## 4 Discussion
However, there are some differences in the absorption and scattering coefficients between the wavelengths used for the excitation of the two fluorophores, and therefore the errors in the concentration ratio estimation increase with an increase in the tissue thickness. Since the abdomen tubes have thicker overlying tissue than the subcutaneous tubes, the inaccuracy that results from not taking into account photon propagation attenuation has a higher effect, causing bigger errors. There are several actions that may be helpful in avoiding high errors in thick tissue. The first is obviously to avoid performing measurements when there are high distances between the needle and the CSF. This may be done by slow insertion of the needle until a sufficiently high fluorescence signal is measured, with an acceptable signal to noise ratio. In addition, we presented the option to use the fluorescence time-resolved measurements for estimating the distance between the needle and the CSF, and the scattering coefficient. These two estimated values may be used as a correction factor that takes into account the tissue thickness and its optical properties without totally neglecting the photon propagation attenuation. Although in some cases, the ratios were estimated with an error of 35%, the sensitivity and specificity still remained high. This may be explained by the fact that for low concentration ratios, an error of 35% still resulted in a relatively low difference between the true and estimated ratio. For instance, in one of the cases, the true ratio was 3.57 and the estimated ratio was 4.86, which is equivalent to 36% error. However, the difference between the true and estimated ratio is 1.29, a rather low difference that will not cause false predictions. In the high concentration ratios, the big errors caused a larger difference between the true and estimated ratio values, but the cutoff value was relatively distant from the true ratio. As a result, in those cases, even big errors did not cause too many false predictions. On the other hand, the concentration ratio values that were close to the cutoff value were estimated with a very high accuracy so the sensitivity and specificity remained high. We can assume that our method requires high accuracy in ratios that are close to the cutoff ratio but can afford bigger errors in the extreme cases of low and high concentration ratios since big errors in these values will not result in false predictions. The fluorescence properties of Cy7 and Cy7.5 probes are not identical to one specific probe developed for AD (presented in Section 1). Cy7 has absorption/emission peaks at 750/773 nm, an extinction coefficient of 199,000 [M\({}^{-1}\)cm\({}^{-1}\)] and quantum yield of 0.3. Cy7.5 has absorption/emission peaks at 788/808 nm and an extinction coefficient of 223,000 [M\({}^{-1}\)cm\({}^{-1}\)]. When comparing the fluorescent properties of the AD probes we see some differences in the absorption/emission peaks but similar orders of magnitudes of the extinction coefficient and quantum yields. For example, AOI987, which was used for imaging A\(\beta\), has an absorption/emission peaks at 650/670 nm, an extinction coefficient of 64,570 [M\({}^{-1}\)cm\({}^{-1}\)], and a quantum yield of 0.4. THK-265 showed similar properties--absorption/emission peak at 630/650 nm, extinction coefficient of 96,198 [M\({}^{-1}\)cm\({}^{-1}\)], and quantum yield of 0.38. CRANAD-58 has a similar absorption peak in 630 nm but an emission peak in 750 nm in the presence of A\(\beta\). For tau imaging, CyDPA2 was presented with an absorption/emission peaks at 826/833 nm, extinction coefficient of 113,553 [M\({}^{-1}\)cm\({}^{-1}\)] and quantum yield of 0.049. The differences in the absorption/emission spectra between the fluorescent probes used in this study and the AD probes may affect the accuracy of the concentration ratio estimation. If the changes between the absorption spectra of the Ab and tau probes are big, the assumption that the optical properties are similar is less accurate.