First investigations on the use of system theory in tissue optics

The system theory was developed from the combination of the operational calculus of N. Wiener and the transfer theory of K. Kuepfmueller. The system theory is the basic for the optical transfer function. With the introduction of a so-called transfer (or system) function, the question arose how to apply this theory to problems in optical tissue diagnostics. Especially the use of the existing basic transfer (or system) function offers possibilities for an approximated evaluation of measured scattering light distributions generated by a well-defined geometry. A possibility for clinical applications is the rheumatoid arthritis (RA) because variations of tissue optics due to different stages of disease lead to divergent scattering light distributions. This is to be investigated by measurements and computational simulations at a relatively simple phantom set. By applying the system theory to scattering media the spatial distribution of the entrance intensity function I(x) was a point source. A focussed laser (675 nm) illuminated the surface of a nearly infinite light scattering slab with a thickness of 30 mm. The optical parameters of the phantom set vary in the range of the optical tissue parameters of healthy and diseased finger joints. At the opposite slab side, the outgoing intensity function O(x) is measured as the result of a convolution of the system and the entrance function (after Laplace transformation). For reference the normalized point spread function is calculated by a new mathematical procedure based on the transport theory under variation of phantom parameters as presented by A. Hielscher/A. Klose. As a first approximation the point spread function of transmitted photon density is confirmed to be proportional to a Gauss distribution as proposed by S. Arridge. Therefore, according to the system theory, a virtual transfer system with a transfer (or system) function in the form of a differential equation of first order was found. The conditions μ_a ≪ μ_s′ and μ_a = const. were assumed. The parameter μ′_s, was determined by linear approximation of the Gauss distribution to the calculated or measured point spread function. For selected patients, the μ_s′ of healthy and diseased finger joints was determined (e.g. 10.1 cm^-1, reap. 26.8 cm^-1) and confirmed the experimental results very well.