Denis J. Doorly

Non-planar curvature and branching of arteries and non-planar-type flow

In this study, magnetic resonance imaging techniques have been used to examine the geometry of arterial curvature and branching in casts and in vivo, and to measure the distribution of axial velocity in the associated flow. It is found, contrary to a widely held view, that the geometry is commonly non-planar. Moreover, relatively small values of the parameters which render the geometry non-planar appear significantly to affect the velocity distribution. The findings suggest that non-planarity is an important factor influencing arterial flows, including wall shear. The implications are not restricted to vascular biology, pathology and surgery, but may extend to the design of general piping systems.

The Influence of Out-of-Plane Geometry on the Flow Within a Distal End-to-Side Anastomosis

This paper describes a computational and experimental investigation of flow in a proto-type model geometry of a fully occluded 45 deg distal end-to-side anastomosis. Previous investigations have considered a similar configuration where the centerlines of the bypass and host vessels lie within a plane, thereby producing a plane of symmetry within the flow. We have extended these investigations by deforming the bypass vessel out of the plane of symmetry, thereby breaking the symmetry of the flow and producing a nonplanar geometry. Experimental data were obtained using magnetic resonance imaging of flow within perspex models and computational data were obtained from simulations using a high-order spectral/hp element method. We found that the nonplanar three-dimensional flow notably alters the distribution of wall shear stress at the bed of the anastomosis, reducing the peak wall shear stress peak by approximately 10 percent when compared with the planar model. Furthermore, an increase in the absolute flux of velocity into the occluded region, proximal to the anastomosis, of 80 percent was observed in the nonplanar geometry when compared with the planar geometry.

Mechanics of airflow in the human nasal airways

The mechanics of airflow in the human nasal airways is reviewed, drawing on the findings of experimental and computational model studies. Modelling inevitably requires simplifications and assumptions, particularly given the complexity of the nasal airways. The processes entailed in modelling the nasal airways (from defining the model, to its production and, finally, validating the results) is critically examined, both for physical models and for computational simulations. Uncertainty still surrounds the appropriateness of the various assumptions made in modelling, particularly with regard to the nature of flow. New results are presented in which high-speed particle image velocimetry (PIV) and direct numerical simulation are applied to investigate the development of flow instability in the nasal cavity. These illustrate some of the improved capabilities afforded by technological developments for future model studies. The need for further improvements in characterising airway geometry and flow together with promising new methods are briefly discussed.

Nasal architecture: form and flow

Current approaches to model nasal airflow are reviewed in this study, and new findings presented. These new results make use of improvements to computational and experimental techniques and resources, which now allow key dynamical features to be investigated, and offer rational procedures to relate variations in anatomical form. Specifically, both replica and simplified airways of a single subject were investigated and compared with the replica airways of two other individuals with overtly differing geometries. Procedures to characterize and compare complex nasal airway geometry are first outlined. It is then shown that coupled computational and experimental studies, capable of obtaining highly resolved data, reveal internal flow structures in both intrinsically steady and unsteady situations. The results presented demonstrate that the intimate relation between nasal form and flow can be explored in greater detail than hitherto possible. By outlining means to compare complex airway geometries and demonstrating the effects of rational geometric simplification on the flow structure, this work offers a fresh approach to studies of how natural conduits guide and control flow. The concepts and tools address issues that are thus generic to flow studies in other physiological systems.

The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anastomosis.

We present an experimental and computational investigation of time-varying flow in an idealized fully occluded 45 degrees distal end-to-side anastomosis. Two geometric configurations are assessed, one where the centerlines of host and bypass vessels lie within a plane, and one where the bypass vessel is deformed out of the plane of symmetry, respectively, termed planar and non-planar. Flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral/hp algorithm. Results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time-averaged peak wall shear stress magnitude by 10% in the non-planar model as compared to the planar configuration. In the planar geometry the stagnation point follows a straight-line path along the host artery bed with a path length of 0.8 diameters. By contrast in the non-planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall, and follows a parabolic path with a 0.7 diameter longitudinal and 0.5 diameter transverse excursion. A definition of the oscillatory shear index (OSI) is introduced that varies between 0 and 0.5 and that accounts for a continuous range of wall shear stress vector angles. In both models, regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow. The mean oscillatory shear magnitude (considering sites where OSI>0.1) in the non-planar geometry was reduced by 22% as compared to the planar configuration. These changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out-of-plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions.

Inflow boundary profile prescription for numerical simulation of nasal airflow

Knowledge of how air flows through the nasal passages relies heavily on model studies, as the complexity and relative inaccessibility of the anatomy prevents detailed in vivo measurement. Almost all models to date fail to incorporate the geometry of the external nose, instead employing a truncated inflow. Typically, flow is specified to enter the model domain either directly at the nares (nostrils), or via an artificial pipe inflow tract attached to the nares. This study investigates the effect of the inflow geometry on flow predictions during steady nasal inspiration. Models that fully replicate the internal and external nasal airways of two anatomically distinct subjects are used as a reference to compare the effects of common inflow treatments on physiologically relevant quantities including regional wall shear stress and particle residence time distributions. Inflow geometry truncation is found to affect flow predictions significantly, though slightly less so for the subject displaying more pronounced passage area contraction up to the internal nasal valve. For both subject geometries, a tapered pipe inflow provides a better approximation to the natural inflow than a blunt velocity profile applied to the nares. Computational modelling issues are also briefly outlined, by comparing quantities predicted using different surface tessellations, and by evaluation of domain-splitting techniques.

Local and Global Geometric Influence on Steady Flow in Distal Anastomoses of Peripheral Bypass Grafts

We consider the effect of geometrical configuration on the steady flow field of representative geometries from an in vivo anatomical data set of end-to-side distal anastomoses constructed as part of a peripheral bypass graft. Using a geometrical classification technique, we select the anastomoses of three representative patients according to the angle between the graft and proximal host vessels (GPA) and the planarity of the anastomotic configuration. The geometries considered include two surgically tunneled grafts with shallow GPAs which are relatively planar but have different lumen characteristics, one case exhibiting a local restriction at the perianastomotic graft and proximal host whilst the other case has a relatively uniform cross section. The third case is nonplanar and characterized by a wide GPA resulting from the graft being constructed superficially from an in situ vein. In all three models the same peripheral resistance was imposed at the computational outflows of the distal and proximal host vessels and this condition, combined with the effect of the anastomotic geometry, has been observed to reasonably reproduce the in vivo flow split. By analyzing the flow fields we demonstrate how the local and global geometric characteristics influences the distribution of wall shear stress and the steady transport of fluid particles. Specifically, in vessels that have a global geometric characteristic we observe that the wall shear stress depends on large scale geometrical factors, e.g., the curvature and planarity of blood vessels. In contrast, the wall shear stress distribution and local mixing is significantly influenced by morphology and location of restrictions, particular when there is a shallow GPA. A combination of local and global effects are also possible as demonstrated in our third study of an anastomosis with a larger GPA. These relatively simple observations highlight the need to distinguish between local and global geometric influences for a given reconstruction. We further present the geometrical evolution of the anastomoses over a series of follow-up studies and observe how the lumen progresses towards the faster bulk flow of the velocity in the original geometry. This mechanism is consistent with the luminal changes in recirculation regions that experience low wall shear stress. In the shallow GPA anastomoses the proximal part of the native host vessel occludes or stenoses earlier than in the case with wide GPA. A potential contribution to this behavior is suggested by the stronger mixing that characterizes anastomoses with large GPA.

Experimental investigation of nasal airflow.

The airway geometry of the nasal cavity is manifestly complex, and the manner in which it controls the airflow to accomplish its various physiological functions is not fully understood. Since the complex morphology and inaccessibility of the nasal passageways precludes detailed in-vivo measurements, either computational simulation or in-vitro experiments are needed to determine how anatomical form and function are related. The fabrication of a replica model of the nasal cavity, of a high optical clarity and derived from in-vivo scan data is described here, together with characteristics of the flow field investigated using particle image velocimetry (PIV) and flow visualization. Flow visualization is shown to be a capable and convenient technique for identifying key phenomena. Specifically the emergence of the jet from the internal nasal valve into the main cavity, how it impacts on the middle turbinate, and the large enhancement of dispersion that accompanies the initial appearance of flow instability are revealed as particularly significant features. The findings from the visualization experiments are complemented by PIV imaging, which provides quantitative detail on the variations in velocity in different regions of the nasal cavity. These results demonstrate the effectiveness of the cavity geometry in partitioning the flow into high shear zones, which facilitate rapid heat transfer and humidification from the nasal mucosa, and slower zones affording greater residence times to facilitate olfactory sensing. The experimental results not only provide a basis for comparison with other computational modelling but also demonstrate an alternative and flexible means to investigate complex flows, relevant to studies in different parts of the respiratory or cardiovascular systems.

Computational modeling of flow and gas exchange in models of the human maxillary sinus

The present study uses numerical modeling to increase the understanding of sinus gas exchange, which is thought to be a factor in sinus disease. Order-of-magnitude estimates and computational fluid dynamics simulations were used to investigate convective and diffusive transport between the nose and the sinus in a range of simplified geometries. The interaction between mucociliary transport and gas exchange was modeled and found to be negligible. Diffusion was the dominant transport mechanism for small ostia and large concentration differences between the sinus and the nose, whereas convection was important for larger ostia or smaller concentration differences. The presence of one or more accessory ostia can increase the sinus ventilation rate by several orders of magnitude, because it allows a net flow through the sinus. Estimates of nitric oxide (NO) transport through the ostium based on measured sinus and nasal NO concentrations suggest that the sinuses cannot supply all the NO in nasally exhaled air.

Large-scale CFD simulations of the transitional and turbulent regime for the large human airways during rapid inhalation

The dynamics of unsteady flow in the human large airways during a rapid inhalation were investigated using highly detailed large-scale computational fluid dynamics on a subject-specific geometry. The simulations were performed to resolve all the spatial and temporal scales of the flow, thanks to the use of massive computational resources. A highly parallel finite element code was used, running on two supercomputers, solving the transient incompressible Navier-Stokes equations on unstructured meshes. Given that the finest mesh contained 350 million elements, the study sets a precedent for large-scale simulations of the respiratory system, proposing an analysis strategy for mean flow, fluctuations and wall shear stresses on a rapid and short inhalation (a so-called sniff). The geometry used encompasses the exterior face and the airways from the nasal cavity, through the trachea and up to the third lung bifurcation; it was derived from a contrast-enhanced computed tomography (CT) scan of a 48-year-old male. The transient inflow produces complex flows over a wide range of Reynolds numbers (Re). Thanks to the high fidelity simulations, many features involving the flow transition were observed, with the level of turbulence clearly higher in the throat than in the nose. Spectral analysis revealed turbulent characteristics persisting downstream of the glottis, and were captured even with a medium mesh resolution. However a fine mesh resolution was found necessary in the nasal cavity to observe transitional features. This work indicates the potential of large-scale simulations to further understanding of airway physiological mechanics, which is essential to guide clinical diagnosis; better understanding of the flow also has implications for the design of interventions such as aerosol drug delivery.