Computational fluid dynamics simulations of particle deposition in large-scale, multigenerational lung models

Computational fluid dynamics (CFD) has emerged as a useful tool for the prediction of airflow and particle transport within the human lung airway. Several published studies have demonstrated the use of Eulerian finite-volume CFD simulations coupled with Lagrangian particle tracking methods to determine local and regional particle deposition rates in small subsections of the bronchopulmonary tree. However, the simulation of particle transport and deposition in large-scale models encompassing more than a few generations is less common, due in part to the sheer size and complexity of the human lung airway. Highly resolved, fully coupled flowfield solution and particle tracking in the entire lung, for example, is currently an intractable problem and will remain so for the foreseeable future. This paper adopts a previously reported methodology for simulating large-scale regions of the lung airway (Walters, D. K., and Luke, W. H., 2010, "A Method for Three-Dimensional Navier-Stokes Simulations of Large-Scale Regions of the Human Lung Airway," ASME J. Fluids Eng., 132(5), p. 051101), which was shown to produce results similar to fully resolved geometries using approximate, reduced geometry models. The methodology is extended here to particle transport and deposition simulations. Lagrangian particle tracking simulations are performed in combination with Eulerian simulations of the airflow in an idealized representation of the human lung airway tree. Results using the reduced models are compared with those using the fully resolved models for an eight-generation region of the conducting zone. The agreement between fully resolved and reduced geometry simulations indicates that the new method can provide an accurate alternative for large-scale CFD simulations while potentially reducing the computational cost of these simulations by several orders of magnitude.     

Does perspective matter? A case study comparing Eulerian and Lagrangian estimates of common murre (Uria aalge) distributions

Studies estimating species' distributions require information about animal locations in space and time. Location data can be collected using surveys within a predetermined frame of reference (i.e., Eulerian sampling) or from animal‐borne tracking devices (i.e., Lagrangian sampling). Integration of observations obtained from Eulerian and Lagrangian perspectives can provide insights into animal movement and habitat use. However, contemporaneous data from both perspectives are rarely available, making examination of biases associated with each sampling approach difficult. We compared distributions of a mobile seabird observed concurrently from ship, aerial, and satellite tag surveys during May, June, and July 2012 in the northern California Current. We calculated utilization distributions to quantify and compare variability in common murre (Uria aalge) space use and examine how sampling perspective and platform influence observed patterns. Spatial distributions of murres were similar in May, regardless of sampling perspective. Greatest densities occurred in coastal waters off southern Washington and northern Oregon, near large murre colonies and the mouth of the Columbia River. Density distributions of murres estimated from ship and aerial surveys in June and July were similar to those observed in May, whereas distributions of satellite‐tagged murres in June and July indicated northward movement into British Columbia, Canada, resulting in different patterns observed from Eulerian and Lagrangian perspectives. These results suggest that the population of murres observed in the northern California Current during spring and summer includes relatively stationary individuals attending breeding colonies and nonstationary, vagile adults and subadults. Given the expected growth of telemetry studies and advances in survey technology (e.g., unmanned aerial systems), these results highlight the importance of considering methodological approaches, spatial extent, and synopticity of distribution data sets prior to integrating data from different sampling perspectives.     

The Lagrangian stochastic model for estimating footprint and water vapor fluxes over inhomogeneous surfaces

This study investigated a two-dimensional Lagrangian stochastic dispersion model for estimating water vapor fluxes and footprint over homogeneous and inhomogeneous surfaces. Over the homogeneous surface, particle trajectories were computed from a 2-D Lagrangian model forced by Eulerian velocity statistics determined by Monin–Obukhov similarity theory (MOST). For an inhomogeneous surface, the velocity and atmospheric stability profiles were computed using a second-order Eulerian closure model, and these local profiles were then used to drive the Lagrangian model. The model simulations were compared with water vapor flux measurements carried out above an irrigated bare soil site and an irrigated potato site. The inhomogeneity involved a step change in surface roughness, humidity, and temperature. Good agreement between eddy-correlation-measured and Lagrangian-model-predicted water vapor fluxes was found for both sites. Hence, this analysis demonstrates the practical utility of second-order closure models in conjunction with Lagrangian analysis to estimate the scalar footprint in planar inhomogeneous flows.     

植被与大气之间物质和能量交换过程的反演理论研究进展

介绍了研究植被与大气之间物质和能量交换过程的一个崭新理论——反演理论,主要包括拉格朗日方法、欧拉方法和欧拉 拉格朗日耦合方法.详细阐述了各种方法的理论框架,并简要说明了其应用范围,最后概述了反演理论的局限性和未来的发展方向.     

Methods for estimating long-distance dispersal

Long-distance dispersal (LDD) includes events in which propagules arrive, but do not necessarily establish, at a site far removed from their origin. Although important in a variety of ecological contexts, the system-specific nature of LDD makes "far removed" difficult to quantify, partly, but not exclusively, because of inherent uncertainty typically involved with the highly stochastic LDD processes. We critically review the main methods employed in studies of dispersal, in order to facilitate the evaluation of their pertinence to specific aspects of LDD research. Using a novel classification framework, we identify six main methodological groups: biogeographical; Eulerian and Lagrangian movement/redistributional; short-term and long-term genetic analyses; and modeling. We briefly discuss the strengths and weaknesses of the most promising methods available for estimation of LDD, illustrating them with examples from current studies.
The rarity of LDD events will continue to make collecting, analyzing, and interpreting the necessary data difficult, and a simple and comprehensive definition of LDD will remain elusive. However, considerable advances have been made in some methodological areas, such as miniaturization of tracking devices, elaboration of stable isotope and genetic analyses, and refinement of mechanistic models. Combinations of methods are increasingly used to provide improved insight on LDD from multiple angles. However, human activities substantially increase the variety of long-distance transport avenues, making the estimation of LDD even more challenging.     

Comparison of blood particle deposition models for non-parallel flow domains

Adhesions of monocytes and platelets to a vascular surface, particularly in regions of flow stagnation, recirculation, and reattachment, are a significant initial event in a broad spectrum of particle-wall interactions that significantly influence the formation of stenotic lesions and mural thrombi. A number of approximations are available for the simulation of both monocyte and platelet interactions with the vascular surface. For the simulation of blood particle adhesion, this study hypothesizes that: (a) the discrete element approach, which accounts for finite particle size and inertia, is advantageous in the context of non-parallel flow domains including stagnation, recirculation, and reattachment; and (b) the likelihood for particle deposition may be effectively approximated as being non-linearly proportional to local particle concentration, residence time, and wall proximity. Models such as wall shear stress correlations, the multicomponent mixture approach, and Lagrangian particle tracking with and without hydrodynamic particle-wall interactions were evaluated. Quantitative performance of the selected models was established by comparisons to available experimental data sets for non-parallel axisymmetric suspension flows of monocytes and platelets. Factors including the convective-diffusive transport of particles, finite particle size and inertia, as well as near-wall hydrodynamic interactions were found to significantly influence blood particle deposition. Of the models studied, the near-wall residence time approach was found to be a particularly effective indicator for the deposition of monocytes (r2=0.74) and platelets (r2=0.57), given that nano-scale physical and biochemical effects must be greatly approximated in computational simulations involving relatively large-scale geometries and complex flow fields.     

Effect of viscoelastic relaxation on moisture transport in foods. Part I: Solution of general transport equation

Within the framework of continuum mechanics, Singh et al. [1] developed an integro-differential equation, which applies to both Darcian (Fickian) and non-Darcian (non-Fickian) modes of fluid transport in swelling biological systems. A dimensionless form of the equation was obtained and transformed from moving Eulerian to the stationary Lagrangian coordinates. Here a solution scheme for the transport equation is developed to predict moisture transport and viscoelastic stresses in spheroidal biopolymeric materials. The equation was solved numerically and results used for predicting drying and sorption curves, moisture profiles, and viscoelastic stresses in soybeans. The Lagrangian solution was obtained by assembling together several schemes: the finite element method was used to discretize the equation in space; non-linearity was addressed using the Newton-Raphson method; the Volterra term was handled via a time integration scheme of Patlashenko et al. [2] and the Galerkin rule was used to solve the time-differential term. The solution obtained in Lagrangian coordinates was transformed back to the Eulerian coordinates. In part II of this sequence we present the numerical results.Revised version: 5 October 2003     

The effects of human movement on the persistence of vector-borne diseases

With the recent resurgence of vector-borne diseases due to urbanization and development there is an urgent need to understand the dynamics of vector-borne diseases in rapidly changing urban environments. For example, many empirical studies have produced the disturbing finding that diseases continue to persist in modern city centers with zero or low rates of transmission. We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) Lagrangian models that mimic human commuting behavior and (ii) Eulerian models that mimic human migration. We determine the basic reproduction number R₀ for both modeling approaches. We show that for both approaches that if the disease-free equilibrium is stable (R₀<1) then it is globally stable and if the disease-free equilibrium is unstable (R₀>1) then there exists a unique positive (endemic) equilibrium that is globally stable among positive solutions. Finally, we prove in general that Lagrangian and Eulerian modeling approaches are not equivalent. The modeling approaches presented provide a framework to explore spatial vector-borne disease dynamics and control in heterogeneous environments. As an example, we consider two patches in which the disease dies out in both patches when there is no movement between them. Numerical simulations demonstrate that the disease becomes endemic in both patches when humans move between the two patches.     

A new drift-flux model for particle transport and deposition in human airways

Particle deposition and transport in human airways isfrequently modeled numerically by the Lagrangian approach. Current formulations of such models always require some ad hoc assumptions, and they are computationally expensive. A new drift-flux model is developed and incorporated into a commercial finite volume code. Because it is Eulerian in nature, the model is able to simulate particle deposition patterns, distribution and transport both spatially and temporally. Brownian diffusion, gravitational settling, and electrostatic force are three major particle deposition mechanisms in human airways. The model is validated against analytical results for three deposition mechanisms in a straight tube prior to applying the method to a single bifurcation G3-G4. Two laminar flows with Reynolds numbers 500 and 2000 are simulated. Particle concentration contour deposition pattern, and enhancement factor are evaluated. To demonstrate how the diffusion and settling influence the deposition and transport along the bifurcation, particle sizes from 1 nm to 10 microm are studied. Different deposition mechanisms can be combined into the mass conversation equation. Combined deposition efficiency for the three mechanisms simultaneously was evaluated and compared with two commonly used empirical expressions.     

A Connectivity-Based Eco-Regionalization Method of the Mediterranean Sea

Ecoregionalization of the ocean is a necessary step for spatial management of marine resources. Previous ecoregionalization efforts were based either on the distribution of species or on the distribution of physical and biogeochemical properties. These approaches ignore the dispersal of species by oceanic circulation that can connect regions and isolates others. This dispersal effect can be quantified through connectivity that is the probability, or time of transport between distinct regions. Here a new regionalization method based on a connectivity approach is described and applied to the Mediterranean Sea. This method is based on an ensemble of Lagrangian particle numerical simulations using ocean model outputs at 1/12° resolution. The domain is divided into square subregions of 50 km size. Then particle trajectories are used to quantify the oceanographic distance between each subregions, here defined as the mean connection time. Finally the oceanographic distance matrix is used as a basis for a hierarchical clustering. 22 regions are retained and discussed together with a quantification of the stability of boundaries between regions. Identified regions are generally consistent with the general circulation with boundaries located along current jets or surrounding gyres patterns. Regions are discussed in the light of existing ecoregionalizations and available knowledge on plankton distributions. This objective method complements static regionalization approaches based on the environmental niche concept and can be applied to any oceanic region at any scale.     

Study of an infant brain subjected to periodic motion via a custom experimental apparatus design and finite element modelling

This paper presents a rig that was specifically designed to simulate the shaking of mechanical models of biological systems, especially those related to shaken baby syndrome (SBS). The scope of this paper includes the testing of an anthropomorphic model that simulates an infant head and provides validation data for complex finite element (FE) modelling using three numerical methods (Lagrangian, Arbitrary-Lagrangian–Eulerian (ALE) and Eulerian method) for fluid structure coupling.The experiments for this study aim to provide an understanding of the influence of two factors on intracranial brain movement of the infant head during violent shaking: (1) the specific paediatric head structure: the anterior fontanelle and (2) the brain–skull interface.The results show that the Eulerian analysis method has significant advantages for the FSI modelling of brain–CSF–skull interactions over the more commonly used methods, e.g. the Lagrangian method. To the knowledge of the authors, this methodology has not been discussed in previous publication.The results indicate that the biomechanical investigation of SBS can provide more accurate results only if the skull with paediatric features and the brain–skull interface are correctly represented, which were overlooked in previous SBS studies.     

Magnetic resonance microscopy analysis of advective transport in a biofilm reactor

In this article we present magnetic resonance microscopy (MRM) characterization of the advective transport in a biofilm capillary reactor. The biofilm generates non-axial flows that are up to 20% of the maximum axial velocity. The presence of secondary velocities of this magnitude alters the mass transport in the bioreactor relative to non-biofilm fouled reactors and questions the applicability of empirical mass transfer coefficient approaches. The data are discussed in the context of simulations and models of biofilm transport and conceptual aspects of transport modeling in complex flows are also discussed. The variation in the residence time distribution due to biofilm growth is calculated from the measured propagator of the motion. Dynamical systems methods applied to model fluid mixing in complex flows are indicated as a template for extending mass transport theory to quantitatively incorporate microscale data on the advection field into macroscale mass transfer models.     

Numerical simulation of pre- and postsurgical flow in a giant basilar aneurysm

Computational modeling of the flow in cerebral aneurysms is an evolving technique that may play an important role in surgical planning. In this study, we simulated the flow in a giant basilar aneurysm before and after surgical takedown of one vertebral artery. Patient-specific geometry and flowrates obtained from magnetic resonance (MR) angiography and velocimetry were used to simulate the flow prior to and after the surgery. Numerical solutions for steady and pulsatile flows were obtained. Highly three-dimensional flows, with strong secondary flows, were computed in the aneurysm in the presurgical and postsurgical conditions. The computational results predicted that occlusion of a vertebral artery would result in a significant increase of the slow flow region formed in the bulge of the aneurysm, where increased particle residence time and velocities lower than 2.5 cms were computed. The region of slow flow was found to have filled with thrombus following surgery. Predictions of numerical simulation methods are consistent with the observed outcome following surgical treatment of an aneurysm. The study demonstrates that computational models may provide hypotheses to test in future studies, and might offer guidance for the interventional treatment of cerebral aneurysms.     

A diversity of beta diversities: straightening up a concept gone awry. Part 2. Quantifying beta diversity and related phenomena

The present two-part review aims to put the different phenomena that have been called "beta diversity" over the years into a common conceptual framework and to explain what each of them measures. The first part (Tuomisto 2010) discussed basic definitions of "beta diversity". Each arises from a different way of combining a definition of "diversity" with a definition of its alpha component and with a mathematical relationship between the alpha and gamma components. This second part assumes that an appropriate basic definition of a beta component (which may or may not be true beta diversity) has been chosen, and the focus here will be on how to quantify it for a given dataset. About twenty different approaches have been used for this purpose. It turns out that only two of these approaches accurately quantify the selected beta component: one does so for the entire dataset, and the other for two sampling units at a time. The other approaches actually quantify other phenomena, such as mean species turnover between sampling units, compositional gradient length (with or without reference to an external gradient), distinctness of a focal sampling unit, rate of species accumulation with increasing sampling effort, rate of compositional turnover along an external gradient, or the rate of decay in compositional similarity with increasing geographical distance. Although most of these phenomena can be expressed as a function of a beta component of diversity, they do not equal a beta component of diversity. Many of these derived variables are not even numerically correlated with the beta component on which they are based, which needs to be taken into account when interpreting the results. The effects of sampling decisions when results are extrapolated beyond the available data will also be discussed.     

Modelling hollow organs for impact conditions: a simplified case study

This study compares the performances of three numerical approaches [Lagrangian (LAG), arbitrary Lagrangian–Eulerian (ALE) and control volume (CV)] for modelling the response of a short cylindrical pipe representing a portion of the intestines subjected to large and rapid compressions. While not being able to simulate sustained fluid flow, the LAG approach provided similar results as the ALE for moderate levels of compression. However, it was the stiffest approach for larger levels and had numerical issues for extreme compressions. While the ALE did not have these issues, its computing cost was very high, which would be problematic for large models. The CV approach had the lowest computing cost and seemed promising for larger compressions. However, its response was the softest and further investigations are needed to define its dependency to modelling parameters.     

Image-based modeling of hemodynamics in coronary artery aneurysms caused by Kawasaki disease

Kawasaki Disease (KD) is the leading cause of acquired pediatric heart disease. A subset of KD patients develops aneurysms in the coronary arteries, leading to increased risk of thrombosis and myocardial infarction. Currently, there are limited clinical data to guide the management of these patients, and the hemodynamic effects of these aneurysms are unknown. We applied patient-specific modeling to systematically quantify hemodynamics and wall shear stress in coronary arteries with aneurysms caused by KD. We modeled the hemodynamics in the aneurysms using anatomic data obtained by multi-detector computed tomography (CT) in a 10-year-old male subject who suffered KD at age 3?years. The altered hemodynamics were compared to that of a reconstructed normal coronary anatomy using our subject as the model. Computer simulations using a robust finite element framework were used to quantify time-varying shear stresses and particle trajectories in the coronary arteries. We accounted for the cardiac contractility and the microcirculation using physiologic downstream boundary conditions. The presence of aneurysms in the proximal coronary artery leads to flow recirculation, reduced wall shear stress within the aneurysm, and high wall shear stress gradients at the neck of the aneurysm. The wall shear stress in the KD subject (2.95-3.81 dynes/sq cm) was an order of magnitude lower than the normal control model (17.10-27.15 dynes/sq cm). Particle residence times were significantly higher, taking 5 cardiac cycles to fully clear from the aneurysmal regions in the KD subject compared to only 1.3 cardiac cycles from the corresponding regions of the normal model. In this novel quantitative study of hemodynamics in coronary aneurysms caused by KD, we documented markedly abnormal flow patterns that are associated with increased risk of thrombosis. This methodology has the potential to provide further insights into the effects of aneurysms in KD and to help risk stratify patients for appropriate medical and surgical interventions.     

One-dimensional numerical simulation of primary production: Lagrangian and Eulerian formulations

It has been argued (Wolf and Woods, in Toward a Theory On Biological-PhysicalInteractions in the World Ocean, Rothschild, (ed.), 1988) (WW88)that phytoplankton growth models are sensitive to Lagrangianeffects because populations at a given depth and time containa wide distribution of photoadaptive properties. On the otherhand, Lande and Lewis (Deep-Sea Research. 36. 1161–1175.1989) (LL89) have claimed that for a different photosyntheticmodel, this distribution of properties can be adequately representedby a mean value in a much simpler and more efficient Eulerianformulation. This study compares Lagrangian and Eulerian integrationsof these two different models of photosynthesis under two mixingregimes. For relatively weak mixing, the growth rate predictedby the different formulations of the two models is small (