Stereoscopic Particle Image Velocimetry Analysis of Healthy and Emphysemic Alveolar Sac Models

Emphysema is a type of chronic obstructive pulmonary disease defined by destruction of the alveolar walls over time. These changes in geometry give rise to changes in the flow fields and resulting particle deposition that are not yet understood. Many studies have examined the flow patterns in the pulmonary regions with increasingly more sophisticated geometries. Tsuda et al. [(1)] performed numerical simulations on a circular channel with expanding torus. Tippe and Tsuda [(2)] presented numerical data on flow in both expanding and nonexpanding alveolated channel flow. Darquenne [(3)] performed a computational fluid dynamic simulation on a static wall geometry consisting of a system of symmetric channels surrounded by triangular shaped alveoli. Karl et al. [(4)] performed both numerical and experimental studies on a nonexpanding channel surrounded by numerous alveoli. Sznitman et al. [(5,6)] completed moving boundary numerical simulations on an alveolated duct with a single alveolus and on a truncated octahedron (14-hedron). Similar to Karl et al. [(4)], van Ertbruggen et al. [(7)] performed both numerical and experimental studies on an alveolated duct. Kumar et al. [(8)] studied two honeycomblike polygonal structures including terminal alveolar sacs. Oakes [(9 10)] performed particle image velocimetry (PIV) studies to measure the flow field in idealized healthy and emphysemic terminal sacs.

Although much work has been done on idealized pulmonary geometry, the work cited in the preceding text has been done on idealized rather than replica geometry. Because in vivo geometry is complex, it is difficult to reconstruct in a typical engineering graphics package. Not until recently has there been numerical [(11)] and experimental [(12)] studies on replica geometry. Berg et. al [(12)]. presented a method of fabrication and experimental flow field results for a healthy replica model that included respiratory bronchioles and five terminal alveolar sacs. Methods presented in Berg et al. were applied in the present work to look at differences between a healthy and emphysematic lung.

Casting techniques of Phalen et al. [(13)] were employed to cast human adult lungs obtained through the Biological Sciences Department at RIT. The left lung of a healthy human was cast in the posterior and lateral basal sections of the lower lobe, while both the superior lower left lobe and the anterior portion of the superior division of the upper left lobe were cast in the emphysemic lung. Both healthy (H) and emphysemic (E) lungs were filled with CO₂ to remove residual air then pumped with approximately 80 ml of saline to dissolve the CO₂. Silicon rubber (10 ml) was then injected into the healthy lung (60 ml of silicon rubber was injected into the emphysemic lung) using a syringe pump, which forced the saline to diffuse through the alveolar membrane. Care was taken during the casting process to ensure that the lung was not overinflated. The casts were set to cure overnight and remained exposed to air for 2 weeks to dry out. Once dry, each lung was soaked in a 4 M NaOH solution for approximately 2 weeks to dissolve the tissue and expose the cast. Based on the quality of the cast, the existence of uniform alveoli, no air bubbles and the presence of a terminating alveolar sac, final healthy and emphysemic sections were chosen. These casts can be seen in Fig. 1. The healthy human alveolar mouth diameters measured from 243 to 378 μm, which was within the range reported by others (approximately 230–330 μm [(14)] or 292–226 μm [(15)]). The measured effective airway diameter of the emphysemic cast measured 1560 μm, which is much larger than reported measurements ranging from 430 to 830 μm [(14)]. This indicated that our model was obtained from a severely diseased lung, which was confirmed during consultation with Dr. Richard Doolittle (Biomedical Professor and Director of the Cadaver Lab, Rochester Institute of Technology).

To create three dimensional (3D) digital models, Micro-CT images were obtained from Micro Photonics (Allentown, PA) for each of the chosen lung casts. Using the 2D images, the casts were reconstructed using 3D Doctor (Able Software: Lexington, MA). Final healthy and emphysematic model reconstructions are shown in Fig. 2. Physical prototypes of the experimental healthy (19.4 times the in vivo size) and emphysemic (8.9 times the in vivo size) models were obtained from Laser Reproductions (Gahanna, OH) using stereolithography techniques at a layer resolution of 152 μm. Two physical prototype models were coated with a semibright nickel finish to reduce bubbles formed during the dipping process. Each of the prototype models were dipped into a bath of melted Ultraflex (Douglas and Sturgess Inc., Richmond, CA) and quickly removed. To ensure uniform thickness, each physical prototype model was rotated once after it was removed from the bath. After cooled to room temperature, the compliant models were removed from the solid prototype, examined for holes, and stored in glycerin. The nickel-plated prototypes for both healthy and emphysemic alveolar sacs are shown in Fig. 3 along with their respective compliant models.

In vivo breathing conditions for a typical healthy human were taken from pulmonary function test (PFT) data previously reviewed and cited by Robinson et al. [(16)]. Using an average functional residual capacity (FRC) of 3050 ml and an average tidal volume (TV) of 483 ml, the calculated in vivo expansion (TV/FRC) is 16%, while the average breathing frequency is 15.7 breath/min for the healthy model. Similarly for emphysema, an FRC of 5135 ml [(17)] and a TV of 560 ml [(18,19)] yields a lung expansion of 11%. A breathing frequency of 16.0 breath/min was used for the emphysemic model [(18)].

Particle image velocimetry (PIV) is an optical measurement technique used to noninvasively obtain instantaneous velocity fields in fluid flows. The fluid is seeded with small reflective tracer particles the motion of which is tracked between images. As with two dimensional (2D) measurements, stereoPIV measures displacements rather than actual velocities but can also calculate out of plane displacements. For each vector, three true displacements (dX, dY, and dZ) are extracted from a pair of 2-dimensional displacements (dx, dy) as seen from the left and right cameras, respectively. Due to perspective distortion occurring from the angle of the cameras with respect to the light sheet, each camera covers a trapezoidal region of the light sheet. Even with careful alignment of the two cameras, their respective fields of view only partly overlap each other. Within the region of overlap, interrogation points are chosen in a rectangular grid to match the spatial resolution of the cameras. The actual stereoscopic measurements begin with conventional 2D PIV processing of simultaneous recordings from left and right cameras. This produces two 2-dimensional vector maps representing the instantaneous flow field as seen from the left and right cameras, respectively. Using known parameters from the perspective calibration (distance from the object to the image, lens focal length, and camera angles), the points in the interrogation grid (overlap area) are mapped from the light sheet plane onto the left and right image planes (camera sensor), respectively. The 2D vector maps are re-sampled in the new interrogation regions to estimate 2D vectors at each point based on the nearest neighbors. The resulting 3D vector map is then calculated.

The experimental setup for stereoPIV analysis is shown in Fig. 4. Images were captured using two IDT Motion Pro X-3 Plus high-speed digital cameras, each equipped with a Tamron macro lens with a focal length of 90 mm, f-number of 2.8, and an image macro magnification ratio of 1:1. Ideally, Scheimpflug mounts are used to focus on planar fields at oblique viewing angles. Because they were not used in this experiment, the camera angles were minimized to allow the entire image to be in focus across the laser sheet. Therefore each camera was angled 15° from the perpendicular to the light sheet and was 7 in. from the center stand (30° between cameras as opposed to the ideal angle of 90°). The distance from the camera lens to the experimental model was chosen as to allow the entire experimental model to fit into the field of view of each camera, resulting in a spatial resolution of 64.23 μm per pixel occurring at the center of the experimental setup and varying as the light sheet location changes. The fluid was illuminated with a New Wave Research Solo II pulsed 532 nm laser and 8 μm red fluorescent polymer microspheres (Duke Scientific Corp.; Palo Alto, CA) were used as tracer particles in 99% glycerin carrier fluid (emitting at 612 nm). A mirror, positioned on a rotation stage, was used to direct the beam from the laser to the optics. A planar laser sheet was created by passing the collimated laser beam through a cylindrical lens, focal length of 25.4 mm, and a spherical lens of focal length 150 mm. The cameras were focused on regions of the experimental models in which the laser sheet’s waist (focal point of the beam) occurred, measuring approximately 1 mm thick and occurring in the center of the model. The cameras and laser were synchronized using a TSI laser pulse synchronizer and triggered with the start of each experiment.

Each compliant model was housed in a glycerin (refractive index of 1.47 ± 2.0E-3) chamber and filled with a glycerin/particle mix of approximately 0.007 gs of particles per 150 ml of glycerin to achieve the appropriate mixture required to minimize PIV processing error [(22)]. A computer controlled syringe pump drew a negative pressure on the chamber fluid, expanding the model and drawing glycerin from the inlet tube into the compliant model. Total model volume changes were verified with pressure sensors placed at the model inlet (MPXV5010GP, Freescale Semiconductor, Inc.; Austin, TX) and at the base of the chamber (PX2300-10DI, Omega Engineering, Inc.; Stamford, CT.

A LabVIEW code was generated to accurately control the syringe pump based on the desired flow conditions. Specifically, the model volume change per unit time was calculated from the initial model volume, percent expansion, and cycle time that would result in the desired Re and Wo for each model. Volume change was converted to linear displacement of the syringe pump based on the cross-sectional area of the syringe. The syringe pump (NE-500, New Era Pump Systems, Inc.; Wantagh, NY) was fitted with a stepper motor and controlled by a motion controller (MBC25081TB, Anaheim Automation; Anaheim, CA), programmed using LabVIEW and a DAQ device (PCI-6025E DAQ, National Instruments Corp.; Austin, TX). The compliant model material properties were not a factor in governing the rate of flow into the model. Each model was run at a flow rate of 1.94 ml/s for a 4 s period corresponding to a 3.15 ml volume change over the inhalation time (1.6 s). These conditions resulted in the Wo and Re previously given in Table 1.

TSI’s Insight 3G (TSI Inc., Shoreview, MN) was used to capture images for each experiment. A single pulse/frame for each camera was used with a frequency of 12.5 Hz (deltaT of 0.08 s between sequential laser pulses and images). For each laser sheet location, a total of three data sets were collected to illustrate the repeatability of the experimental results. Particle displacements were analyzed using Insight 3G (TSI Inc., Shoreview, MN). Correlations were computed using fast Fourier transforms, where the interrogation regions were 32 pixels × 32 pixels, and the velocity vectors were imported into Tecplot (Tecplot Inc., Bellevue, WA) to display the 3D vector maps.

Flow fields were observed real-time throughout the models to identify regions of recirculation that might exist. Figure 5 shows an example of streamlines in a section of the healthy model in which recirculating eddies would be expected based on the presence of distinct alveolar walls. As can be seen in the figure, the streamlines are not recirculating. It was clear from observation that there was no significant amount of flow moving past the alveolar mouth openings that would cause flow inside the alveoli to recirculate, even in regions with well defined alveolar geometry. Instead flow was observed to move in and out of the alveoli along the contours of the model walls. Similar observations were made in all regions of both the healthy and emphysematic models, and no recirculating eddies were found during either inflation or deflation.

To visualize the three-dimensional flow fields, 12 planar locations were analyzed for the healthy (H) model, and 10 planar locations were analyzed for the emphysemic (E) model. Using Eq. 4, the stereoPIV data were scaled to obtain the in vivo velocity magnitudes. A subset of the planes is shown in Figs. 6,7, for the H and E models, respectively. The dimensions in both figures have been scaled back to in vivo dimensions and represent the size of the original lung cast. Note that the in vivo healthy alveolar sac was 1.7 mm × 1.6 mm, while the emphysematic sac was 3 mm × 2.8 mm, about 75% larger. The in vivo velocities in the alveolar sacs ranged over two orders of magnitude (from 0.02 to 0.2 mm/s), for both the H and E models. The maximum velocities occurred near the model inlets (10th location for H and 8th location for E). Distal to the inlet in the H model, the velocities dissipated quickly so that the majority of the alveolar sac was seeing flows that were an order of magnitude lower than the inlet velocities. Specifically, in just 0.25 mm, flow slowed down from 0.23 mm/s to 0.09 mm/s or 60%. However, in the same distance, flow in the E model reduced from 0.24 mm/s to 0.22 mm/s, only 8% (see Fig. 8). Figure 9 represents contour plots with increased resolution for planes nearest to the walls (second location), showing that flow is moving about 50% faster in the emphysemic lung compared to the healthy lung where gas exchange occurs. Although the majority of the flow field was slow moving in both E and H models, the overall flow in the E model averaged around 0.07 mm/s, which was more than three times the magnitude of the H model flow (0.02 mm/s). These differences in the flow fields were consistent with differences in the geometries between H and E models. The H alveolar model divides and branches into smaller alveolar ducts, reducing the flow rate, while the E alveolar model remains one large volume, a result of septa deterioration in the diseased lung.

Using the predominant in vivo velocities of 0.07 mm/s and 0.02 mm/s for H and E models, respectively, the Pelect number was estimated for both models (see Fig. 10). The Pe numbers for the healthy model are consistent with our previous work using a different healthy human subject [(12)] and show diffusion dominated flow for particles less than 0.7 μm in diameter. This is based on previous work by Tan and Hsu [(23)] in which they approximated a transition from diffusive to convective dominated flow for Pelect numbers greater than 200. Using this same critical Peclet number for the transition point, it is clear that the E alveolar model transitions to convective dominated flow at much smaller particle sizes (0.15 μm).

The alveolar sac flow fields presented in this study were obtained experimentally on a larger-than in vivo scale, yet under dynamically similar flow conditions. These dynamically similar conditions were derived from pulmonary function test data gathered from the literature. Therefore, qualitatively, the flow field distributions obtained in this study using stereoPIV provide a good representation of what would be found in vivo. In this study, the normalized data were scaled back to in vivo conditions, based on the original PFT data and cast dimensions, in order to understand actual flow magnitudes present in H and E alveolar sacs.

It should be noted, as was demonstrated here and previously [(12)], that our experimental data can be scaled back to any range of chosen in vivo conditions as long as the Wo and Re for the in vivo conditions are below the convergence limit. The PFT data used in this study yielded Wo and Re that were well below the convergence limit. However, if one was to use heavy or rapid breathing; for example, the increased breathing frequency (f) and lung expansion (E) would increase the Wo and Re, respectively. These values must be checked against the convergence limits before applying dimensional analysis to our results for different breathing conditions.

Major geometric differences were found between the healthy and emphysemic lung during the casting process. In particular, the emphysematic lung contained no distinct alveoli, and it was clear from observation that the alveoli had merged into several large air sacs. Because of the extent of disease in the emphysemic lung, to obtain a complete emphysemic alveolar sac required a section with a much larger volume compared to the healthy alveolar sac cast. If we normalize values by model volume; however, we can realistically compare ventilation rates between H and E alveolar geometry. If we further assume that ventilation is uniform in the pulmonary region, our small alveolar sac models are reasonable representations of any alveolar region in the lung. We apply these normalizations here to make generalized comparisons between healthy and emphysematic subjects. If the breathing conditions from the PFT data are preserved, meaning we assume an 11% lung expansion for E and 16% for H, the emphysemic alveolar sac would receive 11 times the volume of air compared to a healthy person, which translates into a ventilation flow rate that is eight times higher for emphysema than for healthy. However, the ventilation per unit volume for emphysema is 30% smaller than for healthy.

Observations made in this study indicated that recirculation did not exist in the healthy or emphysemic alveolar models. These results confirm what has been predicted previously, based on idealized healthy geometry and what would be expected based on the model geometry and local flow conditions. According to literature, flow rate ratios (ratio of the alveolar to duct flow rate) below about 0.05 produce recirculating flows [(1,2,8)]. These small ratios exist where the ductal flow is large compared to the alveolar flow or in regions where the alveolar mouth diameter is small compared to the alveolar depth. From observation, the emphysemic model did not contain geometry that would induce recirculation. The majority of the emphysemic model was merged into two large sections; none of which contained regions where the alveolar mouth diameter was small compared to the alveolar depth. The healthy model; however, contained multiple, well defined bulb structures with several distinct alveoli. Yet the observed flow fields showed reversible flow throughout the entire healthy human model. Because emphysema is a condition that decreases the definition of individual alveoli, it is reasonable to expect that recirculation would not occur in the terminal alveolar sacs of emphysemic patients. Furthermore, based on these qualitative observations, it is reasonable to expect that recirculation does not occur in vivo in the terminal alveolar sacs of healthy lungs. This study provides further evidence that gas transport in the terminal alveolar sacs is governed by reversible convective flow and diffusion rather than turbulent eddies or chaotic effects [(12)].

Current understanding is that predicted particle deposition efficiency is smaller in emphysema compared to healthy lungs [(9,10 24)]. The flow field results from this study support the idea of reduced deposition in emphysema because the fluid pathlines come closer to the septa walls in the healthy model compared to emphysema model. The emphysemic alveolar sac is so much larger than the healthy sac, that even though the inhaled volume is larger, the net result is that the convected air does not penetrate as far in a single breath. To quantify the effect that these penetration differences have on deposition, a numerical study is needed in which particle diffusion and convection are tracked simultaneously.

Until now, there have been no data to realistically quantify differences in flow between healthy and emphysemic lungs. This study provides experimental velocity distributions for airflow inside expanding emphysemic and healthy terminal alveolar sacs. The velocities were scaled to in vivo conditions based on pulmonary function test data. Results indicate that the emphysematic lung loses its ability to dissipate flow so that the average velocity is larger than in the healthy lung. Furthermore, particle flow is more likely to be governed by convection rather than diffusion, even at smaller particle sizes. Finally, the ventilation flow rate is larger in emphysema, yet ventilation per unit volume is significantly reduced. Emphysemic induced flow changes occurring in the alveolar region could have a profound effect on gas exchange rates, accuracy of dosages of inhaled medications, and disease progressions.

This work was supported by the American Society (RSG-05-021-01-CNE). The authors would like to thank Dr. Richard Doolittle (Assistant Provost for Undergraduate Education, RIT) for his assistance in obtaining samples of healthy and emphysemic human lungs, Professor John Wellin (Department of Mechanical Engineering, RIT) for contributing to the development of the stereoPIV setup, and Dr. Steven Day for his general knowledge of PIV. This work is dedicated to Ted (Teddy) Harding, Jr. (Mechanical Engineering Graduate, RIT) as he greatly influenced the content and success of this research.