Time-Resolved Reflectance Spectroscopy in Turbid Tissues

Monte Carlo simulations illustrate how various absorption μa and scattering μs coefficients influence time-dependent reflectance R(t) from a semi-infinite homogeneous turbid tissue following an impulse of narrow-beam irradiation. The tissue absorption coefficient μa in cm-1 can be obtained from measurements of R(t) after the first 20-200 ps (depends on μs) following an impulse by the expression: μa = −(n/c) d In [R(t)]/dt - 3n/2ct where n is the tissue-refractive index and c is the in vacuo speed of light. Early data in the first 20–200 ps do not conform to this expression or to diffusion theory. Monte Carlo simulations allow study of the early R(t) behavior. The volume of tissue involved in a measurement is specified by a volume radius r that approximately equals (6Dtc(c/n)1/2 where t is the time of measurement and D is the optical diffusion constant D = (3μs(1 - g))−1. At 50 ps and typical values of μs = 100 cm-1 and anisotropy equal to 0.9, r equals 5 mm. The upper limit for measurable μa values is limited by how quickly the reflectance signal is attenuated, and is estimated for current streak camera technology to be μa ≤ 21 cm-1, assuming several measurements are taken over a dynamic range of two orders of magnitude within a 10 ps period.