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The mechanical properties of the sclera play a critical role in supporting the ocular structure and maintaining its shape. However, non-invasive measurements to quantify scleral biomechanics remain challenging. Recently introduced multi-directional optical coherence elastography (OCE) combined with an air-coupled ultrasound transducer for excitation of elastic surface waves was used to estimate phase speed and shear modulus in ex vivo rabbit globes (n = 7). The scleral phase speed (12.1 ± 3.2 m/s) was directional-dependent and higher than for corneal tissue (5.9 ± 1.4 m/s). In the tested locations, the sclera proved to be more anisotropic than the cornea by a factor of 11 in the maximum of modified planar anisotropy coefficient. The scleral shear moduli, estimated using a modified Rayleigh-Lamb wave model, showed significantly higher values in the circumferential direction (65.4 ± 31.9 kPa) than in meridional (22.5 ± 7.2 kPa); and in the anterior zone (27.3 ± 9.3 kPa) than in the posterior zone (17.8 ± 7.4 kPa). The multi-directional scanning approach allowed both quantification and radial mapping of estimated parameters within a single measurement. The results indicate that multi-directional OCE provides a valuable non-invasive assessment of scleral tissue properties that may be useful in the development of improved ocular models, the evaluation of potential myopia treatment strategies, and disease characterization and monitoring.

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Background:Dispersion presents both a challenge and a diagnostic opportunity in shear wave elastography (SWE).Shear Wave Rheometry(SWR) is an inversion technique for processing SWE data acquired using an acoustic radiation force impulse (ARFI) excitation. The main advantage of SWR is that it can characterize the shear properties of homogeneous soft media over a wide frequency range. Assumptions associated with SWR include tissue homogeneity, tissue isotropy, and axisymmetry of the ARFI excitation).Objective:Evaluate the validity of the SWR assumptions in ex vivo bovine liver.Approach:SWR was used to measure the shear properties of bovine liver tissue as function of frequency over a large frequency range. Assumptions associated with SWR (tissue homogeneity, tissue isotropy, and axisymmetry of the ARFI excitation) were evaluated through measurements performed at multiple locations and probe orientations. Measurements focused on quantities that would reveal violations of the assumptions.Main results:Measurements of shear properties were obtained over the 25-250 Hz range, and showed a 4-fold increase in shear storage modulus (from 1 to 4 kPa) and over a 10-fold increase in the loss modulus (from 0.2 to 3 kPa) over that decade-wide frequency range. Measurements under different conditions were highly repeatable, and model error was low in all cases.Significance and Conclusion:SWR depends on modeling the ARFI-induced shear wave as a full vector viscoelastic shear wave resulting from an axisymmetric source; it is agnostic to any specific rheological model. Despite this generality, the model makes three main simplifying assumptions. These results show that the modeling assumptions used in SWR are valid in bovine liver over a wide frequency band.

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The objective of this study is to compare shear modulus of lower limb muscles between children with hypotonia versus typical development (TD) or developmental disorders associated with altered tone. Nineteen children with mild hypotonia (mean age 9.4 ± 2.3y, 13 male) completed assessment of resting shear modulus of rectus femoris, biceps femoris (BF), tibialis anterior (TA) and gastrocnemius lateralis (GL) at short and long lengths using shear wave elastography. Data was compared with previous data from TD children and a scoping review for children with developmental disorders. Data were collated according to Net-Longitudinal Tension Angle (Net-LTA), which is the muscle length expressed as the net proximal and distal joint angles. Effects of Net-LTA (e.g., short, neutral, long) were examined according to sex, age and body mass index (BMI). In children with hypotonia, shear modulus was: higher at longer versus shorter lengths for four muscles (p < 0.01); correlated with age for BF-short (r = 0.60, p < 0.03) and GL-short (r = -0.54, p < 0.03), with BMI for BF-short (r = 0.71, p < 0.05); and not different between sexes (p > 0.05). The shear modulus values for lower limb muscles for children with mild hypotonia were lower than those for children with Duchenne Muscular Dystrophy (TA-neutral), or Cerebral Palsy (GL-neutral), but not TD children (all four muscles). In conclusion, shear modulus increases with longer muscle length (i.e. higher Net-LTA) in mildly hypotonic children. Children with mild hypotonia have lower shear modulus than children with cerebral palsy and Duchenne muscular dystrophy.

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Acoustic radiation force (ARF) is widely used to induce shear waves for evaluating the mechanical properties of biological tissues. Two shear waves can be generated when exciting with ARF: a transverse shear wave, also simply called shear wave (SW), and a longitudinal shear wave (LSW). Shear waves (SWs) have been broadly used to assess the mechanical properties. Some articles have reported that the LSW can be used to evaluate mechanical properties locally. However, existing LSW studies are mainly focused on the group velocity evaluation using optical coherence tomography (OCT). Here, we report that a LSW generated with ARF can be used to probe viscoelastic properties, including shear modulus and viscosity, using ultrasound. We took advantage of the surface boundary effect to reflect the LSW, named RLSW, to address the energy deficiency of LSW induced by ARF. We systematically evaluated the experiments with tissue-mimicking viscoelastic phantoms and validated by numerical simulations. Phase velocity and dispersion comparison between the results induced by a RLSW and a SW exhibit good agreement in both the numerical simulations and experimental results. The Kelvin-Voigt (KV) model was used to determine the shear modulus and viscosity. RLSW shows great potential to evaluate localized viscoelastic properties, which could benefit various biomedical applications such as evaluating the viscoelasticity of heterogeneous materials or microscopic lesions of tissues.

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In order to facilitate the prediction of some physical properties, we propose several simple formulas based on two parameters only, the metallic valence and metallic atomic radii. Knowing the composition, for single-phase alloys, the average parameters can be calculated by the rule of mixture. The input parameters can be obtained from tabulated databases. Adopting from the literature the results of Coulomb crystal model for metals and single-phase high-entropy alloys, we have derived formulas for the shear modulus (G) and the cohesion energy (Ecoh). Based on these parameters separately, we set up two formulas to estimate the hardness in the case of pure metals. For single-phase (solid-solution) HEAs, by simplifying the Maresca and Curtin model, we obtained a formula for estimating the hardness, which takes into account the atomic misfit in addition to G. The maximal hardness for single-phase HEA is approximately 600 kg/mm2 and is obtained for a composition with a valence electron concentration of approximately 6 ÷ 7.

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BACKGROUND: Multifidus is an important lumbar muscle with distinct superficial and deep fibers responsible for torque production and stabilization, respectively. Its mechanical properties change when transitioning from lying to sitting positions, necessitating enhanced stability. It holds crucial clinical relevance to assess these layers separately, especially in the sitting posture, which demands increased neuromuscular control compared to the prone position. OBJECTIVE: To compare lumbar multifidus stiffness in lying versus sitting postures, analyzing both superficial and deep layers. METHODS: Supersonic Shear Imaging captured elastographic images from 26 asymptomatic volunteers in prone and seated positions. RESULTS: Left multifidus shear modulus in lying: 5.98 ± 1.80/7.96 ± 1.59 kPa (deep/superficial) and sitting: 12.58 ± 4.22/16.04 ± 6.65 kPa. Right side lying: 6.08 ± 1.97/7.80 ± 1.76 kPa and sitting: 13.25 ± 4.61/17.95 ± 7.12 kPa. No side differences (lying p= 0.99, sitting p= 0.43). However, significant inter-postural differences occurred. CONCLUSION: Lumbar multifidus exhibits increased stiffness in sitting, both layers affected, with superior stiffness in superficial versus deep fibers. Applying these findings could enhance assessing multifidus stiffness changes, for classifying tension-induced low back pain stages.

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Magnetic resonance elastography (MRE) and diffusion-weighted imaging (DWI) are complementary imaging techniques that detect disease based on viscoelasticity and water mobility, respectively. However, the relationship between viscoelasticity and water diffusion is still poorly understood, hindering the clinical translation of combined DWI-MRE markers. We used DWI-MRE to study 129 biomaterial samples including native and cross-linked collagen, glycosaminoglycans (GAGs) with different sulfation levels, and decellularized specimens of pancreas and liver, all with different proportions of solid tissue, or solid fractions. We developed a theoretical framework of the relationship between mechanical loss and tissue-water mobility based on two parameters, solid and fluid viscosity. These parameters revealed distinct DWI-MRE property clusters characterizing weak, moderate, and strong water-network interactions. Sparse networks interacting weakly with water, such as collagen or diluted decellularized tissue, resulted in marginal changes in water diffusion over increasing solid viscosity. In contrast, dense networks with larger solid fractions exhibited both free and hindered water diffusion depending on the polarity of the solid components. For example, polar and highly sulfated GAGs as well as native soft tissues hindered water diffusion despite relatively low solid viscosity. Our results suggest that two fundamental properties of tissue networks, solid fraction and network polarity, critically influence solid and fluid viscosity in biological tissues. Since clinical DWI and MRE are sensitive to these viscosity parameters, the framework we present here can be used to detect tissue remodeling and architectural changes in the setting of diagnostic imaging. STATEMENT OF SIGNIFICANCE: The viscoelastic properties of biological tissues provide a wealth of information on the vital state of cells and host matrix. Combined measurement of viscoelasticity and water diffusion by medical imaging is sensitive to tissue microarchitecture. However, the relationship between viscoelasticity and water diffusion is still poorly understood, hindering full exploitation of these properties as a combined clinical biomarker. Therefore, we analyzed the parameter space accessible by diffusion-weighted imaging (DWI) and magnetic resonance elastography (MRE) and developed a theoretical framework for the relationship between water mobility and mechanical parameters in biomaterials. Our theory of solid material properties related to particle motion can be translated to clinical radiology using clinically established MRE and DWI.

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A DMA (dynamic mechanical analysis)-like device based on the principle of classical viscoelasticity testing is invented to investigate the in-situ/in-vivo shear-bearing mechanism of plantar soft tissue. Forty-three volunteers were recruited for the shear-strain test in the longitudinal and transverse directions at five anatomical spots on the plantar surface. Several encouraging observations indicated significant variances among different spots and individuals, implying that the outer forefoot surrounding the second, fifth metatarsal head is a more intensive shear-bearing region on the plantar surface compared to the inner forefoot under the first metatarsal head, and drawing the hypothesis of a significant effect of BMI on the shear-bearing property. The speculations agree with our expectations and other previous research. The feasibility and practical value of this novel approach are substantiated, and these intriguing discoveries provide foundational underpinnings for further in-depth investigations.

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To investigate the effects of intentionally minimizing spinal motion and abdominal muscle contractions on intervertebral angles during quadruped upper and lower extremity lift (QULEL). Fifteen healthy men performed the QULEL under four conditions: without any special instructions (basic), with the intention to minimize spinal motion (intentional), with abdominal bracing (bracing), and with abdominal hollowing (hollowing). Each intervertebral angle was calculated from the local coordinate system using the marker data obtained from a motion capture system. Shear moduli, as indicators of the activities of the right transversus abdominis (TrA), internal and external oblique, and rectus abdominis muscles, were assessed using shear wave elastography during QULEL. One-way repeated-measures analysis of variance and multiple comparisons among conditions were used to compare each shear modulus of the abdominal muscle and the changes in thoracic kyphosis (Th1-12), lumbar lordosis (L1-5), and lumbar intervertebral angles from the quadruped position to QULEL. The significance level was set at P < 0.05. Changes in lumbar lordosis and L2/L3 and L3/L4 extension angles were significantly lower under hollowing than under other conditions (effect size ηG2: lumbar lordosis, 0.068; L2/L3, 0.072; L3/L4, 0.043). The change in the L1/L2 extension angle significantly decreased in bracing and hollowing compared with the basic (ηG2 = 0.070). Only the TrA shear modulus significantly increased in bracing and hollowing compared with the basic (ηG2 = 0.146). Abdominal hollowing during the QULEL increased TrA activity and suppressed lumbar extension, except at L4/L5, and may be more effective as a rehabilitation exercise for controlling spinal motion.

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To describe the evolution of residual stresses in epoxy resin during the curing process, a more detailed characterization of its viscoelastic properties is necessary. In this study, we have devised a simplified apparatus for assessing the viscoelastic properties of epoxy resin. This apparatus employs a confining cylinder to restrict the circumferential and radial deformations of the material. Following the application of load by the testing machine, the epoxy resin sample gradually reduces the gap between its surface and the inner wall of the confining cylinder, ultimately achieving full contact and establishing a continuous interface. By recording the circumferential stress-strain on the outer surface of the confining cylinder, we can deduce the variations in material bulk and shear moduli with time. This characterization spans eight temperature points surrounding the glass transition temperature, revealing the bulk and shear relaxation moduli of the epoxy resin. Throughout the experiments, the epoxy resin's viscoelastic response demonstrated a pronounced time-temperature dependency. Below the glass transition temperature, the stress relaxation response progressively accelerated with increasing temperature, while beyond the glass transition temperature, the stress relaxation time underwent a substantial reduction. By applying the time-temperature superposition principle, it is possible to construct the relaxation master curves for the bulk and shear moduli of the epoxy resin. By fitting the data, we can obtain expressions for the constitutive model describing the viscoelastic behavior of the epoxy resin. In order to validate the reliability of the test results, a uniaxial tensile relaxation test was conducted on the epoxy resin casting body. The results show good agreement between the obtained uniaxial relaxation modulus curves and those derived from the bulk and shear relaxation modulus equations, confirming the validity of both the device design and the testing methodology.

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Elastomeric biocomposites based on poly(glycerol adipate urethane) and hydroxyapatite were fabricated for tissue regeneration. The poly(glycerol adipate urethane) (PGAU) elastomeric composite matrices were obtained by chemical crosslinking of the poly(glycerol adipate) prepolymer (pPGA) with diisocyanate derivative of L-lysine. Two series of composites varying in the amount of L-lysine diisocyanate ethyl ester (LDI) used as a crosslinking agent were manufactured. As a ceramic filler both unmodified and L-lysine surface-modified hydroxyapatite (HAP) particles were used. The novelty of our research consists in the manufactured elastomeric materials and characterization of their linear viscoelastic (LVE) properties. The LVE properties of the composites were investigated by means of dynamic thermomechanical analysis. Frequency sweep and amplitude sweep measurements were performed in shear mode. The influence of the crosslinking agent (LDI) amount, HAP content and surface modification of HAP on the LVE properties of the composites was determined based on the analysis of the master curves of storage (G') and loss (G″) moduli and of tanδ of the composites. Depending on the amount of LDI, HAP and surface modification, the materials differ in the values of rubber elasticity plateau modulus (G0) and G' and G″ determined at selected shear frequencies and at the glassy state. G0 ranges from 278 kPa to 3.98 MPa, G' in the glassy state is within the range of 219 MPa-459 MPa. The G0 values of the PGAU-based composites are within the stiffness range of soft tissue. In view of the choice of HAP as the ceramic component and the G0 values, elastomeric composites have the potential to be used as filling materials in small bone defects (due to their mechanical similarity to osteoid) as well as materials for cartilage tissue regeneration.

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BACKGROUND: The intrinsic foot muscles play an important role in medial longitudinal arch support, as well as several extrinsic foot muscles. While various strength training methods specific to intrinsic foot muscles have been conducted, these exercises are associated with certain concerns regarding their effectiveness and difficulty. We developed a new exercise for the intrinsic muscles (MTP flexion exercise). OBJECTIVE: The aim was to compare the shear modulus of the toe flexors as the muscle contraction activity during MTP flexion and short-foot exercises using ultrasound shear wave elastography. METHODS: Eleven healthy participants were included in this study. The shear modulus of the toe flexor muscles was measured during MTP flexion and short-foot exercises using ultrasound shear wave elastography. The muscle shear modulus was statistically compared between the resting phase, and during the two exercises. RESULTS: The shear modulus during MTP flexion exercise was significantly greater than in the resting phase in the abductor hallucis, flexor hallucis brevis, flexor digitorum brevis, quadratus plantae, and flexor digitorum longus. The flexor digitorum longus showed greater shear modulus during MTP flexion exercise than during short-foot exercise. CONCLUSION: MTP flexion exercise showed equivalent or greater contraction activity in certain intrinsic and extrinsic foot muscles when compared with short-foot exercise. This exercise is considered one of the training options for strengthening the intrinsic muscles of the foot.

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OBJECTIVE: Tissue susceptibility to histotripsy disintegration has been reported to depend on its elastic properties. This work was aimed at investigation of histotripsy efficiency for liquefaction of human hematomas, depending on their stiffness and degree of retraction over time (0-10 d). METHODS: As an in vitro hematoma model, anticoagulated human blood samples (200 mL) were recalcified at different temperatures. In one set of samples, the shear modulus was measured by shear wave elastography during blood clotting at 10℃, 22℃ and 37℃, and then daily during further aging. The ultrastructure of the samples was analyzed daily with scanning electron microscopy (SEM). Another set of blood samples (50-200 mL) were recalcified at 37℃ for density and retraction measurements over aging and exposed to histotripsy at varying time points. Boiling histotripsy (2.5 ms pulses) and hybrid histotripsy (0.2 ms pulses) exposures (2 MHz, 1% dc, P+/P-/As = 182/-27/207 MPa in situ) were used to produce either individual cigar-shaped or volumetric (0.8-3 mL) lesions in samples incubated for 3 h, 5 d and 10 d. The obtained lesions were sized, then the lysate aspirated under B-mode guidance was analyzed ultrastructurally and diluted in distilled water for sizing of residual fragments. RESULTS: It was found that clotting time decreased from 113 to 25 min with the increase in blood temperature from 10℃ to 37℃. The shear modulus increased to 0.53 ± 0.17 kPa during clotting and remained constant within 8 d of incubation at 2℃. Sample volumes decreased by 57% because of retraction within 10 d. SEM revealed significant echinocytosis but unchanged ultrastructure of the fibrin meshwork. Liquefaction rate and lesion dimensions produced with the same histotripsy protocols correlated with the increase in the degree of retraction and were lower in retracted samples versus freshly clotted samples. More than 80% of residual fibrin fragments after histotripsy treatment were shorter than 150 µm; the maximum length was 208 µm, allowing for unobstructed aspiration of the lysate with most clinically used needles. CONCLUSION: The results indicate that hematoma susceptibility to histotripsy liquefaction is not entirely determined by its stiffness, and correlates with the retraction degree.

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PURPOSE: This study compares the acute effects of a static stretching and a warmup protocol on the active and passive shear modulus of the hamstring muscles. METHODS: Muscle shear modulus was assessed at rest and during isometric contractions at 20 % of maximal voluntary isometric contraction (MVIC). RESULTS: After stretching, the passive shear modulus pattern was not altered, while at 20 % MVIC the biceps femoris short head (BFsh) and semimembranosus showed a shear modulus increase and decrease, respectively, which resulted on BFsh-SM pair differences (pre: 3.8 ±â€¯16.8 vs. post: 39.3 ±â€¯25.1 kPa; p < 0.001; d = 1.66) which was accompanied by a decrease of 18.3 % on MVIC. Following the warmup protocol, passive shear modulus remained unchanged, while active shear modulus was decreased for the semitendinosus (pre: 65.3 ±â€¯13.5 vs. post: 60.3 ±â€¯12.3 kPa; p = 0.035; d = 0.4). However, this difference was within the standard error of measurement (10.54 kPa), and did not impact the force production, since it increased only 1.4 % after the warmup. CONCLUSIONS: The results of this study suggest that the passive and active shear modulus responses of the individual hamstring muscles to static stretching are muscle-specific and that passive and active hamstring shear modulus are not changed by a standard warmup intervention.

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Objective.Skeletal muscles are organized into distinct layers and exhibit anisotropic characteristics across various scales. Assessing the arrangement of skeletal muscles may provide valuable biomarkers for diagnosing muscle-related pathologies and evaluating the efficacy of clinical interventions.Approach. In this study, we propose a novel ultrafast ultrasound sequence constituted of steered pushing beams was proposed for ultrasound elastography applications in transverse isotropic muscle. Based on the propagation of the shear wave vertical mode, it is possible to fit the experimental results to retrieve in the same imaging plane, the shear modulus parallel to fibers as well as the elastic anisotropy factor (ratio of Young's moduli times the shear modulus perpendicular to fibers).Main results. The technique was demonstratedin vitroin phantoms andex vivoin fusiform beef muscles. At last, the technique was appliedin vivoon fusiform muscles (biceps brachii) and mono-pennate muscles (gastrocnemius medialis) during stretching and contraction.Significance. This novel sequence provides access to new structural and mechanical biomarkers of muscle tissue, including the elastic anisotropy factor, within the same imaging plane. Additionally, it enables the investigation of multiples parameters during muscle active and passive length changes.

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This study aimed to determine whether changes in hamstrings passive and active shear modulus after a warmup protocol are correlated. Twenty males without a history of hamstring strain injury participated. Muscle shear modulus was assessed using ultrasound-based shear wave elastography at rest and during isometric contractions at 20% of maximal voluntary isometric effort before and immediately after a warmup protocol. Changes in passive shear modulus did not seem to be associated with changes in active shear modulus. The results of this study suggest that changes in passive and active hamstring shear modulus are not associated after a standardized warmup intervention.

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Rotator cuff tear is a common shoulder injury that causes shoulder dysfunction and pain. Although surgical repair is the primary treatment for rotator cuff tear, it is well recognized that impaired force exertion of muscles connecting to the involved tendon and subsequent complemental change in the force exertion of synergist muscles persist even after repair. This study aimed to identify the compensation strategy of shoulder abductors by examining how synergist muscles respond to supraspinatus (SSP) muscle force deficit in patients with rotator cuff repair. Muscle shear modulus, an index of muscle force, was assessed for SSP, infraspinatus, upper trapezius, and middle deltoid muscles in repaired and contralateral control shoulders of 15 patients with unilateral tendon repair of the SSP muscle using ultrasound shear wave elastography while the patients passively or actively held their arm in shoulder abduction. In the repaired shoulder, the shear modulus of the SSP muscle declined, whereas that of other synergist muscles did not differ relative to that of the control. To find the association between the affected SSP and each of the synergist muscles, a regression analysis was used to assess the shear moduli at the population level. However, no association was observed between them. At the individual level, there was a tendency of variation among patients with regard to a specific muscle whose shear modulus complementarily increased. These results suggest that the compensation strategy for SSP muscle force deficit varies among individuals, being nonstereotypical in patients with rotator cuff injury.

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Introduction: While shear modulus has been used as an index of muscle elongation, high costs prevent its general adoption. A more general indicator that can quantify muscle elongation non-invasively is needed to develop effective methods for stretching each muscle. The purpose of this study was to determine whether the echo intensity of the muscle changes with muscle elongation compared with the shear modulus. Methods: Sixteen healthy males (24.1 ± 2.8 years) participated in the study. Shear modulus and echo intensity of the medial gastrocnemius were assessed at 20° and 10° of ankle plantar-flexion, and 0°, 10°, and 20° of ankle dorsiflexion (presented as -20°, -10°, and 0°, +10°, +20°, respectively). Shear modulus was measured using ultrasound shear wave elastography. The echo intensity was quantified using the average grayscale value of a given region of interest (RoI) in longitudinal and transverse B-mode images. Grayscale analysis was performed using two RoIs: one which included as much of the muscle as possible (maximum RoI), and a rectangular one whose size and depth was identical for all images (rectangular RoI). Pearson's correlation coefficients between either the shear modulus or echo intensity and the ankle angle and between the echo intensity and shear modulus were calculated separately for each participant. Results: Average Pearson's correlation coefficient between shear modulus and ankle angle of the participants was 0.904. The average Pearson's correlation coefficients between the echo intensity and ankle angle were estimated to be 0.797 and 0.222 for the maximum RoI and 0.698 and 0.323 for the rectangular RoI in the longitudinal and transverse images, respectively. The average Pearson's correlation coefficients between the echo intensity and shear modulus were 0.684 and 0.514 for the maximum RoI, and 0.611 and 0.409 for rectangular RoI in the longitudinal and transverse images, respectively. Discussion: The results indicate that the echo intensity in the longitudinal image of the gastrocnemius, especially when assessed using the maximum RoI, increased with muscle elongation by passive ankle dorsiflexion. Therefore, assessment of the echo intensity using the maximum RoI in the longitudinal image might be useful for quantifying the muscle elongation.

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PURPOSE: This study aimed i) to investigate the mechanical, morphological, and compositional characteristics of the supraspinatus muscle after rotator cuff repair by using ultrasound shear wave elastography (SWE) and B-mode imaging, and ii) to determine whether the morphological or compositional characteristics are associated with the mechanical characteristic of the supraspinatus during contraction. METHODS: Using SWE and B-mode imaging, active and passive shear moduli, muscle thickness, and echo intensity of the supraspinatus were measured from the repaired and contralateral control shoulders of 22 patients with rotator cuff repair. The shear modulus, muscle thickness, and echo intensity were compared between the repaired and control shoulders. The association between the active shear modulus and the other variables was determined. RESULTS: While the active and passive shear moduli were lower in the repaired shoulder compared to the control, the muscle thickness and echo intensity did not vary between them. Interestingly, the passive shear modulus was positively correlated with the active shear modulus only in the control shoulder. CONCLUSION: The mechanical characteristic of supraspinatus remains impaired, even without degenerative changes in the morphological and compositional characteristics after rotator cuff repair. Furthermore, the association between contractile and elastic characteristics in the supraspinatus was deteriorated in control shoulder.

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Timoshenko presented the torsional rigidity of an isotropic rectangular bar, and Lekhnitskii presented that of an orthotropic rectangular bar. The solutions of Timoshenko and Lekhnitskii (T&L) are functions of the bar's length, width, thickness and shear modulus or moduli. However, the functions of T&L solutions become different from their original ones when the width and thickness are swapped. Swapping the width and thickness definitions does not alter the bar's physical properties, named the "rule of swapping" by the authors. In the last century, no research has shown the T&L solutions to satisfy the rule of swapping, an observation hereinafter referred to as the "Timoshenko & Lekhnitskii Puzzle". Roughly 90 years later, Tsai et al. re-solved T&L cases using the TSAI technique. The derived solutions are nearly if not completely identical to T&L's numerically and satisfy the rule of swapping automatically. The rule of swapping is a novel issue and has never been mentioned before. Based on the Weierstrass factorization theorem, this study mathematically proves that they are identical for isotropic and orthotropic bars and satisfy the rule of swapping. The result of a torsional pendulum test is analyzed to support the rule.