Novak S. J. Elliott

Effect of the velopharynx on intraluminal pressures in reconstructed pharynges derived from individuals with and without sleep apnea

The most collapsible part of the upper airway in the majority of individuals is the velopharynx which is the segment positioned behind the soft palate. As such it is an important morphological region for consideration in elucidating the pathogenesis of obstructive sleep apnea (OSA). This study compared steady flow properties during inspiration in the pharynges of nine male subjects with OSA and nine body-mass index (BMI)- and age-matched control male subjects without OSA. The k-ωSST turbulence model was used to simulate the flow field in subject-specific pharyngeal geometric models reconstructed from anatomical optical coherence tomography (aOCT) data. While analysis of the geometry of reconstructed pharynges revealed narrowing at velopharyngeal level in subjects with OSA, it was not possible to clearly distinguish them from subjects without OSA on the basis of pharyngeal size and shape alone. By contrast, flow simulations demonstrated that pressure fields within the narrowed airway segments were sensitive to small differences in geometry and could lead to significantly different intraluminal pressure characteristics between subjects. The ratio between velopharyngeal and total pharyngeal pressure drops emerged as a relevant flow-based criterion by which subjects with OSA could be differentiated from those without.

A lumped-parameter model of the cerebrospinal system for investigating arterial-driven flow in posttraumatic syringomyelia

Fluid transport in syringomyelia has remained enigmatic ever since the disease was first identified some three centuries ago. However, accumulating evidence in the last decade from animal studies implicates arterial pulsations in syrinx formation. In particular, it has been suggested that a phase difference between the pressure pulse in the spinal subarachnoid space and the perivascular spaces, due to a pathologically disturbed cerebrospinal fluid (CSF) or blood supply, could result in a net influx of CSF into the spinal cord (SC). A lumped-parameter model is developed of the cerebrospinal system to investigate this conjecture. It is found that although this phase-lag mechanism may operate, it requires the SC to have an intrinsic storage capacity due to the collapsibility of the contained venous reservoir. This net flux is associated with a higher mean pressure in the SC than the SSS which is maintained in the periodic steady state. According to our simulations the mechanical perturbations of arachnoiditis exacerbate the phase-lag effect, which may be partially alleviated by the presence of a posttraumatic syrinx and more completely by a syringo-subarachnoid shunt.

Large-Amplitude Oscillations of a Finite-Thickness Cantilevered Flexible Plate in Viscous Channel Flow

The broad aim of the present work is to elucidate mechanisms of obstructive breathing disorders (snoring, sleep apnea) in which flow-induced instabilities of the soft palate feature. We use the well-established analogue system model wherein a two-dimensional flexible plate (soft palate) is mounted downstream of a rigid surface that separates upper and lower plane channel (oral and nasal tracts) flows that interact with the plate motion and then combine into a single plane channel (pharynx) flow. For this system, we take the next step towards biomechanical realism by modeling finite-amplitude motions of the flexible plate and incorporating finite thickness in its structure. The structural model makes use of a geometrically nonlinear formulation of the solid mechanics. Viscous flow is modeled at Reynolds numbers giving unsteady laminar flow. The fully-coupled fluid-structure interaction (FSI) model is developed using the open-source finite-element library oomph–lib . We first show the effects of finite amplitude and finite thickness on the in-vacuo modes of the plate through a validation study of the structural mechanics. Thereafter, we use the FSI model to illustrate both stable and unstable motions of the plate. Overall, this paper demonstrates the versatility of the new modeling approach and its suitability for characterizing the dependence of the plate’s stability on the system parameters.© 2010 ASME

Stability of a Cantilevered Flexible Plate with Non-uniform Thickness in Viscous Channel Flow

Most studies analysing the instability of a cantilevered flexible plate in an axial flow are based on models assuming an inviscid flow and uniform properties for the plate. However, for some applications, such as biomechanical fluid-structure interaction (FSI) systems, these simplifications may not be valid due the scale of the problems and the non-uniform geometric and mechanical properties of the soft tissue. In this study, a parametric investigation is conducted to determine the conditions leading to flutter instability of a cantilevered flexible plate with a non-uniform thickness immersed in a two-dimensional viscous channel flow. It is shown that, depending on the mass ratio, the thinning and thickening of the plate free-end can stabilise or destabilise the FSI system and change the critical mode at instability onset.

Syringomyelia and the fluid-structure interactions of a cerebrospinal waveguide

In the disease syringomyelia, fluid-filled cavities, called syrinxes, form in the spinal cord. The expansion of these pathological pressure vessels compresses the surrounding nerve fibers and blood supply, which is associated with neurological damage. We investigate the spinal wave-propagation characteristics, principally to serve as a reference for more anatomically-detailed models. The spinal cord is modeled as an elastic cylinder, which becomes an annulus containing inviscid fluid when a syrinx is included. This is surrounded by an annulus of inviscid fluid, representing the cerebrospinal fluid occupying the subarachnoid space, with an outer rigid boundary approximating the dura mater. The axisymmetric harmonic motion is solved as an eigenvalue problem. We present dispersion diagrams and describe the physical mechanism of each wave mode. We identify potentially damaging syrinx fluid motions and tissue stress concentrations from the eigenvectors. Finally, we determine the dependence of each wave mode on syrinx radius and cord tissue compressibility.Copyright

Stability of a Flexible Wall Separating Two Inviscid Channel Flows

The stability of a finite flexible wall occupying part of a rigid wall that separates two inviscid channel flows is investigated. The two-dimensional system is solved using a boundary-element method coupled with a finite-difference method. The motion of the wall is driven by the transmural pressure while the no-flux condition at the wall provides the kinematic boundary condition for each of the flows. Flows and structure are fully coupled to yield a system equation that is then transformed into state-space form so that its eigenvalues can be analysed. The flow velocities at which divergence and modal-coalescence flutter of the flexible wall occur are then determined as are mode shapes. We show that decreasing the channel heights and increasing the fluid density causes instabilities to occur at lower flow velocities. When the channels flow in opposite directions it is possible to suppress modal-coalescence of the first two modes.Copyright

Arterial-pulsation Driven Flow in Syringomyelia - A Lumped-parameter Model

Syringomyelia is a disease in which highpressure fluid-filled cavities, called syrinxes, form in the spinal cord which can cause progressive loss of sensory and motor functions. Poor treatment outcomes have led to myriad hypotheses for its pathogenesis, which unfortunately are often based on small numbers of patients due to the relative rarity of the disease. However, accumulating evidence in the last decade from animal studies implicates arterial pulsations in syrinx formation. In particular, it has been suggested that a phase difference between the pressure pulse in the spinal subarachnoid space and the perivascular spaces, due to a pathologically disturbed blood supply, could result in a net influx of cerebrospinal fluid (CSF) into the spinal cord (SC). A lumped-parameter model is developed of the cerebrospinal system to investigate this conjecture. It is found that although this phase-lag mechanism may operate, it requires the SC to have an intrinsic storage capacity due to the collapsibility of the contained venous reservoir. If this storage requirement is met then the results presented here suggest that, on mechanical grounds, a syringo-subarachnoid shunt may be a better surgical treatment option than a subarachnoid for post-traumatic syringomyelia.

Eigen-Analysis of an Inviscid Channel Flow with a Finite Flexible Plate in One Wall

A state-space method is used to investigate the surface instabilities of a flexible plate comprising one wall of an inviscid channel flow computationally modelled with a finite-difference method coupled with a boundary-element method. Simple elastic and spring-backed plates are considered and in both cases it is found that reducing the height of the channel causes divergence and modal-coalescence to occur at lower flow velocities. An analytical prediction for an infinitely long plate is also developed and the divergence-onset predictions are compared with those obtained by the state-space method for a spring-backed plate.

Cerebrospinal Fluid-Structure Interactions: The Development of Mathematical Models Accessible to Clinicians

Physical scientists work with clinicians on biomechanical problems, yet the predictive capabilities of mathematical models often remain elusive to clinical collaborators. This is due to both conceptual differences in the research methodologies of each discipline, and the perceived complexity of even simple models. This limits expert medical input, affecting the applicability of the results. Moreover, a lack of understanding undermines the medical practitioner’s confidence in modeling predictions, hampering its clinical application. In this paper we consider the disease syringomyelia, which involves the fluid-structure interaction of pressure vessels and pipes, as a paradigm of the nexus between the modeling approaches of physical scientists and clinicians. The observations made are broadly applicable to cross-disciplinary research between engineers and non-technical specialists, such as may occur in academic-industrial collaborations.Copyright

Flow-Induced Deformantions of a Compliant Insert in Channel Flow: from Small to Large Amplitudes

In this paper we consider a fluid-conveying channel with a compliant insert undergoing large amplitude flow-induced deformations. The objective is to assess the suitability of an open source finite element library oomph-lib for modelling this system. The fundamental system is relevant to a host of applications in both engineered (e.g. flexible-pipes, membrane filters, and general aero-/hydro-elasticity) and biomechanical (e.g. blood flow, airway flow) systems. The structural model uses a geometrically nonlinear formulation of the solid mechanics. Viscous flow is modelled at Reynolds numbers producing unsteady laminar flow. We present a brief summary of previous component validations with oomph-lib. We then focus on the unsteady-state FSI validation by comparing with published results, obtained using different computational schemes. This is done for both small-amplitude and large-amplitude wall deformations. Finally, we look at some preliminary energetics analysis of the flexible wall. The validations demonstrate the suitability and versatility of oomph-lib as a modelling and predictive tool. The flexible wall energetics validation show the possibility of understanding system stability through analysis of the flexible wall and fluid energetics.Copyright