On the Incorporation of Obstacles in a Fluid Flow Problem Using a Navier-Stokes-Brinkman Penalization Approach

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the solids by the moving fluid. Such problems appear in various contexts, ranging from numerous technical applications such as turbines to medical problems such as the regulation of hemodyamics by valves. Typically, the numerical treatment of such problems is posed within a fluid structure interaction (FSI) framework. General FSI models are able to capture bidirectional interactions, but are challenging to solve and computationally expensive. Simplified methods offer a possible remedy by achieving better computational efficiency to broaden the scope to demanding application problems with focus on understanding the effect of solids on altering fluid dynamics. In this study we report on the development of a novel method for such applications. In our method rigid moving obstacles are incorporated in a fluid dynamics context using concepts from porous media theory. Based on the Navier-Stokes-Brinkman equations which augments the Navier-Stokes equation with a Darcy drag term our method represents solid obstacles as time-varying regions containing a porous medium of vanishing permeability. Numerical stabilization and turbulence modeling is dealt with by using a residual based variational multiscale formulation. The key advantages of our approach -- computational efficiency and ease of implementation -- are demonstrated by solving a standard benchmark problem of a rotating blood pump posed by the Food and Drug Administration Agency (FDA). Validity is demonstrated by conducting a mesh convergence study and by comparison against the extensive set of experimental data provided for this benchmark

The influence of bicuspid aortic valves on the dynamic pressure distribution in the ascending aorta: a porcine ex vivo model †

OBJECTIVES The aim of the study was to simulate the effect of different bicuspid aortic valve configurations on the dynamic pressure distribution in the ascending aorta. METHODS Aortic specimens were harvested from adult domestic pigs. In Group 1, bicuspidalization was created by a running suture between the left and the right coronary leaflets (n = 6) and in Group 2 by a running suture between the left and the non-coronary leaflets (n = 6). Eleven tricuspid specimens served as controls. Two intraluminal pressure catheters were positioned at the concavity and the convexity of the ascending aorta. The specimens were connected to a mock circulation (heart rate: 60 bpm, target pressure: 95 mmHg). A comparison of the different conditions was also done in a numerical simulation. RESULTS At a distal mean aortic pressure of 94 ± 10 mmHg, a mean flow rate of 5.2 ± 0.3 l/min was achieved. The difference of maximal dynamic pressure values (which occurred in systole) between locations at the convexity and the concavity was 7.8 ± 2.9 mmHg for the bicuspid and 1.0 ± 0.9 mmHg for the tricuspid specimens (P < 0.001). The numerical simulation revealed an even higher pressure difference between convexity and concavity for bicuspid formation. CONCLUSIONS In this hydrodynamic mock circulation model, we were able to demonstrate that bicuspid aortic valves are associated with significant pressure differences in different locations within the ascending aorta compared with tricuspid aortic valves. These altered pressure distributions and flow patterns may further add to the understanding of aneurismal development in patients with bicuspid aortic valves and might serve to anticipate adverse aortic events due to a better knowledge of the underlying mechanism

Dietary Silicon Deficiency Does Not Exacerbate Diet-Induced Fatty Lesions in Female ApoE Knockout Mice.

BACKGROUND: Dietary silicon has been positively linked with vascular health and protection against atherosclerotic plaque formation, but the mechanism of action is unclear. OBJECTIVES: We investigated the effect of dietary silicon on 1) serum and aorta silicon concentrations, 2) the development of aortic lesions and serum lipid concentrations, and 3) the structural and biomechanic properties of the aorta. METHODS: Two studies, of the same design, were conducted to address the above objectives. Female mice, lacking the apolipoprotein E (apoE) gene, and therefore susceptible to atherosclerosis, were separated into 3 groups of 10-15 mice, each exposed to a high-fat diet (21% wt milk fat and 1.5% wt cholesterol) but with differing concentrations of dietary silicon, namely: silicon-deprived (-Si; <3-μg silicon/g feed), silicon-replete in feed (+Si-feed; 100-μg silicon/g feed), and silicon-replete in drinking water (+Si-water; 115-μg silicon/mL) for 15-19 wk. Silicon supplementation was in the form of sodium metasilicate (feed) or monomethylsilanetriol (drinking water). RESULTS: The serum silicon concentration in the -Si group was significantly lower than in the +Si-feed (by up to 78%; P < 0.003) and the +Si-water (by up to 84%; P < 0.006) groups. The aorta silicon concentration was also lower in the -Si group than in the +Si-feed group (by 65%; P = 0.025), but not compared with the +Si-water group. There were no differences in serum and aorta silicon concentrations between the silicon-replete groups. Body weights, tissue wet weights at necropsy, and structural, biomechanic, and morphologic properties of the aorta were not affected by dietary silicon; nor were the development of fatty lesions and serum lipid concentrations. CONCLUSIONS: These findings suggest that dietary silicon has no effect on atherosclerosis development and vascular health in the apoE mouse model of diet-induced atherosclerosis, contrary to the reported findings in the cholesterol-fed rabbit model

Dietary Silicon Deficiency Does Not Exacerbate Diet-Induced Fatty Lesions in Female ApoE Knockout Mice.

BACKGROUND: Dietary silicon has been positively linked with vascular health and protection against atherosclerotic plaque formation, but the mechanism of action is unclear. OBJECTIVES: We investigated the effect of dietary silicon on 1) serum and aorta silicon concentrations, 2) the development of aortic lesions and serum lipid concentrations, and 3) the structural and biomechanic properties of the aorta. METHODS: Two studies, of the same design, were conducted to address the above objectives. Female mice, lacking the apolipoprotein E (apoE) gene, and therefore susceptible to atherosclerosis, were separated into 3 groups of 10-15 mice, each exposed to a high-fat diet (21% wt milk fat and 1.5% wt cholesterol) but with differing concentrations of dietary silicon, namely: silicon-deprived (-Si; <3-μg silicon/g feed), silicon-replete in feed (+Si-feed; 100-μg silicon/g feed), and silicon-replete in drinking water (+Si-water; 115-μg silicon/mL) for 15-19 wk. Silicon supplementation was in the form of sodium metasilicate (feed) or monomethylsilanetriol (drinking water). RESULTS: The serum silicon concentration in the -Si group was significantly lower than in the +Si-feed (by up to 78%; P < 0.003) and the +Si-water (by up to 84%; P < 0.006) groups. The aorta silicon concentration was also lower in the -Si group than in the +Si-feed group (by 65%; P = 0.025), but not compared with the +Si-water group. There were no differences in serum and aorta silicon concentrations between the silicon-replete groups. Body weights, tissue wet weights at necropsy, and structural, biomechanic, and morphologic properties of the aorta were not affected by dietary silicon; nor were the development of fatty lesions and serum lipid concentrations. CONCLUSIONS: These findings suggest that dietary silicon has no effect on atherosclerosis development and vascular health in the apoE mouse model of diet-induced atherosclerosis, contrary to the reported findings in the cholesterol-fed rabbit model

“overestimation” of catheter gradients by doppler ultrasound in patients with aortic stenosis: a predictable manifestation of pressure recovery

AbstractOBJECTIVESThis study sought to evaluate whether pressure recovery can cause significant differences between Doppler and catheter gradients in patients with aortic stenosis, and whether these differences can be predicted by Doppler echocardiography.BACKGROUNDPressure recovery has been shown to be a source of discrepancy between Doppler and catheter gradients across aortic stenoses in vitro. However, the clinical relevance of this phenomenon for the Doppler assessment of aortic stenosis has not been evaluated in patients.METHODSTwenty-three patients with various degrees of aortic stenosis were studied with Doppler echocardiography and catheter technique within 24 h. Using an equation previously validated in vitro, pressure recovery was estimated from peak transvalvular velocity, aortic valve area and cross-sectional area of the ascending aorta and compared with the observed differences between Doppler and catheter gradients. Doppler gradients were also corrected by subtracting the predicted pressure recovery and then were compared with the observed catheter gradients.RESULTSPredicted differences between Doppler and catheter gradients due to pressure recovery ranged from 5 to 82 mm Hg (mean ± SD, 19 ± 16 mm Hg) and 3 to 54 mm Hg (12 ± 11 mm Hg) for peak and mean gradients, respectively. They compared well with the observed Doppler-catheter gradient differences, ranging from −5 to 75 mm Hg (18 ± 18 mm Hg) and −7 to 48 mm Hg (11 ± 13 mm Hg). Good correlation between predicted pressure recovery and observed gradient differences was found (r = 0.90 and 0.85, respectively). Both the noncorrected and the corrected Doppler gradients correlated well with the catheter gradients (r = 0.93–0.97). However, noncorrected Doppler gradients significantly overestimated the catheter gradients (slopes, 1.36 and 1.25 for peak and mean gradients, respectively), while Doppler gradients corrected for pressure recovery showed good agreement with catheter gradients (slopes, 1.03 and 0.96; standard error of estimate [SEE] 8.1 and 6.9 mm Hg; mean difference ± SD 0.4 ± 8.0 mm Hg and 1.1 ± 6.8 mm Hg for peak and mean gradients, respectively).CONCLUSIONSSignificant pressure recovery can occur in patients with aortic stenosis and can cause discrepancies between Doppler and catheter gradients. However, pressure recovery and the resulting differences between Doppler and catheter measurements may be predicted from Doppler velocity, aortic valve area and size of the ascending aorta