Time-resolved reflectance spectroscopy in turbid tissues.

Monte Carlo simulations illustrate how various absorption mu a and scattering mu s 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 mu a in cm -1 can be obtained from measurements of R (t) after the first 20-200 ps (depends on mu s) following an impulse by the expression: mu a = -(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/n)1/2 where t is the time of measurement and D is the optical diffusion constant D = (3 mu s (1 - g]-1. At 50 ps and typical values of mu s = 100 cm-1 and anisotropy equal to 0.9, r equals 5 mm. The upper limit for measurable mu a values is limited by how quickly the reflectance signal is attenuated, and is estimated for current streak camera technology to be mu a less than or equal to 21 cm-1, assuming several measurements are taken over a dynamic range of two orders of magnitude within a 10 ps period.