The preliminary evaluation of a 1 MHz ultrasound probe for measuring the elastic anisotropy of human cortical bone

Our objective is to evaluate an ultrasound probe for measurements of velocity and anisotropy in human cortical bone (tibia). The anisotropy of cortical bone is a known and mechanically relevant property in the context of osteoporotic fracture risk. Current in vivo quantitative ultrasound devices measuring the velocity of ultrasound in long bones can only be applied in the axial direction. For anisotropy measurements a second direction for velocity measurements preferably perpendicular to the axial direction is necessary. We developed a new ultrasound probe which permits axial transmission measurements with a simultaneous second perpendicular direction (tangential). Anisotropy measurements were performed on isotropic and anisotropic phantoms and two excised human female tibiae (age 63 and 82). Anisotropy ratios (AI; ratio of squared ultrasound velocities in the two directions) were for the isotropic phantom 1.06 ± 0.01 and for the anisotropic phantom 1.14 ± 0.03 (mean ± standard deviation). AI was 1.83 ± 0.29 in the tibia from the older donor and 1.37 ± 0.18 in the tibia from the younger donor. The AIs were in the expected range and differed significantly (p < 0.05, t-test) between the tibiae. Measured sound velocities were reproducible (mean standard deviation of short time precision of both channels for phantom measurements 31 m/s) and in agreement with reported velocities of the phantom material. Our results document the feasibility of anisotropy measurements at long bones using a single probe. Further improvements in the design of the probe and tests in vivo are warranted. If this approach can be evaluated in vivo an additional tool for assessing the bone status is available for clinical use.     

Structure and elastic properties of TeO2-BaF2 glasses

Binary tellurite (100−x)TeO₂-xBaF₂ glasses for different compositions of BaF₂ (x=8, 10, 12, 15, 18 and 20 wt%) have been prepared by rapid quenching method. The velocities and attenuation during the propagation of the ultrasonic waves in all glasses were measured using a transducer operated at a fundamental frequency of 5 MHz at room temperature. A progressive increase in BaF₂ content leads to a decrease in ultrasonic velocities and density, which is followed by an increase in attenuation. The existence of depolymerisation of Te co-ordination leads to the transformation of TeO₄ trigonal bipyramid units through TeO₃₊₁ polyhedron to TeO₃ trigonal pyramid units. This is responsible for the observed decrease in the measured and determined parameters with the addition of the modifier content.     

Investigation of rat bone fracture healing using pulsed 1.5 MHz, 30 mW/cm burst ultrasound – Axial distance dependency

This study investigated the effect of LIPUS on fracture healing when fractures were exposed to ultrasound at three axial distances: z = 0 mm, 60 mm, and 130 mm. We applied LIPUS to rat fracture at these three axial distances mimicking the exposure condition of human fractures at different depths under the soft tissue. Measurement of LIPUS shows pressure variations in near field (nearby transducer); uniform profile was found beyond it (far field). We asked whether different positions of the fracture within the ultrasound field cause inconsistent biological effect during the healing process. Closed femoral fractured Sprague–Dawley rats were randomized into control, near-field (0 mm), mid-near field (60 mm) or far-field (130 mm) groups. Daily LIPUS treatment (plane, but apodized source, see details in the text; 2.2 cm in diameter; 1.5 MHz sine waves repeating at 1 kHz PRF; spatial average temporal average intensity, I_SATA = 30 mW/cm²) was given to fracture site at the three axial distances. Weekly radiographs and endpoint microCT, histomorphometry, and mechanical tests were performed. The results showed that the 130 mm group had the highest tissue mineral density; and significantly higher mechanical properties than control at week 4. The 60 mm and 0 mm groups had significantly higher (i.e. p < 0.05) woven bone percentage than control group in radiological, microCT and histomorphometry measurements. In general, LIPUS at far field augmented callus mineralization and mechanical properties; while near field and mid-near field enhanced woven bone formation. Our results indicated the therapeutic effect of LIPUS is dependent on the axial distance of the ultrasound beam. Therefore, the depth of fracture under the soft tissue affects the biological effect of LIPUS. Clinicians have to be aware of the fracture depth when LIPUS is applied transcutaneously.     

3-D Model of sound pressure field in a meridinal section plane of fruit

A theoretical model was suggested for qualitative evaluation of a sound pressure field in fruit tissue, as affected by ultrasonic probe dimensions and fruit properties. The classic directivity pattern of an ideal fluid model, expressed by Bessel function of the first kind, was extended to include energy dissipation of a real material. The directional characteristics of wave propagation, as influenced by transmitter frequency and diameter, and by fruit properties, were discussed. The model indicates how to select the parameters of the ultrasonic transducer (transducer diameter, frequency and excitation power) to control the magnitude and directivity of the ultrasonic waves in the fruit tissue. The suggested theoretical model represented fairly well the experimental sound wave distribution over the half-cut surface of potato and avocado (R² > 0.862 and 0.977, respectively); the same theoretical model could not represent the sound wave distribution over a half-cut melon. Results of the study were applied in a new probe design for ultrasonic testing of whole fruit.     

Anomalous behavior of ultrasonic properties near 50 K in Rb0.30MoO3 and Rb0.30(Mo1−xVx)O3

Depending on the temperature, the charge density wave (CDW) nonlinear conductivity of the blue bronzes A_0.30MoO₃ (A=K, Rb) shows two different regimes: a strongly damped motion above ∼50 K and motion with almost no damping below ∼50 K. In a search for an elastic signature of this CDW behaviour, we performed ultrasonic measurements on Rb_0.30MoO₃ and Rb_0.30(Mo_1−xV_x)O₃ single crystals between 4 K and 300 K. In Rb_0.30MoO₃, at T∼50 K, upon cooling, a large increase of the sound velocity is observed. The ultrasonic attenuation coefficient shows an increase down to 50 K followed by a plateau. In Rb_0.30(Mo_1−xV_x)O₃ (x=0.4 at%) the anomaly broadens and is shifted towards higher temperatures. The results are discussed in terms of CDW glass.     

Lead-free KNLNT piezoelectric ceramics for high-frequency ultrasonic transducer application

This paper presents the latest development of a lead-free piezoelectric ceramic and its application to transducers suitable for high-frequency ultrasonic imaging. A lead-free piezoelectric ceramic with formula of (K_0.5Na_0.5)_0.97Li_0.03(Nb_0.9 Ta_0.1)O₃ (abbreviated as KNLNT-0.03/0.10) was fabricated and characterized. The material was found to have a clamped dielectric constant ε₃₃^S/ε₀ = 890, piezoelectric coefficient d₃₃ = 245 pC/N, electromechanical coupling factor k_t = 0.42 and Curie temperature T_c > 300 °C. High-frequency (40 MHz) ultrasound transducers were successfully fabricated with the lead-free material. A representative lead-free transducer had a bandwidth of 45%, two-way insertion loss of -18 dB. This performance is comparable to reported performances of popular lead-based transducers. The comparison results suggest that the lead-free piezoelectric material may serve as an alternative to lead-based piezoelectric materials for high-frequency ultrasonic transducer applications.     

Interaction of ultrasonic waves with domain walls on nanocrystalline YIG

The nanocrystalline YIG samples with different particle sizes (20–40 nm) has been prepared using microwave–hydrothermal method. As synthesized powders were characterized using XRD and TEM. The powders were pressed and sintered at three different temperatures i.e., 700 °C/30 min, 800 °C/30 min, 900 °C/30 min, using microwave furnace. The sintered samples were characterized using XRD and TEM. The sintered samples are monophasic in nature with average grain size ranging in between 72 nm and 90 nm. The thermal variation of ultrasonic velocities [longitudinal (V_l) and transverse (V_S)] and longitudinal attenuation (α_l) has been measured on sintered samples by the pulse transmissionmethod at 1 MHz, in the temperature range of 300–600 K. The room temperature velocity is found to be grain size dependent and decreases with increasing temperature, except near the Curie temperature, T_C, where a small anomaly is observed. The longitudinal attenuation (α₁) at room temperature is also found to be more sample dependent. The temperature variation of ultrasonic longitudinal attenuation exhibits a sharp maximum just below Curie temperature (T_C). The above observations were carried on in the demagnetized state, on the application of a saturation field of 380 mT, the anomaly observed in the thermal variation of velocities (longitudinal and transverse) and attenuation is found to disappears. The observed interaction of ultrasonic velocity with domain walls has been qualitatively explained with the help oftemperature variation of magneto-crystalline anisotropy constant (k₁) and Landau’s theory.     

Microstructures, surface bonding states and room temperature ferromagnetisms of Zn0.95Co0.05O thin films doped with copper

Zn_0.95−xCo_0.05Cu_xO (ZCCO, where x = 0, 0.005, 0.01 and 0.015) thin films were deposited on Si (1 0 0) substrates by pulsed laser deposition technique. Crystal structures, surface morphologies, chemical compositions, bonding states and chemical valences of the corresponding elements for ZCCO films were characterized by X-ray diffraction (XRD), field emission scanning electron microscope (FESEM) and X-ray photoelectron spectroscopy (XPS). XRD and FESEM results indicate that crystallite sizes of the highly (0 0 2)-oriented ZCCO films slightly decrease with increasing Cu content. When the Cu content increases from 0 to 0.015, Zn 2p_3/2, Co 2p, Cu 2p_3/2 and O 1s peaks of the ZCCO film shift towards higher or lower binding energy regions, and the reasons for these chemical shifts are investigated by fitting the corresponding XPS narrow-scan spectra. Both in-plane and out-of-plane magnetization-magnetic field hysteresis loops of the ZCCO films reveal that all the films have room temperature ferromagnetisms (RTFMs). The conceivable origin of the RTFM is ascribed to the combined effects of the local structural disorder resulted from (Co²⁺, Cu²⁺, Cu¹⁺)-cations which substitute Zn²⁺ ions in the ZnO matrices, ferromagnetic coupling between coupled dopant atoms caused by Co²⁺ (3d⁷4s⁰) and Cu²⁺ (3d⁹4s⁰) spin states, and exchange interactions between the unpaired electron spins originating from lattice defects induced by Cu doping in the Zn_0.95Co_0.05O matrices.     

Scaling of the viscoelastic shell properties of phospholipid encapsulated microbubbles with ultrasound frequency

Phospholipid encapsulated microbubbles are widely employed as clinical diagnostic ultrasound contrast agents in the 1–5 MHz range, and are increasingly employed at higher ultrasound transmit frequencies. The stiffness and viscosity of the encapsulating “shells” have been shown to play a central role in determining both the linear and nonlinear response of microbubbles to ultrasound. At lower frequencies, recent studies have suggested that shell properties can be frequency dependent. At present, there is only limited knowledge of how the viscoelastic properties of phospholipid shells scale at higher frequencies. In this study, four batches of in-house phospholipid encapsulated microbubbles were fabricated with decreasing volume-weighted mean diameters of 3.20, 2.07, 1.82 and 1.61 μm. Attenuation experiments were conducted in order to assess the frequency-dependent response of each batch, resulting in resonant peaks in response at 4.2, 8.9, 12.6 and 19.5 MHz, respectively. With knowledge of the size measurements, the attenuation spectra were then fitted with a standard linearized bubble model in order to estimate the microbubble shell stiffness S_p and shell viscosity S_f, resulting in a slight increase in S_p (1.53–1.76 N/m) and a substantial decrease in S_f (0.29 × 10⁻⁶–0.08 × 10⁻⁶ kg/s) with increasing frequency. These results performed on a single phospholipid agent show that frequency dependent shell properties persist at high frequencies (up to 19.5 MHz).     

Joint L1/Lp-regularized minimization in video recovery of remote sensing based on compressed sensing

L₁ regularization and L_p regularization are proposed for processing recovered images based on compressed sensing (CS). L₁ regularization can be solved as a convex optimization problem but is less sparse than L_p (0 < p < 1). L_p regularization is sparser than L₁ regularization but is more difficult to solve. This paper proposes joint L₁/L_p (0 < p < 1) regularization, which combines L_p regularization and L₁ regularization. This joint regularization is applied to recover video of remote sensing based on CS. Joint regularization is sparser than L₁ regularization but is as easy to solve as L₁ regularization. A linearized Bregman reweighted iteration algorithm is proposed to solve the joint L₁/L_p regularization problem. The performance and capabilities of the linearized Bregman algorithm and linearized Bregman reweighted algorithm for solving the joint L₁/L_p regularization model are analyzed and compared through numerical simulations.     

Influence of subcutaneous fat in surface heating of ultrasonic diagnostic transducers

The transducers of diagnostic ultrasonic equipment generate undesired local heating at the applied part of the transducer surface. The assessment of this heating is fundamental in warranting patient safety. On the standard IEC 60601-2-37, methods have been established for the reliable measurement of heating, where three tissue models based on tissue-mimicking materials are recommended: soft tissue mimic only, bone mimic close to the surface of soft tissue, and skin mimic at the surface of soft tissue. In the present work, we compared the last-mentioned tissue model with a new one using a layer of porcine subcutaneous fat inserted between the soft tissue and skin-mimicking materials. We verify significant statistical differences between models, with the average temperature rise measured for the tests without subcutaneous fat at 6.7 °C ± 1.7 °C and for the ones with subcutaneous fat at 8.9 °C ± 1.8 °C (k = 2; p = 0.95). For each model, the procedure was performed 10 times in repeatability conditions of measurement. It has been suggested that the influence of subcutaneous fat for external transducers heating evaluation should be considered, as the presence of many millimeters of subcutaneous fat is a common condition in patients. Otherwise, the transducer surface heating and, therefore, the risk to the patient may be underestimated.     

Measurement of the sound velocity in fluids using the echo signals from scattering particles

With conventional methods the sound velocity c in fluids can be determined using the back wall echo. This paper proposes a novel technique, in which the signals reflected by scattering particles suspended in a fluid are analysed instead. The basic idea is that the particles generate the strongest echo signal when being located in the sound field maximum. Therefore the position of the echo signal maximum is a measure for the propagation time to the sound field maximum. Provided that calibration data or sound field simulations for the ultrasonic transducer are available, this propagation time suffices to determine both sound velocity and the location of the sound field maximum. The feasibility of the new approach is demonstrated by different kinds of experiments: (i) Measurements of the sound velocity c in four fluids covering the wide range between 1116 and 2740 m/s. The results show good agreement with values published elsewhere. (ii) Using the dependence of the sound velocity on temperature, it is possible to vary c over the comparatively small range between 1431 and 1555 m/s with increments of less than 10 m/s. The measured statistical variation of 1.4 m/s corresponds to a relative uncertainty not worse than 0.1%. (iii) The focus position, i.e. the distance of the maximum of the sound field from the transducer, was varied by time-shifted superposition of the receive signals belonging to the different elements of an annular array. The results indicate that the novel method is even capable of measuring profiles of the sound velocity along the ultrasonic beam non-invasively.     

Carotid atherosclerotic plaque characterisation by measurement of ultrasound sound speed in vitro at high frequency, 20 MHz

This study aimed to utilise a tissue mimicking material (TMM) in order to embed in vitro carotid plaque tissue so that its acoustic properties could be assessed. Here, an International Electrotechnical Commission (IEC) agar-based TMM was adapted to a clear gel by removal of the particulates. This clear TMM was measured with sound speed at 1540 ms⁻¹ and an attenuation coefficient of 0.15 dB cm⁻¹ MHz⁻¹. Composite sound speed was then measured through the embedded material using a scanning acoustic microscope (SAM). Both broadband reflection and transmission techniques were performed on each plaque specimen in order to ensure the consistency of the measurement of sound speed, both at 21 °C and 37 °C. The plaque was measured at two temperatures to investigate any effect on the lipid content of the plaque. The contour maps from its associated attenuation plots were used to match the speed data to the photographic mask of the plaque outline. This physical matching was then used to derive the sound speed from the percentage composition seen in the histological data by solution of simultaneous equations. Individual speed values for five plaque components were derived; TMM, elastin, fibrous/collagen, calcification and lipid. The results for derived sound speed in the TMM were consistently close to the expected value of soft tissue, 1540 ms⁻¹. The fibrous tissue showed a mean value of 1584 ms⁻¹ at 37 °C. The derived sound speeds for elastic and lipid exhibited large inter-quartile ranges. The calcification had higher sound speed than the other plaque components at 1760–2000 ms⁻¹. The limitations here lay in the difficulties in the matching process caused by the inhomogeneity of the plaque material and shrinkage during the histological process. Future work may concentrate on more homogeneous material in order to derive sound speed data for separate components. Nevertheless, this study increases the known data ranges of the individual components within a plaque. This information may be used help to assess the mechanical properties and structural integrity and its associated vulnerability or risk of embolization in future diagnostic ultrasound techniques.     

Using 1 MHz pulse-echo ultrasound externally applied to detect mastoid effusion: cadaver experiments

The objective of this study is to explore the feasibility of using ultrasound to detect mastoid effusion (ME). In the past, ultrasound has been used to measure middle ear effusion (MEE) by injecting water into the external ear canal to measure echoes from the tympanic membrane, which is uncomfortable for the patient. It has been shown that air cells in the mastoid of patients with MEE are filled with fluid, which implies that ME could be a useful indicator of MEE. This study suggests using ultrasound to detect ME as a potentially noninvasive approach for MEE detection. In vitro experiments were performed on ten cadaver samples of the human ear. A single-element 1 MHz transducer was used to measure the mastoid of each cadaver before and after injecting water into the mastoid. The experimental results showed that the relative amplitudes of ultrasonic signals differed significantly between before (0.24 ± 0.09, mean ± standard deviation) and after (0.15 ± 0.03) the water injection (p < 0.05, t-test), demonstrating that the ultrasonic reflection can be used to detect ME. The location of the human mastoid under the skin behind the ear allows external measurements, and hence ultrasound-based ME detection may be an alternative, noninvasive diagnostic approach to detecting MEE in the future, providing an examination that avoids discomfort.     

Arbitrary shaped, liquid filled reverberators with non-resonant transducers for broadband focusing of ultrasound using Time Reversed Acoustics

The ability to generate short focused ultrasonic pulses with duration on the order of one period of carrier frequency depends on the bandwidth of the transmitter as the pulse duration is inversely proportional to the bandwidth. Conventional focusing arrays used for focusing ultrasound have limited bandwidth due to the resonant nature of the piezoelements generating ultrasound. Theoretically it is possible to build a broadband phased array composed of “non-resonant” elements: wedge-shaped or flat-concave piezotransducers, though there are numerous technical difficulties in designing arrays with hundreds of elements of complex shape. This task is much easier to realize in an alternative technique of ultrasound focusing based on the principles of Time Reversed Acoustics (TRA) because in TRA systems, effective focusing can be achieved with just a few, or even one, transducers. The goal of this study is to demonstrate the possibility of broadband focusing of ultrasonic waves using a TRA system with non-resonant transducers and to explore the factors affecting the performance of such a system. A new type of TRA reverberators, such as water-filled thin-wall plastic vessels, which can be used with the submersible piezotransducers fixed internally in the reverberator, are proposed and tested. The experiments are conducted in a water tank with the walls and bottom covered by a sound absorbing lining. A needle hydrophone mounted on a 3D positioning system is used as a beacon for the TRA focusing and then for measuring the spatial distribution of the focused ultrasound field. The bandwidth and spatial distribution of the signal focused by the TRA system using a single channel with the resonant versus non-resonant transducers have been analyzed. Two types of non-resonant transducers were tested: a flat-concave transducer with a diameter of 30 mm, and a thickness varying from 2 mm in the center to 11 mm at the edge, and a specially designed submersible transducer having an uneven shape with a diameter of about 25 mm and a thickness varying from 2 to 6 mm. It was shown that TRA focusing system using non-resonant transducer had a bandwidth at 10 dB of 500 kHz while the resonant transducer provided about 100 kHz bandwidth. Correspondingly, the extended bandwidth of the TRA focusing system, especially toward higher frequencies, provides a 50% sharper spatial distribution. Furthermore, the relative level of the background ultrasound was reduced by a factor up to 3 as more frequencies were added coherently in focus and incoherently out of focus. Advantages of water-filled reverberators made of thin-wall plastic vessels include easy manufacturing, low costs, extreme simplicity, and good acoustical matching with soft tissues, important for biomedical applications.     

High-frequency ultrasonic transducer based on lead-free BSZT piezoceramics

This paper describes the fabrication and evaluation of a high-frequency (40 MHz) transducer based on lead-free piezoceramics for ultrasonic imaging. The transducer with an aperture size of 0.9 mm has been fabricated using barium strontium zirconate titanate ((Ba_0.95Sr_0.05)(Zr_0.05Ti_0.95)O₃, abbreviated as BSZT) ceramics. The lead-free BSZT has a piezoelectric d₃₃ coefficient of 300 pC/N and an electromechanical coupling factor k_t of 0.45. High-frequency ultrasound transducers were fabricated and a bandwidth of 76.4% has been achieved with an insertion loss of −26 dB. Applications in high resolution biological and medical imaging could be possible with this lead-free material.     

Influence of thickness,width and temperature on critical current density of Nb thin film structures

The density of critical currents j_C in Nb thin films with thickness smaller than 15 nm and width between 100 nm and 10 μm has been measured in a wide temperature range. We have found that the temperature dependencies of j_C in sub-micrometer wide bridges at 0.7T_C < T < T_C are well described by the Ginzburg–Landau de-pairing critical current. In wider bridges already at T < 0.9T_C the j_C value is significantly reduced due to the penetration and de-pinning of magnetic vortices.     

Particle effects on the emissivity and temperature of optically thick, mixed media retrieved by mid-IR emission spectroscopy

Passive diagnostics offer new ways of obtaining real-time data for the control and modeling of industrial furnaces. It has been proposed elsewhere that from the intensity profile between 3.8 and 4.7 μm one may derive the temperature of a gas-particle medium and the particle emissivity (ε_p) at 3.95 μm. This technique applies to large columns of combustion products with enough CO₂. The temperature is retrieved by finding the best fit between Planck's function and the intensity profile between 4.56 and 4.7 μm, which is that of a blackbody due to CO₂ saturation. Here we consider the effect of particles on the intensity profile and, therefore, on the retrieved temperature and particle emissivity. We derive an analytic approximation of the effective emissivity for an optically thick gas-particle mixture that includes emission and absorption due to particles and gases, along with isotropic particle scattering. The derivation follows the method of embedded invariance and has been used already for particle-only clouds. It yields a spectral solution that is applicable in other infrared regions where gas and particle optical thicknesses are large. A key parameter (χ) is the ratio of the gas absorption coefficient to the particle extinction coefficient. For χ=1 and ε_p=0.5, particle effects decrease the gas band profile by 5% from that of a blackbody. For χ<1 and ε_p<0.5, particle effects on the calculated temperature and particle emissivity are noticeable and particle effects should be considered. If χ is known, an iterative procedure may be used to calculate temperature and particle emissivity. We illustrate this procedure with data from a coal-fired boiler. Accounting for particle effects, temperatures were 4% higher (at about 1500 K) and particle emissivities 28% lower (for ε_p within 0.3-05) than without considering these effects.     

Optical measurements of silicon wafer temperature

An optical technique for precise, non-contact, and real time measurement of silicon wafer temperature that uses the polarized reflectivity ratio R_p/R_s is described. The proposed method is based on temperature dependence of the optical functions of silicon. Expected strong temperature sensitivity is obtained near band gap. Simultaneous monitoring of temperature and oxide layer thickness is discussed using measurements at four wavelength 365 nm, 405 nm, 546 nm, and 820 nm.     

In vitro ultrasonic and mechanic characterization of the modulus of elasticity of children cortical bone

The assessment of elastic properties in children’s cortical bone is a major challenge for biomechanical engineering community, more widely for health care professionals. Even with classical clinical modalities such as X-ray tomography, MRI, and/or echography, inappropriate diagnosis can result from the lack of reference values for children bone. This study provides values for elastic properties of cortical bone in children using ultrasonic and mechanical measurements, and compares them with adult values. 18 fibula samples from 8 children (5–16 years old, mean age 10.6 years old ±4.4) were compared to 16 fibula samples from 3 elderly adults (more than 65 years old). First, the dynamic modulus of elasticity (E_dyn) and Poisson’s ratio (ν) are evaluated via an ultrasonic method. Second, the static modulus of elasticity (E_sta) is estimated from a 3-point microbending test. The mean values of longitudinal and transverse wave velocities measured at 10 MHz for the children’s samples are respectively 3.2 mm/μs (±0.5) and 1.8 mm/μs (±0.1); for the elderly adults’ samples, velocities are respectively 3.5 mm/μs (±0.2) and 1.9 mm/μs (±0.09). The mean E_dyn and the mean E_sta for the children’s samples are respectively 15.5 GPa (±3.4) and 9.1 GPa (±3.5); for the elderly adults’ samples, they are respectively 16.7 GPa (±1.9) and 5.8 GPa (±2.1). E_dyn, ν and E_sta are in the same range for children’s and elderly adults’ bone without any parametric statistical difference; a ranking correlation between E_dyn and E_sta is shown for the first time.