Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements.

A numerical model based on the nonlinear, one-dimensional (1-D) equations of pressure and flow wave propagation in conduit arteries is tested against a well-defined experimental 1:1 replica of the human arterial tree. The tree consists of 37 silicone branches representing the largest central systemic arteries in the human, including the aorta, carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs. The set-up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow. Terminal branches end in simple resistance models, consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure. The parameters required by the numerical algorithm are directly measured in the in vitro set-up and no data fitting is involved. Comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1-D time-domain formulation to capture the main features of pulse wave propagation measured throughout the system test. As a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation, the experimental set-up generates waveforms at terminal branches with additional non-physiological oscillations. The frequencies of these oscillations are well captured by the 1-D model, even though amplitudes are overestimated. Adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect, suggesting that wall visco-elasticity might play an important role in the experimental results. Nevertheless, average relative root-mean-square errors between simulations and experimental waveforms are smaller than 4% for pressure and 19% for the flow at all 70 locations studied.

The geometry of unstented and stented pig common carotid artery bypass grafts.

The long-term success of arterial bypass grafting with autologous saphenous veins is limited by neointimal hyperplasia (NIH), which seemingly develops preferentially at sites where hydrodynamic wall shear is low. Placement of a loose-fitting, porous stent around end-to-end, or end-to-side, autologous saphenous vein grafts on the porcine common carotid artery has been found significantly to reduce NIH, but the mechanism is unclear. In a preliminary study, we implanted autologous saphenous vein grafts bilaterally on the common carotid arteries of pigs, placing a stent around one graft and leaving the contralateral graft unstented. At sacrifice 1 month post implantation, the grafts were pressure fixed in situ and resin casts were made. Unstented graft geometry was highly irregular, with non-uniform dilatation, substantial axial lengthening, curvature, kinking, and possible long-pitch helical distortion. In contrast, stented grafts showed no major dilatation, lengthening or curvature, but there was commonly fine corrugation, occasional slight kinking or narrowing of segments, and possible long-pitch helical distortion. Axial growth of grafts against effectively tethered anastomoses could account for these changes. CFD studies are planned, using 3D MR reconstructions, on the effects of graft geometry on the flow. Abnormality of the flow could favour the development of vascular pathology, including NIH.

Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements.

The accuracy of the nonlinear one-dimensional (1-D) equations of pressure and flow wave propagation in Voigt-type visco-elastic arteries was tested against measurements in a well-defined experimental 1:1 replica of the 37 largest conduit arteries in the human systemic circulation. The parameters required by the numerical algorithm were directly measured in the in vitro setup and no data fitting was involved. The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was previously reported in this paper [Matthys et al., 2007. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40, 3476-3486]. In comparison to the purely elastic model, visco-elasticity significantly reduced the average relative root-mean-square errors between numerical and experimental waveforms over the 70 locations measured in the in vitro model: from 3.0% to 2.5% (p<0.012) for pressure and from 15.7% to 10.8% (p<0.002) for the flow rate. In the frequency domain, average relative errors between numerical and experimental amplitudes from the 5th to the 20th harmonic decreased from 0.7% to 0.5% (p<0.107) for pressure and from 7.0% to 3.3% (p<10(-6)) for the flow rate. These results provide additional support for the use of 1-D reduced modelling to accurately simulate clinically relevant problems at a reasonable computational cost.

Modelling pulse wave propagation in the rabbit systemic circulation to assess the effects of altered nitric oxide synthesis.

Pulse wave propagation in the mature rabbit systemic circulation was simulated using the one-dimensional equations of blood flow in compliant vessels. A corrosion cast of the rabbit circulation was manufactured to obtain arterial lengths and diameters. Pulse wave speeds and inflow and outflow boundary conditions were derived from in vivo data. Numerical results captured the main features of in vivo pressure and velocity pulse waveforms in the aorta, brachiocephalic artery and central ear artery. This model was used to elucidate haemodynamic mechanisms underlying changes in peripheral pulse waveforms observed in vivo after administering drugs that alter nitric oxide synthesis in the endothelial cells lining blood vessels. According to our model, these changes can be explained by single or combined alterations of blood viscosity, peripheral resistance and compliance, and the elasticity of conduit arteries.

Automatic reconstruction of a patient-specific high-order surface representation and its application to mesh generation for CFD calculations.

We describe a set of procedures for the shape reconstruction and mesh generation of unstructured high-order spatial discretization of patient-specific geometries from a series of medical images and for the simulation of flows in these meshes using a high-order hp-spectral solver. The reconstruction of the shape of the boundary is based on the interpolation of an implicit function through a set of points obtained from the segmentation of the images. This approach is favoured for its ability of smoothly interpolating between sections of different topology. The boundary of the object is initially represented as an iso-surface of an implicit function defined in terms of radial basis functions. This surface is approximated by a triangulation extracted by the method of marching cubes. The triangulation is then suitably smoothed and refined to improve its quality and permit its approximation by a quilt of bi-variate spline surface patches. Such representation is often the standard input format required for state-of-the-art mesh generators. The generation of the surface patches is based on a partition of the triangulation into Voronoi regions and dual Delaunay triangulations with an even number of triangles. The quality of the triangulation is optimized by imposing that the distortion associated with the energy of deformation by harmonic maps is minimized. Patches are obtained by merging adjacent triangles and this representation is then used to generate a mesh of linear elements using standard generation techniques. Finally, a mesh of high-order elements is generated in a bottom-up fashion by creating the additional points required for the high-order interpolation and projecting them on the edges and surfaces of the quilt of patches. The methodology is illustrated by generating meshes for a by-pass graft geometry and calculating high-order CFD solutions in these meshes.

Three-dimensional reconstruction of autologous vein bypass graft distal anastomoses imaged with magnetic resonance: clinical and research applications.

High-resolution magnetic resonance imaging was combined with computational modeling to create focused three-dimensional reconstructions of the distal anastomotic region of autologous vein peripheral bypass grafts in a preliminary series of patients. Readily viewed on a personal computer or printed as hard copies, a detailed appreciation of in vivo postoperative features of the anastomosis is possible. These reconstructions are suitable for analysis of geometric features, including vessel caliber, tortuosity, anastomotic angles, and planarity. Some potential clinical and research applications of this technique are discussed.