Shear Wave Elasticity Research Articles

Assessment of bending waves in Torsion Hopkinson Bar experiments using Photon Doppler Velocimetry

A Photon Doppler Velocimetry system that measures the propagation of elastic shear waves in a Torsion Hopkinson Bar (THB) system is presented. The method uses multiple fiber optic probes located symmetrically on opposing sides of the apparatus bars, and provides data with high spatial (a laser irradiated spot size of 35μm) and temporal resolution that is ultimately limited by the data acquisition system and used electronic components. A series of validation experiments simulating the movement of the bar subjected to bending and misalignments demonstrated that this approach is effective in detecting and accounting for the bending waves. The THB experiment under non-ideal conditions, where a combination of shear and bending waves propagates in the system, conclusively confirmed that the disturbance in the acquired signals can be properly addressed with the proposed arrangement of the PDV probes. It was reflected in similar measurements of the component of tangential velocity to the strain gauges. This approach shown to be complementary to the conventional strain gauge technique, but can provide better precision and be more robust under loading and/or temperature conditions that may affect the reliability of strain gauge measurements.

Evaluating ECM stiffness and liver cancer radiation response via shear-wave elasticity in 3D culture models

BackgroundThe stiffness of the tumor microenvironment (TME) directly influences cellular behaviors. Radiotherapy (RT) is a common treatment for solid tumors, but the TME can impact its efficacy. In the case of liver cancer, clinical observations have shown that tumors within a cirrhotic, stiffer background respond less to RT, suggesting that the extracellular matrix (ECM) stiffness plays a critical role in the development of radioresistance.MethodsThis study explored the effects of ECM stiffness and the inhibition of lysyl oxidase (LOX) isoenzymes on the radiation response of liver cancer in a millimeter-sized three-dimensional (3D) culture. We constructed a cube-shaped ECM-based millimeter-sized hydrogel containing Huh7 human liver cancer cells. By modulating the collagen concentration, we produced two groups of samples with different ECM stiffnesses to mimic the clinical scenarios of normal and cirrhotic livers. We used a single-transducer system for shear-wave-based elasticity measurement, to derive Young’s modulus of the 3D cell culture to investigate how the ECM stiffness affects radiosensitivity. This is the first demonstration of a workflow for assessing radiation-induced response in a millimeter-sized 3D culture.ResultsIncreased ECM stiffness was associated with a decreased radiation response. Moreover, sonoporation-assisted LOX inhibition with BAPN (β-aminopropionitrile monofumarate) significantly decreased the initial ECM stiffness and increased RT-induced cell death. Inhibition of LOX was particularly effective in reducing ECM stiffness in stiffer matrices. Combining LOX inhibition with RT markedly increased radiation-induced DNA damage in cirrhotic liver cancer cells, enhancing their response to radiation. Furthermore, LOX inhibition can be combined with sonoporation to overcome stiffness-related radioresistance, potentially leading to better treatment outcomes for patients with liver cancer.ConclusionsThe findings underscore the significant influence of ECM stiffness on liver cancer’s response to radiation. Sonoporation-aided LOX inhibition emerges as a promising strategy to mitigate stiffness-related resistance, offering potential improvements in liver cancer treatment outcomes.

Using Poisson’s ratio and acoustic anisotropy parameter to assess damage and accumulated plastic strain during fatigue loading of austenitic steel

The work investigated the effect of fatigue failure on the elastic characteristics of metastable austenitic steel AISI 321: Poisson’s ratio and acoustic anisotropy parameter. The elastic characteristics were calculated using ultrasonic measurements of the propagation time of longitudinal and shear elastic waves. The volume fraction of strain-induced martensite was determined by the eddy current method. Theoretical studies have shown that the main factors influencing Poisson’s ratio are the accumulation of microdamages and changes in phase composition. The change in the acoustic anisotropy parameter is associated with the influence of cyclic deformation on the crystallographic texture of the material matrix and the formation of oriented crystals of strain-induced martensite. Based on the analysis of experimental results, expressions were obtained for calculating damage and relative accumulated plastic deformation based on acoustic measurement data, which are widely used in engineering practice to determine the fatigue life of structural materials.

Weakened by an infinite system of transverse periodic cracks piezoelectric waveguide as a filter of electroacoustic waves

Abstract The problem of propagation of an electroactive unidirectional elastic shear wave signal in an infinite piezoelectric waveguide weakened by a periodic system of transverse cracks is considered. Wave formation is investigated in cases of different anisotropies of the piezoelectric material, under different electromechanical conditions on the waveguide surfaces. In contrast to the case of a homogeneous waveguide, the presence of a system of periodic cracks leads to the formation of Floquet waves with a periodic structure. Different anisotropies and asymmetric electromechanical conditions on the waveguide surface lead to different localization of wave energy over the thickness of the waveguide, as well as to the presence of different zones of acceptable frequencies. A comparative analysis of the influence of the presence of a periodic system of transverse cracks on the frequency transmittance of the waveguide is carried out.

Modeling the Dispersion of Waves in a Multilayered Inhomogeneous Membrane with Fractional-Order Infusion

The dispersion of elastic shear waves in multilayered bodies is a topic of extensive research due to its significance in contemporary science and engineering. Anti-plane shear motion, a two-dimensional mathematical model in solid mechanics, effectively captures shear wave propagation in elastic bodies with relative mathematical simplicity. This study models the vibration of elastic waves in a multilayered inhomogeneous circular membrane using the Helmholtz equation with fractional-order infusion, effectively leveraging the anti-plane shear motion equation to avoid the computational complexity of universal plane motion equations. The method of the separation of variables and the conformable Bessel equation are utilized for the analytical examination of the model’s resulting vibrational displacements, as well as the dispersion relation. Additionally, the influence of various wave phenomena, including the dependencies of the wavenumber on the frequency and the phase speed on the wavenumber, respectively, with the variational effect of the fractional order on wave dispersion is considered. Numerical simulations of prototypical cases validate the formulated model, illustrating its applicability and effectiveness. The study reveals that fractional-order infusion significantly impacts the dispersion of elastic waves in both single- and multilayer membranes. The effects vary depending on the membrane’s structure and the wave propagation regime (long-wave vs. short-wave). These findings underscore the potential of fractional-order parameters in tailoring wave behavior for diverse scientific and engineering applications.

Quantitative diagnosis of early acute compartment syndrome using two-dimensional shear wave elastography in a rabbit model.

This study explored the association of the elasticity modulus and shear wave velocity (SWV) of the tibialis anterior muscle, as measured by two-dimensional shear wave elastography (2D-SWE), with the intracompartmental pressure (ICP) determined using the Whitesides method in a New Zealand rabbit model of acute compartment syndrome (ACS). Additionally, it evaluated the viability of 2D-SWE as a noninvasive, quantitative tool for the early detection of ACS. An ACS model was established through direct external compression by applying pressure bandaging to the lower legs of 15 New Zealand rabbits using neonatal blood pressure cuffs. Another five animals represented a non-modeled control group. To measure the elasticity modulus and SWV of the tibialis anterior muscles, 2D-SWE was employed. Blood oxygen saturation, serum creatine kinase (CK), and myoglobin levels were monitored. Subsequently, the anterior tibial compartment was dissected, and the tibialis anterior was removed for hematoxylin and eosin staining to assess muscle injury. The elasticity modulus and SWV of the tibialis anterior muscle increased with compression duration, as did serum CK and myoglobin levels. ICP was strongly positively correlated with these parameters, particularly mean velocity (r=0.942, P<0.001) and CK (r=0.942, P<0.001). Blood oxygen saturation was negatively correlated with ICP (r=-0.887, P<0.001). Histological analysis indicated progressive muscle cell swelling over time, with damage transitioning from reversible to irreversible and culminating in necrosis. In a rabbit ACS model, ICP was strongly positively correlated with muscle elasticity modulus/SWV. Consequently, 2D-SWE may represent a novel tool for assessing early-phase ACS.

Modified TI-RADS Coupled with BRAFV600E Enhances Diagnostic Efficiency in Papillary Thyroid Carcinoma: Prospective Study.

Thyroid disorders, relatively common diseases of the endocrine system, have risen gradually in recent years. Early detection and accurate diagnosis of thyroid cancer hold exceptional importance. This study aimed to determine the efficacy of a modified TI-RADS and BRAFV600E mutation testing for thyroid cancer (PTC) diagnosis. Ninety five thyroid nodules (48 benign and 47 malignant) from 81 patients were examined using Kwak Thyroid Imaging Reporting and Data System (TI-RADS) were subjected to shear wave elasticity (SWE), BRAFV600E genotyping and fine needle aspiration (FNA) cytology. The modified TI-RADS exhibited superior diagnostic accuracy compared to TI-RADS in differentiating benign nodules from malignant thyroid nodules. Moreover, the AUC of modified TI-RADS in conjunction with BRAFV600E was the highest at 95% CI (0.898-0.992, p=0.003), surpassing other diagnostic methods in enhanced sensitivity and maintaining high specificity. The diagnostic efficiency of this combination surpassed that of individual diagnostic methods.

Reflected shear wave computed tomography for elasticity imaging of 3D cell cultures using a single-element transducer

Shear wave elasticity imaging (SWEI) has long been used to quantify tissue stiffness in clinical diagnoses. In comparison with conventional bulk-based measurement methods, SWEI offers the distinct advantage of nondestructive sampling, thereby enabling the spatiotemporal monitoring of stiffness variations. However, applying SWEI to assessing millimeter-scale three-dimensional (3D) cell environments has faced limitations despite its potential in mechanobiology, and the existing techniques are insufficient for imaging inhomogeneous media environments. In this study, we investigated a computed tomography technique specifically designed for reflected SWEI (called R-SWCT) by rotational scanning in a sample using a 20-MHz ultrasound single-element transducer. We focused on samples containing a single inclusion with higher stiffness than the surrounding medium, mimicking the situation of a tumor sphere embedded in a 3D gel. Our method reconstructs the stiffness distribution using a curve-fitting method, wherein coefficients of Gaussian curves are fitted to the wavefronts of simulated signals. This reconstruction method yielded coefficients that closely approximated the wavefronts obtained experimentally, with a maximum difference between the measured and predicted shear wave speeds of only 0.1 m/s for phantom samples and 0.2 m/s for cell samples. The system and methodologies proposed in this research have demonstrated the feasibility of employing R-SWCT to study the remodeling dynamics of a cell group within its surrounding matrix in an in vitro setting. This noninvasive method also facilitates an exploration of how irradiation dosage used in radiation therapy can induce temporal alterations in the shear wave speed in 3D cancer cell cultures.

Thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load

Considering the importance of understanding the propagation of transient waves in the piezomagnetic solids, the thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load is investigated analytically in this paper. Using one-sided, two-sided Laplace transformation and Cagniard–de Hoop (CH) technique, an efficient and accurate analytical derivation for the solution of the anti-plane displacement, shear stress, magnetic potential, and induction in Laplace domain is presented. The study shows that the thermal stresses developed in x-axis and y-axis directions have significant influence on the transient response of the half-space. The magnetic induction B x increases obviously when the thermal stress is applied in x-axis direction, while it decreases when the thermal stress is applied in y-axis direction. Approaching time of magnetic induction B x and B y will become longer with higher thermal stress in x-axis direction. With the growth of the thermal stress in x-direction, contribution from the electromagnetic–elastic head (EH) wave increases, while the contribution from the shear elastic (SE) wave and the static value of shear stress decrease.

Evaluation of Carotid Stiffness in Metabolic Syndrome by Real-Time Shear Wave Elasticity Imaging and Ultrafast Pulse Wave Velocity

ObjectiveThis study utilized real-time shear wave elasticity imaging (SWE) and ultrafast pulse wave velocity (ufPWV) to assess carotid arterial stiffness, aiming to predict atherosclerosis risk in patients with metabolic syndrome (MS). MethodsIn this study, 181 patients with metabolic syndrome (MS group) were compared with 73 healthy adults. The MS group was divided into three groups: MS I group: CIMT was normal (CIMT < 1.0 mm, no plaque, n = 61); MS II group: CIMT thickening (1.0 mm ≤ CIMT<1.5 mm, no plaque, n = 39); MS III group: plaque group (CIMT ≥ 1.5 mm, plaque, n = 81). Concurrently, the group of 73 healthy individuals was designated as the control set (NC). Parameters assessed include carotid intima-media thickness (CIMT), elastic modulus values of the carotid artery's anterior and posterior walls (Mean, Max, Min), pulse wave velocity at systole's commencement (PWV-BS), and pulse wave velocity at systole's termination (PWV-ES). Differences, distribution characteristics, and correlations across these groups were analyzed. ResultsA significant association was found between PWV-BS, PWV-ES, and arteriosclerosis severity, with these factors gaining importance as arteriosclerosis progressed. Notably, PWV-ES differences were significant across the four groups (p < 0.05). Both MS III and MS II groups exhibited higher PWV-ES values compared to the MS I group and controls. Statistically significant differences were observed between MS III, MS II, and MS I groups relative to the control group (p < 0.05). Additionally, the Mean, Max, and Min values of the anterior and posterior carotid walls in the MS III group surpassed those of the other groups. ConclusionReal-time shear wave elasticity imaging and ultrafast pulse wave velocity are valuable tools for assessing atherosclerosis risk in MS patients. These non-invasive, safe, and reproducible imaging techniques can quantitatively evaluate the stiffness of the common carotid artery's wall, offering important insights into cardiovascular risk assessment.

Endometrial Elasticity is an Ultrasound Marker for Predicting Clinical Pregnancy Outcomes after Embryo Transfer.

Endometrial elasticity is a potential new marker for assessing endometrial receptivity and pregnancy outcomes based on endometrial thickness and type. Currently, little research has been conducted on the elasticity of the endometrium using shear wave elasticity imaging (SWEI). This study aimed to explore whether endometrial elasticity is an ultrasound marker for predicting clinical pregnancy outcomes after embryo transfer. A total of 245 infertile women underwent ultrasonography before embryo transfer at the Peking University Third Hospital. We compared the endometrial elasticity and sub-endometrial blood flow rate using SWEI in the groups with different pregnancy outcomes. Trends in clinical pregnancy outcomes across the quartiles of endometrial elasticity in the fundus of the uterus (E1) were assessed. Logistic regression analysis was performed to obtain odds ratios for clinical pregnancy outcomes based on the quartiles of E1, with or without adjusting for potential confounding variables. Women in the clinical pregnancy group had higher E1 values and sub-endometrial blood flow rates in the uterine fundus than those in the non-pregnancy group. Women in the highest quartile of E1 had the most favorable clinical pregnancy rates. Endometrial elasticity measured using SWEI is a promising ultrasound marker for predicting clinical pregnancy outcomes after embryo transfer.

Diagnostic value of ultrasound elastography in polycystic ovary syndrome: a systematic review and meta-analysis

Objective The main purpose of this systematic review and meta-analysis was to investigate the diagnostic value of ultrasound elastography in the evaluation of polycystic ovary syndrome (PCOS). Methods A comprehensive and methodical investigation was carried out in the databases of PubMed, EMBASE, Cochrane, Scopus, Web of Science, and China National Knowledge Infrastructure, covering the entire duration of these databases until October 18, 2023. The primary purpose of this research was to evaluate and contrast ovarian tissue elasticity in people with and without PCOS. The elasticity of ovarian tissue was quantified using standardized mean difference (SMD). Results A total of eight studies were ultimately selected for systematic evaluation and meta-analysis. Five studies used shear wave elastography (SWE) as a diagnostic tool, and it was discovered that women with PCOS had higher levels of ovarian shear wave elasticity than their healthy counterparts. The SMD was determined to be 1.86 kilopascal (95% CI: 1.27 to 2.44). Three studies were conducted using strain elastography (SE) to compare the ovarian strain ratio of patients with PCOS to that of a healthy control group. The SMD for the PCOS group was 2.07 (95% CI: 1.79 to 2.34), which indicated that the ovarian strain ratio was significantly higher in that group. Conclusion This systematic review and meta-analysis found that women with PCOS had stiffer ovarian tissue than women without the disorder. Ultrasound elastography may provide clinicians with value beyond 2D ultrasound in the diagnosis of PCOS.

Ultrasonic shear wave elastography predicts the quality of the residual tendon before the rotator cuff repair

Background and purposeEffective evaluation of rotator cuff tear residual tendon quality is the key to surgical repair. However, until now, the evaluation of rotator cuff tissue by ultrasonic shear wave elasticity (SWE) has been controversial. This prospective study analyzed the association between preoperative SWE and arthroscopic residual tendon quality scores.MethodsThe shear wave velocity (SWV) of the deltoid muscle, the supraspinatus tendon, and the supraspinatus muscle were measured in full-thickness rotator cuff tear patients. Tendon quality was scored according to tear size, tendon margin, tendon thickness, and footprint coverage during arthroscopy. The arthroscopic scores were used as the gold standard, and the SWV ratio of tendon and muscle (supraspinatus tendon/deltoid and supraspinatus muscle/deltoid) were calculated and correlated with the arthroscopic scores.ResultEighty-nine patients (129 shoulders) were enrolled, including 89 operation shoulders and 40 control shoulders. In the group of operation shoulders, both the SWV ratios of tendon (SWV-RT) and the SWV ratio of muscle (SWV-RM) were negatively correlated with arthroscopic scores (The correlation coefficient (R) ranged from -0.722 to -0.884 and -0.569 to -0.689). The SWV-RT and SWV-RM of the operation shoulders were significantly lower than that of the control shoulders (p < 0.05).ConclusionSWE could be used to predict the quality of the residual tendon before the rotator cuff repair. SWV of the supraspinatus tendon and muscle was a useful parameter to predict the quality of the residual tendon.Critical relevance statementMeasuring the shear wave velocity of the supraspinatus tendon and muscle with SWE is useful for predicting the quality of the residual tendon which is one of the key factors for a successful rotator cuff repair.Key points• Evaluating the quality of the residual tendon is important before surgery.• Elasticity measurements were negatively correlated with the arthroscopic score.• SWE is useful for predicting the quality of the residual tendon.Graphical

Skin Elasticity Measurement Using Finite Element Simulation with Shear Wave Elasticity Imaging

Skin Elasticity Measurement Using Finite Element Simulation with Shear Wave Elasticity Imaging

Robust elastic shear wave transport in membrane-type topological metamaterials induced by material difference

Novel membrane-type topological metamaterials induced by material difference are investigated in this work. Different from previous common method to break spatial inversion symmetry and realize topological phase transition, choosing different materials is more convenient and shows more complex topological properties. Not all combinations of different materials can open the topological band gap. Interestingly, not only the topological interface modes but also the conventional interface modes are found in this system. Although strong energy localization capacity is found near the interface, both kinds of interface modes show different robustness against defects. To further enhance adaptability to environmental variations and broaden the working frequency range, the thermal field is introduced in membrane-type topological metamaterials to tune the dispersion relations. Fortunately, not only interface modes can be tuned to a lower frequency range, but also the energy localization of interface modes can be remained at a high level. The temperature can act as a switch to turn on/off the robust shear wave transport in membrane-type topological metamaterials. Given that, novel temperature-controlled topological metamaterials are expected to open new avenues for active elastic multifunctional devices.

Role of Shear Wave Elastography of Placenta in Prediction of Preeclampsia in High-Risk Pregnancy.

The aim of our study was to compare the placental elasticity values between normal pregnancies and preeclamptic pregnancies and evaluate the utility of shear-wave elastography of the placenta as a predictor for preeclampsia in high-risk pregnancy. A prospective study was performed with 90 singleton high-risk pregnancies having any of the 7 risk factors for developing preeclampsia (primigravida, history of preeclampsia, family history of preeclampsia, history of pregestational diabetes, chronic hypertension, advanced maternal age [≥40 years], and body mass index ≥26 kg/m 2 ) were enrolled in the study. Shear-wave elastography was performed in all patients at 20 to 24 weeks' gestation and at 34 to 36 weeks' gestation, at 2 sites: center and edge of the placenta. The patients were divided into 2 groups: normal pregnancies (group A) or developed preeclampsia (group B). Women with posterior placentation, obstetric disorders other than preeclampsia, or multiple gestation were excluded from the study. Group comparisons were done using the χ2 test or Fisher exact test. Shear-wave elasticity values at 20 to 24 weeks' gestation for group B at the center of the placenta (21.73 vs 9.72 kPa) and at the edge of the placenta (21.6 kPa vs 10.15 kPa) were significantly higher than those for group A ( P < 0.05). Similar results were seen at 34 to 36 weeks' gestation. With a cutoff of 13.1 kPa, we attained sensitivity of 95.2%, specificity of 92.8% and diagnostic accuracy of 93.3% for predicting development of preeclampsia. Patients with preeclampsia have a significantly higher stiffness of the placenta. Shear-wave elastography is useful to evaluate placental function. Elastography can be used as a supplementary tool for prediction of preeclampsia.

Shear Waves in an Elastic Plate with a Hole Resting on a Rough Base

The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite elastic thin plate with a circular orifice of radius r0 lying on a rough base. Considering the friction forces and their influence on the sample of wave propagation in extended rods or thin plates is important for calculating the stress–strain state in them and the size of the area of motion. An exact analytical solution of a nonlinear boundary value problem for tangential stresses and velocities is obtained in quadratures by the Laplace transform, with respect to time. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance r* from the center of the orifice, and an elementary formula is given for this distance (the case of tangential shock stresses suddenly applied to the orifice boundary is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the stopping (trailing) wave fronts are calculated. After passing them, a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual stresses is established in the region r0≤r≤r*. For the first time, a precise analytical solution was obtained for the boundary value problem of the propagation of elastic shear waves in an infinite isotropic space with a cylindrical cavity, when a tangential shock load is set on its surface.

Shear Wave Elastography for Assessment of Changes in Abdominal Soft Tissues after Lipoabdominoplasty.

The changes in the elasticity of the abdominal skin, subcutaneous tissues and muscles after lipoabdominoplasty are still unknown. The aim of this study was to provide an objective assessment of tissue elasticity after lipoabdominoplasty using ultrasound elastography. A total of 21 female patients (31-41 years old) who underwent lipoabdominoplasty from Oct 2019 to Mar 2022 were included in this retrospective study. The elastography values of the skin, subcutaneous tissues and abdominal muscles were obtained with the ultrasound shear wave elasticity imaging system pre-operation (Pre) and 6 months post-operation (Post) at four different points. Twenty-one female patients were included. The elasticity of the abdominal skin, subcutaneous tissues, rectus abdominis and external oblique abdominis significantly increased at 6 months post-operation. The improvements in abdominal soft tissue elasticity were not uniform across the examined points. Significant changes in the elasticity of the abdominal skin, subcutaneous tissues and muscles were observed after lipoabdominoplasty. Ultrasound elastographic assessment was objective and feasible for evaluating the effect of lipoabdominoplasty on abdominal soft tissue. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Rotational 3D shear wave elasticity imaging: Effect of knee flexion on 3D shear wave propagation in in vivo vastus lateralis

Skeletal muscle is a complex tissue, exhibiting not only direction-dependent material properties (commonly modeled as a transversely isotropic material), but also changes in observed material properties due to factors such as contraction and passive stretch. In this work, we evaluated the effect of muscle passive stretch on shear wave propagation along and across the muscle fibers using a rotational 3D shear wave elasticity imaging system and automatic analysis methods. We imaged the vastus lateralis of 10 healthy volunteers, modulating passive stretch by imaging at 8 different knee flexion angles (controlled by a BioDex system). In addition to demonstrating the ability of this acquisition and automatic processing system to estimate muscle shear moduli over a range of values, we evaluated potential higher order biomarkers for muscle health that capture the change in muscle stiffness along and across the fibers with changing knee flexion. The median within-subject variability of these biomarkers is found to be <16%, suggesting promise as a repeatable clinical metric. Additionally, we report an unexpected observation: that shear wave signal amplitude along the fibers increases with increasing flexion and muscle stiffness, which is not predicted by transversely isotropic (TI) material simulations. This observation may point to an additional potential biomarker for muscle health or inform other material modeling choices for muscle.

Effect of Anisotropy of Elastic Energy and Shear Waves on Electron–Phonon Relaxation and Electrical Resistivity of Noble Metals. Review 4

Effect of Anisotropy of Elastic Energy and Shear Waves on Electron–Phonon Relaxation and Electrical Resistivity of Noble Metals. Review 4