We report on the first three-dimensional, volumetric, tomographic localization of vascular reactivity in the brain. To this end we developed a model-based iterative image reconstruction scheme that employs adjoint differentiation methods to minimize the difference between measured and predicted data. The necessary human-head geometry and optode locations were determined with a photogrammetric method. To illustrate the performance of the technique, the three-dimensional distribution of changes in the concentration of oxyhemoglobin, deoxyhemoglobin, and total hemoglobin during a Valsalva maneuver were visualized. The observed results are consistent with previously reported effects concerning optical responses to hemodynamic perturbations.

Diffuse optical tomography (DOT) is emerging as a viable new biomedical imaging modality. Using near-infrared (NIR) light, this technique probes absorption as well as scattering properties of biological tissues. First commercial instruments are now available that allow users to obtain cross-sectional and volumetric views of various body parts. Currently, the main applications are brain, breast, limb, joint, and fluorescence/bioluminescence imaging. Although the spatial resolution is limited when compared with other imaging modalities, such as magnetic resonance imaging (MRI) or X-ray computerized tomography (CT), DOT provides access to a variety of physiological parameters that otherwise are not accessible, including sub-second imaging of hemodynamics and other fast-changing processes. Furthermore, DOT can be realized in compact, portable instrumentation that allows for bedside monitoring at relatively low cost. In this paper, we present an overview of current state-of-the -art technology, including hardware and image-reconstruction algorithms, and focus on applications in brain and joint imaging. In addition, we present recent results of work on optical tomographic imaging in small animals.

We present an algorithm that provides a frequency-domain solution of the equation of radiative transfer (ERT) for heterogeneous media of arbitrary shape. Although an ERT is more accurate than a diffusion equation, no ERT code for the widely employed frequency-domain case has been developed to date. In this work the ERT is discretized by a combination of discrete-ordinate and finite-volume methods. Two numerical simulations are presented.

We report on the implementation of an augmented Lagrangian approach for solving the inverse problems in diffuse optical tomography (DOT). The forward model of light propagation is the radiative transport equation (RTE). The inverse problem is formulated as a minimization problem with the RTE being considered as an equality constraint on the set of 'optical properties-radiance' pairs. This approach allows the incorporation of the recently developed technique of PDE-constrained optimization, which has shown great promise in many applications that can be formulated as infinite-dimensional optimization problems. Compared to the traditional unconstrained optimization approaches for optical tomographic imaging where one solves several forward and adjoint problems at each optimization iteration, the method proposed in this work solves the forward and inverse problems simultaneously. We found in initial studies, using synthetic data, that the image reconstruction time can typically be reduced by a factor of 10 to 30, which depends on a combination of noise level, regularization parameter, mesh size, initial guess, optical properties and system geometry.