Fast and Accurate Pressure-Drop Prediction in Straightened Atherosclerotic Coronary Arteries

A novel physics-based model for fast computation of blood flow in coronary arteries

Blood flow and pressure calculated using the currently available methods have shown the potential to predict the progression of pathology, guide treatment strategies and help with postoperative recovery. However, the conspicuous disadvantage of these methods might be the time-consuming nature due to the simulation of virtual interventional treatment. The purpose of this study is to propose a fast novel physics-based model, called FAST, for the prediction of blood flow and pressure. More specifically, blood flow in a vessel is discretized into a number of micro-flow elements along the centerline of the artery, so that when using the equation of viscous fluid motion, the complex blood flow in the artery is simplified into a one-dimensional (1D) steady-state flow. We demonstrate that this method can compute the fractional flow reserve (FFR) derived from coronary computed tomography angiography (CCTA). 345 patients with 402 lesions are used to evaluate the feasibility of the FAST simulation through a comparison with three-dimensional (3D) computational fluid dynamics (CFD) simulation. Invasive FFR is also introduced to validate the diagnostic performance of the FAST method as a reference standard. The performance of the FAST method is comparable with the 3D CFD method. Compared with invasive FFR, the accuracy, sensitivity and specificity of FAST is 88.6%, 83.2% and 91.3%, respectively. The AUC of FFR_FAST is 0.906. This demonstrates that the FAST algorithm and 3D CFD method show high consistency in predicting steady-state blood flow and pressure. Meanwhile, the FAST method also shows the potential in detecting lesion-specific ischemia.

Comparison of LBM and FVM in the estimation of LAD stenosis

The finite volume method (FVM)-based computational fluid dynamics (CFD) technology has been applied in the non-invasive diagnosis of coronary artery stenosis. Nonetheless, FVM is a time-consuming process. In addition to FVM, the lattice Boltzmann method (LBM) is used in fluid flow simulation. Unlike FVM solving the Navier-Stokes equations, LBM directly solves the simplified Boltzmann equation, thus saving computational time. In this study, 12 patients with left anterior descending (LAD) stenosis, diagnosed by CTA, are analysed using FVM and LBM. The velocities, pressures, and wall shear stress (WSS) predicted using FVM and LBM for each patient is compared. In particular, the ratio of the average and maximum speed at the stenotic part characterising the degree of stenosis is compared. Finally, the golden standard of LAD stenosis, invasive fractional flow reserve (FFR), is applied to justify the simulation results. Our results show that LBM and FVM are consistent in blood flow simulation. In the region with a high degree of stenosis, the local flow patterns in those two solvers are slightly different, resulting in minor differences in local WSS estimation and blood speed ratio estimation. Notably, these differences do not result in an inconsistent estimation. Comparison with invasive FFR shows that, in most cases, the non-invasive diagnosis is consistent with FFR measurements. However, in some cases, the non-invasive diagnosis either underestimates or overestimates the degree of stenosis. This deviation is caused by the difference between physiological and simulation conditions that remains the biggest challenge faced by all CFD-based non-invasive diagnostic methods.

A zero-dimensional predictive model for the pressure drop in the stenotic coronary artery based on its geometric characteristics

The diameter- or area-reduction ratio measured from coronary angiography, commonly used in clinical practice, is not accurate enough to represent the functional significance of the stenosis, i.e., the pressure drop across the stenosis. We propose a new zero-dimensional model for the pressure drop across the stenosis considering its geometric characteristics and flow rate. To identify the geometric parameters affecting the pressure drop, we perform three-dimensional numerical simulations for thirty-three patient-specific coronary stenoses. From these numerical simulations, we show that the pressure drop is mostly determined by the curvature as well as the area-reduction ratio of the stenosis before the minimal luminal area (MLA), but heavily depends on the area-expansion ratio after the MLA due to flow separation. Based on this result, we divide the stenosis into the converging and diverging parts in the present zero-dimensional model. The converging part is segmented into a series of straight and curved pipes with curvatures, and the loss of each pipe is estimated by an empirical relation between the total pressure drop, flow rate, and pipe geometric parameters (length, diameter, and curvature). The loss in the diverging part is predicted by a relation among the total pressure drop, Reynolds number, and area expansion ratio with the coefficients determined by a machine learning method. The pressure drops across the stenoses predicted by the present zero-dimensional model agree very well with those obtained from three-dimensional numerical simulations.

Reduced order models for transstenotic pressure drop in the coronary arteries

The efficacy of reduced order modeling for transstenotic pressure drop in the coronary arteries is presented. Coronary artery disease is a leading cause of death worldwide and the computation of fractional flow reserve from computed tomography (FFRct) has become a standard for evaluating the functional significance of a coronary stenosis. FFRct uses 3D computational fluid dynamics to simulate coronary blood flow in order to compute transstenotic pressure drop during simulated hyperemia. In this study, we evaluate different fidelity hydrodynamic models and their ability to compute transstenotic pressure drop and FFRct in the coronary arteries. Models range from simple algebraic formulae to 1D, 2D and 3D time-dependent computational fluid dynamic simulations. Although several algebraic pressure-drop formulae have been proposed in the literature, these models were found to exhibit wide variation in predictions. Nonetheless, we demonstrate an algebraic formula that provides reliable predictions over a range of stenosis severity, morphology, location and flow rate when compared to the current standard for FFRct. The accounting of viscous dissipation, flow separation and pulsatile inertial effects were found to be the most significant contributions to accurate reduce order modeling of transstenotic coronary hemodynamics.

Uncertainty Quantification in a Patient-Specific One-Dimensional Arterial Network Model: EnKF-Based Inflow Estimator

Successful clinical use of patient-specific models for cardiovascular dynamics depends on the reliability of the model output in the presence of input uncertainties. For 1D fluid dynamics models of arterial networks, input uncertainties associated with the model output are related to the specification of vessel and network geometry, parameters within the fluid and wall equations, and parameters used to specify inlet and outlet boundary conditions. This study investigates how uncertainty in the flow profile applied at the inlet boundary of a 1D model affects area and pressure predictions at the center of a single vessel. More specifically, this study develops an iterative scheme based on the ensemble Kalman filter (EnKF) to estimate the temporal inflow profile from a prior distribution of curves. The EnKF-based inflow estimator provides a measure of uncertainty in the size and shape of the estimated inflow, which is propagated through the model to determine the corresponding uncertainty in model predictions of area and pressure. Model predictions are compared to ex vivo area and blood pressure measurements in the ascending aorta, the carotid artery, and the femoral artery of a healthy male Merino sheep. Results discuss dynamics obtained using a linear and a nonlinear viscoelastic wall model.

The effects of curvature and constriction on airflow and energy loss in pathological tracheas

This paper considers factors that play a significant role in determining inspiratory pressure and energy losses in the human trachea. Previous characterisations of pathological geometry changes have focussed on relating airway constriction and subsequent pressure loss, however many pathologies that affect the trachea cause deviation, increased curvature, constriction or a combination of these. This study investigates the effects of these measures on tracheal flow mechanics, using the compressive goitre (a thyroid gland enlargement) as an example. Computational fluid dynamics simulations were performed in airways affected by goitres (with differing geometric consequences) and a normal geometry for comparison. Realistic airways, derived from medical images, were used because idealised geometries often oversimplify the complex anatomy of the larynx and its effects on the flow. Two mechanisms, distinct from stenosis, were found to strongly affect airflow energy dissipation in the pathological tracheas. The jet emanating from the glottis displayed different impingement and breakdown patterns in pathological geometries and increased loss was associated with curvature.

Influence of the Accuracy of Angiography-Based Reconstructions on Velocity and Wall Shear Stress Computations in Coronary Bifurcations: A Phantom Study

INTRODUCTION

Wall shear stress (WSS) plays a key role in the onset and progression of atherosclerosis in human coronary arteries. Especially sites with low and oscillating WSS near bifurcations have a higher propensity to develop atherosclerosis. WSS computations in coronary bifurcations can be performed in angiography-based 3D reconstructions. It is essential to evaluate how reconstruction errors influence WSS computations in mildly-diseased coronary bifurcations. In mildly-diseased lesions WSS could potentially provide more insight in plaque progression.

MATERIALS METHODS

Four Plexiglas phantom models of coronary bifurcations were imaged with bi-plane angiography. The lumens were segmented by two clinically experienced readers. Based on the segmentations 3D models were generated. This resulted in three models per phantom: one gold-standard from the phantom model itself, and one from each reader. Steady-state and transient simulations were performed with computational fluid dynamics to compute the WSS. A similarity index and a noninferiority test were used to compare the WSS in the phantoms and their reconstructions. The margin for this test was based on the resolution constraints of angiography.

RESULTS

The reconstruction errors were similar to previously reported data; in seven out of eight reconstructions less than 0.10 mm. WSS in the regions proximal and far distal of the stenosis showed a good agreement. However, the low WSS areas directly distal of the stenosis showed some disagreement between the phantoms and the readers. This was due to small deviations in the reconstruction of the stenosis that caused differences in the resulting jet, and consequently the size and location of the low WSS area.

DISCUSSION

This study showed that WSS can accurately be computed within angiography-based 3D reconstructions of coronary arteries with early stage atherosclerosis. Qualitatively, there was a good agreement between the phantoms and the readers. Quantitatively, the low WSS regions directly distal to the stenosis were sensitive to small reconstruction errors.

Functional and anatomical measures for outflow boundary conditions in atherosclerotic coronary bifurcations

The aim of this research was finding the influence of anatomy-based and functional-based outflow boundary conditions for computational fluid dynamics (CFD) on fractional flow reserve (FFR) and wall shear stress (WSS) in mildly diseased coronary bifurcations. For 10 patient-specific bifurcations three simulations were set up with different outflow conditions, while the inflow was kept constant. First, the outflow conditions were based on the diameter of the outlets. Second, they were based on the volume estimates of the myocardium that depended on the outlets. Third, they were based on a myocardial flow measure derived from computed tomography perfusion imaging (CTP). The difference in outflow ratio between the perfusion-based and the diameter-based approach was -7 p.p. [-14 p.p.:7 p.p.] (median percentage point and interquartiles), and between the perfusion-based and volume-based this was -2 p.p. [-2 p.p.:1 p.p.]. Despite of these differences the computed FFRs matched very well. A quantitative analysis of the WSS results showed very high correlations between the methods with an r(2) ranging from 0.90 to 1.00. But despite the high correlations the diameter-based and volume-based approach generally underestimated the WSS compared to the perfusion-based approach. These differences disappeared after normalization. We demonstrated the potential of CTP for setting patient-specific boundary conditions for atherosclerotic coronary bifurcations. FFR and normalized WSS were unaffected by the variations in outflow ratios. In order to compute absolute WSS a functional measure to set the outflow ratio might be of added value in this type of vessels.