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Research Papers

The Impact of Simplified Boundary Conditions and Aortic Arch Inclusion on CFD Simulations in the Mouse Aorta: A Comparison With Mouse-specific Reference Data

[+] Author and Article Information
Bram Trachet1

 IBiTech - bioMMeda, Ghent University, BE-9000 Ghent, Belgiumbram.trachet@ugent.be IBiTech - Medisip, Ghent University - IBBT, BE-9000 Ghent, Belgiumbram.trachet@ugent.be Centre for Medical Genetics, Ghent University, BE-9000 Ghent, Belgium; Centre of Medical Genetics, Antwerp University Hospital, BE-2000 Antwerp, Belgiumbram.trachet@ugent.be IBiTech - bioMMeda, Ghent University, BE-9000 Ghent, Belgiumbram.trachet@ugent.be

Joris Bols, Gianluca De Santis, Stefaan Vandenberghe, Bart Loeys, Patrick Segers

 IBiTech - bioMMeda, Ghent University, BE-9000 Ghent, Belgium IBiTech - Medisip, Ghent University - IBBT, BE-9000 Ghent, Belgium Centre for Medical Genetics, Ghent University, BE-9000 Ghent, Belgium; Centre of Medical Genetics, Antwerp University Hospital, BE-2000 Antwerp, Belgium IBiTech - bioMMeda, Ghent University, BE-9000 Ghent, Belgium

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Corresponding author.

J Biomech Eng 133(12), 121006 (Dec 23, 2011) (13 pages) doi:10.1115/1.4005479 History: Received September 20, 2011; Revised November 22, 2011; Published December 23, 2011; Online December 23, 2011

Computational fluid dynamics (CFD) simulations allow for calculation of a detailed flow field in the mouse aorta and can thus be used to investigate a potential link between local hemodynamics and disease development. To perform these simulations in a murine setting, one often needs to make assumptions (e.g. when mouse-specific boundary conditions are not available), but many of these assumptions have not been validated due to a lack of reference data. In this study, we present such a reference data set by combining high-frequency ultrasound and contrast-enhanced micro-CT to measure (in vivo) the time-dependent volumetric flow waveforms in the complete aorta (including seven major side branches) of 10 male ApoE -/- deficient mice on a C57Bl/6 background. In order to assess the influence of some assumptions that are commonly applied in literature, four different CFD simulations were set up for each animal: (i) imposing the measured volumetric flow waveforms, (ii) imposing the average flow fractions over all 10 animals, presented as a reference data set, (iii) imposing flow fractions calculated by Murray’s law, and (iv) restricting the geometrical model to the abdominal aorta (imposing measured flows). We found that – even if there is sometimes significant variation in the flow fractions going to a particular branch – the influence of using average flow fractions on the CFD simulations is limited and often restricted to the side branches. On the other hand, Murray’s law underestimates the fraction going to the brachiocephalic trunk and strongly overestimates the fraction going to the distal aorta, influencing the outcome of the CFD results significantly. Changing the exponential factor in Murray’s law equation from 3 to 2 (as suggested by several authors in literature) yields results that correspond much better to those obtained imposing the average flow fractions. Restricting the geometrical model to the abdominal aorta did not influence the outcome of the CFD simulations. In conclusion, the presented reference dataset can be used to impose boundary conditions in the mouse aorta in future studies, keeping in mind that they represent a subsample of the total population, i.e., relatively old, non-diseased, male C57Bl/6 ApoE -/- mice.

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Figures

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Figure 2

Redistribution scheme for two typical cases (top: AA2, bottom: AA6). Solid lines represent original (measured) volumetric flow waveforms (averaged over three cardiac cycles and corrected for the time lag present in the measurements). Dashed lines represent redistributed volumetric flow waveforms. As described in the Methods section, redistribution is split into two different parts (proximal and distal aorta). Volumetric flow in the thoracic aorta is fixed in the abdominal part to guarantee a correct mass balance using exactly the same outlet boundary conditions in those simulations in which only the abdominal aorta is considered. Mind that the scale is different for proximal (left) and distal (right) parts of the figure.

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Figure 3

Boxplots showing the nodal distribution of TAWSS, OSI and RRT, visualizing the 25th, 50th and 75th percentile (box) as well as the 10th and 90th percentile (whiskers) and the 5th and 95th percentile (outliers). (a) The nodal distribution is compared over the entire aorta for three different BC schemes: white boxes (left) show the golden standard, i.e., the distribution when the measured outflow velocity waveforms are imposed. Light gray boxes (middle) show the distribution when the average flow ratios over all 10 animals are imposed, and dark gray boxes (right) show the distribution when Murray’s law (using an exponential factor 3) is used to determine the outflow ratios towards the branches. (b). The nodal distribution is compared over the abdominal aorta for two different geometrical settings: white boxes (left) show the golden standard, i.e., the distribution over the abdominal aorta when the entire aorta is included into the numerical model. Dark gray boxes (right) show the distribution when the proximal and thoracic aorta are omitted from the model, thus imposing a flow velocity waveform directly at the inlet of the abdominal model (see also Fig. 7). Measured outflow velocity waveforms were used as boundary conditions in both cases.

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Figure 4

TAWSS distribution compared for three different outlet BC schemes. The left panels show the TAWSS distribution when measured outflow velocity waveforms are imposed, middle panels when the average flow ratios over all 10 animals are imposed, and right panels when Murray’s law (using an exponential factor 3) is used to determine the imposed outflow ratios. Top: Influence of BC outlet scheme on TAWSS distribution for maximal Cohen’s distance (AA2). Bottom: Influence of BC outlet scheme on TAWSS distribution for minimal Cohen’s distance (AA8).

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Figure 5

OSI distribution compared for three different outlet BC schemes. The left panels show the OSI distribution when measured outflow velocity waveforms are imposed, middle panels when the average flow ratios over all 10 animals are imposed, and right panels when Murray’s law (using an exponential factor 3) is used to determine the imposed outflow ratios. Top: Influence of BC outlet scheme on OSI distribution for maximal Cohen’s distance (AA3). Bottom: influence of BC outlet scheme on OSI distribution for minimal Cohen’s distance (AA1).

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Figure 6

RRT distribution compared for three different outlet BC schemes. The left panels show the RRT distribution when measured outflow velocity waveforms are imposed, middle panels when the average flow ratios over all 10 animals are imposed, and right panels when Murray’s law (using an exponential factor 3) is used to determine the imposed outflow ratios. Top: Influence of BC outlet scheme on RRT distribution for maximal Cohen’s distance (AA9). Bottom: Influence of BC outlet scheme on RRT distribution for minimal Cohen’s distance (AA8).

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Figure 7

Spatial TAWSS, OSI and RRT distribution compared for two different geometrical settings. Distributions are shown for the case with highest Cohen’s distance (AA5). Top: CFD results over the abdominal aorta when the entire aorta is included into the geometrical model. Bottom: CFD results when the geometrical model is restricted to the abdominal aorta, imposing a (measured) parabolic flow velocity waveform at the inlet of the model.

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Figure 8

Lambda-2 isosurfaces (indicating the location of vortex cores) and velocity vector profiles shown at the aortic deceleration phase for the case with highest Cohen’s distance (AA5). Top: The entire aorta is included into the geometrical model. Vortex cores are located at the arch and in the curvature of the thoracic aorta and a skewed velocity profile enters the abdominal aorta. Bottom: The geometrical model is restricted to the abdominal aorta. Vortex cores are located near the side branches, at the same locations as when the entire aorta was included into the aorta. A (measured) parabolic flow velocity waveform is imposed at the inlet of the model but proximal to the first branch (coeliac artery) the velocity profile is no longer different from the one that is obtained when the entire aorta is included into the model.

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Figure 1

Pulsed Doppler ultrasound flow velocity measurements as they are acquired throughout the arterial tree. On the left hand side, indicated with white dots and dotted lines, are the measurements performed in all seven side branches of the aorta. On the right hand side, indicated with black dots and dashed lines, shows the measurements performed at eight different locations throughout the aorta itself. Mind that the shown images represent flow velocity waveforms as they were measured, which implies that the scale is different for each measurement location.

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