Sensitivity of the shear wave speed-stress relationship to soft tissue material properties and fiber alignment.

The use of shear wave propagation to noninvasively measure material properties and loading in tendons and ligaments is a growing area of interest in biomechanics. Prior models and experiments suggest that shear wave speed primarily depends on the apparent shear modulus (i.e., shear modulus accounting for contributions from all constituents) at low loads, and then increases with axial stress when axially loaded. However, differences in the magnitudes of shear wave speeds between ligaments and tendons, which have different substructures, suggest that the tissue's composition and fiber alignment may also affect shear wave propagation. Accordingly, the objectives of this study were to (1) characterize changes in the apparent shear modulus induced by variations in constitutive properties and fiber alignment, and (2) determine the sensitivity of the shear wave speed-stress relationship to variations in constitutive properties and fiber alignment. To enable systematic variations of both constitutive properties and fiber alignment, we developed a finite element model that represented an isotropic ground matrix with an embedded fiber distribution. Using this model, we performed dynamic simulations of shear wave propagation at axial strains from 0% to 10%. We characterized the shear wave speed-stress relationship using a simple linear regression between shear wave speed squared and axial stress, which is based on an analytical relationship derived from a tensioned beam model. We found that predicted shear wave speeds were both in-range with shear wave speeds in previous in vivo and ex vivo studies, and strongly correlated with the axial stress (R2 = 0.99). The slope of the squared shear wave speed-axial stress relationship was highly sensitive to changes in tissue density. Both the intercept of this relationship and the apparent shear modulus were sensitive to both the shear modulus of the ground matrix and the stiffness of the fibers' toe-region when the fibers were less well-aligned to the loading direction. We also determined that the tensioned beam model overpredicted the axial tissue stress with increasing load when the model had less well-aligned fibers. This indicates that the shear wave speed increases likely in response to a load-dependent increase in the apparent shear modulus. Our findings suggest that researchers may need to consider both the material and structural properties (i.e., fiber alignment) of tendon and ligament when measuring shear wave speeds in pathological tissues or tissues with less well-aligned fibers.

Calibration of the shear wave speed-stress relationship in ex vivo tendons.

It has recently been shown that shear wave speed in tendons is directly dependent on axial stress. Hence, wave speed could be used to infer tendon load provided that the wave speed-stress relationship can be calibrated and remains robust across loading conditions. The purpose of this study was to investigate the effects of loading rate and fluid immersion on the wave speed-stress relationship in ex vivo tendons, and to assess potential calibration techniques. Tendon wave speed and axial stress were measured in 20 porcine digital flexor tendons during cyclic (0.5, 1.0 and 2.0 Hz) or static axial loading. Squared wave speed was highly correlated to stress (r2avg = 0.98) and was insensitive to loading rate (p = 0.57). The constant of proportionality is the effective density, which reflects the density of the tendon tissue and additional effective mass added by the adjacent fluid. Effective densities of tendons vibrating in a saline bath averaged 1680 kg/m3 and added mass effects caused wave speeds to be 22% lower on average in a saline bath than in air. The root-mean-square error between predicted and measured stress was 0.67 MPa (6.7% of maximum stress) when using tendon-specific calibration parameters. These errors increased to 1.31 MPa (13.1% of maximum stress) when calibrating based on group-compiled data from ten tendons. These results support the feasibility of calculating absolute tendon stresses from wave speed squared based on linear calibration relationships.

Gauging force by tapping tendons.

Muscles are the actuators that drive human movement. However, despite many decades of work, we still cannot readily assess the forces that muscles transmit during human movement. Direct measurements of muscle-tendon loads are invasive and modeling approaches require many assumptions. Here, we introduce a non-invasive approach to assess tendon loads by tracking vibrational behavior. We first show that the speed of shear wave propagation in tendon increases with the square root of axial stress. We then introduce a remarkably simple shear wave tensiometer that uses micron-scale taps and skin-mounted accelerometers to track tendon wave speeds in vivo. Tendon wave speeds are shown to modulate in phase with active joint torques during isometric exertions, walking, and running. The capacity to non-invasively assess muscle-tendon loading can provide new insights into the motor control and biomechanics underlying movement, and could lead to enhanced clinical treatment of musculoskeletal injuries and diseases.

Advanced age brings a greater reliance on visual feedback to maintain balance during walking.

We implemented a virtual reality system to quantify differences in the use of visual feedback to maintain balance during walking between healthy young (n=12, mean age: 24 years) and healthy old (n=11, 71 years) adults. Subjects walked on a treadmill while watching a speed-matched, virtual hallway with and without mediolateral visual perturbations. A motion capture system tracked center of mass (CoM) motion and foot kinematics. Spectral analysis, detrended fluctuation analysis, and local divergence exponents quantified old and young adults' dynamic response to visual perturbations. Old and young adults walked normally with comparable CoM spectral characteristics, lateral step placement temporal persistence, and local divergence exponents. Perturbed visual flow induced significantly larger changes in mediolateral CoM motion in old vs. young adults. Moreover, visual perturbations disrupted the control of lateral step placement and compromised local dynamic stability more significantly in old than young adults. Advanced age induces a greater reliance on visual feedback to maintain balance during waking, an effect that may compensate for degradations in somatosensation. Our findings are relevant to the early diagnosis of sensory-induced balance impairments and also point to the potential use of virtual reality to evaluate sensory rehabilitation and balance training programs for old adults.

Error in dynamic spring constant calibration of atomic force microscope probes due to nonuniform cantilevers.

Many common atomic force microscope (AFM) spring constant calibration methods regard the AFM probe as a uniform cantilever, neglecting the tip mass and any nonuniformity in the thickness of the probe along its length. This work quantifies the error in the spring constant estimated by the Sader and thermal calibration methods due to nonuniformity in the thickness of the cantilever and the influence of the mass loading effect of the probe tip. Formulae are presented that can be used to compute the uncertainty in cantilever calibration for an arbitrary thickness nonuniformity, or to correct the calibration methods if the thickness nonuniformity is known. The results show that both methods are quite sensitive to nonuniformity. When the first dynamic mode is used in the calibration, the error in the spring constant estimated by either method is between - 4% and 9% for a cantilever whose thickness increases or decreases linearly by 30% along its length. The errors are several times larger if the second or higher dynamic modes are used. To illustrate the proposed methods, a commercial AFM probe that has significant nonuniformity is considered and the error in calibrating this probe is quantified and discussed. For this particular probe, variations in the thickness of the probe over the last 15% of its length are found to significantly reduce the accuracy of the calibration when the thermal method is used, since that method is sensitive to changes in the shape of the eigenmode of the probe near its free end.