We introduce two model-based iterative methods to obtain shear modulus images of tissue using magnetic resonance elastography. The first method jointly finds the displacement field that best fits tissue displacement data and the corresponding shear modulus. The displacement satisfies a viscoelastic wave equation constraint, discretized using the finite element method. Sparsifying regularization terms in both shear modulus and displacement are used in the cost function minimized for the best fit. The second method extends the first method for multifrequency tissue displacement data. The formulated problems are bi-convex. Their solution can be obtained iteratively by using the alternating direction method of multipliers. Sparsifying regularizations and the wave equation constraint filter out sensor noise and compressional waves. Our methods do not require bandpass filtering as a preprocessing step and converge fast irrespective of the initialization. We evaluate our new methods in multiple in silico and phantom experiments, with comparisons with existing methods, and we show improvements in contrast to noise and signal-to-noise ratios. Results from an in vivo liver imaging study show elastograms with mean elasticity comparable to other values reported in the literature.

Quantitative ultrasound (QUS) offers a non-invasive and objective way to quantify tissue health. We recently presented a spatially adaptive regularization method for reconstruction of a single QUS parameter, limited to a two dimensional region. That proof-of-concept study showed that regularization using homogeneity prior improves the fundamental precision-resolution trade-off in QUS estimation. Based on the weighted regularization scheme, we now present a multiparametric 3D weighted QUS (3D QUS) method, involving the reconstruction of three QUS parameters: attenuation coefficient estimate (ACE), integrated backscatter coefficient (IBC) and effective scatterer diameter (ESD). With the phantom studies, we demonstrate that our proposed method accurately reconstructs QUS parameters, resulting in high reconstruction contrast and therefore improved diagnostic utility. Additionally, the proposed method offers the ability to analyze the spatial distribution of QUS parameters in 3D, which allows for superior tissue characterization. We apply a three-dimensional total variation regularization method for the volumetric QUS reconstruction. The 3D regularization involving N planes results in a high QUS estimation precision, with an improvement of standard deviation over the theoretical 1/N rate achievable by compounding N independent realizations. In the in vivo liver study, we demonstrate the advantage of adopting a multiparametric approach over the single parametric counterpart, where a simple quadratic discriminant classifier using feature combination of three QUS parameters was able to attain a perfect classification performance to distinguish between normal and fatty liver cases.

Magnetic resonance elastography (MRE) is commonly regarded as the imaging-based gold-standard for liver fibrosis staging, comparable to biopsy. While ultrasound-based elastography methods for liver fibrosis staging have been developed, they are confined to a 1D or a 2D region of interest and to a limited depth. 3D Shear Wave Absolute Vibro-Elastography (S-WAVE) is a steady-state, external excitation, volumetric elastography technique that is similar to MRE, but has the additional advantage of multi-frequency excitation. We present a novel ultrasound matrix array implementation of S-WAVE that takes advantage of 3D imaging. We use a matrix array transducer to sample axial multi-frequency steady-state tissue motion over a volume, using a Color Power Angiography sequence. Tissue motion with the frequency components (40, 50,60) and (45, 55, 65) Hz are acquired over a (90° lateral)×(40° elevational)×(16 cm depth) sector with an acquisition time of 12 seconds. We compute the elasticity map in 3D using local spatial frequency estimation. We characterize this new approach in tissue phantoms against measurements obtained with transient-elastography and MRE. Six healthy volunteers and eight patients with chronic liver disease were imaged. Their MRE and S-WAVE volumes were aligned using T1 to B-mode registration for direct comparison in common regions of interest. S-WAVE and MRE results are correlated with R2= 0.92, while MRE and TE results are correlated with R2= 0.71. Our findings show that S-WAVE with matrix array has the potential to deliver a similar assessment of liver fibrosis as MRE in a more accessible, inexpensive way, to a broader set of patients.

This paper evaluates the feasibility of a novel optical sensing concept to measure forces applied at the tip of daVinci EndoWrist instruments. An optical slit is clamped onto the instrument shaft, in-line with an infrared LED-bicell pair. Deflection of the shaft moves the slit with respect to the LED-bicell pair and modulates the light incident on each active element of the bicell. The differential photocurrent is conditioned and monitored to estimate the tip forces. The feasibility evaluation consists of a flexible beam model to quantify the required sensor performance, experimental results with a 3D printed prototype and estimation of the sensor limitations including the measurement bandwidth due to the structural dynamics. The proposed approach requires no modifications to the instrument, is adaptable to different instruments and robot platforms, and leads to high-resolution, high-dynamic range sensing without hysteresis.

In quantitative elastography, maps of the mechanical properties of soft tissue, or elastograms, are calculated from the measured displacement data by solving an inverse problem. The model assumptions have a significant effect on elastograms. Motivated by the high sensitivity of imaging results to the model assumptions for in vivo magnetic resonance elastography of the prostate, we compared elastograms obtained with four different methods. Two finite-element method (FEM)-based methods developed by our group were compared with two other commonly used methods, local frequency estimator (LFE) and curl-based direct inversion (c-DI). All the methods assume a linear isotropic elastic model, but the methods vary in their assumptions, such as local homogeneity or incompressibility, and in the specific approach used. We report results using simulations, phantom, and ex vivo and in vivo data. The simulation and phantom studies show, for regions with an inclusion, that the contrast to noise ratio (CNR) for the FEM methods is about three to five times higher than the CNR for the LFE and c-DI and the rms error is about half. The LFE method produces very smooth results (i.e., low CNR) and is fast. c-DI is faster than the FEM methods but it is only accurate in areas where elasticity variations are small. The artifacts resulting from the homogeneity assumption in c-DI is detrimental in regions with large variations. The ex vivo and in vivo results also show similar trends as the simulation and phantom studies. The c-FEM method is more sensitive to noise compared with the mixed-FEM due to higher orders derivatives. This is especially evident at lower frequencies, where the wave curvature is smaller and it is more prone to such error, causing a discrepancy in the absolute values between the mixed-FEM and c-FEM in our in vivo results. In general, the proposed FEMs use fewer simplifying assumptions and outperform the other methods but they are computationally more expensive.

In elasticity imaging, the shear modulus is obtained from measured tissue displacement data by solving an inverse problem based on the wave equation describing the tissue motion. In most inversion approaches, the wave equation is simplified using local homogeneity and incompressibility assumptions. This causes a loss of accuracy and therefore imaging artifacts in the resulting elasticity images. In this paper we present a new curl-based finite element method inversion technique that does not rely upon these simplifying assumptions. As done in previous research, we use the curl operator to eliminate the dilatational term in the wave equation, but we do not make the assumption of local homogeneity. We evaluate our approach using simulation data from a virtual tissue phantom assuming time harmonic motion and linear, isotropic, elastic behavior of the tissue. We show that our reconstruction results are superior to those obtained using previous curl-based methods with homogeneity assumption. We also show that with our approach, in the 2-D case, multi-frequency measurements provide better results than single-frequency measurements. Experimental results from magnetic resonance elastography of a CIRS elastography phantom confirm our simulation results and further demonstrate, in a quantitative and repeatable manner, that our method is accurate and robust.

In this paper, a novel approach to the problem of elasticity reconstruction is introduced. In this approach, the solution of the wave equation is expanded as a sum of waves travelling in different directions sharing a common wave number. In particular, the solutions for the scalar and vector potentials which are related to the dilatational and shear components of the displacement respectively are expanded as sums of travelling waves. This solution is then used as a model and fitted to the measured displacements. The value of the shear wave number which yields the best fit is then used to find the elasticity at each spatial point. The main advantage of this method over direct inversion methods is that, instead of taking the derivatives of noisy measurement data, the derivatives are taken on the analytical model. This improves the results of the inversion. The dilatational and shear components of the displacement can also be computed as a byproduct of the method, without taking any derivatives. Experimental results show the effectiveness of this technique in magnetic resonance elastography. Comparisons are made with other state-of-the-art techniques.