We establish the feasibility of imaging the linear and nonlinear elastic properties of soft tissue using ultrasound. We report results for breast tissue where it is conjectured that these properties may be used to discern malignant tumors from benign tumors. We consider and compare three different quantities that describe nonlinear behavior, including the variation of strain distribution with overall strain, the variation of the secant modulus with overall applied strain and finally the distribution of the nonlinear parameter in a fully nonlinear hyperelastic model of the breast tissue.

We reconstruct the in vivo spatial distribution of linear and nonlinear elastic parameters in ten patients with benign (five) and malignant (five) tumors. The mechanical behavior of breast tissue is represented by a modified Veronda–Westmann model with one linear and one nonlinear elastic parameter. The spatial distribution of these elastic parameters is determined by solving an inverse problem within the region of interest (ROI). This inverse problem solution requires the knowledge of the displacement fields at small and large strains. The displacement fields are measured using a free-hand ultrasound strain imaging technique wherein, a linear array ultrasound transducer is positioned on the breast and radio frequency echo signals are recorded within the ROI while the tissue is slowly deformed with the transducer. Incremental displacement fields are determined from successive radio-frequency frames by employing cross-correlation techniques. The rectangular regions of interest were subjectively selected to obtain low noise displacement estimates and therefore were variables that ranged from 346 to 849.6 mm2. It is observed that malignant tumors stiffen at a faster rate than benign tumors and based on this criterion nine out of ten tumors were correctly classified as being either benign or malignant.

We have recently developed and tested an efficient algorithm for solving the nonlinear inverse elasticity problem for a compressible hyperelastic material. The data for this problem are the quasi-static deformation fields within the solid measured at two distinct overall strain levels. The main ingredients of our algorithm are a gradient based quasi-Newton minimization strategy, the use of adjoint equations and a novel strategy for continuation in the material parameters. In this paper we present several extensions to this algorithm. First, we extend it to incompressible media thereby extending its applicability to tissues which are nearly incompressible under slow deformation. We achieve this by solving the forward problem using a residual-based, stabilized, mixed finite element formulation which circumvents the Ladyzenskaya–Babuska–Brezzi condition. Second, we demonstrate how the recovery of the spatial distribution of the nonlinear parameter can be improved either by preconditioning the system of equations for the material parameters, or by splitting the problem into two distinct steps. Finally, we present a new strain energy density function with an exponential stress-strain behavior that yields a deviatoric stress tensor, thereby simplifying the interpretation of pressure when compared with other exponential functions. We test the overall approach by solving for the spatial distribution of material parameters from noisy, synthetic deformation fields.

Altered blood flow during embryonic development has been shown to cause cardiac defects; however, the mechanisms by which the resulting haemodynamic forces trigger heart malformation are unclear. This study used heart outflow tract banding to alter normal haemodynamics in a chick embryo model at HH18 and characterized the immediate blood flow response versus the degree of band tightness. Optical coherence tomography was used to acquire two-dimensional longitudinal structure and Doppler velocity images from control (n ¼ 16) and banded (n ¼ 25, 6-64% measured band tightness) embryos, from which structural and velocity data were extracted to estimate haemodynamic measures. Peak blood flow velocity and wall shear rate (WSR) initially increased linearly with band tightness ( p , 0.01), but then velocity plateaued between 40% and 50% band tightness and started to decrease with constriction greater than 50%, whereas WSR continued to increase up to 60% constriction before it began decreasing with increased band tightness. Time of flow decreased with constriction greater than 20% ( p , 0.01), while stroke volume in banded embryos remained comparable to control levels over the entire range of constriction ( p . 0.1). The haemodynamic dependence on the degree of banding reveals immediate adaptations of the early embryonic cardiovascular system and could help elucidate a range of cardiac adaptations to gradually increased load.

Hemodynamic conditions play a critical role in embryonic cardiovascular development, and altered blood flow leads to congenital heart defects. Chicken embryos are frequently used as models of cardiac development, with abnormal blood flow achieved through surgical interventions such as outflow tract (OFT) banding, in which a suture is tightened around the heart OFT to restrict blood flow. Banding in embryos increases blood pressure and alters blood flow dynamics, leading to cardiac malformations similar to those seen in human congenital heart disease. In studying these hemodynamic changes, synchronization of data to the cardiac cycle is challenging, and alterations in the timing of cardiovascular events after interventions are frequently lost. To overcome this difficulty, we used ECG signals from chicken embryos (Hamburger-Hamilton stage 18, ∼3 days of incubation) to synchronize blood pressure measurements and optical coherence tomography images. Our results revealed that, after 2 h of banding, blood pressure and pulse wave propagation strongly depend on band tightness. In particular, while pulse transit time in the heart OFT of control embryos is ∼10% of the cardiac cycle, after banding (35% to 50% band tightness) it becomes negligible, indicating a faster OFT pulse wave velocity. Pulse wave propagation in the circulation is likewise affected; however, pulse transit time between the ventricle and dorsal aorta (at the level of the heart) is unchanged, suggesting an overall preservation of cardiovascular function. Changes in cardiac pressure wave propagation are likely contributing to the extent of cardiac malformations observed in banded hearts.