Solution of the nonlinear elasticity imaging inverse problem: The incompressible case

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.     

Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis

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.     

Equilibrium distributions of key components of spearmint oil in sub/supercritical carbon dioxide

Effects of temperature (at 35, 45 or 55°C) and pressure (10–110 atm) on the relative distribution coefficients of the twelve key components of spearmint oil (essential oil ofMentha cardiaca; Scotch spearmint) at equilibrium in dense CO₂ were investigated under conditions ranging from subcritical to supercritical regions. Effects of vapor pressure, molecular weight and polarity of the key components on their equilibrium distributions in sub/supercritical CO₂ are discussed. At 35°C, all key components of spearmint oil are equally soluble in dense CO₂ within the 12–102 atm pressure region. At 45 and 55°C, the key components are equally soluble for pressures greater than about 60 atm. However, around either 45°C/27 atm or 55°C/35 atm conditions, the relative distribution coefficients of all monoterpene hydrocarbons and of isomenthone (an oxygenated monoterpene) exhibit maxima, which are due to significantly higher vapor pressures of these components and significantly lower solvating power of the dense-gas solvent at these particular temperatures and pressures. Vapor-pressure effects, coupled with the decrease in solvating power, dominate the effects of polarity and molecular mass of the key components. Deterpenation of spearmint oil with dense CO₂ is possible around either 45°C/27 atm or 55°C/35 atm, where the monoterpene hydrocarbons tend to concentrate in the CO₂-rich phase.     

Blood flow dynamics reflect degree of outflow tract banding in Hamburger–Hamilton stage 18 chicken embryos

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 = 16) and banded (n = 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.     

Supercritical carbon dioxide extraction of spearmint oil from mint-plant leaves

Spearmint oil (essential oil of Mentha spicata) was extracted from Turkish mint-plant leaves using supercritical CO₂ in a basket-type extractor. Effects of temperature, pressure, extraction time, amount of CO₂, and entrainer (ethanol) concentration on composition of essential-oil extracts and oil yield, relative to hydro-distillation, were investigated. Relative yields were as high as 80%. Monoterpenes fraction in extracts was inversely correlated with relative oil yields. Monoterpenes were preferentially extracted by CO₂ due to their high vapor pressure, low molar mass and low polarity. Supercritical extraction presented advantages over the conventional hydro-distillation by yielding extracts lower in monoterpenes fraction and by enabling high yields at temperatures safe for the heat-sensitive essential oil.     

Diagnostic ultrasound tooth imaging using fractional Fourier transform

An ultrasound contact imaging method is proposed to measure the enamel thickness in the human tooth. A delay-line transducer with a working frequency of 15 MHz is chosen to achieve a minimum resolvable distance of 400 μm in human enamel. To confirm the contact between the tooth and the transducer, a verification technique based on the phase shift upon reflection is used. Because of the high attenuation in human teeth, linear frequency-modulated chirp excitation and pulse compression are exploited to increase the penetration depth and improve the SNR. Preliminary measurements show that the enamel-dentin boundary creates numerous internal reflections, which cause the applied chirp signals to interfere arbitrarily. In this work, the fractional Fourier transform (FrFT) is employed for the first time in dental imaging to separate chirp signals overlapping in both time and frequency domains. The overlapped chirps are compressed using the FrFT and matched filter techniques. Micro-computed tomography is used for validation of the ultrasound measurements for both techniques. For a human molar, the thickness of the enamel layer is measured with an average error of 5.5% after compressing with the FrFT and 13.4% after compressing with the matched filter based on the average speed of sound in human teeth.     

Peculiarities of establishment of steady-state frontal polymerization of vinyl monomers

Frontal radical polymerization of vinyl monomers in non-stationary mode is investigated theoretically. It is shown that the formation and the time of establishment of steady-state polymerization heat autowaves considerably depend on the initial temperature, T_i. When T_i is less than the adiabatic heating temperature (T_a), the excess heat and relatively high conversion foster front formation before the non-stationary one. Whereas, for T_i > T_a, steady-state frontal polymerization regime is established, when the heat flow from the outer source is considerably less than the heat evolving due to the chemical reaction.     

Conversion of propylene into cyclohexane on PtGaZr/SiO2 catalyst

The light olefins present in Delay Coker and fluid catalytic cracker dry gas can be valorized into naphthenes using a new PtGaZr/SiO₂ catalyst. This catalyst was compared to a GaZrSiO₂ catalyst prepared with the same methodology. Both were characterized by XRD, and FTIR, XPS, ⁷¹Ga, ²⁹Si and ¹H NMR spectroscopies. Propylene is treated in the presence of CS₂, hydrogen, and benzene in a semi-batch type reactor and the product composition is analyzed by GC and MS techniques. The different operating variables were explored to study the effect of Pt on activity, selectivity and catalyst stability. The spent catalysts after 10 cycles in operation were analyzed using ¹³C NMR, ¹H NMR, IR, and XPS spectroscopies. The paper discusses the catalytic surface composition, the effect of temperature, contact time, hydrogen partial pressure and benzene in the feed. The study demonstrated that the effect of Pt, hydrogen and benzene is crucial to orient the reaction toward naphthenes production.     

Achieving zT > 1 in Inexpensive Zintl Phase Ca9Zn4+xSb9 by Phase Boundary Mapping

Complex multinary compounds (ternary, quaternary, and higher) offer countless opportunities for discovering new semiconductors for applications such as photovoltaics and thermoelectrics. However, controlling doping has been a major challenge in complex semiconductors as there are many possibilities for charged intrinsic defects (e.g., vacancies, interstitials, antisite defects) whose energy depends on competing impurity phases. Even in compounds with no apparent deviation from a stoichiometric nominal composition, such defects commonly lead to free carrier concentrations in excess of 10²⁰ cm^?3. Nevertheless, by slightly altering the nominal composition, these defect concentrations can be tuned with small variation of the chemical potentials (composition) of each element. While the variation of chemical composition is undetectable, it is shown that the changes can be inferred by mapping (in nominal composition space) the boundaries where different competing impurity phases form. In the inexpensive Zintl compound Ca₉Zn_4+x Sb₉, the carrier concentrations can be finely tuned within three different three‐phase regions by altering the nominal composition (x = 0.2–0.8), enabling the doubling of thermoelectric performance (zT). Because of the low thermal conductivity, the zT can reach as high as 1.1 at 875 K, which is one of the highest among the earth abundant p‐type thermoelectrics with no ion conducting.