Reconstructing 3-D maps of the local viscoelastic properties using a finite-amplitude modulated radiation force

A modulated acoustic radiation force, produced by two confocal tone-burst ultrasound beams of slightly different frequencies (i.e. 2.0 MHz ± Δf/2, where Δf is the difference frequency), can be used to remotely generate modulated low-frequency (Δf ? 500 Hz) shear waves in attenuating media. By appropriately selecting the duration of the two beams, the energy of the generated shear waves can be concentrated around the difference frequency (i.e., Δf ± Δf/2). In this manner, neither their amplitude nor their phase information is distorted by frequency-dependent effects, thereby, enabling a more accurate reconstruction of the viscoelastic properties. Assuming a Voigt viscoelastic model, this paper describes the use of a finite-element-method model to simulate three-dimensional (3-D) shear-wave propagation in viscoelastic media containing a spherical inclusion. Nonlinear propagation is assumed for the two ultrasound beams, so that higher harmonics are developed in the force and shear spectrum. Finally, an inverse reconstruction algorithm is used to extract 3-D maps of the local shear modulus and viscosity from the simulated shear-displacement fields based on the fundamental and second-harmonic component. The quality of the reconstructed maps is evaluated using the contrast between the inclusion and the background and the contrast-to-noise ratio (CNR). It is shown that the shear modulus can be accurately reconstructed based on the fundamental component, such that the observed contrast deviates from the true contrast by a root-mean-square-error (RMSE) of only 0.38 and the CNR is greater than 30 dB. If the second-harmonic component is used, the RMSE becomes 1.54 and the corresponding CNR decreases by approximately 10–15 dB. The reconstructed shear viscosity maps based on the second harmonic are shown to be of higher quality than those based on the fundamental. The effects of noise are also investigated and a fusion operation between the two spectral components is applied to enhance the reconstruction quality. Finally, a modified shear-wave spectroscopy technique, shown to be more robust to noise, is described for the estimation of the viscoelastic properties inside and outside the spherical inclusion under conditions of increased noise.     

Accessing lanthanide-based,in situ illuminated optical turn-on probes by modulation of the antenna triplet state energy

Luminescent lanthanides possess ideal properties for biological imaging, including long luminescent lifetimes and emission within the optical window. Here, we report a novel approach to responsive luminescent Tb(iii) probes that involves direct modulation of the antenna excited triplet state energy. If the triplet energy lies too close to the ⁵D₄ Tb(iii) excited state (20 500 cm⁻¹), energy transfer to ⁵D₄ competes with back energy transfer processes and limits lanthanide-based emission. To validate this approach, a series of pyridyl-functionalized, macrocyclic lanthanide complexes were designed, and the corresponding lowest energy triplet states were calculated using density functional theory (DFT). Subsequently, three novel constructs L3 (nitro-pyridyl), L4 (amino-pyridyl) and L5 (fluoro-pyridyl) were synthesized. Photophysical characterization of the corresponding Gd(iii) complexes revealed antenna triplet energies between 25 800 and 30 400 cm⁻¹ and a 500-fold increase in quantum yield upon conversion of Tb(L3) to Tb(L4) using the biologically relevant analyte H₂S. The corresponding turn-on reaction can be monitored using conventional, small-animal optical imaging equipment in presence of a Cherenkov radiation emitting isotope as an in situ excitation source, demonstrating that antenna triplet state energy modulation represents a viable approach to biocompatible, Tb-based optical turn-on probes.

The rational, analyte-mediated modulation of the relative energy of the lanthanide-sensitizing triplet state produces Tb-based luminescence, observable by a conventional optical imager in presence of the Cherenkov radiation emitting radioisotope ¹⁸F.     

Improved Bounds on the Dimensions of Sets that Avoid Approximate Arithmetic Progressions

Journal of Fourier Analysis and Applications - In this paper we construct a wavelet basis in $$L^{2}({\mathbb {R}}^{n};\mu )$$ possessing vanishing moments of a fixed order for a general locally...