CFD Simulation and Experimental Validation of Fluid Flow and Particle Transport in a Model of Alveolated Airways.

Accurate modeling of air flow and aerosol transport in the alveolated airways is essential for quantitative predictions of pulmonary aerosol deposition. However, experimental validation of such modeling studies has been scarce. The objective of this study is to validate CFD predictions of flow field and particle trajectory with experiments within a scaled-up model of alveolated airways. Steady flow (Re = 0.13) of silicone oil was captured by particle image velocimetry (PIV), and the trajectories of 0.5 mm and 1.2 mm spherical iron beads (representing 0.7 to 14.6 mum aerosol in vivo) were obtained by particle tracking velocimetry (PTV). At twelve selected cross sections, the velocity profiles obtained by CFD matched well with those by PIV (within 1.7% on average). The CFD predicted trajectories also matched well with PTV experiments. These results showed that air flow and aerosol transport in models of human alveolated airways can be simulated by CFD techniques with reasonable accuracy.

Modeling the Progression of Epithelial Leak Caused by Overdistension.

Mechanical ventilation is necessary for treatment of the acute respiratory distress syndrome but leads to overdistension of the open regions of the lung and produces further damage. Although we know that the excessive stresses and strains disrupt the alveolar epithelium, we know little about the relationship between epithelial strain and epithelial leak. We have developed a computational model of an epithelial monolayer to simulate leak progression due to overdistension and to explain previous experimental findings in mice with ventilator-induced lung injury. We found a nonlinear threshold-type relationship between leak area and increasing stretch force. After the force required to initiate the leak was reached, the leak area increased at a constant rate with further increases in force. Furthermore, this rate was slower than the rate of increase in force, especially at end-expiration. Parameter manipulation changed only the leak-initiating force; leak area growth followed the same trend once this force was surpassed. These results suggest that there is a particular force (analogous to ventilation tidal volume) that must not be exceeded to avoid damage and that changing cell physical properties adjusts this threshold. This is relevant for the development of new ventilator strategies that avoid inducing further injury to the lung.

A Computational Model of Cellular Engraftment on Lung Scaffolds.

The possibility that stem cells might be used to regenerate tissue is now being investigated for a variety of organs, but these investigations are still essentially exploratory and have few predictive tools available to guide experimentation. We propose, in this study, that the field of lung tissue regeneration might be better served by predictive tools that treat stem cells as agents that obey certain rules of behavior governed by both their phenotype and their environment. Sufficient knowledge of these rules of behavior would then, in principle, allow lung tissue development to be simulated computationally. Toward this end, we developed a simple agent-based computational model to simulate geographic patterns of cells seeded onto a lung scaffold. Comparison of the simulated patterns to those observed experimentally supports the hypothesis that mesenchymal stem cells proliferate preferentially toward the scaffold boundary, whereas alveolar epithelial cells do not. This demonstrates that a computational model of this type has the potential to assist in the discovery of rules of cellular behavior.

Quantified aneurysm shape and rupture risk.

OBJECT: The authors investigated whether quantified shape or size indices could better discriminate between ruptured and unruptured aneurysms. METHODS: Several custom algorithms were created to quantifiy the size and shape indices of intracranial aneurysms by using three-dimensional computerized tomography angiography models of the brain vasculature. Data from 27 patients with ruptured or unruptured aneurysms were evaluated in a blinded fashion to determine whether aneurysm size or shape better discriminated between the ruptured and unruptured groups. Five size and eight shape indices were calculated for each aneurysm. Two-tailed independent Student t-tests (significance p < 0.05) were used to determine statistically significant differences between ruptured and unruptured aneurysm groups for all 13 indices. Receiver-operating characteristic-area under curve analyses were performed for all indices to quantify the predictability of each index and to identify optimal threshold values. None of the five size indices were significantly different between the ruptured and unruptured aneurysms. Five of the eight shape indices were significantly different between the two lesion groups, and two other shape indices showed a trend toward discriminating between ruptured and unruptured aneurysms, although these differences did not reach statistical significance. CONCLUSIONS: Quantified shape is more effective than size in discriminating between ruptured and unruptured aneurysms. Further investigation will determine whether quantified aneurysm shape will prove to be a reliable predictor of aneurysm rupture.

Resistance to alveolar shape change limits range of force propagation in lung parenchyma.

We have recently shown that if the lung parenchyma is modeled in 2 dimensions as a network of springs arranged in a pattern of repeating hexagonal cells, the distortional forces around a contracting airway propagate much further from the airway wall than classic continuum theory predicts. In the present study we tested the hypothesis that this occurs because of the negligible shear modulus of a hexagonal spring network. We simulated the narrowing of an airway embedded in a hexagonal network of elastic alveolar walls when the hexagonal cells of the network offered some resistance to a change in shape. We found that as the forces resisting shape change approach about 10% of the forces resisting length change of an individual spring the range of distortional force propagation in the spring network fell of rapidly as in an elastic continuum. We repeated these investigations in a 3-dimensional spring network composed of space-filling polyhedral cells and found similar results. This suggests that force propagation away from a point of local parenchymal distortion also falls off rapidly in real lung tissue.

Mechanical interactions between adjacent airways in the lung.

The forces of mechanical interdependence between the airways and the parenchyma in the lung are powerful modulators of airways responsiveness. Little is known, however, about the extent to which adjacent airways affect each other's ability to narrow due to distortional forces generated within the intervening parenchyma. We developed a two-dimensional computational model of two airways embedded in parenchyma. The parenchyma itself was modeled in three ways: 1) as a network of hexagonally arranged springs, 2) as a network of triangularly arranged springs, and 3) as an elastic continuum. In all cases, we determined how the narrowing of one airway was affected when the other airway was relaxed vs. when it narrowed to the same extent as the first airway. For the continuum and triangular network models, interactions between airways were negligible unless the airways lay within about two relaxed diameters of each other, but even at this distance the interactions were small. By contrast, the hexagonal spring network model predicted that airway-airway interactions mediated by the parenchyma can be substantial for any degree of airway separation at intermediate values of airway contraction forces. Evidence to date suggests that the parenchyma may be better represented by the continuum model, which suggests that the parenchyma does not mediate significant interactions between narrowing airways.

A progressive rupture model of soft tissue stress relaxation.

A striking feature of stress relaxation in biological soft tissue is that it frequently follows a power law in time with an exponent that is independent of strain even when the elastic properties of the tissue are highly nonlinear. This kind of behavior is an example of quasi-linear viscoelasticity, and is usually modeled in a purely empirical fashion. The goal of the present study was to account for quasi-linear viscoelasticity in mechanistic terms based on our previously developed hypothesis that it arises as a result of isolated micro-yield events occurring in sequence throughout the tissue, each event passing the stress it was sustaining on to other regions of the tissue until they themselves yield. We modeled stress relaxation computationally in a collection of stress-bearing elements. Each element experiences a stochastic sequence of either increases in elastic equilibrium length or decreases in stiffness according to the stress imposed upon it. This successfully predicts quasi-linear viscoelastic behavior, and in addition predicts power-law stress relaxation that proceeds at the same slow rate as observed in real biological soft tissue.

Airway-parenchymal interdependence in the lung slice.

The explanted lung slice has become a popular in vitro system for studying how airways contract. Because the forces of airway-parenchymal interdependence are such important modulators of airway narrowing, it is of significant interest to understand how the parenchyma around a constricting airway in a lung slice behaves. We have previously shown that the predictions of the 2-dimensional distortion field around a constricting airway are substantially different depending on whether the parenchyma is modeled as an elastic continuum versus a network of hexagonally arranged springs, which raises the question as to which model best explains the lung slice. We treated lung slices with methacholine and then followed the movement of a set of parenchymal landmarks around the airway as it narrowed. The resulting parenchymal displacement field was compared to the displacement fields predicted by the continuum and hexagonal spring network models. The predictions of the continuum model were much closer to the measured data than were those of the hexagonal spring network model, suggesting that the parenchyma in the lung slice behaves like an elastic continuum rather than a network of discrete springs. This may be because the alveoli of the lung slice are filled with agarose in order to provide structural stability, causing the parenchyma in the slice to act like a true mechanical continuum. How the air-filled parenchyma in the intact lung behave in vivo remains an open question.

Influence of parenchymal heterogeneity on airway-parenchymal interdependence.

To estimate the influence of parenchymal heterogeneities on airway-parenchymal interdependence, we considered a circular airway embedded within elastic parenchyma modeled as (1) a hexagonal spring network, (2) a triangular spring network, or (3) a continuum. The deformation in the parenchyma due to active airway contraction was simulated using the finite element method. Random perturbations of elastic moduli in the parenchyma did not significantly affect the overall pattern of force transmission. By contrast, when elastic moduli were increased along a path projecting radially outward from the airway, the hexagonal spring network model predicted significantly increased force along this line as the airway contracted, but this was not observed in other two models. These results indicate that tissue heterogeneities generally have minimal effect on the global nature of airway-parenchymal interdependence. However, in the exceptional circumstance of scar tissue aligned radially from the airway wall, parenchymal distortion forces may propagate much farther from the airway wall than was previously thought.

Aerosol bolus dispersion in acinar airways--influence of gravity and airway asymmetry.

The aerosol bolus technique can be used to estimate the degree of convective mixing in the lung; however, contributions of different lung compartments to measured dispersion cannot be differentiated unambiguously. To estimate dispersion in the distal lung, we studied the effect of gravity and airway asymmetry on the dispersion of 1 µm-diameter particle boluses in three-dimensional computational models of the lung periphery, ranging from a single alveolar sac to four-generation (g4) structures of bifurcating airways that deformed homogeneously during breathing. Boluses were introduced at the beginning of a 2-s inhalation, immediately followed by a 3-s exhalation. Dispersion was estimated by the half-width of the exhaled bolus. Dispersion was significantly affected by the spatial orientation of the models in normal gravity and was less in zero gravity than in normal gravity. Dispersion was strongly correlated with model volume in both normal and zero gravity. Predicted pulmonary dispersion based on a symmetric g4 acinar model was 391 ml and 238 ml under normal and zero gravity, respectively. These results accounted for a significant amount of dispersion measured experimentally. In zero gravity, predicted dispersion in a highly asymmetric model accounted for ∼20% of that obtained in a symmetric model with comparable volume and number of alveolated branches, whereas normal gravity dispersions were comparable in both models. These results suggest that gravitational sedimentation and not geometrical asymmetry is the dominant factor in aerosol dispersion in the lung periphery.

Continuum vs. spring network models of airway-parenchymal interdependence.

The outward tethering forces exerted by the lung parenchyma on the airways embedded within it are potent modulators of the ability of the airway smooth muscle to shorten. Much of our understanding of these tethering forces is based on treating the parenchyma as an elastic continuum; yet, on a small enough scale, the lung parenchyma in two dimensions would seem to be more appropriately described as a discrete spring network. We therefore compared how the forces and displacements in the parenchyma surrounding a contracting airway are predicted to differ depending on whether the parenchyma is modeled as an elastic continuum or as a spring network. When the springs were arranged hexagonally to represent alveolar walls, the predicted parenchymal stresses and displacements propagated substantially farther away from the airway than when the springs were arranged in a triangular pattern or when the parenchyma was modeled as a continuum. Thus, to the extent that the parenchyma in vivo behaves as a hexagonal spring network, our results suggest that the range of interdependence forces due to airway contraction may have a greater influence than was previously thought.

Aerosol deposition characteristics in distal acinar airways under cyclic breathing conditions.

Although the major mechanisms of aerosol deposition in the lung are known, detailed quantitative data in anatomically realistic models are still lacking, especially in the acinar airways. In this study, an algorithm was developed to build multigenerational three-dimensional models of alveolated airways with arbitrary bifurcation angles and spherical alveolar shape. Using computational fluid dynamics, the deposition of 1- and 3-µm aerosol particles was predicted in models of human alveolar sac and terminal acinar bifurcation under rhythmic wall motion for two breathing conditions (functional residual capacity = 3 liter, tidal volume = 0.5 and 0.9 liter, breathing period = 4 s). Particles entering the model during one inspiration period were tracked for multiple breathing cycles until all particles deposited or escaped from the model. Flow recirculation inside alveoli occurred only during transition between inspiration and expiration and accounted for no more than 1% of the whole cycle. Weak flow irreversibility and convective transport were observed in both models. The average deposition efficiency was similar for both breathing conditions and for both models. Under normal gravity, total deposition was ~33 and 75%, of which ~67 and 96% occurred during the first cycle, for 1- and 3-µm particles, respectively. Under zero gravity, total deposition was ~2-5% for both particle sizes. These results support previous findings that gravitational sedimentation is the dominant deposition mechanism for micrometer-sized aerosols in acinar airways. The results also showed that moving walls and multiple breathing cycles are needed for accurate estimation of aerosol deposition in acinar airways.

Effects of recruitment/derecruitment dynamics on the efficacy of variable ventilation.

Variable (or noisy) ventilation (VV) has been demonstrated in animal models of acute lung injury to be superior to constant (or conventional) ventilation (CV), in terms of improved gas exchange and mitigation of lung injury, for reasons that are not entirely clear. We hypothesized that the efficacy of VV is related to the fact that recruitment and derecruitment of lung units are dynamic processes. To test this hypothesis, we modeled the lung computationally as a symmetrically bifurcating airway tree terminating in elastic units. Each airway was fully open or completely closed, at any point in time, according to its pressure history. The model is able to accurately mimic previous experimental measurements showing that the lungs of mice injured by acid aspiration are better recruited after 60 min of VV than CV. The model also shows that recruitment/derecruitment dynamics contribute to the relative efficacy of VV, provided lung units open more rapidly than they close once a critical opening or closing pressure threshold has been crossed. We conclude that the dynamics of recruitment and derecruitment in the lung may be important factors responsible for the benefits of VV compared with CV.

Modeling the complex dynamics of derecruitment in the lung.

Recruitment maneuvers using deep inflations (DI) have long been used clinically with the objective of recruiting collapsed regions of the lung. Considerable uncertainty continues to exist, however, as to how best to employ recruitment maneuvers or even if they should be used routinely at all for patients receiving mechanical ventilation. Much of this uncertainty may arise from a lack of understanding about the dynamic nature of recruitment and derecruitment. To shed some light on this complex issue, we developed a time-dependent computational model of recruitment and derecruitment in the lung based on a symmetrically bifurcating airway tree in which each branch has a critical closing and opening pressure as well as pressure-dependent opening and closing speeds. Starting from the fully open state, the model underwent regular ventilation for 8 min followed by a series of identical DIs separated by 5 min of identical regular ventilation. We found that the geographical nature and extent of derecruitment before and 5 min after each DI were not always the same, demonstrating that the model exhibits multiple stable states. We conclude that the effectiveness of a recruitment maneuver is not only simply a function of the duration and magnitude of a DI, but may also have an unpredictable component arising from the distributed bi-stable nature of the derecruitment process itself.

CFD simulation of aerosol deposition in an anatomically based human large-medium airway model.

Quantitative data on aerosol deposition in the human respiratory tract are useful for understanding the causes of certain lung diseases and for designing efficient drug delivery systems via inhalation. In this study, aerosol deposition in a 3D anatomically based human large-medium airway model was simulated using computational fluid dynamics (CFD). The model extended from mouth to generation 10 and included two-thirds of the airways obtained by multi-detector row computed tomography (MDCT) imaging on normal healthy human subjects. Steady oral inhalation (15, 30, and 60 L/min) and aerosol (1-30 micrometer) deposition were computed by CFD using the realizable k-epsilon turbulence model. Based on the mean turbulence flow field, the computed extrathoracic deposition, ratio of left to right lung deposition, and deposition efficiency at each generation compared favorably with existing in vivo and in vitro experiments. The significant deposition in the large-medium airway model showed that the total tracheobronchial deposition is dominated by the large-medium airways for micrometer-sized aerosol particles. These quantitative data and the methods developed in this study provided valuable means toward subject-specific modeling of aerosol deposition in the human lung based on realistic lung geometry.

Nonlinear anisotropic stress analysis of anatomically realistic cerebral aneurysms.

BACKGROUND: Static deformation analysis and estimation of wall stress distribution of patient-specific cerebral aneurysms can provide useful insights into the disease process and rupture. METHOD OF APPROACH: The three-dimensional geometry of saccular cerebral aneurysms from 27 patients (18 unruptured and nine ruptured) was reconstructed based on computer tomography angiography images. The aneurysm wall tissue was modeled using a nonlinear, anisotropic, hyperelastic material model (Fung-type) which was incorporated in a user subroutine in ABAQUS. Effective material fiber orientations were assumed to align with principal surface curvatures. Static deformation of the aneurysm models were simulated assuming uniform wall thickness and internal pressure load of 100 mm Hg. RESULTS: The numerical analysis technique was validated by quantitative comparisons to results in the literature. For the patient-specific models, in-plane stresses in the aneurysm wall along both the stiff and weak fiber directions showed significant regional variations with the former being higher. The spatial maximum of stress ranged from as low as 0.30 MPa in a small aneurysm to as high as 1.06 MPa in a giant aneurysm. The patterns of distribution of stress, strain, and surface curvature were found to be similar. Sensitivity analyses showed that the computed stress is mesh independent and not very sensitive to reasonable perturbations in model parameters, and the curvature-based criteria for fiber orientations tend to minimize the total elastic strain energy in the aneurysms wall. Within this small study population, there were no statistically significant differences in the spatial means and maximums of stress and strain values between the ruptured and unruptured groups. However, the ratios between the stress components in the stiff and weak fiber directions were significantly higher in the ruptured group than those in the unruptured group. CONCLUSIONS: A methodology for nonlinear, anisotropic static deformation analysis of geometrically realistic aneurysms was developed, which can be used for a more accurate estimation of the stresses and strains than previous methods and to facilitate prospective studies on the role of stress in aneurysm rupture.

An anatomically based hybrid computational model of the human lung and its application to low frequency oscillatory mechanics.

Lung input impedance measured via forced oscillation over low frequency range has been confirmed as sensitive to the degree and the heterogeneity of lung disease. In this study we advanced an image-based, multi-scale computational model for the human lung, which includes upper and central airways, small airways and alveoli tissue unit. A three-dimensional (3-D) realistic model of the upper airway (reconstructed from MRI images) was combined with an anatomically based 3-D model of the central airways (based on MDCT images) to form a 3-D model of the large airways (from mouth to generation 6, incomplete for generations 4-6). The small airway trees distal to the central branches were based on a hypothetical airway tree for a normal healthy lung. A constant phase viscoelastic model was assumed for the alveolar tissue unit. Unsteady airflows in the large airways were simulated based on computational fluid dynamics (CFD). An experimentally measured broadband forcing flow was applied at the mouth. The impedance of the small airways was computed based on a one-dimensional transmission line model. The computed overall dynamic lung resistance and elastance compared very well with experimental values. Results showed that unsteady 3-D simulation and realistic geometry of the upper and large airways up to generations 4-6 can provide a reasonably accurate estimation of lung input impedance. The impedance of the upper airway constitutes a significant part of the total lung input impedance. The resistance of the upper airway accounts for 45-70% of the total lung resistance at frequencies between 0 and 1 Hz, and 70-81% at frequencies between 1 and 8 Hz.

Non-invasive determination of zero-pressure geometry of arterial aneurysms.

Arterial aneurysms are in a pre-deformed state in vivo under non-zero pressure. The ability to determine their zero pressure geometry may help in improving accuracy of determination of stress distribution and reverse estimation of material properties from dynamic imaging data. An approximate method to recover the zero pressure geometry of the AAA is proposed. This method is motivated by the observation that the patterns in displacement field for a given AAA are strikingly consistent in an AAA under all physiological pressures. The basic principle is to leverage this observation to iteratively identify the geometry that when subjected to the in vivo pressure, will recover the geometry reconstructed from in vivo imaging. The methodology is demonstrated and validated using patient-specific AAA models.

Three-dimensional geometrical characterization of cerebral aneurysms.

The risk of rupture of cerebral aneurysms has been correlated with the size of the aneurysm sac. It is conceivable that geometrical shape, not just size may also be related to aneurysm rupture potential. Further, aneurysm shape may also be a factor in deciding on treatment modalities, i.e., to clip or coil. However, our ability to make use of available information on aneurysm shape remains poor. In this study, methods were developed to quantify the seemingly arbitrary three-dimensional geometry of the aneurysm sac, using differential and computational geometry techniques. From computed tomography angiography (CTA) data, the three-dimensional geometry of five unruptured human cerebral aneurysms was reconstructed. Various indices (maximum diameter, neck diameter, height, aspect ratio, bottleneck factor, bulge location, volume, surface area, Gaussian and mean curvatures, isoperimetric ratio, and convexity ratio) were utilized to characterize the geometry of these aneurysm surfaces and four size-matched hypothetical control aneurysms. The physical meanings of various indices and their possible role as prognosticators for rupture risk and presurgical planning were discussed.