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.

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.

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.

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.

From fetus to neonate: A review of cardiovascular modeling in early life.

Computational modeling has well-established utility in the study of cardiovascular hemodynamics, with applications in medical research and, increasingly, in clinical settings to improve the diagnosis and treatment of cardiovascular diseases. Most cardiovascular models developed to date have been of the adult circulatory system; however, the perinatal period is unique as cardiovascular physiology undergoes drastic changes from the fetal circulation, during the birth transition, and into neonatal life. There may also be further complications in this period: for example, preterm birth (defined as birth before 37 completed weeks of gestation) carries risks of short-term cardiovascular instability and is associated with increased lifetime cardiovascular risk. Here, we review computational models of the cardiovascular system in early life, their applications to date and potential improvements and enhancements of these models. We propose a roadmap for developing an open-source cardiovascular model that spans the fetal, perinatal, and postnatal periods. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Congenital Diseases > Computational Models.

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.

Impact of baseline coronary flow and its distribution on fractional flow reserve prediction.

Model-based prediction of fractional flow reserve (FFR) in the context of stable coronary artery disease (CAD) diagnosis requires a number of modelling assumptions. One of these assumptions is the definition of a baseline coronary flow, ie, total coronary flow at rest prior to the administration of drugs needed to perform invasive measurements. Here we explore the impact of several methods available in the literature to estimate and distribute baseline coronary flow on FFR predictions obtained with a reduced-order model. We consider 63 patients with suspected stable CAD, for a total of 105 invasive FFR measurements. First, we improve a reduced-order model with respect to previous results and validate its performance versus results obtained with a 3D model. Next, we assess the impact of a wide range of methods to impose and distribute baseline coronary flow on FFR prediction, which proved to have a significant impact on diagnostic performance. However, none of the proposed methods resulted in a significant improvement of prediction error standard deviation. Finally, we show that intrinsic uncertainties related to stenosis geometry and the effect of hyperemic inducing drugs have to be addressed in order to improve FFR prediction accuracy.

The Effects of Cerebral Vasospasm on Cerebral Blood Flow and the Effects of Induced Hypertension: A Mathematical Modelling Study.

BACKGROUND: Induced hypertension has been used to promote cerebral blood flow under vasospastic conditions although there is no randomised clinical trial to support its use. We sought to mathematically model the effects of vasospasm on the cerebral blood flow and the effects of induced hypertension. METHODS: The Anatomically Detailed Arterial Network (ADAN) model is employed as the anatomical substrate in which the cerebral blood flow is simulated as part of the simulation of the whole body arterial circulation. The pressure drop across the spastic vessel is modelled by inserting a specific constriction model within the corresponding vessel in the ADAN model. We altered the degree of vasospasm, the length of the vasospastic segment, the location of the vasospasm, the pressure (baseline mean arterial pressure [MAP] 90 mm Hg, hypertension MAP 120 mm Hg, hypotension), and the presence of collateral supply. RESULTS: Larger decreases in cerebral flow were seen for diffuse spasm and more severe vasospasm. The presence of collateral supply could maintain cerebral blood flow, but only if the vasospasm did not occur distal to the collateral. Induced hypertension caused an increase in blood flow in all scenarios, but did not normalise blood flow even in the presence of moderate vasospasm (30%). Hypertension in the presence of a complete circle of Willis had a marginally greater effect on the blood flow, but did not normalise flow. CONCLUSION: Under vasospastic condition, cerebral blood flow varies considerably. Hypertension can raise the blood flow, but it is unable to restore cerebral blood flow to baseline.

On the anatomical definition of arterial networks in blood flow simulations: comparison of detailed and simplified models.

The goal of this work is to assess the impact of vascular anatomy definition degree in the predictions of blood flow models of the arterial network. To this end, results obtained with an anatomically detailed network containing over 2000 vessels are systematically compared with those obtained with an anatomically simplified network containing the main 86 vessels, the latter being a truncated version of the former one. The comparison is performed quantitatively and qualitatively in terms of pressure and flow rate waveforms, wave intensity analysis and impedance analysis. Comparisons are performed under physiological conditions and for the case of common carotid artery occlusion. Mechanisms of blood flow delivery to the brain, as well as different blood flow steal phenomena, are unveiled in light of model predictions. Results show that detailed and simplified models are in reasonable agreement regarding the hemodynamics in larger vessels and in healthy scenarios. The anatomically detailed arterial network features improved predictive capabilities at peripheral vessels. Moreover, discrepancies between models are substantially accentuated in the case of anatomical variations or abnormal hemodynamic conditions. We conclude that physiologically meaningful agreement between models is obtained for normal hemodynamic conditions. This agreement rapidly deteriorates for abnormal blood flow conditions such as those caused by total arterial occlusion. Differences are even larger when modifications of the vascular anatomy are considered. This rational comparison allows us to gain insight into the need for anatomically detailed arterial networks when addressing complex hemodynamic interactions.

Reduced-Order Unscented Kalman Filter With Observations in the Frequency Domain: Application to Computational Hemodynamics.

OBJECTIVE: The aim of this paper is to assess the potential of the reduced-order unscented Kalman's filter (ROUKF) in the context of computational hemodynamics, in order to estimate cardiovascular model parameters when employing real patient-specific data. METHODS: The approach combines an efficient blood flow solver for one-dimensional networks (for the forward problem) with the parameter estimation problem cast in the frequency space. Namely, the ROUKF is used to correct model parameters after each cardiac cycle, depending on the discrepancies of model outputs with respect to available observations properly mapped into the frequency space. RESULTS: First we validate the filter in frequency domain applying it in the context of a set of experimental measurements for an in vitro model. Second, we perform different numerical experiments aiming at parameter estimation using patient-specific data. CONCLUSION: Our results demonstrate that the filter in frequency domain allows a faster and more robust parameter estimation, when compared to its time-domain counterpart. Moreover, the proposed approach allows to estimate parameters that are not directly related to the network, but are crucial for targeting inter-individual parameter variability (e.g., parameters that characterize the cardiac output). SIGNIFICANCE: The ROUKF in frequency domain provides a robust and flexible tool for estimating parameters related to cardiovascular mathematical models using in vivo data.

Uncertainty Quantification and Sensitivity Analysis for Computational FFR Estimation in Stable Coronary Artery Disease.

PURPOSE: The main objectives of this study are to validate a reduced-order model for the estimation of the fractional flow reserve (FFR) index based on blood flow simulations that incorporate clinical imaging and patient-specific characteristics, and to assess the uncertainty of FFR predictions with respect to input data on a per patient basis. METHODS: We consider 13 patients with symptoms of stable coronary artery disease for which 24 invasive FFR measurements are available. We perform an extensive sensitivity analysis on the parameters related to the construction of a reduced-order (hybrid 1D-0D) model for FFR predictions. Next we define an optimal setting by comparing reduced-order model predictions with solutions based on the 3D incompressible Navier-Stokes equations. Finally, we characterize prediction uncertainty with respect to input data and identify the most influential inputs by means of sensitivity analysis. RESULTS: Agreement between FFR computed by the reduced-order model and by the full 3D model was satisfactory, with a bias ([Formula: see text]) of [Formula: see text] at the 24 measured locations. Moreover, the uncertainty related to the factor by which peripheral resistance is reduced from baseline to hyperemic conditions proved to be the most influential parameter for FFR predictions, whereas uncertainty in stenosis geometry had greater effect in cases with low FFR. CONCLUSION: Model errors related to solving a simplified reduced-order model rather than a full 3D problem were small compared with uncertainty related to input data. Improved measurement of coronary blood flow has the potential to reduce uncertainty in computational FFR predictions significantly.

Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations.

We propose a detailed CellML model of the human cerebral circulation that runs faster than real time on a desktop computer and is designed for use in clinical settings when the speed of response is important. A lumped parameter mathematical model, which is based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, is constructed using a bond graph formulation to ensure mass conservation and energy conservation. The model includes arterial vessels with geometric and anatomical data based on the ADAN circulation model. The peripheral beds are represented by lumped parameter compartments. We compare the hemodynamics predicted by the bond graph formulation of the cerebral circulation with that given by a classical one-dimensional Navier-Stokes model working on top of the whole-body ADAN model. Outputs from the bond graph model, including the pressure and flow signatures and blood volumes, are compared with physiological data.

Blood pressure gradients in cerebral arteries: a clue to pathogenesis of cerebral small vessel disease.

RATIONALE: The role of hypertension in cerebral small vessel disease is poorly understood. At the base of the brain (the 'vascular centrencephalon'), short straight arteries transmit blood pressure directly to small resistance vessels; the cerebral convexity is supplied by long arteries with many branches, resulting in a drop in blood pressure. Hypertensive small vessel disease (lipohyalinosis) causes the classically described lacunar infarctions at the base of the brain; however, periventricular white matter intensities (WMIs) seen on MRI and WMI in subcortical areas over the convexity, which are often also called 'lacunes', probably have different aetiologies. OBJECTIVES: We studied pressure gradients from proximal to distal regions of the cerebral vasculature by mathematical modelling. METHODS AND RESULTS: Blood flow/pressure equations were solved in an Anatomically Detailed Arterial Network (ADAN) model, considering a normotensive and a hypertensive case. Model parameters were suitably modified to account for structural changes in arterial vessels in the hypertensive scenario. Computations predict a marked drop in blood pressure from large and medium-sized cerebral vessels to cerebral peripheral beds. When blood pressure in the brachial artery is 192/113 mm Hg, the pressure in the small arterioles of the posterior parietal artery bed would be only 117/68 mm Hg. In the normotensive case, with blood pressure in the brachial artery of 117/75 mm Hg, the pressure in small parietal arterioles would be only 59/38 mm Hg. CONCLUSION: These findings have important implications for understanding small vessel disease. The marked pressure gradient across cerebral arteries should be taken into account when evaluating the pathogenesis of small WMIs on MRI. Hypertensive small vessel disease, affecting the arterioles at the base of the brain should be distinguished from small vessel disease in subcortical regions of the convexity and venous disease in the periventricular white matter.

Computer-aided quantification of microvascular networks: Application to alterations due to pathological angiogenesis in the hamster.

Angiogenesis is both a physiological and a pathological process of great complexity, which is difficult to measure objectively and automatically. The hamster cheek pouch (HCP) prepared for intravital-microscopy (IVM) has been used to characterize microvascular functions in many studies and was chosen to investigate microvascular characteristics observed in normal non-infected hamsters as compared to those HCPs parasitized by Trypanosoma cruzi. Images of HCPs captured at IVM were subjected to computer based measurements of angiogenesis and histamine-induced macromolecular (FITC-dextran) leakage with an image segmentation approach that has the capacity to discriminate between fluorescence emitted by macromolecular tracers inside the vasculature and in the extravascular space. We present such an automatic segmentation methodology using known tools from image processing field that, to our knowledge, have not been tested in IVM images. We have compared this methodology with a recently published segmentation strategy based on image intensity thresholding. Our method renders an accurate and robust segmentation of blood vessels for different microvascular scenarios, normal and pathological. Application of the proposed strategy for objective and automatic measurement of angiogenesis detection was explored in detail.

Assessment of reduced-order unscented Kalman filter for parameter identification in 1-dimensional blood flow models using experimental data.

This work presents a detailed investigation of a parameter estimation approach on the basis of the reduced-order unscented Kalman filter (ROUKF) in the context of 1-dimensional blood flow models. In particular, the main aims of this study are (1) to investigate the effects of using real measurements versus synthetic data for the estimation procedure (i.e., numerical results of the same in silico model, perturbed with noise) and (2) to identify potential difficulties and limitations of the approach in clinically realistic applications to assess the applicability of the filter to such setups. For these purposes, the present numerical study is based on a recently published in vitro model of the arterial network, for which experimental flow and pressure measurements are available at few selected locations. To mimic clinically relevant situations, we focus on the estimation of terminal resistances and arterial wall parameters related to vessel mechanics (Young's modulus and wall thickness) using few experimental observations (at most a single pressure or flow measurement per vessel). In all cases, we first perform a theoretical identifiability analysis on the basis of the generalized sensitivity function, comparing then the results owith the ROUKF, using either synthetic or experimental data, to results obtained using reference parameters and to available measurements.

Roadmap for cardiovascular circulation model.

Computational models of many aspects of the mammalian cardiovascular circulation have been developed. Indeed, along with orthopaedics, this area of physiology is one that has attracted much interest from engineers, presumably because the equations governing blood flow in the vascular system are well understood and can be solved with well-established numerical techniques. Unfortunately, there have been only a few attempts to create a comprehensive public domain resource for cardiovascular researchers. In this paper we propose a roadmap for developing an open source cardiovascular circulation model. The model should be registered to the musculo-skeletal system. The computational infrastructure for the cardiovascular model should provide for near real-time computation of blood flow and pressure in all parts of the body. The model should deal with vascular beds in all tissues, and the computational infrastructure for the model should provide links into CellML models of cell function and tissue function. In this work we review the literature associated with 1D blood flow modelling in the cardiovascular system, discuss model encoding standards, software and a model repository. We then describe the coordinate systems used to define the vascular geometry, derive the equations and discuss the implementation of these coupled equations in the open source computational software OpenCMISS. Finally, some preliminary results are presented and plans outlined for the next steps in the development of the model, the computational software and the graphical user interface for accessing the model.

A high-order local time stepping finite volume solver for one-dimensional blood flow simulations: application to the ADAN model.

In recent years, the complexity of vessel networks for one-dimensional blood flow models has significantly increased, because of enhanced anatomical detail or automatic peripheral vasculature generation, for example. This fact, along with the application of these models in uncertainty quantification and parameter estimation poses the need for extremely efficient numerical solvers. The aim of this work is to present a finite volume solver for one-dimensional blood flow simulations in networks of elastic and viscoelastic vessels, featuring high-order space-time accuracy and local time stepping (LTS). The solver is built on (i) a high-order finite volume type numerical scheme, (ii) a high-order treatment of the numerical solution at internal vertexes of the network, often called junctions, and (iii) an accurate LTS strategy. The accuracy of the proposed methodology is verified by empirical convergence tests. Then, the resulting LTS scheme is applied to arterial networks of increasing complexity and spatial scale heterogeneity, with a number of one-dimensional segments ranging from a few tens up to several thousands and vessel lengths ranging from less than a millimeter up to tens of centimeters, in order to evaluate its computational cost efficiency. The proposed methodology can be extended to any other hyperbolic system for which network applications are relevant. Copyright © 2016 John Wiley & Sons, Ltd.

Impact of Jugular Vein Valve Function on Cerebral Venous Haemodynamics.

We quantify the effect of internal-jugular vein function on intracranial venous haemodynamics, with particular attention paid to venous reflux and intracranial venous hypertension. Haemodynamics in the head and neck is quantified by computing the velocity, flow and pressure fields, and vessel cross-sectional area in all major arteries and veins. For the computations we use a global, closed-loop multi-scale mathematical model for the entire human circulation, recently developed by the first two authors. Validation of the model against in vitro and in vivo Magnetic Resonance Imaging (MRI) measurements have been reported elsewhere. Here, the circulation model is equipped with a sub-model for venous valves. For the study, in addition to a healthy control, we identify two venous-valve related conditions, namely valve incompetence and valve obstruction. A parametric study for subjects in the supine position is carried out for nine cases. It is found that valve function has a visible effect on intracranial venous haemodynamics, including dural sinuses and deep cerebral veins. In particular, valve obstruction causes venous reflux, redirection of flow and intracranial venous hypertension. The clinical implications of the findings are unknown, though they may relate to recent hypotheses linking some neurological conditions to extra-cranial venous anomalies.

A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling.

Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.