In this paper, we study anisotropic scattering and light propagation models applicable to diffuse optical tomography. We propose a model for anisotropic scattering in the radiative transfer framework and derive the corresponding anisotropic diffusion model. To verify the anisotropic diffusion model, we consider the case of a simple anisotropic scattering model also presentable within the diffusion approximation. For numerical computations, we present a three-dimensional (3D) anisotropic Monte Carlo model and 2D finite element and boundary element solutions of the anisotropic diffusion model, and compare the results of the simulations.

We propose an approach for the estimation of the optical absorption coefficient in medical optical tomography in the presence of geometric mismodelling. We focus on cases in which the boundaries of the measurement domain or the optode positions are not accurately known. In general, geometric distortion of the domain produces anisotropic changes for the material parameters in the model. Hence, geometric mismodelling in an isotropic case may correspond to an anisotropic model. We seek to approximate the errors due to geometric mismodelling as extraneous additive noise and to pose a simple anisotropic model for the diffusion coefficient. We show that while geometric mismodelling may deteriorate the estimates of the absorption coefficient significantly, using the proposed model enables the recovery of the main features.

In this paper we present a model for anisotropic light propagation and reconstructions of optical absorption coefficient in the presence of anisotropies. To model the anisotropies, we derive the diffusion equation in an anisotropic case, and present the diffusion matrix as an eigenvalue decomposition. The inverse problem considered in this paper is to estimate the optical absorption when the directions of anisotropy are known, but the strength may vary. To solve this inverse problem, two approaches are taken. First, we assume that the strength of anisotropy is known, and compare maximum a posteriori reconstructions using a fixed value for the strength when the value for the strength is both correct and incorrect. We then extend the solution to allow an uncertainty of the strength of the anisotropy by choosing a prior distribution for the strength and calculating the marginal posterior density. Numerical examples of maximum a posteriori estimates are again presented. The results in this paper suggest that the anisotropy of the body is a property that cannot be ignored in the estimation of the absorption coefficient.

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Steady state flux balance analysis (FBA) for cellular metabolism is used, e.g., to seek information on the activity of the different pathways under equilibrium conditions, or as a basis for kinetic models. In metabolic models, the stoichiometry of the system, commonly completed with bounds on some of the variables, is used as the constraint in the search of a meaningful solution. As model complexity and number of constraints increase, deterministic approach to FBA is no longer viable: a multitude of very different solutions may exist, or the constraints may be in conflict, implying that no precise solution can be found. Moreover, the solution may become overly sensitive to parameter values defining the constraints. Bayesian FBA treats the unknowns as random variables and provides estimates of their probability density functions. This stochastic setting naturally represents the variability which can be expected to occur over a population and helps to circumvent the drawbacks of the classical approach, but its implementation can be quite tedious for users without background in statistical computations. This article presents a software package called METABOLICA for performing Bayesian FBA for complex multi-compartment models and visualization of the results.