Fluorescence lifetime optical tomography with Discontinuous Galerkin discretisation scheme.

We develop discontinuous Galerkin framework for solving direct and inverse problems in fluorescence diffusion optical tomography in turbid media. We show the advantages and the disadvantages of this method by comparing it with previously developed framework based on the finite volume discretization. The reconstruction algorithm was used with time-gated experimental dataset acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Optical parameters, quantum yield and lifetime were simultaneously reconstructed. Reconstruction results are presented and discussed.

Statistical modelling of the whole human femur incorporating geometric and material properties.

When analysing the performance of orthopaedic implants the vast majority of computational studies use either a single or limited number of bone models. The results are then extrapolated to the population as a whole, overlooking the inherent and large interpatient variability in bone quality and geometry. This paper describes the creation of a three dimensional, statistical, finite element analysis (FEA) ready model of the femur using principal component analysis. To achieve this a registration scheme based on elastic surface matching and a mesh morphing algorithm has been developed. This method is fully automated enabling registration and generation of high resolution models. The variation in both geometry and material properties was extracted from 46 computer tomography scans and captured by the statistical model. Analysis of mesh quality showed this was maintained throughout the model generation and sampling process. Reconstruction of the training femurs showed 35 eigenmodes were required for accurate reproduction. A set of unique, anatomically realistic femur models were generated using the statistical model, with a variation comparable to that seen in the population. This study illustrates a methodology with the potential to generate femur models incorporating material properties for large scale multi-femur finite element studies.

Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.

In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.