A study on Rayleigh wave dispersion in bone according to Mindlin's Form II gradient elasticity.

The classical elasticity cannot effectively describe bone's mechanical behavior since only homogeneous media and local stresses are assumed. Additionally, it cannot predict the dispersive nature of the Rayleigh wave which has been reported in experimental studies and was also demonstrated in a previous computational study by adopting Mindlin's Form II gradient elasticity. In this work Mindlin's theory is employed to analytically determine the dispersion of Rayleigh waves in a strain gradient elastic half-space. An isotropic semi-infinite space is considered with properties equal to those of bone and dynamic behavior suffering from microstructural effects. Microstructural effects are considered by incorporating four intrinsic parameters in the stress analysis. The results are presented in the form of group and phase velocity dispersion curves and compared with existing computational results and semi-analytical curves calculated for a simpler case of Rayleigh waves in dipolar gradient elastic half-spaces. Comparisons are also performed with the velocity of the first-order antisymmetric mode propagating in a dipolar plate so as to observe the Rayleigh asymptotic behavior. It is shown that Mindlin's Form II gradient elasticity can effectively describe the dispersive nature of Rayleigh waves. This study could be regarded as a step toward the ultrasonic characterization of bone.

Dendritic brushes under theta and poor solvent conditions.

The effects of solvent quality on the internal stratification of polymer brushes formed by dendron polymers up to third generation were studied by means of molecular dynamics simulations with Langevin thermostat. The distributions of polymer units, of the free ends, the radii of gyration, and the back folding probabilities of the dendritic spacers were studied at the macroscopic states of theta and poor solvent. For high grafting densities we observed a small decrease in the height of the brush as the solvent quality decreases. The internal stratification in theta solvent was similar to the one we found in good solvent, with two and in some cases three kinds of populations containing short dendrons with weakly extended spacers, intermediate-height dendrons, and tall dendrons with highly stretched spacers. The differences increase as the grafting density decreases and single dendron populations were evident in theta and poor solvent. In poor solvent at low grafting densities, solvent micelles, polymeric pinned lamellae, spherical and single chain collapsed micelles were observed. The scaling dependence of the height of the dendritic brush at high density brushes for both solvents was found to be in agreement with existing analytical results.

A quasi-lumped model for the peripheral distortion of the arterial pulse.

As blood circulates through the arterial tree, the flow and pressure pulse distort. Principal factors to this distortion are reflections form arterial bifurcations and the viscous character of the flow of the blood. Both of them are expounded in the literature and included in our analysis. The nonlinearities of inertial effects are usually taken into account in numerical simulations, based on Navier-Stokes like equations. Nevertheless, there isn't any qualitative, analytical formula, which examines the role of blood's inertia on the distortion of the pulse. We derive such an analytical nonlinear formula. It emanates from a generalized Bernoulli's equation for an an-harmonic, linear, viscoelastic, Maxwell fluid flow in a linear, viscoelastic, Kelvin-Voigt, thin, cylindrical vessel. We report that close to the heart, convection effects related to the change in the magnitude of the velocity of blood dominate the alteration of the shape of the pressure pulse, while at remote sites of the vascular tree, convection of vorticity, related to the change in the direction of the velocity of blood with respect to a mean axial flow, prevails. A quantitative comparison between the an-harmonic theory and related pressure measurements is also performed.

Velocity dispersion of guided waves propagating in a free gradient elastic plate: application to cortical bone.

The classical linear theory of elasticity has been largely used for the ultrasonic characterization of bone. However, linear elasticity cannot adequately describe the mechanical behavior of materials with microstructure in which the stress state has to be defined in a non-local manner. In this study, the simplest form of gradient theory (Mindlin Form-II) is used to theoretically determine the velocity dispersion curves of guided modes propagating in isotropic bone-mimicking plates. Two additional terms are included in the constitutive equations representing the characteristic length in bone: (a) the gradient coefficient g, introduced in the strain energy, and (b) the micro-inertia term h, in the kinetic energy. The plate was assumed free of stresses and of double stresses. Two cases were studied for the characteristic length: h=10(-4) m and h=10(-5) m. For each case, three subcases for g were assumed, namely, g>h, g

The effect of boundary conditions on guided wave propagation in two-dimensional models of healing bone.

Guided wave propagation has recently drawn significant interest in the ultrasonic characterization of bone. In this work, we present a two-dimensional computational study of ultrasound propagation in healing bones aiming at monitoring the fracture healing process. In particular, we address the effect of fluid loading boundary conditions on the characteristics of guided wave propagation, using both time and time-frequency (t-f) signal analysis techniques, for three study cases. In the first case, the bone was assumed immersed in blood which occupied the semi-infinite spaces of the upper and lower surfaces of the plate. In the second case, the bone model was assumed to have the upper surface loaded by a 2mm thick layer of blood and the lower surface loaded by a semi-infinite fluid with properties close to those of bone marrow. The third case, involves a three-layer model in which the upper surface of the plate was again loaded by a layer of blood, whereas the lower surface was loaded by a 2mm layer of a fluid which simulated bone marrow. The callus tissue was modeled as an inhomogeneous material and fracture healing was simulated as a three-stage process. The results clearly indicate that the application of realistic boundary conditions has a significant effect on the dispersion of guided waves when compared to simplified models in which the bone's surfaces are assumed free.