Method for estimating pulsatile wall shear stress from one-dimensional velocity waveforms.

Wall shear stress (WSS)-a key regulator of endothelial function-is commonly estimated in vivo using simplified mathematical models based on Poiseuille's flow, assuming a quasi-steady parabolic velocity distribution, despite evidence that more rapidly time-varying, pulsatile blood flow during each cardiac cycle modulates flow-mediated dilation (FMD) in large arteries of healthy subjects. More exact and accurate models based on the well-established Womersley solution for rapidly changing blood flow have not been adopted clinically, potentially because the Womersley solution relies on the local pressure gradient, which is difficult to measure non-invasively. We have developed an open-source method for automatic reconstruction of unsteady, Womersley-derived velocity profiles, and WSS in conduit arteries. The proposed method (available online at https://doi.org/10.5281/zenodo.7576408) requires only the time-averaged diameter of the vessel and time-varying velocity data available from non-invasive imaging such as Doppler ultrasound. Validation of the method with subject-specific computational fluid dynamics and application to synthetic velocity waveforms in the common carotid, brachial, and femoral arteries reveals that the Poiseuille solution underestimates peak WSS 38.5%-55.1% during the acceleration and deceleration phases of systole and underestimates or neglects retrograde WSS. Following evidence that oscillatory shear significantly augments vasodilator production, it is plausible that mischaracterization of the shear stimulus by assuming parabolic flow leads to systematic underestimates of important biological effects of time-varying blood velocity in conduit arteries.

Transport of nitrite from large arteries modulates regional blood flow during stress and exercise.

Background: Acute cardiovascular stress increases systemic wall shear stress (WSS)-a frictional force exerted by the flow of blood on vessel walls-which raises plasma nitrite concentration due to enhanced endothelial nitric oxide synthase (eNOS) activity. Upstream eNOS inhibition modulates distal perfusion, and autonomic stress increases both the consumption and vasodilatory effects of endogenous nitrite. Plasma nitrite maintains vascular homeostasis during exercise and disruption of nitrite bioavailability can lead to intermittent claudication. Hypothesis: During acute cardiovascular stress or strenuous exercise, we hypothesize enhanced production of nitric oxide (NO) by vascular endothelial cells raises nitrite concentrations in near-wall layers of flowing blood, resulting in cumulative NO concentrations in downstream arterioles sufficient for vasodilation. Confirmation and implications: Utilizing a multiscale model of nitrite transport in bifurcating arteries, we tested the hypothesis for femoral artery flow under resting and exercised states of cardiovascular stress. Results indicate intravascular transport of nitrite from upstream endothelium could result in vasodilator-active levels of nitrite in downstream resistance vessels. The hypothesis could be confirmed utilizing artery-on-a-chip technology to measure NO production rates directly and help validate numerical model predictions. Further characterization of this mechanism may improve our understanding of symptomatic peripheral artery occlusive disease and exercise physiology.

Hemodynamic modeling of the circle of Willis reveals unanticipated functions during cardiovascular stress.

The circle of Willis (CW) allows blood to be redistributed throughout the brain during local ischemia; however, it is unlikely that the anatomic persistence of the CW across mammalian species is driven by natural selection of individuals with resistance to cerebrovascular disease typically occurring in elderly humans. To determine the effects of communicating arteries (CoAs) in the CW on cerebral pulse wave propagation and blood flow velocity, we simulated young, active adult humans undergoing different states of cardiovascular stress (i.e., fear and aerobic exercise) using discrete transmission line segments with stress-adjusted cardiac output, peripheral resistance, and arterial compliance. Phase delays between vertebrobasilar and carotid pulses allowed bidirectional shunting through CoAs: both posteroanterior shunting before the peak of the pulse waveform and anteroposterior shunting after internal carotid pressure exceeded posterior cerebral pressure. Relative to an absent CW without intact CoAs, the complete CW blunted anterior pulse waveforms, although limited to 3% and 6% reductions in peak pressure and pulse pressure, respectively. Systolic rate of change in pressure (i.e., ∂P/∂t) was reduced 15%-24% in the anterior vasculature and increased 23%-41% in the posterior vasculature. Bidirectional shunting through posterior CoAs was amplified during cardiovascular stress and increased peak velocity by 25%, diastolic-to-systolic velocity range by 44%, and blood velocity acceleration by 134% in the vertebrobasilar arteries. This effect may facilitate stress-related increases in blood flow to the cerebellum (improving motor coordination) and reticular-activating system (enhancing attention and focus) via a nitric oxide-dependent mechanism, thereby improving survival in fight-or-flight situations.NEW & NOTEWORTHY Hemodynamic modeling reveals potential evolutionary benefits of the intact circle of Willis (CW) during fear and aerobic exercise. The CW equalizes pulse waveforms due to bidirectional shunting of blood flow through communicating arteries, which boosts vertebrobasilar blood flow velocity and acceleration. These phenomena may enhance perfusion of the brainstem and cerebellum via nitric oxide-mediated vasodilation, improving performance of the reticular-activating system and motor coordination in survival situations.

Computational modeling of flow-altering surgeries in basilar aneurysms.

In cases where surgeons consider different interventional options for flow alterations in the setting of pathological basilar artery hemodynamics, a virtual model demonstrating the flow fields resulting from each of these options can assist in making clinical decisions. In this study, image-based computational fluid dynamics (CFD) models were used to simulate the flow in four basilar artery aneurysms in order to evaluate postoperative hemodynamics that would result from flow-altering interventions. Patient-specific geometries were constructed using MR angiography and velocimetry data. CFD simulations carried out for the preoperative flow conditions were compared to in vivo phase-contrast MRI measurements (4D Flow MRI) acquired prior to the interventions. The models were then modified according to the procedures considered for each patient. Numerical simulations of the flow and virtual contrast transport were carried out in each case in order to assess postoperative flow fields and estimate the likelihood of intra-aneurysmal thrombus deposition following the procedures. Postoperative imaging data, when available, were used to validate computational predictions. In two cases, where the aneurysms involved vital pontine perforator arteries branching from the basilar artery, idealized geometries of these vessels were incorporated into the CFD models. The effect of interventions on the flow through the perforators was evaluated by simulating the transport of contrast in these vessels. The computational results were in close agreement with the MR imaging data. In some cases, CFD simulations could help determine which of the surgical options was likely to reduce the flow into the aneurysm while preserving the flow through the basilar trunk. The study demonstrated that image-based computational modeling can provide guidance to clinicians by indicating possible outcome complications and indicating expected success potential for ameliorating pathological aneurysmal flow, prior to a procedure.

Flow residence time and regions of intraluminal thrombus deposition in intracranial aneurysms.

Thrombus formation in intracranial aneurysms, while sometimes stabilizing lesion growth, can present additional risk of thrombo-embolism. The role of hemodynamics in the progression of aneurysmal disease can be elucidated by patient-specific computational modeling. In our previous work, patient-specific computational fluid dynamics (CFD) models were constructed from MRI data for three patients who had fusiform basilar aneurysms that were thrombus-free and then proceeded to develop intraluminal thrombus. In this study, we investigated the effect of increased flow residence time (RT) by modeling passive scalar advection in the same aneurysmal geometries. Non-Newtonian pulsatile flow simulations were carried out in base-line geometries and a new postprocessing technique, referred to as "virtual ink" and based on the passive scalar distribution maps, was used to visualize the flow and estimate the flow RT. The virtual ink technique clearly depicted regions of flow separation. The flow RT at different locations adjacent to aneurysmal walls was calculated as the time the virtual ink scalar remained above a threshold value. The RT values obtained in different areas were then correlated with the location of intra-aneurysmal thrombus observed at a follow-up MR study. For each patient, the wall shear stress (WSS) distribution was also obtained from CFD simulations and correlated with thrombus location. The correlation analysis determined a significant relationship between regions where CFD predicted either an increased RT or low WSS and the regions where thrombus deposition was observed to occur in vivo. A model including both low WSS and increased RT predicted thrombus-prone regions significantly better than the models with RT or WSS alone.

Numerical modeling of the flow in intracranial aneurysms: prediction of regions prone to thrombus formation.

The deposition of intralumenal thrombus in intracranial aneurysms adds a risk of thrombo-embolism over and above that posed by mass effect and rupture. In addition to biochemical factors, hemodynamic factors that are governed by lumenal geometry and blood flow rates likely play an important role in the thrombus formation and deposition process. In this study, patient-specific computational fluid dynamics (CFD) models of blood flow were constructed from MRA data for three patients who had fusiform basilar aneurysms that were thrombus free and then proceeded to develop intralumenal thrombus. In order to determine whether features of the flow fields could suggest which regions had an elevated potential for thrombus deposition, the flow was modeled in the baseline, thrombus-free geometries. Pulsatile flow simulations were carried out using patient-specific inlet flow conditions measured with MR velocimetry. Newtonian and non-Newtonian blood behavior was considered. A strong similarity was found between the intra-aneurysmal regions with CFD-predicted slow, recirculating flows and the regions of thrombus deposition observed in vivo in the follow-up MR studies. In two cases with larger aneurysms, the agreement between the low velocity zones and clotted-off regions improved when non-Newtonian blood behavior was taken into account. A similarity was also found between the calculated low shear stress regions and the regions that were later observed to clot.