Abstract
Optical tomography is a non-invasive medical imaging modality that utilizes measurements of transmitted near-infrared light to reconstruct the distribution of optical properties
inside the human body, such as for the determination of blood oxygenation, functional imaging of brain activities, and early diagnosis of rheumatoid arthritis in finger joints.
The majority of currently applied image reconstruction schemes rely on the validity of the diffusion equation for the description of light propagation in tissue. Unfortunately, the diffusion equation does not accurately describe light propagation in media that contain low-scattering regions.
This work addresses these shortcomings by developing a novel model-based iterative image reconstruction scheme for optical tomography. It consists of two major parts: (1) a forward model for light propagation and (2) an inverse model.
The forward model predicts the detector readings on the tissue boundary given a source and distribution of optical parameters inside the medium. The equation of radiative transfer, unlike the diffusion equation, describes correctly as a forward model the photon propagation in turbid media containing low-scattering areas. The equation of radiative transfer is numerically solved by means of a finite difference discrete ordinates method.
In contrast, the inverse model determines the optical parameters inside tissue, given a set of detector readings on the boundary of tissue. The inverse model is viewed as a large-scale nonlinear optimization problem. The measured fluence on the boundary is compared to the predicted detector readings by defining an objective function. The objective function is iteratively minimized by a nonlinear conjugate gradient technique, or by quasi-Newton methods. These techniques use the first derivative of the objective function with respect to the optical parameters for calculating search directions towards the minimum. Forward and inverse model are iteratively employed until self-consistency is reached.
A major obstacle is the computationally efficient calculation of the first derivative of the objective function with respect to the optical parameters because the objective function depends on approximately 10,000 unknown optical parameters. We calculate the derivative by utilizing an adjoint differentiation technique that is a particular numerical implementation of an adjoint model. We apply the adjoint differentiation technique for the first time to the equation of radiative transfer.
We show reconstructed sagittal images of optical parameters of a human finger joint. We emphasize the potential application for the early diagnosis of rheumatoid arthritis in a numerical study. |
