One-Dimensional Haemodynamic Modeling and Wave Dynamics in the Entire Adult Circulation

A review of computational methodologies to predict the fractional flow reserve in coronary arteries with stenosis

Computational methodologies for predicting the fractional flow reserve (FFR) in coronary arteries with stenosis have gained significant attention due to their potential impact on healthcare outcomes. Coronary artery disease is a leading cause of mortality worldwide, prompting the need for accurate diagnostic and treatment approaches. The use of medical image-based anatomical vascular geometries in computational fluid dynamics (CFD) simulations to evaluate the hemodynamics has emerged as a promising tool in the medical field. This comprehensive review aims to explore the state-of-the-art computational methodologies focusing on the possible considerations. Key aspects include the rheology of blood, boundary conditions, fluid-structure interaction (FSI) between blood and the arterial wall, and multiscale modelling (MM) of stenosis. Through an in-depth analysis of the literature, the goal is to obtain an overview of the major achievements regarding non-invasive methods to compute FFR and to identify existing gaps and challenges that inform further advances in the field. This research has the major objective of improving the current diagnostic capabilities and enhancing patient care in the context of cardiovascular diseases.

Efficient uncertainty quantification in a spatially multiscale model of pulmonary arterial and venous hemodynamics

Pulmonary hypertension (PH) is a debilitating disease that alters the structure and function of both the proximal and distal pulmonary vasculature. This alters pressure-flow relationships in the pulmonary arterial and venous trees, though there is a critical knowledge gap in the relationships between proximal and distal hemodynamics in disease. Multiscale computational models enable simulations in both the proximal and distal vasculature. However, model inputs and measured data are inherently uncertain, requiring a full analysis of the sensitivity and uncertainty of the model. Thus, this study quantifies model sensitivity and output uncertainty in a spatially multiscale, pulse-wave propagation model of pulmonary hemodynamics. The model includes fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. We quantify uncertainty in blood pressure, blood flow rate, wave intensity, wall shear stress, and cyclic stretch. The latter two are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal arterial and venous circulations.

Computational haemodynamics for pulmonary valve replacement by means of a reduced fluid-structure interaction model

Pulmonary valve replacement (PVR) consists of substituting a patient's original valve with a prosthetic one, primarily addressing pulmonary valve insufficiency, which is crucially relevant in Tetralogy of Fallot repairment. While extensive clinical and computational literature on aortic and mitral valve replacements is available, PVR's post-procedural haemodynamics in the pulmonary artery and the impact of prosthetic valve dynamics remain significantly understudied. Addressing this gap, we introduce a reduced Fluid-Structure Interaction (rFSI) model, applied for the first time to the pulmonary valve. This model couples a three-dimensional computational representation of pulmonary artery haemodynamics with a one-degree-of-freedom model to account for valve structural mechanics. Through this approach, we analyse patient-specific haemodynamics pre and post PVR. Patient-specific geometries, reconstructed from CT scans, are virtually equipped with a template valve geometry. Boundary conditions for the model are established using a lumped-parameter model, fine-tuned based on clinical patient data. Our model accurately reproduces patient-specific haemodynamic changes across different scenarios: pre-PVR, six months post-PVR, and a follow-up condition after a decade. It effectively demonstrates the impact of valve implantation on sustaining the diastolic pressure gradient across the valve. The numerical results indicate that our valve model is able to reproduce overall physiological and/or pathological conditions, as preliminary assessed on two different patients. This promising approach provides insights into post-PVR haemodynamics and prosthetic valve effects, shedding light on potential implications for patient-specific outcomes.

Impact of Pressure Guidewire on Model-Based FFR Prediction

INTRODUCTION

Fractional Flow Reserve (FFR) is used to characterize the functional significance of coronary artery stenoses. FFR is assessed under hyperemic conditions by invasive measurements of trans-stenotic pressure thanks to the insertion of a pressure guidewire across the coronary stenosis during catheterization. In order to overcome the potential risk related to the invasive procedure and to reduce the associated high costs, three-dimensional blood flow simulations that incorporate clinical imaging and patient-specific characteristics have been proposed.

PURPOSE

Most CCTA-derived FFR models neglect the potential influence of the guidewire on computed flow and pressure. Here we aim to quantify the impact of taking into account the presence of the guidewire in model-based FFR prediction.

METHODS

We adopt a CCTA-derived FFR model and perform simulations with and without the guidewire for 18 patients with suspected stable CAD.

RESULTS

Presented results show that the presence of the guidewire leads to a tendency to predict a lower FFR value. The FFR reduction is prominent in cases of severe stenoses, while the influence of the guidewire is less pronounced in cases of moderate stenoses.

CONCLUSION

From a clinical decision-making point of view, including of the pressure guidewire is potentially relevant only for intermediate stenosis cases.

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.

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.

A data-driven computational methodology towards a pre-hospital Acute Ischaemic Stroke screening tool using haemodynamics waveforms

BACKGROUND AND OBJECTIVE

Acute Ischaemic Stroke (AIS), a significant global health concern, results from occlusions in cerebral arteries, causing irreversible brain damage. Different type of treatments exist depending on the size and location of the occlusion. Challenges persist in achieving faster diagnosis and treatment, which needs to happen in the first hours after the onset of symptoms to maximize the chances of patient recovery. The current diagnostic pipeline, i.e. "drip and ship", involves diagnostic via advanced imaging tools, only available in large clinical facilities, which poses important delays. This study investigates the feasibility of developing a machine learning model to diagnose and locate occluding blood clots from velocity waveforms, which can be easily be obtained with portable devices such as Doppler Ultrasound. The goal is to explore this approach as a cost-effective and time-efficient alternative to advanced imaging techniques typically available only in large hospitals.

METHODS

Simulated haemodynamic data is used to conduct blood flow simulations representing healthy and different AIS scenarios using a population-based database. A Machine Learning classification model is trained to solve the inverse problem, this is, detect and locate a potentially occluding thrombus from measured waveforms. The classification process involves two steps. First, the region where the thrombus is located is classified into nine groups, including healthy, left or right large vessel occlusion, left or right anterior cerebral artery, and left or right posterior cerebral artery. In a second step, the bifurcation generation of the thrombus location is classified as small, medium, or large vessel occlusion.

RESULTS

The proposed methodology is evaluated for data without noise, achieving a true prediction rate exceeding 95% for both classification steps mentioned above. The inclusion of up to 20% noise reduces the true prediction rate to 80% for region detection and 70% for bifurcation generation detection.

CONCLUSIONS

This study demonstrates the potential effectiveness and efficiency of using haemodynamic data and machine learning to detect and locate occluding thrombi in AIS patients. Although the geometric and topological data used in this study are idealized, the results suggest that this approach could be applicable in real-world situations with appropriate adjustments. Source code is available in https://github.com/ahmetsenemse/Acute-Ischaemic-Stroke-screening-tool-.

Non-invasive pressure-volume loops using the elastance model and CMR: a porcine validation at transient pre-loads

Aims

Pressure-volume (PV) loops have utility in the evaluation of cardiac pathophysiology but require invasive measurements. Recently, a time-varying elastance model to derive PV loops non-invasively was proposed, using left ventricular (LV) volume by cardiovascular magnetic resonance (CMR) and brachial cuff pressure as inputs. Validation was performed using CMR and pressure measurements acquired on the same day, but not simultaneously, and without varying pre-loads. This study validates the non-invasive elastance model used to estimate PV loops at varying pre-loads, compared with simultaneous measurements of invasive pressure and volume from real-time CMR, acquired concurrent to an inferior vena cava (IVC) occlusion.

Methods and results

We performed dynamic PV loop experiments under CMR guidance in 15 pigs (n = 7 naïve, n = 8 with ischaemic cardiomyopathy). Pre-load was altered by IVC occlusion, while simultaneously acquiring invasive LV pressures and volumes from real-time CMR. Pairing pressure and volume signals yielded invasive PV loops, and model-based PV loops were derived using real-time LV volumes. Haemodynamic parameters derived from invasive and model-based PV loops were compared. Across 15 pigs, 297 PV loops were recorded. Intra-class correlation coefficient (ICC) agreement was excellent between model-based and invasive parameters: stroke work (bias = 0.007 ± 0.03 J, ICC = 0.98), potential energy (bias = 0.02 ± 0.03 J, ICC = 0.99), ventricular energy efficiency (bias = -0.7 ± 2.7%, ICC = 0.98), contractility (bias = 0.04 ± 0.1 mmHg/mL, ICC = 0.97), and ventriculoarterial coupling (bias = 0.07 ± 0.15, ICC = 0.99). All haemodynamic parameters differed between naïve and cardiomyopathy animals (P < 0.05). The invasive vs. model-based PV loop dice similarity coefficient was 0.88 ± 0.04.

Conclusion

An elastance model-based estimation of PV loops and associated haemodynamic parameters provided accurate measurements at transient loading conditions compared with invasive PV loops.

Validation of a Multiscale Computational Model Using a Mock Circulatory Loop to Simulate Cardiogenic Shock

The objectives of this study are to characterize the hemodynamics of cardiogenic shock (CS) through a computational model validated using a mock circulatory loop (MCL) and to perform sensitivity analysis and uncertainty propagation studies after the American Society of Mechanical Engineers (ASME) Validation and Verification (V&V) guidelines. The uncertainties in cardiac cycle time ( ), total resistance ( ), and total volume ( ) were quantified in the MCL and propagated in the computational model. Both models were used to quantify the pressure in the left atrium, aorta (Ao), and left ventricle (LV), along with the flow through the aortic valve, reaching a good agreement. The results suggest that 1) is the main source of uncertainty in the variables under study, 2) showed its greatest impact on the uncertainty of Ao hemodynamics, and 3) mostly affected the uncertainty of LV pressure and Ao flow at the late-systolic phase. Comparison of uncertainty levels in the computational and experimental results was used to infer the presence of additional contributing factors that were not captured and propagated during a first analysis. Future work will expand upon this study to analyze the impact of mechanical circulatory support devices, such as ventricular assist devices, under CS conditions.

Modeling essential hypertension with a closed-loop mathematical model for the entire human circulation

Arterial hypertension, defined as an increase in systemic arterial pressure, is a major risk factor for the development of diseases affecting the cardiovascular system. Every year, 9.4 million deaths worldwide are caused by complications arising from hypertension. Despite well-established approaches to diagnosis and treatment, fewer than half of all hypertensive patients have adequately controlled blood pressure. In this scenario, computational models of hypertension can be a practical approach for better quantifying the role played by different components of the cardiovascular system in the determination of this condition. In the present work we adopt a global closed-loop multi-scale mathematical model for the entire human circulation to reproduce a hypertensive scenario. In particular, we modify the model to reproduce alterations in the cardiovascular system that are cause and/or consequence of the hypertensive state. The adaptation does not only affect large systemic arteries and the heart but also the microcirculation, the pulmonary circulation and the venous system. Model outputs for the hypertensive scenario are validated through assessment of computational results against current knowledge on the impact of hypertension on the cardiovascular system.

Mechanistic insights on age-related changes in heart-aorta-brain hemodynamic coupling using a pulse wave model of the entire circulatory system

Age-related changes in aortic biomechanics can impact the brain by reducing blood flow and increasing pulsatile energy transmission. Clinical studies have shown that impaired cardiac function in patients with heart failure is associated with cognitive impairment. Although previous studies have attempted to elucidate the complex relationship between age-associated aortic stiffening and pulsatility transmission to the cerebral network, they have not adequately addressed the effect of interactions between aortic stiffness and left ventricle (LV) contractility (neither on energy transmission nor on brain perfusion). In this study, we use a well-established and validated one-dimensional blood flow and pulse wave computational model of the circulatory system to address how age-related changes in cardiac function and vasculature affect the underlying mechanisms involved in the LV-aorta-brain hemodynamic coupling. Our results reveal how LV contractility affects pulsatile energy transmission to the brain, even with preserved cardiac output. Our model demonstrates the existence of an optimal heart rate (near the normal human heart rate) that minimizes pulsatile energy transmission to the brain at different contractility levels. Our findings further suggest that the reduction in cerebral blood flow at low levels of LV contractility is more prominent in the setting of age-related aortic stiffening. Maintaining optimal blood flow to the brain requires either an increase in contractility or an increase in heart rate. The former consistently leads to higher pulsatile power transmission, and the latter can either increase or decrease subsequent pulsatile power transmission to the brain.NEW & NOTEWORTHY We investigated the impact of major aging mechanisms of the arterial system and cardiac function on brain hemodynamics. Our findings suggest that aging has a significant impact on heart-aorta-brain coupling through changes in both arterial stiffening and left ventricle (LV) contractility. Understanding the underlying physical mechanisms involved here can potentially be a key step for developing more effective therapeutic strategies that can mitigate the contributions of abnormal LV-arterial coupling toward neurodegenerative diseases and dementia.

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.

Cardiac contractility is a key factor in determining pulse pressure and its peripheral amplification

Background

Arterial stiffening and peripheral wave reflections have been considered the major determinants of raised pulse pressure (PP) and isolated systolic hypertension, but the importance of cardiac contractility and ventricular ejection dynamics is also recognised.

Methods

We examined the contributions of arterial compliance and ventricular contractility to variations in aortic flow and increased central (cPP) and peripheral (pPP) pulse pressure, and PP amplification (PPa) in normotensive subjects during pharmacological modulation of physiology, in hypertensive subjects, and in silico using a cardiovascular model accounting for ventricular-aortic coupling. Reflections at the aortic root and from downstream vessels were quantified using emission and reflection coefficients, respectively.

Results

cPP was strongly associated with contractility and compliance, whereas pPP and PPa were strongly associated with contractility. Increased contractility by inotropic stimulation increased peak aortic flow (323.9 ± 52.8 vs. 389.1 ± 65.1 ml/s), and the rate of increase (3193.6 ± 793.0 vs. 4848.3 ± 450.4 ml/s2) in aortic flow, leading to larger cPP (36.1 ± 8.8 vs. 59.0 ± 10.8 mmHg), pPP (56.9 ± 13.1 vs. 93.0 ± 17.0 mmHg) and PPa (20.8 ± 4.8 vs. 34.0 ± 7.3 mmHg). Increased compliance by vasodilation decreased cPP (62.2 ± 20.2 vs. 45.2 ± 17.8 mmHg) without altering d P / d t , pPP or PPa. The emission coefficient changed with increasing cPP, but the reflection coefficient did not. These results agreed with in silico data obtained by independently changing contractility/compliance over the range observed in vivo.

Conclusions

Ventricular contractility plays a key role in raising and amplifying PP, by altering aortic flow wave morphology.

The Impact of Left Ventricular Performance and Afterload on the Evaluation of Aortic Valve Stenosis: A 1D Mathematical Modeling Approach

The transaortic valvular pressure gradient (TPG) plays a central role in decision-making for patients suffering from severe aortic stenosis. However, the flow-dependence nature of the TPG makes the diagnosis of aortic stenosis challenging since the markers of cardiac performance and afterload present high physiological interdependence and thus, isolated effects cannot be measured directly in vivo. We used a validated 1D mathematical model of the cardiovascular system, coupled with a model of aortic stenosis, to assess and quantify the independent effect of the main left ventricular performance parameters (end-systolic (Ees) and end-diastolic (Eed) elastance) and principal afterload indices (total vascular resistance (TVR) and total arterial compliance (TAC)) on the TPG for different levels of aortic stenosis. In patients with critical aortic stenosis (aortic valve area (AVA) ≤ 0.6 cm2), a 10% increase of Eed from the baseline value was associated with the most important effect on the TPG (−5.6 ± 0.5 mmHg, p < 0.001), followed by a similar increase of Ees (3.4 ± 0.1 mmHg, p < 0.001), in TAC (1.3 ±0.2 mmHg, p < 0.001) and TVR (−0.7 ± 0.04 mmHg, p < 0.001). The interdependence of the TPG left ventricular performance and afterload indices become stronger with increased aortic stenosis severity. Disregarding their effects may lead to an underestimation of stenosis severity and a potential delay in therapeutic intervention. Therefore, a comprehensive evaluation of left ventricular function and afterload should be performed, especially in cases of diagnostic challenge, since it may offer the pathophysiological mechanism that explains the mismatch between aortic severity and the TPG.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

A predictive patient-specific computational model of coronary artery bypass grafts for potential use by cardiac surgeons to guide selection of graft configurations

Cardiac surgeons face a significant degree of uncertainty when deciding upon coronary artery bypass graft configurations for patients with coronary artery disease. This leads to significant variation in preferred configuration between different surgeons for a particular patient. Additionally, for the majority of cases, there is no consensus regarding the optimal grafting strategy. This situation results in the tendency for individual surgeons to opt for a “one size fits all” approach and use the same grafting configuration for the majority of their patients neglecting the patient-specific nature of the diseased coronary circulation. Quantitative metrics to assess the adequacy of coronary bypass graft flows have recently been advocated for routine intraoperative use by cardiac surgeons. In this work, a novel patient-specific 1D-0D computational model called “COMCAB” is developed to provide the predictive haemodynamic parameters of functional graft performance that can aid surgeons to avoid configurations with grafts that have poor flow and thus poor patency. This model has significant potential for future expanded applications.

Insights from computational modeling on the potential hemodynamic effects of sinus rhythm versus atrial fibrillation

Atrial fibrillation (AF) is the most common clinical tachyarrhythmia, posing a significant burden to patients, physicians, and healthcare systems worldwide. With the advent of more effective rhythm control strategies, such as AF catheter ablation, an early rhythm control strategy is progressively demonstrating its superiority not only in symptoms control but also in prognostic terms, over a standard strategy (rate control, with rhythm control reserved only to patients with refractory symptoms). This review summarizes the different impacts exerted by AF on heart mechanics and systemic circulation, as well as on cerebral and coronary vascular beds, providing computational modeling-based hemodynamic insights in favor of pursuing sinus rhythm maintenance in AF patients.

Optimised design of an arterial network model reproduces characteristic central and peripheral hemodynamic waveform features in young adults

Abstract

The arterial network in healthy young adults is thought to be structured to optimize wave reflection in the arterial system, producing an ascending aortic pressure waveform with three key features: early systolic peak, negative systolic augmentation and diastolic hump. One‐dimensional computer models have provided significant insights into arterial haemodynamics, but no previous models of the young adult have exhibited these three features. Given that this issue was likely to be related to unrepresentative or non‐optimized impedance properties of the model arterial networks, we developed a new ‘YoungAdult’ model that incorporated the following features: (i) a new and more accurate empirical equation for approximating wave speeds, based on area and relative distance to elastic–muscular arterial transition points; (ii) optimally matched arterial junctions; and (iii) an improved arterial network geometry that eliminated ‘within‐segment’ taper (which causes wave reflection in conduit arteries) whilst establishing ‘impedance‐preserving’ taper. These properties of the model led to wave reflection occurring predominantly at distal vascular beds, rather than in conduit arteries. The model predicted all three typical characteristics of an ascending aortic pressure waveform observed in young adults. When compared with non‐invasively acquired pressure and velocity measurements (obtained via tonometry and Doppler ultrasound in seven young adults), the model was also shown to reproduce the typical waveform morphology observed in the radial, brachial, carotid, temporal, femoral and tibial arteries. The YoungAdult model provides support for the concept that the arterial tree impedance in healthy young adults is exquisitely optimized, and it provides an important baseline model for investigating cardiovascular changes in ageing and disease states.

Key points

The origin of wave reflection in the arterial system is controversial, but reflection properties are likely to give rise to characteristic haemodynamic features in healthy young adults, including an early systolic peak, negative systolic augmentation and diastolic hump in the ascending aortic pressure waveform, and triphasic velocity profiles in peripheral arteries. Although computational modelling provides insights into arterial haemodynamics, no previous models have predicted all these features.

An established arterial network model was optimized by incorporating the following features: (i) a more accurate representation of arterial wave speeds; (ii) precisely matched junctions; and (iii) impedance‐preserving tapering, thereby minimizing wave reflection in conduit arteries in the forward direction. Comparison with in vivo data (n = 7 subjects) indicated that the characteristic waveform features in young adults were predicted accurately.

Our findings strongly imply that a healthy young arterial system is structured to optimize wave reflection in the main conduit arteries and that reflection of forward waves occurs primarily in the vicinity of vascular beds.

A coupling strategy for a first 3D-1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function

A key factor governing the mechanical performance of the heart is the bidirectional coupling with the vascular system, where alterations in vascular properties modulate the pulsatile load imposed on the heart. Current models of cardiac electromechanics (EM) use simplified 0D representations of the vascular system when coupling to anatomically accurate 3D EM models is considered. However, these ignore important effects related to pulse wave transmission. Accounting for these effects requires 1D models, but a 3D-1D coupling remains challenging. In this work, we propose a novel, stable strategy to couple a 3D cardiac EM model to a 1D model of blood flow in the largest systemic arteries. For the first time, a personalised coupled 3D-1D model of left ventricle and arterial system is built and used in numerical benchmarks to demonstrate robustness and accuracy of our scheme over a range of time steps. Validation of the coupled model is performed by investigating the coupled system's physiological response to variations in the arterial system affecting pulse wave propagation, comprising aortic stiffening, aortic stenosis or bifurcations causing wave reflections. Our first 3D-1D coupled model is shown to be efficient and robust, with negligible additional computational costs compared to 3D-0D models. We further demonstrate that the calibrated 3D-1D model produces simulated data that match with clinical data under baseline conditions, and that known physiological responses to alterations in vascular resistance and stiffness are correctly replicated. Thus, using our coupled 3D-1D model will be beneficial in modelling studies investigating wave propagation phenomena.

Inter-arm differences in regional arterial stiffness and geometry lead to inter-arm systolic blood pressure differences: A modelling study

An inter-arm systolic blood pressure difference (ISBPD), if substantial in magnitude (typically defined as ≥10 mmHg), is a potential cardiovascular risk factor in adults, due to its association with cardiovascular events/mortality. A substantial ISBPD occurs in approximately 10% of the adult population, and, although associations with vascular disease and elevated stiffness have been reported, the mechanisms underlying ISBPD remain unknown. The aim of this study was to investigate whether inter-arm differences in segmental pulse wave velocity, cross-sectional area, or vascular bed compliance/resistance could give rise to substantial differences in brachial pressures between arms; for example, due to differences in pulse wave transmission and reflection. Using an established one-dimensional model of the major systemic arteries, pulse wave velocity (PWV) was uniformly increased or decreased in arteries of 1) the supra-aortic region leading up to the arm, 2) the brachial region, 3) the forearm, and 4) all of these (entire arm pathway); for the left arm, right arm, and both arms. Cross-sectional area and vascular bed compliance and resistance of the arms were similarly varied. Inter-arm differences in segmental PWV and cross-sectional area (but not bilateral changes) led to associated substantial inter-arm SBP differences, which were observed with changes to brachial, forearm and/or entire arm pathways and were related to altered transmission of forward waves and amplitude/timing of reflected waves. Vascular bed compliance and resistance had minimal influence. We conclude that inter-arm differences in arterial stiffness and geometry may contribute to inter-arm systolic blood pressure differences, warranting further investigation.

Automating fractional flow reserve (FFR) calculation from CT scans: A rapid workflow using unsupervised learning and computational fluid dynamics

Fractional flow reserve (FFR) provides the functional relevance of coronary atheroma. The FFR-guided strategy has been shown to reduce unnecessary stenting, improve overall health outcome, and to be cost-saving. The non-invasive, coronary computerised tomography (CT) angiography-derived FFR (cFFR) is an emerging method in reducing invasive catheter based measurements. This computational fluid dynamics-based method is laborious as it requires expertise in multidisciplinary analysis of combining image analysis and computational mechanics. In this work, we present a rapid method, powered by unsupervised learning, to automatically calculate cFFR from CT scans without manual intervention.

A Closed-Loop Modeling Framework for Cardiac-to-Coronary Coupling

The mechanisms by which cardiac mechanics effect coronary perfusion (cardiac-to-coronary coupling) remain incompletely understood. Several coronary models have been proposed to deepen our understanding of coronary hemodynamics, but possibilities for in-depth studies on cardiac-to-coronary coupling are limited as mechanical properties like myocardial stress and strain are most often neglected. To overcome this limitation, a mathematical model of coronary mechanics and hemodynamics was implemented in the previously published multi-scale CircAdapt model of the closed-loop cardiovascular system. The coronary model consisted of a relatively simple one-dimensional network of the major conduit arteries and veins as well as a lumped parameter model with three transmural layers for the microcirculation. Intramyocardial pressure was assumed to arise from transmission of ventricular cavity pressure into the myocardial wall as well as myocardial stiffness, based on global pump mechanics and local myofiber mechanics. Model-predicted waveforms of global epicardial flow velocity, as well as of intramyocardial flow and diameter were qualitatively and quantitatively compared with reported data. Versatility of the model was demonstrated in a case study of aortic valve stenosis. The reference simulation correctly described the phasic pattern of coronary flow velocity, arterial flow impediment, and intramyocardial differences in coronary flow and diameter. Predicted retrograde flow during early systole in aortic valve stenosis was in agreement with measurements obtained in patients. In conclusion, we presented a powerful multi-scale modeling framework that enables realistic simulation of coronary mechanics and hemodynamics. This modeling framework can be used as a research platform for in-depth studies of cardiac-to-coronary coupling, enabling study of the effect of abnormal myocardial tissue properties on coronary hemodynamics.

Cardiovascular Response to Posture Changes: Multiscale Modeling and in vivo Validation During Head-Up Tilt

In spite of cardiovascular system (CVS) response to posture changes have been widely studied, a number of mechanisms and their interplay in regulating central blood pressure and organs perfusion upon orthostatic stress are not yet clear. We propose a novel multiscale 1D-0D mathematical model of the human CVS to investigate the effects of passive (i.e., through head-up tilt without muscular intervention) posture changes. The model includes the main short-term regulation mechanisms and is carefully validated against literature data and in vivo measures here carried out. The model is used to study the transient and steady-state response of the CVS to tilting, the effects of the tilting rate, and the differences between tilt-up and tilt-down. Passive upright tilt led to an increase of mean arterial pressure and heart rate, and a decrease of stroke volume and cardiac output, in agreement with literature data and present in vivo experiments. Pressure and flow rate waveform analysis along the arterial tree together with mechano-energetic and oxygen consumption parameters highlighted that the whole system approaches a less stressed condition at passive upright posture than supine, with a slight unbalance of the energy supply-demand ratio. The transient dynamics is not symmetric in tilt-up and tilt-down testing, and is non-linearly affected by the tilting rate, with stronger under- and overshoots of the hemodynamic parameters as the duration of tilt is reduced. By enriching the CVS response to posture changes, the present modeling approach shows promise in a number of applications, ranging from autonomic system disorders to spaceflight deconditioning.

Numerical predictions of shear stress and cyclic stretch in pulmonary hypertension due to left heart failure

Isolated post-capillary pulmonary hypertension (Ipc-PH) occurs due to left heart failure, which contributes to 1 out of every 9 deaths in the United States. In some patients, through unknown mechanisms, Ipc-PH transitions to combined pre-/post-capillary PH (Cpc-PH) and is associated with a dramatic increase in mortality. Altered mechanical forces and subsequent biological signaling in the pulmonary vascular bed likely contribute to the transition from Ipc-PH to Cpc-PH. However, even in a healthy pulmonary circulation, the mechanical forces in the smallest vessels (the arterioles, capillary bed, and venules) have not been quantitatively defined. This study is the first to examine this question via a computational fluid dynamics model of the human pulmonary arteries, arterioles, venules, and veins. Using this model, we predict temporal and spatial dynamics of cyclic stretch and wall shear stress with healthy and diseased hemodynamics. In the normotensive case for large vessels, numerical simulations show that large arteries have higher pressure and flow than large veins, as well as more pronounced changes in area throughout the cardiac cycle. In the microvasculature, shear stress increases and cyclic stretch decreases as vessel radius decreases. When we impose an increase in left atrial pressure to simulate Ipc-PH, shear stress decreases and cyclic stretch increases as compared to the healthy case. Overall, this model predicts pressure, flow, shear stress, and cyclic stretch that providing a way to analyze and investigate hypotheses related to disease progression in the pulmonary circulation.

A computational analysis of atrial fibrillation effects on coronary perfusion across the different myocardial layers

Patients with atrial fibrillation (AF) may present ischemic chest pain in the absence of classical obstructive coronary disease. Among the possible causes, the direct hemodynamic effect exerted by the irregular arrhythmia has not been studied in detail. We performed a computational fluid dynamics analysis by means of a 1D-0D multiscale model of the entire human cardiovascular system, enriched by a detailed mathematical modeling of the coronary arteries and their downstream distal microcirculatory districts (subepicardial, midwall and subendocardial layers). Three mean ventricular rates were simulated (75, 100, 125 bpm) in both sinus rhythm (SR) and atrial fibrillation, and an inter-layer and inter-frequency analysis was conducted focusing on the ratio between mean beat-to-beat blood flow in AF compared to SR. Our results show that AF exerts direct hemodynamic consequences on the coronary microcirculation, causing a reduction in microvascular coronary flow particularly at higher ventricular rates; the most prominent reduction was seen in the subendocardial layers perfused by left coronary arteries (left anterior descending and left circumflex arteries).

Impact of Respiratory Fluctuation on Hemodynamics in Human Cardiovascular System: A 0-1D Multiscale Model

To explore hemodynamic interaction between the human respiratory system (RS) and cardiovascular system (CVS), here we propose an integrated computational model to predict the CVS hemodynamics with consideration of the respiratory fluctuation (RF). A submodule of the intrathoracic pressure (ITP) adjustment is developed and incorporated in a 0-1D multiscale hemodynamic model of the CVS specified for infant, adolescent, and adult individuals. The model is verified to enable reasonable estimation of the blood pressure waveforms accounting for the RF-induced pressure fluctuations in comparison with clinical data. The results show that the negative ITP caused by respiration increases the blood flow rates in superior and inferior vena cavae; the deep breathing improves the venous return in adolescents but has less influence on infants. It is found that a marked reduction in ITP under pathological conditions can excessively increase the flow rates in cavae independent of the individual ages, which may cause the hemodynamic instability and hence increase the risk of heart failure. Our results indicate that the present 0-1D multiscale CVS model incorporated with the RF effect is capable of providing a useful and effective tool to explore the physiological and pathological mechanisms in association with cardiopulmonary interactions and their clinical applications.

Cerebrospinal fluid dynamics coupled to the global circulation in holistic setting: Mathematical models, numerical methods and applications

This paper presents a mathematical model of the global, arterio-venous circulation in the entire human body, coupled to a refined description of the cerebrospinal fluid (CSF) dynamics in the craniospinal cavity. The present model represents a substantially revised version of the original Müller-Toro mathematical model. It includes one-dimensional (1D), non-linear systems of partial differential equations for 323 major blood vessels and 85 zero-dimensional, differential-algebraic systems for the remaining components. Highlights include the myogenic mechanism of cerebral blood regulation; refined vasculature for the inner ear, the brainstem and the cerebellum; and viscoelastic, rather than purely elastic, models for all blood vessels, arterial and venous. The derived 1D parabolic systems of partial differential equations for all major vessels are approximated by hyperbolic systems with stiff source terms following a relaxation approach. A major novelty of this paper is the coupling of the circulation, as described, to a refined description of the CSF dynamics in the craniospinal cavity, following Linninger et al. The numerical solution methodology employed to approximate the hyperbolic non-linear systems of partial differential equations with stiff source terms is based on the Arbitrary DERivative Riemann problem finite volume framework, supplemented with a well-balanced formulation, and a local time stepping procedure. The full model is validated through comparison of computational results against published data and bespoke MRI measurements. Then we present two medical applications: (i) transverse sinus stenoses and their relation to Idiopathic Intracranial Hypertension; and (ii) extra-cranial venous strictures and their impact in the inner ear circulation, and its implications for Ménière's disease.

Ventricular wall stress and wall shear stress homeostasis predicts cardiac remodeling during pregnancy: A modeling study

Pregnancy is a unique and dynamic process characterized by significant changes in the maternal cardiovascular system that are required to satisfy the increased maternal and fetal metabolic demands. Profound structural and hemodynamic adaptations occur during healthy pregnancy that allows the mother to maintain healthy hemodynamics and provide an adequate uteroplacental blood circulation to ensure physiological fetal development. Investigating these adaptations is crucial for understanding the physiology of pregnancy and may provide important insights for the management of high-risk pregnancies. However, no previous modeling studies have investigated the maternal cardiac structural changes that occur during gestation. This study, therefore, had two aims. The first was to develop a lumped parameter model of the whole maternal circulation that is suitable for studying global hemodynamics and cardiac function at different stages of gestation. The second was to test the hypothesis that myofiber stress and wall shear stress homeostasis principles can be used to predict cardiac remodeling that occurs during normal pregnancy. Hemodynamics and cardiac variables predicted from simulations with and without controlled cardiac remodeling algorithms were compared and evaluated with reference clinical data. While both models reproduced the hemodynamic variations that arise in pregnancy, importantly, we show that the structural changes that occur with pregnancy could be predicted by assuming invariant homeostatic "target" values of myocardial wall stress and chamber wall shear stress.

Wave Intensity Analysis Combined With Machine Learning can Detect Impaired Stroke Volume in Simulations of Heart Failure

Heart failure is treatable, but in the United Kingdom, the 1-, 5- and 10-year mortality rates are 24.1, 54.5 and 75.5%, respectively. The poor prognosis reflects, in part, the lack of specific, simple and affordable diagnostic techniques; the disease is often advanced by the time a diagnosis is made. Previous studies have demonstrated that certain metrics derived from pressure-velocity-based wave intensity analysis are significantly altered in the presence of impaired heart performance when averaged over groups, but to date, no study has examined the diagnostic potential of wave intensity on an individual basis, and, additionally, the pressure waveform can only be obtained accurately using invasive methods, which has inhibited clinical adoption. Here, we investigate whether a new form of wave intensity based on noninvasive measurements of arterial diameter and velocity can detect impaired heart performance in an individual. To do so, we have generated a virtual population of two-thousand elderly subjects, modelling half as healthy controls and half with an impaired stroke volume. All metrics derived from the diameter-velocity-based wave intensity waveforms in the carotid, brachial and radial arteries showed significant crossover between groups-no one metric in any artery could reliably indicate whether a subject's stroke volume was normal or impaired. However, after applying machine learning to the metrics, we found that a support vector classifier could simultaneously achieve up to 99% recall and 95% precision. We conclude that noninvasive wave intensity analysis has significant potential to improve heart failure screening and diagnosis.

An efficient, localised approach for the simulation of elastic blood vessels using the lattice Boltzmann method

Many numerical studies of blood flow impose a rigid wall assumption due to the simplicity of its implementation compared to a full coupling with a solid mechanics model. In this paper, we present a localised method for incorporating the effects of elastic walls into blood flow simulations using the lattice Boltzmann method implemented by the open-source code HemeLB. We demonstrate that our approach is able to more accurately capture the flow behaviour expected in elastic walled vessels than ones with rigid walls. Furthermore, we show that this can be achieved with no loss of computational performance and remains strongly scalable on high performance computers. We finally illustrate that our approach captures the same trends in wall shear stress distribution as those observed in studies using a rigorous coupling between fluid dynamics and solid mechanics models to solve flow in personalised vascular geometries. These results demonstrate that our model can be used to efficiently and effectively represent flows in elastic blood vessels.

Closed-Loop Multiscale Computational Model of Human Blood Circulation. Applications to Ballistocardiography

Cardiac mechanical activity leads to periodic changes in the distribution of blood throughout the body, which causes micro-oscillations of the body's center of mass and can be measured by ballistocardiography (BCG). However, many of the BCG findings are based on parameters whose origins are poorly understood. Here, we generate simulated multidimensional BCG signals based on a more exhaustive and accurate computational model of blood circulation than previous attempts. This model consists in a closed loop 0D-1D multiscale representation of the human blood circulation. The 0D elements include the cardiac chambers, cardiac valves, arterioles, capillaries, venules, and veins, while the 1D elements include 55 systemic and 57 pulmonary arteries. The simulated multidimensional BCG signal is computed based on the distribution of blood in the different compartments and their anatomical position given by whole-body magnetic resonance angiography on a healthy young subject. We use this model to analyze the elements affecting the BCG signal on its different axes, allowing a better interpretation of clinical records. We also evaluate the impact of filtering and healthy aging on the BCG signal. The results offer a better view of the physiological meaning of BCG, as compared to previous models considering mainly the contribution of the aorta and focusing on longitudinal acceleration BCG. The shape of experimental BCG signals can be reproduced, and their amplitudes are in the range of experimental records. The contributions of the cardiac chambers and the pulmonary circulation are non-negligible, especially on the lateral and transversal components of the velocity BCG signal. The shapes and amplitudes of the BCG waveforms are changing with age, and we propose a scaling law to estimate the pulse wave velocity based on the time intervals between the peaks of the acceleration BCG signal. We also suggest new formulas to estimate the stroke volume and its changes based on the BCG signal expressed in terms of acceleration and kinetic energy.

Parallel generation of extensive vascular networks with application to an archetypal human kidney model

Given the relevance of the inextricable coupling between microcirculation and physiology, and the relation to organ function and disease progression, the construction of synthetic vascular networks for mathematical modelling and computer simulation is becoming an increasingly broad field of research. Building vascular networks that mimic in vivo morphometry is feasible through algorithms such as constrained constructive optimization (CCO) and variations. Nevertheless, these methods are limited by the maximum number of vessels to be generated due to the whole network update required at each vessel addition. In this work, we propose a CCO-based approach endowed with a domain decomposition strategy to concurrently create vascular networks. The performance of this approach is evaluated by analysing the agreement with the sequentially generated networks and studying the scalability when building vascular networks up to 200 000 vascular segments. Finally, we apply our method to vascularize a highly complex geometry corresponding to the cortex of a prototypical human kidney. The technique presented in this work enables the automatic generation of extensive vascular networks, removing the limitation from previous works. Thus, we can extend vascular networks (e.g. obtained from medical images) to pre-arteriolar level, yielding patient-specific whole-organ vascular models with an unprecedented level of detail.

High fidelity blood flow in a patient-specific arteriovenous fistula

An arteriovenous fistula, created by artificially connecting segments of a patient’s vasculature, is the preferred way to gain access to the bloodstream for kidney dialysis. The increasing power and availability of supercomputing infrastructure means that it is becoming more realistic to use simulations to help identify the best type and location of a fistula for a specific patient. We describe a 3D fistula model that uses the lattice Boltzmann method to simultaneously resolve blood flow in patient-specific arteries and veins. The simulations conducted here, comprising vasculatures of the whole forearm, demonstrate qualified validation against clinical data. Ongoing research to further encompass complex biophysics on realistic time scales will permit the use of human-scale physiological models for basic and clinical medicine.

Parameter estimation for closed-loop lumped parameter models of the systemic circulation using synthetic data

Physics-based models can be applied to describe mechanisms in both health and disease, which has the potential to accelerate the development of personalized medicine. The aim of this study was to investigate the feasibility of personalizing a model of systemic hemodynamics by estimating model parameters. We investigated the feasibility of estimating model parameters for a closed-loop lumped parameter model of the left heart and systemic circulation using the step-wise subset reduction method. This proceeded by first investigating the structural identifiability of the model parameters. Secondly we performed sensitivity analysis to determine which parameters were most influential on the most relevant model outputs. Finally, we constructed a sequence of progressively smaller subsets including parameters based on their ranking by model output influence. The model was then optimized to data for each set of parameters to evaluate how well the parameters could be estimated for each subset. The subsequent results allowed assessment of how different data sets, and noise affected the parameter estimates. In the noiseless case, all parameters could be calibrated to less than 10^-3% error using time series data, while errors using clinical index data could reach over 100%. With 5% normally distributed noise the accuracy was limited to be within 10% error for the five most sensitive parameters, while the four least sensitive parameters were unreliably estimated for waveform data. The three least sensitive parameters were particularly challenging to estimate so these should be prioritised for measurement. Cost functions based on time series such as pressure waveforms, were found to give better parameter estimates than cost functions based on standard indices used in clinical assessment of the cardiovascular system, for example stroke volume (SV) and pulse pressure (PP). Averaged parameter estimate errors were reduced by several orders of magnitude by choosing waveforms for noiseless synthetic data. Also when measurement data were noisy, the parameter estimation procedure based on continuous waveforms was more accurate than that based on clinical indices. By application of the step-wise subset reduction method we demonstrated that by the addition of venous pressure to the cost function, or conversely fixing the systemic venous compliance parameter at an accurate value improved all parameter estimates, especially the diastolic filling parameters which have least influence on the aortic pressure.

Sensitivity analysis and uncertainty quantification of 1-D models of pulmonary hemodynamics in mice under control and hypertensive conditions

Pulmonary hypertension (PH), defined as an elevated mean blood pressure in the main pulmonary artery (MPA) at rest, is associated with vascular remodeling of both large and small arteries. PH has several sub-types that are all linked to high mortality rates. In this study, we use a one-dimensional (1-D) fluid dynamics model driven by in vivo measurements of MPA flow to understand how model parameters and network size influence MPA pressure predictions in the presence of PH. We compare model predictions with in vivo MPA pressure measurements from a control and a hypertensive mouse and analyze results in three networks of increasing complexity, extracted from micro-computed tomography (micro-CT) images. We introduce global scaling factors for boundary condition parameters and perform local and global sensitivity analysis to calculate parameter influence on model predictions of MPA pressure and correlation analysis to determine a subset of identifiable parameters. These are inferred using frequentist optimization and Bayesian inference via the Delayed Rejection Adaptive Metropolis (DRAM) algorithm. Frequentist and Bayesian uncertainty is computed for model parameters and MPA pressure predictions. Results show that MPA pressure predictions are most sensitive to distal vascular resistance and that parameter influence changes with increasing network complexity. Our outcomes suggest that PH leads to increased vascular stiffness and decreased peripheral compliance, congruent with clinical observations.

Personalising cardiovascular network models in pregnancy: A two-tiered parameter estimation approach

Uterine artery Doppler waveforms are often studied to determine whether a patient is at risk of developing pathologies such as pre-eclampsia. Many uterine waveform indices have been developed, which attempt to relate characteristics of the waveform with the physiological adaptation of the maternal cardiovascular system, and are often suggested to be an indicator of increased placenta resistance and arterial stiffness. Doppler waveforms of four patients, two of whom developed pre-eclampsia, are compared with a comprehensive closed-loop model of pregnancy. The closed-loop model has been previously validated but has been extended to include an improved parameter estimation technique that utilises systolic and diastolic blood pressure, cardiac output, heart rate, and pulse wave velocity measurements to adapt model resistances, compliances, blood volume, and the mean vessel areas in the main systemic arteries. The shape of the model-predicted uterine artery velocity waveforms showed good agreement with the characteristics observed in the patient Doppler waveforms. The personalised models obtained now allow a prediction of the uterine pressure waveforms in addition to the uterine velocity. This allows for a more detailed mechanistic analysis of the waveforms, eg, wave intensity analysis, to study existing clinical indices. The findings indicate that to accurately estimate arterial stiffness, both pulse pressure and pulse wave velocities are required. In addition, the results predict that patients who developed pre-eclampsia later in pregnancy have larger vessel areas in the main systemic arteries compared with the two patients who had normal pregnancy outcomes.

Validation of an aging virtual population for the study of carotid hemodynamics

The analysis of carotid ultrasound (US) flow, velocity, and diameter waveforms provides important information about cardiovascular and circulatory health. These can be used to derive clinical indices of atherosclerosis, vascular aging, and hemodynamic status. To derive clinical insight from carotid waveforms, it is essential to understand the relationship of the observed variability in morphology with the underlying hemodynamic status and cardiovascular properties. For this purpose, using a one-dimensional modeling approach, we have developed and validated a virtual population that is able to realistically simulate carotid waveforms of healthy subjects aged between 10 and 80 years old.Clinical Relevance-Our virtual population of carotid waveforms can support the interpretation of US patient data. It can be used, e.g., to investigate how waveform morphology and derived indices relate to individual arterial and cardiac properties.

Impact of ductus arteriosus constriction and restrictive foramen ovale on global hemodynamics for term fetuses with d-TGA

The ductus arteriosus (DA) constriction and restrictive foramen ovale (FO) are known as the leading cause of compromise and death of fetuses with dextro-transposition of the great arteries (d-TGA). Although the d-TGA fetal hemodynamics is of great importance in making diagnosis and management of the congenital heart defect, it remains poorly understood, particularly in terms of abnormal DA and FO. In this study, we developed a closed-loop 0-1D multiscale model of the fetal cardiovascular system (CVS) specified for the d-TGA circulation and conducted a systematic study of the impact of the DA constriction and restrictive FO on fetal hemodynamics. We found that the DA constriction led to a pronounced increase in the pulmonary artery pressure, pulmonary and mitral valve (PV and MV) regurgitation as well as left heart volume; the restrictive FO was responsible for reducing MV E/A ratio, ie, the ratio of peak early filling and late diastolic filling velocities, and PV peak systolic flow (PSV) but could increase both aortic valve (AV) PSV and aortic isthmus systolic index (ISI). Moreover, the amount of blood flowing through the DA was observed equivalent to that through the FO; the influence of DA constriction on the cerebral and placental perfusions are larger than that of the FO. Our results demonstrate that the proposed fetal cardiovascular model may be a useful tool for studying the underlying mechanisms associated with d-TGA fetal circulation and providing insights into its complex physiology and pathology.

Total Effective Vascular Compliance of a Global Mathematical Model for the Cardiovascular System

In this work, we determined the total effective vascular compliance of a global closed-loop model for the cardiovascular system by performing an infusion test of 500 mL of blood in four minutes. Our mathematical model includes a network of arteries and veins where blood flow is described by means of a one-dimensional nonlinear hyperbolic PDE system and zero-dimensional models for other cardiovascular compartments. Some mathematical modifications were introduced to better capture the physiology of the infusion test: (1) a physiological distribution of vascular compliance and total blood volume was implemented, (2) a nonlinear representation of venous resistances and compliances was introduced, and (3) main regulatory mechanisms triggered by the infusion test where incorporated into the model. By means of presented in silico experiment, we show that effective total vascular compliance is the result of the interaction between the assigned constant physical vascular compliance and the capacity of the cardiovascular system to adapt to new situations via regulatory mechanisms.

A Solution of the Junction Riemann Problem for 1D Hyperbolic Balance Laws in Networks including Supersonic Flow Conditions on Elastic Collapsible Tubes

The numerical modeling of one-dimensional (1D) domains joined by symmetric or asymmetric bifurcations or arbitrary junctions is still a challenge in the context of hyperbolic balance laws with application to flow in pipes, open channels or blood vessels, among others. The formulation of the Junction Riemann Problem (JRP) under subsonic conditions in 1D flow is clearly defined and solved by current methods, but they fail when sonic or supersonic conditions appear. Formulations coupling the 1D model for the vessels or pipes with other container-like formulations for junctions have been presented, requiring extra information such as assumed bulk mechanical properties and geometrical properties or the extension to more dimensions. To the best of our knowledge, in this work, the JRP is solved for the first time allowing solutions for all types of transitions and for any number of vessels, without requiring the definition of any extra information. The resulting JRP solver is theoretically well-founded, robust and simple, and returns the evolving state for the conserved variables in all vessels, allowing the use of any numerical method in the resolution of the inner cells used for the space-discretization of the vessels. The methodology of the proposed solver is presented in detail. The JRP solver is directly applicable if energy losses at the junctions are defined. Straightforward extension to other 1D hyperbolic flows can be performed.

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

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

Personalized 0D-1D multiscale hemodynamic modeling and wave dynamics analysis of cerebral circulation for an elderly patient with dementia

Senile dementia is associated with pronounced alterations in cerebral circulation. A fundamental understanding of intracranial hemodynamics and wave dynamics is essential for assessing dementia risk. Recent findings suggest that higher carotid artery wave intensity (WI) can predict future cognitive impairments in the elderly. However, wave power (WP) is more advantageous for assessing the risk of cognitive impairment and dementia because of its conservative form, which allows quantification of detailed WP distribution among the entire cerebrovascular network. Unfortunately, intracranial hemodynamics and wave dynamics in elderly patients with dementia remain poorly understood due to ethical issues and technical challenges. In this paper, we proposed a novel and easily achievable personalized methodology for the 0D-1D model of cerebral circulation using widely available clinical data on transcranial Doppler ultrasonography velocity, cerebral artery anatomy from magnetic resonance imaging, and brachial artery pressure. Using the proposed model, we simulated the cerebral blood flows and compared the wave dynamics between a healthy elderly subject and one living with dementia. Moreover, we performed a variance-based global sensitivity analysis to quantify the model-predicted WI and WP sensitivity to the uncertainties of model inputs. This provided more precise information for model personalization and further insights into the wave dynamics of cerebral circulation. In conclusion, the proposed personalized model framework provides a practical approach for patient-specific modeling and WI/WP analysis of cerebral circulation through noninvasive clinical data. The wave dynamics features of higher WI and lower WP in cerebral arteries may be an invaluable biomarker for assessing dementia risk.

The effect of left ventricular contractility on arterial hemodynamics: A model-based investigation

Ventricular-arterial coupling is a major determinant of cardiovascular performance, however, there are still inherent difficulties in distinguishing ventricular from vascular effects on arterial pulse phenotypes. In the present study, we employed an extensive mathematical model of the cardiovascular system to investigate how sole changes in cardiac contractility might affect hemodynamics. We simulated two physiologically relevant cases of high and low contractility by altering the end-systolic elastance, E_es, (3 versus 1 mmHg/mL) under constant cardiac output and afterload, and subsequently performed pulse wave analysis and wave separation. The aortic forward pressure wave component was steeper for high E_es, which led to the change of the total pressure waveform from the characteristic Type A phenotype to Type C, and the decrease in augmentation index, AIx (-2.4% versus +18.1%). Additionally, the increase in E_es caused the pulse pressure amplification from the aorta to the radial artery to rise drastically (1.86 versus 1.39). Our results show that an increase in cardiac contractility alone, with no concomitant change in arterial properties, alters the shape of the forward pressure wave, which, consequently, changes central and peripheral pulse phenotypes. Indices based on the pressure waveform, like AIx, cannot be assumed to reflect only arterial properties.

Multiscale Coupling of One-dimensional Vascular Models and Elastic Tissues

We present a computational multiscale model for the efficient simulation of vascularized tissues, composed of an elastic three-dimensional matrix and a vascular network. The effect of blood vessel pressure on the elastic tissue is surrogated via hyper-singular forcing terms in the elasticity equations, which depend on the fluid pressure. In turn, the blood flow in vessels is treated as a one-dimensional network. Intravascular pressure and velocity are simulated using a high-order finite volume scheme, while the elasticity equations for the tissue are solved using a finite element method. This work addresses the feasibility and the potential of the proposed coupled multiscale model. In particular, we assess whether the multiscale model is able to reproduce the tissue response at the effective scale (of the order of millimeters) while modeling the vasculature at the microscale. We validate the multiscale method against a full scale (three-dimensional) model, where the fluid/tissue interface is fully discretized and treated as a Neumann boundary for the elasticity equation. Next, we present simulation results obtained with the proposed approach in a realistic scenario, demonstrating that the method can robustly and efficiently handle the one-way coupling between complex fluid microstructures and the elastic matrix.

Fractional-order model representations of apparent vascular compliance as an alternative in the analysis of arterial stiffness: anin-silicostudy

Objective. Recent studies have demonstrated the advantages of fractional-order calculus tools for probing the viscoelastic properties of collagenous tissue, characterizing the arterial blood flow and red cell membrane mechanics, and modeling the aortic valve cusp. In this article, we present novel lumped-parameter equivalent circuit models for apparent arterial compliance using a fractional-order capacitor (FOC). FOCs, which generalize capacitors and resistors, display a fractional-order behavior that can capture both elastic and viscous properties through a power-law formulation.Approach. The proposed framework describes the dynamic relationship between the blood-pressure input and the blood volume, using linear fractional-order differential equations.Main results. The results show that the proposed models present a reasonable fit with thein-silicodata of more than 4000 subjects. Additionally, strong correlations have been identified between the fractional-order parameter estimates and the central hemodynamic determinants as well as the pulse-wave velocity indexes.Significance. Therefore, the fractional-order-based paradigm for arterial compliance shows notable potential as an alternative tool in the analysis of arterial stiffness.

Cardiac Magnetic Resonance Imaging in Pulmonary Arterial Hypertension: Ready for Clinical Practice and Guidelines?

Purpose of Review

Pulmonary arterial hypertension (PAH) is a progressive disease with high mortality. A greater understanding of the physiology and function of the cardiovascular system in PAH will help improve survival. This review covers the latest advances within cardiovascular magnetic resonance imaging (CMR) regarding diagnosis, evaluation of treatment, and prognostication of patients with PAH.

Recent Findings

New CMR measures that have been proven relevant in PAH include measures of ventricular and atrial volumes and function, tissue characterization, pulmonary artery velocities, and arterio-ventricular coupling.

Summary

CMR markers carry prognostic information relevant for clinical care such as treatment response and thereby can affect survival. Future research should investigate if CMR, as a non-invasive method, can improve existing measures or even provide new and better measures in the diagnosis, evaluation of treatment, and determination of prognosis of PAH.

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.