Computational fluid dynamics models are increasingly proposed for assisting the diagnosis and management of vascular diseases. Ideally, patient-specific flow measurements are used to impose flow boundary conditions. When patient-specific flow measurements are unavailable, mean values of flow measurements across small cohorts are used as normative values. In reality, both the between-subjects and within-subject flow variabilities are large. Consequently, neither one-shot flow measurements nor mean values across a cohort are truly indicative of the flow regime in a given person. We develop models for both the between-subjects and within-subject variability of internal carotid flow. A log-linear mixed effects model is combined with a Gaussian process to model the between-subjects flow variability, while a lumped parameter model of cerebral autoregulation is used to model the within-subject flow variability in response to heart rate and blood pressure changes. The model parameters are identified from carotid ultrasound measurements in a cohort of 103 elderly volunteers. We use the models to study intracranial aneurysm flow in 54 subjects under rest and exercise and conclude that OSI, a common wall shear-stress derived quantity in vascular CFD studies, may be too sensitive to flow fluctuations to be a reliable biomarker.KEYWORDS cerebrovascular disease, computational fluid dynamics, Gaussian process models, patient-specific models, uncertainty quantification Numerous computational fluid dynamics (CFD) models of human cardiovascular and cerebrovascular physiology are published every year, but few of them make any impact in clinical practice. This inconvenient truth has been blamed on the improper use of CFD solvers, 1 insufficient validation of biomechanics models, 2 and lack of understanding of the clinical decision-making process by the biomedical engineers building the models. 3 One additional explanation is that many "patient-specific" CFD models fail to consider the physiological variability of vascular flow, confounding interpretation of model results and producing overly confident predictions of flow quantities.Patient-specific modelling of vascular flow requires an accurate description of the lumen plus the definition of boundary conditions. The latter is done by measuring patient-specific flow waveforms using either phase contrast magnetic resonance imaging (pcMRI) or ultrasound-based flow measurement techniques. When patient-specific flow measurements are not available, cohort-averaged values of flow from the literature are often used. For example, the small-scale studies 4-6 Int J Numer Meth Biomed Engng. 2020;36:e3271.wileyonlinelibrary.com/journal/cnm
Our objective is to study the collimation of solar jets by nonlinear forces corresponding to torsional Alfvén waves together with external forces. We consider a straight, initially non-rotating, untwisted magnetic cylinder embedded in a plasma with a straight magnetic field, where a shear between the internal and external flows exists. By implementing magnetohydrodynamic theory and taking into account the second-order thin flux tube approximation, the balance between the internal nonlinear forces is visualized. The nonlinear differential equation containing the ponderomotive, magnetic tension, and centrifugal forces in the presence of the shear flow is obtained. The solution presents the scale of influence of the propagating torsional Alfvén wave on compressive perturbations. Explicit expressions for the compressive perturbations caused by the forces connected to the torsional Alfvén wave show that, in the presence of a shear flow, the magnetic tension and centrifugal forces do not cancel each other’s effects as they did in its absence. This shear flow plays in favor of the magnetic tension force, resulting in a more efficient collimation. Regarding the ponderomotive force, the shear flow has no effect. The phase relations highlight the interplay of the shear flow and the plasma-β. As the shear flow and plasma-β increase, compressive perturbation amplitudes emerge. We conclude that the jet collimation due to the torsional Alfvén wave highly depends on the location of the jet. The shear flow tightens the collimation as the jet elevates up to the solar corona.
The aim of this study is to model the nature of nonlinear torsional magnetohydrodynamic waves propagating in solar jets as they are elevated to the outer solar atmosphere. The contribution of sequential processes to the transfer of energy is taken under consideration: the nonlinear cascade and shock formation. Thus a straight magnetic cylinder embedded in a plasma with an initial magnetic field and parallel flow to the cylinder axis is implemented. To resemble a jet where the oscillation wavelength highly exceeds the radius, the second-order thin flux tube approximation proves adequate. A Cohen–Kulsrud type equation is presented, and its solution highly depends on the parameter presented in this study, which itself is constituted of various environmental and equilibrium conditions that affect the perturbations of the variables as well as the nonlinear forces connected to Alfvén wave propagation. The shock formation time of torsional waves is inversely proportional to the density contrast of the jet, while the efficiency of energy transfer to shorter scales is directly proportional to the density contrast. While the parallel flow with a shear at the boundary expedites shock formation, its efficiency regarding energy transfer is dramatically enhanced by the plasma-β, significantly contributing to coronal heating. The observational and seismological aspect of the present study is that faster jets are less probable for observations at higher altitudes, as they experience energy transfer mostly at the base of the corona, while slow speed jets may be observed at higher altitudes contributing to solar wind acceleration.
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