## 3 Results
### Time-Resolved Results  
Our proposed method involves with fewer risks and side effects than the lumbar puncture process required for CSF collection and for the measurement of amyloid-beta and tau concentration ratio. However, the method still requires an insertion of a needle to the epidural fat in the lumbar section. A feedback system for the needle distance from the CSF can assist in reducing almost completely any complications and risks involved in such a procedure.  
Fluorescence lifetime measurements, which may be taken simultaneously with the fluorescence intensity measurements, may provide the basis for such a feedback system. The fluorescence intensity time-resolved curve is affected both by the intrinsic fluorescence lifetime value and by the photon propagation time. The propagation time depends on the tissue optical properties and on the physical distance between the fluorophore and the source and detector. Since the shape of the time-resolved curve is affected by the distance between the fluorophore and the source and detector we can utilize this curve in order to extract the distance of the needle from the CSF. The extracted distance will provide physicians with real-time information about the needle location, thus avoiding penetration of the dura matter.  
In our previous report [31] we demonstrated in vitro the effect of variations in the thickness and scattering coefficient of the overlying phantom layer on two features extracted from the fluorescence intensity time-resolved curve. The first feature is \(t_{\text{max}}\), which represents the time in which the intensity reached its maximal value and is related directly to the photon path-length. The value of \(t_{\text{max}}\) increases with an increase in the thickness of the overlying medium due to the longer photon path-length required for the fluorescent photons reach the detector. The second feature is the absolute value of the slope of the decaying part of the intensity curve, in logarithmic scale, which decreases with an increase in the thickness of the overlying medium. In other words, there is a steeper decline in the intensity in thin phantoms or tissues compared to the thicker phantoms or tissues. When the thickness of the overlying media increases, there are more scattering events causing more photons arriving at later times, thus reducing the absolute slope of the intensity decay curve.  
The time-resolved curves were measured using the TCSPC system during the animal experiments. The fluorescent tubes implanted in the abdomen were located deeper than the tubes implanted subcutaneously. Since the photon path length of the abdomen tubes is bigger than in the subcutaneous tubes, \(t_{\text{max}}\) is expected to be higher too. Figure 3 presents the time-resolved fluorescence curve measured from the two tubes implanted in one of the mice: the abdomen tube and the subcutaneous tube. The time-resolved curves were normalized in order to emphasize the difference in \(t_{\text{max}}\). As expected, the time in which the abdomen fluorescence reaches its maximal value is higher than the time in which the subcutaneous fluorescence reaches the maximum value: \(t_{\text{max}}\) (abdomen) = 1.28 ns and \(t_{\text{max}}\) (subcutaneous) = 1.15 ns.  
The absolute value of the slope of the intensity decay curve, in logarithmic scale was also calculated for both cases. For the subcutaneous tubes the absolute value of the slope was 0.75 [1/ns], and for the abdomen tubes the absolute slope was 0.74 [1/ns]. As expected, the absolute value of the slope decreases with an increase in the thickness of the tissue overlying the fluorescent tubes.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cutoff Value** & **TN** & **FN** & **TP** & **FP** & **Sensitivity** & **Specificity** \\ \hline concentration ratio \textless{} 6.5 & 14 & 0 & 24 & 3 & 100\% & 82\% \\ concentration ratio \textless{} 6.16 & 15 & 0 & 24 & 2 & 100\% & 88\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Sensitivity and specificity calculation.