Parameter and Structure Identification in Optical Tomography

This project is funded under EPSRC Grant EP/E034950/1. Principal investigator: Simon R. Arridge. Other investigators: Adam P. Gibson, Jem. C. Hebden, Simon J. D. Prince.

Synopsis

Diffuse optical tomography (DOT) is a non-invasive technique for imaging the optical properties of biological tissue. It operates my measuring light transmission though the body between different points on the surface. The distribution of photons in these boundary measurements, as well as the temporal dispersion and spectral information, can be used to reconstruct images of the internal distribution of optical absorption and scattering coefficients. DOT is faster and cheaper than alternative imaging methods. The hardware is compact, allowing use in clinical settings where other imaging modalities are impractical.

The resulting images support a wide range of clinical applications. These include the non-invasive detection of breast tumours, functional imaging of muscle and brain activity, estimation of cerebral oxygenation and haemodynamics, measurement of cytochrome oxidase and mitrochondrial energetics, investigation of oxidative metabolism in muscle, measurement of tissue viability in transplantation of organs, and detection of abnormalities in joints of arthritic patients.

DOT is generally recognised as a nonlinear inverse problem. We construct a physically accurate model that describes the progress of photons from the source optodes through the media and to the detector optodes. This is termed the forward problem. This model is parameterised by the spatial distribution of scattering and absorption properties in the media. We adjust these properties iteratively until the predicted measurements from the forward model match the physical measurements from the device. This is termed the inverse problem.

This project

Despite its advantages, DOT is not yet widely used in clinical practice. Its major drawback is the relatively slow and inaccurate image reconstruction process. Previous funding has concentrated on the development of experimental methods and numerical tools for solving the forward problem. This project adresses the image reconstruction problem and proposes methods to make it faster, more accurate and more robust. Three strategies are pursued:

Model reduction

The construction of a sufficiently accurate forward model can be computationally prohibitive or fundamentally impossible. In the approximation error method we abandon the need to produce an “exact model”. Instead, we attempt to determine the statistical properties of the modelling errors and compensate for them by incorporating them into the image reconstruction using a Bayesian approach that can operate on a “coarse model” by describing its statistical properties in comparison with a high-fidelity model. Preliminary studies have shown that this approach can produce results comparable with a significanly more accurate forward model, while being an order of magnitude more efficient.

In this project we will develop the approximation error method for OT under a wide range of simplified models, with the aim of improving speed (Problem 1) and reconstruction fidelity (Problem 2).

Incorporating Prior Knowledge

The ill-posedness of the inverse problem in DOT makes it necessary to apply regularisation to stabilise the reconstruction. The Bayesian approach provides a rigorous framework in which the reconstructed images are chosen to belong to a distribution with principled characteristics (the prior).

In this project we are investigating two types of prior information: generic priors which are based on the expected local image statistics without explicit knowledge of the particular structures, and anatomical priors, which take explicit account of known anatomical features. A new and very promising advance in OT is its combination with other imaging modalities such as MRI or Ultrasound. In principle, data from these other modalities can act as priors for optical reconstruction. However, there are two major problems. First, the quantitative values from the other modality may not have a simple relationship (i.e. are incommensurate) with those from OT. Secondly, the other modality must be spatially registered with the optical data. In this project we are applying a series of increasingly sophisticated priors to the reconstruction problem, with the aim of increasing the accuracy and robustness of imaging (Problem 2).

Combined analysis and reconstruction

Optical tomography is an example of a parameter identification problem because the reconstructed images represent the parameters of a model of light propagation. In common with many medical imaging modalities, the reconstructed images are not an end in themselves; they need to be analyzed for structural and functional information, including classification of regions, segmentation and cross validation with other modalities. In the particular case of DOT, this post-processing step has some drawbacks. In reconstruction, we use small sets of measurements to reconstruct a large image with many parameters. In the subsequent analysis stage we analyze these parameters to categorise the image into only a few discrete categories e.g. to estimate a classification into discrete regions, or to determine the parameters of a low-dimensional shape model. In each case, the final result is of considerably smaller dimensionality than the intermediate reconstruction.

An alternative approach is the integration of classification or segmentation with the reconstruction. This problem may be better posed than the two-stage approach, as we are only moving from the sparse measurements to another low-dimensional space. In this project we are improving segmentation and classification methods (Problem 3) by performing these tasks simultaneously with reconstruction rather than considering them as a post-processing step.