Session T15: Biological Fluid Dynamics: Physiological

Oscillatory Flow Networks with Valves

To first approximation, fluidic networks are modeled as linear resistor networks, allowing for a straightforward calculation of the flows depending on the driving pressures, which can be steady or oscillating. However, when valves are present, the flow response is nonlinear such that the flow along one direction is prefered. This mechanism is utilized by the lymphatic system, which consists of a network of contracting lymphangions and one-way valves that allow the lymph to incrementally overcome a negative pressure gradient even when the peristaltic pumping direction is opposite that of the mean flow. Modeling a chain of lymphangions in series allows one to understand the cooperation between peristalsis and valves. However, this alone is insufficient to study complications that arise at the network level, when the network contains loops and branches. The orientation induced by valves must compete with the orientation given by the sign of the mean pressure drop. In order to achieve positive flow in a network with unfavorable pressure conditions, the placement of the valves in the network becomes important.   

Mechanical response in elastic fluid flow networks

Optimization of transport networks is a ubiquitous problem that can be found in a variety of natural and artificial systems. In the case of systems such as the animal vasculature, the transport of fluids is not only hindered by the inherent resistance to flow but also kept in a dynamic state by the pulsatile nature of the heart and elastic properties of the vessel walls. By linearizing the Navier-Stokes equation, we show that while this imparted pulsatility necessarily increases the dissipation of energy caused by the resistance, the vessel elasticity helps to reduce overall dissipation by attenuating the amplitude of the pulsatile components of the flow. However, we find that this reduction in energy loss comes at the price of increasing the time required to respond to changes in the flow boundary conditions. Dissipation and response time are found to obey a simple power law scaling relation in single vessels as well as hierarchically structured networks with relatively few loops.   

Pressure – area loop based phenotypic classification and mechanics of esophagogastric junction physiology

The esophagogastric junction (EGJ) is located at the distal end of the esophagus, and acts as a valve allowing swallowed materials to enter the stomach and preventing acid reflux. Weakening of the EGJ muscles results in a more compliant valve, which changes its opening and closing patterns and can progress into esophageal diseases. Therefore, understanding the physics behind the opening and closing cycle of the EGJ provides a mechanistic insight into its function and can help identify the underlying conditions that cause its degradation. From clinical data, we plotted the pressure-area hysteresis at the EGJ location and identified two major loop types, one with opening curve above closing, and the other with closing curve above the opening. The following study aimed to identify the key characteristics that define each loop type and find what causes the inversion between one loop to another. To do so, the clinical observations were reproduced using simulations and the work done by the EGJ was calculated. This work was separated into active and passive parts which revealed the competing mechanisms that dictate the loop type. These parameters are esophagus stiffness, fluid viscosity, and the EGJ relaxation pattern.   

Viscoelastic model of tissue mechanics in 3D with active surfaces

Epithelia are biological tissues made up of a large number of cells arranged as a connected monolayer.  They are one of the most critical and often-studied structures in animal bodies; yet their mechanics are still not well-understood.  In particular, until recently, epithelia had frequently been modeled as a two-dimensional, planar system.  However, recent microscopic technologies have begun to reveal dynamics in the third dimension of the tissue.  With these dynamics in mind, we have developed a self-sculpting, three-dimensional model of epithelia whose dynamics are driven by active forces on its surface.  The model describes mechanical properties such as viscoelasticity, as well as active forcing, biologically relevant tissue geometry, and fluid surroundings.  We represent epithelia in a continuum framework as a Stokes fluid with extra viscoelastic stress.  We present analytical and numerical solutions of the system, including its response to various forms of driving.  Employing this model, we can make quantitative predictions about cell shapes and cell dynamics in a three-dimensional setting, allowing for physics-based studies of animal morphogenesis and development of body plans.   

Esophageal virtual disease landscape for disease pathogenesis and diagnostics using mechanics-informed machine learning

The mechanical behavior of the esophagus plays a major role in its physiology. But most diagnostic devices cannot estimate this mechanical behavior directly. We present a method that combines fluid mechanics and machine learning to identify and differentiate different esophageal disorders and maps them onto a parameter space which we call the virtual disease landscape (VDL). We have developed a one-dimensional mechanics-based inverse model that predicts the mechanical "health" of the esophagus through mechanics-based parameters such as esophageal wall properties and contractile behavior using the output from an esophageal diagnostic device called EndoFLIP. These predicted mechanical parameters are then used to train a variational autoencoder (VAE) that generates a latent space where different esophageal disorders get clustered into different regions and forms the VDL. This network also has a side network to predict the work done by the esophagus during bolus transport which also acts as a metric for differentiating various esophageal disorders. The VDL helps to quantify the extent of an esophageal disorder as well as disease progression in time. Thus, the VDL can potentially be used to guide treatment procedures and quantify their effectiveness.   

The Chemo-Fluid Dynamics of Digestion in the Stomach: Insights from Computational Modeling

The stomach acts simultaneously as a mixer, grinder, siever, and bioprocessor of food, and the chemo-fluid dynamics of the digestion process in the stomach are central to our health. The peristaltic motion of the stomach walls combines with the secretion of enzymes to break down food (proteins, lipids, and carbohydrates) into lower molecular weight components that are ejected into the duodenum for digestion. Computational modeling of this phenomenon can fill the gaps left behind by the experimental approaches. In this study, the digestion of a protein shake in an MR derived model of the human stomach is simulated using a newly developed in-silico model “StomachSim”. In the current model, pepsin, the enzyme that hydrolyses protein, is secreted from the proximal region of the stomach walls and allowed to react with the contents of the stomach. The mixing of the contents, the extent of hydrolysis, and the emptying from the stomach are quantified for a healthy stomach, as well as for a stomach affected by gastroparesis. The findings demonstrate the potential of computational approaches to provide  data and insights that are complementary to in-vivo or in-vitro methods.   

The Fluid Dynamics of the Dissolution of an Oral Drug in the Human Stomach

The oral route is used most frequently for drug administration in human due to its safety, reduced cost, and high degree of patient compliance, but it is also the most complex way for an active pharmaceutical ingredient to enter the body. This complexity is because drug absorption via the gastrointestinal tract depends not only on factors related to the drug and its formulation, but also the contents and motility of the stomach. Also, the dynamic physiological environment of the stomach generates complex pill trajectories and non-uniform rate of dissolution and emptying of the drug into the duodenum, which potentially affects drug bioavailability. These issues pose several challenges to the design of drug delivery systems from R&D, clinical, and regulatory perspectives. These are particularly relevant for disease conditions that are associated with alterations in the anatomy and/or physiology of the stomach as current clinical approaches to assess the efficacy of oral drugs are limited in their ability to elucidate the relationship between bioavailability and altered stomach. We employ "StomachSim", a CFD model of human stomach, to investigate the effect of body posture and stomach motility on drug bioavailability and understand the fluid-dynamic mechanisms of drug dissolution.   

Large-scale cortex-core structure formation in brain organoids

Brain organoids recapitulate several brain properties, including neuronal diversity. However,

do they recapitulate brain shape? Using a hydrodynamic description for cell nuclei as particles

interacting via an attractive field generated by the surrounding active cell cytoskeleton, we quantify

shape development in brain organoids. Regions of cell nuclei overdensity in the linear regime drive

the initial seeding for cortex-core structures, which emerge in the non-linear regime with elongated

cell nuclei and thus, cell shape, in the cortex. We then use an extended version of the buckling

without bending morphogenesis model to predict scalloped foliations/folds of the cortex in the

presence of nonlinearity due to elongated cells actively regulating strain. In addition to laying

new groundwork for the design of more familiar and less familiar brain shapes, our work provides an

intriguing quantitative connection with large-scale structure formation in the universe.    

Oscillating flow past a streamwise periodic array of cylinders

As a simple two-dimensional model to investigate effects of nerve roots on the flow and transport in the spinal canal, we consider the flow induced by the interaction of a periodically oscillating stream and an infinite array of equally spaced identical cylinders aligned with the unperturbed flow. Specific attention is given to flows involving small values of the ratio e of the stroke length to the cylinder radius, when the time-averaged Lagrangian motion can be described as the sum of a steady-streaming component and a Stokes-drift component, which are determined for selected values of the relevant Womersley number. Also, consideration is given to configurations with order-unity values of e and inharmonic velocity oscillations. Numerical integrations are used to characterize the resulting flow for  different values of the inter-cylinder distance.   

Mathematical modelling and in vitro studies of high shear blood clot formation in a microfluidic system

Arterial blood clot formation (thrombosis) is the leading cause of both stroke and heart attack. Accurate prediction of clotting dynamics under high shear is a key part of developing safe and effective treatments. We use in vitro and mathematical modelling to examine high shear thrombosis in a microfluidic system. Thrombosis under pathologically high shear stresses relies on the protein Von Willebrand Factor (VWF). At high shear VWF unfolds, which exposes binding sites, and facilitates rapid platelet deposition and clot formation.

In vitro, platelets and VWF flow over collagen in a rectangular stenosis model. Platelet deposition over time is measured for a range of flow rates. The in vitro data is used to parameterise a continuum mathematical model which examines the early stages of thrombosis. The model includes a novel mechanistic description of VWF dynamics using a dilute limit of a viscoelastic fluid model. We exploit the small aspect ratio of the microfluidic system to construct a reduced model. The reduced model is used to investigate the effect of varying stenosis geometry and blood flow conditions on the unfolding of VWF and subsequent platelet binding. This allows for effective prediction of the location and timescale platelet deposition for a given stenosis.   

Modelling Perfusion and Temperature Effects of Ischaemic Stroke using Expanded Discrete Cerebral Vasculature in a Vascular-Porous Model

Modelling of the effects of ischaemic stroke requires vasculature of a resolution that is unobtainable from conventional cerebral-vasculature imaging techniques. We have developed a technique to generate additional vasculature to complement the obtainable vasculature and together form a hybrid 1D vasculature. This is then combined with our existing Vascular-Porous (VaPor) model to fully simulate the cerebral geometry, crucially including the ischaemic region. In the VaPor model, the hybrid 1D vasculature is embedded into a 3D porous tissue. The additional 1D vasculature is created using an algorithm that has been developed to procedurally generate new nodes based on the main arterial territories and tissue type. A variety of severities of ischaemic stroke can be simulated by obstructing any given vessel segment in the arterial tree. The resulting occlusion geometry, perfusion, and thermal effects are then calculated by solving mass, momentum, and energy equations. Our results show discrete vessels are important in modelling cerebral temperature and perfusion, and particularly the effects of stroke. Visual 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. The presence of additional vasculature in our model leads to greater homogeneity in the resulting temperature profiles. Using our model, a temperature rise of the order of 0.5 °C can be observed in the affected region following ischaemic stroke. Further, our model shows that direct brain cooling via the scalp may be more effective at reducing cerebral temperatures than previously thought.   

Fractional-order Modeling of the Complex and Frequency-dependent Arterial Compliance: In Human and Animal Validation

Recently, experimental and theoretical studies have recognized the power of fractional calculus to perceive viscoelastic blood vessel structure and bio-mechanical properties. This work presents five fractional-order model representations to describe the dynamic relationship between the aortic blood pressure input and blood volume. Each configuration incorporates a fractional-order capacitor element (FOC) to lump the apparent arterial compliance's complex and frequency dependence properties. FOC combines both resistive and capacitive attributes within a single component, which can be controlled through the fractional differentiation order factor, alpha. Besides, the equivalent capacitance of FOC is by its very nature frequency-dependent, compassing the complex properties using only a few parameters. The proposed representations have been compared with generalized integer-order models of arterial compliance. Both model's structures have been applied and validated using different aortic pressure and flow rate data acquired from various species such as humans, pigs, and dogs. The results have shown that the fractional-order framework is able to reconstruct the overall dynamic of the complex and frequency-dependent apparent compliance dynamic and reduce the complexity. The physiological relevance of the proposed models' parameters as well as the models' calibration were assessed by evaluating a variance-based global sensitivity analysis. The results show that this new paradigm confers a prominent potential to be adopted in clinical practice and basic cardiovascular mechanics research.