements. In this paper, we investigate biomarker extraction methods based on two ERP experiments. First, we derive average ERPs from the electroencephalography (EEG) recorded during each experiment and store them in third-order tensors with subjects, channels and time samples along the three modes. Then, we extract biomarkers from these datasets via tensor decompositions. We compare single tensor decompositions and joint tensor decompositions that fuse the data from the individual tensors. In a simulated ERP experiment we compare the benefits and limitations of different tensor-based data fusion methods. Finally, we investigate their performance on a real dataset obtained from schizophrenia patients.

Recent advancements in wearable EEG devices have highlighted the importance of accurate seizure detection algorithms, yet the ever-increasing size of the generated datasets poses a significant challenge to existing seizure detection methods based on kernel machines. Typically, this problem is mitigated by significantly undersampling the majority class, but in practice, these methods tend to suffer from too many false alarms. Recent works have proposed tensor networks to enable large-scale classification with kernel machines. In this paper, we explore the use of a probabilistic tensor method, the tensor-network Kalman filter for LS-SVMs (TNKF-LSSVM), for seizure detection, as we hypothesize that using more data will improve the detection performance. We show that the TNKF-LSSVM performs comparably to a regular LSSVM in detecting seizures when both are trained on the same dataset. Additionally, the TNKF-LSSVM can provide meaningful uncertainty quantification, and it is able to handle large-scale datasets beyond the capabilities of the LS-SVM (i.e., $N \gt 10 ^{5})$. However, for the presented model configuration detection performance does not seem to improve with more input data.

Functional ultrasound (fUS) is an emerging neuroimaging modality that indirectly measures neural activity by detecting fluctuations in local blood dynamics. fUS acquisitions typically rely on the use of a 1D array transducer, which records hemodynamic activity in a single plane. A new technique named swept-3D fUS imaging obtains a full 3D volume of the brain by continuously moving a 1D array back-and-forth over the volume of interest. The standard procedure in fUS imaging involves filtering and averaging a number of ultrasound frames obtained at a single location to compute power-Doppler images, yet, in case of swept-3D fUS, the location of the recorded slice shifts at each time instant due to probe motion. In this work, we aim at discovering task-relevant components from 3D fUS data while taking into account the spatiotemporal differences in adjacent slices. We propose an alternating optimization scheme with general liner model-based regularization, and validate our method on swept-3D fUS data by identifying active regions and time traces within the mouse brain during a visual experiment.

Functional ultrasound (fUS) is a high-sensitivity neuroimaging technique that images cerebral blood volume changes, which reflect neuronal activity in the corresponding brain area. fUS measures hemodynamic changes which are typically modeled as the output of a linear time-invariant system, characterized by an impulse response known as the hemodynamic response function (HRF), and a binary representation of the stimulus signal as input. In this work, we quantify the difference between a linear and a nonlinear time-invariant HRF model in terms of data fitting and prediction performance. Our results on fUS data obtained from two mice reveal that: (a) including nonlinearities in the HRF achieves a significantly more precise modeling of the fUS signal compared to the linear assumption under certain stimulus conditions and (b) a second-order Volterra series approximation can be used to characterize the nonlinear model and predict responses to stimuli.

Functional ultrasound (fUS) is a novel neuroimaging technique that measures brain hemodynamics through a time series of Doppler images. The measured spatiotemporal hemodynamic changes reflect changes in neural activity through the neurovascular coupling (NVC). Often, such image time series is used to analyze dynamic functional connectivity (dFC) by directly computing a connectivity metric between the measured hemodynamic signals, ignoring the functional connectomics of underlying neural populations. This work proposes a novel fUS signal model, consisting of a hidden Markov model (HMM) cascaded with a convolutive model, that captures how fUS signals arise from a generative perspective while incorporating high-level biological functioning of neural populations. Consequently, the developed model enables inference of functional connectivity networks, being co-activation patterns (CAPs) of neural populations. Our results show that our methods can identify biologically plausible networks of functional connectivity. Furthermore, this method captures a difference in brain dynamics between wild-type and ${Shank2}^{-/-}$ mouse mutants.