Flow of aerosol in 3D alveolated bifurcations: experimental measurements by Particle Image Velocimetry and Particle Tracking Velocimetry

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1 Flow o aerosol in 3D alveolated biurcations: experimental measurements by Particle Image Velocimetry and Particle Tracking Velocimetry Vincent Ruwet, Patricia Corieri, Ra Theunissen, Baoshun Ma, Michel L. Riethmuller, Chantal Darquenne : von Karman Institute or Fluid Dynamics, Rhode-Saint-Genèse, Belgium, ruwet@vki.ac.be : University o Caliornia-San Diego, Department o Medicine, San Diego, USA, cdarquenne@ucsd.edu Abstract Studies related to aerosol transport and deposition in the alveolar region o the lung have been mostly restricted to numerical studies, which require urther experimental validation. Indeed, there are ew experimental studies with quantitative data due to the complexity o measurements in extremely low Reynolds-numbers (in the order o 0.) encountered in the lower lung airways. This article describes the experimental measurements perormed in a model o multiple lung biurcations with cylindrical cavities representing the alveoli. Both velocity ield and aerosol trajectories were measured with Particle Image Velocimetry (PIV) and 3D Particle Tracking Velocimetry (PTV), respectively. Silicon oil was used as carrier luid to satisy Reynolds similarity. Small iron beads o. mm and 0.5 mm were used to simulate aerosols o 5.3 µm and µm, respectively. Steady low velocity distributions were measured by PIV using 0µm iron particles as tracers. The images were processed with an algorithm that used a combination o the advanced interrogation method with an ensemble averaging procedure. Displacement rom 0.0 to 0 pixel were detected covering a velocity range o 0.0 to 0 mm/s. Two cameras were used in the PTV measurements to track the aerosol particles in three dimensions. All the particles trajectories were parallel to the biurcation plane and only ew 0.5 mm beads did not deposit inside the model. The trajectories deviated rom the low streamlines mainly under the eect o gravity. Finally, velocities measured by PIV were used in the equation describing small particle motions in Stokes low and accurately predicted the particles trajectories measured by PTV. In conclusion, both the PIV and PTV techniques can reliably be used in uture investigations o aerosol behavior in more complex acinar models Introduction Understanding the transport o inhaled particles in the alveolar region o the lung is important whether particle exposure results rom pollution or inhaled drug therapy. Aerosol transport mechanisms are however not yet ully understood despite their investigation in numerous computational studies. Furthermore, because o the absence o in-vivo measurements to quantiy the aerosol behavior in each acinar duct, these computational studies lack experimental validation. Due to the complexity o measurements made in extremely low Reynolds-numbers (in the order o 0.) encountered in the lower lung airways, only ew experimental studies have been reported where quantitative data o alveolar low has been measured. Recently Lee et al. (005) analyzed the respiratory low dynamics in a rigid model o the human lung spanning generation 8 to using a Micro-PIV system. Their model was made o smooth cylinders and did not include any alveolar cavities. Tsuda et al. (003) demonstrated through low visualization studies that chaotic mixing may be key to particle motion within the alveolar lung regions. Karl et al. (004) investigated viscous low through ducts with rigid cavities o dierent aspect ratios and showed that the low is extremely sensitive to the alveolar geometry. All o these in-vitro experiments ocused on the low velocity distribution or were limited to only one alveolus. Theunissen et al. (006) examined experimentally particle trajectories in low Reynolds number lows (Re 0.07) using a threedimensional scaled up rigid model o a bend tube, i.e. a hal biurcation, with alveolar cavities.

2 These data were used successully to validate numerical predictions obtained by computational luid dynamics (CFD) in a similar model (van Ertbruggen et al., 008) We built a 3D scaled-up model o multiple biurcations o airways with circular cavities representative o the alveolar region o the lung in which both low velocities and aerosol trajectories were measured by PIV and 3D PTV. Measurements provide a comprehensive dataset or validation o numerical simulations perormed in a similar model. The goal o the study was not to exactly relect the behavior o the human lung, but to take into account as many essential characteristics o alveolar structures as well as o aerosols. Experimental set-up. Experimental model A 3D model o acinar lung biurcations was manuactured at the von Karman Institute (VKI). This model consisted o two successive biurcations o cylindrical pipes (Figure ) representative o airway lumen in generations 0, and o the human lung (Weibel 963). Each o these pipes were surrounded with three circular rings to model the alveoli. The model was about 70 times larger than average airspaces in the alveolar region o the human lung. The lumen diameter was 0 mm and the alveolar rings had a diameter o 45 mm. The total height o the model was 30 cm. The model was built using a lost-model technique. The core o the model consisted o a lowmelting point metal alloy (Low 58 Alchemy Castings). The cast itsel was made o a mixture o silicone and curing agent (Sylgard 84, Dow Corning). This material was chosen or its very good transparency and or its reractive index ( n ~.43) matching that o the carrier luid (silicon oil). This manuacturing technique allowed to obtain an alveolated model with a complex geometry that was optically clear as shown on Figure.. Figure : Alveolated model o two successive lung biurcations

3 . Experimental acility The carrier luid used was silicon oil (47 V 000 rom Dow Corning). It has a kinematic viscosity o 000 mm²/s and a density o about 970 kg/m³. This high viscosity luid allowed or the Reynolds similarity. The optical properties o the luid matched the reractive index o the model. The experimental acility is depicted in Figure (let). The low inside the model was established by gravity. From an upstream reservoir, the luid was brought to the model with a circular pipe () and entered the model () on the top. Each outlet o the model was connected to a valve (4) in order to control the low rates in the two biurcations. The low exiting each outlet pass through a lowmeter (5) to measure the low rate in each o the three branches (Figure right). The luid was inally collected in a reservoir downstream and pumped to the top reservoir ml/s.0 ml/s ml/s ml/s Figure : Experimental acility (let) and low rates in the biurcation model (right) Because o the low low rates and high viscosity o silicon oil, commercially available lowmeters based on inertia driven mechanical systems were not appropriate. Flowmeters were developed at the VKI and consisted o a load cell which allows to determine the low rate by measuring weight o the luid passing on a slide. In the irst series o experiments, low rates calculated rom the velocities measured by PIV did not match those measured by the lowmeters. Dierences o almost 0 % were measured. It was observed that the alveolar cavities deormed under the hydrostatic pressure o the luid column above the model inlet A inite-element analysis (Figure 3) was perormed with the inite element sotware Samce Field, to estimate the model deormation under an internal pressure corresponding to a liquid height o.5 m ( Δp ~ 0.05 N/mm² ). The Young s modulus o the model material (Sylgard 84 rom Dow Corning) was evaluated to be about.6 MPa and the Poisson ratio to be about The inite-element computation predicts a maximal deormation o 0.4 mm or 4% or the diameter o one alveolus meaning that the area o the cross section o the pipes becomes 8% larger under the hydrostatic pressure. Because the low rates computed rom the measured velocities were obtained by integrating the velocity over the nominal non-deormed cross-section, this deormation could explain the dierence with the low rates measured by the balances. 3

4 To avoid this undesirable deormation, a Plexiglas box was built around the model and illed with the same carrier luid at the same pressure as inside the model. The nominal geometry was recovered with this technique. The dierence between the low rate measured with the balances and the low rate computed rom the velocity measurements remained below 3 %. Figure 3 : Model walls displacements under an internal pressure o 0.05 MPa computed by inite element analysis (Samce Field).3 Flow and aerosols similarity The Reynolds number or generation 0 to deep in the lung is about 0.. The dimensionless equation governing the motion o a small sphere in Stokes low is given by : d p p St u = ( p) u u u g () dt U ρ pdu p p Where St =, u p = u, = u U u, t = t, g = g 8μ D U U d g ( ρ ρ ) g d and up = up u = 8μ p p u u In equation (), U represents the mean luid velocity in the airway o diameter D; ρ p and d p are the density and the diameter o the aerosol particle travelling in a luid o dynamic viscosity μ. Finally, g is the gravitational acceleration. Two non-dimensional numbers appear in equation () : the Stokes number (St) which governs the ratio between the inertia o the particle and the viscous drag and the ratio between the relative particle s terminal velocity u p and the mean low velocity U. To simulate aerosol trajectories, particles used under experimental conditions must show a similar behavior as aerosols inhaled in the lung. Aerodynamic similarity was ensured by applying the real Reynolds numbers in the model or both the lung low and aerosols. As none o the two conditions (St and u p /U) could be satisied simultaneously it was opted to ocus only on the imposed velocity ratio between terminal velocity and low velocity (Theunissen et al., 006). Spherical iron particles o. mm and 0.5 mm in diameter were chosen. Based on their terminal velocities, the equivalent p 4

5 aerosol diameter would be 5.3 μm and µm, respectively. The iron spheres had relaxation times o 64 μs. Such number ensured that the particles would not ollow the low streamlines. 3 Particle Image Velocimetry 3. PIV measurement set up The luid was seeded with iron particles o 0 µm in diameter. These particles have a relaxation time o s and can be assumed to be neutrally buoyant Figure 4 : PIV illumination with laser sheet (let) and an example o recorded PIV image (right) A continuous Innova 70C Argon laser supplied the coherent light source with a wavelength o 54 nm. The laser beam was passing through an optical iber, and transormed into a thin laser sheet by a conventional optical system (Figure 4 let). The scattered light intensities were recorded with a standard digital PCO pixelly camera, equipped with a 50mm ocal length Nikon lens. Because o the very low velocities o the low (about 0 mm/s), a PIV camera was not needed. Since the low velocity is lower than 0 mm/s, an exposure time o 5 ms ensured the capture o rozen tracer patterns (Figure 4 right). Although most parts o the model were optically clear, some regions, especially the inter-alveolar regions suered rom a lower optical access and only ew tracers were visible there. An image acquisition rate o 0 Hz was imposed by an external trigger, which was connected to a host computer where the camera sotware was installed. The images themselves had a typical resolution o pixel and an average o 00 successive images were recorded. 3. Processing algorithm Processing o the images was perormed with the VKI cross-correlation algorithm WiDIM (Scarano and Riethmuller 999), using iterative image deormation. The algorithm displaced the second exposure interrogation-area with sub-pixel accuracy by gaussian itting and optimized it within an iterative structure.. During the iterative procedure, the size o the interrogating windows was gradually reduced (the windows were halved in both directions), yielding a iner resolution in space compared with one step interrogation methods and thereby increasing the spatial resolution. When evaluating digital PIV recordings with conventional correlation algorithms, a suicient number o particle images per interrogation window is required to perorm a reliable crosscorrelation. Typically, an average o ten particle images suice to ensure a reliable and accurate 5

6 measurement. In the current PIV experiments, it was diicult to ensure a high seeding concentration, especially in the cavities. Since the low could be considered as steady due to the low Reynolds number, the present study used a combination o the advanced interrogation method (WiDIM) with an ensemble averaging procedure. The common procedure to enhance the quality o the spatial-average displacement is to ensemble average the correlations o corresponding windows in successive image pairs. I φk(m, n) is the correlation unction o a single image pair the average (or ensemble) correlation unction or N PIV recording pairs is given by as: N φens ( mn, ) = φk ( mn, ) () N k= A total o 50 images were used or the ensemble averaging procedure. The initial windows size was set to 80x80 pixels and two window reinements were made during the iterative procedure leading to a inal size o 0x0 pixels. With an overlapping actor o 50 %, the inal spatial resolution was about vector each 0 pixels corresponding to one vector each 0.6 mm. 4 3D Particle Tracking Velocimetry 4. PTV measurement set-up The aerosol trajectories were measured with time resolved 3D PTV. Two cameras were needed to track the aerosol particles in three dimensions. The irst camera was placed in ront o the model and the second had its optical axis perpendicular to the bottom o the model to track the 3D motion o the particle in the irst biurcation (Figure 5). Figure 5 : Camera conigurations or 3D Particle Tracking Velocimetry The small iron spheres (0.5 and. mm diameter) were released in the low with an electromagnetic magnet upstream the test section. This particle release unit was suiciently ar rom the inlet o the model to avoid any induced low perturbations. Two cameras (Pixelly rom PCO) identical to the camera used or the PIV measurements were synchronized with an external trigger unit. Both cameras record images at the same time with an acquisition requency o 9 Hz. A white light illuminated volume was used to allow the aerosol particle to scatter a suicient amount o light (Bilka 006). 6

7 4. Time-resolved particle tracking algorithm The recorded images ollowed a background subtraction process to improve the particle signal. The developed algorithm makes use o reerence images (I 0 ), i.e. recorded images without seeding, to produce a background image. I the instantaneous pixel intensity (I) ulils the criterion mentioned in equation, it is classiied as part o a particle. The center o the eventual particle image is determined by a three point Gaussian it on the intensities in case o a local maximum or by calculating the center o gravity o the intensity distribution (Cowen and Monismith 997). 0 [ ] I( i, j) I ( x, y) + 4. RMS I ( x, y) (3) As no displacement ield was available or the particles, the tracking procedure was initialized by the our-rame method proposed by Malik et al. (993). A search area was built around each particle o the irst rame. All particle images o the second rame located within the area were considered to be possible partners. Based on the assumption that the particles would travel between successive rames the same distance on the same path, search areas in the third and ourth rame were located at the linear extrapolated positions rom the two previous rames. Eventually the path with the minimum acceleration was selected rom the collection o possible trajectories. In case o pairing conlicts, the particle lying closest to the predicted position was considered to be correct. Once a trajectory was established, the participating particles were taken out o consideration in the tracking o the remaining particles. Since numerous trajectories had to be compared, the our-rame method was quite laborious. Ater the our-rame method, all position predictions were thereore made rom a linear extrapolation o the previous particle positions. Again the particle link was perormed with the particle located closest to the predicted position. 0 5 Experimental Results and Discussion 5. Flow measurements Figure 6 depicts the contour plot o the velocity magnitude inside the biurcation plane o the model, resulting rom the ensemble average cross-correlation o 50 images. The poor optical quality o the model in the inter-alveoli regions lead to very low signal to noise ratio in these areas (black areas in ig. 6). These have been omitted rom the analysis. In the other regions o the measurement plane, the signal to noise ratio was almost always larger than 3. The PIV measurements show good agreement with previous studies (Theunissen 006). In the lumen, velocity proiles agreed with Poiseuille low and the integration o the parabolic proile lead to similar low rates than that measured with the lowmeters, within 3% o uncertainty. The velocity in the center o the lumen was about 0 mm/s or the 0 th generation, 5 mm/s in the branch modelling the st generation and about.5 mm/s in both branches o the nd generation. The Reynolds number at the inlet o the model was 0.3 and was reduced to 0.05 or the two last branches o generation. Because o this very low Reynolds number, the velocity proiles reestablish almost immediately ater the biurcations. 7

8 Figure 6 : Velocity ield in the biurcation plane (PIV measurements) Figure 7 : Velocity measurements in three alveoli ( let to right: streamlines; central alveolus : velocity vectors) Flow ields were characterised by a curvilinear separation streamline at the alveolar openings, indicating little convective exchange between the alveoli and the lumen. The recirculation region, typical o a cavity low, was identiied. A strong velocity gradient existed between the lumen and the inlet o the alveolus (Fig.7, middle alveolus). The velocities o the slowly rotating luid inside an alveolus were only about 0.0 mm/s (Figure 8 let) while the velocities in the center o the lumen were about 0 mm/s. Because o the very low velocities in the alveolar cavities, images in these areas were recorded with a larger magniication to improve the accuracy o the measurements. Figure 8 compares measurements inside an alveolus using images o the whole low ield (magniication actor ~ 0.06 mm/pixel) and that obtained with a larger magniication in a zoomed image (magniication actor ~ mm/pixel). The displacement in the center o the alveolus was about 0.3 pixels in the zoomed images which is 0 times larger than the displacement measured on the whole ield images (0.03 pixels). Although the luid displacement in the alveolus or the whole low ield measurement is 0.03 pixels (Figure 8 right), the maximum velocity dierence with the zoomed ield measurement (much more accurate) is only 0.0 mm/s (Figure 8 let). For the whole ield images, 0.0mm/s 8

9 corresponds to a displacement about 0.05 pixels, meaning that the advanced interrogation technique can measure displacements about / pixels. It is remarkable that the PIV technique used here allows to reach an accuracy o 0.05 pixels (displacement o µm only). With the whole low ield measurement, the iterative windows deormation procedure is able to measure in the same ield o view, velocities o 0 mm/s (window displacement o 7 pixels) and velocities o about 0.0 mm/s (window displacement o 0.03 pixels). In a given PIV image, a dynamic range o displacements covering three orders o magnitude can be measured. Integrating the proile on the whole cross section, the low rate measured by the balances is retrieved with % dierences.. Figure 8 : Velocity proile in the alveolus along the radial direction in mm/s (let) and corresponding displacement measured in pixel (right) 5. Aerosol trajectories Trajectories o iron particles o both. and 0.5 mm in diameter were measured. Figure 9 shows such a trajectory or a 0.5 mm-diameter particle. The aerosol particles do not ollow the stream lines. The curvature o the trajectories because o gravity was the predominant deposition mechanism. The gravity could explain that the particles deposit only in the inclined duct. Whatever the initial release location, all the. mm particles deposit beore the second biurcation while some o the 0.5 mm particles exit the structure. Figure 9 presents the 3D PTV results. Trajectories o two particles A and B were tracked. From images taken by camera ( Figure 9 (d) ), the trajectories in the vertical plane were obtained (Figure 9 (a) ). Looking rom the bottom, camera (Figure 9 (d) ) allows to record the iron spheres images in the irst biurcation. The corresponding measured trajectories are shown in Figure 9 (b). In supplement, the sum o the PTV images taken by camera are depicted in Figure 9 (c). In (c), the successive positions o the iron spheres are visible and correspond to the measured trajectories shown in Figure 9 (b). The trajectories in the horizontal plane (Figure 9 (b) and (c)), obtained by camera, showed that the particle trajectories were almost parallel to the biurcation plane. In the neighbourhood o an alveolus, the trajectory was curved because o the low curvature at the cavity inlet. The small iron spheres o 0.5 mm were able to cross the whole model i released in the biurcation plane in the let part o the model. The particles passing in the center o the lumen o the second branch can acquire suicient horizontal velocity to reach the second biurcation. I the particle entered an alveolus, where the velocities were very small (Figure 7), it deposited on the alveolus wall almost immediately, the settling velocity being much higher than low velocities in the cavity. 9

10 4 Model boundaries (a) (b) 3 4 (c) (d) Figure 9 : 3D PTV trajectories: (a) trajectories in the vertical plane obtained by camera ; (b) trajectories projected on the horizontal plane taken by camera (particle motion is towards the reader rom right to let); (c) sum o PTV recorded images rom camera ; (d) positions o camera and camera or PTV. Labels: : lumen; : irst alveolar ring o the st generation; 3: particles images/trajectories; 4: third alveolar ring o the 0 th generation To validate the measurements, Equation () was solved or a particle initially released in the biurcation plane. Because the PTV measurements in the third dimension have shown that the trajectories are almost parallel to the biurcation plane, we can assume that the particle remains in the laser sheet plane o the PIV measurements, i.e. the biurcation plane. Deducting u (in equation 0

11 ) rom the PIV measurements, the particle trajectory can be easily computed and compared to the PTV measurements (Figure 0). Both approaches show very good agreement and the aerosol particles behavior under Stokes low conditions can be easily predicted rom the luid velocity measurements with high accuracy. Figure 0 : 0.5 mm iron sphere trajectory obtained rom PTV and predicted rom PIV measurements 6 Conclusion In the present article, the investigation o aerosol particles behavior in three generations o the human acinus was perormed. A 3D scaled up model made o pipes and circular cavities representing the alveoli in the deepest part o the lung was built to model lung generations 0 to (Re ~ 0.). Silicon oil was used as carrier luid and the low rates inside the two biurcations were adjusted precisely with lowmeters in order to satisy the Reynolds similarity. Small iron spheres o. mm and 0.5 mm diameter were used to simulate aerosols o 5.3 and µm respectively. An ensemble average correlation algorithm was used because o the poor quality o the images in such complex geometry. This algorithm incorporates window distortion and reduction o the interrogation windows within an iterative structure. The adapted algorithm allowed the extraction o valuable velocity inormation with relatively high spatial resolution, even in regions o poor image quality and low seeding. An existing particle tracking algorithm was modiied to allow the tracking o the aerosol particles in the three dimensions. Two synchronized cameras placed in ront o two sides o the model recorded images simultaneously to extract the time resolved aerosol 3D trajectories and velocities.

12 A curvilinear separation streamline at the alveolar openings characterized the low ield and indicated little convective exchange with the lumen low. In the center o the tube, measured velocity proiles showed good agreement with the theoretical Poiseuille low. The velocity inside the alveoli was about two orders o magnitude smaller compared to the mean lumen velocity. Through the advanced interrogation methodology even the slow rotating luid elements, located at the center o each cavity could be properly identiied. The whole velocity range could be accurately measured because the advanced PIV algorithm was able to measure displacements as small as 0.0 pixels. In a given PIV image displacements rom 0 to 0.0 pixels have been measured covering a velocity range o 0 to 0.0 mm/s. The 3D measurements o the aerosol trajectories have shown that the aerosols remain in a vertical plane parallel to the plane o the biurcation. Only some o the 0.5 mm particles were able to travel inside the whole model without depositing. All the other particles studied deposited in the structure with gravity being the dominating deposition mechanism. We also showed that PIV measurements could be used to accurately compute the particle trajectories using an equation describing small particle motion in Stokes low. Both the PIV and PTV techniques can thereore reliably be used in uture investigations o aerosol behavior in more complex acinar models. 7 Reerences Cowen E.A. and Monismith S.G.(997) A hybrid digital particle tracking velocimetry technique, Experiments in Fluids,, 99- Bilka M. (006) Experimental investigation o 3D aerosol motion within an alveolated duct. VKI DC Project Report Darquenne C. (00) A realistic two-dimensional model o aerosol transport and deposition in the alveolar zone o a human lung, J. o Aerosol Science, 3, 6-74 Darquenne C. (00) Heterogenity o aerosol deposition in a two-dimensional model o human alveolated ducts, J. o Aerosol Science, 33, 6-78 Haber S., Yitzhak D., Tsuda A. (003) Gravitational deposition in a rhythmically expanding and contracting alveolus, Journal o Applied Physiology, 95, Karl A., Henry F.S., Tsuda A. (004) Low Reynolds number viscous low in an alveolated duct, ASME, 6, pp Lee W.J., Kawahashi M., Hirahara H. (005) Analysis o respiratory low dynamics in a model o human terminal airway biurcation using Micro PIV, Proc. 6th Int. Symp. Particle Image Velocimetry, Pasadena, Caliornia, September -3 Malik N.A., Dracos T., Papantoniou D.A. (993) Particle Tracking Velocimetry in threedimensional lows Part II: Particle tracking, Experiments in Fluids, 5, Meinhart C.D., Wereley S.T., Santiago J.G. (000) A PIV algorithm or estimating time-average velocity ields, J. o Fluids Engineering,, Issue, Scarano F. and Riethmuller M.L. (999), Iterative Multigrid approach in PIV image processing with discrete window oset, Experiments in Fluids, 6, Theunissen R., Buchmann N., Corieri P., Riethmuller M.L., Darquenne C. (006), Experimental Investigation o Aerosol Deposition in Alveolar Lung Airways, 3th Int Symposium on Applications o Laser Techniques to Fluid Mechanics van Ertbruggen C., Corieri P., Theunissen R., Riethmuller M.L., Darquenne C. (008), Validation o CFD predictions o low in a 3D alveolated bend with experimental data, Journal o Biomechanics, 4, Issue, Weibel E.R. (963) Morphology o the human lung, Springer Verlag, Heidelberg