Guide Fluid Structure Interaction II: Modelling, Simulation, Optimization

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Modelling, Simulation, Optimization

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During preliminary experiments, pressure measurements inside the FSI section were obtained using a catheter. Unfortunately, disturbance of the flow field and artifacts in the acquired MRI data could not be fully avoided. Thus, pressure recordings were omitted during the two phases of data acquisition. Further, Hessenthaler et al 49 showed that the hydrostatic pressure component can be removed from the modeled FSI system via a substitution in the pressure variable, such that pressure measurements are not imperative.

Measurement error in the velocity data extracted from PC MRI can be challenging and is often not determinable from the images directly. Further, precise geometry definition was achieved using CAD tools, and experimental design aimed to minimize errors. For example, fluid temperature was recorded during the experiments to improve measurement accuracy of fluid material parameters. Nevertheless, measurement errors occurred, and manufacturing tolerances existed.

Known weights were added to the sample to cause elongation. Thus, measurements accuracy depended on the accuracy of the used Vernier caliper and balance, and the relative error is larger at small stretches. A list of known sources of experimental error is given in Table 5 along with error intervals. To illustrate the FSI phenomena observed in phases I and II of the experiment, a qualitative description of steady and transient solid motion and fluid flow is given in this section.

Experimental results extracted from imaging data are presented. We note that extracted experimental values are available in the online supplement. Increasing the inflow velocity decreased the peak deflection for moderate inflow velocities because of surrounding flow and fluid shear stresses being exerted onto the solid.

Further, increases in inflow led to little change in deflection until the flow became turbulent, at which point the filament exhibited unsteady deflection.

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Observed profiles were parabolic in nature as expected on the basis of Poiseuille flow in a cylindrical tube. The steady silicone filament deflection under constant inflow conditions was approximately Velocity components v x are given in the left column, v y in the middle column, and v z in the right column. Peak values for each time frame were obtained on the basis of a best fit to a parabolic profile. Phase II, recorded inflow boundary condition data. B, Raw image data cropped at flow phantom wall of inlet velocity profiles at peak inflow. Note that flow in the v y direction was observed only in the upper inlet.

It is noted that peak values of flow are observed at different time instants and that reflow regions develop near the long axis of the flow phantom model. Once flow decelerates, gravitational forces become more dominant and the silicone filament moves back upwards. It performs a swing before reaching its initial position. Note that the resting position under zero flow conditions is significantly different to the position of the silicone filament at the beginning of each flow cycle.

Key characteristics of the FSI experiment were designed to be comparable with those of many biomedical engineering problems. For example, flow rates were selected such that resulting flow was in the laminar regime. The chosen fluid is moderately viscous and incompressible, and the solid material exhibits nonlinear incompressible material characteristics. Importantly, MRI has been used for data acquisition as it is often used in translational biomedical engineering applications.

Testing also includes the correct spatial prediction of solid position and flow as well as testing of the coupling scheme. As opposed to phase I, modeling of the dynamics of the fluid and the solid as well as the coupled FSI problem becomes of prime importance. Significant variation in solid motion is observed as well as changes to flow dynamics.

This phase thus presents additional challenges for example, coupling of time integration schemes for both subsystems on top of the first phase. Postprocessed data were presented in this paper and are available in the online supplement. For further details, see the work of Gaddum et al. The experimental design was optimized, and additional data acquired to minimize measurement errors and assist with correct modeling of the FSI problem. Of course, measurement errors could not be fully avoided. For example, tolerances during manufacture eg, 3D printing and measurement eg, viscometer impact precision as outlined in Table 5.

In general, MRI measurements of flow velocity and solid position represent volume and time averages due to finite voxel size and acquisition time.

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For example, measurement errors in recorded flow fields are generally a fraction of the selected VENC value, such that the relative error increases with decreasing flow velocity in unsteady flow cases. Nevertheless, due to optimizing VENC values for each flow velocity components, measurement errors could be minimized.

The representation of inflow boundary conditions by parabolic profiles for each time frame is an approximation to simplify prescription of boundary conditions in the numerical setting. A modest improvement of the description of the inflow can be achieved by fitting the multifrequency Womersley solution see Appendix A.

The use of MRI also constrained the experimental design. The temporal resolution of MRI sequences used was also limited to avoid prolonged data acquisition.

arbitrary lagrangian eulerian and fluid structure interaction numerical simulation Manual

In this regard, PIV may provide better performance and would be less prone to averaging effects than MRI because of the underlying technology of tracing particles to obtain an instantaneous velocity map. An additional advantage of MRI over PIV is the lack for optical requirements, for example, accounting for the refraction index of the flow phantom material, as well as the less intrusive approach no tracer particles required.

Further, MRI tends to provide the input data commonly used in biomedical engineering research geared toward translation. Hence, the definition of input data and comparison of end results are considered a valuable step for translational FSI applications. For further details on PIV, see previous works. Gravitational forces make an important contribution to the mechanism that is employed to obtain a repeatable deflection pattern see Section 3.

To yield such behavior, however, the frequency of the oscillating flow rate was selected to be relatively small as compared to the normal heart rate of an adult at rest, which ranges from 1 to 1. Therefore, future improvements or test cases could be obtained by investigating frequencies more closely related to human heart rate, eg, by employing a different FSI mechanism. We note that the solid material exhibits viscoelastic behavior.

However, viscous effects are minimal at low frequency and were thus deemed negligible in this study. Focus of the experiment was on aspects encountered in typical biomedical engineering applications. For example, flow was in the laminar regime with biologically relevant Reynolds numbers. A moderately viscous incompressible Newtonian fluid interacts with a nonlinear incompressible isotropic solid in a fully 3D setting under the influence of gravitational forces. Like in many biomedical engineering applications, MRI was used for acquisition.

A comprehensive data set comprising of geometry and flow images quantifying fluid and solid motion in space and time was obtained and is made available in the online supplement. Stuttgart, Germany. Once the inflow boundary scans were acquired and registered, the centers of either inlet were identified. Then, a multifrequency Womersley solution was fit in a local coordinate frame with respect to radius r , ie, distance to center point for each velocity component individually,.

The fit was obtained as follows. Firstly, we interpolated the data at equispaced time points. Secondly, the mean square error at each data point was weighted by the variance of the data as well as the number of data points per radius r. Further, the weighted mean square error of the parabolic fits see Section 2. Hessenthaler, N. Gaddum and O.

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Holub share first authorship to this work. National Center for Biotechnology Information , U. Published online Jan Hessenthaler , 1 N. Gaddum , 2 O. Holub , 2 R. Sinkus , 2 O. Nordsletten 2. Author information Article notes Copyright and License information Disclaimer. Hessenthaler, Email: ed.

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Corresponding author. Email: ed. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Associated Data Supplementary Materials supporting info item.

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Table 1 Selection of popular FSI benchmark test cases in publication order with specification of Reynolds number R e and whether the benchmark is based on an experiment. Open in a separate window. Figure 1. FSI section Numerical experiments were performed in 2D and 3D to review and optimize geometry and experimental design and explore suitable sets of materials. Table 3 Experimentally determined fluid and solid material parameters.

Material selection and material properties A key aspect of the experimental design was the selection of the fluid.

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