Alberto M Gambaruto

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.

Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology

Newtonian and generalized Newtonian mathematical models for blood flow are compared in two different reconstructions of an anatomically realistic geometry of a saccular aneurysm, obtained from rotational CTA and differing to within image resolution. The sensitivity of the flow field is sought with respect to geometry reconstruction procedure and mathematical model choice in numerical simulations. Taking as example a patient specific intracranial aneurysm located on an outer bend under steady state simulations, it is found that the sensitivity to geometry variability is greater, but comparable, to the one of the rheological model. These sensitivities are not quantifiable a priori. The flow field exhibits a wide range of shear stresses and slow recirculation regions that emphasize the need for careful choice of constitutive models for the blood. On the other hand, the complex geometrical shape of the vessels is found to be sensitive to small scale perturbations within medical imaging resolution. The sensitivity to mathematical modeling and geometry definition are important when performing numerical simulations from in vivo data, and should be taken into account when discussing patient specific studies since differences in wall shear stress range from 3% to 18%.

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.

Dynamics of airflow in a short inhalation.

During a rapid inhalation, such as a sniff, the flow in the airways accelerates and decays quickly. The consequences for flow development and convective transport of an inhaled gas were investigated in a subject geometry extending from the nose to the bronchi. The progress of flow transition and the advance of an inhaled non-absorbed gas were determined using highly resolved simulations of a sniff 0.5 s long, 1 l s−1 peak flow, 364 ml inhaled volume. In the nose, the distribution of airflow evolved through three phases: (i) an initial transient of about 50 ms, roughly the filling time for a nasal volume, (ii) quasi-equilibrium over the majority of the inhalation, and (iii) a terminating phase. Flow transition commenced in the supraglottic region within 20 ms, resulting in large-amplitude fluctuations persisting throughout the inhalation; in the nose, fluctuations that arose nearer peak flow were of much reduced intensity and diminished in the flow decay phase. Measures of gas concentration showed non-uniform build-up and wash-out of the inhaled gas in the nose. At the carina, the form of the temporal concentration profile reflected both shear dispersion and airway filling defects owing to recirculation regions.

Wall shear stress and near-wall convective transport: Comparisons with vascular remodelling in a peripheral graft anastomosis

Fluid dynamic properties of blood flow are implicated in cardiovascular diseases. The interaction between the blood flow and the wall occurs through the direct transmission of forces, and through the dominating influence of the flow on convective transport processes. Controlled, in vitro testing in simple geometric configurations has provided much data on the cellular-level responses of the vascular walls to flow, but a complete, mechanistic explanation of the pathogenic process is lacking. In the interim, mapping the association between local haemodynamics and the vascular response is important to improve understanding of the disease process and may be of use for prognosis. Moreover, establishing the haemodynamic environment in the regions of disease provides data on flow conditions to guide investigations of cellular-level responses. This work describes techniques to facilitate comparison between the temporal alteration in the geometry of the vascular conduit, as determined by in vivo imaging, with local flow parameters. Procedures to reconstruct virtual models from images by means of a partition-of-unity implicit function formulation, and to align virtual models of follow-up scans to a common coordinate system, are outlined. A simple Taylor series expansion of the Lagrangian dynamics of the near-wall flow is shown to provide both a physical meaning to the directional components of the flow, as well as demonstrating the relation between near-wall convection in the wall normal direction and spatial gradients of the wall shear stress. A series of post-operative follow-up MRI scans of two patient cases with bypass grafts in the peripheral vasculature are presented. These are used to assess how local haemodynamic parameters relate to vascular remodelling at the location of the distal end-to-side anastomosis, i.e. where the graft rejoins the host artery. Results indicate that regions of both low wall shear stress and convective transport towards the wall tend to be more associated with regions of inward remodelling. A strong point-wise correlation was not found to exist however between local changes in wall location and either quantity.

Sensitivity to outflow boundary conditions and level of geometry description for a cerebral aneurysm.

Mathematical models, namely the flow boundary conditions, as well as the detail of the bounding geometry, can highly influence the computed flow field. In this work, an anatomically realistic portion of cerebral vasculature with a saccular aneurysm, and its geometric idealisation, are considered. The importance of the geometric description, namely including the side branches or modelling them as holes in the main vessel, is studied. Several approaches to prescribe the outflow boundary conditions at the side branches are analysed, including the traction-free condition, zero velocity (hence neglecting the side-branch), and the coupling with simple zero-dimensional and one-dimensional models. Results of the effects of outflow boundary modelling choice on computed haemodynamic parameters are used to identify appropriateness of the models based on the physical interpretation. Estimated range of error-bars associated to outflow boundary model choice and the level of geometric details are presented for patient-specific computational haemodynamics, and can serve as invitation for future studies. The zero-dimensional and one-dimensional models are shown to provide good representations of the side branches in the case of the clipped geometry.

Computational haemodynamics of small vessels using the Moving Particle Semi-implicit (MPS) method

The simulation of whole blood stands as a complex multi-body problem. The Moving Particle Semi-implicit method, a Lagrangian particle method to solve the incompressible Navier-Stokes (NS) equations, is developed to perform simulations in complex periodic domains. Red blood cells are modelled using the spring network approach, that act as body force terms in the NS equations. Detailed presentation and derivation of both the MPS method and different spring network models is given. An adaptive time step and an implicit scheme are adopted, improving the stability and overall computational efficiency.The findings from the simulations show evidence that in proximity to the vessel wall, the red blood cells expose a larger surface area by orientation and deformation, due to the presence of a high velocity gradient. The greatest membrane internal stresses occur in the core region of the flow. The intra-cell interaction is driven by a complex flow field that can be visualised in a Lagrangian framework, and highlights vortex structures in the wakes and in between the cells. The stresses the blood exerts on the vessel wall are influenced by this complex flow field and by the presence of red blood cells.

Decomposition and Description of the Nasal Cavity Form

Patient-specific studies of physiological flows rely on anatomically realistic or idealized models. Objective comparison of datasets or the relation of specific to idealized geometries has largely been performed in an ad hoc manner. Here, two rational procedures (based respectively on Fourier descriptors and medial axis (MA) transforms) are presented; each provides a compact representation of a complex anatomical region, specifically the nasal airways. The techniques are extended to furnish average geometries. These retain a sensible anatomical form, facilitating the identification of a specific anatomy as a set of weighted perturbations about the average. Both representations enable a rapid translation of the surface description into a virtual model for computation of airflow, enabling future work to comprehensively investigate the relation between anatomic form and flow-associated function, for the airways or for other complex biological conduits. The methodology based on MA transforms is shown to allow flexible geometric modeling, as illustrated by a local alteration in airway patency. Computational simulations of steady inspiratory flow are used to explore the relation between the flow in individual vs. averaged anatomical geometries. Results show characteristic flow measures of the averaged geometries to be within the range obtained from the original three subjects, irrespective of averaging procedure. However the effective regularization of anatomic form resulting from the shape averaging was found to significantly reduce trans-nasal pressure loss and the mean shear stress in the cavity. It is suggested that this may have implications in attempts to relate model geometries and flow patterns that are broadly representative.

Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms

Disease in human physiology is often related to cardiovascular mechanics. Impressively, strokes are one of the leading causes of death in developed countries, and they might occur as a result of an aneurysm rupture, which is a sudden event in the majority of cases. On the basis of several autopsy and angiography series, it is estimated that 0.4–6 % of the general population harbors one or more intracranial aneurysms, and on average the incidence of an aneurysmal rupture is of 10 per 100,000 population per year, with tendency to increase in patients with multiple aneurysms [14, 20].

Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows.

Near-wall transport is of utmost importance in connecting blood flow mechanics with cardiovascular disease progression. The near-wall region is the interface for biologic and pathophysiologic processes such as thrombosis and atherosclerosis. Most computational and experimental investigations of blood flow implicitly or explicitly seek to quantify hemodynamics at the vessel wall (or lumen surface), with wall shear stress (WSS) quantities being the most common descriptors. Most WSS measures are meant to quantify the frictional force of blood flow on the vessel lumen. However, WSS also provides an approximation to the near-wall blood flow velocity. We herein leverage this fact to compute a wall shear stress exposure time (WSSET) measure that is derived from Lagrangian processing of the WSS vector field. We compare WSSET against the more common relative residence time (RRT) measure, as well as a WSS divergence measure, in several applications where hemodynamics are known to be important to disease progression. Because these measures seek to quantify near-wall transport and because near-wall transport is important in several cardiovascular pathologies, surface concentration computed from a continuum transport model is used as a reference. The results show that compared to RRT, WSSET is able to better approximate the locations of near-wall stagnation and concentration build-up of chemical species, particularly in complex flows. For example, the correlation to surface concentration increased on average from 0.51 (RRT) to 0.79 (WSSET) in abdominal aortic aneurysm flow. Because WSSET considers integrated transport behavior, it can be more suitable in regions of complex hemodynamics that are traditionally difficult to quantify, yet encountered in many disease scenarios.