The temporal profile of the time-resolvedreflectancecurveisanalysedusing a solution of the radiative transport equationunderthediffusionapproximationfor a semi-infinite homogeneous medium11,12
where /?(p,i) is the number of photons perunittime (i)andareare-emittedfrom the tissue at a distance p from the injectionpoint. p isthesource-detectordis-tance (or interfibre distance), v = c/n is thespeedoflightinthemedium, n isthe refraction index, D = (3|ms')-1 is the diffusion coefficient, z0 = (|ms')-1 is the iso-tropisation length, ze is the extrapolated distance which takes into account the refraction index mismatch at the surface.
The experimental curve is fitted with a convolution of the theoretical function with the instrumental response function (IRF). The best fit is reached minimising the c2 varying both |ma, and |ms' using a Levenberg-Marquardt iterative procedure. Owing to the lower accuracy of the models in earlier times, the range of the fit includes all the points on the experimental curve with a number of counts higher than 80% of the peak value on the rising edge of the curve and 1% of the peak value on the falling edge. Figure 8.3 shows the best fit of a typical experimental curve. The instrumental transfer function is also shown for comparison (dashed line).
The fitting procedure can automatically analyse a full batch of experimental curves on a standard PC (Athlon AMD, 1GHz) at a speed of 10 curves per second. Synchronisation of the analysis and measurement PCs over the network permits on-line processing of the experimental data, so that the absorption and scattering coefficients are shown on the screen in real time while the measurement is inprogress.
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