Varying perivascular astroglial endfoot dimensions along the vascular tree maintain perivascular-interstitial flux through the cortical mantle.

The glymphatic system is a recently defined brain-wide network of perivascular spaces along which cerebrospinal fluid (CSF) and interstitial solutes exchange. Astrocyte endfeet encircling the perivascular space form a physical barrier in between these two compartments, and fluid and solutes that are not taken up by astrocytes move out of the perivascular space through the junctions in between astrocyte endfeet. However, little is known about the anatomical structure and the physiological roles of the astrocyte endfeet in regulating the local perivascular exchange. Here, visualizing astrocyte endfoot-endfoot junctions with immunofluorescent labeling against the protein megalencephalic leukoencephalopathy with subcortical cysts-1 (MLC1), we characterized endfoot dimensions along the mouse cerebrovascular tree. We observed marked heterogeneity in endfoot dimensions along vessels of different sizes, and of different types. Specifically, endfoot size was positively correlated with the vessel diameters, with large vessel segments surrounded by large endfeet and small vessel segments surrounded by small endfeet. This association was most pronounced along arterial, rather than venous segments. Computational modeling simulating vascular trees with uniform or varying endfeet dimensions demonstrates that varying endfoot dimensions maintain near constant perivascular-interstitial flux despite correspondingly declining perivascular pressures along the cerebrovascular tree through the cortical depth. These results describe a novel anatomical feature of perivascular astroglial endfeet and suggest that endfoot heterogeneity may be an evolutionary adaptation to maintain perivascular CSF-interstitial fluid exchange through deep brain structures.

Competitive resource allocation to metabolic pathways contributes to overflow metabolisms and emergent properties in cross-feeding microbial consortia.

Resource scarcity is a common stress in nature and has a major impact on microbial physiology. This review highlights microbial acclimations to resource scarcity, focusing on resource investment strategies for chemoheterotrophs from the molecular level to the pathway level. Competitive resource allocation strategies often lead to a phenotype known as overflow metabolism; the resulting overflow byproducts can stabilize cooperative interactions in microbial communities and can lead to cross-feeding consortia. These consortia can exhibit emergent properties such as enhanced resource usage and biomass productivity. The literature distilled here draws parallels between in silico and laboratory studies and ties them together with ecological theories to better understand microbial stress responses and mutualistic consortia functioning.

Spatiotemporal modeling of laser tissue soldering using photothermal nanocomposites.

OBJECTIVE: Laser tissue soldering using photothermal solders is a technology that facilitates rapid sealing using heat-induced changes in the tissue and the solder material. The solder material is made of gold nanorods embedded in a protein matrix patch that can be placed over the tissue rupture site and heated with a laser. Although laser tissue soldering is an attractive approach for surgical repair, potential photothermal damage can limit the success of this approach. Development of predictive mathematical models of photothermal effects including cell death, can lead to more efficient approaches in laser-based tissue repair. METHODS: We describe an experimental and modeling investigation into photothermal solder patches for sealing porcine and mouse cadaver intestine sections using near-infrared laser irradiation. Spatiotemporal changes in temperature were determined at the surface as well as various depths below the patch. A mathematical model, based on the finite element method, predicts the spatiotemporal temperature distribution in the patch and surrounding tissue, as well as concomitant cell death in the tissue is described. RESULTS: For both the porcine and mouse intestine systems, the model predicts temperatures that are quantitatively similar to the experimental measurements with the model predictions of temperature increase often being within a just a few degrees of experimental measurements. CONCLUSION: This mathematical model can be employed to identify optimal conditions for minimizing healthy cell death while still achieving a strong seal of the ruptured tissue using laser soldering. Lasers Surg. Med. 50:143-152, 2018. © 2017 Wiley Periodicals, Inc.

Quantifying the effects of the division of labor in metabolic pathways.

Division of labor is commonly observed in nature. There are several theories that suggest diversification in a microbial community may enhance stability and robustness, decrease concentration of inhibitory intermediates, and increase efficiency. Theoretical studies to date have focused on proving when the stable co-existence of multiple strains occurs, but have not investigated the productivity or biomass production of these systems when compared to a single 'super microbe' which has the same metabolic capacity. In this work we prove that if there is no change in the growth kinetics or yield of the metabolic pathways when the metabolism is specialized into two separate microbes, the biomass (and productivity) of a binary consortia system is always less than that of the equivalent monoculture. Using a specific example of Escherichia coli growing on a glucose substrate, we find that increasing the growth rates or substrate affinities of the pathways is not sufficient to explain the experimentally observed productivity increase in a community. An increase in pathway efficiency (yield) in specialized organisms provides the best explanation of the observed increase in productivity.

Effect of model selection on prediction of periodic behavior in gene regulatory networks.

One of the current challenges for cell biology is understanding of the system level cellular behavior from the knowledge of a network of the individual subcellular agents. We address a question of how the model selection affects the predicted dynamic behavior of a gene network. In particular, for a fixed network structure, we compare protein-only models with models in which each transcriptional activation is represented both by mRNA and protein concentrations. We compare linear behavior near equilibria for both cyclic feedback systems and a general system. We show that, in general, explicit inclusion of the mRNA in the model weakens the stability of equilibria. We also study numerically dynamics of a particular gene network and show significant differences in global dynamics between the two types of models.

Environment Constrains Fitness Advantages of Division of Labor in Microbial Consortia Engineered for Metabolite Push or Pull Interactions.

Fitness benefits from division of labor are well documented in microbial consortia, but the dependency of the benefits on environmental context is poorly understood. Two synthetic Escherichia coli consortia were built to test the relationships between exchanged organic acid, local environment, and opportunity costs of different metabolic strategies. Opportunity costs quantify benefits not realized due to selecting one phenotype over another. The consortia catabolized glucose and exchanged either acetic or lactic acid to create producer-consumer food webs. The organic acids had different inhibitory properties and different opportunity costs associated with their positions in central metabolism. The exchanged metabolites modulated different consortial dynamics. The acetic acid-exchanging (AAE) consortium had a "push" interaction motif where acetic acid was secreted faster by the producer than the consumer imported it, while the lactic acid-exchanging (LAE) consortium had a "pull" interaction motif where the consumer imported lactic acid at a comparable rate to its production. The LAE consortium outperformed wild-type (WT) batch cultures under the environmental context of weakly buffered conditions, achieving a 55% increase in biomass titer, a 51% increase in biomass per proton yield, an 86% increase in substrate conversion, and the complete elimination of by-product accumulation all relative to the WT. However, the LAE consortium had the trade-off of a 42% lower specific growth rate. The AAE consortium did not outperform the WT in any considered performance metric. Performance advantages of the LAE consortium were sensitive to environment; increasing the medium buffering capacity negated the performance advantages compared to WT. IMPORTANCE Most naturally occurring microorganisms persist in consortia where metabolic interactions are common and often essential to ecosystem function. This study uses synthetic ecology to test how different cellular interaction motifs influence performance properties of consortia. Environmental context ultimately controlled the division of labor performance as shifts from weakly buffered to highly buffered conditions negated the benefits of the strategy. Understanding the limits of division of labor advances our understanding of natural community functioning, which is central to nutrient cycling and provides design rules for assembling consortia used in applied bioprocessing.

Biofilm deformation in response to fluid flow in capillaries.

Biofilms are complex mixtures of microorganisms and extracellular matrix that exist on many wetted surfaces. Recently, magnetic resonance microscopy has been used to measure fluid velocities near biofilms that are attached to the walls of capillary channels. These velocity measurements showed unexpectedly high secondary velocities (i.e., high velocity magnitudes perpendicular to the direction of bulk flow and perpendicular to the surface that the biofilm is attached), and the presence of high secondary velocities near a biofilm could increase the delivery of substrates to the biofilm. A mathematical model, based on the immersed boundary method, is used here to examine the physical interaction between a biofilm and a moving fluid in a capillary and to analyze possible factors that may contribute to the elevated secondary velocities observed experimentally. The simulation predicts the formation of a recirculation downstream of a biofilm, and this recirculation deforms and lifts the biofilm upward from the surface to which the biofilm is attached. Changing the mechanical properties (i.e., stiffness) of the biofilm impacts both the lifting of the biofilm and the magnitude of the secondary velocities. The maximum lifting of the biofilm occurs when the biofilm properties are similar to previous experimental measurements, which indicates that the mechanical properties of the biofilm may be tuned for the generation of maximum secondary velocity magnitude and transport of substrates to the biofilm.

Flow velocity vector fields by ultrasound particle imaging velocimetry: in vitro comparison with optical flow velocimetry.

OBJECTIVES: We performed an in vitro study to assess the precision and accuracy of particle imaging velocimetry (PIV) data acquired using a clinically available portable ultrasound system via comparison with stereo optical PIV. METHODS: The performance of ultrasound PIV was compared with optical PIV on a benchmark problem involving vortical flow with a substantial out-of-plane velocity component. Optical PIV is capable of stereo image acquisition, thus measuring out-of-plane velocity components. This allowed us to quantify the accuracy of ultrasound PIV, which is limited to in-plane acquisition. The system performance was assessed by considering the instantaneous velocity fields without extracting velocity profiles by spatial averaging. RESULTS: Within the 2-dimensional correlation window, using 7 time-averaged frames, the vector fields were found to have correlations of 0.867 in the direction along the ultrasound beam and 0.738 in the perpendicular direction. Out-of-plane motion of greater than 20% of the in-plane vector magnitude was found to increase the SD by 11% for the vectors parallel to the ultrasound beam direction and 8.6% for the vectors perpendicular to the beam. CONCLUSIONS: The results show a close correlation and agreement of individual velocity vectors generated by ultrasound PIV compared with optical PIV. Most of the measurement distortions were caused by out-of-plane velocity components.

Quantitative analysis of macroscopic solute transport in the murine brain.

BACKGROUND: Understanding molecular transport in the brain is critical to care and prevention of neurological disease and injury. A key question is whether transport occurs primarily by diffusion, or also by convection or dispersion. Dynamic contrast-enhanced (DCE-MRI) experiments have long reported solute transport in the brain that appears to be faster than diffusion alone, but this transport rate has not been quantified to a physically relevant value that can be compared to known diffusive rates of tracers. METHODS: In this work, DCE-MRI experimental data is analyzed using subject-specific finite-element models to quantify transport in different anatomical regions across the whole mouse brain. The set of regional effective diffusivities ([Formula: see text]), a transport parameter combining all mechanisms of transport, that best represent the experimental data are determined and compared to apparent diffusivity ([Formula: see text]), the known rate of diffusion through brain tissue, to draw conclusions about dominant transport mechanisms in each region. RESULTS: In the perivascular regions of major arteries, [Formula: see text] for gadoteridol (550 Da) was over 10,000 times greater than [Formula: see text]. In the brain tissue, constituting interstitial space and the perivascular space of smaller blood vessels, [Formula: see text] was 10-25 times greater than [Formula: see text]. CONCLUSIONS: The analysis concludes that convection is present throughout the brain. Convection is dominant in the perivascular space of major surface and branching arteries (Pe > 1000) and significant to large molecules (> 1 kDa) in the combined interstitial space and perivascular space of smaller vessels (not resolved by DCE-MRI). Importantly, this work supports perivascular convection along penetrating blood vessels.

Antimicrobial laser-activated sealants for combating surgical site infections.

Surgical-site infections (SSIs) occur in 2-5% of patients undergoing surgery in the US alone, impacting 300 000-500 000 lives each year, and presenting up to 11 times greater risk of death compared to patients without SSIs. The most common cause of SSI is Staphylococcus aureus, and methicillin-resistant S. aureus (MRSA) is the most common pathogen in community hospitals. Current clinical devices used for approximating incisions and traumatic lacerations include sutures, adhesives, tapes, or staples with or without antimicrobial incorporation. However, current closure technologies may not provide adequate protection against infection, are susceptible to wound dehiscence, and can result in delayed biomechanical recoveries. Laser-activated tissue repair is a sutureless technique in which chromophore-loaded sealants convert laser light energy to heat in order to induce rapid tissue sealing. Here, we describe the generation and evaluation of laser-activated sealant (LASE) biomaterials, in which, indocyanine green (ICG), an FDA-approved dye, was embedded in a silk fibroin matrix and cast into films as wound sealants. Silk-ICG films were subjected to different near-infrared (NIR) laser powers to identify temperatures optimal for laser sealing of soft tissues. A mathematical model was developed in order to determine the photothermal conversion efficiency of LASEs following laser irradiation. NIR laser activation of silk-ICG LASEs increased the recovery of skin biomechanical strength compared to sutured skin in full-thickness incisional wounds in immunocompetent mice, and live animal imaging indicated persistence of silk-ICG LASEs over several days. LASEs loaded with the antibiotic vancomycin demonstrated higher efficacies for combating MRSA infections in a mouse model of surgical site infection compared to antibacterial sutures. Our results demonstrate that LASEs can be loaded with antimicrobial drugs and may serve as new multifunctional biomaterials for rapid tissue sealing, repair and surgical site protection following surgery.

Impact of pericardial adhesions on diastolic function as assessed by vortex formation time, a parameter of transmitral flow efficiency.

BACKGROUND: Pericardial adhesions are a pathophysiological marker of constrictive pericarditis (CP), which impairs cardiac filling by limiting the total cardiac volume compliance and diastolic filling function. We studied diastolic transmitral flow efficiency as a new parameter of filling function in a pericardial adhesion animal model. We hypothesized that vortex formation time (VFT), an index of optimal efficient diastolic transmitral flow, is altered by patchy pericardial-epicardial adhesions. METHODS: In 8 open-chest pigs, the heart was exposed while preserving the pericardium. We experimentally simulated early pericardial constriction and patchy adhesions by instilling instant glue into the pericardial space and using pericardial-epicardial stitches. We studied left ventricular (LV) function and characterized intraventricular blood flow with conventional and Doppler echocardiography at baseline and following the experimental intervention. RESULTS: Significant decreases in end-diastolic volume, ejection fraction, stroke volume, and late diastolic filling velocity reflected the effects of the pericardial adhesions. The mean VFT value decreased from 3.61 ± 0.47 to 2.26 ± 0.45 (P = 0.0002). Hemodynamic variables indicated the inhibiting effect of pericardial adhesion on both contraction (decrease in systolic blood pressure and +dP/dt decreased) and relaxation (decrease in the magnitude of -dP/dt and prolongation of Tau) function. CONCLUSION: Patchy pericardial adhesions not only negatively impact LV mechanical functioning but the decrease of VFT from normal to suboptimal value suggests impairment of transmitral flow efficiency.

An experimentally validated immersed boundary model of fluid-biofilm interaction.

Biofllms are colonies of microorganisms that live on wetted surfaces in a matrix consisting of polysaccharides, proteins, and nucleic acids. According to the National Institute of Health (NIH), biofilms play a role in over 80 percent of microbial infections in the body and these infections are remarkably difficult to treat with antimicrobial compounds. The objective here is to understand and predict the physical interaction between a biofilm and the surrounding fluid flow. We have developed a biofilm-fluid interaction model, based on the Immersed Boundary Method, to simulate the interaction between the biofilm and a moving fluid. The model predictions of biofilm deformation quantitatively agree with experimental measurements for a range of biofilms using a simple immersed elastic solid to model the biofilm matrix. An immersed viscoelastic solid model is also developed and compared with experimental measurements. The results show that the viscoelastic behaviour inherent in the immersed boundary method (even when using a simple immersed elastic solid) is sufficient for some biofilms, but a slightly viscoelastic solid gives more general agreement with experimental measurements.

Increase in the late diastolic filling force is associated with impaired transmitral flow efficiency in acute moderate elevation of left ventricular afterload.

OBJECTIVE: Analysis of intraventricular flow force and efficiency is a novel concept of quantitatively assessing left ventricular (LV) hemodynamic performance. We have parametrically characterized diastolic filling flow by early inflow force, late inflow force, and total inflow force and by vortex formation time (VFT), a fundamental parameter of fluid transport efficiency. The purpose of this study was to determine what changes in inflow forces characterize a decrease in diastolic blood transport efficiency in acute moderate elevation of LV afterload. METHODS: In 8 open-chested pigs, the flow force and VFT parameters were calculated from conventional and flow Doppler echocardiographic measurements at baseline and during a brief (3-minute) moderate elevation of afterload induced by increasing the systolic blood pressure to 130% of the baseline value. RESULTS: Systolic LV function decreased significantly during elevated afterload. Early inflow force did not significantly change, whereas late inflow force increased from 5,822.09 +/- 1,656.5 (mean +/- SD) to 13,948.25 +/- 9,773.96 dyne (P = .049), and total inflow force increased from 13,783.35 +/- 4,816.58 to 21,836.67 +/- 8,635.33 dyne (P = .031). Vortex formation time decreased from 4.09 +/- 0.29 to 2.79 +/- 1.1 (P = .0068), confirming suboptimal flow transport efficiency. CONCLUSIONS: Even a brief moderate increase of LV afterload causes a significant increase in late diastolic filling force and impairs transmitral flow efficiency.

In response to "Is solute movement within the extracellular spaces of brain gray matter brought about primarily by diffusion or flow?"

In our work, "Analysis of Convective and Diffusive Transport in the Brain Interstitium", published in this journal (2019, 16:6), we estimate the interstitial superficial velocity by comparison of transport model simulations to published experimental Real-Time Iontophoresis (RTI) data. In the Discussion section, we calculate a value for perfusion rate, or volumetric flow rate per unit mass of tissue, from these fundamental results of superficial velocity. Drs. Hladky and Barrand have proposed an alternative method for choosing the surface area per volume used to calculate perfusion rate from superficial velocity, using our model domain. Their method seems reasonable to us, as does ours. Upon reflection, a range of volumetric flow per unit mass values should have been reported in our paper, 1-40 µL/min-g. The value calculated using Drs. Hladky and Barrand surface area is a likely upper-bound on this range and the value in the paper is a low estimate at the bottom of the range. We are confident in the estimates of interstitial velocity reported in our article, using the assumptions of the model. Peclet (Pe) numbers, which compare convective and diffusive transport rates for different molecules, were calculated using the superficial velocity estimates; and we continue to believe these values are correct along with all other major results and conclusions presented in the paper.

Analysis of convective and diffusive transport in the brain interstitium.

BACKGROUND: Despite advances in in vivo imaging and experimental techniques, the nature of transport mechanisms in the brain remain elusive. Mathematical modelling verified using available experimental data offers a powerful tool for investigating hypotheses regarding extracellular transport of molecules in brain tissue. Here we describe a tool developed to aid in investigation of interstitial transport mechanisms, especially the potential for convection (or bulk flow) and its relevance to interstitial solute transport, for which there is conflicting evidence. METHODS: In this work, we compare a large body of published experimental data for transport in the brain to simulations of purely diffusive transport and simulations of combined convective and diffusive transport in the brain interstitium, incorporating current theories of perivascular influx and efflux. RESULTS: The simulations show (1) convective flow in the interstitium potentially of a similar magnitude to diffusive transport for molecules of interest and (2) exchange between the interstitium and perivascular space, whereby fluid and solutes may enter or exit the interstitium, are consistent with the experimental data. Simulations provide an upper limit for superficial convective velocity magnitude (approximately [Formula: see text] = 50 µm min-1), a useful finding for researchers developing techniques to measure interstitial bulk flow. CONCLUSIONS: For the large molecules of interest in neuropathology, bulk flow may be an important mechanism of interstitial transport. Further work is warranted to investigate the potential for bulk flow.

In vivo comparison of epithelial responses for S-8 versus JP-8 jet fuels below permissible exposure limit.

This study was designed to characterize and compare the pulmonary effects in distal lung from a low-level exposure to jet propellant-8 fuel (JP-8) and a new synthetic-8 fuel (S-8). It is hypothesized that both fuels have different airway epithelial deposition and responses. Consequently, male C57BL/6 mice were nose-only exposed to S-8 and JP-8 at average concentrations of 53mg/m(3) for 1h/day for 7 days. A pulmonary function test performed 24h after the final exposure indicated that there was a significant increase in expiratory lung resistance in the S-8 mice, whereas JP-8 mice had significant increases in both inspiratory and expiratory lung resistance compared to control values. Neither significant S-8 nor JP-8 respiratory permeability changes were observed compared to controls, suggesting no loss of epithelial barrier integrity. Morphological examination and morphometric analysis of airway tissue demonstrated that both fuels showed different patterns of targeted epithelial cells: bronchioles in S-8 and alveoli/terminal bronchioles in JP-8. Collectively, our data suggest that both fuels may have partially different deposition patterns, which may possibly contribute to specific different adverse effects in lung ventilatory function.

Combining existing numerical models with data assimilation using weighted least-squares finite element methods.

A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd.

Effects of Spatial Localization on Microbial Consortia Growth.

Microbial consortia are commonly observed in natural and synthetic systems, and these consortia frequently result in higher biomass production relative to monocultures. The focus here is on the impact of initial spatial localization and substrate diffusivity on the growth of a model microbial consortium consisting of a producer strain that consumes glucose and produces acetate and a scavenger strain that consumes the acetate. The mathematical model is based on an individual cell model where growth is described by Monod kinetics, and substrate transport is described by a continuum-based, non-equilibrium reaction-diffusion model where convective transport is negligible (e.g., in a biofilm). The first set of results focus on a single producer cell at the center of the domain and surrounded by an initial population of scavenger cells. The impact of the initial population density and substrate diffusivity is examined. A transition is observed from the highest initial density resulting in the greatest cell growth to cell growth being independent of initial density. A high initial density minimizes diffusive transport time and is typically expected to result in the highest growth, but this expected behavior is not predicted in environments with lower diffusivity or larger length scales. When the producer cells are placed on the bottom of the domain with the scavenger cells above in a layered biofilm arrangement, a similar critical transition is observed. For the highest diffusivity values examined, a thin, dense initial scavenger layer is optimal for cell growth. However, for smaller diffusivity values, a thicker, less dense initial scavenger layer provides maximal growth. The overall conclusion is that high density clustering of members of a food chain is optimal under most common transport conditions, but under some slow transport conditions, high density clustering may not be optimal for microbial growth.

Computational evaluation of the role of accommodation in pigmentary glaucoma.

PURPOSE: Accommodation has been proposed as the cause of the bowing of the posterior iris that occurs in eyes with pigmentary dispersion syndrome. A mathematical model of the anterior eye is needed to explore the elastohydrodynamic effects of accommodation on both the aqueous humor dynamics and the contour of the iris. METHODS: A mathematical model of the coupled aqueous humor-iris system was used to predict the effects of accommodation on the iris position and pressure distribution in the aqueous humor. RESULTS: The mathematical model predicts that accommodation produces a pressure reversal--the anterior chamber pressure being higher than the posterior chamber--and iris movement into a more concave configuration. Total time for accommodation, iris modulus, iris attachment point, and trabecular meshwork permeability all had little or no effect on the iris contour and pressure change. The amount of accommodation, however, had a dramatic effect on both the amount of iris curvature and especially the pressure reversal. For accommodation resulting in a 0.6-mm change in anterior chamber depth, the pressure in the anterior chamber was more than 1.0 mm Hg higher than that in the posterior chamber, compared with a pressure difference of less than 0.1 mm Hg for accommodation resulting in a 0.2-mm change in anterior chamber depth. CONCLUSIONS: The results confirm that accommodation produces bowing of the posterior iris and the magnitude of the bowing is a strong function of the amount of accommodation.

Simulation of nanoparticle transport in airways using Petrov-Galerkin finite element methods.

The transport and deposition properties of nanoparticles with a range of aerodynamic diameters ( 1 nm ≤ d ≤ 150 nm) were studied for the human airways. A finite element code was developed that solved both the Navier-Stokes and advection-diffusion equations monolithically. When modeling nanoparticle transport in the airways, the finite element method becomes unstable, and, in order resolve this issue, various stabilization methods were considered in terms of accuracy and computational cost. The stabilization methods considered here include the streamline upwind, streamline upwind Petrov-Galerkin, and Galerkin least squares approaches. In order to compare the various stabilization approaches, the approximate solution from each stabilization approach was compared to the analytical Graetz solution, which is a model for monodispersed, dilute particle transport in a straight cylinder. The optimal stabilization method, especially with regard to accuracy, was found to be the Galerkin least squares approach for the Graetz problem when the Péclet number was larger than 10(4). In the human airways geometry, the Galerkin least squares stabilization approach once more provided the most accurate approximate solution for particles with an aerodynamic diameter of 10 nm or larger, but mesh size had a much greater effect on accuracy than the choice of stabilization method. The choice of stabilization method had a greater impact than mesh size for particles with an aerodynamic diameter 10 nm or smaller, but the most accurate stabilization method was streamline upwind Petrov-Galerkin in these cases.