Preface: Biofluid mechanics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87903/2/031401_1.pd

The steady propagation of a surfactant-laden liquid plug in a two-dimensional channel

In this study, we investigate the steady propagation of a liquid plug in a two-dimensional channel lined by a uniform, thin liquid film. The liquid contains soluble surfactant that can exist both in the bulk fluid and on the air-liquid interface. The Navier-Stokes equations with free-surface boundary conditions and the surfactant transport equations are solved using a finite volume numerical scheme. The adsorption/desorption process of the surfactant is modeled based on pulmonary surfactant properties. As the plug propagates, the front meniscus sweeps preexisting interfacial surfactant from the precursor film, and the surfactant accumulates on the front meniscus interface. As the front meniscus converges on the precursor film from the region where the interfacial surfactant concentration is maximized, the Marangoni stress opposes the flow. In this region, the Marangoni stress results in nearly zero surface velocity, which causes the precursor film thickness near the meniscus to be thicker than the leading film thickness. Since the peaks of wall pressure and wall shear stress occur due to narrowing of the film thickness, the observed increase of the minimum film thickness weakens these stresses. In the thicker film region, however, the drag forces increase due to an increase in the surfactant concentration. This causes the overall pressure drop across the plug to increase as a result of the increasing surfactant concentration. A recirculation flow forms inside the plug core and is skewed toward the rear meniscus as the Reynolds number increases. When no surfactant exists, the recirculation flow is in contact with both the front and the rear interfaces. As the surfactant concentration increases, the Marangoni stress begins to rigidify the front interface and forces the recirculation flow away from the front interface. Subsequently, the recirculation flow is directed away from the rear interface in a manner similar to that for the front interface. When the plug length is shorter, this change in recirculation pattern occurs at a smaller surfactant concentration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87308/2/082102_1.pd

The Propagation of a Liquid Bolus Through an Elastic Tube and Airway Reopening

We use lubrication theory and matched asymptotic expansions to model the quasi-steady propagation of a liquid bridge through an elastic tube. In the limit of small capillary number, asymptotic expressions are found for the pressure drop across the bridge and the thickness of the liquid film left behind, as functions of the capillary number, the thickness of the liquid lining ahead of the bridge and the elastic characteristics of the tube wall. For a given precursor thickness, we find a critical propagation speed, and hence a critical imposed pressure drop, above which the bridge will eventually burst, and hence the tube will reopen

A model of flow and surfactant transport in an oscillatory alveolus partially filled with liquid

The flow and transport in an alveolus are of fundamental importance to partial liquid ventilation, surfactant transport, pulmonary drug administration, cell-cell signaling pathways, and gene therapy. We model the system in which an alveolus is partially filled with liquid in the presence of surfactants. By assuming a circular interface due to sufficiently strong surface tension and small surfactant activity, we combine semianalytical and numerical techniques to solve the Stokes flow and the surfactant transport equations. In the absence of surfactants, there is no steady streaming because of reversibility of Stokes flow. The presence of surfactants, however, induces a nontrivial cycle-averaged surfactant concentration gradient along the interface that generates steady streaming. The steady streaming patterns (e.g., number of vortices) particularly depend on the ratio of inspiration to expiration periods (I:EI:E ratio) and the sorption parameter KK. For an insoluble surfactant, a single vortex is formed when the I:EI:E ratio is either smaller or larger than 1:1, but the recirculations have opposite directions in the two cases. A soluble surfactant can lead to more complex flow patterns such as three vortices or saddle-point flow structures. The estimated unsteady velocity is 10−3 cm/s10−3cm∕s, and the corresponding Péclet number for transporting respiratory gas is O(1)O(1). For a cell-cell signaling molecule such as surfactant-associated protein-A for regulating surfactant secretion, the Péclet number could be O(10)O(10) or higher. Convection is either comparable to or more dominant than diffusion in these processes. The estimated steady velocity ranges from 10−6 to 10−4 cm/s10−6to10−4cm∕s, depending on I:EI:E and KK, and the corresponding steady Péclet number is between 10−8/Dm10−8∕Dm and 10−6/Dm10−6∕Dm (DmDm is the molecular diffusivity with units of cm2/scm2∕s). Therefore, for Dm ⩽ 10−8 cm2/sDm⩽10−8cm2∕s, the convective transport dominates.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87925/2/031510_1.pd

The effect of age and demographics on rib shape

Elderly populations have a higher risk of rib fractures and other associated thoracic injuries than younger adults, and the changes in body morphology that occur with age are a potential cause of this increased risk. Rib centroidal path geometry for 20 627 ribs was extracted from computed tomography (CT) scans of 1042 live adult subjects, then fitted to a six‐parameter mathematical model that accurately characterizes rib size and shape, and a three‐parameter model of rib orientation within the body. Multivariable regression characterized the independent effect of age, height, weight, and sex on the rib shape and orientation across the adult population, and statistically significant effects were seen from all demographic factors (P < 0.0001). This study reports a novel aging effect whereby both the rib end‐to‐end separation and rib aspect ratio are seen to increase with age, producing elongated and flatter overall rib shapes in elderly populations, with age alone explaining up to 20% of population variability in the aspect ratio of mid‐level ribs. Age was not strongly associated with overall rib arc length, indicating that age effects were related to shape change rather than overall bone length. The rib shape effect was found to be more strongly and directly associated with age than previously documented age‐related changes in rib angulation. Other demographic results showed height and sex being most strongly associated with rib size, and weight most strongly associated with rib pump‐handle angle. Results from the study provide a statistical model for building rib shapes typical of any given demographic by age, height, weight, and sex, and can be used to help build population‐specific computational models of the thoracic rib cage. Furthermore, results also quantify normal population ranges for rib shape parameters which can be used to improve the assessment and treatment of rib skeletal deformity and disease.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137729/1/joa12632_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137729/2/joa12632.pd

Peristaltic flow in the glymphatic system.

The flow inside the perivascular space (PVS) is modeled using a first-principles approach in order to investigate how the cerebrospinal fluid (CSF) enters the brain through a permeable layer of glial cells. Lubrication theory is employed to deal with the flow in the thin annular gap of the perivascular space between an impermeable artery and the brain tissue. The artery has an imposed peristaltic deformation and the deformable brain tissue is modeled by means of an elastic Hooke\u27s law. The perivascular flow model is solved numerically, discovering that the peristaltic wave induces a steady streaming to/from the brain which strongly depends on the rigidity and the permeability of the brain tissue. A detailed quantification of the through flow across the glial boundary is obtained for a large parameter space of physiologically relevant conditions. The parameters include the elasticity and permeability of the brain, the curvature of the artery, its length and the amplitude of the peristaltic wave. A steady streaming component of the through flow due to the peristaltic wave is characterized by an in-depth physical analysis and the velocity across the glial layer is found to flow from and to the PVS, depending on the elasticity and permeability of the brain. The through CSF flow velocity is quantified to be of the order of micrometers per seconds

Microprinted feeder cells guide embryonic stem cell fate

We introduce a non‐contact approach to microprint multiple types of feeder cells in a microarray format using immiscible aqueous solutions of two biopolymers. Droplets of cell suspension in the denser aqueous phase are printed on a substrate residing within a bath of the immersion aqueous phase. Due to their affinity to the denser phase, cells remain localized within the drops and adhere to regions of the substrate underneath the drops. We show the utility of this technology for creating duplex heterocellular stem cell niches by printing two different support cell types on a gel surface and overlaying them with mouse embryonic stem cells (mESCs). As desired, the type of printed support cell spatially direct the fate of overlaid mESCs. Interestingly, we found that interspaced mESCs colonies on differentiation‐inducing feeder cells show enhanced neuronal differentiation and give rise to dense networks of neurons. This cell printing technology provides unprecedented capabilities to efficiently identify the role of various feeder cells in guiding the fate of stem cells. Biotechnol. Bioeng. 2011;108: 2509–2516. © 2011 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86949/1/23190_ftp.pd

Effects of Surface Tension and Yield Stress on Mucus Plug Rupture: a Numerical Study

We study the effects of surface tension and yield stress on mucus plug rupture. A three-dimensional simplified configuration is employed to simulate mucus plug rupture in a collapsed lung airway of the 10 th generation. The Herschel-Bulkley model is used to take into account the non-Newtonian viscoplastic fluid properties of mucus. Results show that the maximum wall shear stress greatly changes right prior to the rupture of the mucus plug. The surface tension influences mainly the late stage of the rupture process when the plug deforms greatly and the curvature of the mucus-air interface becomes significant. High surface tension increases the wall shear stress and the time needed to rupture since it produces a resistance to the rupture, as well as strong stress and velocity gradients across the mucus-air interface. The yield stress effects are pronounced mainly at the beginning. High yield stress makes the plug take long time to yield and slows down the whole rupture process. When the effects induced by the surface tension and yield forces are comparable, dynamical quantities strongly depend on the ratio of the two forces. The pressure difference (the only driving in the study) contributes to wall shear stress much more than yield stress and surface tension per unit length. Wall shear stress is less sensitive to the variation in yield stress than that in surface tension. In general, wall shear stress can be effectively reduced by the smaller pressure difference and surface tension

Splitting of a three-dimensional liquid plug at an airway bifurcation

Employing the moving particles' semi-implicit (MPS) method, this study presents a numerical framework for solving the Navier–Stokes equations for the propagation and the split of a liquid plug through a three-dimensional air-filled bifurcating tube, where the inner surface is coated by a thin fluid film, and surface tension acts on the air–liquid interface. The detailed derivation of a modified MPS method to handle the air–liquid interface of liquid plugs is presented. When the front air–liquid interface of the plug splits at the bifurcation, the interface deforms quickly and causes large wall shear stress. We observe that the presence of a transverse gravitational force causes asymmetries in plug splitting, which becomes more pronounced as the capillary number decreases or the Bond number increases. We also observe that there exists a critical capillary number below which the plug does not split into two daughter tubes but propagates into the lower daughter tube only. In order to deliver the plug into the upper daughter tube, the driving pressure to push the plug is required to overcome the hydrostatic pressure due to gravity. These tendencies agree with our previous experimental and theoretical studies

Effect of Ventilation Rate on Instilled Surfactant Distribution in the Pulmonary Airways of Rats

Liquid can be instilled into the pulmonary airways during medical procedures such as surfactant replacement therapy, partial liquid ventilation, and pulmonary drug delivery. For all cases, understanding the dynamics of liquid distribution in the lung will increase the efficacy of treatment. A recently developed imaging technique for the study of real-time liquid transport dynamics in the pulmonary airways was used to investigate the effect of respiratory rate on the distribution of an instilled liquid, surfactant, in a rat lung. Twelve excised rat lungs were suspended vertically, and a single bolus (0.05 ml) of exogenous surfactant (Survanta, Ross Laboratories, Columbus, OH) mixed with radiopaque tracer was instilled as a plug into the trachea. The lungs were ventilated with a 4-ml tidal volume for 20 breaths at one of two respiratory rates: 20 or 60 breaths/min. The motion of radiodense surfactant was imaged at 30 frames/s with a microfocal X-ray source and an image intensifier. Dynamics of surfactant distribution were quantified for each image by use of distribution statistics and a homogeneity index. We found that the liquid distribution depended on the time to liquid plug rupture, which depends on ventilation rate. At 20 breaths/min, liquid was localized in the gravity-dependent region of the lung. At 60 breaths/min, the liquid coated the airways, providing a more vertically uniform liquid distribution