Kristiaan Riemslagh

Computer Simulation of Intraventricular Flow and Pressure Gradients During Diastole

A two-dimensional axisymmetric computer model is developed for the simulation of the filling flow in the left ventricle (LV). The computed results show that vortices are formed during the acceleration phases of the filling waves. During the deceleration phases these are amplified and convected into the ventricle. The ratio of the maximal blood velocity at the mitral valve (peak E velocity) to the flow wave propagation velocity (WPV) of the filling wave is larger than 1. This hemodynamic behavior is also observed in experiments in vitro (Steen and Steen, 1994, Cardiovasc. Res., 28, pp. 1821-1827) and in measurements in vivo with color M-mode Doppler echocardiography (Stugaard et al., 1994, J. Am. Coll. Cardiol., 24, 663-670). Computed intraventricular pressure profiles are similar to observed profiles in a dog heart (Courtois et al., 1988, Circulation, 78, pp. 661-671). The long-term goal of the computer model is to study the predictive value of noninvasive parameters (e.g., velocities measured with Doppler echocardiography) on invasive parameters (e.g., pressures, stiffness of cardiac wall, time constant of relaxation). Here, we show that higher LV stiffness results in a smaller WPV for a given peak E velocity. This result may indicate an inverse relationship between WPV and LV stiffness, suggesting that WPV may be an important noninvasive index to assess LV diastolic stiffness, LV diastolic pressure and thus atrial pressure (preload).

Computational Treatment of Source Terms in Two-Equation Turbulence Models

The source terms in turbulence models require careful treatment to obtain a stable discretization. The choice between implicit and explicit treatment has to be made. This can be done either on the basis of individual terms or on the basis of the exact Jacobian of the source terms. A comparison of both methods shows that the latter is generally applicable and superior to the first, approximate method with respect to convergence speed. This comes from the possibility of using the multigrid technique with the exact method, whereas this is not always possible with the approximate method. In principle, for robustness a time-step restriction for the source terms has to be introduced to prevent the turbulence quantities from becoming negative or infinitely large. An approximation of the appropriate time step is calculated. Practical results, however, indicate that the time-step restriction is not always necessary. Different two-equation turbulence models are investigated confirming the generality of the approach

A three-dimensional analysis of flow in the pivot regions of an ATS bileaflet valve.

Bileaflet heart valves are currently the most commonly implanted type of mechanical prosthetic valve, because of their low transvalvular pressure drop, centralised flow and durability. However, in common with all mechanical heart valves, implanted bileaflet valves show an inherent tendency for blood clot formation at the valve site. Fluid dynamical phenomena associated with blood clotting are elevated blood shear stresses and regions of persistent blood recirculation, particularly when both occur together. Using three-dimensional CFD modelling, combined with enlarged scale experimental modelling, we investigated the blood flow through the ATS bileaflet valve during forward flow, with particular attention to the leaflet pivot regions. Recirculating regions were found both within and downstream of the valve housing ring. Qualitative assessment of the entire cardiac cycle suggested that recirculating blood within the housing ring will be washed away whilst the valve is closed, but as with all bileaflet valve designs recirculating blood downstream of the valve may have a residence time much longer than one cardiac cycle.

An arbitrary Lagrangian-Eulerian finite-volume method for the simulation of rotary displacement pump flow

Abstract A method is described that allows the simulation of the flow of an incompressible fluid through rotary displacement pumps. The two-dimensional incompressible Navier–Stokes equations in arbitrary Lagrangian–Eulerian formulation are discretized on a triangular grid using a finite-volume method. Fully implicit time integration makes the method stable for any time step. Central differencing is used for the diffusive fluxes. Upwind differencing based on flux-difference splitting is used for the convective fluxes. A detailed description is given of the grid generation process.

Left-ventricular pressure gradients: a computer-model simulation

Both invasive left-ventricular pressure measurements and non-invasive colour M-mode echographic measurements have shown the existence of intraventricular pressure gradients (IVPGs) during early filling. The mechanisms responsible for these IVPG cannot be completely explained by the experiments. Therefore a one-dimensional numerical model is developed and validated. The model describes filling (both velocities and pressures) along a left ventricular (LV) base-apex axis. Blood-wall interaction in the left ventricle with moving boundaries is taken into account. The computational results for a canine heart indicate that the observed IVPGs during filling are the consequence of a complex interaction between, on the one hand, pressure waves travelling in the LV and, on the other hand, LV geometry, relaxation and compliance. The computational results indicate the pressure dependency of wavespeed (0.77–1.90 m−1 s) for different mean intraventricular pressures (0.88–5.00 mmHg) and IVPGs up to 2 mmHg, independent of the ratio of end systolic volume and equilibrium volume. Increasing relaxation rate not only decreases minimum basal pressure (2.8 instead of 3.6 mmHg) but also has a strong influence on the time delay between the minimum basal and apical pressures (14 ms instead of 49 ms). The results sustain the hypothesis that pressure-wave propagation determines IVPGs and that IVPGs are no proof of elastic recoil.

An assessment of ductus venosus tapering and wave transmission from the fetal heart

Pressure and flow pulsations in the fetal heart propagate through the precordial vein and the ductus venosus (DV) but are normally not transmitted into the umbilical vein (UV). Pulsations in the umbilical vein do occur, however, in early pregnancy and in pathological conditions. Such transmission into the umbilical vein is not well understood. In particular, the effect of the impedance changes in the DV due to its tapered geometry is not known. This paper presents a mathematical model that we developed to study the transmission of pulsations, originating in the fetal heart, through the DV to the umbilical vein. In our model, the tapered geometry of the DV was found to be of minor importance and the only effective reflection site in the DV appears to be at the DV inlet. Differences between the DV inlet and outlet flow were also found to be minor for medium to large umbilical vein–DV diameter ratios. Finally, the results of a previously proposed lumped model were found to agree well with the present model of the DV–umbilical vein bifurcation.

Two-dimensional incompressible Navier-Stokes calculations in complex-shaped moving domains

A method is described that allows the simulation of the flow of an incompressible fluid through complex-shaped two-dimensional domains which move in any prescribed time-varying way. The incompressible Navier-Stokes equations in arbitrary Lagrangian—Eulerian form are discretized on a triangular grid by means of a finite-volume method. Fully implicit time integration makes the method stable for any time step. Central differencing is used for the diffusive fluxes. Upwind differencing based on flux-difference splitting is used for the convective fluxes. A detailed description is provided for the discretization in two dimensions, with a collocated arrangement of pressure and velocity components as dependent variables. A description of the grid-generation process is given. Results are shown for the flow in a rotating-lobe pump.

Treatment of All Speed Flows and High Aspect Ratios in CFD Applications

An AUSM (Advection Upstream Splitting Method) based discretization method, using an explicit third-order discretization for the convective part, a line-implicit central discretization for the acoustic part and for the diffusive part, has been developed for incompressible and low speed compressible Navier-Stokes equations. The lines are chosen in the direction of the gridpoints with shortest connection. The semi-implicit line method is used in multistage form because of the explicit third-order discretization of the convective part. Multigrid is used as acceleration technique. Due to the implicit treatment of the acoustic and the diffusive terms, the stiffness otherwise caused by high aspect ratio cells is removed. Low Mach number stiffness is treated by a preconditioning technique. To ensure physical correct behaviour of the discretization for vanishing Mach number, extreme care has been taken. For vanishing Mach number, stabilization terms are added to the mass flux. Pressure and temperature stabilization terms are necessary. The coefficients of these terms are chosen so that correct scaling with Mach number is obtained. A blend of the low speed algorithm with the original AUSM algorithm developed for high speed applications has been constructed so that the resulting algorithm can be used at all speeds.

Computer simulation of left ventricular filling flow: impact study on echocardiograms

A 2D axisymmetrical computer model is developed describing left ventricular (LV) flow during filling. The unsteady Navier-Stokes equations in a LV geometry with moving walls are solved. The relaxation and compliance of the LV wall and the fluid-wall interaction are taken into account. The method is used to simulate the filling of a canine heart. The computed results show intraventricular flow and pressure patterns during filling. From a calculated colour M-mode Doppler echocardiogram, it can be seen that both early and atrial filling waves travel from base to apex. The maximal blood velocity during the early filling wave is 70 cm/s and the propagation velocity of the filling wave which corresponds with the propagation of a ring vortex, is 45 cm/s. The ratio is 1.56. Slower relaxation and higher LV stiffness result in a slower wave propagation.

A finite volume method for viscous compressible flows in low and high speed applications

An AUSM (Advection Upstream Splitting Method) based discretization method, using an explicit third-order discretization for the convective part, a line-implicit central discretization for the acoustic part and for the diffusive part, has been developed for incompressible and low speed compressible flow. The lines are chosen in the direction of the gridpoints with shortest connection. The semi-implicit line method is used in multistage form because of the explicit third-order discretization of the convective part, Multigrid is used as an acceleration technique. Due to the implicit treatment of the acoustic and the diffusive terms, the stiffness otherwise caused by high aspect ratio cells is removed. Low Mach number stiffness is treated by a preconditioning technique. To ensure physically correct behaviour of the discretization for vanishing Mach number, extreme care has been taken. For vanishing Mach number, stabilization terms are added to the mass flux. Pressure and temperature stabilization terms are necessary. The coefficients of these terms are chosen so that correct scaling with Mach number is obtained. A blend of the low speed algorithm with the original AUSM algorithm developed for high speed applications has been constructed so that the resulting algorithm can be used at all speeds.