A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models

Fluid-structure interaction analysis of a healthy aortic valve and its surrounding haemodynamics

The opening and closing dynamics of the aortic valve (AV) has a strong influence on haemodynamics in the aortic root, and both play a pivotal role in maintaining normal physiological functions of the valve. The aim of this study was to establish a subject-specific fluid-structure interaction (FSI) workflow capable of simulating the motion of a tricuspid healthy valve and the surrounding haemodynamics under physiologically realistic conditions. A subject-specific aortic root was reconstructed from magnetic resonance (MR) images acquired from a healthy volunteer, whilst the valve leaflets were built using a parametric model fitted to the subject-specific aortic root geometry. The material behaviour of the leaflets was described using the isotropic hyperelastic Ogden model, and subject-specific boundary conditions were derived from 4D-flow MR imaging (4D-MRI). Strongly coupled FSI simulations were performed using a finite volume-based boundary conforming method implemented in FlowVision. Our FSI model was able to simulate the opening and closing of the AV throughout the entire cardiac cycle. Comparisons of simulation results with 4D-MRI showed a good agreement in key haemodynamic parameters, with stroke volume differing by 7.5% and the maximum jet velocity differing by less than 1%. Detailed analysis of wall shear stress (WSS) on the leaflets revealed much higher WSS on the ventricular side than the aortic side and different spatial patterns amongst the three leaflets.

Global sensitivity analysis with multifidelity Monte Carlo and polynomial chaos expansion for vascular haemodynamics

Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample-based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol' sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three-dimensional fluid-structure interaction simulations with affordable one- and zero-dimensional reduced-order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi- (1D/0D) and tri-fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single-fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol' indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response.

Guidelines for mechanistic modeling and analysis in cardiovascular research

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Critical role of arterial constitutive model in predicting blood pressure from pulse wave velocity

BACKGROUND

A promising approach to cuff-less, continuous blood pressure monitoring is to estimate blood pressure (BP) from Pulse Wave Velocity (PWV). However, most existing PWV-based methods rely on empirical BP-PWV relations and have large prediction errors, which may be caused by the implicit assumption of thin-walled, linear elastic arteries undergoing small deformations. Our objective is to understand the BP-PWV relationship in the absence of such limiting assumptions.

METHOD

We performed Fluid-Structure Interaction (FSI) simulations of the radial artery and the common carotid artery under physiological flow conditions. In these dynamic simulations, we employed two constitutive models for the arterial wall: the linear elastic model, implying a thin-walled linear elastic artery undergoing small deformations, and the Holzapfel-Gasser-Ogden (HGO) model, accounting for the nonlinear effects of collagen fibers and their orientations on the large arterial deformation.

RESULTS

Despite the changing BP, the linear elastic model predicts a constant PWV throughout a cardiac cycle, which is not physiological. The HGO model correctly predicts a positive BP-PWV correlation by capturing the nonlinear deformation of the artery, showing up to 50 % variations of PWV in a cardiac cycle.

CONCLUSION

Dynamic FSI simulations reveal that the BP-PWV relationship strongly depends on the arterial constitutive model, especially in the radial artery. To infer BP from PWV, one must account for the varying PWV, a consequence of the nonlinear arterial response due to collagen fibers. Future efforts should be directed towards robust measurement of time-varying PWV if it is to be used to predict BP.

A new method for scaling inlet flow waveform in hemodynamic analysis of aortic dissection

Computational fluid dynamics (CFD) simulations have shown great potentials in cardiovascular disease diagnosis and postoperative assessment. Patient-specific and well-tuned boundary conditions are key to obtaining accurate and reliable hemodynamic results. However, CFD simulations are usually performed under non-patient-specific flow conditions due to the absence of in vivo flow and pressure measurements. This study proposes a new method to overcome this challenge by tuning inlet boundary conditions using data extracted from electrocardiogram (ECG). Five patient-specific geometric models of type B aortic dissection were reconstructed from computed tomography (CT) images. Other available data included stoke volume (SV), ECG, and 4D-flow magnetic resonance imaging (MRI). ECG waveforms were processed to extract patient-specific systole to diastole ratio (SDR). Inlet boundary conditions were defined based on a generic aortic flow waveform tuned using (1) SV only, and (2) with ECG and SV (ECG + SV). 4D-flow MRI derived inlet boundary conditions were also used in patient-specific simulations to provide the gold standard for comparison and validation. Simulations using inlet flow waveform tuned with ECG + SV not only successfully reproduced flow distributions in the descending aorta but also provided accurate prediction of time-averaged wall shear stress (TAWSS) in the primary entry tear (PET) and abdominal regions, as well as maximum pressure difference, ∆Pmax, from the aortic root to the distal false lumen. Compared with simulations with inlet waveform tuned with SV alone, using ECG + SV in the tuning method significantly reduced the error in false lumen ejection fraction at the PET (from 149.1% to 6.2%), reduced errors in TAWSS at the PET (from 54.1% to 5.7%) and in the abdominal region (from 61.3% to 11.1%), and improved ∆Pmax prediction (from 283.1% to 18.8%) However, neither of these inlet waveforms could be used for accurate prediction of TAWSS in the ascending aorta. This study demonstrates the importance of SDR in tailoring inlet flow waveforms for patient-specific hemodynamic simulations. A well-tuned flow waveform is essential for ensuring that the simulation results are patient-specific, thereby enhancing the confidence and fidelity of computational tools in future clinical applications.

Efficient Cardiovascular Parameters Estimation for Fluid-Structure Simulations Using Gappy Proper Orthogonal Decomposition

As full-scale detailed hemodynamic simulations of the entire vasculature are not feasible, numerical analysis should be focused on specific regions of the cardiovascular system, which requires the identification of lumped parameters to represent the patient behavior outside the simulated computational domain. We present a novel technique for estimating cardiovascular model parameters using gappy Proper Orthogonal Decomposition (g-POD). A POD basis is constructed with FSI simulations for different values of the lumped model parameters, and a linear operator is applied to retain information that can be compared to the available patient measurements. Then, the POD coefficients of the reconstructed solution are computed either by projecting patient measurements or by solving a minimization problem with constraints. The POD reconstruction is then used to estimate the model parameters. In the first test case, the parameter values of a 3-element Windkessel model are approximated using artificial patient measurements, obtaining a relative error of less than 4.2%. In the second case, 4 sets of 3-element Windkessel are approximated in a patient's aorta geometry, resulting in an error of less than 8% for the flow and less than 5% for the pressure. The method shows accurate results even with noisy patient data. It automatically calculates the delay between measurements and simulations and has flexibility in the types of patient measurements that can handle (at specific points, spatial or time averaged). The method is easy to implement and can be used in simulations performed in general-purpose FSI software.

Estimating pulmonary arterial remodeling via an animal-specific computational model of pulmonary artery stenosis

Pulmonary artery stenosis (PAS) often presents in children with congenital heart disease, altering blood flow and pressure during critical periods of growth and development. Variability in stenosis onset, duration, and severity result in variable growth and remodeling of the pulmonary vasculature. Computational fluid dynamics (CFD) models enable investigation into the hemodynamic impact and altered mechanics associated with PAS. In this study, a one-dimensional (1D) fluid dynamics model was used to simulate hemodynamics throughout the pulmonary arteries of individual animals. The geometry of the large pulmonary arteries was prescribed by animal-specific imaging, whereas the distal vasculature was simulated by a three-element Windkessel model at each terminal vessel outlet. Remodeling of the pulmonary vasculature, which cannot be measured in vivo, was estimated via model-fitted parameters. The large artery stiffness was significantly higher on the left side of the vasculature in the left pulmonary artery (LPA) stenosis group, but neither side differed from the sham group. The sham group exhibited a balanced distribution of total distal vascular resistance, whereas the left side was generally larger in the LPA stenosis group, with no significant differences between groups. In contrast, the peripheral compliance on the right side of the LPA stenosis group was significantly greater than the corresponding side of the sham group. Further analysis indicated the underperfused distal vasculature likely moderately decreased in radius with little change in stiffness given the increase in thickness observed with histology. Ultimately, our model enables greater understanding of pulmonary arterial adaptation due to LPA stenosis and has potential for use as a tool to noninvasively estimate remodeling of the pulmonary vasculature.

Effect of veno-arterial extracorporeal membrane oxygenation lower-extremity cannulation on intra-arterial flow characteristics, oxygen content, and thrombosis risk

PURPOSE

This study aimed to investigate the effects of lower-extremity cannulation on the intra-arterial hemodynamic environment, oxygen content, blood damage, and thrombosis risk under different levels of veno-arterial (V-A) ECMO support.

METHODS

Computational fluid dynamics methods were used to investigate the effects of different levels of ECMO support (ECMO flow ratios supplying oxygen-rich blood 100-40 %). Flow rates and oxygen content in each arterial branch were used to determine organ perfusion. A new thrombosis model considering platelet activation and deposition was proposed to determine the platelet activation and thrombosis risk at different levels of ECMO support. A red blood cell damage model was used to explore the risk of hemolysis.

RESULTS

Our study found that partial recovery of cardiac function improved the intra-arterial hemodynamic environment, with reduced impingement of the intra-arterial flow field by high-velocity blood flow from the cannula, a flow rate per unit time into each arterial branch closer to physiological levels, and improved perfusion in the lower extremities. Partial recovery of cardiac function helps reduce intra-arterial high shear stress and residence time, thereby reducing blood damage. The overall level of hemolysis and platelet activation in the aorta decreased with the gradual recovery of cardiac contraction function. The areas at high risk of thrombosis under V-A ECMO femoral cannulation support were the aortic root and the area distal to the cannula, which moved to the descending aorta when cardiac function recovered to 40-60 %. However, with the recovery of cardiac contraction function, hypoxic blood pumped by the heart is insufficient in supplying oxygen to the front of the aortic arch, which may result in upper extremity hypoxia.

CONCLUSION

We developed a thrombosis risk prediction model applicable to ECMO cannulation and validated the model accuracy using clinical data. Partial recovery of cardiac function contributed to an improvement in the aortic hemodynamic environment and a reduction in the risk of blood damage; however, there is a potential risk of insufficient perfusion of oxygen-rich blood to organs.

Age and sex-dependent sensitivity analysis of a common carotid artery model

The common carotid artery (CCA) is an accessible and informative site for assessing cardiovascular function which makes it a prime candidate for clinically relevant computational modelling. The interpretation of supplemental information possible through modelling is encumbered by measurement uncertainty and population variability in model parameters. The distribution of model parameters likely depends on the specific sub-population of interest and delineation based on sex, age or health status may correspond to distinct ranges of typical parameter values. To assess this impact in a 1D-CCA-model, we delineated specific sub-populations based on age, sex and health status and carried out uncertainty quantification and sensitivity analysis for each sub-population. We performed a structured literature review to characterize sub-population-specific variabilities for eight model parameters without consideration of health status; variations for a healthy sub-populations were based on previously established references values. The variabilities of diameter and distensibility found in the literature review differed from those previously established in a healthy population. Model diameter change and pulse pressure were most sensitive to variations in distensibility, while pressure was most sensitive to resistance in the Windkessel model for all groups. Uncertainties were lower when variabilities were based on a healthy sub-population; however, the qualitative distribution of sensitivity indices was largely similar between the healthy and general population. Average sensitivity of the pressure waveform showed a moderate dependence on age with decreasing sensitivity to distal resistance and increasing sensitivity to distensibility and diameter. The female population was less sensitive to variations in diameter but more sensitive to distensibility coefficient than the male population. Overall, as hypothesized input variabilities differed between sub-populations and resulted in distinct uncertainties and sensitivities of the 1D-CCA-model outputs, particularly over age for the pressure waveform and between males and females for pulse pressure.

Patient-specific closed-loop model of the fontan circulation: Calibration and validation

The Fontan circulation, designed for managing patients with a single functional ventricle, presents challenges in long-term outcomes. Computational methods offer potential solutions, yet their application in cardiology practice remains largely unexplored. Our aim was to assess the ability of a patient-specific, closed-loop, reduced-order blood flow model to simulate pulsatile blood flow in the Fontan circulation. Using one-dimensional models, we simulated the aorta, superior and inferior venae cavae, and right and left pulmonary arteries, while lumping heart chambers and remaining vessels into zero-dimensional models. The model was calibrated with patient-specific haemodynamic data from combined cardiac catheterisation and magnetic resonance exams, using a novel physics-based stepwise methodology involving simpler open-loop models. Testing on a 10-year-old, anesthetised patient, demonstrated the model's capability to replicate pulsatile pressure and flow in the larger vessels and ventricular pressure. Average relative errors in mean pressure and flow were 2.9 % and 3.6 %, with average relative point-to-point errors (RPPE) in pressure and flow at 5.2 % and 16.0 %. Comparing simulation results to measurements, mean aortic pressure and flow values were 50.7 vs. 50.4 mmHg and 41.6 vs. 41.9 ml/s, respectively, while ventricular pressure values were 28.7 vs. 27.4 mmHg. The model accurately described time-varying ventricular volume with a RPPE of 2.9 %, with mean, minimum, and maximum ventricular volume values for simulation results vs. measurements at 59.2 vs. 58.2 ml, 38.0 vs. 37.6 ml, and 76.0 vs. 74.4 ml, respectively. It provided physiologically realistic predictions of haemodynamic changes from pulmonary vasodilation and atrial fenestration opening. The new model and calibration methodology are freely available, offering a platform to virtually investigate the Fontan circulation's response to clinical interventions and explore potential mechanisms of Fontan failure. Future efforts will concentrate on broadening the model's applicability to a wider range of patient populations and clinical scenarios, as well as testing its effectiveness.

Blood flow and emboli transport patterns during venoarterial extracorporeal membrane oxygenation: A computational fluid dynamics study

PROBLEM

Despite advances in Venoarterial Extracorporeal Membrane Oxygenation (VA-ECMO), a significant mortality rate persists due to complications. The non-physiological blood flow dynamics of VA-ECMO may lead to neurological complications and organ ischemia. Continuous retrograde high-flow oxygenated blood enters through a return cannula placed in the femoral artery which opposes the pulsatile deoxygenated blood ejected by the left ventricle (LV), which impacts upper body oxygenation and subsequent hyperoxemia. The complications underscore the critical need to comprehend the impact of VA-ECMO support level and return cannula size, as mortality remains a significant concern.

AIM

The aim of this study is to predict and provide insights into the complications associated with VA-ECMO using computational fluid dynamics (CFD) simulations. These complications will be assessed by characterising blood flow and emboli transport patterns through a comprehensive analysis of the influence of VA-ECMO support levels and arterial return cannula sizes.

METHODS

Patient-specific 3D aortic and major branch models, derived from a male patient's CT scan during VA-ECMO undergoing respiratory dysfunction, were analyzed using CFD. The investigation employed species transport and discrete particle tracking models to study ECMO blood (oxygenated) mixing with LV blood (deoxygenated) and to trace emboli transport patterns from potential sources (circuit, LV, and aorta wall). Two cannula sizes (15 Fr and 19 Fr) were tested alongside varying ECMO pump flow rates (50%, 70%, and 90% of the total cardiac output).

RESULTS

Cannula size did not significantly affect oxygen transport. At 90% VA-ECMO support, all arteries distal to the aortic arch achieved 100% oxygen saturation. As support level decreased, oxygen transport to the upper body also decreased to a minimum saturation of 73%. Emboli transport varied substantially between emboli origin and VAECMO support level, with the highest risk of cerebral emboli coming from the LV with a 15 Fr cannula at 90% support.

CONCLUSION

Arterial return cannula sizing minimally impacted blood oxygen distribution; however, it did influence the distribution of emboli released from the circuit and aortic wall. Notably, it was the support level alone that significantly affected the mixing zone of VA-ECMO and cardiac blood, subsequently influencing the risk of embolization of the cardiogenic source and oxygenation levels across various arterial branches.

An in silico study of the effects of cardiovascular aging on carotid flow waveforms and indexes in a virtual population

Cardiovascular aging is strongly associated with increased risk of cardiovascular disease and mortality. Moreover, health and lifestyle factors may accelerate age-induced alterations, such as increased arterial stiffness and wall dilation, beyond chronological age, making the clinical assessment of cardiovascular aging an important prompt for preventative action. Carotid flow waveforms contain information about age-dependent cardiovascular properties, and their ease of measurement via noninvasive Doppler ultrasound (US) makes their analysis a promising tool for the routine assessment of cardiovascular aging. In this work, the impact of different aging processes on carotid waveform morphology and derived indexes is studied in silico, with the aim of establishing the clinical potential of a carotid US-based assessment of cardiovascular aging. One-dimensional (1-D) hemodynamic modeling was employed to generate an age-specific virtual population (VP) of N = 5,160 realistic carotid hemodynamic waveforms. The resulting VP was statistically validated against in vivo aging trends in waveforms and indexes from the literature, and simulated waveforms were studied in relation to age and underlying cardiovascular parameters. In our study, the carotid flow augmentation index (FAI) significantly increased with age (with a median increase of 50% from the youngest to the oldest age group) and was strongly correlated to local arterial stiffening (r = 0.94). The carotid pulsatility index (PI), which showed less pronounced age variation, was inversely correlated with the reflection coefficient at the carotid branching (r = -0.88) and directly correlated with carotid net forward wave energy (r = 0.90), corroborating previous literature where it was linked to increased risk of cerebrovascular damage in the elderly. There was a high correlation between corrected carotid flow time (ccFT) and cardiac output (CO) (r = 0.99), which was not affected by vascular age. This study highlights the potential of carotid waveforms as a valuable tool for the assessment of cardiovascular aging.NEW & NOTEWORTHY An age-specific virtual population was generated based on a 1-D model of the arterial circulation, including newly defined literature-based specific age variations in carotid vessel properties. Simulated carotid flow/velocity waveforms, indexes, and age trends were statistically validated against in vivo data from the literature. A comprehensive study of the impact of aging on carotid flow waveform morphology was performed, and the mechanisms influencing different carotid indexes were elucidated. Notably, flow augmentation index (FAI) was found to be a strong indicator of local carotid stiffness.

Central Artery Hemodynamics in Angiotensin II-Induced Hypertension and Effects of Anesthesia

Systemic hypertension is a strong risk factor for cardiovascular, neurovascular, and renovascular diseases. Central artery stiffness is both an initiator and indicator of hypertension, thus revealing a critical relationship between the wall mechanics and hemodynamics. Mice have emerged as a critical animal model for studying effects of hypertension and much has been learned. Regardless of the specific mouse model, data on changes in cardiac function and hemodynamics are necessarily measured under anesthesia. Here, we present a new experimental-computational workflow to estimate awake cardiovascular conditions from anesthetized data, which was then used to quantify effects of chronic angiotensin II-induced hypertension relative to normotension in wild-type mice. We found that isoflurane anesthesia had a greater impact on depressing hemodynamics in angiotensin II-infused mice than in controls, which led to unexpected results when comparing anesthetized results between the two groups of mice. Through comparison of the awake simulations, however, in vivo relevant effects of angiotensin II-infusion on global and regional vascular structure, properties, and hemodynamics were found to be qualitatively consistent with expectations. Specifically, we found an increased in vivo vascular stiffness in the descending thoracic aorta and suprarenal abdominal aorta, leading to increases in pulse pressure in the distal aorta. These insights allow characterization of the impact of regionally varying vascular remodeling on hemodynamics and mouse-to-mouse variations due to induced hypertension.

Tube law parametrization using in vitro data for one-dimensional blood flow in arteries and veins: TUBE LAW PARAMETRIZATION IN ARTERIES AND VEINS

The deformability of blood vessels in one-dimensional blood flow models is typically described through a pressure-area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena. Here, we present a novel mathematical-property-preserving approach for the estimation of the parameters of the elastic and viscoelastic tube laws. Our goal was to estimate the parameters by using ovine and human in vitro data, while constraining them to meet prescribed mathematical properties. Results show that both elastic and viscoelastic tube laws accurately describe experimental pressure-area data concerning both quantitative and qualitative aspects. Additionally, the viscoelastic tube law can provide a qualitative explanation for the observed hysteresis cycles. The two models were evaluated using two approaches: (i) allowing all parameters to freely vary within their respective ranges and (ii) fixing some of the parameters. The former approach was found to be the most suitable for reproducing pressure-area curves.

Development of a 3D Vascular Network Visualization Platform for One-Dimensional Hemodynamic Simulation

Recent advancements in computational performance and medical simulation technology have made significant strides, particularly in predictive diagnosis. This study focuses on the blood flow simulation reduced-order models, which provide swift and cost-effective solutions for complex vascular systems, positioning them as practical alternatives to 3D simulations in resource-limited medical settings. The paper introduces a visualization platform for patient-specific and image-based 1D-0D simulations. This platform covers the entire workflow, from modeling to dynamic 3D visualization of simulation results. Two case studies on, respectively, carotid stenosis and arterial remodeling demonstrate its utility in blood flow simulation applications.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Modeling and evaluation of biomechanics and hemodynamic based on patient-specific small intracranial aneurysm using fluid-structure interaction

BACKGROUND AND OBJECTIVE

Rupture of small intracranial aneurysm (IA) often leads to the development of highly fatal clinical syndromes such as subarachnoid hemorrhage. Due to the patient specificity of small IA, there are many difficulties in evaluating the rupture risk of small IA such as multiple influencing factors, high clinical experience requirements and poor reusability.

METHODS

In this study, clinical methods such as transcranial doppler (TCD) and magnetic resonance imaging (MRI) are used to obtain patient-specific parameters, and the fluid-structure interaction method (FSI) is used to model and evaluate the biomechanics and hemodynamics of patient-specific small IA.

RESULTS

The results show that a spiral vortex stably exists in the patient-specific small IA. Due to the small size of the patient-specific small IA, the blood flow velocity still maintains a high value with maximum reaching 3 m/s. The inertial impact of blood flow and vortex convection have certain influence on hemodynamic and biomechanics parameters. They cause three high value areas of WSSM on the patient-specific small IA with maximum of 180 Pa, 130 Pa and 110 Pa, respectively. They also cause two types of WSS concentration points, positive normal stress peak value areas and negative normal stress peak value areas to appear.

CONCLUSION

This paper found that the factors affecting hemodynamic parameters and biomechanical parameters are different. Unlike hemodynamic parameters, biomechanical parameters are also affected by blood pressure in addition to blood flow velocity. This study reveals the relationship between the flow field distribution and changes of patient-specific small IA, biomechanics and hemodynamics.

Accelerated simulation methodologies for computational vascular flow modelling

Vascular flow modelling can improve our understanding of vascular pathologies and aid in developing safe and effective medical devices. Vascular flow models typically involve solving the nonlinear Navier-Stokes equations in complex anatomies and using physiological boundary conditions, often presenting a multi-physics and multi-scale computational problem to be solved. This leads to highly complex and expensive models that require excessive computational time. This review explores accelerated simulation methodologies, specifically focusing on computational vascular flow modelling. We review reduced order modelling (ROM) techniques like zero-/one-dimensional and modal decomposition-based ROMs and machine learning (ML) methods including ML-augmented ROMs, ML-based ROMs and physics-informed ML models. We discuss the applicability of each method to vascular flow acceleration and the effectiveness of the method in addressing domain-specific challenges. When available, we provide statistics on accuracy and speed-up factors for various applications related to vascular flow simulation acceleration. Our findings indicate that each type of model has strengths and limitations depending on the context. To accelerate real-world vascular flow problems, we propose future research on developing multi-scale acceleration methods capable of handling the significant geometric variability inherent to such problems.

A comparative study of altered hemodynamics in iliac vein compression syndrome

Introduction: Iliac vein compression syndrome (IVCS) is present in over 20% of the population and is associated with left leg pain, swelling, and thrombosis. IVCS symptoms are thought to be induced by altered pelvic hemodynamics, however, there currently exists a knowledge gap on the hemodynamic differences between IVCS and healthy patients. To elucidate those differences, we carried out a patient-specific, computational modeling comparative study. Methods: Computed tomography and ultrasound velocity and area data were used to build and validate computational models for a cohort of IVCS (N = 4, Subject group) and control (N = 4, Control group) patients. Flow, cross-sectional area, and shear rate were compared between the right common iliac vein (RCIV) and left common iliac vein (LCIV) for each group and between the Subject and Control groups for the same vessel. Results: For the IVCS patients, LCIV mean shear rate was higher than RCIV mean shear rate (550 ± 103 s-1 vs. 113 ± 48 s-1, p = 0.0009). Furthermore, LCIV mean shear rate was higher in the Subject group than in the Control group (550 ± 103 s-1 vs. 75 ± 37 s-1, p = 0.0001). Lastly, the LCIV/RCIV shear rate ratio was 4.6 times greater in the Subject group than in the Control group (6.56 ± 0.9 vs. 1.43 ± 0.6, p = 0.00008). Discussion: Our analyses revealed that IVCS patients have elevated shear rates which may explain a higher thrombosis risk and suggest that their thrombus initiation process may share aspects of arterial thrombosis. We have identified hemodynamic metrics that revealed profound differences between IVCS patients and Controls, and between RCIV and LCIV in the IVCS patients. Based on these metrics, we propose that non-invasive measurement of shear rate may aid with stratification of patients with moderate compression in which treatment is highly variable. More investigation is needed to assess the prognostic value of shear rate and shear rate ratio as clinical metrics and to understand the mechanisms of thrombus formation in IVCS patients.

Modelling large scale artery haemodynamics from the heart to the eye in response to simulated microgravity

We investigated variations in haemodynamics in response to simulated microgravity across a semi-subject-specific three-dimensional (3D) continuous arterial network connecting the heart to the eye using computational fluid dynamics (CFD) simulations. Using this model we simulated pulsatile blood flow in an upright Earth gravity case and a simulated microgravity case. Under simulated microgravity, regional time-averaged wall shear stress (TAWSS) increased and oscillatory shear index (OSI) decreased in upper body arteries, whilst the opposite was observed in the lower body. Between cases, uniform changes in TAWSS and OSI were found in the retina across diameters. This work demonstrates that 3D CFD simulations can be performed across continuously connected networks of small and large arteries. Simulated results exhibited similarities to low dimensional spaceflight simulations and measured data-specifically that blood flow and shear stress decrease towards the lower limbs and increase towards the cerebrovasculature and eyes in response to simulated microgravity, relative to an upright position in Earth gravity.

Learning reduced-order models for cardiovascular simulations with graph neural networks

Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience loss in accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 3% for pressure and flow rate, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models while maintaining high efficiency at inference time.

A hemodynamic analysis of fenestrated physician-modified endograft repair for complicated aortic dissections involving the visceral arteries

OBJECTIVE

The aim of this study is to perform patient-specific hemodynamic simulations of the patients with complicated aortic dissection underwent Physician-modified endograft (PMEG) and evaluate the treatment outcome.

METHOD

12 patient-specific models were reconstructed from computed tomography angiography (CTA) data of 6 patients with complicated aortic dissection before and after the PMEG. Hemodynamic simulations were conducted with the same time-varying volumetric flow rate extracted from the literature and 3-element Windkessel model (3 EWM) boundary conditions were applied at the aortic outlet. Hemodynamic indicators such as time-averaged wall shear stress (TAWSS), relative residence time (RRT) and endothelial cell activation potential (ECAP) were obtained to evaluate the postoperative effect of PMEG.

RESULTS

Comparing with the preoperative models, the flow rates of most visceral arteries were increased in the postoperative models (PSMA = 0.012, PRRA = 0.013, and PLRA = 0.005). Pressure and TAWSS in visceral regions were significantly reduced (PP = 0.003 and PTAWSS = 0.017). With the false lumens (FL) covered by the stent grafts, the average TAWSS level increased in the regions of postoperative abdominal aorta (P = 0.002), and the average RRT and ECAP values decreased significantly (PRRT = 0.02 and PECAP = 0.003).

CONCLUSION

This study shows that PMEG, as a new technique for the treatment of complicated aortic dissection involving the distal tears in the visceral region, can effectively restore the abnormal blood supply of the visceral arteries, reduce the risk of aortic rupture, the formation of aortic dissection aneurysm (ADA), and thrombosis. This corresponds well with clinical retrospective studies and 1-year follow-up outcomes. The findings of this study are of great significance for the development of PMEG.

Numerical coupling of 0D and 1D models in networks of vessels including transonic flow conditions. Application to short-term transient and stationary hemodynamic simulation of postural changes

When modeling complex fluid networks using one-dimensional (1D) approaches, boundary conditions can be imposed using zero-dimensional (0D) models. An application case is the modeling of the entire human circulation using closed-loop models. These models can be considered as a tool to investigate short-term transient and stationary hemodynamic responses to postural changes. The first shortcoming of existing 1D modeling methods in simulating these sudden maneuvers is their inability to deal with rapid variations in flow conditions, as they are limited to the subsonic case. On the other hand, numerical modeling of 0D models representing microvascular beds, venous valves or heart chambers is also currently modeled assuming subsonic flow conditions in 1D connecting vessels, failing when transonic and supersonic flow conditions appear. Therefore, if numerical simulation of sudden maneuvers is a goal in closed-loop models, it is necessary to reformulate the current methodologies used when coupling 0D and 1D models, allowing the correct handling of flow evolution for both subsonic and transonic conditions. This work focuses on the extension of the general methodology for the Junction Riemann Problem (JRP) when coupling 0D and 1D models. As an example of application, the short-term transient response to head-up tilt (HUT) from supine to upright position of a closed-loop model is shown, demonstrating the potential, capability and necessity of the presented numerical models when dealing with sudden maneuvers.

Liver fibrosis emulation: Impact of the vascular fibrotic alterations on hemodynamics

The liver circulatory system comprises two blood supply vascular trees (the hepatic artery and portal venous networks), microcirculation through the hepatic capillaries (the sinusoids), and a blood drainage vascular tree (the hepatic vein network). Vasculature changes due to fibrosis -located predominantly at the microcirculation level- lead to a marked increase in resistance to flow causing an increase in portal pressure (portal hypertension). Here, we present a liver fibrosis/cirrhosis model. We build on our 1D model of the healthy hepatic circulation, which considers the elasticity of the vessels walls and the pulsatile character of blood flow and pressure, and recreate the deteriorated liver vasculature due to fibrosis. We emulate altered sinusoids by fibrous tissue (stiffened, compressed and splitting) and propose boundary conditions to investigate the impact of fibrosis on hemodynamic variables within the organ. We obtain that the sinusoids stiffness leads to changes in the amplitude and shape of the blood flow and pressure waveforms but not in their mean value. For the compressed and splitting sinusoids, we observe significant increases in the mean value and amplitude of the pressure waveform in the altered sinusoids and in the portal venous network. In other words, we obtain the portal hypertension clinically observed in fibrotic/cirrhotic patients. We also study the extent of the spreading fibrosis by performing the structural fibrotic changes in an increasingly number of sinusoids. Finally, we calculate the portal pressure gradient (PPG) in the model and obtain values in agreement with those reported in the literature for fibrotic/cirrhotic patients.

Signatures of obstructions and expansions in the arterial frequency response

BACKGROUND AND OBJECTIVE

The blood pressure and flow waveforms carry valuable information about the condition of the cardiovascular system and a patient's health. Waveform analysis in health and pathological conditions can be performed in the time or frequency domains; the information to be emphasised defines the use of either domain. However, physicians are more familiar with the time domain, and the changes in the waveforms due to cardiovascular diseases and ageing are better characterised in such domain. On the other hand, the analysis of the vascular and geometrical variables determining the signatures in the frequency response of local vascular anomalies, such as aneurysms and stenoses, has not been thoroughly explored. This paper aims to characterise the signatures of obstructions (stenoses) and expansions (aneurysms) in the frequency response of tapered arteries.

METHODS

The first step in our methodology was to incorporate the viscous response of the arterial wall into a one-dimensional elastic formulation that solves the governing equations in the frequency domain. As a second step, we imposed a volumetric flow excitation in arteries simulating the aorta with increasing geometry complexity: from straight to tapered arteries with local expansions or obstructions; and we assessed the frequency response.

RESULTS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that are distinguishable from a health condition. The signatures of obstruction and expansions differ; the obstructions increase the magnitude of fundamental frequency and work as a close boundary condition. On the other hand, the expansions diminish the fundamental frequency and work as an open boundary condition. Furthermore, such signatures correlate to the distance between the artery's inlet and the anomaly's starting point and have the potential to pinpoint abnormalities non-invasively.

CONCLUSIONS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that have the potential to detect and follow up on the development of vascular abnormalities. For the latter purpose, constant monitoring may be required; despite this not being a common clinical practice, the new wearable technology offers the possibility of continuous monitoring of biophysical markers such as the pressure waveform.

The Impact of Left Ventricular Assist Device Outflow Graft Positioning on Aortic Hemodynamics: Improving Flow Dynamics to Mitigate Aortic Insufficiency

Heart failure is a global health concern with significant implications for healthcare systems. Left ventricular assist devices (LVADs) provide mechanical support for patients with severe heart failure. However, the placement of the LVAD outflow graft within the aorta has substantial implications for hemodynamics and can lead to aortic insufficiency during long-term support. This study employs computational fluid dynamics (CFD) simulations to investigate the impact of different LVAD outflow graft locations on aortic hemodynamics. The introduction of valve morphology within the aorta geometry allows for a more detailed analysis of hemodynamics at the aortic root. The results demonstrate that the formation of vortex rings and subsequent vortices during the high-velocity jet flow from the graft interacted with the aortic wall. Time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) indicate that modification of the outflow graft location changes mechanical states within the aortic wall and aortic valve. Among the studied geometric factors, both the height and inclination angle of the LVAD outflow graft are important in controlling retrograde flow to the aortic root, while the azimuthal angle primarily determines the rotational direction of blood flow in the aortic arch. Thus, precise positioning of the LVAD outflow graft emerges as a critical factor in optimizing patient outcomes by improving the hemodynamic environment.

An ultrasound imaging and computational fluid dynamics protocol to assess hemodynamics in iliac vein compression syndrome

OBJECTIVE

Elevated shear rates are known to play a role in arterial thrombosis; however, shear rates have not been thoroughly investigated in patients with iliac vein compression syndrome (IVCS) owing to imaging limitations and assumptions on the low shear nature of venous flows. This study was undertaken to develop a standardized protocol that quantifies IVCS shear rates and can aid in the diagnosis and treatment of patients with moderate yet symptomatic compression.

METHODS

Study patients with and without IVCS had their iliac vein hemodynamics measured via duplex ultrasound (US) at two of the following three vessel locations: infrarenal inferior vena cava (IVC), right common iliac vein, and left common iliac vein, in addition to acquiring data at the right and left external iliac veins. US velocity spectra were multiplied by a weighted cross-sectional area calculated from US and computed tomography (CT) data to create flow waveforms. Flow waveforms were then scaled to enforce conservation of flow across the IVC and common iliac veins. A three-dimensional (3D), patient-specific model of the iliac vein anatomy was constructed from CT and US examination. Flow waveforms and the 3D model were used as a basis to run a computational fluid dynamics (CFD) simulation. Owing to collateral vessel flow and discrepancies between CT and US area measurements, flows in internal iliac veins and cross-sectional areas of the common iliac veins were calibrated iteratively against target common iliac flow. Simulation results on mean velocity were validated against US data at measurement locations. Simulation results were postprocessed to derive spatial and temporal values of quantities such as velocity and shear rate.

RESULTS

Using our modeling protocol, we were able to build CFD models of the iliac veins that matched common iliac flow splits within 2% and measured US velocities within 10%. Proof-of-concept analyses (1 subject, 1 control) have revealed that patients with IVCS may experience elevated shear rates in the compressed left common iliac vein, more typical of the arterial rather than the venous circulation. These results encourage us to extend this protocol to a larger group of patients with IVCS and controls.

CONCLUSIONS

We developed a protocol that obtains hemodynamic measurements of the IVC and iliac veins from US, creates patient-specific 3D reconstructions of the venous anatomy using CT and US examinations, and computes shear rates using calibrated CFD methods. Proof-of-concept results have indicated that patients with IVCS may experience elevated shear rates in the compressed left common iliac vein. Larger cohorts are needed to assess the relationship between venous compression and shear rates in patients with IVCS as compared with controls with noncompressed iliac veins. Further studies using this protocol may also give promising insights into whether or not to treat patients with moderate, yet symptomatic compression.

Haemodynamic changes in visceral hybrid repairs of type III and type V thoracoabdominal aortic aneurysms

The visceral hybrid procedure combining retrograde visceral bypass grafting and completion endovascular stent grafting is a feasible alternative to conventional open surgical or wholly endovascular repairs of thoracoabdominal aneurysms (TAAA). However, the wide variability in visceral hybrid configurations means that a priori prediction of surgical outcome based on haemodynamic flow profiles such as velocity pattern and wall shear stress post repair remain challenging. We sought to appraise the clinical relevance of computational fluid dynamics (CFD) analyses in the setting of visceral hybrid TAAA repairs. Two patients, one with a type III and the other with a type V TAAA, underwent successful elective and emergency visceral hybrid repairs, respectively. Flow patterns and haemodynamic parameters were analysed using reconstructed pre- and post-operative CT scans. Both type III and type V TAAAs showed highly disturbed flow patterns with varying helicity values preoperatively within their respective aneurysms. Low time-averaged wall shear stress (TAWSS) and high endothelial cell action potential (ECAP) and relative residence time (RRT) associated with thrombogenic susceptibility was observed in the posterior aspect of both TAAAs preoperatively. Despite differing bypass configurations in the elective and emergency repairs, both treatment options appear to improve haemodynamic performance compared to preoperative study. However, we observed reduced TAWSS in the right iliac artery (portending a theoretical risk of future graft and possibly limb thrombosis), after the elective type III visceral hybrid repair, but not the emergency type V repair. We surmise that this difference may be attributed to the higher neo-bifurcation of the aortic stent graft in the type III as compared to the type V repair. Our results demonstrate that CFD can be used in complicated visceral hybrid repair to yield potentially actionable predictive insights with implications on surveillance and enhanced post-operative management, even in patients with complicated geometrical bypass configurations.

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models

PURPOSE

The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model.

METHOD

The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation.

RESULTS

The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress.

CONCLUSION

Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.

An anatomically detailed arterial-venous network model. Cerebral and coronary circulation

In recent years, several works have addressed the problem of modeling blood flow phenomena in veins, as a response to increasing interest in modeling pathological conditions occurring in the venous network and their connection with the rest of the circulatory system. In this context, one-dimensional models have proven to be extremely efficient in delivering predictions in agreement with in-vivo observations. Pursuing the increase of anatomical accuracy and its connection to physiological principles in haemodynamics simulations, the main aim of this work is to describe a novel closed-loop Anatomically-Detailed Arterial-Venous Network (ADAVN) model. An extremely refined description of the arterial network consisting of 2,185 arterial vessels is coupled to a novel venous network featuring high level of anatomical detail in cerebral and coronary vascular territories. The entire venous network comprises 189 venous vessels, 79 of which drain the brain and 14 are coronary veins. Fundamental physiological mechanisms accounting for the interaction of brain blood flow with the cerebro-spinal fluid and of the coronary circulation with the cardiac mechanics are considered. Several issues related to the coupling of arterial and venous vessels at the microcirculation level are discussed in detail. Numerical simulations are compared to patient records published in the literature to show the descriptive capabilities of the model. Furthermore, a local sensitivity analysis is performed, evidencing the high impact of the venous circulation on main cardiovascular variables.

1D-model of the human liver circulatory system

BACKGROUND AND OBJECTIVE

Blood flow rate and pressure can be measured in vivo by invasive and non-invasive techniques in the large vessels of the hepatic vasculature, but it is not possible to do so along the entire liver circulatory system. Here, we develop a novel 1D model of the liver circulatory system to obtain the hemodynamic signals from macrocirculation to microcirculation with a very low computational cost.

METHODS

The model considers structurally well-defined elements that constitute the entire hepatic circulatory system, the hemodynamics (the temporal-dependence of the blood flow rate and pressure), and the elasticity of the vessel walls.

RESULTS

Using flow rate signals from in vivo measurements as inputs in the model, we obtain pressure signals within their physiological range of values. Furthermore, the model allows to get and analyze the blood flow rate and pressure signals along any vessel of the hepatic vasculature. The impact of the elasticity of the different model components on the inlet pressures is also tested.

CONCLUSIONS

A 1D model of the entire blood vascular system of the human liver is presented for the first time. The model allows to obtain the hemodynamic signals along the hepatic vasculature at a low computational cost. The amplitude and shape of the flow and pressure signals has hardly been studied in the small liver vessels. In this sense, the proposed model is a useful non-invasive exploration tool of the characteristics of the hemodynamic signals. In contrast to models that partially address the hepatic vasculature or those using an electrical analogy, the model presented here is made entirely of structurally well-defined elements. Future works will allow to directly emulate structural vascular alterations due to hepatic diseases and studying their impact on pressure and blood flow signals at key locations of the vasculature.

Calibration of patient-specific boundary conditions for coupled CFD models of the aorta derived from 4D Flow-MRI

Introduction: Patient-specific computational fluid dynamics (CFD) models permit analysis of complex intra-aortic hemodynamics in patients with aortic dissection (AD), where vessel morphology and disease severity are highly individualized. The simulated blood flow regime within these models is sensitive to the prescribed boundary conditions (BCs), so accurate BC selection is fundamental to achieve clinically relevant results. Methods: This study presents a novel reduced-order computational framework for the iterative flow-based calibration of 3-Element Windkessel Model (3EWM) parameters to generate patient-specific BCs. These parameters were calibrated using time-resolved flow information derived from retrospective four-dimensional flow magnetic resonance imaging (4D Flow-MRI). For a healthy and dissected case, blood flow was then investigated numerically in a fully coupled zero dimensional-three dimensional (0D-3D) numerical framework, where the vessel geometries were reconstructed from medical images. Calibration of the 3EWM parameters was automated and required ~3.5 min per branch. Results: With prescription of the calibrated BCs, the computed near-wall hemodynamics (time-averaged wall shear stress, oscillatory shear index) and perfusion distribution were consistent with clinical measurements and previous literature, yielding physiologically relevant results. BC calibration was particularly important in the AD case, where the complex flow regime was captured only after BC calibration. Discussion: This calibration methodology can therefore be applied in clinical cases where branch flow rates are known, for example, via 4D Flow-MRI or ultrasound, to generate patient-specific BCs for CFD models. It is then possible to elucidate, on a case-by-case basis, the highly individualized hemodynamics which occur due to geometric variations in aortic pathology high spatiotemporal resolution through CFD.

One-dimensional analysis method of pulsatile blood flow in arterial network for REBOA operations

Based on the generalized Darcy model, here we develop a linear one-dimensional (1D) composite model to predict the effects of the inserted balloon under REBOA operations on the dynamic characteristics of blood flow in flexible arterial networks. We first consider the effect of the decrease of cardiac output under different degrees of blood loss through employing the fourth-order lumped parameter model of cardiovascular system. Then, the effect of the inserted balloon is included by developing the relation between flow resistance and occlusion ratio with the neural network approach. Finally, the accuracy of the developed 1D composite model for REBOA operations, which can be solved analytically in the frequency domain, is verified by comparing to computational fluid dynamics (CFD) simulations. It is demonstrated that the 1D model is able to reproduce main features of the systemic circulation under balloon occlusion of the aorta during REBOA surgery. The 1D composite model could substantially reduce the computational time, which makes it possible to give the instant prediction of the working parameters during RABOA operations.

The effect of arterial cannula tip position on differential hypoxemia during venoarterial extracorporeal membrane oxygenation

Interaction between native ventricular output and venoarterial extracorporeal membrane oxygenation (VA ECMO) flow may hinder oxygenated blood flow to the aortic arch branches, resulting in differential hypoxemia. Typically, the arterial cannula tip is placed in the iliac artery or abdominal aorta. However, the hemodynamics of a more proximal arterial cannula tip have not been studied before. This study investigated the effect of arterial cannula tip position on VA ECMO blood flow to the upper extremities using computational fluid dynamics simulations. Four arterial cannula tip positions (P1. common iliac, P2. abdominal aorta, P3. descending aorta and P4. aortic arch) were compared with different degrees of cardiac dysfunction and VA ECMO support (50%, 80% and 90% support). P4 was able to supply oxygenated blood to the arch vessels at all support levels, while P1 to P3 only supplied the arch vessels during the highest level (90%) of VA ECMO support. Even during the highest level of support, P1 to P3 could only provide oxygenated VA-ECMO flow at 0.11 L/min to the brachiocephalic artery, compared with 0.5 L/min at P4. This study suggests that cerebral perfusion of VA ECMO flow can be increased by advancing the arterial cannula tip towards the aortic arch.

Comparative Analysis of Patient-Specific Aortic Dissections through Computational Fluid Dynamics Suggests Increased Likelihood of Degeneration in Partially Thrombosed False Lumen

Aortic dissection is a life-threatening vascular disease associated with high rates of morbidity and mortality, especially in medically underserved communities. Understanding patients’ blood flow patterns is pivotal for informing evidence-based treatment as they greatly influence the disease outcome. The present study investigates the flow patterns in the false lumen of three aorta dissections (fully perfused, partially thrombosed, and fully thrombosed) in the chronic phase, and compares them to a healthy aorta. Three-dimensional geometries of aortic true and false lumens (TLs and FLs) are reconstructed through an ad hoc developed and minimally supervised image analysis procedure. Computational fluid dynamics (CFD) is performed through a finite volume unsteady Reynolds-averaged Navier–Stokes approach assuming rigid wall aortas, Newtonian and homogeneous fluid, and incompressible flow. In addition to flow kinematics, we focus on time-averaged wall shear stress and oscillatory shear index that are recognized risk factors for aneurysmal degeneration. Our analysis shows that partially thrombosed dissection is the most prone to false lumen degeneration. In all dissections, the arteries connected to the false lumen are generally poorly perfused. Further, both true and false lumens present higher turbulence levels than the healthy aorta, and critical stagnation points. Mesh sensitivity and a thorough comparison against literature data together support the reliability of the CFD methodology. Image-based CFD simulations are efficient tools to assess the possibility of aortic dissection to lead to aneurysmal degeneration, and provide new knowledge on the hemodynamic characteristics of dissected versus healthy aortas. Similar analyses should be routinely included in patient-specific hemodynamics investigations, to plan and design tailored therapeutic strategies, and to timely assess their effectiveness.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

Wave reflection quantification analysis and personalized flow wave estimation based on the central aortic pressure waveform

Pulse wave reflections reflect cardiac afterload and perfusion, which yield valid indicators for monitoring cardiovascular status. Accurate quantification of pressure wave reflections requires the measurement of aortic flow wave. However, direct flow measurement involves extra equipment and well-trained operator. In this study, the personalized aortic flow waveform was estimated from the individual central aortic pressure waveform (CAPW) based on pressure-flow relations. The separated forward and backward pressure waves were used to calculate wave reflection indices such as reflection index (RI) and reflection magnitude (RM), as well as the central aortic pulse transit time (PTT). The effectiveness and feasibility of the method were validated by a set of clinical data (13 participants) and the Nektar1D Pulse Wave Database (4,374 subjects). The performance of the proposed personalized flow waveform method was compared with the traditional triangular flow waveform method and the recently proposed lognormal flow waveform method by statistical analyses. Results show that the root mean square error calculated by the personalized flow waveform approach is smaller than that of the typical triangular and lognormal flow methods, and the correlation coefficient with the measured flow waveform is higher. The estimated personalized flow waveform based on the characteristics of the CAPW can estimate wave reflection indices more accurately than the other two methods. The proposed personalized flow waveform method can be potentially used as a convenient alternative for the measurement of aortic flow waveform.

Effect of lower extremity amputation on cardiovascular hemodynamic environment: An in vitro study

Lower extremity amputation (LEA) was associated with a greater risk of cardiovascular disease, but its hemodynamic mechanisms have not been fully studied. Therefore, to clarify the interrelationship between them, and figure out the potential pathogenesis, the exploration of the hemodynamic environment change of patients after LEA was premeditatedly executed. A near-physiological mock circulatory system (MCS) was employed in the present work to replicate the cardiovascular circulation after LEA in a short time and the unsteady-state numerical simulation was utilized as an auxiliary method to observe the changes of the hemodynamic environment inside the blood vessel. Higher severity of LEA leads to higher peripheral vascular impedance, higher blood pressure, and more obvious redistribution of blood perfusion volume. In addition, higher severity of LEA leads to lower wall shear stress (WSS), higher oscillatory shear index (OSI), and higher relative residence time (RRT) appeared in the infrarenal abdominal aorta and the iliac artery, while these changes are closely related to the higher probability of cardiovascular diseases. Results showed that different degrees of LEA (varying heights, unilateral/bilateral) have diverse effects on the patient's hemodynamic environment. This study explained the potential pathogenesis of cardiovascular diseases after LEA from a hemodynamic perspective and provided a certain reference value for the improvement of the cardiovascular hemodynamic environment and the prevention of cardiovascular diseases in lower extremity amputees.

The effect of cardiac properties on arterial pulse waves: An in-silico study

This study investigated the effects of cardiac properties variability on arterial pulse wave morphology using blood flow modelling and pulse wave analysis. A lumped-parameter model of the left part of the heart was coupled to a one-dimensional model of the arterial network and validated using reference pulse waveforms in turn verified by comparison with in vivo measurements. A sensitivity analysis was performed to assess the effects of variations in cardiac parameters on central and peripheral pulse waveforms. Results showed that left ventricle contractility, stroke volume, cardiac cycle duration, and heart valves impairment are determinants of central waveforms morphology, pulse pressure and its amplification. Contractility of the left atrium has negligible effects on arterial pulse waves. Results also suggested that it might be possible to infer left ventricular dysfunction by analysing the timing of the dicrotic notch and cardiac function by analysing PPG signals. This study has identified cardiac properties that may be extracted from in vivo central and peripheral pulse waves to assess cardiac function.

Computational fluid dynamics model to predict the dynamical behavior of the cerebrospinal fluid through implementation of physiological boundary conditions

Cerebrospinal fluid (CSF) dynamics play an important role in maintaining a stable central nervous system environment and are influenced by different physiological processes. Multiple studies have investigated these processes but the impact of each of them on CSF flow is not well understood. A deeper insight into the CSF dynamics and the processes impacting them is crucial to better understand neurological disorders such as hydrocephalus, Chiari malformation, and intracranial hypertension. This study presents a 3D computational fluid dynamics (CFD) model which incorporates physiological processes as boundary conditions. CSF production and pulsatile arterial and venous volume changes are implemented as inlet boundary conditions. At the outlets, 2-element windkessel models are imposed to simulate CSF compliance and absorption. The total compliance is first tuned using a 0D model to obtain physiological pressure pulsations. Then, simulation results are compared with in vivo flow measurements in the spinal subarachnoid space (SAS) and cerebral aqueduct, and intracranial pressure values reported in the literature. Finally, the impact of the distribution of and total compliance on CSF pressures and velocities is evaluated. Without respiration effects, compliance of 0.17 ml/mmHg yielded pressure pulsations with an amplitude of 5 mmHg and an average value within the physiological range of 7-15 mmHg. Also, model flow rates were found to be in good agreement with reported values. However, when adding respiration effects, similar pressure amplitudes required an increase of compliance value to 0.51 ml/mmHg, which is within the range of 0.4-1.2 ml/mmHg measured in vivo. Moreover, altering the distribution of compliance over the four different outlets impacted the local flow, including the flow through the foramen magnum. The contribution of compliance to each outlet was directly proportional to the outflow at that outlet. Meanwhile, the value of total compliance impacted intracranial pressure. In conclusion, a computational model of the CSF has been developed that can simulate CSF pressures and velocities by incorporating boundary conditions based on physiological processes. By tuning these boundary conditions, we were able to obtain CSF pressures and flows within the physiological range.

Parametric analysis of an efficient boundary condition to control outlet flow rates in large arterial networks

Substantial effort is being invested in the creation of a virtual human-a model which will improve our understanding of human physiology and diseases and assist clinicians in the design of personalised medical treatments. A central challenge of achieving blood flow simulations at full-human scale is the development of an efficient and accurate approach to imposing boundary conditions on many outlets. A previous study proposed an efficient method for implementing the two-element Windkessel model to control the flow rate ratios at outlets. Here we clarify the general role of the resistance and capacitance in this approach and conduct a parametric sweep to examine how to choose their values for complex geometries. We show that the error of the flow rate ratios decreases exponentially as the resistance increases. The errors fall below 4% in a simple five-outlets model and 7% in a human artery model comprising ten outlets. Moreover, the flow rate ratios converge faster and suffer from weaker fluctuations as the capacitance decreases. Our findings also establish constraints on the parameters controlling the numerical stability of the simulations. The findings from this work are directly applicable to larger and more complex vascular domains encountered at full-human scale.

Patient-Specific Computational Modeling of Different Cannulation Strategies for Extracorporeal Membrane Oxygenation

Institution of extracorporeal membrane oxygenation (ECMO) results in unique blood flow characteristics to the end-organ vascular beds. We studied the interplay between cardiac-driven and extracorporeal membrane oxygenation (ECMO)-driven flow to vascular beds in different ECMO configurations using a patient-specific computational fluid dynamics (CFD) analysis. A computational ECMO model (femoral artery cannulation [FAC]) was constructed using patient-specific imaging and hemodynamic data. Following model calibration, we augmented the 3D geometrical model to represent alternative ECMO configurations (ascending aorta cannulation [AAC] and subclavian artery cannulation [SAC]). We performed CFD analyses, including a novel virtual color-dye analysis to compare global and regional blood flow and pressure characteristics as well as contributions of cardiac and ECMO-derived flow to the various vascular beds. Flow waveforms at all the aortic branch vessels were pulsatile, despite low cardiac output and predominant nonpulsatile ECMO-driven hemodynamics. Virtual color-dye analysis revealed differential contribution of cardiac and ECMO-derived flow to the end-organ vascular beds in the FAC model, while this was more evenly distributed in the AAC and SAC models. While global hemodynamics were relatively similar between various ECMO configurations, several distinct hemodynamic indices, in particular wall shear stress and oscillatory shear patterns, as well as differential contribution of ECMO-derived flow to various vascular beds, showed remarkable differences. The clinical impact of this study highlighting the relevance of CFD modeling in assessment of complex hemodynamics in ECMO warrants further evaluation.

Automated generation of 0D and 1D reduced-order models of patient-specific blood flow

Three-dimensional (3D) cardiovascular fluid dynamics simulations typically require hours to days of computing time on a high-performance computing cluster. One-dimensional (1D) and lumped-parameter zero-dimensional (0D) models show great promise for accurately predicting blood bulk flow and pressure waveforms with only a fraction of the cost. They can also accelerate uncertainty quantification, optimization, and design parameterization studies. Despite several prior studies generating 1D and 0D models and comparing them to 3D solutions, these were typically limited to either 1D or 0D and a singular category of vascular anatomies. This work proposes a fully automated and openly available framework to generate and simulate 1D and 0D models from 3D patient-specific geometries, automatically detecting vessel junctions and stenosis segments. Our only input is the 3D geometry; we do not use any prior knowledge from 3D simulations. All computational tools presented in this work are implemented in the open-source software platform SimVascular. We demonstrate the reduced-order approximation quality against rigid-wall 3D solutions in a comprehensive comparison with N = 72 publicly available models from various anatomies, vessel types, and disease conditions. Relative average approximation errors of flows and pressures typically ranged from 1% to 10% for both 1D and 0D models, measured at the outlets of terminal vessel branches. In general, 0D model errors were only slightly higher than 1D model errors despite requiring only a third of the 1D runtime. Automatically generated ROMs can significantly speed up model development and shift the computational load from high-performance machines to personal computers.

Data-driven computational models of ventricular-arterial hemodynamics in pediatric pulmonary arterial hypertension

Pulmonary arterial hypertension (PAH) is a complex disease involving increased resistance in the pulmonary arteries and subsequent right ventricular (RV) remodeling. Ventricular-arterial interactions are fundamental to PAH pathophysiology but are rarely captured in computational models. It is important to identify metrics that capture and quantify these interactions to inform our understanding of this disease as well as potentially facilitate patient stratification. Towards this end, we developed and calibrated two multi-scale high-resolution closed-loop computational models using open-source software: a high-resolution arterial model implemented using CRIMSON, and a high-resolution ventricular model implemented using FEniCS. Models were constructed with clinical data including non-invasive imaging and invasive hemodynamic measurements from a cohort of pediatric PAH patients. A contribution of this work is the discussion of inconsistencies in anatomical and hemodynamic data routinely acquired in PAH patients. We proposed and implemented strategies to mitigate these inconsistencies, and subsequently use this data to inform and calibrate computational models of the ventricles and large arteries. Computational models based on adjusted clinical data were calibrated until the simulated results for the high-resolution arterial models matched within 10% of adjusted data consisting of pressure and flow, whereas the high-resolution ventricular models were calibrated until simulation results matched adjusted data of volume and pressure waveforms within 10%. A statistical analysis was performed to correlate numerous data-derived and model-derived metrics with clinically assessed disease severity. Several model-derived metrics were strongly correlated with clinically assessed disease severity, suggesting that computational models may aid in assessing PAH severity.

High-resolution cerebral blood flow simulation with a domain decomposition method and verified by the TCD measurement

BACKGROUND

An efficient and accurate blood flow simulation can be useful for understanding many vascular diseases. Accurately resolving the blood flow velocity based on patient-specific geometries and model parameters is still a major challenge because of complex geomerty and turbulence issues. In addition, obtaining results in a short amount of computing time is important so that the simulation can be used in the clinical environment. In this work, we present a parallel scalable method for the patient-specific blood flow simulation with focuses on its parallel performance study and clinical verification.

METHODS

We adopt a fully implicit unstructured finite element method for a patient-specific simulation of blood flow in a full precerebral artery. The 3D artery is constructed from MRI images, and a parallel Newton-Krylov method preconditioned with a two-level domain decomposition method is adopted to solve the large nonlinear system discretized from the time-dependent 3D Navier-Stokes equations in the artery with an integral outlet boundary condition. The simulated results are verified using the clinical data measured by transcranial Doppler ultrasound, and the parallel performance of the algorithm is studied on a supercomputer.

RESULTS

The simulated velocity matches the clinical measured data well. Other simulated blood flow parameters, such as pressure and wall shear stress, are within reasonable ranges. The results show that the parallel algorithm scales up to 2160 processors with a 49% parallel efficiency for solving a problem with over 20 million unstructured elements on a supercomputer. For a standard cerebral blood flow simulation case with approximately 4 million finite elements, the calculation of one cardiac cycle can be finished within one hour with 1000 processors.

CONCLUSION

The proposed method is able to perform high-resolution 3D blood flow simulations in a patient-specific full precerebral artery within an acceptable time, and the simulated results are comparable with the clinical measured data, which demonstrates its high potential for clinical applications.

Inverse problems in blood flow modeling: A review

Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.

Uncertainty quantification in cerebral circulation simulations focusing on the collateral flow: Surrogate model approach with machine learning

Collateral circulation in the circle of Willis (CoW), closely associated with disease mechanisms and treatment outcomes, can be effectively investigated using one-dimensional–zero-dimensional hemodynamic simulations. As the entire cardiovascular system is considered in the simulation, it captures the systemic effects of local arterial changes, thus reproducing collateral circulation that reflects biological phenomena. The simulation facilitates rapid assessment of clinically relevant hemodynamic quantities under patient-specific conditions by incorporating clinical data. During patient-specific simulations, the impact of clinical data uncertainty on the simulated quantities should be quantified to obtain reliable results. However, as uncertainty quantification (UQ) is time-consuming and computationally expensive, its implementation in time-sensitive clinical applications is considered impractical. Therefore, we constructed a surrogate model based on machine learning using simulation data. The model accurately predicts the flow rate and pressure in the CoW in a few milliseconds. This reduced computation time enables the UQ execution with 100 000 predictions in a few minutes on a single CPU core and in less than a minute on a GPU. We performed UQ to predict the risk of cerebral hyperperfusion (CH), a life-threatening condition that can occur after carotid artery stenosis surgery if collateral circulation fails to function appropriately. We predicted the statistics of the postoperative flow rate increase in the CoW, which is a measure of CH, considering the uncertainties of arterial diameters, stenosis parameters, and flow rates measured using the patients’ clinical data. A sensitivity analysis was performed to clarify the impact of each uncertain parameter on the flow rate increase. Results indicated that CH occurred when two conditions were satisfied simultaneously: severe stenosis and when arteries of small diameter serve as the collateral pathway to the cerebral artery on the stenosis side. These findings elucidate the biological aspects of cerebral circulation in terms of the relationship between collateral flow and CH.

Using a reduced-order model to investigate the effect of the heart rate on the aortic dissection

The computational cost of a three-dimensional (3D) fluid-structure interaction (FSI) simulation of a dissected aorta has prevented researchers from investigating the effect of a wide range of the heart rate on the hemodynamic quantities in the disease. We have presented a systematic procedure to develop a zero-dimensional (0D) model for a dissected aorta. A series of numerical experiments were used to calculate the values for the resistance, inertance, and compliance of each lumen with irregular geometries. Having validated the results from the 0D model against those from the 3D model for one heart rate, we used the 0D model to investigate the effect of the heart rate of 50-150 bpm on the flow rates and the pressures in an idealized geometry of an aortic dissection. The 0D model showed acceptable accuracy when compared with the 3D FSI simulation. For instance, at peak systole, 7.18% relative error in the flow rate in the true lumen was observed for 0D and 3D simulations. The flow rate in the true lumen showed a stronger dependency on the heart rate, that is, 300% for the true lumen and 1.5% for the false lumen. The pressure difference between the lumina increased non-monotonically as the heart beats faster. Because of its efficiency, the reported procedure can be used for uncertainty and sensitivity analysis of the hemodynamic quantities in a diseased aorta with complex geometries such as that of the aortic dissection.

Tissue engineered in-vitro vascular patch fabrication using hybrid 3D printing and electrospinning

Three-dimensional (3D) engineered cardiovascular tissues have shown great promise to replace damaged structures. Specifically, tissue engineering vascular grafts (TEVG) have the potential to replace biological and synthetic grafts. We aimed to design an in-vitro patient-specific patch based on a hybrid 3D print combined with vascular smooth muscle cells (VSMC) differentiation. Based on the medical images of a 2 months-old girl with aortic arch hypoplasia and using computational modelling, we evaluated the most hemodynamically efficient aortic patch surgical repair. Using the designed 3D patch geometry, the scaffold was printed using a hybrid fused deposition modelling (FDM) and electrospinning techniques. The scaffold was seeded with multipotent mesenchymal stem cells (MSC) for later maturation to derived VSMC (dVSMC). The graft showed adequate resistance to physiological aortic pressure (burst pressure 101 ​± ​15 ​mmHg) and a porosity gradient ranging from 80 to 10 ​μm allowing cells to infiltrate through the entire thickness of the patch. The bio-scaffolds showed good cell viability at days 4 and 12 and adequate functional vasoactive response to endothelin-1. In summary, we have shown that our method of generating patient-specific patch shows adequate hemodynamic profile, mechanical properties, dVSMC infiltration, viability and functionality. This innovative 3D biotechnology has the potential for broad application in regenerative medicine and potentially in heart disease prevention.