Computational models to predict stenosis growth in carotid arteries: Which is the role of boundary conditions?

Differential sensitivities to blood pressure variations in internal carotid and intracranial arteries: a numerical approach to stroke prediction

Stroke remains a global health concern, necessitating early prediction for effective management. Atherosclerosis-induced internal carotid and intra cranial stenosis contributes significantly to stroke risk. This study explores the relationship between blood pressure and stroke prediction, focusing on internal carotid artery (ICA) branches: middle cerebral artery (MCA), anterior cerebral artery (ACA), and their role in hemodynamics. Computational fluid dynamics (CFD) informed by the Windkessel model were employed to simulate patient-specific ICA models with introduced stenosis. Central to our investigation is the impact of stenosis on blood pressure, flow velocity, and flow rate across these branches, incorporating Fractional Flow Reserve (FFR) analysis. Results highlight differential sensitivities to blood pressure variations, with M1 branch showing high sensitivity, ACA moderate, and M2 minimal. Comparing blood pressure fluctuations between ICA and MCA revealed heightened sensitivity to potential reverse flow compared to ICA and ACA comparisons, emphasizing MCA's role. Blood flow adjustments due to stenosis demonstrated intricate compensatory mechanisms. FFR emerged as a robust predictor of stenosis severity, particularly in the M2 branch. In conclusion, this study provides comprehensive insights into hemodynamic complexities within major intracranial arteries, elucidating the significance of blood pressure variations, flow attributes, and FFR in stenosis contexts. Subject-specific data integration enhances model reliability, aiding stroke risk assessment and advancing cerebrovascular disease understanding.

Personalised simulation of hemodynamics in cerebrovascular disease: lessons learned from a study of diagnostic accuracy

Intracranial atherosclerotic disease (ICAD) poses a significant risk of subsequent stroke but current prevention strategies are limited. Mechanistic simulations of brain hemodynamics offer an alternative precision medicine approach by utilising individual patient characteristics. For clinical use, however, current simulation frameworks have insufficient validation. In this study, we performed the first quantitative validation of a simulation-based precision medicine framework to assess cerebral hemodynamics in patients with ICAD against clinical standard perfusion imaging. In a retrospective analysis, we used a 0-dimensional simulation model to detect brain areas that are hemodynamically vulnerable to subsequent stroke. The main outcome measures were sensitivity, specificity, and area under the receiver operating characteristics curve (ROC AUC) of the simulation to identify brain areas vulnerable to subsequent stroke as defined by quantitative measurements of relative mean transit time (relMTT) from dynamic susceptibility contrast MRI (DSC-MRI). In 68 subjects with unilateral stenosis >70% of the internal carotid artery (ICA) or middle cerebral artery (MCA), the sensitivity and specificity of the simulation were 0.65 and 0.67, respectively. The ROC AUC was 0.68. The low-to-moderate accuracy of the simulation may be attributed to assumptions of Newtonian blood flow, rigid vessel walls, and the use of time-of-flight MRI for geometric representation of subject vasculature. Future simulation approaches should focus on integrating additional patient data, increasing accessibility of precision medicine tools to clinicians, addressing disease burden disparities amongst different populations, and quantifying patient benefit. Our results underscore the need for further improvement of mechanistic simulations of brain hemodynamics to foster the translation of the technology to clinical practice.

An analytical method informed by clinical imaging data for estimating outlet boundary conditions in computational fluid dynamics analysis of carotid artery blood flow

Stroke occur mainly due to arterial thrombosis and rupture of cerebral blood vessels. Previous studies showed that blood flow-induced wall shear stress is an essential bio marker for estimating atherogenesis. It is a common practice to use computational fluid dynamics (CFD) simulations to calculate wall shear stress and to quantify blood flow. Reliability of predicted CFD results greatly depends on the accuracy of applied boundary conditions. Previously, the boundary conditions were estimated by varying values so that they matched the clinical data. It is applicable upon the availability of clinical data. Meanwhile, in most cases all that can be accessed are arterial geometry and inflow rate. Consequently, there is a need to devise a tool to estimate boundary values such as resistance and compliance of arteries. This study proposes an analytical framework to estimate the boundary conditions for a carotid artery based on the geometries of the downstream arteries available from clinical images.

Patient-Specific Cerebral Blood Flow Simulation Based on Commonly Available Clinical Datasets

Cerebral hemodynamics play an important role in the development of cerebrovascular diseases. In this work, we propose a numerical framework for modeling patient-specific cerebral blood flow, using commonly available clinical datasets. Our hemodynamic model was developed using Simscape Fluids library in Simulink, based on a block diagram language. Medical imaging data obtained from computerized tomography angiography (CTA) in 59 patients with aneurysmal subarachnoid hemorrhage was used to extract arterial geometry parameters. Flow information obtained from transcranial Doppler (TCD) measurement was employed to calibrate input parameters of the hemodynamic model. The results show that the proposed numerical model can reproduce blood flow in the circle of Willis (CoW) per patient per measurement set. The resistance at the distal end of each terminal branch was the predominant parameter for the flow distribution in the CoW. The proposed model may be a promising tool for assessing cerebral hemodynamics in patients with cerebrovascular disease.

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan circulations.

Suitability of lattice Boltzmann inlet and outlet boundary conditions for simulating flow in image-derived vasculature

The lattice Boltzmann method (LBM) is a popular alternative to solving the Navier-Stokes equations for modeling blood flow. When simulating flow using the LBM, several choices for inlet and outlet boundary conditions exist. While boundary conditions in the LBM have been evaluated in idealized geometries, there have been no extensive comparisons in image-derived vasculature, where the geometries are highly complex. In this study, the Zou-He (ZH) and finite difference (FD) boundary conditions were evaluated in image-derived vascular geometries by comparing their stability, accuracy, and run times. The boundary conditions were compared in four arteries: a coarctation of the aorta, dissected aorta, femoral artery, and left coronary artery. The FD boundary condition was more stable than ZH in all four geometries. In general, simulations using the ZH and FD method showed similar convergence rates within each geometry. However, the ZH method proved to be slightly more accurate compared with experimental flow using three-dimensional printed vasculature. The total run times necessary for simulations using the ZH boundary condition were significantly higher as the ZH method required a larger relaxation time, grid resolution, and number of time steps for a simulation representing the same physiological time. Finally, a new inlet velocity profile algorithm is presented for complex inlet geometries. Overall, results indicated that the FD method should generally be used for large-scale blood flow simulations in image-derived vasculature geometries. This study can serve as a guide to researchers interested in using the LBM to simulate blood flow.

A velocity tracking approach for the data assimilation problem in blood flow simulations

Several advances have been made in data assimilation techniques applied to blood flow modeling. Typically, idealized boundary conditions, only verified in straight parts of the vessel, are assumed. We present a general approach, on the basis of a Dirichlet boundary control problem, that may potentially be used in different parts of the arterial system. The relevance of this method appears when computational reconstructions of the 3D domains, prone to be considered sufficiently extended, are either not possible, or desirable, because of computational costs. On the basis of taking a fully unknown velocity profile as the control, the approach uses a discretize then optimize methodology to solve the control problem numerically. The methodology is applied to a realistic 3D geometry representing a brain aneurysm. The results show that this data assimilation approach may be preferable to a pressure control strategy and that it can significantly improve the accuracy associated to typical solutions obtained using idealized velocity profiles.

Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging

Blood flow patterns and local hemodynamic parameters have been widely associated with the onset and progression of atherosclerosis in the carotid artery. Assessment of these parameters can be performed noninvasively using cine phase-contrast (PC) magnetic resonance imaging (MRI). In addition, in the last two decades, computational fluid dynamics (CFD) simulation in three dimensional models derived from anatomic medical images has been employed to investigate the blood flow in the carotid artery. This study developed a workflow of a subject-specific CFD analysis using MRI to enhance estimating hemodynamics of the carotid artery. Time-of-flight (TOF) MRI scans were used to construct three-dimensional computational models. PC-MRI measurements were utilized to impose the boundary condition at the inlet and a 0-dimensional lumped parameter model was employed for the outflow boundary condition. The choice of different viscosity models of blood flow as a source of uncertainty was studied, by means of the axial velocity, wall shear stress, and oscillatory shear index. The sequence of workflow in CFD analysis was optimized for a healthy subject using PC-MRI. Then, a patient with carotid artery stenosis and its hemodynamic parameters were examined. The simulations indicated that the lumped parameter model used at the outlet gives physiologically reasonable values of hemodynamic parameters. Moreover, the dependence of hemodynamics parameters on the viscosity models was observed to vary for different geometries. Other factors, however, may be required for a more accurate CFD analysis, such as the segmentation and smoothness of the geometrical model, mechanical properties of the artery's wall, and the prescribed velocity profile at the inlet.

Recent advances in computational methodology for simulation of mechanical circulatory assist devices

Ventricular assist devices (VADs) provide mechanical circulatory support to offload the work of one or both ventricles during heart failure. They are used in the clinical setting as destination therapy, as bridge to transplant, or more recently as bridge to recovery to allow for myocardial remodeling. Recent developments in computational simulation allow for detailed assessment of VAD hemodynamics for device design and optimization for both children and adults. Here, we provide a focused review of the recent literature on finite element methods and optimization for VAD simulations. As VAD designs typically fall into two categories, pulsatile and continuous flow devices, we separately address computational challenges of both types of designs, and the interaction with the circulatory system with three representative case studies. In particular, we focus on recent advancements in finite element methodology that have increased the fidelity of VAD simulations. We outline key challenges, which extend to the incorporation of biological response such as thrombosis and hemolysis, as well as shape optimization methods and challenges in computational methodology.

Simulation based planning of surgical interventions in pediatric cardiology

Hemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.

Hemodynamics analysis of patient-specific carotid bifurcation: a CFD model of downstream peripheral vascular impedance

The study of cardiovascular models was presented in this paper based on medical image reconstruction and computational fluid dynamics. Our aim is to provide a reality platform for the purpose of flow analysis and virtual intervention outcome predication for vascular diseases. By connecting two porous mediums with transient permeability at the downstream of the carotid bifurcation branches, a downstream peripheral impedance model was developed, and the effect of the downstream vascular bed impedance can be taken into consideration. After verifying its accuracy with a healthy carotid bifurcation, this model was implemented in a diseased carotid bifurcation analysis. On the basis of time-averaged wall shear stress, oscillatory shear index, and the relative residence time, fractions of abnormal luminal surface were highlighted, and the atherosclerosis was assessed from a hemodynamic point of view. The effect of the atherosclerosis on the transient flow division between the two branches because of the existence of plaque was also analysed. This work demonstrated that the proposed downstream peripheral vascular impedance model can be used for computational modelling when the outlets boundary conditions are not available, and successfully presented the potential of using medical imaging and numerical simulation to provide existing clinical prerequisites for diagnosis and therapeutic treatment.

A black-box decomposition approach for coupling heterogeneous components in hemodynamics simulations

This work presents a generic and efficient black-box approach for the strong iterative coupling of dimensionally heterogeneous flow models in computational hemodynamics. A heterogeneous model of the cardiovascular system is formed by several vascular black-box components, which are connected through coupling equations. The associated system of equations is solved using the Broyden algorithm. In addition, a multiple time-stepping strategy is introduced to meet different component requirements. The proposed algorithm is employed to split a 3D-1D-0D closed-loop model of the cardiovascular system into corresponding black-box components standing for the 3D (specific vessels), 1D (systemic arteries/peripheral vessels), and 0D (venous/cardiac/pulmonary circulation) components. Examples of application are presented showing the robustness and suitability of this novel approach.

Effect of head posture on the healthy human carotid bifurcation hemodynamics

Head and neck postures may cause morphology changes to the geometry of the carotid bifurcation (CB) that alter the low and oscillating wall shear stress (WSS) regions previously reported as important in the development of atherosclerosis. Here the right and left CB were imaged by MRI in two healthy subjects in the neutral head posture with the subject in the supine position and in two other head postures with the subject in the prone position: (1) rightward rotation up to 80°, and (2) leftward rotation up to 80°. Image-based computational models were constructed to investigate the effect of posture on arterial geometry and local hemodynamics. The area exposure to unfavorable hemodynamics, based on thresholds set for oscillatory shear index (OSI), WSS and relative residence time, was used to quantify the hemodynamic impact on the wall. Torsion of the head was found to: (1) cause notable changes in the bifurcation and internal carotid artery angles and, in most cases, on cross-sectional area ratios for common, internal and external carotid artery, (2) change the spatial distribution of wall regions exposed to unfavorable hemodynamics, and (3) cause a marked change in the hemodynamic burden on the wall when the OSI was considered. These findings suggest that head posture may be associated with the genesis and development of atherosclerotic disease as well as complications in stenotic and stented vessels.

Fluid-structure interaction simulations of the Fontan procedure using variable wall properties

Children born with single ventricle heart defects typically undergo a staged surgical procedure culminating in a total cavopulmonary connection (TCPC) or Fontan surgery. The goal of this work was to perform physiologic, patient-specific hemodynamic simulations of two post-operative TCPC patients by using fluid-structure interaction (FSI) simulations. Data from two patients are presented, and post-op anatomy is reconstructed from MRI data. Respiration rate, heart rate, and venous pressures are obtained from catheterization data, and inflow rates are obtained from phase contrast MRI data and are used together with a respiratory model. Lumped parameter (Windkessel) boundary conditions are used at the outlets. We perform FSI simulations by using an arbitrary Lagrangian-Eulerian finite element framework to account for motion of the blood vessel walls in the TCPC. This study is the first to introduce variable elastic properties for the different areas of the TCPC, including a Gore-Tex conduit. Quantities such as wall shear stresses and pressures at critical locations are extracted from the simulation and are compared with pressure tracings from clinical data as well as with rigid wall simulations. Hepatic flow distribution and energy efficiency are also calculated and compared for all cases. There is little effect of FSI on pressure tracings, hepatic flow distribution, and time-averaged energy efficiency. However, the effect of FSI on wall shear stress, instantaneous energy efficiency, and wall motion is significant and should be considered in future work, particularly for accurate prediction of thrombus formation.

Three-dimensional simulations in Glenn patients: clinically based boundary conditions, hemodynamic results and sensitivity to input data

While many congenital heart defects can be treated without significant long term sequelae, some achieve successful palliation as their definitive endpoints. The single-ventricle defect is one such defect and leaves the child with only one operational ventricle, requiring the systemic and the pulmonary circulations to be placed in series through several operations performed during early childhood. Numerical simulations may be used to investigate these hemodynamic conditions and their relation to post-operative sequelae; however, they rely heavily on boundary condition prescription. In this study, we investigate the impact of hemodynamic input data uncertainties on simulation results. Imaged-based patient-specific models of the multi-branched pulmonary arteries and superior vena cava were built for five cavopulmonary connection (i.e. Glenn) patients. Magnetic resonance imaging and catheterization data were acquired for each patient prior to their Fontan surgery. Inflow and outflow boundary conditions were constructed to match available clinical data and resulted in the development of a framework to incorporate these types of clinical data into patient-specific simulations. Three-dimensional computational fluid dynamics simulations were run and hemodynamic indicators were computed. Power loss was low (and efficiency very high) and a linear correlation was found between power loss and cardiac index among the five patients. Other indicators such as low wall shear stress were considered to better characterize these patients. Flow was complex and oscillatory near the anastomosis, and laminar in the smaller branches. While common trends were seen among patients, results showed differences among patients, especially in the 3D maps, strengthening the importance of patient-specific simulations. A sensitivity analysis was performed to investigate the impact of input data (clinical and modeling) to construct boundary conditions on several indicators. Overall, the sensitivity of the output indicators to the input data was small but non-negligible. The sensitivity of commonly used hemodynamic indicators to compare patients is discussed in this context. Power efficiency was much more sensitive to pressure variation than power loss. To increase the precision of such indicators, mean flow split between right and left lungs needs to be measured with more accuracy with higher priority than refining the model of how the flow is distributed on average among the smaller branches. Although ± 10% flow split imprecision seemed reasonable in terms of patient comparison, this study suggests that the common practice of imposing a right pulmonary artery/left pulmonary artery flow split of 55%/45% when performing patient specific simulations should be avoided. This study constitutes a first step towards understanding the hemodynamic differences between pre- and post Fontan surgery, predicting these differences, and evaluating surgical outcomes based on preoperative data.

Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation

Mounting evidence suggests that the pulsatile character of blood pressure and flow within large arteries plays a particularly important role as a mechano-biological stimulus for wall growth and remodeling. Nevertheless, understanding better the highly coupled interactions between evolving wall geometry, structure, and properties and the hemodynamics will require significantly more experimental data. Computational fluid-solid-growth models promise to aid in the design and interpretation of such experiments and to identify candidate mechanobiological mechanisms for the observed arterial adaptations. Motivated by recent aortic coarctation models in animals, we used a computational fluid-solid interaction model to study possible local and systemic effects on the hemodynamics within the thoracic aorta and coronary, carotid, and cerebral arteries due to a distal aortic coarctation and subsequent spatial variations in wall adaptation. In particular, we studied an initial stage of acute cardiac compensation (i.e., maintenance of cardiac output) followed by early arterial wall remodeling (i.e., spatially varying wall thickening and stiffening). Results suggested, for example, that while coarctation increased both the mean and pulse pressure in the proximal vessels, the locations nearest to the coarctation experienced the greatest changes in pulse pressure. In addition, after introducing a spatially varying wall adaptation, pressure, left ventricular work, and wave speed all increased. Finally, vessel wall strain similarly experienced spatial variations consistent with the degree of vascular wall adaptation.

Sequential Structural and Fluid Dynamic Numerical Simulations of a Stented Bifurcated Coronary Artery

Despite their success, stenting procedures are still associated to some clinical problems like sub-acute thrombosis and in-stent restenosis. Several clinical studies associate these phenomena to a combination of both structural and hemodynamic alterations caused by stent implantation. Recently, numerical models have been widely used in the literature to investigate stenting procedures but always from either a purely structural or fluid dynamic point of view. The aim of this work is the implementation of sequential structural and fluid dynamic numerical models to provide a better understanding of stenting procedures in coronary bifurcations. In particular, the realistic geometrical configurations obtained with structural simulations were used to create the fluid domains employed within transient fluid dynamic analyses. This sequential approach was applied to investigate the final kissing balloon (FKB) inflation during the provisional side branch technique. Mechanical stresses in the arterial wall and the stent as well as wall shear stresses along the arterial wall were examined before and after the FKB deployment. FKB provoked average mechanical stresses in the arterial wall almost 2.5 times higher with respect to those induced by inflation of the stent in the main branch only. Results also enlightened FKB benefits in terms of improved local blood flow pattern for the side branch access. As a drawback, the FKB generates a larger region of low wall shear stress. In particular, after FKB the percentage of area characterized by wall shear stresses lower than 0.5 Pa was 79.0%, while before the FKB it was 62.3%. For these reasons, a new tapered balloon dedicated to bifurcations was proposed. The inclusion of the modified balloon has reduced the mechanical stresses in the proximal arterial vessel to 40% and the low wall shear stress coverage area to 71.3%. In conclusion, these results show the relevance of the adopted sequential approach to study the wall mechanics and the hemodynamics created by stent deployment.

Outflow Conditions for Image-Based Hemodynamic Models of the Carotid Bifurcation: Implications for Indicators of Abnormal Flow

Computational fluid dynamics (CFD) models have become very effective tools for predicting the flow field within the carotid bifurcation, and for understanding the relationship between local hemodynamics, and the initiation and progression of vascular wall pathologies. As prescribing proper boundary conditions can affect the solutions of the equations governing blood flow, in this study, we investigated the influence to assumptions regarding the outflow boundary conditions in an image-based CFD model of human carotid bifurcation. Four simulations were conducted with identical geometry, inlet flow rate, and fluid parameters. In the first case, a physiological time-varying flow rate partition at branches along the cardiac cycle was obtained by coupling the 3D model of the carotid bifurcation at outlets with a lumped-parameter model of the downstream vascular network. Results from the coupled model were compared with those obtained by imposing three fixed flow rate divisions (50/50, 60/40, and 70/30) between the two branches of the isolated 3D model of the carotid bifurcation. Three hemodynamic wall parameters were considered as indicators of vascular wall dysfunction. Our findings underscore that the overall effect of the assumptions done in order to simulate blood flow within the carotid bifurcation is mainly in the hot-spot modulation of the hemodynamic descriptors of atherosusceptible areas, rather than in their distribution. In particular, the more physiological, time-varying flow rate division deriving from the coupled simulation has the effect of damping wall shear stress (WSS) oscillations (differences among the coupled and the three fixed flow partition models are up to 37.3% for the oscillating shear index). In conclusion, we recommend to adopt more realistic constraints, for example, by coupling models at different scales, as in this study, when the objective is the outcome prediction of alternate therapeutic interventions for individual patients, or to test hypotheses related to the role of local fluid dynamics and other biomechanical factors in vascular diseases.

Recent advances in the application of computational mechanics to the diagnosis and treatment of cardiovascular disease

During the last 30 years, research into the pathogenesis and progression of cardiovascular disease has had to employ a multidisciplinary approach involving a wide range of subject areas, from molecular and cell biology to computational mechanics and experimental solid and fluid mechanics. In general, research was driven by the need to provide answers to questions of critical importance for disease management. Ongoing improvements in the spatial resolution of medical imaging equipment coupled to an exponential growth in the capacity, flexibility and speed of computational techniques have provided a valuable opportunity for numerical simulations and complex experimental techniques to make a contribution to improving the diagnosis and clinical management of many forms of cardiovascular disease. This paper contains a review of recent progress in the numerical simulation of cardiovascular mechanics, focusing on three particular areas: patient-specific modeling and the optimization of surgery in pediatric cardiology, evaluating the risk of rupture in aortic aneurysms, and noninvasive characterization of intraventricular flow in the management of heart failure.