Jenni Heino

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.

Estimation of optical absorption in anisotropic background

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.

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.

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.

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.

Diffuse Optical Imaging

Diffuse optical imaging is a functional medical imaging modality which takes advantage of the relatively low attenuation of near-infrared light to probe the internal optical properties of tissue. The optical properties are affected by parameters related to physiology such as the concentrations of oxy- and deoxyhemoglobin. Instrumentation that is used for optical imaging is generally able to measure changes in the attenuation of light at several wavelengths, and in the case of time- and frequency-domain instrumentation, the time-of-flight of the photons in tissue.

Computational modelling of cellular level metabolism

The steady and stationary state inverse problems consist of estimating the reaction and transport fluxes, blood concentrations and possibly the rates of change of some of the concentrations based on data which are often scarce noisy and sampled over a population. The Bayesian framework provides a natural setting for the solution of this inverse problem, because a priori knowledge about the system itself and the unknown reaction fluxes and transport rates can compensate for the insufficiency of measured data, provided that the computational costs do not become prohibitive. This article identifies the computational challenges which have to be met when analyzing the steady and stationary states of multicompartment model for cellular metabolism and suggest stable and efficient ways to handle the computations. The outline of a computational tool based on the Bayesian paradigm for the simulation and analysis of complex cellular metabolic systems is also presented.

Topographical brain activation studies using diffuse optical imaging in the frequency domain

The design of a four-channel frequency-domain instrument developed for various applications of diffuse optical imaging is presented. We also report an imaging technique applied for topographical brain-activation studies. Preliminary results of these studies using motor and auditory stimuli are given. Activation areas have been successfully located on the cortex.