RESUMEN
Bone healing involves a series of complicated cellular and molecular mechanisms that result in bone formation. Several mechanobiological models have been developed to simulate these cellular mechanisms via diffusive processes. In most cases solution to diffusion equations is accomplished using the Finite Element Method (FEM) which however requires global remeshing in problems with moving or new born surfaces or material phases. This limitation is addressed in meshless methods in which no background cells are needed for the numerical solution of the integrals. In this study a new meshless Local Boundary Integral Equation (LBIE) method is employed for deriving predictions of cell proliferation during bone healing. First a benchmark problem is presented to assess the accuracy of the method. Then the LBIE method is utilized for the solution of cell diffusion problem in a two-dimensional (2D) model of fractured model. Our findings indicate that the proposed here LBIE method can successfully predict cell distributions during fracture healing.
Asunto(s)
Algoritmos , Curación de Fractura , Fracturas Óseas/patología , Callo Óseo/fisiología , Movimiento Celular , Proliferación Celular , Análisis de Elementos Finitos , Humanos , Células Madre Mesenquimatosas/citología , Modelos Biológicos , Factores de TiempoRESUMEN
In low flow rates, red blood cells (RBCs) fasten together along their axis of symmetry and form a so-called rouleaux. The scattering of He-Ne laser light by a rouleau consisting of n (2 < or = n < or = 8) average-sized RBCs is investigated. The interaction problem is treated numerically by means of an advanced axisymmetric boundary element--fast Fourier transform methodology. The scattering problem of one RBC was solved first, and the results showed that the influence of the RBC's membrane on the scattering patterns is negligible. Thus the rouleau is modeled as an axisymmetric, homogeneous, low-contrast dielectric cylinder, on the surface of which appears, owing to aggregated RBCs, a periodic roughness along the direction of symmetry. The direction of the incident laser light is considered to be perpendicular to the scatterer's axis of symmetry. The differential scattering cross sections in both perpendicular and parallel scattering planes and for all the scattering angles are calculated and presented in detail.