Session W06: Biological Fluid Dynamics: Physiological (10:00am - 10:45am CST)

Viscous flow in a slit between two elastic plates

Soft plates immersed in fluids appear in many biological processes, including swimming, flying, and breathing. The plate deforms in response to fluid flows, yet fluid stresses are in turn influenced by the plate's deformation. We present a mathematical model examining the flow of a viscous fluid in a narrow slit formed by two rectangular elastic plates, and demonstrate a strongly nonlinear flow response. The volumetric flow rate first increases linearly with pressure; however, the bending of the plates causes the corners to approach. This in turn reduces the flow rate. In some cases, the corners meet and the slit no longer permits flow. Our model, which is based on low-Reynolds-number hydrodynamics and linear plate theory, yields insights into two competing effects: While the plate bending generally reduces the slit aperture, it also causes the two plates to move apart, thus increasing the gap. Relations to biomedical flows are outlined and potential applications to flow control in man-made systems are considered.   

Transport of Concentrated Particles in Successively Bifurcating Vessels

With evolving imaging and computing technologies, the flow characteristics in successive bifurcating conduits have been extensively investigated to understand transport in the respiratory and cardiovascular systems. Specifically for tumor embolization, the ability to predict the fate of injected particles in bifurcating vessels is highly desirable to enable physicians to reach target sites. Predicting particle transport in such complex geometries is a challenging problem, and most past studies focused on very dilute regimes in which particles are not expected to alter the underlying flow. In the present study, we use particle tracking velocimetry to investigate the spatial distribution, velocity, acceleration, and dispersion of finite-size particles in a 4-generation bifurcating model. We consider a regime especially relevant to vascular embolization: a physiologic range of bulk flow Reynolds number and a suspension of neutrally buoyant particles of non-negligible size compared to the vessel diameter, reaching volume fractions up to a few percent. We explore how particles distribute among the distal branches and the influence of the release location. In addition, the effect of particle volume fraction is studied through Lagrangian statistics of the particle trajectories.   

Multiscale Lagrangian Cell-Resolved Simulations of Red Blood Cells

The stress and deformation of red blood cells (RBCs) can have a significant impact on their behavior and lifespan. For example, RBCs under large stresses for long periods of time may rupture in a process known as hemolysis. Broadly, simulations of RBCs fall into two categories: macroscale simulations of large vessels that use a constitutive model to represent the effect of the RBCs (and other particles) as a whole on the fluid dynamics in the vessel, and particle-resolved simulations that track the stress and deformation on the individual RBCs. However, due to a large separation in scales, it is infeasible to track the deformation and stresses of individual particles in large blood vessels. The aim of the present work is to overcome this barrier by simulating blood flow in these vessels using a constitutive model, and then calculate the stress and deformation of a limited number of RBCs as they are passively advected through this flow. The velocity and velocity gradient at the location of the particle are used in a boundary element formulation to obtain the hydrodynamic stress on the particles, which is subsequently used to calculate the cell's deformation and stress to predict RBC trauma.   

Tear film dynamics during blinking and contact lens wear

We use a thin film model based on lubrication theory to describe the dynamics of the pre-lens tear film on a contact lens during blinking. During a blink, the upper eyelid drives motion of the contact lens. The motion of the lid and contact lens together influence the observed dynamics of the pre-lens tear film. We compare tear film dynamics with and without contact lens wear and also explore different types of voluntary and involuntary motion of the eye that can further influence the contact lens motion and tear film dynamics.   

Multiphase Flow Modellingof Magnetically Targeted Stem Cell Delivery

Targeting delivery of stem cells to the site of an injury is a key challenge in regenerative medicine. One possible approach is to inject cells implanted with magnetic nanoparticles into the blood stream. Cells can then be targeted to the delivery site by an external magnetic field. At the injury site, it is of critical importance that the cells do not form an aggregate which could significantly occlude the vessel.We develop a multiphase flow model for the transport of magnetically tagged cells in blood under the action of an external magnetic field. We consider a two phase system of blood and stem cells in a single vessel. We exploit the small aspect ratio of the vessel to examine the system asymptotically. We consider the system for a range of magnetic field strengths and varying strengths of the drag coefficient between the phases. We examine the dynamics close the magnet as the captured stem cells form a porous mass. We explore the different regimes of the model and determine the optimal conditions for the effective delivery of stem cells while minimising vessel occlusion.   

Mechanics-informed radiology, fluoroscopy, and endoscopy enabled by deep learning techniques

The functioning of many organs depends on their mechanical properties, and deducing these properties based on data from routinely used diagnostic techniques can help understand the ``mechanical health'' of an organ and to predict the future course of a pathology. Here we consider flexible tubular organs that are common in a human body, specifically, the esophagus. We develop a one-dimensional fluid-structure numerical model that predicts the shape of the tube, and the fluid velocity and pressure inside it. Using data from the fluid-structure model, we train a variational autoencoder (VAE) that generates a latent space. The model data gets clustered into different regions of the latent space. We find that the locations of the clusters, relative to each other, represent similarities and differences between the modes of bolus transport through the esophagus. The VAE also consists of a side network that we train to predict the physical parameters of the model. We also show that the trained VAE can be used with clinical data from MRI, Fluoroscopy, EndoFLIP (an endoscopy technique), and thus provide fundamental understanding of the underlying physics of various disorders of any flexible tubular organ.   

Fluid mechanics-informed clinical practice in gastroenterology

The upper gastrointestinal (GI) tract is a complex mechanical system that displays rich fluid/solid dynamics during the transport and breakdown of ingested contents. Recently, dilation catheters have been increasingly used to visualize the esophageal wall and measure fluid pressure during contractile activity. In this abstract, we report the development of three mechanics-based “physiomarkers” (or metrics) to quantify the physiological functioning of this organ system using data captured by such catheters. These metrics are used to understand the variation of mechanical work done during peristalsis and emptying of fluid into the stomach. Following the analysis of individual subjects, these metrics have been used to quantify differences in pumping activity and wall stiffness between several disease groups. In addition to providing mechanical insights between various disease states, these metrics can be used during surgical procedures to precisely quantify the extent of intervention needed to restore normal function in the upper GI tract.   

Peristaltic regimes in esophageal transport

An EndoFLIP device, which is a balloon catheter, gives cross-sectional area along the length of the esophagus vs. time and one pressure measurement. Deducing mechanical properties of the esophagus including wall material properties, contraction strength, and wall relaxation from this data is a challenging inverse problem. Knowing mechanical properties can change how clinical decisions are made because of its potential for in-vivo mechanistic insights. To obtain such information, we conducted a parametric study to identify peristaltic regimes and applied it to clinical data. The results gave insightful information about the effect of relaxation pattern, relaxation strength, tube stiffness, and fluid/bolus density on the resulting esophagus shape. Our analysis also revealed the mechanics of the opening of the contraction area as a function of bolus flow resistance. Our eventual goal is to use these insights to develop a mechanics-informed deep learning technique that is clinically relevant. This will represent a new class of diagnostic tools for esophageal disease classification.   

A Simple Model for Biological Valves

Valves play an important role in promoting unidirectional transport of biological fluids in the venous and lymphatic systems, yet the complex nonlinear fluid-structure interaction makes them challenging to model. The current simplest treatment of valves assumes that the valves behave as diodes preventing backflow when the pressure drop is unfavorable, but it is unclear how this electronic analogue arises from local pressure and flow rules at the valves. Thus, there is a need to construct a general valve theory, universal enough to capture the function of valves in a variety of systems yet simple enough to incorporate them into large-scale network models. By employing a one-dimensional model for pulsatile flow in compliant~vessels, this work shows how diode-like pressure-flow relationships can arise from valve mechanics and fluid dynamics near the valves. When the time the valves spend open is comparable to the time spent closed, the effective resistance depends on the properties of the pressure wave as well as the location of the valves. In this regime, resonances caused by reflections off valves near the pumping source play an important role in determining the flow.   

Influence of Discrete Cerebral Vasculature on 3D Perfusion and Temperature Maps Using a Vascular-Porous Model Following Ischaemic Stroke

Modelling the brain volume with an arterial blockage requires detailed vasculature of a resolution not readily available from cerebral-vessel imaging. We have developed a Vascular-Porous (VaPor) model to fully simulate the cerebral geometry, including the ischaemic region. Here we embed a 1D hybrid vasculature, representing the larger vessels, in a 3D porous tissue. Our hybrid vasculature is created by taking vessel centrelines extracted from cerebral-vascular imaging and expanding them using an algorithm weighted by the tissue type and constrained by the perfusion territory. An ischaemic stroke is then simulated by obstructing a selected vessel in the arterial tree, allowing varying stroke severities. The resulting occlusion geometry and thermal effects can then be calculated by solving the mass, momentum and energy equations. We show that discrete vessels are important in modelling thermal and perfusion effects of stroke. Good agreement can be seen between 3D perfusion maps obtained from VaPor and those from in-vivo cerebral imaging of stroke, including the presence of potentially salvageable penumbral tissue. We further show a temperature increase in the ischaemic region of around 0.5$^{\circ}$C following stroke.   

Zebrafish as a model organism to evaluation graphene material toxicity

Graphene materials constitute one of the most promising types of nanomaterials used in different fields, due to their unique physicochemical properties. This has increased concerns associated with the potential toxicity of graphite materials to humans and the environments. Their accumulation in the aquatic environment generates complications to aquatic habitats as well as to food chains. However, the specific organ toxicity triggered by graphite materials to the developing zebrafish (Danio rerio) model and the fundamental mechanisms are yet to be elucidated. Zebrafish is being increasingly employed as a model organism to study graphene material biocompatibility. Thus, in the present study, the toxicity of graphene materials (graphene oxide (GO) and pristine graphene (pG)) on specific organ defects was assessed using zebrafish model. Zebrafish embryos were circulated into the control with treatment of pG and GO, in different environmental concentrations were assessed under numerous toxicity endpoints such as developmental abnormalities, apoptosis, cardiovascular deformities, hepatic formation faults, and neurogenic disruption.   

Coupled Chemo-Fluidic Computational Modeling of Drug Dissolution in the Human Stomach

The oral route is used most frequently for drug administration in humans but it is also the most complex way for an active pharmaceutical ingredient (API) to enter the body. This complexity is because drug absorption via the gastrointestinal tract depends not only on factors related to the drug, but also the fluid dynamics and stomach motility. The current approach to quantifying drug dissolution relies primarily on in-vitro models, but a variety of studies have shown the significant shortcomings of in-vitro devices for mimicking the conditions of the stomach. Computational modeling of drug dissolution in biomimetic models of the stomach have the potential to overcome many limitations of in-vitro models. In this study, we model the drug dissolution in the anatomical model of stomach using the immersed boundary method based, fluid-structure interaction simulations. The pill dissolution and release of API are resolved by directly solving the convection-diffusion equation. The pill trajectory, local API concentration, and the interaction with the flow on the dissolution characteristics are analyzed.   

A Computational Method for Simulating Electro-diffusion-Mediated Swelling of Gastric Mucus

Gastric mucus is a polyelectrolyte gel that serves as the primary defense of the stomach lining against acid and digestive enzymes. Experiments show that the mucus gel may swell explosively within a short time period, accompanied by a massive transport of monovalent cations from the extracellular environment into the densely packed mucus in exchange for divalent calcium that had ‘cross-linked’ the negatively-charged mucus fibers. We propose a 2D computational method for simulating mucus swelling with a two-fluid model. The model includes electro-diffusive transport of ionic species, the coupled motion of the glycoprotein network and hydrating fluid, and chemical interactions between the network and dissolved ions. Each ionic species in the solvent phase is subject to a Nernst–Planck type equation. Together with the electro-neutrality constraint, these equations constitute a system of non-linear parabolic PDEs subject to an algebraic constraint. The discretized system is solved by a Schur complement reduction scheme. Numerical results indicate that the method is very efficient, robust and accurate, even for problems which exhibit large spatial variations in the concentration of ions. Computational investigation of swelling dynamics will be presented.