Inverse Problem Approach to Aberration Correction for in vivo Transcranial Imaging Based on a Sparse Representation of Contrast-enhanced Ultrasound Data

TL;DR

This work presents IPAC, an inverse-problem framework that corrects skull-induced aberrations in transcranial CEUS and ULM by exploiting the sparsity of microbubble signals. A forward model links the sparse MB medium and a phase-screen aberrator to the recorded RF signals, and a linearized formulation enables a least-squares inversion to recover the aberration function, which is then incorporated into beamforming. IPAC is validated in silico with plane and divergent waves and demonstrated in vivo in five mice, showing improvements in CEUS contrast (4.6 dB) and ULM spatial resolution (from $21.1\,\mu$m to $18.3\,\mu$m), as well as enhanced hemodynamic quantification. The method proves robust to MB concentration and outperforms a coherence-based approach under challenging conditions, highlighting its potential to enable reliable non-invasive transcranial ultrasound imaging.

Abstract

Transcranial ultrasound imaging is currently limited by attenuation and aberration induced by the skull. First used in contrast-enhanced ultrasound (CEUS), highly echoic microbubbles allowed for the development of novel imaging modalities such as ultrasound localization microscopy (ULM). Herein, we develop an inverse problem approach to aberration correction (IPAC) that leverages the sparsity of microbubble signals. We propose to use the \textit{a priori} knowledge of the medium based upon microbubble localization and wave propagation to build a forward model to link the measured signals directly to the aberration function. A standard least-squares inversion is then used to retrieve the aberration function. We first validated IPAC on simulated data of a vascular network using plane wave as well as divergent wave emissions. We then evaluated the reproducibility of IPAC \textit{in vivo} in 5 mouse brains. We showed that aberration correction improved the contrast of CEUS images by 4.6 dB. For ULM images, IPAC yielded sharper vessels, reduced vessel duplications, and improved the resolution from 21.1 $μ$m to 18.3 $μ$m. Aberration correction also improved hemodynamic quantification for velocity magnitude and flow direction.

Figures (11)

• Figure 1: Schematic representation of the inverse problem approach. (a) A linear probe is used to image a scattering medium $\mathbf{\Gamma}$ in presence of a phase screen aberrator $\mathbf{u}$. The acquired signal is then given by $\mathbf{s}$. (b) $\mathbf{\Gamma}$ can be inferred from microbubble positions. A forward model $\hat{\mathbf{M}}$ based on wave propagation can then be built, linking the medium $\mathbf{\Gamma}$ and aberration $\mathbf{u}$ to the measured signal $\mathbf{s}$. The transmit operator $\mathbf{T}$ is used to link the transmitted field of the probe to each scatterer. The reflection operator $\mathbf{R}$ then links the scatterer signals back to each element of the probe. (c) Computing the gradient term $\nabla_{\mathbf{u}}\hat{\mathbf{M}}$ allows to write the forward model in matrix form $\mathbf{K}$ (d). In the Fourier domain, the forward model with the matrix $\mathbf{K}$ links directly the received signal $\mathbf{s}$ to the aberration function $\mathbf{u}$ in a linear form. Applying inversion strategies such as least-square minimization is used to solve $\mathbf{u}$.
• Figure 2: General framework for in vivo phase aberration correction. (1) A SVD filter is applied to raw RF channel data to isolate microbubble hyperbolas. (2) Microbubble positions are localized on beamformed data to construct the forward model $\mathbf{K}$. The aberration function is then retrieved by using a least-squares minimization. Delays associated to the aberration function are included into the beamformer to perform correction. This step can be performed in an iterative manner to correct for microbubble positions, which return a more precise $\mathbf{K}$ matrix. (3) After convergence of the iterative step, the final aberration function is used to perform correction on either power Doppler or ULM images.
• Figure 3: Aberration correction on in silico data using a linear probe. (a) Simulation ground truth of the vascular network. (b) Simulated magnitude of RF channel signals with aberration for different SNR. (c) Aberration functions retrieved with the correction method for different SNR and iterative steps. (d) Comparison of Power Doppler images before and after correction for different SNR.
• Figure 4: Aberration correction on in silico data using a phased array probe. (a) Simulation ground truth of the vascular network. (b) Simulated magnitude of RF channel signals with aberration for different SNR. (c) Aberration functions retrieved with the correction method for different SNR and iterative steps. (d) Comparison of Power Doppler images before and after correction for different SNR.
• Figure 5: Example of in vivo microbubble signals used for aberration correction. (a) Microbubbles detection and localization on a mouse brain. (b) In vivo RF channel signals compared to the simulated magnitude of RF channel signals with the forward model. (c) Forward model matrix $\mathbf{K}$ associated to the RF channel data. (d) Microbubbles after correction.