Comparison of steady and unsteady exhalation using multiplane-stereo PIV

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1 Comparison of steady and unsteady exhalation using multiplane-stereo PIV Franka Schröder 1,*, Susanna Bordin 1, Sven Härtel 1, Mark Washausen 1, Michael Klaas 1, Wolfgang Schröder 1 1: Institute of Aerodynamics, RWTH Aachen University, Aachen, Germany * correspondent author: f.schroeder@aia.rwth-aachen.de Abstract A analysis of the flow field in a realistic, transparent model of the human lung is presented in this experimental study. The model consists of the bronchial tree up to the third generation of bifurcation. The spatial focus is on the first bifurcation especially the left main bronchus, whereas the temporal focus is on the exhalation for steady und unsteady flow. Due to the highly three-dimensional and asymmetric character of the flow field time resolved 3D-3C measurements are performed using multiplane-stereo particle-image velocimetry (PIV) and a refractive-index matched fluid. The velocity field is recorded in 13 measurement planes within the human lung for steady exhalation and exhalation during a breathing cycle. The investigated Reynolds number of Re D = 600 is based on the hydraulic diameter and the bulk velocity. The measurements in the left bronchus evidence the development of highly three-dimensional vortical structures which are analyzed by the helicity distribution. The superposition of the observed vortical structures with the upstream fluid transport generates a spiral like flow in both test cases and lead to a wash-out hypothesis of aerosol particles in the human lung. 1. Introduction Chronic obstructive pulmonary disease, also known as COPD, is one of the most deadly and prevalent chronic diseases and is the fourth most common cause of death worldwide. According to the predictions of the World Health Organization (WHO) it will be the third by the year 2030 (WHO, 2008). Amongst other features, COPD is characterized by airflow obstruction, shortness of breath, and acute exacerbations. Hence, COPD treatment requires an early diagnosis. One possible approach to achieve this goal is to establish a non-invasive diagnostics and clinical monitoring of COPD based on the analysis of exhaled aerosols (Haslbeck et al., 2010). To obtain a detailed knowledge about the particle transport in the human lung it is a must to analyze the temporal and spatial development of the flow structures in the human airways. Numerous studies have been conducted to analyze the flow within the human lung. Große et al. (Große et al., 2007, Große et al., 2008) analyzed the steady and unsteady flow in a realistic model of the first six bifurcations using two-dimensional/two-component (2D/2C) particle-image velocimetry. In a first step, they focused on the center plane of the first bifurcation and analyzed the flow field during steady inspiration and expiration for two Reynolds numbers. These measurements indicated that the Reynolds number possesses a minor influence on the spatial extension of the flow phenomena as long as it is higher than Re D = 800. In a second step, they measured the velocity distribution in 13 parallel planes in the first bifurcation during steady inspiration at a Reynolds number of Re D = 1,700. They detected a superposition of the fluid transport in the downstream direction and a pair of counter-rotating vortices to spiral-like shaped vortices. Eitel et al. (Eitel et al., 2010) compared numerical and experimental data for oscillating flow. The experimental investigations were conducted using 2D-2C PIV in the same lung model that had been used by Große et al. (Große et al., 2007, Große et al., 2008) for the analysis of the flow in the first bifurcation. The numerical simulation of the flow in the first six generations was based on the Lattice-Boltzmann method. The authors confirmed that the qualitative structure of the complex flow field remains unchanged if a critical mass flux rate is exceeded. Furthermore, the primary flow - 1 -

2 distribution during expiration, which is more homogeneous than the inspiration flow distribution and possesses a higher level of vorticity, is interpreted as a natural particle washout. To overcome restrictions due to planar data sets and two-dimensional data, Soodt et al. (Soodt et al., 2012) performed stereo scanning particle-image velocimetry measurements for the transition from inspiration to expiration in the right main bronchus and the subsequent lobe bronchi for two nondimensional frequencies, i.e., Womersley numbers (α 1 = 3.35, α 2 = 4.11), at a peak Reynolds number of Re D =1,420. These measurements showed an increased mass flux into the right superior bronchus for the higher Womersley number, a frequency-dependent phase shift of the flow structures, and a heterogeneous outflow at the beginning of the expiration phase. These studies show the necessity to measure and analyze the unsteady three-dimensional flow field in the upper generations of the human lung and to juxtapose unsteady and steady flow field to evidence the impact of the time derivative on the flow structure. Since it is expected that especially the wash-out mechanism is influenced by the unsteadiness, the discussion focuses on the unsteady expiration phase. In other words, the scope of this study is to gain detailed information on the spatial structures of the flow field in the first two bifurcations during steady and unsteady exhalation using multiplane stereo PIV. The paper is organized as follows. Firstly, the flow problem and experimental equipment are described. Secondly, the results of the multiplane-stereo PIV measurements are presented and discussed. Finally, these findings are summarized and conclusions are drawn. 2. Experimental Setup 2.1 Lung model The experiments were conducted in a realistic, three-dimensional, transparent lung model that extends to the 3rd generation of the bronchial system. The lung model is made from transparent silicone (RTV 615) to allow perfect optical access. Figure 1a depicts a photograph of the hollow lung model in the silicone block. At inspiration the fluid enters the lung through the anatomically shaped trachea as illustrated in Figure 1b. At unsteady and steady expiration the flow direction is reversed and the flow enters the lung model through a net of pipes, which have the same diameter as the branches of the 3rd generation of the lung model. They are drilled into the silicone block such that they can be considered straight extensions of these branches. Fig. 1 a Dorsal view of the lung model (left). b Geometry of the inlet cross section (center). c Green representing the measurement planes in the lung model (right)

3 Fig. 2 a Schematic of the experimental setup for steady flow (left). b Schematic of the experimental setup for oscillating flow (right). 2.2 Flow parameters Figure 2 shows schematics of the experimental setup for steady and oscillatory flow. The measurements at steady expiration were performed using a closed-circuit flow facility (Figure 2a). Since a homogeneous flow circulation has to be guaranteed for an idealized flow distribution in the lung model, the fluid supply for the tank is carefully positioned. Measurements at oscillating flow, which were designed to simulate a breathing cycle, were conducted with an open-circuit flow facility (Figure 2b). In the latter case, a fluid movement as shown in Figure 2 was realized using a linearly moving piston. The piston movement to data measured during deposition experiments for a patient at Frauenhofer ITEM Hannover. A water/glycerin mixture with a refractive index of n=1.411 being identical to that of the silicone block of the lung model was used as fluid to ensure optical access without distortion. The optimum mixture for the refractive index of this study model was found to be 40 mass percent water and 60 mass percent glycerin. 2.3 Tracer particles Since solid tracers possess a strong tendency to deposit on the inner surfaces of the model, which led to a considerable decrease in image quality, air-bubbles at a size of 5 to 20µm generated by a micro-bubble generator with Venturi type mechanism served as tracer particles. 2.4 Measurement equipment and image evaluation All experiments of this study were carried out using the stereo scanning PIV system shown in Figure 4. A multipulse Quantel Twins BSL 140 laser operating at a wavelength of λ=532 nm was - 3 -

4 Fig. 3 Motor curve of the breathing cycle for a patient. used as light source. A combination of three lenses (I: convex lens; II: cylindrical lens; III: convex lens) generated the light sheet. The light sheet optics was mounted on a micrometer calliper to guarantee the positioning and movement of the lightsheet in 1mm-steps. Two Photron SA3-120K high-speed cameras were mounted on a Scheimpflug adapter and were synchronized with the laser system by an ILA high-speed synchronizer. The flow was recorded at a sampling frequency of 30 Hz. To guarantee constant path lengths from the object plane to the image plane and as such to keep the image perpendicular to the optical axis, the front walls of the tank had an angle of aperture of α=100. The image post-processing included decomposing of the images into three parts. A multipass crosscorrelation and several filters, i.e., window velocity filter, which filters velocity vectors that are outside an adjustable range, and a normalized local median filter as described in Westerweel and Scarano (Westerweel and Scarano, 2005), were used to determine to obtain the velocity fields (VidPIV, Intelligent Laser Applications). The final window size was 32 pixel x 32 pixel with an overlap of 50%. This led to a vector spacing of 0.6mm with 98% of valid vectors. The lateral spacing of the vector field was 1mm and the light sheet thickness was 0.7mm. Fig. 4 Top view of the optical setup

5 3. Results and Discussion To analyze the influence of the unsteadiness of the flow on the wash-out process multiplane-stereo PIV measurements have been performed for steady and unsteady flow during exhalation. On the one hand, the three-dimensional velocity has been measured for steady expiration and a set of Reynolds numbers Re D in the range of 150 Re D 1,150 and in 13 measurement planes. On the other hand, PIV measurements were carried out in 12 parallel measurement planes during the exhalation phase of a breathing cycle, the motor curve of which is shown in Figure 3. In both cases, the Reynolds number Re D is based on the bulk velocity U and the hydraulic diameter D of the trachea. For the comparison of the two cases, a Reynolds number of Re D =600 has been chosen. As far as the measurements of a breathing cycle are concerned, the velocity of the piston can be assumed to be constant provided that the temporal distance to the beginning of the exhalation phase is large enough. Since the constant slope of the motor curve starts 1.33s and ends 7.6s after the beginning of the beginning of the expiration, the exhalation phase with a constant mass flux has a duration of 6.27s for this patient. This might assume a steady flow field during the exhalation phase of a breathing cycle. However, it is necessary to compare the results for steady and unsteady exhalation. Figure 5 shows the averaged velocity field in 13 parallel measurement planes for steady exhalation at Re D =600 in the left bronchus. The position and size of the measurement planes are indicated by the sketch in the lower corner of the figure. The vectors in Figure 5 represent the normalized inplane velocity components u/v abs and v/v abs, whereas the colormap represents the normalized out-of- Fig. 5 Velocity distribution in 13 measurement planes normal to the z-direction in the left bronchus at Re D = 600 for steady exhalation. The vectors indicate the in-plane velocity (u, v), the colormap represents the out-of-plane velocity component w

6 a b c d Fig. 6 Velocity distribution for oscillating flow in the center plane of the lung model for a t=1,33s, b t=3,33s, c t=5,33s, and d t=7,33s after the beginning of exhalation. The vectors denote the inplane velocity (u, v), the color map represents the absolute velocity v abs. a b c d Fig. 7 Velocity distribution for oscillating flow in the center plane of the lung model for a t=1,33s, b t=3,33s, c t=5,33s, and d t=7,33s after the beginning of exhalation. The vectors denote the inplane velocity (u, v), the color map represents the velocity component w

7 a b Fig. 8 a Velocity distribution during exhalation for a breathing cycle in the center plane of the lung model. In red (+): u, green (x): v, blue (o): w, black: v abs b investigated point mark in the left bronchus. plane velocity component w/v abs. The velocity magnitude v abs is defined as v abs = (u²+v²+w²) 1/2. The analysis of the flow field in the left bronchus shows two predominant vortices. The first vortex center can be seen is in the measurement planes This vortex is located at the outer wall and rotates counter-clockwise. The center of the second vortex, which is also rotating counterclockwise, is located in the measurement planes 5-9 at the inner wall. Both vortices are generated by the inflow from the upstream branch of this bifurcation generation which forms a u-shaped pipe with the left lobe bronchus and the second upper inlet pipe. A high negative out-of- plane velocity can be observed in the measurement plane 7. In conjunction with the high positive out-of-plane velocity in the measurement planes 4 and 5, the results indicate a second vortex pair. In Figures 6 and 7, the velocity distribution in the center plane z=12mm of the lung model being identical to the measurement plane 8 for steady flow in Figure 5 is shown for different time steps of a breathing cycle. The comparison of the absolute velocity shows that the flow field in the trachea changes as a function of time. In the trachea a change of the absolute velocity can be observed. The field in the left bronchus varies over time. The in-plane velocities show a comparable behavior to that for steady flow. Figure 7 shows the distribution for the out-of-plane component. A considerable change of the out-of-plane velocity during exhalation can be observed which already indicates a difference in the vortical structures of the steady and unsteady flow. Figure 8a depicts the temporal evolution of all three velocity components and the absolute velocity in time steps of Δt=0,03s for a fixed position in the left bronchus. The plus sign in the schematic shown in Figure 8 illustrates the position of this measurement point. The rms-value for all components is less than 5% for all three velocity components and for the absolute velocity. Nevertheless a significant change of the velocity components versus time can be detected. Thus, although the steady motion of the piston over an extended time span leads to the assumption of a steady flow field the structures show the flow to be determined by the time derivative. In the following, mean velocity fields of 6 breathing cycles for a constant phase angle of the piston of 5, i.e., for a constant bulk Reynolds number of Re D = 600 are investigated and compared to the results from the measurements of steady flow with the same Reynolds number. This corresponds to a situation 1,33s after the beginning of the exhalation. For clarity, only every second measurement plane is displayed. A highly three-dimensional flow pattern different to that at steady flow can be observed. Moreover, two areas possessing peak values for the absolute velocity can be detected. Those areas are located in the trachea and in the left bronchus. The maximum can be detected in the measurement planes 5 to 7. Concerning the out-of-plane component, the highest values occur in the left bronchus. In this area, the velocity field is influenced by the inflow of the lower branches. By comparison of the measurement plane 8 for steady (Figure 5) and measurement plane 5 for unsteady flow two completely different flow patterns can be seen

8 16th Int Symp on Applications of Laser Techniques to Fluid Mechanics Fig. 9 Velocity distribution in 9 measurement planes normal to the z-direction of the first bifurcation at ReD = 600 during exhalation for a breathing cycle. The vectors indicate the in-plane velocity (u, v), the color map denote out-of-plane the velocity component w. Fig. 10 Velocity distribution in 9 measurement planes normal to the z-direction of the first bifurcation at ReD = 600 during exhalation for a breathing cycle. The vectors indicate the in-plane velocity (u, v), the color map denote absolute velocity vabs. -8-

9 Fig. 11 Helicity distribution in the left bronchus at steady exhalation (left). Four slices of the volumetric helicity distribution (right). To visualize the three-dimensional flow structures, the results of 13 measurement planes that are parallel to the x-y-plane and possess a lateral spacing of Δz=1mm are combined to form a threedimensional volume. To gain a better understanding of the vortical structures, the helicity is analyzed. The helicity is a measure for the strength of helical structures and is defined as the scalar product of the velocity vector and the vorticity H = v ( v). The color code represents the sense of rotation. Red indicates a clockwise rotation and blue the counter-clockwise rotation. Figure 11 shows the helicity in the left bronchus for steady exhalation and a Reynolds number of Re D =600 in a three-dimensional view (left) and four slices that have been extracted from this view (right). The three-dimensional helicity plot evidences three pairs of vortices. The helicity of the steady flow case illustrates that multiple pairs of counter rotating vortices form in the left bronchus. In slice S1, three pairs of counter rotating vortices can be detected. Further upstream, two counter rotating vortices vanish and only three pairs are left, where the two on the outer wall of the bronchus are more pronounced than the remaining pair on the inner wall. Fig. 12 Helicity distribution in the first bifurcation at expiration for a breathing cycle at a Reynolds number Re D =

10 Figure 12 shows the helicity for Re D =600 during a breathing cycle from two different viewing angles. The vortical structures for this case are dissimilar for those for the steady flow presented in Figure 11. Two pairs of counter rotating vortices can be observed. The first pair of vortices has its origin in the subbranches coming from the upper-left lobe, the second vortex pair originates from the lower subbranches. The swirl of the flow is also evidenced by the extracted slices in Figure 13. The comparison of Figure 11 and 13 do illustrate the impact of the unsteadiness on the flow structure that was indicated by the juxtaposition of the out-of-plane component distributions in Figure 5 and 7. S1 S2 S3 S4 Fig. 13 Helicity distribution in four slices at Re D = 600 during exhalation for a breathing cycle in the left bronchus. The position of the extracted slices matches those of the steady exhalation. 4. Conclusion and Outlook Multiplane stereo PIV measurements have been performed in several parallel planes within the first two bifurcations of a realistic model of the human lung. Three-dimensional velocity fields for steady expiration and for exhalation during a breathing cycle have been presented and compared. The velocity fields show that the flow in the lung possesses a highly three-dimensional character. The flow in the trachea is strongly influenced by the inlet velocity from the subbranches. The flow field in the left bronchus is different for steady expiration and expiration during a breathing cycle. These results lead to the hypothesis that the human lung possesses a natural wash-out process in specific regions. To investigate this wash-out process it is necessary to analyze to flow field for unsteady exhalation during a breathing cycle. Although 61% of the excitation of the exhalation cycle can be assumed steady it was shown that the flow field is time-dependent and unsteady

11 Acknowledgement The funding of the Deutsche Forschungsgemeinschaft in the frame of the joint program EXHALAT is gratefully acknowledged. 5. References Eitel, G., Soodt, T., Schröder, W. (2010) Investigation of pulsatile flow in the upper human airways. Int J Des Nat Ecodyn 5(4): Große, S., Schröder, W., Klaas, M., Klöckner, A., Roggenkamp, J. (2007) Time Resolved Analysis of Steady and Oscillating Flow in the Upper Human Airways. Exp. Fluids 42(6): Große, S., Schröder, W., Klaas, M., Klöckner, A., Roggenkamp, J. (2008) Time-resolved PIV measurements of vortical structures in the upper human airways. Topics of applied physics: Particle image velocimetry new developments and recent applications, editors Schröder, A., Willert, C., Springer:35-53 Haslbeck, K. Schwarz, K., Hohlfeld, J. M., Seume, J. R., Koch, W. (2010) Submicron droplet formation in the human lung. J Aerosol Sci, 41: Soodt, T., Schröder, F., Klaas, M., van Overbrüggen, T., Schröder, W. (2012) Experimental investigation into the transitional bronchial velocity distribution using stereoscanning PIV. Exp. Fluids 52(3): Westerweel, J., Scarano, F. (2005) Universal outlier detection for PIV data. Exp Fluids 39(6): WHO. (2008) World Health Statistics Schwitzerland: World Health Organization