Discrepancies between cardiovascular magnetic resonance and Doppler echocardiography in the measurement of transvalvular gradient in aortic stenosis: the effect of flow vorticity

Background

Valve effective orifice area EOA and transvalvular mean pressure gradient (MPG) are the most frequently used parameters to assess aortic stenosis (AS) severity. However, MPG measured by cardiovascular magnetic resonance (CMR) may differ from the one measured by transthoracic Doppler-echocardiography (TTE). The objectives of this study were: 1) to identify the factors responsible for the MPG measurement discrepancies by CMR versus TTE in AS patients; 2) to investigate the effect of flow vorticity on AS severity assessment by CMR; and 3) to evaluate two models reconciling MPG discrepancies between CMR/TTE measurements.

Methods

Eight healthy subjects and 60 patients with AS underwent TTE and CMR. Strouhal number (St), energy loss (EL), and vorticity were computed from CMR. Two correction models were evaluated: 1) based on the Gorlin equation (MPG_CMR-Gorlin); 2) based on a multivariate regression model (MPG_{CMR-Predicted}).

Results

MPG_CMR underestimated MPG_TTE (bias = −6.5 mmHg, limits of agreement from −18.3 to 5.2 mmHg). On multivariate regression analysis, St (p = 0.002), EL (p = 0.001), and mean systolic vorticity (p < 0.001) were independently associated with larger MPG discrepancies between CMR and TTE. MPG_CMR-Gorlin and MPG_TTE correlation and agreement were r = 0.7; bias = −2.8 mmHg, limits of agreement from −18.4 to 12.9 mmHg. MPG_{CMR-Predicted} model showed better correlation and agreement with MPG_TTE (r = 0.82; bias = 0.5 mmHg, limits of agreement from −9.1 to 10.2 mmHg) than measured MPG_CMR and MPG_CMR-Gorlin.

Conclusion

Flow vorticity is one of the main factors responsible for MPG discrepancies between CMR and TTE.     

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr = 0.7 and in liquid mercury at Pr = 0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications.Turbulent convection depends strongly on the material properties of the working fluid that are quantified by the Prandtl number, the ratio of kinematic viscosity of the fluid to thermal diffusivity of the temperature, Pr = ν/κ. Compared with the vast number of investigations at Pr ≥ 1 (1, 2), the very-low-Pr regime appears almost as a “terra incognita” despite many applications. Turbulent convection in the Sun is present at Prandtl numbers Pr < 10^?3 (3–5). The Prandtl number in the liquid metal core of the Earth is Pr ～ 10^?2 (6). Convection in material processing (7), nuclear engineering (8), or liquid metal batteries (9) has Prandtl numbers between 3 × 10^?2 and 10^?3. Rayleigh–Bénard convection (RBC), a fluid flow in a layer that is cooled from above and heated from below, is a paradigm for all of these examples. One reason for significantly fewer low-Pr RBC studies is that laboratory measurements have to be conducted in opaque liquid metals such as mercury or gallium at Pr = 0.021 (10–12). The lowest value for a Prandtl number that can be obtained in optically transparent fluids is Pr = 0.2 for binary gas mixtures (13), i.e., an order of magnitude larger than in liquid metals. Direct numerical simulations (DNS) are currently the only way to gain access to the full 3D convective turbulent fields in low-Pr convection (14–18). These simulations turn out to become very demanding if the small-scale structure of turbulence is to be studied, even for moderate Rayleigh number Ra, the parameter that quantifies the thermal driving in turbulent convection (19, 20). Whereas heat transport is reduced in low-Pr convection, the production of vorticity and shear are enhanced significantly, which amplifies the small-scale intermittency in these flows. An analysis of vorticity generation mechanisms in such flows and a comparison with other turbulent flows, which requires the resolution of spatial derivatives of the turbulent fields, is still missing. These details are, however, essential to improve parameterizations of the small-scale turbulence in low-Prandtl-number fluids such as algebraic heat flux and other subgrid-scale models (21, 22).In the present work, we investigate the reasons for this enhanced vorticity generation in low-Pr convection and compare and contrast the enstrophy production to turbulent convection at Pr ～ 1. Our studies are based on high-resolution 3D DNS. Rather than studying the Pr dependence of convection at a fixed Rayleigh number Ra, as is usually done, we compare two simulations at the same Grashof number Gr, which is defined byGr=gαΔTH3ν2=RaPr.[1]Here, g is the acceleration due to gravity, α is the thermal expansion coefficient, and ΔT is the total temperature difference across the cell height H. In such a comparison, Ra and Pr are varied now simultaneously and the corresponding dimensionless momentum equations (Eq. 4) remain unchanged. This implies that the strongly differing Prandtl numbers show up only in the advection–diffusion equation [5] for temperature. We demonstrate this perspective for two simulations at one Grashof number. We also mention that a similar discussion was emphasized in 2D quasi-geostrophic DNS (20). Fig. 1 illustrates our point of view. In Fig. 1 A and C, we show snapshots of temperature (Fig. 1 A and C, Left) and velocity magnitude (Fig. 1 A and C, Right) for the two runs. Compared with convection in air (Fig. 1 A), the temperature field in the liquid metal flow is much more diffusive, which is indicated by the smoother changes in color. The thickness of the thermal boundary layerδT=H2Nu[2]is significantly enhanced with Nu being the Nusselt number that measures turbulent heat transfer. This large thermal diffusivity is in line with an enhanced fluid turbulence level as seen by a comparison of Fig. 1 A and C, Right. The red line in Fig. 1B illustrates our pathway in the plane, which is spanned by the Prandtl and Rayleigh numbers.Open in a separate windowFig. 1.Comparison of two turbulent convection runs. (A, Left) Vertical slice cut of temperature; (A, Right) corresponding velocity magnitude. Data are for run RB1 at Pr = 0.7. (B) Sketch of the Prandtl–Rayleigh-number plane illustrating our parameter variation between runs RB1 and RB2 (more details in 相似文献   

Novel totally implantable trans-ventricular and cross-valvular cannular pump with rolling bearings and purge system for recovery therapy

In the early 1990s, Yamazaki et al. developed a partly intra-ventricular pump, which was inserted into the left ventricle via the apex and then into the aorta through the aortic valve. The pump delivered blood flow directly from the left ventricle to the aorta, like a natural heart, and needed no inflow and outflow connecting tubes; it could be weaned off after the left ventricle had been recovered. The shortcomings were that the driving DC motor remained outside of the ventricle, causing an anatomic space problem, and the sealing and bearing were not appropriate for a durable device. Recently, a totally implantable trans-ventricular pump has been developed in the authors' laboratory. The device has a motor and a pump entirely contained within one cannula. The motor has a motor coil with iron core and a rotor with four-pole magnet; the pump has an impeller and an outflow guide vane. The motor part is 60 mm in length and 13 mm in diameter; the pump part is 55 mm in length and 11 mm in diameter. The total length of the device is therefore 115 mm. The total weight of the device is 53 g. The motor uses rolling bearing with eight needles on each side of the rotor magnets. A special purge system is devised for the infusion of saline mixed with heparin through bearing to the pump inlet (30 – 50 cc per hour). Thus neither mechanical wear nor thrombus formation along the bearing will occur. In haemodynamic testing, the pump can produce a flow of 4 l min^?1 with 60 mmHg pressure increase, at a pump rotating speed of 12 500 rpm. At zero flow rate, corresponding to the diastolic period of the heart, the pump can maintain aortic blood pressure over 80 mmHg at the same rotating speed. This novel pump can be quickly inserted in an emergency and easily removed after recovery of natural heart. It will be useful for patients with acute left ventricular failure.     

微型轴流风扇不同流量下的损失对比

以一种电子元件冷却用的单级微型轴流风扇为研究对象,数值模拟研究了该风扇级的流场,分析了设计转速下驼峰曲线右侧4种流量下损失差异的产生原因。研究结果表明:在转子通道内,损失主要发生在泄漏涡通过的区域(I区)、压力侧边界层区域(II区)以及吸力侧边界层区域(III区)。随着流量的增加,I区叶尖涡系的影响范围变小,但涡量强度的最大值Ω₀变大且都发生在叶顶间隙中,相应地在该区域高损失范围变小,但在其中心区域损失系数ζ_pt值变大;II区高涡强范围及其Ω₀值均变大,相应地该区域高损失范围及其ζ_pt值也变大;III区高涡强范围及其Ω₀值变化不大,相应地该区域高损失范围及其ζ_pt值变化也不大。综上可知:在转子通道内损失随着流量的增加而变大。在静子通道内损失随着流量的增加变化较小,所以级环境下全压效率随着流量的增加而减小。