Local 3D scaling properties for the analysis of trabecular bone extracted from high-resolution magnetic resonance imaging of human trabecular bone: comparison with bone mineral density in the prediction of biomechanical strength in vitro.

Rationale And Objectives: A novel, nonlinear morphologic measure [DeltaP(alpha)] based on local 3D scaling properties was applied to high-resolution magnetic resonance images (HR-MRI) of human trabecular bone to predict biomechanical strength in vitro.

Methods: We extracted DeltaP(alpha) and traditional morphologic parameters (apparent trabecular volume fraction, apparent trabecular separation) from HR-MR images of 32 femoral and 13 spinal bone specimens. Furthermore, bone mineral density (BMD) and maximum compressive strength (MCS) were determined.

First-order irreversible phase transitions in a nonequilibrium system: mean-field analysis and simulation results.

First-order irreversible phase transitions (IPT's) between an active regime and an absorbing state are studied in a single-component, two-dimensional interacting particle system by means of both simulations and a mean-field analysis. Several features obtained using the mean-field approximation such as the presence of a first-order IPT and hysteresis effects, are in excellent agreement with simulation results. In addition, extensive epidemic simulations show that the dynamical critical behavior of the system is by no means scale invariant.

Competitive growth model involving random deposition and random deposition with surface relaxation.

A deposition model that considers a mixture of random deposition with surface relaxation and a pure random deposition is proposed and studied. As the system evolves, random deposition with surface relaxation (pure random deposition) take place with probability p and (1-p), respectively. The discrete (microscopic) approach to the model is studied by means of extensive numerical simulations, while continuous equations are used in order to investigate the mesoscopic properties of the model.