On the Deformation of a Hyperelastic Tube Due to Steady Viscous Flow Within

In this chapter, we analyze the steady-state microscale fluid--structure interaction (FSI) between a generalized Newtonian fluid and a hyperelastic tube. Physiological flows, especially in hemodynamics, serve as primary examples of such FSI phenomena. The small scale of the physical system renders the flow field, under the power-law rheological model, amenable to a closed-form solution using the lubrication approximation. On the other hand, negligible shear stresses on the walls of a long vessel allow the structure to be treated as a pressure vessel. The constitutive equation for the microtube is prescribed via the strain energy functional for an incompressible, isotropic Mooney--Rivlin material. We employ both the thin- and thick-walled formulations of the pressure vessel theory, and derive the static relation between the pressure load and the deformation of the structure. We harness the latter to determine the flow rate--pressure drop relationship for non-Newtonian flow in thin- and thick-walled soft hyperelastic microtubes. Through illustrative examples, we discuss how a hyperelastic tube supports the same pressure load as a linearly elastic tube with smaller deformation, thus requiring a higher pressure drop across itself to maintain a fixed flow rate.Comment: 19 pages, 3 figures, Springer book class; v2: minor revisions, final form of invited contribution to the Springer volume entitled "Dynamical Processes in Generalized Continua and Structures" (in honour of Academician D.I. Indeitsev), eds. H. Altenbach, A. Belyaev, V. A. Eremeyev, A. Krivtsov and A. V. Porubo

A viscoelastic deadly fluid in carnivorous pitcher plants

Background : The carnivorous plants of the genus Nepenthes, widely distributed in the Asian tropics, rely mostly on nutrients derived from arthropods trapped in their pitcher-shaped leaves and digested by their enzymatic fluid. The genus exhibits a great diversity of prey and pitcher forms and its mechanism of trapping has long intrigued scientists. The slippery inner surfaces of the pitchers, which can be waxy or highly wettable, have so far been considered as the key trapping devices. However, the occurrence of species lacking such epidermal specializations but still effective at trapping insects suggests the possible implication of other mechanisms. Methodology/Principal Findings : Using a combination of insect bioassays, high-speed video and rheological measurements, we show that the digestive fluid of Nepenthes rafflesiana is highly viscoelastic and that this physical property is crucial for the retention of insects in its traps. Trapping efficiency is shown to remain strong even when the fluid is highly diluted by water, as long as the elastic relaxation time of the fluid is higher than the typical time scale of insect movements. Conclusions/Significance : This finding challenges the common classification of Nepenthes pitchers as simple passive traps and is of great adaptive significance for these tropical plants, which are often submitted to high rainfalls and variations in fluid concentration. The viscoelastic trap constitutes a cryptic but potentially widespread adaptation of Nepenthes species and could be a homologous trait shared through common ancestry with the sundew (Drosera) flypaper plants. Such large production of a highly viscoelastic biopolymer fluid in permanent pools is nevertheless unique in the plant kingdom and suggests novel applications for pest control

Perfluorocarbon induced alterations in pulmonary mechanics

Perfluorocarbon (PFC) compounds induce pulmonary hyperinflation and respiratory distress in some animals following intravenous administration. This study was designed to quantify the effects of two PFC emulsions on lung volumes and compliance and to identify the mechanism of pulmonary hyperinflation. New Zealand White rabbits received isotonic saline (3 ml/kg), Fluosol (15 ml/kg) or Oxygent (90% perfluorooctyl-bromide emulsion, 3 ml/kg). After seven days we measured functional residual capacity, vital capacity, lung compliance and thoracic gas volume. Gross and microscopic histologic examination of the lungs was performed. Functional residual capacity after Fluosol administration was 16.0 +/- 4.0 ml/kg, significantly greater than after saline (3.4 +/- 1.0 ml/kg) or Oxygent (4.0 +/- 1.4 ml/kg). Vital capacity was lower with Fluosol (30 +/- 5.0 ml/kg) than after saline (37 +/- 3.0 ml/kg) or Oxygent (37 +/- 2.0 ml/kg). Thoracic gas volume increased from 9 +/- 1.0 ml/kg (saline) to 16 +/- 13 ml/kg (Oxygent) and 33 +/- 7.0 ml/kg (Fluosol). Lung compliance was the same after saline (1.6 +/- 0.5 ml.cm H2O-1.kg-1) and Oxygent (1.5 +/- 0.3 ml.cm H2O-1.kg-1) but lower after Fluosol (0.9 +/- 0.1 ml.cm H2O-1.kg-1). Gross pathology demonstrated foam exudation from airways of animals receiving PFCs and intra-alveolar foam was identified by light microscopy. These results show intra-airway foam formation causes gas trapping and shifts tidal breathing to a less compliant region of the pressure-volume curve

A Macroscopic Model for Simulating the Mucociliary Clearance in a Bronchial Bifurcation: The Role of Surface Tension

The mucociliary clearance in the bronchial tree is the main mechanism by which the lungs clear themselves of deposited particulate matter. In this work, a macroscopic model of the clearance mechanism is proposed. Lubrication theory is applied for thin films with both surface tension effects and a moving wall boundary. The flow field is computed by the use of a finite-volume scheme on an unstructured grid that replicates a bronchial bifurcation. The carina in bronchial bifurcations is of special interest because it is a location of increased deposition of inhaled particles. In this study, the mucus flow is computed for different values of the surface tension. It is found that a minimal surface tension is necessary for efficiently removing the mucus while maintaining the mucus film thickness at physiological levels.http://deepblue.lib.umich.edu/bitstream/2027.42/175169/2/Manolidis J Biomech Eng 2016.pdfPublished versio

A new index for characterizing micro-bead motion in a flow induced by ciliary beating: Part II, modeling

Mucociliary clearance is one of the major lines of defense of the human respiratory system. The mucus layer coating the airways is constantly moved along and out of the lung by the activity of motile cilia, expelling at the same time particles trapped in it. The efficiency of the cilia motion can experimentally be assessed by measuring the velocity of micro-beads traveling through the fluid surrounding the cilia. Here we present a mathematical model of the fluid flow and of the micro-beads motion. The coordinated movement of the ciliated edge is represented as a continuous envelope imposing a periodic moving velocity boundary condition on the surrounding fluid. Vanishing velocity and vanishing shear stress boundary conditions are applied to the fluid at a finite distance above the ciliated edge. The flow field is expanded in powers of the amplitude of the individual cilium movement. It is found that the continuous component of the horizontal velocity at the ciliated edge generates a 2D fluid velocity field with a parabolic profile in the vertical direction, in agreement with the experimental measurements. Conversely, we show than this model can be used to extract microscopic properties of the cilia motion by extrapolating the micro-bead velocity measurement at the ciliated edge. Finally, we derive from these measurements a scalar index providing a direct assessment of the cilia beating efficiency. This index can easily be measured in patients without any modification of the current clinical procedures.http://deepblue.lib.umich.edu/bitstream/2027.42/175167/2/A new index for characterizing micro-bead motion in a flow induced by ciliary beating Part II, modeling.pdfPublished versionDescription of A new index for characterizing micro-bead motion in a flow induced by ciliary beating Part II, modeling.pdf : Published versio

Surfactant delivery in rat lungs: Comparing 3D geometrical simulation model with experimental instillation

Surfactant Replacement Therapy (SRT), which involves instillation of a liquid-surfactant mixture directly into the lung airway tree, is a major therapeutic treatment in neonatal patients with respiratory distress syndrome (RDS). This procedure has proved to be remarkably effective in premature newborns, inducing a five-fold decrease of mortality in the past 35 years. Disappointingly, its use in adults for treating acute respiratory distress syndrome (ARDS) experienced initial success followed by failures. Our recently developed numerical model has demonstrated that transition from success to failure of SRT in adults could, in fact, have a fluid mechanical origin that is potentially reversible. Here, we present the first numerical simulations of surfactant delivery into a realistic asymmetric conducting airway tree of the rat lung and compare them with experimental results. The roles of dose volume (VD), flow rate, and multiple aliquot delivery are investigated. We find that our simulations of surfactant delivery in rat lungs are in good agreement with our experimental data. In particular, we show that the monopodial architecture of the rat airway tree plays a major role in surfactant delivery, contributing to the poor homogeneity of the end distribution of surfactant. In addition, we observe that increasing VD increases the amount of surfactant delivered to the acini after losing a portion to coating the involved airways, the coating cost volume, VCC. Finally, we quantitatively assess the improvement resulting from a multiple aliquot delivery, a method sometimes employed clinically, and find that a much larger fraction of surfactant reaches the alveolar regions in this case. This is the first direct qualitative and quantitative comparison of our numerical model with experimental studies, which enhances our previous predictions in adults and neonates while providing a tool for predicting, engineering, and optimizing patient-specific surfactant delivery in complex situations.http://deepblue.lib.umich.edu/bitstream/2027.42/175166/2/Surfactant delivery in rat lungs Comparing 3D geometrical simulation model with experimental instillation.pdfPublished versionDescription of Surfactant delivery in rat lungs Comparing 3D geometrical simulation model with experimental instillation.pdf : Published versio

A new index for characterizing micro-bead motion in a flow induced by ciliary beating: Part I, experimental analysis

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 experimental measurements, the shear stress exerted by the cilia is deduced. Finally, this shear stress, which can easily be measured in the clinical setting, is proposed as a new index for characterizing the efficiency of ciliary beating.http://deepblue.lib.umich.edu/bitstream/2027.42/175168/2/A new index for characterizing micro-bead motion in a flow induced by ciliary beating Part I, experimental analysis.pdfPublished versionDescription of A new index for characterizing micro-bead motion in a flow induced by ciliary beating Part I, experimental analysis.pdf : Published versio