Finite element modelling strategy for determining directivity of thermoelastically generated laser ultrasound.

Laser ultrasound (LU) is a contactless and couplant-free remote non-destructive (NDE) technique, which uses lasers for ultrasonic generation and detection rather than conventional piezoelectric transducers. For a transducer, an important characteristic is the directivity, the angle-dependent amplitude of the ultrasonic waves generated in the material. In the non-destructive thermoelastic regime, LU source has been widely modelled as a surface force dipole. However, the directivity of LU in more complex material, where there is an increasing demand for NDE, such as carbon fibre reinforced plastic (CFRP), is yet to be understood. In the current paper, a finite element (FE) modelling methodology to obtain the directivity of LU in complex material is presented. The method is applied to a conductive isotropic material (aluminium, Al) for validation against an existing analytical solution and then applied to a heterogeneous anisotropic material (carbon-fibre reinforced plastic, CFRP). To get the directivity of a specific wave mode, the signal for that mode needs to be resolved in time from other modes at all angles. This is challenging for shear (S) waves in a small model domain due to the head wave, so a technique for suppressing the head wave is shown. The multi-physics model solves for thermal expansion, which models the laser source as a surface heat flux for the Al case, and a buried heat source for the CFRP case, according to where the energy is deposited in the material. The same ultrasound generation pattern can be obtained by using a suitable pure elastodynamic loading, which is shown to be a surface force dipole as per the validation case for Al, and a buried quadrupole for the CFRP case. The modelled directivities are scaled and fitted to experimental measurements using maximum likelihood, and the goodness of fit is discussed. For the Al case, the S wave is preferred over the longitudinal (L) wave for inspection due to greater signal amplitude. For the CFRP case, the quasi-longitudinal (qL) wave in CFRP shows a maximum amplitude directly below the source, and has a greater amplitude than the quasi-shear (qS) wave, suggesting a better choice for inspection.

A porosity model for medical image segmentation of vessels.

A physics-based medical image segmentation method is developed. Specifically, the image greyscale intensity is used to infer the voxel partial volumes and subsequently formulate a porous medium analogy. The method involves first translating the medical image volumetric data into a three-dimensional computational domain of a porous material. A velocity field is then obtained from numerical simulations of incompressible fluid flow in the porous material, and finally a velocity iso-surface provides the surface description of the target object. The approach is tested on CT images of eight patient-specific cases, where cerebral aneurysms, nasal cavities (NC), and an aortic arch (AA) are the objects of interest. In the aneurysm cases, the results are compared against constant greyscale thresholding and manual segmentation. The manual segmentations of the aneurysms are validated by a clinical practitioner. Only a qualitative comparison is available for the NC, and the AA geometries. The results show that the proposed method is effective and capable of extracting the target object in a noisy domain. A sensitivity study is carried out to verify the method's performance with respect to modelling or user choices. The segmentation by the proposed method is also evaluated by performing computational fluid dynamics simulation, including a near-wall flow analysis, to ensure that the segmented geometry and the resulting computed solution are representative and meaningful.

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.

Flow structures and red blood cell dynamics in arteriole of dilated or constricted cross section.

Vessel with 'circular' or 'star-shaped' cross sections are studied, representing respectively dilated or constricted cases where endothelial cells smoothly line or bulge into the lumen. Computational haemodynamics simulations are carried out on idealised periodic arteriole-sized vessels, with red blood cell 'tube' hematocrit value=24%. A further simulation of a single red blood cell serves for comparison purposes. The bulk motion of the red blood cells reproduces well-known effects, including the presence of a cell-free layer and the apparent shear-thinning non-Newtonian rheology. The velocity flow field is analysed in a Lagrangian reference frame, relative to any given red blood cell, hence removing the bulk coaxial motion and highlighting instead the complex secondary flow patterns. An aggregate formation becomes apparent, continuously rearranging and dynamic, brought about by the inter-cellular fluid mechanics interactions and the deformability properties of the cells. The secondary flow field induces a vacillating radial migration of the red blood cells. At different radial locations, the red blood cells express different residence times, orientation and shape. The shear stresses exerted by the flow on the vessel wall are influenced by the motion of red blood cells, despite the presence of the cell-free layer. Spatial (and temporal) variations of wall shear stress patters are observed, especially for the 'circular' vessel. The 'star-shaped' vessel bears considerable stress at the protruding endothelial cell crests, where the stress vectors are coaxially aligned. The bulging endothelial cells hence regularise the transmission of stresses on the vessel wall.

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.

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%.

Study of geometrical uncertainty stemming from different reconstruction procedures on the flow field for a peripheral bypass graft.

The geometry of conduits derived from in vivo image data is subject to acquisition and reconstruction errors. This results in a degree of uncertainty in defining the bounding geometry for a patient-specific anatomical conduit. The impact of the conduit geometry uncertainty should be considered with respect to haemodynamic clinically relevant measures that may alter the perception and evaluation of prognosis and diagnosis. These are commonly fluid mechanic stresses on or near the wall. Taking an example of a peripheral bypass graft configuration, we examine the effects of image threshold on the geometry. Thresholding approaches are chosen from the existing image segmentation community and are based on clustering schemes. Two novel methods are also introduced. The geometries are reconstructed using a partition-of-unity implicit function approach from the stack of segmented cross-sections that yields a piecewise linear triangulated mesh. Methods to quantify the differences resulting in the virtual model reconstruction from the different thresholding methods are based on the distance between the models and the surface mean curvature.