Rheumatoid arthritis (RA) is one of the most common diseases of human joints. This progressive disease is characterized by an inflammation process that originates in the inner membrane (synovalis) of the capsule and spreads to other parts of the joint. In early stages the synovalis thickness and the permeability of this membrane changes. This leads to changes in the optical parameters of the synovalis and the synovial fluid (synovia), which occupies the space between the bones. The synovia changes from a clear yellowish fluid to a turbid grayish substance. In this work we present two and three-dimensional reconstruction schemes for optical tomography of the finger joints. Our reconstruction algorithm is based on the diffusion approximation and employs adjoint differentiation techniques for the gradient calculation of the objective function with respect to the spatial distribution of optical properties. In this way, the spatial distribution of optical properties within the joints is reconstructed with high efficiency and precision. Volume information concerning the synovial space and the capsula are provided. Furthermore, it is shown that small changes of the scattering coefficients can be monitored. Therefore, optical tomography has the potential of becoming a useful tool for the early diagnosis and monitoring of disease progression in RA.
Keywords: optical tomography, image reconstruction, adjoint differentiation, rheumatoid arthritis
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