## 3 Results and Discussion
### Viscoelastic Properties  
#### 3.2.1 Particle Tracking Microrheology  
The MSDs and absolute viscoelastic properties, G' and G'', which are referred to the rigidity of the mucus samples, varied over four orders of magnitude and report the diversity of human laryngeal mucus. Based on the absolute MSDs, the according diffusive exponents and corresponding viscoelastic characteristics, especially a crossover of the storage and loss modulus (G', G''), the results led to a subdivision of the mucus samples into three groups: a, b and c, see Figure 2. The mean MSDs and the mean storage and loss moduli, including their slopes over the four data points near the evaluation limits, were calculated for each group, see Figure 3. The according mean absolute MSDs and viscoelastic properties at the evaluation limits (i.e., \(\tau\) = 5.14 ms, \(\tau\) = 1662 ms and \(\omega\) = 0.6 s\({}^{-1}\), \(\omega\) = 195 s\({}^{-1}\)) are given in Table 2.  
Group a mucus samples were characterized by the lowest MSDs and highest storage and loss moduli compared to group b and group c mucus samples, see Figure 2. This can be seen more distinct in the direct comparison of the mean curves of the groups, see Figure 3. The according characteristic parameters of the MSD and viscoelasticity at the evaluation limits, see Table 2, underline the visualization. Group a mucus samples revealed the lowest diffusive exponents \(\alpha\). Information about the rigidity of gels at rest, the long-term behavior, is given by G' and G'' at the lowest evaluated frequency. These are higher for group a than for the other two groups: At (\(\omega\) = 0.6 s\({}^{-1}\)), G' = 12.28 Pa and G'' = 4.19 Pa. Nevertheless, the mean G' and G'' revealed high standard deviations, which are caused by varying absolute moduli of the samples within the group, see Figure 2. In this context, the extreme cases of group a were mucus samples a1 and a7. The extreme cases caused a range of G' from 3.0 Pa \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Gender**} & \multicolumn{2}{c}{**Male**} & \multicolumn{2}{c}{**Female**} \\ \cline{2-5}  & \multicolumn{2}{c}{12} & \multicolumn{2}{c}{7} \\ \cline{2-5}  & \(<\)**50** & **50–59** & **60–69** & \(\geq\)**70** \\ \hline \multirow{2}{*}{**Age**} & 3 & 8 & 5 & 3 \\ \cline{2-5}  & \multicolumn{2}{c}{**Healthy**} & \multicolumn{2}{c}{**Pathologic**} \\ \cline{2-5}  & \multicolumn{2}{c}{14} & \multicolumn{2}{c}{5} \\ \cline{2-5}  & \multicolumn{2}{c}{**Non-Smokers**} & \multicolumn{2}{c}{**Former Smokers**} & \multicolumn{2}{c}{**Smokers**} \\ \hline \multirow{2}{*}{**Smoking Behavior**} & 5 & \multicolumn{2}{c}{2} & \multicolumn{2}{c}{12} \\ \cline{2-5}  & \multicolumn{2}{c}{} & \multicolumn{2}{c}{2} & \multicolumn{2}{c}{12} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Demographic data of the patients belonging to the 19 mucus samples measured by particle tracking microrheology (PTM). Number of evaluated samples based on gender, age, larynx status and smoking behavior. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & _Group a_ & _Group b_ & _Group c_ \\ \hline
**MSD Parameters** & & & & \\ \(\tau\) = 5.14 ms: & MSD [nm\({}^{2}\)] & 73 \(\pm\) 41 & 451 \(\pm\) 128 & 1420 \(\pm\) 341 \\ \(\tau\) = 5.14 ms: & \(\alpha\) & 0.33 \(\pm\) 0.04 & 0.57 \(\pm\) 0.07 & 0.76 \(\pm\) 0.04 \\ \(\tau\) = 1662 ms: & MSD [nm\({}^{2}\)] & 300 \(\pm\) 191 & 3489 \(\pm\) 1709 & 34036 \(\pm\) 8632 \\ \(\tau\) = 1662 ms: & \(\alpha\) & 0.21 \(\pm\) 0.03 & 0.22 \(\pm\) 0.04 & 0.32 \(\pm\) 0.07 \\
**Viscoelasticity Parameters** & & & & \\ G’ [Pa] & 12.28 \(\pm\) 12.89 & 0.80 \(\pm\) 0.43 & 0.05 \(\pm\) 0.02 \\ \(\omega\) = 0.6 s\({}^{-1}\) (at rest): & G’ [Pa] & 4.19 \(\pm\) 4.60 & 0.28 \(\pm\) 0.15 & 0.03 \(\pm\) 0.00 \\  & tan \(\delta\) & 0.34 \(\pm\) 0.05 & 0.36 \(\pm\) 0.06 & 0.55 \(\pm\) 0.15 \\ \(\omega\) = 195 s\({}^{-1}\): & tan \(\delta\) & 0.58 \(\pm\) 0.09 & 1.21 \(\pm\) 0.30 & 2.57 \(\pm\) 0.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristic mean parameters of the MSDs and viscoelasticity.