Evoked Component Analysis (ECA): Decomposing Functional Ultrasound Signals Based on GLM Regularization

Background

The analysis of functional neuroimaging data aims to uncover spatial and temporal patterns of brain activity. Existing data analysis methods mainly fall into two categories: fully data-driven analysis methods and methods that rely on prior information, such as analyzing brain activity using stimulus time courses. Generally, using stimulus signals can help identify active brain regions, but the brain’s response to stimuli often exhibits nonlinear and time-varying characteristics. Therefore, relying solely on stimulus signals to describe the temporal response of the brain may lead to a limited understanding of brain function.

Against this background, the authors propose a new technique called Evoked Component Analysis (ECA), which utilizes prior information as a guiding factor. By introducing a General Linear Model (GLM) design matrix as a regularization term within a low-rank decomposition framework, ECA aims to decompose functional ultrasound signals in both spatial and temporal dimensions.

Source of the Paper

The paper is authored by Aybuke Erol, Bastian Generowicz, Pieter Kruizinga, and Borbala Hunyadi, who are affiliated with the Signal Processing Systems Group at Delft University of Technology and the Center for Ultrasound and Brain imaging (CUBE) at Erasmus University Medical Center in the Netherlands. The paper is published in the IEEE Transactions on Biomedical Engineering journal, with an expected release date in 2024.

Research Workflow and Methods

2D Functional Ultrasound Experiments

The study first conducts 2D functional ultrasound (FUS) experiments on mice. The authors demonstrate how to perform ECA decomposition under various regularization strengths (λ) to highlight the importance of prior information. The experiments use multiple hemodynamic response functions from the GLM design matrix to delve into the characteristics of evoked activities in different regions. The workflow is as follows:

1. Experimental Design: Conducting functional ultrasound experiments on the brain regions of mice, showing twenty 4-second visual stimulus blocks, with random intervals of 10 to 15 seconds between each stimulus block. Imaging is performed transversely using an ultrasound probe.
2. Data Acquisition and Preprocessing: The obtained 2D images are subjected to Singular Value Decomposition (SVD) to remove irrelevant tissue noise, followed by Power Doppler Imaging (PDI), collecting the time series for each pixel.
3. ECA Decomposition: Decomposing the data under different regularization levels to observe its impact on the responses of the visual cortex (VIS), lateral geniculate nucleus (LGN), and primary motor cortex (M1).

3D Scanning Functional Ultrasound Experiments

Subsequently, swept 3D functional ultrasound (Swept-3D FUS) experiments are conducted on five mice participating in two different visual tasks. This method involves sequential imaging of the brain by moving the probe, with each imaging result separated by time points. The workflow is as follows:

1. Experimental Design: Using LED lights as stimuli, flashing at 3 Hz for 5 seconds, followed by random rest intervals of 10 to 16 seconds. Monitoring the 3D volumetric images of the mice’s brains during the experiment.
2. Data Processing and Modeling: Standardizing the acquired data and using the ECA algorithm to perform 3D decomposition, estimating the factor matrix at each time point, and comparing it with GLM and correlation analysis methods.

Main Results and Analysis

2D Functional Ultrasound Experiment Results

Through the 2D FUS experiment, the study shows that as the regularization strength decreases (λ decreases from 5000 to 100), the changes in brain responses captured by the Evoked Component Analysis algorithm across different epochs significantly increase. Under high regularization, the responses of LGN and VIS are more notable, whereas under low regularization, the activation level of the primary motor cortex (M1) is higher. Moreover, modeling the non-regularized components (noise and background activity) indicates that these components are mainly associated with vascular activity.

3D Scanning Functional Ultrasound Experiment Results

In experiments with five mice, the study applied the ECA algorithm to separate brain activities evoked by left-eye and right-eye stimuli. The results show that using the ECA algorithm can more accurately describe the temporal and spatial responses of the brain. Compared to traditional correlation analysis and GLM methods, the statistical results in visual processing pathways (such as the superior colliculus, LGN, and visual cortex) are more significant, with higher t-statistic data than those obtained through correlation analysis and GLM.

Conclusion and Value

The Evoked Component Analysis (ECA) algorithm proposed in this study holds significant value in the field of biomedical engineering for functional ultrasound research. Its main contributions include:

1. Innovative Method: ECA utilizes the General Linear Model design matrix within a low-rank decomposition framework, making reasonable use of prior information while avoiding total reliance on prior information, thereby capturing brain activity effectively.
2. Superior Performance: ECA demonstrates superior decomposition results on both 2D FUS and 3D FUS data, better describing the temporal and spatial responses of the brain and yielding higher t-statistic data.
3. Broad Application Potential: This method can be extended beyond mouse experiments to other neuroimaging studies, providing significant insights into the dynamic changes of stimulus-evoked brain activities.

Evoked Component Analysis (ECA) combines the advantages of both model-guided and data-driven approaches, providing new tools and perspectives for the complex analysis of neuroimaging data. It enriches the methods for understanding and analyzing brain functions.