J. Grotberg - Academia.edu (original) (raw)

Papers by J. Grotberg

Respiratory Physiology & Neurobiology, 2008

We describe the mechanisms by which liquids and surfactants can be delivered into the pulmonary a... more We describe the mechanisms by which liquids and surfactants can be delivered into the pulmonary airways. These are instilled and transported throughout the lung in clinical therapies such as surfactant replacement therapy, partial liquid ventilation and drug delivery. The success of these treatments is contingent on the liquid distribution and the delivery to targeted regions of the lung. The targeting of a liquid plug can be influenced by a variety of factors such as the physical properties of the liquid, the interfacial activity, the gravitational orientation, instillation method and propagation speed. We provide a review of experimental and theoretical studies that examine these effects in single tubes or channels, in tubes with single bifurcations and in the whole lung.

Journal of Fluid Mechanics, 2003

A simplified model is developed for an alveolar liquid lining undergoing cyclic stretching which ... more A simplified model is developed for an alveolar liquid lining undergoing cyclic stretching which mimics breathing motions. A thin, viscous film coats an extensible alveolar wall with small aspect ratio, ε. Scaling analysis and asymptotic theory are used to describe the interface profile and surfactant distribution during the oscillation cycle for either insoluble or soluble surfactants. The flow consists of two distinct regimes: an outer region away from the rigid endwalls where flow is near-parallel and a boundary-layer region at the rigid endwalls where flow is non-parallel. The system is solved asymptotically in the limit of ε 1 and small strain amplitudes, ∆ 1. For leading order in ε, steady streaming vortical flows are found at O(∆ 2) and their size, number and flow direction depend on the system parameter values. This preliminary model can be useful for understanding alveolar transport characteristics for slowly diffusing molecules with large Péclet number, such as endogenous surfactants and proteins as well as delivered surfactants, drugs and genetic material that may occur in various therapies or partial liquid ventilation. The flow pattern also provides a pathway for cell-cell signalling within the alveolus.

ABSTRACT Particle transport and deposition associated with flow over a wedge is investigated as a... more ABSTRACT Particle transport and deposition associated with flow over a wedge is investigated as a model for particle transport and flow at an airway bifurcation. Using matched asymptotics, a uniformly valid solution is obtained to represent the high Reynolds number flow over a wedge which considers both the viscous boundary layer near the wedge and the outer inviscid region, and is then used to solve the particle transport equations. The phenomenon of boundary layer shielding is investigated and is characterized by a positive normal velocity component near the wall that pushes particles in the boundary layer away from the wall and prevents particle impaction. Additionally, deposition efficiency and relative distribution of impacted particles are presented. The present model compares well to more complex ones that consider the three dimensional structure of an airway, but is advantageous in that the boundary layer phenomena can be closely investigated.

The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. Thi... more The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid which is modeled here as a Jeffreys fluid. To examine the role of mucus alone, we model a single layer of a visco-elastic fluid. Nonlinear evolution equations are derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Solutions of the nonlinear evolution equations reveal that the closure time, defined to be the time required for a plug to form, decreases with increasing film thickness and viscoelasticity. Some results obtained from direct numerical simulations are also presented and compared with the lubrication theory model.

Journal of Fluid Mechanics, 1996

APL Bioengineering

Paper published as part of the special topic on Microphysiological Systems Note: This paper is pa... more Paper published as part of the special topic on Microphysiological Systems Note: This paper is part of the special topic on Microphysiological Systems. This paper was selected as an Editor's Pick ARTICLES YOU MAY BE INTERESTED IN AAV-mediated gene therapy targeting TRPV4 mechanotransduction for inhibition of pulmonary vascular leakage APL Bioengineering 3, 046103 (2019);

Journal of Biomechanical Engineering

We study the effects of surface tension and yield stress on mucus plug rupture. A three-dimension... more 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 10th 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 remarkably 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. W...

Journal of Anatomy

Elderly populations have a higher risk of rib fractures and other associated thoracic injuries th... more 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.

PLoS computational biology, 2017

Mucociliary clearance is one of the major lines of defense of the respiratory system. The mucus l... more Mucociliary clearance is one of the major lines of defense of the respiratory system. The mucus layer coating the pulmonary airways is moved along and out of the lung by the activity of motile cilia, thus expelling the particles trapped in it. Here we compare ex vivo measurements of a Newtonian flow induced by cilia beating (using micro-beads as tracers) and a mathematical model of this fluid flow, presented in greater detail in a second companion article. Samples of nasal epithelial cells placed in water are recorded by high-speed video-microscopy and ciliary beat pattern is inferred. Automatic tracking of micro-beads, used as markers of the flow generated by cilia motion, enables us also to assess the velocity profile as a function of the distance above the cilia. This profile is shown to be essentially parabolic. The obtained experimental data are used to feed a 2D mathematical and numerical model of the coupling between cilia, fluid, and micro-bead motion. From the model and the...

43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005

The NASA Bioscience and Engineering Institute at the University of Michigan is a multicomponent i... more The NASA Bioscience and Engineering Institute at the University of Michigan is a multicomponent initiative of research, education and outreach which addresses important issues in microgravity environments which are at the interface of biology and engineering sciences. Currently there are 9 research projects involving 26 faculty members and 11 students/postdocs. A description of these projects is made with the goal of introducing the AIAA community to these efforts which can benefit from collaborative approaches between scientists skilled in aeronautical and astronautical areas with biologists and biomedical engineers. Also the goals of outreach and education are discussed. Details of the projects are also available at www.umnbei.umich.edu.

Biomicrofluidics, 2015

Fluid dynamics of mucus plug rupture is important to understand mucus clearance in lung airways a... more Fluid dynamics of mucus plug rupture is important to understand mucus clearance in lung airways and potential effects of mucus plug rupture on epithelial cells at lung airway walls. We established a microfluidic model to study mucus plug rupture in a collapsed airway of the 12th generation. Mucus plugs were simulated using Carbopol 940 (C940) gels at concentrations of 0.15%, 0.2%, 0.25%, and 0.3%, which have non-Newtonian properties close to healthy and diseased lung mucus. The airway was modeled with a polydimethylsiloxane microfluidic channel. Plug motion was driven by pressurized air. Global strain rates and shear stress were defined to quantitatively describe plug deformation and rupture. Results show that a plug needs to overcome yield stress before deformation and rupture. The plug takes relatively long time to yield at the high Bingham number. Plug length shortening is the more significant deformation than shearing at gel concentration higher than 0.15%. Although strain rates increase dramatically at rupture, the transient shear stress drops due to the shear-thinning effect of the C940 gels. Dimensionless time-averaged shear stress, T xy , linearly increases from 3.7 to 5.6 times the Bingham number as the Bingham number varies from 0.018 to 0.1. The dimensionless time-averaged shear rate simply equals to T xy /2. In dimension, shear stress magnitude is about one order lower than the pressure drop, and one order higher than yield stress. Mucus with high yield stress leads to high shear stress, and therefore would be more likely to cause epithelial cell damage. Crackling sounds produced with plug rupture might be more detectable for gels with higher concentration.

Pulmonary surfactant in bronchoalveolar lavage fluid (BALF) and induced sputum from adults with s... more Pulmonary surfactant in bronchoalveolar lavage fluid (BALF) and induced sputum from adults with stable asthma (n ϭ 36) and healthy controls (n ϭ 12) was analyzed for phospholipid and protein compositions and function. Asthmatic subjects were graded as mild, moderate, or severe. Phospholipid compositions of BALF and sputum from control subjects were similar and characteristic of surfactant. For asthmatic subjects, the proportion of dipalmitoyl phosphatidylcholine (16:0/16:0PC), the major phospholipid in surfactant, decreased in sputum (P Ͻ 0.05) but not in BALF. 1 In BALF, mole percent 16:0/16:0PC correlated with surfactant function measured in a capillary surfactometer, and sputum mole percent 16:0/16:0PC correlated with lung function (forced expiratory volume in 1 s). Neither surfactant protein A nor total protein concentration in either BALF or sputum was altered in asthma. These results suggest altered phospholipid composition and function of airway (sputum) but not alveolar (BALF) surfactant in stable asthma. Such underlying surfactant dysfunction may predispose asthmatic subjects to further surfactant inhibition by proteins or aeroallergens in acute asthma episodes and contribute to airway closure in asthma. Consequently, administration of an appropriate therapeutic surfactant could provide clinical benefit in asthma.

Integrative and comparative biology, 2014

Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many ch... more Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many challenges. The complex rheology of the fluids, interaction between fluids and structures, and complicated multi-scale geometry all add to the complexity of the problem. We provide a brief overview of approaches used to model three aspects of pulmonary fluid and flow: the surfactant layer in the deep branches of the lung, the mucus layer in the upper airway branches, and closure/reopening of the airway. We discuss models of each aspect, the potential to capture biological and therapeutic information, and open questions worthy of further investigation. We hope to promote multi-disciplinary collaboration by providing insights into mathematical descriptions of fluid-mechanics in the lung and the kinds of predictions these models can make.

Physics of Fluids, 2005

In this study, we investigate the steady propagation of a liquid plug in a two-dimensional channe... more 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.

Physics of Fluids, 2002

This paper considers the propagation of a liquid plug, forced by a driving pressure ⌬P, within a ... more This paper considers the propagation of a liquid plug, forced by a driving pressure ⌬P, within a rigid tube. The tube is already lined with a liquid precursor film of thickness h 2. Both the plug and the precursor film, as well as the interface, contain small amounts of surfactant whose concentrations are assumed to be near equilibrium. Since the motions are slow, we seek asymptotic solutions for small capillary number, CaӶ1, and also assume that sorption kinetics control the surfactant flux to the interface compared to bulk diffusion. An additional asymptotic assumption is that the Stanton number, St, is sufficiently large such that ␤ϰCa 1/3 /StӶ1, which relates the importance of sorption kinetics to convection. The surfactant strength is measured by the surface elasticity, EϭM /␤ where M is the Marangoni number. The results of the analysis are that, for a given plug Ca, ⌬P increases with increasing E but decreases with increasing h 2. The trailing film thickness, h 1 , increases with ⌬P, but at a slower rate when E is larger. For h 1 Ͻh 2 , criteria for plug rupture are established. This model is relevant to delivery of surfactants into the lung by direct instillation into the bronchial network as is done in surfactant replacement therapy and the use of surfactant solutions to carry other substances ͑e.g., genetic material͒ into the airways.

This article covers several aspects of respiratory fluid mechanics that have been actively invest... more This article covers several aspects of respiratory fluid mechanics that have been actively investigated by our group over the years. For the most part, the topics involve two-phase flows in the respiratory system with applications to normal and diseased lungs, as well as therapeutic interventions. Specifically, the topics include liquid plug flow in airways and at airway bifurcations as it relates to surfactant, drug, gene, or stem cell delivery into the lung; liquid plug rupture and its damaging effects on underlying airway epithelial cells as well as a source of crackling sounds in the lung; airway closure from “capillary-elastic instabilities,” as well as nonlinear stabilization from oscillatory core flow which we call the “oscillating butter knife;” liquid film, and surfactant dynamics in an oscillating alveolus and the steady streaming, and surfactant spreading on thin viscous films including our discovery of the Grotberg–Borgas–Gaver shock.

Journal of Fluid Mechanics, 2012

We study numerically the steady creeping motion of Bingham liquid plugs in two-dimensional channe... more We study numerically the steady creeping motion of Bingham liquid plugs in two-dimensional channels as a model of mucus behaviour during airway reopening in pulmonary airways. In addition to flow analysis related to propagation of the plug, the stress distribution on the wall is studied for better understanding of potential airway epithelial cell injury mechanisms. The yield stress behaviour of the fluid was implemented through a regularized constitutive equation. The capillary number, mathitCa\mathit{Ca}mathitCa, and the Bingham number, mathitBn\mathit{Bn}mathitBn, which is the ratio of the yield stress to a characteristic viscous stress, varied over the ranges 0.025–0.1 and 0–1.5, respectively. For the range of parameters studied, it was found that, while the yield stress reduces the magnitude of the shearing along the wall, it can magnify the amplitude of the wall shear stress gradient significantly, and also it can elevate the magnitude of the wall shear stress and wall pressure gradient up to 30 % and 15 ...

Journal of Biomechanical Engineering, 2001

Both theoretical and experimental studies of pleural fluid dynamics and lung buoyancy during stea... more Both theoretical and experimental studies of pleural fluid dynamics and lung buoyancy during steady-state, apneic conditions are presented. The theory shows that steady-state, top-to-bottom pleural-liquid flow creates a pressure distribution that opposes lung buoyancy. These two forces may balance, permitting dynamic lung floating, but when they do not, pleural–pleural contact is required. The animal experiments examine pleural-liquid pressure distributions in response to simulated reduced gravity, achieved by lung inflation with perfluorocarbon liquid as compared to air. The resulting decrease in lung buoyancy modifies the force balance in the pleural fluid, which is reflected in its vertical pressure gradient. The data and model show that the decrease in buoyancy with perfluorocarbon inflation causes the vertical pressure gradient to approach hydrostatic. In the microgravity analogue, the pleural pressures would be toward a more uniform distribution, consistent with ventilation st...