Four-dimensional flow cardiovascular magnetic resonance aortic cross-sectional pressure changes and their associations with flow patterns in health and ascending thoracic aortic aneurysm.

BACKGROUND: Ascending thoracic aortic aneurysm (ATAA) is a silent and threatening dilation of the ascending aorta (AscAo). Maximal aortic diameter which is currently used for ATAA patients management and surgery planning has been shown to inadequately characterize risk of dissection in a large proportion of patients. Our aim was to propose a comprehensive quantitative evaluation of aortic morphology and pressure-flow-wall associations from four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) data in healthy aging and in patients with ATAA. METHODS: We studied 17 ATAA patients (64.7 ± 14.3 years, 5 females) along with 17 age- and sex-matched healthy controls (59.7 ± 13.3 years, 5 females) and 13 younger healthy subjects (33.5 ± 11.1 years, 4 females). All subjects underwent a CMR exam, including 4D flow and three-dimensional anatomical images of the aorta. This latter dataset was used for aortic morphology measurements, including AscAo maximal diameter (iDMAX) and volume, indexed to body surface area. 4D flow MRI data were used to estimate 1) cross-sectional local AscAo spatial (∆PS) and temporal (∆PT) pressure changes as well as the distance (∆DPS) and time duration (∆TPT) between local pressure peaks, 2) AscAo maximal wall shear stress (WSSMAX) at peak systole, and 3) AscAo flow vorticity amplitude (VMAX), duration (VFWHM), and eccentricity (VECC). RESULTS: Consistency of flow and pressure indices was demonstrated through their significant associations with AscAo iDMAX (WSSMAX:r = -0.49, p < 0.001; VECC:r = -0.29, p = 0.045; VFWHM:r = 0.48, p < 0.001; ∆DPS:r = 0.37, p = 0.010; ∆TPT:r = -0.52, p < 0.001) and indexed volume (WSSMAX:r = -0.63, VECC:r = -0.51, VFWHM:r = 0.53, ∆DPS:r = 0.54, ∆TPT:r = -0.63, p < 0.001 for all). Intra-AscAo cross-sectional pressure difference, ∆PS, was significantly and positively associated with both VMAX (r = 0.55, p = 0.002) and WSSMAX (r = 0.59, p < 0.001) in the 30 healthy subjects (48.3 ± 18.0 years). Associations remained significant after adjustment for iDMAX, age, and systolic blood pressure. Superimposition of ATAA patients to normal aging trends between ∆PS and WSSMAX as well as VMAX allowed identifying patients with substantially high pressure differences concomitant with AscAo dilation. CONCLUSION: Local variations in pressures within ascending aortic cross-sections derived from 4D flow MRI were associated with flow changes, as quantified by vorticity, and with stress exerted by blood on the aortic wall, as quantified by wall shear stress. Such flow-wall and pressure interactions might help for the identification of at-risk patients.

Computational Analysis of Flow Structures in Turbulent Ventricular Blood Flow Associated With Mitral Valve Intervention.

Cardiac disease and clinical intervention may both lead to an increased risk for thrombosis events due to a modified blood flow in the heart, and thereby a change in the mechanical stimuli of blood cells passing through the chambers of the heart. Specifically, the degree of platelet activation is influenced by the level and type of mechanical stresses in the blood flow. In this article we analyze the blood flow in the left ventricle of the heart through a computational model constructed from patient-specific data. The blood flow in the ventricle is modelled by the Navier-Stokes equations, and the flow through the mitral valve by a parameterized model which represents the projected opening of the valve. A finite element method is used to solve the equations, from which a simulation of the velocity and pressure of the blood flow is constructed. The intraventricular blood flow is complex, in particular in diastole when the inflow jet from the atrium breaks down into turbulent flow on a range of scales. A triple decomposition of the velocity gradient tensor is then used to distinguish between rigid body rotational flow, irrotational straining flow, and shear flow. The triple decomposition enables the separation of three fundamentally different flow structures, that each generates a distinct type of mechanical stimulus on the blood cells in the flow. We compare the results in a simulation where a mitral valve clip intervention is modelled, which leads to a significant modification of the intraventricular flow. Further, we perform a sensitivity study of the results with respect to the positioning of the clip. It was found that the shear in the simulation cases treated with clips increased more compared to the untreated case than the rotation and strain did. A decrease in valve opening area of 64% in one of the cases led to a 90% increase in rotation and strain, but a 150% increase in shear. The computational analysis opens up for improvements in models of shear-induced platelet activation, by offering an algorithm to distinguish shear from other modalities in intraventricular blood flow.

Uncertainty quantification of a thrombosis model considering the clotting assay PFA-100®.

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100®). The analysis is facilitated thanks to time-evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of 15 parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity, and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA-100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

A Graph Clustering Approach to Localization for Adaptive Covariance Tuning in Data Assimilation Based on State-Observation Mapping.

An original graph clustering approach for the efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here, the localization term is very generic and refers to the idea of breaking up a global assimilation into subproblems. This unsupervised localization technique based on a linearized state-observation measure is general and does not rely on any prior information such as relevant spatial scales, empirical cutoff radii or homogeneity assumptions. Localization is performed via graph theory, a branch of mathematics emerging as a powerful approach to capturing complex and highly interconnected Earth and environmental systems in computational geosciences. The novel approach automatically segregates the state and observation variables in an optimal number of clusters, and it is more amenable to scalable data assimilation. The application of this method does not require underlying block-diagonal structures of prior covariance matrices. To address intercluster connectivity, two alternative data adaptations are proposed. Once the localization is completed, a covariance diagnosis and tuning are performed within each cluster, whose contribution is sequentially integrated into the entire covariance matrix. Numerical twin experiment tests show the reduced cost and added flexibility of this approach compared to global covariance tuning, and more accurate results yielded for both observation- and background-error parameter tuning.

Reduced-order modeling of hemodynamics across macroscopic through mesoscopic circulation scales.

We propose a hemodynamic reduced-order model bridging macroscopic and mesoscopic blood flow circulation scales from arteries to capillaries. In silico tree-like vascular geometries, mathematically described by graphs, are synthetically generated by means of stochastic growth algorithms constrained by statistical morphological and topological principles. Scale-specific pruning gradation of the tree is then proposed in order to fit computational budget requirement. Different compliant structural models with respect to pressure loads are used depending on vessel walls thicknesses and structures, which vary considerably from macroscopic to mesoscopic circulation scales. Nonlinear rheological properties of blood are also included, and microcirculation network responses are computed for different rheologies. Numerical results are in very good agreement with available experimental measurements. The computational model captures the dynamic transition between large- to small-scale flow pulsatility speeds and magnitudes and wall shear stresses, which have wide-ranging physiological influences.

Kinetics of the coagulation cascade including the contact activation system: sensitivity analysis and model reduction.

Thrombus formation is one of the main issues in the development of blood-contacting medical devices. This article focuses on the modeling of one aspect of thrombosis, the coagulation cascade, which is initiated by the contact activation at the device surface and forms thrombin. Models exist representing the coagulation cascade by a series of reactions, usually solved in quiescent plasma. However, large parameter uncertainty involved in the kinetic models can affect the predictive capabilities of this approach. In addition, the large number of reactions of the kinetic models prevents their use in the simulation of complex flow configurations encountered in medical devices. In the current work, both issues are addressed to improve the applicability and fidelity of kinetic models. A sensitivity analysis is performed by two different techniques to identify the most sensitive parameters of an existing detailed kinetic model of the coagulation cascade. The results are used to select the form of a novel reduced model of the coagulation cascade which relies on eight chemical reactors only. Then, once its parameters have been calibrated thanks to the Bayesian inference, this model shows good predictive capabilities for different initial conditions.

Analysis of aortic pressure fields from 4D flow MRI in healthy volunteers: Associations with age and left ventricular remodeling.

BACKGROUND: Aging-related arterial stiffness is associated with substantial changes in global and local arterial pressures. The subsequent early return of reflected pressure waves leads to an elevated left ventricular (LV) afterload and ultimately to a deleterious concentric LV remodeling. PURPOSE: To compute aortic time-resolved pressure fields of healthy subjects from 4D flow MRI and to define relevant pressure-based markers while investigating their relationship with age, LV remodeling, as well as tonometric augmentation index (AIx) and pulse wave velocity (PWV). STUDY TYPE: Retrospective. POPULATION: Forty-seven healthy subjects (age: 49.5 ± 18 years, 24 women). FIELD STRENGTH/SEQUENCE: 3 T/4D flow MRI. ASSESSMENT: Spatiotemporal pressure fields were computed by integrating velocity-derived pressure gradients using Navier-Stokes equations, while assuming zero pressure at the sino-tubular junction. To quantify aortic pressure spatiotemporal variations, we defined the following markers: 1) volumetric aortic pressure propagation rates ΔP E1 /ΔV and ΔP E2 /ΔV, representing variations of early and late systolic relative pressure peaks along the aorta, respectively, according to the cumulated aortic volume; 2) ΔA PE1-PE2 defined in four aortic regions as the absolute difference between early and late systolic relative pressure peaks amplitude. STATISTICAL TESTS: Linear regression, Wilcoxon rank sum test, Bland-Altman analysis, and intraclass correlation coefficients (ICC). RESULTS: Spatiotemporal variations of aortic pressure peaks were moderately to highly reproducible (ICC ≥0.50) and decreased significantly with age, in terms of absolute magnitude: ΔP E1 /ΔV (r = 0.70, P < 0.005), ΔP E2 /ΔV (r = -0.45, P < 0.005) and ΔA PE1-PE2 (|r| > 0.39, P < 0.005). ΔP E1 /ΔV was associated with LV remodeling (r = 0.53, P < 0.001) and ascending aorta ΔA PE1-PE2 was associated with AIx (r = -0.59, P < 0.001). Both associations were independent of age and systolic blood pressures. Only weak associations were found between pressure indices and PWV (r ≤ 0.40). DATA CONCLUSION: 4D flow MRI relative aortic pressures were consistent with physiological knowledge as demonstrated by their significant volumetric and temporal variations with age and their independent association with LV remodeling and augmentation index. Level of Evidence 2 Technical Efficacy Stage 3 J. Magn. Reson. Imaging 2019;50:982-993.

Uncertainty quantification of inflow boundary condition and proximal arterial stiffness-coupled effect on pulse wave propagation in a vascular network.

This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic simulations of a reduced-order pulse wave propagation model. A simple pulsatile output form is used to reproduce the most relevant cardiac features with a minimum number of parameters associated with left ventricle dynamics. Another source of significant uncertainty is the spatial heterogeneity of the aortic compliance, which plays a key role in the propagation and damping of pulse waves generated at each cardiac cycle. A continuous representation of the aortic stiffness in the form of a generic random field of prescribed spatial correlation is then considered. Making use of a stochastic sparse pseudospectral method, we investigate the sensitivity of the pulse pressure and waves reflection magnitude over the arterial tree with respect to the different model uncertainties. Results indicate that uncertainties related to the shape and magnitude of the prescribed inlet flow in the proximal aorta can lead to potent variation of both the mean value and standard deviation of blood flow velocity and pressure dynamics due to the interaction of different wave propagation and reflection features. Lack of accurate knowledge in the stiffness properties of the aorta, resulting in uncertainty in the pulse wave velocity in that region, strongly modifies the statistical response, with a global increase in the variability of the quantities of interest and a spatial redistribution of the regions of higher sensitivity. These results will provide some guidance in clinical data acquisition and future coupling of arterial pulse wave propagation reduced-order model with more complex beating heart models.

A Robust and Subject-Specific Hemodynamic Model of the Lower Limb Based on Noninvasive Arterial Measurements.

Cardiovascular diseases are currently the leading cause of mortality in the population of developed countries, due to the constant increase in cardiovascular risk factors, such as high blood pressure, cholesterol, overweight, tobacco use, lack of physical activity, etc. Numerous prospective and retrospective studies have shown that arterial stiffening is a relevant predictor of these diseases. Unfortunately, the arterial stiffness distribution across the human body is difficult to measure experimentally. We propose a numerical approach to determine the arterial stiffness distribution of an arterial network using a subject-specific one-dimensional model. The proposed approach calibrates the optimal parameters of the reduced-order model, including the arterial stiffness, by solving an inverse problem associated with the noninvasive in vivo measurements. An uncertainty quantification analysis has also been carried out to measure the contribution of the model input parameters variability, alone or by interaction with other inputs, to the variation of clinically relevant hemodynamic indices, here the arterial pulse pressure. The results obtained for a lower limb model, demonstrate that the numerical approach presented here can provide a robust and subject-specific tool to the practitioner, allowing an early and reliable diagnosis of cardiovascular diseases based on a noninvasive clinical examination.

How to estimate aortic characteristic impedance from magnetic resonance and applanation tonometry data?

OBJECTIVES: Compare seven previous methods for the estimation of aortic characteristic impedance, which contributes to left ventricle pulsatile load, from phase-contrast cardiovascular magnetic resonance (CMR) and applanation tonometry data. METHODS: We studied 77 healthy (43 ±â€Š16 years) individuals and 16 hypertensive (61 ±â€Š9 years) patients, who consecutively underwent ascending aorta CMR and carotid tonometry, resulting in flow and pressure waveforms, respectively. Characteristic impedance was semi-automatically estimated in time domain from these latter waveforms, using seven methods. The methods were based on the following: methods 1-4, magnitudes at specific times; method 5, early-systolic up-slope; method 6, time-derivatives peak; and method 7, pressure-flow loop early-systolic slope. RESULTS: Aortic characteristic impedance was significantly increased in hypertensive patients when compared to elderly controls (n = 32) with a similar mean age of (59 ±â€Š8 years) when using methods based on 95% of peak flow, up-slopes, and derivatives peaks (P < 0.05). When considering healthy individuals, impedance indices were significantly correlated to central pulse pressure for all methods (P < 0.005). Finally, characteristic impedance was correlated to the frequency-domain reference values (r > 0.65, P < 0.0001), with a slight superiority for the same three methods as above (r > 0.82, P < 0.0001). CONCLUSIONS: This is the first study demonstrating phase-contrast CMR and tonometry usefulness in aortic characteristic impedance temporal estimation. Methods based on 95% of peak flow, as well as those based on derivative peaks and up-slopes, which are fast and independent of curve preprocessing, were slightly superior. They can be easily integrated in a clinical workflow and may help to understand the complementarity of this pulsatile index with other CMR aortic geometry and stiffness measures in the setting of left ventricle-aortic coupling.

Noisy inflows cause a shedding-mode switching in flow past an oscillating cylinder.

Vortex streets formed behind oscillating bluff bodies consist of arrays of groups of two, three, or four vortices classified as 2S, P+S, and 2P shedding modes, respectively. The prevailing dominant mode depends primarily on the amplitude and the frequency of the oscillation and on the Reynolds number. We investigate the effect of noise at the inflow on the stability of these vortex modes in laminar flow past a circular cylinder. We employ stochastic simulations based on a new polynomial chaos method to study the shedding-mode switching from a P+S pattern to a 2S mode in the presence of noise.