## 3 Results and Discussion
### Viscoelastic Properties
#### 3.2.1 Particle Tracking Microrheology
MSD parameters: absolute MSD and diffusive exponent at the evaluation limits \(\tau\) = 5.14 ms and \(\tau\) = 1662 ms. Viscoelasticity parameters: Storage modulus G’, loss modulus G′′ and tan\(\delta\) at \(\omega\) = 0.6 s\({}^{-1}\) (at rest) and tan\(\delta\) at \(\omega\) = 195 s\({}^{-1}\). to 42.07 Pa and G\" from 1.24 Pa to 14.76 Pa at the lower evaluation limit (\(\omega\) = 0.6 s\({}^{-1}\)) and G' from 11.71 Pa to 131.30 Pa and G\" from 7.54 Pa to 57.72 Pa at the higher evaluation limit (\(\omega\) = 194 s\({}^{-1}\)), see Appendix A, Table A1. The loss factor tan\(\delta\) = G\"/G', which describes the relationship of the moduli, was throughout smaller than 1 for group a mucus samples. G' and G\" increased with increasing frequency. The slope of the mean G', given in Figure 3, revealed a decrease which resulted in a flattening of the curve, whereas the slope of G\" increased over frequency. Figure 2: MSDs and viscoelastic properties of mucus samples, subdivided into three groups. (**a**) MSD group a; (**b**) viscoelasticity group a; (**c**) MSD group b; (**d**) viscoelasticity group b; (**e**) MSD group c; (**f**) viscoelasticity group c. Group a mucus samples revealed the lowest MSDs, the highest loss and storage moduli and throughout gel character. MSDs increased from group a over b to c. Hence the storage and loss moduli decrease. Group b and c mucus samples revealed a crossover of the moduli. The abbreviations in the brackets give information about the patients’ demographic data belonging to the mucus samples: 1. digit: gender (f: female, m: male); 2. digit: larynx status (h: healthy, p: pathologic); 3. digit: smoking behavior (s: smoker, f: former smoker, n: non-smokers); 4/5. digit: age. Group a mucus samples revealed classic gel character. The elastic modulus G' was higher than the storage modulus G'' over the whole range of evaluated frequencies, which reveals solid-like, elastic-dominant character (G' > G''). This is in accordance with bulk-rheology measurements of different kinds of mucus reported previously [14; 15; 16; 17]. The absolute storage and loss modulus varied within the samples in group a. However, their range cover rigidity of native human airway mucus [14; 15; 16] and native intestinal mucus of pigs [16] found before. Group b mucus samples revealed higher MSDs than group a, lower MSDs than group c mucus samples and vice versa lower storage and loss moduli than group a and higher than group c, see Figures 2 and 3. Additionally, a crossover at frequencies \(\omega\) > 10 s\({}^{-1}\) can be seen. The crossover led to a change from tan\(\delta\) < 1 at the lower evaluation limit to tan\(\delta\) > 1 at the higher limit, see Table 2. The mean diffusive exponent \(\alpha\) lies between group a and group c at the lowest lag-time \(\tau\) = 5.14 ms, but is almost equal to group a and lower than group c at the highest lag-time. The rigidity at rest (G' and G'' at \(\omega\) = 0.6 s\({}^{-1}\)) lies in between group a and c: G' = 0.80 Pa, G'' = 0.28 Pa. Extreme cases in this group could be found according to the absolute moduli and the crossover frequency. The highest absolute moduli were found for mucus sample b1 and the lowest moduli were found for mucus sample b7 and b8, depending on the frequency. This leads to a range of G' from 0.26 Pa to 1.62 Pa and G'' from 0.1 Pa to 0.59 Pa at the lower evaluation limit (\(\omega\) = 0.6 s\({}^{-1}\)) and G' from 1.57 Pa to 5.86 Pa and G'' from 2.43 Pa to 5.97 Pa at the higher evaluation limit (\(\omega\) = 194 s\({}^{-1}\)), see Appendix A, Table A1. The crossover at the lowest frequency was found for mucus sample b8, followed by sample b3, which showed slightly different characteristics within the group. For these two samples, the crossover happened between frequencies of \(\omega\) = 10 s\({}^{-1}\) and \(\omega\) = 100 s\({}^{-1}\). For the other samples, the crossover happened at frequencies \(\omega\) > 100 s\({}^{-1}\). The slopes of the mean curves of G' and G'', given in Figure 3, reveal an increase over frequency.