$\textbf{Purpose:}$ To develop and evaluate an operator learning framework for nonlinear inversion (NLI) of brain magnetic resonance elastography (MRE) data, which enables real-time inversion of elastograms with comparable spatial accuracy to NLI. $\textbf{Materials and Methods:}$ In this retrospective study, 3D MRE data from 61 individuals (mean age, 37.4 years; 34 female) were used for development of the framework. A predictive deep operator learning framework (oNLI) was trained using 10-fold cross-validation, with the complex curl of the measured displacement field as inputs and NLI-derived reference elastograms as outputs. A structural prior mechanism, analogous to Soft Prior Regularization in the MRE literature, was incorporated to improve spatial accuracy. Subject-level evaluation metrics included Pearson's correlation coefficient, absolute relative error, and structural similarity index measure between predicted and reference elastograms across brain regions of different sizes to understand accuracy. Statistical analyses included paired t-tests comparing the proposed oNLI variants to the convolutional neural network baselines. $\textbf{Results:}$ Whole brain absolute percent error was 8.4 $\pm$ 0.5 ($μ'$) and 10.0 $\pm$ 0.7 ($μ''$) for oNLI and 15.8 $\pm$ 0.8 ($μ'$) and 26.1 $\pm$ 1.1 ($μ''$) for CNNs. Additionally, oNLI outperformed convolutional architectures as per Pearson's correlation coefficient, $r$, in the whole brain and across all subregions for both the storage modulus and loss modulus (p < 0.05). $\textbf{Conclusion:}$ The oNLI framework enables real-time MRE inversion (30,000x speedup), outperforming CNN-based approaches and maintaining the fine-grained spatial accuracy achievable with NLI in the brain.

Abdominal aortic aneurysms (AAA) pose a significant clinical risk due to their potential for rupture, which is often asymptomatic but can be fatal. Although maximum diameter is commonly used for risk assessment, diameter alone is insufficient as it does not capture the properties of the underlying material of the vessel wall, which play a critical role in determining the risk of rupture. To overcome this limitation, we propose a deep learning-based framework for elasticity imaging of AAAs with 2D ultrasound. Leveraging finite element simulations, we generate a diverse dataset of displacement fields with their corresponding modulus distributions. We train a model with U-Net architecture and normalized mean squared error (NMSE) to infer the spatial modulus distribution from the axial and lateral components of the displacement fields. This model is evaluated across three experimental domains: digital phantom data from 3D COMSOL simulations, physical phantom experiments using biomechanically distinct vessel models, and clinical ultrasound exams from AAA patients. Our simulated results demonstrate that the proposed deep learning model is able to reconstruct modulus distributions, achieving an NMSE score of 0.73\%. Similarly, in phantom data, the predicted modular ratio closely matches the expected values, affirming the model's ability to generalize to phantom data. We compare our approach with an iterative method which shows comparable performance but higher computation time. In contrast, the deep learning method can provide quick and effective estimates of tissue stiffness from ultrasound images, which could help assess the risk of AAA rupture without invasive procedures.

We present a novel extension of the Weak Neural Variational Inference (WNVI) framework for probabilistic material property estimation that explicitly quantifies model errors in PDE-based inverse problems. Traditional approaches assume the correctness of all governing equations, including potentially unreliable constitutive laws, which can lead to biased estimates and misinterpretations. Our proposed framework addresses this limitation by distinguishing between reliable governing equations, such as conservation laws, and uncertain constitutive relationships. By treating all state variables as latent random variables, we enforce these equations through separate sets of residuals, leveraging a virtual likelihood approach with weighted residuals. This formulation not only identifies regions where constitutive laws break down but also improves robustness against model uncertainties without relying on a fully trustworthy forward model. We demonstrate the effectiveness of our approach in the context of elastography, showing that it provides a structured, interpretable, and computationally efficient alternative to traditional model error correction techniques. Our findings suggest that the proposed framework enhances the accuracy and reliability of material property estimation by offering a principled way to incorporate uncertainty in constitutive modeling.

In the field of neuroimaging, accurate brain age prediction is pivotal for uncovering the complexities of brain aging and pinpointing early indicators of neurodegenerative conditions. Recent advancements in self-supervised learning, particularly in contrastive learning, have demonstrated greater robustness when dealing with complex datasets. However, current approaches often fall short in generalizing across non-uniformly distributed data, prevalent in medical imaging scenarios. To bridge this gap, we introduce a novel contrastive loss that adapts dynamically during the training process, focusing on the localized neighborhoods of samples. Moreover, we expand beyond traditional structural features by incorporating brain stiffness--a mechanical property previously underexplored yet promising due to its sensitivity to age-related changes. This work presents the first application of self-supervised learning to brain mechanical properties, using compiled stiffness maps from various clinical studies to predict brain age. Our approach, featuring dynamic localized loss, consistently outperforms existing state-of-the-art methods, demonstrating superior performance and laying the way for new directions in brain aging research.

Medical applications of robots are increasingly popular to objectivise and speed up the execution of several types of diagnostic and therapeutic interventions. Particularly important is a class of diagnostic activities that require physical contact between the robotic tool and the human body, such as palpation examinations and ultrasound scans. The practical application of these techniques can greatly benefit from an accurate estimation of the biomechanical properties of the patient's tissues. In this paper, we evaluate the accuracy and precision of a robotic device used for medical purposes in estimating the elastic parameters of different materials. The measurements are evaluated against a ground truth consisting of a set of expanded foam specimens with different elasticity that are characterised using a high-precision device. The experimental results in terms of precision are comparable with the ground truth and suggest future ambitious developments.

Computer-aided detection (CAD) of benign and malignant breast lesions becomes increasingly essential in breast ultrasound (US) imaging. The CAD systems rely on imaging features identified by the medical experts for their performance, whereas deep learning (DL) methods automatically extract features from the data. The challenge of the DL is the insufficiency of breast US images available to train the DL models. Here, we present an ensemble transfer learning model to classify benign and malignant breast tumors using B-mode breast US (B-US) and strain elastography breast US (SE-US) images. This model combines semantic features from AlexNet & ResNet models to classify benign from malignant tumors. We use both B-US and SE-US images to train the model and classify the tumors. We retrospectively gathered 85 patients' data, with 42 benign and 43 malignant cases confirmed with the biopsy. Each patient had multiple B-US and their corresponding SE-US images, and the total dataset contained 261 B-US images and 261 SE-US images. Experimental results show that our ensemble model achieves a sensitivity of 88.89% and specificity of 91.10%. These diagnostic performances of the proposed method are equivalent to or better than manual identification. Thus, our proposed ensemble learning method would facilitate detecting early breast cancer, reliably improving patient care.

It is known that changes in the mechanical properties of tissues are associated with the onset and progression of certain diseases. Ultrasound elastography is a technique to characterize tissue stiffness using ultrasound imaging either by measuring tissue strain using quasi-static elastography or natural organ pulsation elastography, or by tracing a propagated shear wave induced by a source or a natural vibration using dynamic elastography. In recent years, deep learning has begun to emerge in ultrasound elastography research. In this review, several common deep learning frameworks in the computer vision community, such as multilayer perceptron, convolutional neural network, and recurrent neural network are described. Then, recent advances in ultrasound elastography using such deep learning techniques are revisited in terms of algorithm development and clinical diagnosis. Finally, the current challenges and future developments of deep learning in ultrasound elastography are prospected.

Ultrasound elastography is used to estimate the mechanical properties of the tissue by monitoring its response to an internal or external force. Different levels of deformation are obtained from different tissue types depending on their mechanical properties, where stiffer tissues deform less. Given two radio frequency (RF) frames collected before and after some deformation, we estimate displacement and strain images by comparing the RF frames. The quality of the strain image is dependent on the type of motion that occurs during deformation. In-plane axial motion results in high-quality strain images, whereas out-of-plane motion results in low-quality strain images. In this paper, we introduce a new method using a convolutional neural network (CNN) to determine the suitability of a pair of RF frames for elastography in only 5.4 ms. Our method could also be used to automatically choose the best pair of RF frames, yielding a high-quality strain image. The CNN was trained on 3,818 pairs of RF frames, while testing was done on 986 new unseen pairs, achieving an accuracy of more than 91%. The RF frames were collected from both phantom and in vivo data.

Time delay estimation (TDE) is a critical and challenging step in all ultrasound elastography methods. A growing number of TDE techniques require an approximate but robust and fast method to initialize solving for TDE. Herein, we present a fast method for calculating an approximate TDE between two radio frequency (RF) frames of ultrasound. Although this approximate TDE can be useful for several algorithms, we focus on GLobal Ultrasound Elastography (GLUE), which currently relies on Dynamic Programming (DP) to provide this approximate TDE. We exploit Principal Component Analysis (PCA) to find the general modes of deformation in quasi-static elastography, and therefore call our method PCA-GLUE. PCA-GLUE is a data-driven approach that learns a set of TDE principal components from a training database in real experiments. In the test phase, TDE is approximated as a weighted sum of these principal components. Our algorithm robustly estimates the weights from sparse feature matches, then passes the resulting displacement field to GLUE as initial estimates to perform a more accurate displacement estimation. PCA-GLUE is more than ten times faster than DP in estimation of the initial displacement field and yields similar results.

Traditionally, nonlinear inversion, direct inversion, or wave estimation methods have been used for reconstructing images from MRE displacement data. In this work, we propose a convolutional neural network architecture that can map MRE displacement data directly into elastograms, circumventing the costly and computationally intensive classical approaches. In addition to the mean squared error reconstruction objective, we also introduce a secondary loss inspired by the MRE mechanical models for training the neural network. Our network is demonstrated to be effective for generating MRE images that compare well with equivalents from the nonlinear inversion method.