Understanding the mechanisms that underpin learning effects remains a central goal in neuroscience, with functional neuroimaging offering a powerful avenue for observing brain activity. This work is situated within the domain of haemodynamic functional neuroimaging, with a specific focus on functional ultrasound (fUS)—a relatively novel modality that combines high spatio-temporal resolution and portability. The goal of this project is to investigate the capacity of tensor-decomposition-based techniques to extract meaningful, interpretable representations of stimulus-evoked learning effects from a multi-subject fUS dataset while being robust to the non-idealities present in said data. While numerous approaches exist for analysing neuroimaging data, many are limited by scalability, interpretability, or an inability to capture changing neurological patterns. This work is thus motivated by the need for methods capable of handling large, dynamic datasets while extracting interpretable results. Tensor decompositions offer such a framework but their ability to capture subject-specific time-varying effects and their application to functional ultrasound is still under-explored. Several tensor decomposition algorithms are examined, assessed in terms of their learning effect extraction capabilities and robustness to non-idealities, and a novel shifted canonical polyadic decomposition variant is developed to address time-varying effects. Results from synthetic data analysis demonstrate that tensor decompositions are robust to non-idealities in functional ultrasound data (to varying degrees) and can recover interpretable latent components. Due to the data's partial scan coverage, no novel signatures of learning were identified in the real data; however, the extracted components further substantiate the potential of these algorithms and highlight a promising direction for analysing learning effects in functional neuroimaging data.

In the last decade, the new functional neuroimaging technique functional ultrasound (fUS) has emerged as a potential new tool for clinical and neuroscientific applications. Unlike several conventional methods for functional brain imaging, fUS offers an unparalleled combination of submillimeter-subsecond spatiotemporal resolution and the ability to penetrate deep into brain tissue and capture large areas of interest. This makes fUS an exceptionally valuable tool for investigating brain function. The principal physiological mechanism utilized by fUS imaging is neurovascular coupling, which connects neuronal activity with local hemodynamic changes. Within the brain, increased neuronal activity results in the dilation of nearby blood vessels, subsequently leading to an increased local blood flow and volume.
In fUS, the increase in blood volume is measured by the intensity of the Doppler signal caused by the Doppler effect. To obtain relevant information from functional neuroimaging data, blind source separation (BSS) is often used. BSS is the separation of a set of source signals from a set of mixed signals, without the aid of information about the source signals or the mixing process. A commonly used BSS method for identifying brain networks and artifacts in functional neuroimaging techniques like fMRI is independent component analysis, which is a low-rank matrix decomposition. This work explores the use of canonical polyadic decomposition (CPD), a low-rank tensor decomposition, for BSS of fUS data. The CPD approximates a 3rd-order tensor, consisting of a space, frequency, and time dimension, by a sum of rank-1 tensors. The proposed method offers three key advantages that make it highly relevant to the field of fUS signal processing: 1) Tensor-based BSS by CPD allows for frequency as a third dimension to complement the spatial and temporal dimensions; 2) Tensor-based BSS by CPD allows for the use of all raw fUS data (compound images) rather than only power doppler images, exploiting more available information; and 3) Tensor-based BSS by CPD allows for a BSS method without strong constraints such as the case with matrix-based methods like independent component analysis. The full processing pipeline developed in this work consists of four distinct stages. In stage one, pre-processing is carried out through SVD filtering, temporal demeaning, and pixel-based normalization. During the SVD filtering, normalization of the singular values is performed, which is novel. In stage two, compression is performed using truncated multilinear singular value decomposition. In stage three, BSS is carried out using CPD on the compressed data. In stage four, stable components are extracted by running the CPD 100 times and clustering the resulting components. These clusters were then averaged to create mean components. The CPD rank was estimated based on two quantifiable aspects: 1) Correlation between mean components and 2) Frequency of occurrence of mean components. The method is entirely data-driven, can be applied to entire raw fUS datasets, and can run on a laptop with standard RAM. Application to task experiment data of a mouse verified that activity that is temporally correlated with the stimulus can be extracted in expected regions. The components also indicate expected functional connectivity, which is often not the case for matrix-based methods. Moreover, frequency spectra showed different characteristics for different types of components, which displays the relevance of this dimension for BSS, especially for nuisance components. In conclusion, the proposed tensor-based blind source separation pipeline for raw fUS data was able to identify artifacts and meaningful neurological components based on distinctive characteristics in the temporal, spatial, and spectral domains. This work serves as a starting point for more advanced denoising, the identification of novel brain networks, and the comparison of brain networks across healthy and pathological conditions. Nevertheless, further research is necessary to ensure the utility of the method.

The brain is one of the most important organs of the human body, yet it remains poorly understood. The anatomical connections between different brain regions facilitate the transmission of electrical signals across the brain, forming the basis of higher functionalities such as speech, vision, comprehension, and sensory perception. During brain tumor surgery, it is critical to preserve vital connections within the brain while resecting as much of the tumor as possible. Therefore, accurately locating and mapping functional tracts within the brain is crucial for optimal patient outcomes. This thesis focuses on the exploration and application of electrocorticography (ECoG) and Cortico-Cortical Evoked Potentials (CCEP) to enhance our understanding of brain connectivity to ultimately aid in the improvement of tumor resection.

The Background chapter provides all necessary information on the electrophysiological brain, intraoperative neuromonitoring, ECoG, and CCEP. By explaining the fundamental concepts and technological aspects, the chapter sets the stage for understanding how ECoG and CCEP can be utilized to study brain connectivity and improve surgical outcomes.

Chapter 1 establishes the foundation of the research. It uses data from a study on brain transmission speeds involving 74 patients who underwent epilepsy surgery. The chapter explains the composition and structure of the raw data, explaining the processes of data loading and preprocessing, including the construction of epochs and evoked objects from the raw data. The peak detection algorithm, the primary analysis method used to extract amplitude and latency parameters from registered CCEP N1 peaks, is illustrated. These results, a combination of the CCEP connections between electrodes and their corresponding amplitude and latency, form the basis for further chapters.

In Chapter 2, the research primarily addresses the analysis of CCEP responses measured with ECoG across a population. The analysis made a construction of brain connectivity graphs based on Destrieux labels and individual electrodes. The peak detection algorithm identified various CCEP responses and highlighted connections between stimulating and recording electrodes. Notably, connections between temporal and parietal brain regions, and between parietal and frontal regions, were found. These findings corresponded with known white matter tracts, demonstrating the capability of CCEP measurements to reflect connectivity, comparable to standard DTI measurements.

Chapter 3 shifts focus to the visualization of these CCEP responses at an individual patient level for clinical translation. Stimulation of electrodes in the parietal region revealed both local responses and distant connections in the frontal and temporal regions of an exemplary patient. These visualizations provide intuitive insights into the brain's connectivity. An animation illustrating the temporal progression of signal propagation offers a basis for personalized visualizations of connectivity based on CCEP measurements.

In summary, this work contributes to the field of neuroscience by providing robust methods for visualizing and analyzing brain connectivity, ultimately enhancing our ability to translate these findings into practical clinical applications.

Doppler ultrasound imaging of cerebral blood flow faces challenges arising from a low signal-to-noise ratio (SNR) and a wide dynamic range. Echo signals received from blood cells are significantly weaker compared to surrounding tissues, such as the skull or brain soft tissue, resulting in inhibited visualization of small blood vessels and deep brain areas. To address this issue, this thesis explored the feasibility of employing and improving coded excitation techniques to enhance the SNR of Doppler ultrasound images. Furthermore, an optimized code for Doppler ultrasound imaging is designed, represented by a generalized encoding matrix.
The research begins with the definition of a linear signal model that incorporates the encoding matrix. Subsequently, a trace-constraint optimization problem is formulated based on maximizing the Fisher information matrix to find the optimized encoding matrix. The feasibility and performance of the optimized encoding matrix are assessed through simulations on both small and large array settings, which operate above Nyquist sampling frequency and under Nyquist sampling frequency respectively. The imaging results indicate that the optimized code exhibits higher SNR in deep image regions compared to existing coded excitation methods like Barker code while using the same number of transmissions, bit length, and same average transmit energy, albeit with a trade-off of decreased axial resolution. Nonetheless, this resolution degradation can be mitigated through the application of the iterative imaging technique LSQR. Finally, the optimized code is tested in a clinical transducer setting, and a blood flow simulation is conducted. The outcomes showcase the capacity of the proposed optimized code to enable higher SNR in Doppler ultrasound imaging and more accurate and informative clinical assessments.

To better understand how brain signals are processed and even how the human mind works, analyzing the hemodynamic signal model is one of the most essential steps. In the CUBE group of Erasmus MC, functional ultrasound (fUS) data of a mouse’s brain is recorded. By using this fUS dataset, this thesis will solve the problem regarding the joint estimation of hemodynamic response function (HRF) and the underlying stimulus. Usually, hemodynamic responses are investigated in the time domain, while this thesis provides another perspective
from frequency domain signal processing.

We consider the hemodynamic response as a convolutive signal mixture, then try to transform it into an instantaneous mixing model by converting the context into the frequency domain. By applying independent vector analysis (IVA), this estimation problem can be solved without facing permutation ambiguity which is a well-unknown problem regarding independent component analysis (ICA). Additional steps before and after IVA are also discussed so that a whole estimation road map is formed.

Both simulation and experimental analysis are provided to validate this estimation algorithm. Results show that by using this method, both stimulus and HRF estimation can be achieved satisfyingly in a suitable experimental setting. This thesis provides insights and future potentials for IVA to be further investigated in neural signal processing problems.

Functional ultrasound is by now a well-established technique in the neuroscience community to measure brain activity. However, the transcranial application of functional ultrasound on humans, with the exception of the acoustic windows in the skull, remains a huge challenge because of the properties of the cranial bone the acoustic waves will reflect, refract, attenuate or will cause aberration. Therefore, the signal-to-noise ratio (SNR) of the incoming signal is too low for transcranial functional ultrasound (TCfUS). This thesis tries to overcome the SNR problem of TCfUS with the design of a 64-channel ultrasound acquisition system that is focused on achieving the highest SNR possible. This is achieved by placing the analog front-end (AFE) chips as near to the transducer elements as possible and by oversampling the incoming signal with a factor of 25, a theoretical increase of 15 dB of the signal-to-quantization-noise ratio over the current state-of-the-art is estimated. The proposed design is a receive-only system where the transmission of the ultrasound pulses is carried out by a separate ultrasound system. The design splits the acquisition system into a front-end and a back-end subsystem, where the front-end system is implemented using four AFE58JD48 analog front-end chips from Texas Instruments. From here the data samples are transported over fiber optics to the back-end subsystem, which consists of a VCK190 FPGA board from Xilinx, where the samples are processed and/or transported to a workstation for storage. Because the system organization differentiates from more conventional research ultrasound systems, a trade-off is introduced between processing and throughput, resulting in three processing configurations for the FPGA with each a different focus: raw RF data sampling, real-time processing, and hardware processing. Due to time and resource constraints, no measurements and results are available on the SNR and decimation. However, a theoretical exploration has been done on the expandability of the number of channels which was found to be 192 channels for the VCK190.

At the Center for Ultrasound and Brain imaging at Erasmus MC in Rotterdam, a mouse's visual cortex had been imaged using the fUS technique. The mouse had been exposed to different visual stimuli. The stimuli varied in position, size, and shape. We investigate how the measured task-based fUS signals differ depending on the visual stimuli presented to the mouse. For that purpose, we decompose the fUS data with four different methods giving different levels of sparsity. This thesis compares the performance of the four methods, and provides neurological insights obtained with these methods. For modeling the data, we consider four data-driven decomposition methods: ICA and three sDL variants. The methods decompose the data into better interpretable spatial maps and time courses. Every decomposition is further examined by training L1-regularized prediction models that optimize for sparsity. The goal is to predict the presented stimulus based on the decomposed data. Furthermore, the potential of group lasso regularization in prediction models is illustrated. The decompositions extract spatial maps anatomically linked to the visual cortex, superior colliculus and the hippocampus. All decompositions achieve considerable performance in the position prediction but have low success in the size and shape prediction. ICA outperformed the three sDL variants in all prediction tasks. Furthermore, group lasso regularization is found to be a useful tool to obtain discriminatory information in the time dynamics.

Detailed imaging of blood flow may improve the understanding of brain functions. The state-of-the-art non-invasive flow imaging of the brain is limited to a one-dimensional Doppler setting. We propose a method to estimate the two-dimensional flow vector in the fine vascular network of the brain by using a speckle tracking technique. The framework of Orthogonal Matching Pursuit is used for speckle tracking and modified to include prior constraints to guide the matching process among two frames, called as Guided Orthogonal Matching Pursuit. Prior constraint is in the form of a directional constraint which determines the probability of vector flow in all the directions according to the orientation of the vessels. The orientation of the vessels is computed using Power Doppler Imaging. In this work, the proposed method for two-dimensional vector estimation is compared with the standard block matching technique of Normalized Cross-Correlation. We see that the variance of the final velocity estimates has reduced when compared to the standard speckle tracking method and the direction of blood flow is found within the curvature of the vessel.

Previous work [1] has demonstrated the possibility of high resolution imaging through the use of a single element and a aberration mask. This thesis will expand on the previous work by examining the proposed method for errors in the creation of the model. The analysis is preformed by examining the various aspects of the measurements setup and underlying theoretical model, after which measurements are performed to determine their contribution and correctness with regard to the model. Results demonstrated a systematic error of a non-linear frequency scaling and semi-linear phase shift. The origin of the error lies in the unwanted addition of transfer functions of some of the components. A Tikhonov regularized least squares method is proposed to estimate this transfer function and supply compensation based on all the measurements. The results of application of this method on the uncalibrated model are demonstrated through 1D imaging experiments. The result of which show a signicant improvement over the previous uncalibrated results. After which the possibility of calibration due to a singular measurement is explored and a adaptation of the Tikhonov regularized least squares method is proposed for close approximation of the previously found transfer function. Further to obtain an indication of possible remaining hurdles and successes with this method, extensive simulations are preformed to examine the individual impact of various sources of noise and interference.

Understanding the hidden organizational principles existing in the human brain was always one of the great challenges in Neuroscience. To uncover the way the brain functions, advancements in the fields of Medical Imaging and Computational Science have been of great importance. Powerful imaging tools, such as functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), have already enabled scanning the whole brain volume and visualizing the brain functioning, both at rest and during task execution, to a significant degree. However, several limitations especially in spatiotemporal resolution led to the need for further advancements in the field of functional imaging. An alternative technique, that overcomes most of the previously existing problems, is functional ultrasound (fUS). fUS is capable of imaging even the microvasculature blood-flow dynamics in response to brain activation with high spatiotemporal resolution. The wealth of fUS-acquired data calls for advanced data-analytic methods to uncover new information, beyond the well-applied simple univariant correlation method. This is the main goal of this MSc thesis, to use a proper analysis technique, mainly borrowed from the same-principle fMRI technique, in order to produce powerful inferences. For this reason, a detailed literature review regarding fUS imaging and fMRI analysis methods is introduced. Then, the main analysis part is focused on the Independent Component Analysis (ICA) method, trying to segregate the brain into spatially independent components that share a similar activity response. Here, the whole processing pipeline is established, describing all the necessary preprocessing steps along with ICA parameters and approaches (single- and group-ICA) using the ICASSO software package. As a post-processing step, functional images-to-Allen brain atlas registration is also performed in order to identify the different regions represented in the ICA-derived spatial components. The effectiveness of the methods is assessed based on the collected results on different datasets, obtained from 2D visual-stimulation as well as 3D resting-state experiments conducted on mice at the Neuroscience department of the Erasmus MC. As a conclusion, ICA was able to separate different anatomical and functional sub-networks. More specifically, from the visual-stimulation experiments, brain regions such as Lateral geniculate nucleus (LGN) that play a role in the visual pathway are identified, while from the resting-state the spatial continuity of different regions is confirmed.

The application of Compressive Sampling (CS) in the medical ultrasound has been widely studied in recent years with the growing requirement of reconstructing high-quality images with smaller data size. Most of the current studies with successful CS reconstruction are mainly focusing on the mathematical applications of CS theory in ultrasound imaging. However, the randomized mechanisms in these studies are hard to be fully fulfilled in hardware. In addition, some of the studies try to discover the sparse representation of signals by ignoring a part of information rather than compressing all data. We propose a new compression scheme for fast image acquisition in ultrasound imaging using a method, which is similar in style to CS. Our scheme is based on the formulation of an inverse scattering problem (ISP), where the Born approximation have been used during its derivation. In our system, the ultrasound image are represented by a collection of hypothetical points, what can be called pixels. These points are identified by their unique spatial impulse responses relative to the elements in the transducer. The randomized linear combinations of the spatial impulse responses from the view of elements can be maintained the uniquenesses of these points, which is similar to the coding techniques in data compression. Hence, our compression scheme can be more controllable than the conventional CS, which can achieve the real-time compression of data during the acquisition stage in hardware. We employ L2-regularization to solve the ill-posed ISP rather than the L1-regularization CS since there is no any assumption of signal sparsity. In our work, we finally achieve the acceptable reconstructions by compressing the raw data to 12.5% of its original size. The results are better than 12.5% with multiplexing the received signals from 12.5% elements in the array and almost as good as 25% with multiplexing the received signals from 25% elements in the array.