Methods for Postprocessing in Single-Step Diffuse Optical Tomography

The methods of computed tomography – X-ray computed tomography, magnetic resonance imaging, single-photon emission computed tomography, positron emission tomography, ultrasonic reflectivity tomography and others (Webb, 1998) are now widely used in the practice of medical imaging and their importance increasingly grows. These methods allow the real time reproduction and visual analysis of the inner spatial structure of tissue on the display, which on whole helps increase the quality of diagnostics. However, in the context of problems to be resolved in oncology, the efficiency of currently available commercial tomography methods remains relatively low. One of the reasons is the lack of methods that would allow reliable differentiation between malignant and benign tumors on reconstructed tomograms. The recent clinical studies (Boas et al., 2001; Gibson et al., 2005) show that rapidly developing diffuse optical tomography (DOT) is very likely to help out. DOT is unique in its ability to separately reconstruct the spatial distributions of optical parameters (absorption and scattering coefficients) which helps visualize the spatial pattern of blood volume and oxygen saturation. As a result, it becomes possible to differentiate and spatially localize such phenomena as cancerous tissue vascularisation and angiogenesis and hence detect cancer in the early stage of its development. DOT implies that tissue is probed by near-infrared radiation from the so-called therapeutic window (700-900 nm) where absorption by tissue is minimal. Position dependent measurements are taken, i.e. near-infrared light from an array of sources is observed with an array of receivers. Then an inverse problem, i.e. the tomographic reconstruction problem is solved to infer the spatially localized optical properties of tissue. The main problem of DOT is the low spatial resolution because of the multiple scattering of photons that do not have regular trajectories and are distributed in the entire volume V being probed. As a result, each volume element significantly contributes to the detected signal. The basic equation of DOT is written as