## 3 Results and Discussion
### Comparisons of Deposition Efficiency Predictions Using DPM Approach
#### 3.2.1 Tissue Visco-Elasticity  
Many researchers disregard the some important part of alveolar modelling, including both actual particle dynamics and tissue-driven wall motion challenges. Therefore, significant advantages of our 3D developed model are the efficient particle tracking system and the capability of coupling of the FSI technique for modelling the alveolar accurately. Although this approach, which produces the airflow by applying an oscillatory pressure to the tissue, is computationally intensive, it has several desirable features. These features are not available in other studies that used prescribed airflow conditions [22; 23]. As a result, the wall motion achieved by the elasticity or viscosity of tissue properties can influence the alveolar flow patterns and particle pathways. The relative effect of tissue mechanical properties on particle deposition efficiency can be investigated in two major parts; the elastic and visco-elastic tissues.  
Figure 7 shows particle deposition efficiency vs. various tissue elasticity and Figure 8 shows the particle deposition efficiency vs. tissue visco-elasticity values for 1 and 5 \(\upmu\)m particle diameter by two-way coupling method on 18-22 generations. For the investigation of the case of elastic tissue, wall deformation is limited due to increasing stiffness (higher E) of tissue, and it causes lower-velocity airflow, which is produced by a negative pressure gradient. Decreasing the airflow velocity causes lower convective forces. Thus, the lower-velocity air flow pulls the particles into the radial alveoli. As a result, the effects of particle inertia and Brownian diffusion are magnified in higher generations by increasing the elasticity of tissue and cause more particles to pass out of streamlines and become deposited on the walls.  
In the other case of the visco-elasticity tissue, it is seen that increasing the tissue viscosity does not have any significant effects on the deposition efficiency or particle dynamic transport. The latter is affected by tissue visco-elastic properties, which alter the system's response for changing and loading the convective dynamics of particles. Suitable physiologic values of tissue viscosity (\(\upeta\)) are adjusted for providing approximately 0.15 to 1 ratio of tissue stress relaxation time to breathing period [9]. According to the results in Figure 6, the variation in time delay of the tissue response in actual conditions, which include gravitational effects, has no significant effect on the particle deposition efficiency and particle dynamics. Under actual conditions, on which the current study is based, the gravitational effects dominate the particle dynamics more than the diffusion effects. In addition, when the size of particles is increased, the particles are driven more strongly by gravity and become less susceptible to diffusion forces [18]. Therefore, changing the visco-elasticity or time delay of the tissue response has a milder effect on the obtained results. Furthermore, increasing the generation number causes a lower-velocity airflow produced by the total volumetric flow rate of the generations. Decreasing the airflow velocity causes lower convective forces. By increasing the generation number, the effects of tissue elasticity become more pronounced. Thus, a lower-velocity airflow pulls the particles into the radial alveoli. Note that E = 40,000 dyn/cm\({}^{2}\) and \(\upeta\) = 30,000 g/cms are the chosen values for tissue visco-elastic properties in the investigation of other deposition parameters [9].  
Figure 7: Particle deposition efficiency of 1 and 5 \(\upmu\)m, two-way coupling particles vs. various tissue elasticity values on (**a**) 18 st, (**b**) 19 st, (**c**) 20 st, (**d**) 21 st and (**e**) 22 st generations.