In the past decade, near-infrared sampling of tissue has become a large field of study, which has been called by many names (Photon migration, photon random walk, photon density waves, photon diffusion) encompassing work in spectroscopy and imaging of tissue. In this special issue, the focus is on diffuse optical tomography as it applies to medicine and biology. Diffuse optical tomography involves processing of near-infrared light measurements taken from tissue to create images of the interior.

Diffusion tomography is unique in medical imaging, in that measurements of a diffuse field of light are taken and require application of the appropriate model to deconvolve an image of the region. As a comparison, x-ray tomography utilizes Beer's law for the model of propagation through tissue, permitting inversion of the data analytically. However, solving the diffusion or the radiation transport equations do not lead to analytic inverse solutions for arbitrary geometries, and requires either analytic approximation or numerical solution. Thus the field of partial differential equation (PDE) model-based image reconstruction has to be developed along with the technological advances in the optical measurement systems. While there are relatively few successful applications of model-based image reconstruction being used routinely in the clinic, this will change as the problems of matching new models to the measurements are solved in specific situations. With this extra work, measurements of diffuse light propagation in tissue can provide fundamentally new information to the medical field about blood dynamics, cytochromes, lipids, water, tissue metabolism, and blood transport phenomenon.

This research field is quite diverse, with many researchers producing fundamentally new results in theoretical models, computational tomography programs, and experimental systems to study pathology and physiology. As seen in many instances of this special issue, the imaging results obtained from measurements can depend upon (i) the particular theory used to interpret the data, (ii) the computational algorithm used to reconstruct the region, and (iii) the hardware configuration used to measure the light. Only through an integrated approach can diffuse optical tomography be realized to produce accurate images of tissue. The articles in this issue are arranged in order of (i) theoretical development going towards (ii) computational design and ending with (iii) applications. These papers have been solicited to provide a representation of the field, covering a diverse range of aspects in diffuse optical tomography.

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