Ultrasound frame rate requirements for cardiac elastography: experimental and in vivo results

Cardiac elastography using radiofrequency echo signals can provide improved 2D strain information compared to B-mode image data, provided data are acquired at sufficient frame rates. In this paper, we evaluate ultrasound frame rate requirements for unbiased and robust estimation of tissue displacements and strain. Both tissue-mimicking phantoms under cyclic compressions at rates that mimic the contractions of the heart and in vivo results are presented. Sinusoidal compressions were applied to the phantom at frequencies ranging from 0.5 to 3.5 cycles/sec, with a maximum deformation of 5% of the phantom height. Local displacements and strains were estimated using both a two-step one-dimensional and hybrid two-dimensional cross-correlation method. Accuracy and repeatability of local strains were assessed as a function of the ultrasound frame rate based on signal-to-noise ratio values.The maximum signal-to-noise ratio obtained in a uniformly elastic phantom is 20 dB for both a 1.26 Hz and a 2 Hz compression frequency when the radiofrequency echo acquisition is at least 12 Hz and 20 Hz respectively. However, for compression frequencies of 2.8 Hz and 4 Hz the maximum signal-to-noise ratio obtained is around 16 dB even for a 40 Hz frame rate. Our results indicate that unbiased estimation of displacements and strain require ultrasound frame rates greater than ten times the compression frequency, although a frame rate of about two times the compression frequency is sufficient to estimate the compression frequency imparted to the tissue-mimicking phantom. In vivo results derived from short-axis views of the heart acquired from normal human volunteers also demonstrate this frame rate requirement for elastography.     

Ground-state constants, ab initio anharmonic force field, and equilibrium structure of F2BOH

The millimeterwave spectra of F₂¹⁰BOH and F₂¹¹BOH (difluorohydroxyborane) have been measured in their ground vibrational state. Accurate rotational and centrifugal distortion constants have been determined. The equilibrium geometry and anharmonic force fields have been calculated at the CCSD(T) level of theory. The ab initio centrifugal distortion constants and rotation-vibration interaction constants are compared to the experimental values. Some discrepancies are found and discussed. Particularly, it is explained why the semi-experimental structure is not reliable. The best equilibrium structure is: r_e(BF_cis) = 132.29 pm, r_e(BF_trans) = 131.29 pm, r_e(BO) = 134.48 pm, r_e(OH) = 95.74 pm, ∠_e(FBF) = 118.36°, ∠_e(F_cisBO) = 122.25°, and ∠_e(BOH) = 113.14°.     

Fourier transform emission spectroscopy of the EΠ-XΣ transition of CaH and CaD

The emission spectra of CaH and CaD have been recorded at high resolution using a Fourier transform spectrometer and bands belonging to the E²Π-X²Σ⁺ transition have been measured in the 20 100-20 700 cm⁻¹ region. A rotational analysis of 0-0 and 1-1 bands of both the isotopologues has been carried out. The present measurements have been combined with the previously available pure rotation and vibration-rotation data to provide improved spectroscopic constants for the E²Π state. The constants ΔG(½) = 1199.8867(34) cm⁻¹, B_e = 4.345032(49) cm⁻¹, α_e = 0.122115(92) cm⁻¹, r_e = 1.986633(11) Å for CaH, and ΔG(½)=868.7438(46) cm⁻¹, B_e = 2.212496(51) cm⁻¹, α_e = 0.036509(97) cm⁻¹, r_e = 1.993396(23) Å for CaD have been determined.     

Submillimeter-wave spectroscopy of HN2 and DN2 in the excited vibrational states

The pure rotational transitions of HN₂⁺ and DN₂⁺ in the first excited vibrational states for all the fundamental vibrational modes have been observed in the range of 300-750 GHz. The molecular constants determined are much more accurate compared with those obtained from the infrared spectroscopy. The equilibrium rotational constants, B_e = 46832.45 (71) MHz for HN₂⁺ and B_e = 38708.38 (58) MHz for DN₂⁺, have been determined by correcting for the higher-order vibration-rotation interaction effects, γ_ij, obtained by an infrared investigation. The equilibrium bond lengths are derived from these equilibrium rotational constants: r_e(H-N) = 1.03460 (14) Å and r_e (N-N) = 1.092698 (26) Å.     

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.     

Thermally stimulated current study of electron-irradiation induced defects in semi-insulating InP obtained by multiple-step wafer annealing

Electron-irradiation induced defects in semi-insulating (SI) InP wafers with Fe concentration ranging from 1.5×10¹⁵ to 2.5×10¹⁵ cm⁻³, which have been obtained by multiple-step wafer annealing (MWA) under phosphorus vapor pressure, were studied using a thermally stimulated current (TSC) method. New traps, e₁, e₂, e₃, e₄ and e₅, with activation energies of 0.22, 0.28, 0.37, 0.44 and 0.46 eV, respectively, were observed. Based upon the annealing behavior of traps and the calculated defect levels, traps e₁ and e₅ produced by the irradiation with electron doses above 1×10¹⁵ cm⁻² were linked to In_P and P_In antisite defects, respectively, that probably form complexes. Traps e₃ and e₄ produced by the irradiation with doses above 1×10¹⁴ cm⁻² were associated with In and P vacancy related defects, respectively.     

Er-Yb co-doped glass waveguide amplifiers using ion exchange and field-assisted annealing

Er³⁺-Yb³⁺ co-doped waveguide amplifiers fabricated using thermal two-step ion-exchange are demonstrated. K⁺-Na⁺ ion-exchange process was first carried out in pure KNO₃ molten bath, and then field-assisted annealing (FAA) was used to make the buried waveguides. The effective buried depth is estimated to be ∼3.4 μm for the buried FAA waveguides. With the use of cut-back method, the fiber-to-guide coupling loss of ∼4.38 dB, the waveguide loss of ∼2.27 dB/cm, and Er³⁺ absorption loss ∼5.7 dB were measured for a ∼1.24-cm-long waveguide. Peak relative gain of ∼7.0 dB is obtained for a ∼1.24-cm-long waveguide. The potential for the fabrication of compact optical amplifiers operating in the range of 1520-1580 nm is also demonstrated.     

Infrared emission studies of the AΣ-XΠ electronic transition of the SiC radical

The gas phase infrared emission spectrum of the A³Σ⁻-X³Π electronic transition of SiC has been observed using a high resolution Fourier transform spectrometer. Three bands ν′ − ν″ = 0-1, 0-0, and 1-0 have been observed in the 2770, 3723, and 4578 cm⁻¹ regions, where the 0-1 and 0-0 bands were observed for the first time. The SiC radical was generated by a dc discharge in a flowing mixture of hexamethyl disilane [(CH₃)₆Si₂] and He. A total of 1074 rotational transitions assigned to the 0-1, 0-0, and 1-0 bands have been combined in a simultaneous analysis with previously reported pure rotational data to determine the molecular constants for SiC in the two electronic states. The principal equilibrium molecular constants for the A³Σ⁻ state are: B_e = 0.6181195(18) cm⁻¹, α_e = 0.0051921(20) cm⁻¹, r_e = 1.8020884(26) Å, and T_e = 3773.31(17) cm⁻¹, with one standard deviation given in parentheses. The effect of a perturbation was recognized between the ν = 4 level of X³Π and the ν = 0 level of A³Σ, and the analysis was carried out to determine the interaction parameter between the two states.     

Subharmonic aided pressure estimation for monitoring interstitial fluid pressure in tumours – In vitro and in vivo proof of concept

The feasibility of using subharmonic aided pressure estimation (SHAPE) to noninvasively estimate interstitial fluid pressure (IFP) was studied. In vitro, radiofrequency signals, from 0.2 ml/l of Definity (Lantheus Medical Imaging, N Billerica, MA) were acquired within a water-tank with a Sonix RP ultrasound scanner (Analogic Ultrasound, Richmond, BC, Canada; f_T/R = 6.7/3.35 MHz and f_T/R = 10/5 MHz) and the subharmonic amplitudes of the signals were compared over 0–50 mmHg. In vivo, five swine with naturally occurring melanomas were studied. Subharmonic signals were acquired from tumours and surrounding tissue during infusion of Definity and compared to needle-based pressure measurements. Both in vitro and in vivo, an inverse linear relationship between hydrostatic pressure and subharmonic amplitude was observed with r² = 0.63–0.95; p < 0.05, maximum amplitude drop 11.36 dB at 10 MHz and −8 dB, and r² as high as 0.97; p < 0.02 (10 MHz and −4/−8 dB most promising), respectively, indicating that SHAPE may be useful in monitoring IFP.     

Fourier transform infrared emission spectra of MnH and MnD

Fourier transform infrared emission spectra of MnH and MnD were observed in the ground X⁷Σ⁺ electronic state. The vibration-rotation bands from v = 1 → 0 to v = 3 → 2 for MnH and from v = 1 → 0 to v = 4 → 3 for MnD were recorded at an instrumental resolution of 0.0085 cm⁻¹. Spectroscopic constants were determined for each vibrational level and equilibrium constants were found from a Dunham-type fit. The equilibrium vibrational constant (ω_e) for MnH was found to be 1546.84518(65) cm⁻¹, the equilibrium rotational constant (B_e) is 5.6856789(103) cm⁻¹ and the eqilibrium bond distance (r_e) was determined to be 1.7308601(47) Å.     

Observation of nonstationary effects in saturation spectroscopy

We have studied the nonstationary effects in saturated absorption spectroscopy of the ⁸⁷Rb D₂ line. Varying the size of the σ⁺ polarized pump laser beam, we observed saturated absorption spectra for the σ^± polarized probe beam. For equal polarizations of the pump and probe beams, we found that the resonance signal for the F_g = 1 → F_e = 2 line, and the crossover lines between F_g = 1 → F_e = 2 and F_g = 1 → F_e = 1 (and 0) lines increased to a greater extent than the others. This observation can be understood from the calculated time evolution of the populations of the ground-state sublevels by means of a rate equation model. We also compared experimental data for other conditions with the calculated results. We found good agreement between the calculated results and the data.     

Simulative analysis of pre- and post-compensation using CRZ format in WDM optical transmission link

This paper reports the effects of pre- and post-compensation using CRZ modulation format in long-haul WDM optical transmission link using wavelengths in three bandwidths viz. 1537.4; 1550; 1562.6 nm at per channel bit rates of 10 Gbit/s. It has been investigated here that optimization of dispersion map results in improved management of nonlinear effects in long-haul light wave systems operating in the quasi-linear regime. In addition, pre- and post-dispersion compensation was applied at the transmitter and receiver depending on the signal wavelength, which resulted in improvement of performance metrics viz. Q² (dB), BER and OSNR over longer transmission distances. It is reported here that optimum values of Q² dB of 17.1 dB, BER of 8.4933e⁻⁰¹⁵ and OSNR of 30.1 dB are obtained at 1550 nm at a transmission distance of 7360 km with pre- and post-compensation using CRZ modulation format.     

Large amplitude bending motion in CsOH, studied through ab initio-based three-dimensional potential energy functions

The large-amplitude bending motion in CsOH, a ‘classical’ molecule whose microwave spectrum was first recorded in 1967, has been studied ab initio. The three-dimensional potential energy surface has been calculated at the RCCSD(T)_DK3/[QZP + g ANO-RCC (Cs, O, H)] level of theory and employed in MORBID calculations of the rotation-vibration energies and intensities. The ground electronic state is ¹Σ⁺ with the equilibrium structure r_e(Cs-O) = 2.3930 Å, r_e(O-H) = 0.9587 Å, and ∠_e(Cs-O-H) = 180.0°. The O-H moiety is bound to Cs by an ionic bond and the molecule can be described as Cs^δ+(OH)^δ-. Hence, the bending potential is shallow and gives rise to large-amplitude bending motion. The ro-vibrationally averaged structural parameters, determined as expectation values over MORBID wavefunctions, are 〈r(Cs-O)〉₀ = 2.3987 Å, 〈r(O-H)〉₀ = 0.9754 Å, and 〈∠(Cs-O-H)〉₀ = 163°. Although the averaged structure in the vibrational ground state is far from being linear, the Yamada-Winnewissi-linearity parameter for CsOH is γ₀≈-1.0, the value characteristic for a linear molecule.     

Tetragonal distortion of InAsPSb film grown on InAs substrate studied by Rutherford backscattering/channeling and synchrotron X-ray diffraction

Rutherford backscattering/channeling spectrometry and synchrotron X-ray diffraction are employed to characterize the structural properties of the InAsPSb epilayer grown on the InAs substrate. The results indicate that a 975-nm thick InAs_0.668P_0.219Sb_0.113 layer has a quite good crystalline quality (χ_min=6.1%). The channeling angular scan around an off-normal 〈1 1 1〉 axis in the (0 1? 1) plane of the sample is used to determine the tetragonal distortion e_T, which is caused by elastic strain in the layer. The results show that the InAsPSb layer is subjected to an elastic strain at the interfacial layer, and the strain decreases gradually moving towards the near-surface layer. It is expected that an epitaxial InAsPSb layer with the thickness of around 1700 nm will be fully relaxed (e_T=0). The magnitude difference of e_T deduced from angular scans and X-ray diffraction implies some structure (like dislocations) may play a role.     

Theoretical investigation of the intrinsic piezoelectric properties for tetragonal BaTiO3 epitaxial films

The orientation dependences of the converse longitudinal piezoelectric constant d_33,f, and the in-plane converse piezoelectric constant e_31,f, are calculated for tetragonal barium titanate epitaxial films. The calculations demonstrate that both e_31,f and d_33,f have their maximum values along an axis close to the (1 1 1) direction of the pseudo-cubic system, which are similar to the orientation dependence results for a tetragonal BaTiO₃ single crystal. The calculated piezoelectric constants for a (1 1 1) oriented BaTiO₃ epitaxial film (e_31,f = −23 C/m², d_33,f = 124 pm/V) suggest that it is a good candidate material for lead-free MEMS applications.     

The analysis of combination and overtone states of BF3 from 1650 to 4600 cm

High-resolution (0.0015-0.0035 cm⁻¹) infrared spectra of isotopically enriched ¹¹BF₃ have been examined in detail. The analysis of the combination and overtone states within the region of study, from 1650 to 4600 cm⁻¹, led to the assignment of over 25,000 transitions. The major perturbations were due to the Fermi resonances between states possessing one quantum of v₃ and three quanta of v₄. With corrections through the quadratic rotational terms, the equilibrium B_e and C_e values have been determined; 0.3462679(7) cm⁻¹ and 0.1731151(6) cm⁻¹, respectively. An improved set of equilibrium rotational constants for ¹⁰BF₃, consistent with this analysis of ¹¹BF₃ are also given. The averaged equilibrium values for both isotopomers lead to a B-F bond distance of r_e = 130.704 ± 0.005 pm. All of the quadratic anharmonic constants, with the exception of x³³ were independently determined from experiment. For the first time for BF₃, a normal force field analysis was performed that utilized the experimentally determined, fundamental harmonic vibrational frequencies.     

Mean work functions effective for negative-ionic, electronic and positive-ionic emissions from polycrystalline surfaces

To elucidate the thermionic property of polycrystalline surfaces, a further study is made on the mean work functions (φ⁻, φ^e and φ⁺) effective for negative-ionic, electronic and positive-ionic emissions. Comparison between theoretical analyses and experimental data yields the conclusions as follows. (1) The equation of φ⁻ = φ^e holds always with both mono- and polycrystalline surfaces. (2) The relation of φ⁻ = φ^e < φ⁺ applies to polycrystalline surfaces because they bear the thermionic contrast (Δφ^* ≡ φ⁺ − φ^e > 0). (3) The value of Δφ^* ranges from ∼0.4 to 0.9 eV depending upon the surface species of polycrystalline metals (e.g., W, Re and Pt), whilst Δφ^* = 0 for monocrystalline surfaces. (4) When the degree of monocrystallization (δ_m) is less than ∼50%, the theoretical value of Δφ^* is virtually independent of δ_m and agrees well with experimental data, nearly the same within ±0.1 eV among the so-called “polycrystalline” surfaces of W. (5) As δ_m increases beyond ∼80 up to 100%, Δφ^* decreases rapidly down to 0 eV, showing again a good agreement between theory and experiment. (6) Our theoretical model is valid in evaluating the effective mean work functions, irrespective of the range of δ_m.     

Rotational spectra of isotopic species of SO2F2: experimental and ab initio structures

The rotational spectra of ³⁴SO₂F₂ and S¹⁸O¹⁶OF₂ have been measured in their ground vibrational state between 9 and 110 GHz. Accurate rotational constants have been derived. Various experimental structures including the average structure have been determined. The ab initio structure has been calculated at the CCSD(T) level of theory. The different structures are compared and the best equilibrium structure is the ab initio structure: r_e(SO)=1.401 (3) Å, r_e(SF)=1.532 (3) Å, ∠_e(OSO)=124.91(20)°, ∠_e(FSF)=95.53 (20)°.     

A theoretical study of FeNC in the Δ electronic ground state

We report an ab initio calculation, at the MR-SDCI + Q + E_rel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] level of theory, of the potential energy surface for ⁶Δ_i FeNC. From the ab initio results, we have computed values for the standard spectroscopic parameters of FeN¹²C and FeN¹³C. Analytical representations of the potential energy surfaces have been fitted through the ab initio points, and the resulting functions have been used for directly solving the rotation-vibration Schrödinger equation by means of the MORBID program and by means of an adiabatic-separation method. For ⁶Δ_i FeNC, our ab initio calculations show that the equilibrium structure is linear with r_e (Fe-N) = 1.9354 Å and r_e (N-C) = 1.1823 Å. We find that the bending potential is very shallow, and the MORBID calculations show that the zero-point averaged structure is bent with the expectation values 〈r (Fe-N)〉 = 1.9672 Å, 〈r(N-C)〉 = 1.1866 Å, and . The experimentally derived bond length r₀ (N-C) = 1.03(8) Å reported for ⁶Δ_i FeNC by Lie and Dagdigian [J. Chem. Phys. 114 (2001) 2137-2143] is much shorter than the corresponding ab initio r_e-value and the averaged value from MORBID. Our calculations suggest that this discrepancy is caused by the inadequate treatment of the large-amplitude bending motion of ⁶Δ_i FeNC. It would appear that for floppy triatomic molecules such as FeNC, r₀-values have little physical meaning, at least when they are determined with the effects of the large-amplitude bending motion being ignored, i.e., under the assumption that the r₀ structure is linear.     

Theoretical investigation of the molecular structure and transition dipole moments of the NaK low lying electronic states

The electronic structure and the spectroscopic constants of the low lying electronic states of the NaK⁺ ionic molecule have been determined through using an ab initio approach involving a non-empirical pseudopotential for the Na and K cores and core valence correlation correction. The potential energy of nearly 26 electronic states of ²Σ⁺, ²Π, and ²Δ symmetries has been calculated up to their dissociation limit Na(4d) + K⁺ and Na⁺ + K(6s). Their spectroscopic constants (R_e, D_e, T_e, ω_e, ω_eχ_e, and B_e) are derived and compared with the few available theoretical studies. A good agreement has been found for the ground state and few excited states with previous works. New potential energy curves were presented, for the first time, for the higher excited states. Numerous avoided crossing between electronic states of ²Σ⁺, ²Π symmetries have been localized and analyzed. Their existences are related to the charge transfer between the two ionic molecules Na⁺K and NaK⁺. Furthermore, we have determined the transition dipole moments for several states and analyzed the avoided crossings related to charge transfer between alkaline atoms.