Metabolica: a statistical research tool for analyzing metabolic networks.

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.

Bayesian flux balance analysis applied to a skeletal muscle metabolic model.

In this article, the steady state condition for the multi-compartment models for cellular metabolism is considered. The problem is to estimate the reaction and transport fluxes, as well as the concentrations in venous blood when the stoichiometry and bound constraints for the fluxes and the concentrations are given. The problem has been addressed previously by a number of authors, and optimization-based approaches as well as extreme pathway analysis have been proposed. These approaches are briefly discussed here. The main emphasis of this work is a Bayesian statistical approach to the flux balance analysis (FBA). We show how the bound constraints and optimality conditions such as maximizing the oxidative phosphorylation flux can be incorporated into the model in the Bayesian framework by proper construction of the prior densities. We propose an effective Markov chain Monte Carlo (MCMC) scheme to explore the posterior densities, and compare the results with those obtained via the previously studied linear programming (LP) approach. The proposed methodology, which is applied here to a two-compartment model for skeletal muscle metabolism, can be extended to more complex models.

Comparison between a time-domain and a frequency-domain system for optical tomography.

The quality of phase and amplitude data from two medical optical tomography systems were compared. The two systems are a 32-channel time-domain system developed at University College London (UCL) and a 16-channel frequency-domain system developed at Helsinki University of Technology (HUT). Difference data measured from an inhomogeneous and a homogeneous phantom were compared with a finite-element method (diffusion equation) and images of scattering and absorption were reconstructed based on it. The measurements were performed at measurement times between 1 and 30 s per source. The mean rms errors in the data measured by the HUT system were 3.4% for amplitude and 0.51 deg for phase, while the corresponding values for the UCL data were 6.0% and 0.46 deg, respectively. The reproducibility of the data measured with the two systems was tested with a measurement time of 5 s per source. It was 0.4% in amplitude for the HUT system and 4% for the UCL system, and 0.08 deg in phase for both systems. The image quality of the reconstructions from the data measured with the two systems were compared with several quantitative criteria. In general a higher contrast was observed in the images calculated from the HUT data.

Compensation for geometric mismodelling by anisotropies in optical tomography.

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.

A modelling error approach for the estimation of optical absorption in the presence of anisotropies.

Optical tomography is an emerging method for non-invasive imaging of human tissues using near-infrared light. Generally, the tissue is assumed isotropic, but this may not always be true. In this paper, we present a method for the estimation of optical absorption coefficient allowing the background to be anisotropic. To solve the forward problem, we model the light propagation in tissue using an anisotropic diffusion equation. The inverse problem consists of the estimation of the absorption coefficient based on boundary measurements. Generally, the background anisotropy cannot be assumed to be known. We treat the uncertainties in the background anisotropy parameter values as modelling error, and include this in our model and reconstruction. We present numerical examples based on simulated data. For reference, examples using an isotropic inversion scheme are also included. The estimates are qualitatively different for the two methods.

Anisotropic effects in highly scattering media.

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.