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.

In this work we propose to validate the predictive capabilities of one-dimensional (1D) blood flow models with full three-dimensional (3D) models in the context of patient-specific coronary hemodynamics in hyperemic conditions. Such conditions mimic the state of coronary circulation during the acquisition of the Fractional Flow Reserve (FFR) index. Demonstrating that 1D models accurately reproduce FFR estimates obtained with 3D models has implications in the approach to computationally estimate FFR. To this end, a sample of 20 patients was employed from which 29 3D geometries of arterial trees were constructed, 9 obtained from coronary computed tomography angiography (CCTA) and 20 from intra-vascular ultrasound (IVUS). For each 3D arterial model, a 1D counterpart was generated. The same outflow and inlet pressure boundary conditions were applied to both (3D and 1D) models. In the 1D setting, pressure losses at stenoses and bifurcations were accounted for through specific lumped models. Comparisons between 1D models (FFR1D) and 3D models (FFR3D) were performed in terms of predicted FFR value. Compared to FFR3D, FFR1D resulted with a difference of 0.00 ± 0.03 and overall predictive capability AUC, Acc, Spe, Sen, PPV and NPV of 0.97, 0.98, 0.90, 0.99, 0.82, and 0.99, with an FFR threshold of 0.8. We conclude that inexpensive FFR1D simulations can be reliably used as a surrogate of demanding FFR3D computations.

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.

An extension of a total variation diminishing (TVD) scheme to solve one-dimensional (1D) blood flow for human circulation is proposed. This method is simple as it involves only a few modifications to existing shock-capturing TVD schemes. We have applied the method to a wide range of test cases including a complete simulation of the human vascular network. Excellent solutions have been demonstrated for problems involving varying and discontinuous mechanical properties of blood vessels. For 1D network simulations, the method has been shown to agree well with the reported computational results. Finally, the method has been demonstrated to compare favorably with in vivo experiments set up to study the impact of circle of Willis anomalies on flow patterns in the cerebral arterial system.

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.