Dynamic X-ray elastography using a pulsed photocathode source

X-ray absorption of breast cancers and surrounding healthy tissue can be very similar, a situation that sometimes leads to missed cancers or false-positive diagnoses. To increase the accuracy of mammography and breast tomosynthesis, we describe dynamic X-ray elastography using a novel pulsed X-ray source. This new imaging modality provides both absorption and mechanical properties of the imaged material. We use a small acoustic speaker to vibrate the sample while a synchronously pulsed cold cathode X-ray source images the mechanical deformation. Using these stroboscopic images, we derive two-dimensional stiffness maps of the sample in addition to the conventional X-ray image. In a breast phantom composed of ZrO2 powder embedded in gel, dynamic elastography derived stiffness maps were able to discriminate a hard inclusion from surrounding material with a contrast-to-noise ratio (CNR) of 4.5. The CNR on the corresponding absorption image was 1.1. This demonstrates the feasibility of dynamic X-ray elastography with a synchronously pulsed X-ray source.

Deformating of a viscoelastic disk rotating with acceleration

Рассматривается деформирование вязкоупругого диска, вращающегося с изменяющейся скоростью (разгон, торможение и вращение с постоянной скоростью). Для математического моделирования процесса деформирования используется теория течения. При предположении плоского напряженного состояния получена система дифференциальных уравнений для определения полей напряжений, обратимых и необратимых деформаций и перемещений. Численное решение этой системы уравнений найдено с помощью конечно-разностного метода. В случае решения осесимметричной задачи используется метод конечных элементов, реализованный в пакете Freefem++. Рассмотрено деформирование полого диска и диска с жестким включением, как постоянной толщины, так и переменной. The deformation of a viscoelastic disk rotating with a changing speed is considered. Within the framework of the theory of flow, relations are obtained that allow one to calculate the fields of stresses, strains, displacements, and velocities. To solve these equations in the case of a plane stress state, the finite-difference method is used, in the case of an axisymmetric problem, the finite element method implemented in the Freefem ++ package is used. Acceleration, braking and rotation at a constant speed are considered. The deformation of a hollow disk and a disk with a hard inclusion of both a constant thickness and a variable is considered.

Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

An equilibrium problem of the Kirchhoff–Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing the width of the inclusion ε as εN with N<1. The passage to the limit as the parameter ε tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion (N<−1) and elastic inclusion (N=−1). The inhomogeneity disappears in the case of N∈(−1,1).

Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

An equilibrium problem of the Kirchhoff-Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing width of the inclusion $\varepsilon$ as $\varepsilon^N$ with $N&lt;1$. The passage to the limit as the parameter $\varepsilon$ tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion ($N&lt;-1$) and elastic inclusion ($N=-1$). The inhomogeneity disappears in the case of $N\in (-1,1)$.

On the Effects of Constitutive Properties and Roughness of a Hard Inclusion in Soft Tissue on B-mode Images

We perform finite element modeling of pulse-echo ultrasound of a hard inclusion in a soft tissue to gain a better understanding of B-mode image brightness characteristics. We simulate a pressure wave emitted by an ultrasound transducer through the inclusion-tissue medium by prescribing suitable boundary conditions, and collect the scattered wave response to simulate the behavior of the transducer array used for pulse-echo ultrasound. We form B-mode images from simulated channel data using standard delay and sum beamforming. We establish the accuracy of the finite element model by comparing the point spread function with that obtained from Field II ultrasound simulation program. We also demonstrate qualitative validation by comparing the brightness characteristics of rough and smooth surfaced circular inclusions with experimental images of a cylindrical metal tool immersed in a water tank. We next conduct simulation studies to evaluate changes in B-mode image brightness intensity and contrast related to different constitutive properties, namely, compressibility of the inclusion, impedance contrast between the host and inclusion, and surface roughness of the inclusion. We find that the intensity observed behind a hard inclusion in the axial direction is strongly affected by the compressibility and roughness of the inclusion. Also, the perceived width of the stone based on the intensity is greater for rougher stones. Our study indicates that imaging of compressible inclusions may benefit from targeted B-mode image forming algorithms. Our modeling framework can potentially be useful in differentiating hard inclusions from surrounding parenchyma, and for classifying kidney stones or gallstones.

A Preliminary Two-Dimensional Palpation Mechanics for Detecting a Hard Inclusion by Indentation of a Soft Matrix Under Large Strain

A rigid inclusion is embedded at a finite depth in a soft layer resting on a rigid substrate. A spherical indenter presses vertically onto the surface, deforming the matrix and displacing the inclusion. A subsurface inclusion initially near the indentation axis moves primarily downward, until an unstable lateral jump occurs to minimize the energy stored in the elastic medium. Such an instability is unique to soft materials undergoing large deformation. A two-dimensional plane-strain finite element analysis is used to simulate the 3D phenomenon.

Formation Mechanism of Voids around Hard Inclusion during Hot Rolling Processes

To investigate the mechanism by which voids form around hard inclusions, the deformations of a plastic slab with hard and soft inclusions that form inside it during the hot rolling process have been simulated with a finite element method. By comparing plastic strain distributions, the relative displacements of contact surfaces, and the deformations between hard and soft inclusions have preceded analysis of the formation mechanism of these voids. The variations of strain measurements between the matrix and hard inclusions cause relative displacement of their contact surfaces. Therefore, voids occur at the front and rear of the hard inclusions. Trials on the slab deformations using a titanium ball instead of the soft inclusion inside the slab during the hot rolling process are conducted. The simulated shapes of the soft inclusions with different reductions mostly agree with the experimental results.