Analysis of blood flow through a modelled artery with an aneurysm

The intention of the present work is to carry out a systematic analysis of flow features in a tube, modelled as artery, having a local aneurysm in presence of haematocrit. The arterial model is treated to be axi-symmetric and rigid. The blood, flowing through the modelled artery, is treated to be Newtonian and non-homogeneous. For a thorough quantitative analysis of the flow characteristics such as wall pressure, flow velocity, wall shear stress, the unsteady incompressible Navier-Stokes equations in cylindrical polar co-ordinates under the laminar flow conditions are solved by using the finite-difference method. Finally, the numerical illustrations presented in this paper provide an effective measure to estimate the combined influence of haematocrit and aneurysm on flow characteristics. It is found that the magnitude of wall shear stress and also the length of separation increase with increasing values of the haematocrit parameter. The length of flow separation increases but the peak value of wall shear stress decreases with the increasing length of aneurysm. The peak value of wall shear stress as well as the length of separation increases with the increasing height of the aneurysm.     

Investigation of the effects of two parallel wires' non-uniform magnetic field on heat and biomagnetic fluid flow in an aneurysm

ABSTRACT

In this paper, effects of two wires magnetic field on heat transfer and biomagnetic fluid flow in an aneurysm have been investigated using the ferrohydrodynamics model. Using the finite volume method and the SIMPLE algorithm, the governing equations have been discretised. Simulations have been carried out for both conditions of wires in the same and opposite directions and different magnetic numbers of 41 and 82. Results show that the magnetic field causes a decrease in heat transfer of blood flow towards the walls. Moreover, major energy loss or pressure drop, arising from mean wall shear stress, decreases but local or minor energy loss, arising from aneurysm vortexes, increases. Furthermore, risk factors of aneurysm rupture is decreased under the effect of the magnetic field. The effective contact surface between drug-coated magnetic nanoparticles and the aneurysm tissue may increase and residence time of drug on the cells of the region would decrease.     

Post-bifurcation analysis of a thin-walled hyperelastic tube under inflation

We consider the problem of bulging, or necking, of an infinite thin-walled hyperelastic tube that is inflated by an internal pressure, with the axial stretch at infinity maintained at unity. We present a simple procedure that can be used to derive the bifurcation condition and to determine the near-critical behaviour analytically. It is shown that there is a bifurcation with zero mode number and that the associated axial variation of near-critical bifurcated configurations is governed by a first-order differential equation that admits a locally bulging or necking solution. This result suggests that the corresponding bifurcation pressure can be identified with the so-called initiation pressure which featured in recent experimental studies. This is supported by good agreement between our theoretical predictions and one set of experimental data. It is also shown that the Gent material model can support both bulging and necking solutions whereas the Varga and Ogden material models can only support bulging solutions. Relevance of the present method to the study of non-linear wave propagation in a fluid-filled distensible tube is also discussed.     

Hemodynamic analysis of intracranial aneurysms using phase-contrast magnetic resonance imaging and computational fluid dynamics

Additional hemodynamic parameters are highly desirable in the clinical management of intracranial aneurysm rupture as static medical images cannot demonstrate the blood flow within aneurysms. There are two ways of obtaining the hemodynamic information—by phase-contrast magnetic resonance imaging(PCMRI) and computational fluid dynamics(CFD). In this paper, we compared PCMRI and CFD in the analysis of a stable patient's specific aneurysm.The results showed that PCMRI and CFD are in good agreement with each other. An additional CFD study of two stable and two ruptured aneurysms revealed that ruptured aneurysms have a higher statistical average blood velocity,wall shear stress, and oscillatory shear index(OSI) within the aneurysm sac compared to those of stable aneurysms.Furthermore, for ruptured aneurysms, the OSI divides the positive and negative wall shear stress divergence at the aneurysm sac.     

Simulation of unsteady laminar flow in models of terminal aneurysm of the basilar artery

Blood flow dynamics play an important role in the pathogenesis and treatment of intracranial aneurysms. The evaluation of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils, in addition the temporal and spatial variations of wall shear stress in the aneurysm are correlated with its growth and rupture. The present numerical investigation describes the hemodynamics in two models of terminal aneurysm of the basilar artery. Aneurysm models with an aspect ratio of 1.0 and 1.67 were studied. Each model was subject to a steady, sinusoidal and physiologically representative waveform of inflow for a mean Reynolds number of 560. Symmetric and asymmetric outflow conditions in the branches were also studied.

The three-dimensional continuity and the Navier-Stokes equations for incompressible, unsteady laminar flow with Newtonian properties were solved with a commercial software using non structured grids with 61334 and 65961 cells for models 1 and 2, respectively. The grids were primarily composed of tetrahedral elements.

The intra-aneurysmal flow was unsteady for all input conditions and in both models, the flow always showed a complex vortex structure. The inflow and outflow zones in the aneurysm neck were determined. The wall shear stress on the aneurysm showed large temporal and spatial variations. The asymmetric outflow increased the wall shear stress in both models.     

Localized bulging in an inflated cylindrical tube of arbitrary thickness – the effect of bending stiffness

We study localized bulging of a cylindrical hyperelastic tube of arbitrary thickness when it is subjected to the combined action of inflation and axial extension. It is shown that with the internal pressure P and resultant axial force F viewed as functions of the azimuthal stretch on the inner surface and the axial stretch, the bifurcation condition for the initiation of a localized bulge is that the Jacobian of the vector function $(P,F)$ should vanish. This is established using the dynamical systems theory by first computing the eigenvalues of a certain eigenvalue problem governing incremental deformations, and then deriving the bifurcation condition explicitly. The bifurcation condition is valid for all loading conditions, and in the special case of fixed resultant axial force it gives the expected result that the initiation pressure for localized bulging is precisely the maximum pressure in uniform inflation. It is shown that even if localized bulging cannot take place when the axial force is fixed, it is still possible if the axial stretch is fixed instead. The explicit bifurcation condition also provides a means to quantify precisely the effect of bending stiffness on the initiation pressure. It is shown that the (approximate) membrane theory gives good predictions for the initiation pressure, with a relative error less than 5%, for thickness/radius ratios up to 0.67. A two-term asymptotic bifurcation condition for localized bulging that incorporates the effect of bending stiffness is proposed, and is shown to be capable of giving extremely accurate predictions for the initiation pressure for thickness/radius ratios up to as large as 1.2.     

MRI postoperative monitoring in patients surgically treated for aortic dissection

In most cases, surgery of aortic dissections repairs only the ascending portion of the aorta, leaving a residual dissection in the arch and descending aorta. We studied 17 patients operated upon for type A aortic dissection. A total of 42 magnetic resonance imaging (MRI) examinations were performed, with two to five studies per patient (mean 2.47). The studies were done between 5 weeks and 47 months (mean 17.5 months) after surgery. The patients were evaluated by MRI using gated spin-echo and gradient-echo sequences on axial and oblique sagittal views, and in selected cases, coronal views. A high incidence of abnormalities was observed. Pericardial hematoma was observed in 11% of cases, aortic and branch involvement in 41%, abdominal aortic branch involvement in 47%, dilatation of native aorta in 58%, and extension of dissection in 10%. New complications were detected during follow-up in 53% of patients. MRI was helpful in the follow-up of patients operated upon for aortic dissections, owing to its noninvasiveness and multiplanarity. By means of this technique, it was possible to obtain information about the natural history of the disease, as well as information useful for subsequent treatment.     

Instability analysis in pressurized transversely isotropic Saint-Venant–Kirchhoff and neo-Hookean cylindrical thick shells

Under the effect of an inner pressure, a thick hyperelastic shell cylinder is susceptible to developing mechanical instabilities, leading to a bifurcated shape that no longer has the initial cylindrical symmetry. The considered problem has a strong resonance in a biomedical context, considering pathologies encountered for arteries, such as aneurysm. In this contribution, the mechanical behavior of thick elastic shells has been analyzed, considering a thick-walled cylindrical hyperelastic model material obeying a transversely isotropic behavior, first in a large-displacement situation and then in a large-deformation case. The response of the material is assumed to be instantaneous, so that time-dependent effects shall not be considered in this paper. The case of a Saint-Venant–Kirchhoff material is considered with special emphasis to exemplify a large-displacement small-strain situation; the neo-Hookean behavior is next considered to enlarge the constitutive law toward consideration of large strains. The stability conditions of the shell are studied and bifurcation conditions formulated in terms of the applied pressure and of the geometrical and mechanical parameters that characterize the shell. Analytical solutions of some bifurcation points are evidenced and calculated when the direction of the fibers coincide with the cylinder axis.     

Numerical simulation of solitary blood waves in an elastic tube subjected to a localised deformation

In order to well apprehend what really happens in a locally deformed elastic tube, a numerical analysis of the liquid flow in such a media has been undertaken. A cylindrical tube with constant rigidity subjected to a localised dilatation is first considered and results obtained help to understand the behaviour and the developing process of aneurysm. The analysis of the effects of stenoses on blood flow is also done.