An H∞ Strategy for Strain Estimation in Ultrasound Elastography Using Biomechanical Modeling Constraint

Abstract

The purpose of ultrasound elastography is to identify lesions by reconstructing the hardness characteristics of tissue reconstructed from ultrasound data. Conventional quasi-static ultrasound elastography is easily applied to obtain axial strain components along the compression direction, with the results inverted to represent the distribution of tissue hardness under the assumption of constant internal stresses. However, previous works of quasi-static ultrasound elastography have found it difficult to obtain the lateral and shear strain components, due to the poor lateral resolution of conventional ultrasound probes. The physical nature of the strain field is a continuous vector field, which should be fully described by the axial, lateral, and shear strain components, and the clinical value of lateral and shear strain components of deformed tissue is gradually being recognized by both engineers and clinicians. Therefore, a biomechanical-model-constrained filtering framework is proposed here for recovering a full displacement field at a high spatial resolution from the noisy ultrasound data. In our implementation, after the biomechanical model constraint is integrated into the state-space equation, both the axial and lateral displacement components can be recovered at a high spatial resolution from the noisy displacement measurements using a robust filter, which only requires knowledge of the worst-case noise levels in the measurements. All of the strain components can then be calculated by applying a gradient operator to the recovered displacement field. Numerical experiments on synthetic data demonstrated the robustness and effectiveness of our approach, and experiments on phantom data and in-vivo clinical data also produced satisfying results.

High-Pitch, Low-Voltage and Low-Iodine-Concentration CT Angiography of Aorta: Assessment of Image Quality and Radiation Dose with Iterative Reconstruction

“…Thus, it is of paramount importance to implement low-dose CTA protocol in aortic imaging. Although ultrasound is increasingly used to follow-up endovascular repair of aortic aneurysm as it does not involve ionizing radiation [ 44 – 46 ], CTA still remains the preferred method in the current clinical practice.…”

2D tissue strain tensor imaging in quasi-static ultrasound elastography

“…These RF images include lateral oscillations, resulting from a particular beamforming. Other work focuses instead on the estimation method itself to reduce noise in elastograms, notably with the development of regularization-based approaches [12][13][14][15]. Guo et al [16] recently proposed a partial differential equation (PDE)-based regularization method to smooth the displacement fields using the (quasi) incompressibility property of soft tissues [17].…”

Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation

“…Many different types of soft tissue can be assumed to be incompressible because they are mostly composed of water. A fifth approach, pursued in [21] is to constrain the displacements to satisfy the momentum equations.…”

“…Among the existing approaches, the incompressibility processing method introduced in [31], and the momentum equation based processing method [21] are arguably the most similar in spirit to the method presented here to reconstruct better lateral displacements. In [31], the authors assumed that the deformation is linear, incompressible, and plane strain in character.…”

“…In [21], the authors constrain the measured displacements to satisfy the plane strain elasticity equations. Using only the measured axial displacements, and an H ∞ filtering strategy, they are able to reconstruct the full displacement field.…”