SUMMARYHaemodynamical 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 threedimensional 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.

We present a framework for the estimation of the Fractional Flow Reserve index based on blood ow simulations that incorporate clinical imaging and patient-specic characteristics. The process of model design implies making choices in order to build a suitable mathematical model, e.g. simulating a 3D domain versus a 1D domain, modeling of peripheral resistances, determining the regions of interest, etc. Here we thoroughly evaluate the impact of such choices on FFR prediction accuracy by reduced-order models with respect to more complete models by means of uncertainty quantication and sensitivity analysis. Moreover, we assess the uncertainty of FFR predictions based on our framework with respect to input data, and further determine the most inuential inputs with sensitivity analysis, aiming at increasing the clinical usability of predictions by providing information on the reliability of model output on a per case basis. Analysis is carried out for a population of 13 patients for which 24 invasive FFR measurements are available. Our analysis conrms previously observed sources of uncertainty and provides insight into aspects to be improved in any model-based non-invasive FFR estimation method.

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.

As computational models of the cardiovascular system are applied in modern personalized medicine, maximizing certainty of model input becomes crucial. A model with a high number of arterial segments results in a more realistic description of the system, but also requires a high number of parameters with associated uncertainties. In this paper, we present a method to optimize/reduce the number of arterial segments included in one-dimensional blood flow models, while preserving key features of flow and pressure waveforms. We quantify the preservation of key flow features for the optimal network with respect to the baseline networks (a 96-artery and a patient-specific coronary network) by various metrics and quantities like average relative error, pulse pressure and augmentation pressure. Furthermore, various physiological and pathological states are considered. For the aortic root and larger systemic artery pressure waveforms a network with minimal description of lower and upper limb arteries and no cerebral arteries, sufficiently captures important features such as pressure augmentation and pulse pressure. Discrepancies in carotid and middle cerebral artery flow waveforms that are introduced by describing the arterial system in a minimalistic manner are small compared with errors related to uncertainties in blood flow measurements obtained by ultrasound.

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