Based on contact fractal theory, a modified MB fractal model, and from the energy dissipation point and considering the mechanism of energy dissipation of joint interfaces, tangential damping and its dissipation factor models of joint interfaces are proposed. Numerical simulations reveal the varying relations of tangential damping and its dissipation factor versus corresponding parameters such as fractal dimension, fractal roughness, friction factor, and plastic index. A micro convex nonlinear relation (when fractal dimension is between 1.1 and 1.4) or near linear relation(when fractal dimension is between 1.4 and 1.9) between dimensionless tangential damping and dimensionless normal contact force over the joint interfaces varies with the fractal dimension of the surface profiles, dimensionless tangential damping increases(when fractal dimension is between 1.1 and 1.7) or decreases (when fractal dimension is between 1.7 and 1.9) with the increment of fractal dimension, and decreases with the increase of dimensionless fractal roughness. While the influences of plastic index, the ratio of hardness to yield strength, and the ratio of total tangential force to total normal force on dimensionless tangential damping are similar, and a concave nonlinear relation between tangential damping dissipation factor and the normal contact force over the joint interfaces, the tangential damping dissipation factor, meanwhile, decreases with the increment of the friction factor. In addition, the validation of the tangential contact damping model is implemented in indirect ways, which make comparison between the proposed tangential stiffness model and the literature.

Accurate simulation of temperature distribution in tumors induced by gold nanorods during laser photothermal therapy relies on precise measurements of thermal, optical, and physiological properties of the tumor with or without nanorods present. In this study, a computational Monte Carlo simulation algorithm is developed to simulate photon propagation in a spherical tumor to calculate laser energy absorption in the tumor and examine the effects of the absorption (μa) and scattering (μs) coefficients of tumors on the generated heating pattern in the tumor. The laser-generated energy deposition distribution is then incorporated into a 3D finite-element model of prostatic tumors embedded in a mouse body to simulate temperature elevations during laser photothermal therapy using gold nanorods. The simulated temperature elevations are compared with measured temperatures in PC3 prostatic tumors in our previous in vivo experimental studies to extract the optical properties of PC3 tumors containing different concentrations of gold nanorods. It has been shown that the total laser energy deposited in the tumor is dominated by μa, while both μa and μs shift the distribution of the energy deposition in the tumor. Three sets of μa and μs are extracted, representing the corresponding optical properties of PC3 tumors containing different concentrations of nanorods to laser irradiance at 808 nm wavelength. With the injection of 0.1 cc of a 250 optical density (OD) nanorod solution, the total laser energy absorption rate is increased by 30% from the case of injecting 0.1 cc of a 50 OD nanorod solution, and by 125% from the control case without nanorod injection. Based on the simulated temperature elevations in the tumor, it is likely that after heating for 15 min, permanent thermal damage occurs in the tumor injected with the 250 OD nanorod solution, while thermal damage to the control tumor and the one injected with the 50 OD nanorod solution may be incomplete.