Two- and Three-Dimensional Optical Tomography of Finger Joints for Diagnostics of Rheumatoid Arthritis Alexander D. Klose 1 , Andreas H. Hielscher 1 , Kenneth M. Hanson 2 and Jürgen Beuthan 3 1 SUNY Health Science Center at Brooklyn, Dept. of Pathology, Brooklyn, NY 11203, USA 2 Los Alamos National Laboratory, Hydrodynamic Applications, Los Alamos, NM 87545, USA 3 FU Berlin, Institut für Medizinische Physik, 12207 Berlin, Germany ABSTRACT 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 1. INTRODUCTION In recent years, considerable research effort has been devoted to the development of techniques and methods for optical tomography (OT). The technology for making optical tomographic measurement on human subjects is nowadays readily available 1 , 2 , 3 , 4 , 5 and has been applied in a variety of pilot studies concerned with monitoring of blood oxygenation, 6,7 , 8 , 9 , 10 , 11 , 12 , 13 hemorrhage detection, 3, 14 , 15 , 16 functional imaging of brain activities 17 , 18 , 19 , 20 , 21 , Alzheimer diagnosis 22 , 23 and breast cancer detection. 2, 24 , 25 , 26 , 27 , 28 , 29 Another possible application of OT is the investigation of human finger joints for early rheumatoid diagnostics and for monitoring the inflammation process. 30 , 31 The small dimensions involved, the diameter of a joint is approximately 1-2 cm, make this an ideal application for photon migration imaging. 32 A major challenge remains the development of computer algorithms that transform these measurements into useful images of the interior of large organs. Other than x-rays, the near-infrared photons used in PMT do not cross the medium on a straight line from the source to the detector. Light is scattered and absorbed throughout the system. Hence, standard backprojection method have only limited success, 33 , 34 and other analytical reconstruction methods are only available for highly restrictive problems. 35,36,37,38,39 In general, either the optical properties of a reference medium have to be known, or/and it has to be assumed that the heterogeneities constitute only a small perturbation in a homogeneous background medium. In the special case of the finger joint, large differences in the scattering and absorption coefficients occur, which prohibits the use of perturbation-theory-based reconstruction schemes. Furthermore, these schemes are computationally very expensive since they require the inversion of large, full, ill-conditioned Jacobian matrices. To overcome the limitations of perturbation-based reconstruction algorithm, we have introduced in the past a non-perturbation, model-based iterative reconstruction (MOBIIR) schemes. 40,41 In this work we extend our MOBIIR code to include 3D data. Before we will present details on the 3D- reconstruction scheme, we will first give some background information on rheumatoid arthritis of finger joints. We will show that the MOBIIR algorithm is capable of reconstructing optically highly inhomogeneous finger joints. Therefore, Optical Tomography has the potential to assist in the early diagnosis and monitoring of rheumatoid arthritis.