Comparison of 1D and 3D Models for the Estimation of Fractional Flow Reserve

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

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

Establishing the longitudinal hemodynamic mapping framework for wearable-driven coronary digital twins

Understanding the evolving nature of coronary hemodynamics is crucial for early disease detection and monitoring progression. We require digital twins that mimic a patient's circulatory system by integrating continuous physiological data and computing hemodynamic patterns over months. Current models match clinical flow measurements but are limited to single heartbeats. To this end, we introduced the longitudinal hemodynamic mapping framework (LHMF), designed to tackle critical challenges: (1) computational intractability of explicit methods; (2) boundary conditions reflecting varying activity states; and (3) accessible computing resources for clinical translation. We show negligible error (0.0002-0.004%) between LHMF and explicit data of 750 heartbeats. We deployed LHMF across traditional and cloud-based platforms, demonstrating high-throughput simulations on heterogeneous systems. Additionally, we established LHMFC, where hemodynamically similar heartbeats are clustered to avoid redundant simulations, accurately reconstructing longitudinal hemodynamic maps (LHMs). This study captured 3D hemodynamics over 4.5 million heartbeats, paving the way for cardiovascular digital twins.

Computational framework for the generation of one-dimensional vascular models accounting for uncertainty in networks extracted from medical images

One-dimensional (1D) cardiovascular models offer a non-invasive method to answer medical questions, including predictions of wave-reflection, shear stress, functional flow reserve, vascular resistance and compliance. This model type can predict patient-specific outcomes by solving 1D fluid dynamics equations in geometric networks extracted from medical images. However, the inherent uncertainty in in vivo imaging introduces variability in network size and vessel dimensions, affecting haemodynamic predictions. Understanding the influence of variation in image-derived properties is essential to assess the fidelity of model predictions. Numerous programs exist to render three-dimensional surfaces and construct vessel centrelines. Still, there is no exact way to generate vascular trees from the centrelines while accounting for uncertainty in data. This study introduces an innovative framework employing statistical change point analysis to generate labelled trees that encode vessel dimensions and their associated uncertainty from medical images. To test this framework, we explore the impact of uncertainty in 1D haemodynamic predictions in a systemic and pulmonary arterial network. Simulations explore haemodynamic variations resulting from changes in vessel dimensions and segmentation; the latter is achieved by analysing multiple segmentations of the same images. Results demonstrate the importance of accurately defining vessel radii and lengths when generating high-fidelity patient-specific haemodynamics models. KEY POINTS: This study introduces novel algorithms for generating labelled directed trees from medical images, focusing on accurate junction node placement and radius extraction using change points to provide haemodynamic predictions with uncertainty within expected measurement error. Geometric features, such as vessel dimension (length and radius) and network size, significantly impact pressure and flow predictions in both pulmonary and aortic arterial networks. Standardizing networks to a consistent number of vessels is crucial for meaningful comparisons and decreases haemodynamic uncertainty. Change points are valuable to understanding structural transitions in vascular data, providing an automated and efficient way to detect shifts in vessel characteristics and ensure reliable extraction of representative vessel radii.

Guidelines for mechanistic modeling and analysis in cardiovascular research

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

Patient-specific in silico 3D coronary model in cardiac catheterisation laboratories

Coronary artery disease is caused by the buildup of atherosclerotic plaque in the coronary arteries, affecting the blood supply to the heart, one of the leading causes of death around the world. X-ray coronary angiography is the most common procedure for diagnosing coronary artery disease, which uses contrast material and x-rays to observe vascular lesions. With this type of procedure, blood flow in coronary arteries is viewed in real-time, making it possible to detect stenoses precisely and control percutaneous coronary interventions and stent insertions. Angiograms of coronary arteries are used to plan the necessary revascularisation procedures based on the calculation of occlusions and the affected segments. However, their interpretation in cardiac catheterisation laboratories presently relies on sequentially evaluating multiple 2D image projections, which limits measuring lesion severity, identifying the true shape of vessels, and analysing quantitative data. In silico modelling, which involves computational simulations of patient-specific data, can revolutionise interventional cardiology by providing valuable insights and optimising treatment methods. This paper explores the challenges and future directions associated with applying patient-specific in silico models in catheterisation laboratories. We discuss the implications of the lack of patient-specific in silico models and how their absence hinders the ability to accurately predict and assess the behaviour of individual patients during interventional procedures. Then, we introduce the different components of a typical patient-specific in silico model and explore the potential future directions to bridge this gap and promote the development and utilisation of patient-specific in silico models in the catheterisation laboratories.

Rapid and Precise Computation of Fractional Flow Reserve from Routine Two-Dimensional Coronary Angiograms Based on Fluid Mechanics: The Pilot FFR2D Study

Objective: To present a novel pipeline for rapid and precise computation of fractional flow reserve from an analysis of routine two-dimensional coronary angiograms based on fluid mechanics equations (FFR2D). Material and methods: This was a pilot analytical study that was designed to assess the diagnostic performance of FFR2D versus the gold standard of FFR (threshold ≤ 0.80) measured with a pressure wire for the physiological assessment of intermediate coronary artery stenoses. In a single academic center, consecutive patients referred for diagnostic coronary angiography and potential revascularization between 1 September 2020 and 1 September 2022 were screened for eligibility. Routine two-dimensional angiograms at optimal viewing angles with minimal overlap and/or foreshortening were segmented semi-automatically to derive the vascular geometry of intermediate coronary lesions, and nonlinear pressure-flow mathematical relationships were applied to compute FFR2D. Results: Some 88 consecutive patients with a single intermediate coronary artery lesion were analyzed (LAD n = 74, RCA n = 9 and LCX n = 5; percent diameter stenosis of 45.7 ± 11.0%). The computed FFR2D was on average 0.821 ± 0.048 and correlated well with invasive FFR (r = 0.68, p < 0.001). There was very good agreement between FFR2D and invasive-wire FFR with minimal measurement bias (mean difference: 0.000 ± 0.048). The overall accuracy of FFR2D for diagnosing a critical epicardial artery stenosis was 90.9% (80 cases classified correctly out of 88 in total). FFR2D identified 24 true positives, 56 true negatives, 4 false positives, and 4 false negatives and predicted FFR ≤ 0.80 with a sensitivity of 85.7%, specificity of 93.3%, positive likelihood ratio of 13.0, and negative likelihood ratio of 0.15. FFR2D had a significantly better discriminatory capacity (area under the ROC curve: 0.95 [95% CI: 0.91-0.99]) compared to 50%DS on 2D-QCA (area under the ROC curve: 0.70 [95% CI: 0.59-0.82]; p = 0.0001) in predicting wire FFR ≤ 0.80. The median time of image analysis was 2 min and the median time of computation of the FFR2D results was 0.1 s. Conclusion: FFR2D may rapidly derive a precise image-based metric of fractional flow reserve with high diagnostic accuracy based on a single two-dimensional coronary angiogram.

Computational framework for the generation of one-dimensional vascular models accounting for uncertainty in networks extracted from medical images

One-dimensional (1D) cardiovascular models offer a non-invasive method to answer medical questions, including predictions of wave-reflection, shear stress, functional flow reserve, vascular resistance, and compliance. This model type can predict patient-specific outcomes by solving 1D fluid dynamics equations in geometric networks extracted from medical images. However, the inherent uncertainty in in-vivo imaging introduces variability in network size and vessel dimensions, affecting hemodynamic predictions. Understanding the influence of variation in image-derived properties is essential to assess the fidelity of model predictions. Numerous programs exist to render three-dimensional surfaces and construct vessel centerlines. Still, there is no exact way to generate vascular trees from the centerlines while accounting for uncertainty in data. This study introduces an innovative framework employing statistical change point analysis to generate labeled trees that encode vessel dimensions and their associated uncertainty from medical images. To test this framework, we explore the impact of uncertainty in 1D hemodynamic predictions in a systemic and pulmonary arterial network. Simulations explore hemodynamic variations resulting from changes in vessel dimensions and segmentation; the latter is achieved by analyzing multiple segmentations of the same images. Results demonstrate the importance of accurately defining vessel radii and lengths when generating high-fidelity patient-specific hemodynamics models.

Accelerated simulation methodologies for computational vascular flow modelling

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

CT-derived Fractional Flow Reserve: How, When, and Where to use this Novel Cardiac Imaging Tool

Fractional flow reserve computed tomography (FFRCT) is a novel imaging modality. It utilizes computational fluid dynamics analysis of coronary blood flow obtained from CCTA images to estimate the decrease in pressure across coronary stenosis during the maximum hyperemia. The FFRCT can serve as a valuable tool in the assessment of coronary artery disease (CAD). This non-invasive option can be used as an alternative to the invasive fractional Flow Reserve (FFR) evaluation, which is presently considered the gold standard for evaluating the physiological significance of coronary stenoses. It can help in several clinical situations, including Assessment of Acute and stable chest pain, virtual planning for coronary stenting, and treatment decision-making. Although FFRCT has demonstrated potential clinical applications as a non-invasive imaging technique, it is also crucial to acknowledge its limitations in clinical practice. As a result, it is imperative to meticulously evaluate the advantages and drawbacks of FFRCT individually and contemplate its application in combination with other diagnostic examinations and clinical data.

High-Speed On-Site Deep Learning-Based FFR-CT Algorithm: Evaluation Using Invasive Angiography as the Reference Standard

BACKGROUND. Estimation of fractional flow reserve from coronary CTA (FFR-CT) is an established method of assessing the hemodynamic significance of coronary lesions. However, clinical implementation has progressed slowly, partly because of off-site data transfer with long turnaround times for results. OBJECTIVE. The purpose of this study was to evaluate the diagnostic performance of FFR-CT computed on-site with a high-speed deep learning-based algorithm with invasive hemodynamic indexes as the reference standard. METHODS. This retrospective study included 59 patients (46 men, 13 women; mean age, 66.5 ± 10.2 years) who underwent coronary CTA (including calcium scoring) followed within 90 days by invasive angiography with invasive fractional flow reserve (FFR) and/or instantaneous wave-free ratio measurements from December 2014 to October 2021. Coronary artery lesions were considered to have hemodynamically significant stenosis in the presence of invasive FFR of 0.80 or less and/or instantaneous wave-free ratio of 0.89 or less. A single cardiologist evaluated the CTA images using an on-site deep learning-based semiautomated algorithm entailing a 3D computational flow dynamics model to determine FFR-CT for coronary artery lesions detected with invasive angiography. Time for FFR-CT analysis was recorded. FFR-CT analysis was repeated by the same cardiologist in 26 randomly selected examinations and by a different cardiologist in 45 randomly selected examinations. Diagnostic performance and agreement were assessed. RESULTS. A total of 74 lesions were identified with invasive angiography. FFR-CT and invasive FFR had strong correlation (r = 0.81) and, in Bland-Altman analysis, bias of 0.01 and 95% limits of agreement of -0.13 to 0.15. FFR-CT had AUC for hemodynamically significant stenosis of 0.975. At a cutoff of 0.80 or less, FFR-CT had 95.9% accuracy, 93.5% sensitivity, and 97.7% specificity. In 39 lesions with severe calcifications (≥ 400 Agatston units), FFR-CT had AUC of 0.991 and at a cutoff of 0.80, 94.7% sensitivity, 95.0% specificity, and 94.9% accuracy. Mean analysis time per patient was 7 minutes 54 seconds. Intraobserver agreement (intraclass correlation coefficient, 0.85; bias, -0.01; 95% limits of agreement, -0.12 and 0.10) and interobserver agreement (intraclass correlation coefficient, 0.94; bias, -0.01; 95% limits of agreement, -0.08 and 0.07) were good to excellent. CONCLUSION. A high-speed on-site deep learning-based FFR-CT algorithm had excellent diagnostic performance for hemodynamically significant stenosis with high reproducibility. CLINICAL IMPACT. The algorithm should facilitate implementation of FFR-CT technology into routine clinical practice.

A novel physics-based model for fast computation of blood flow in coronary arteries

Blood flow and pressure calculated using the currently available methods have shown the potential to predict the progression of pathology, guide treatment strategies and help with postoperative recovery. However, the conspicuous disadvantage of these methods might be the time-consuming nature due to the simulation of virtual interventional treatment. The purpose of this study is to propose a fast novel physics-based model, called FAST, for the prediction of blood flow and pressure. More specifically, blood flow in a vessel is discretized into a number of micro-flow elements along the centerline of the artery, so that when using the equation of viscous fluid motion, the complex blood flow in the artery is simplified into a one-dimensional (1D) steady-state flow. We demonstrate that this method can compute the fractional flow reserve (FFR) derived from coronary computed tomography angiography (CCTA). 345 patients with 402 lesions are used to evaluate the feasibility of the FAST simulation through a comparison with three-dimensional (3D) computational fluid dynamics (CFD) simulation. Invasive FFR is also introduced to validate the diagnostic performance of the FAST method as a reference standard. The performance of the FAST method is comparable with the 3D CFD method. Compared with invasive FFR, the accuracy, sensitivity and specificity of FAST is 88.6%, 83.2% and 91.3%, respectively. The AUC of FFR_FAST is 0.906. This demonstrates that the FAST algorithm and 3D CFD method show high consistency in predicting steady-state blood flow and pressure. Meanwhile, the FAST method also shows the potential in detecting lesion-specific ischemia.

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

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

Validity and Diagnostic Performance of Computing Fractional Flow Reserve From 2-Dimensional Coronary Angiography Images

BACKGROUND

Measurement of fractional flow reserve (FFR) is the gold standard for determining the physiologic significance of coronary artery stenosis, but newer software programs can calculate the FFR from 2-dimensional angiography images.

METHODS

A retrospective analysis was conducted using the records of patients with intermediate coronary stenoses who had undergone adenosine FFR (aFFR). To calculate the computed FFR, a software program used simulated coronary blood flow using computational geometry constructed using at least 2 patient-specific angiographic images. Two cardiologists reviewed the angiograms and determined the computational FFR independently. Intraobserver variability was measured using κ analysis and the intraclass correlation coefficient. The correlation coefficient and Bland-Altman plots were used to assess the agreement between the calculated FFR and the aFFR.

RESULTS

A total of 146 patients were included, with 95 men and 51 women, with a mean (SD) age of 61.1 (9.5) y. The mean (SD) aFFR was 0.847 (0.072), and 41 patients (27.0%) had an aFFR of 0.80 or less. There was a strong intraobserver correlation between the computational FFRs (r = 0.808; P < .001; κ = 0.806; P < .001). There was also a strong correlation between aFFR and computational FFR (r = 0.820; P < .001) and good agreement on the Bland-Altman plot. The computational FFR had a high sensitivity (95.1%) and specificity (90.1%) for detecting an aFFR of 0.80 or less.

CONCLUSION

A novel software program provides a feasible method of calculating FFR from coronary angiography images without resorting to pharmacologically induced hyperemia.

Analysis identifying minimal governing parameters for clinically accurate in silico fractional flow reserve

Background

Personalized hemodynamic models can accurately compute fractional flow reserve (FFR) from coronary angiograms and clinical measurements (FFR baseline ), but obtaining patient-specific data could be challenging and sometimes not feasible. Understanding which measurements need to be patient-tuned vs. patient-generalized would inform models with minimal inputs that could expedite data collection and simulation pipelines.

Aims

To determine the minimum set of patient-specific inputs to compute FFR using invasive measurement of FFR (FFR invasive ) as gold standard.

Materials and Methods

Personalized coronary geometries ( N = 50 ) were derived from patient coronary angiograms. A computational fluid dynamics framework, FFR baseline , was parameterized with patient-specific inputs: coronary geometry, stenosis geometry, mean arterial pressure, cardiac output, heart rate, hematocrit, and distal pressure location. FFR baseline was validated against FFR invasive and used as the baseline to elucidate the impact of uncertainty on personalized inputs through global uncertainty analysis. FFR streamlined was created by only incorporating the most sensitive inputs and FFR semi-streamlined additionally included patient-specific distal location.

Results

FFR baseline was validated against FFR invasive via correlation ( r = 0.714 , p < 0.001 ), agreement (mean difference: 0.01 ± 0.09 ), and diagnostic performance (sensitivity: 89.5%, specificity: 93.6%, PPV: 89.5%, NPV: 93.6%, AUC: 0.95). FFR semi-streamlined provided identical diagnostic performance with FFR baseline . Compared to FFR baseline vs. FFR invasive , FFR streamlined vs. FFR invasive had decreased correlation ( r = 0.64 , p < 0.001 ), improved agreement (mean difference: 0.01 ± 0.08 ), and comparable diagnostic performance (sensitivity: 79.0%, specificity: 90.3%, PPV: 83.3%, NPV: 87.5%, AUC: 0.90).

Conclusion

Streamlined models could match the diagnostic performance of the baseline with a full gamut of patient-specific measurements. Capturing coronary hemodynamics depended most on accurate geometry reconstruction and cardiac output measurement.

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

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

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.

Global Sensitivity Analysis For Clinically Validated 1D Models of Fractional Flow Reserve

Computation of Fractional Flow Reserve (FFR) through computational fluid dynamics (CFD) is used to guide intervention and often uses a number of clinically-derived metrics, but these patient-specific data could be costly and difficult to obtain. Understanding which parameters can be approximated from population averages and which parameters need to be patient-specific is important and remains largely unexplored. In this study, we performed a global sensitivity study on two 1D models of FFR to identify the most influential patient parameters. Our results indicated that vessel compliance, cardiac cycle period, flow rate, density, viscosity, and elastic modulus contributed minimally to the variance in FFR and may be approximated from population averages. On the other hand, outlet resistance (i.e., microvascular resistance), stenosis degree, and percent stenosis length contributed the most to FFR computation and needed to be tuned to the patient of interest. Selective measuring of patient-specific parameters may significantly reduce costs and streamline the simulation pipeline without reducing accuracy.

CT-based fractional flow reserve: development and expanded application

Computations of fractional flow reserve, based on CT coronary angiography and computational fluid dynamics (CT-based FFR) to assess the severity of coronary artery stenosis, was introduced around a decade ago and is now one of the most successful applications of computational fluid dynamic modelling in clinical practice. Although the mathematical modelling framework behind this approach and the clinical operational model vary, its clinical efficacy has been demonstrated well in general. In this review, technical elements behind CT-based FFR computation are summarised with some key assumptions and challenges. Examples of these challenges include the complexity of the model (such as blood viscosity and vessel wall compliance modelling), whose impact has been debated in the research. Efforts made to address the practical challenge of processing time are also reviewed. Then, further application areas—myocardial bridge, renal stenosis and lower limb stenosis—are discussed along with specific challenges expected in these areas.

An improved reduced-order model for pressure drop across arterial stenoses

Quantification of pressure drop across stenotic arteries is a major element in the functional assessment of occlusive arterial disease. Accurate estimation of the pressure drop with a numerical model allows the calculation of Fractional Flow Reserve (FFR), which is a haemodynamic index employed for guiding coronary revascularisation. Its non-invasive evaluation would contribute to safer and cost-effective diseases management. In this work, we propose a new formulation of a reduced-order model of trans-stenotic pressure drop, based on a consistent theoretical analysis of the Navier-Stokes equation. The new formulation features a novel term that characterises the contribution of turbulence effect to pressure loss. Results from three-dimensional computational fluid dynamics (CFD) showed that the proposed model produces predictions that are significantly more accurate than the existing reduced-order models, for large and small symmetric and eccentric stenoses, covering mild to severe area reductions. FFR calculations based on the proposed model produced zero classification error for three classes comprising positive (≤ 0.75), negative (≥ 0.8) and intermediate (0.75 − 0.8) classes.

Model order reduction of flow based on a modular geometrical approximation of blood vessels

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g., straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by Proper Orthogonal Decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier-Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton-Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.

A multiscale model of vascular function in chronic thromboembolic pulmonary hypertension

Chronic thromboembolic pulmonary hypertension (CTEPH) is caused by recurrent or unresolved pulmonary thromboemboli, leading to perfusion defects and increased arterial wave reflections. CTEPH treatment aims to reduce pulmonary arterial pressure and reestablish adequate lung perfusion, yet patients with distal lesions are inoperable by standard surgical intervention. Instead, these patients undergo balloon pulmonary angioplasty (BPA), a multisession, minimally invasive surgery that disrupts the thromboembolic material within the vessel lumen using a catheter balloon. However, there still lacks an integrative, holistic tool for identifying optimal target lesions for treatment. To address this insufficiency, we simulate CTEPH hemodynamics and BPA therapy using a multiscale fluid dynamics model. The large pulmonary arterial geometry is derived from a computed tomography (CT) image, whereas a fractal tree represents the small vessels. We model ring- and web-like lesions, common in CTEPH, and simulate normotensive conditions and four CTEPH disease scenarios; the latter includes both large artery lesions and vascular remodeling. BPA therapy is simulated by simultaneously reducing lesion severity in three locations. Our predictions mimic severe CTEPH, manifested by an increase in mean proximal pulmonary arterial pressure above 20 mmHg and prominent wave reflections. Both flow and pressure decrease in vessels distal to the lesions and increase in unobstructed vascular regions. We use the main pulmonary artery (MPA) pressure, a wave reflection index, and a measure of flow heterogeneity to select optimal target lesions for BPA. In summary, this study provides a multiscale, image-to-hemodynamics pipeline for BPA therapy planning for patients with inoperable CTEPH. NEW & NOTEWORTHY This article presents novel computational framework for predicting pulmonary hemodynamics in chronic thromboembolic pulmonary hypertension. The mathematical model is used to identify the optimal target lesions for balloon pulmonary angioplasty, combining simulated pulmonary artery pressure, wave intensity analysis, and a new quantitative metric of flow heterogeneity.

Seven Mathematical Models of Hemorrhagic Shock

Although mathematical modelling of pressure-flow dynamics in the cardiocirculatory system has a lengthy history, readily finding the appropriate model for the experimental situation at hand is often a challenge in and of itself. An ideal model would be relatively easy to use and reliable, besides being ethically acceptable. Furthermore, it would address the pathogenic features of the cardiovascular disease that one seeks to investigate. No universally valid model has been identified, even though a host of models have been developed. The object of this review is to describe several of the most relevant mathematical models of the cardiovascular system: the physiological features of circulatory dynamics are explained, and their mathematical formulations are compared. The focus is on the whole-body scale mathematical models that portray the subject's responses to hypovolemic shock. The models contained in this review differ from one another, both in the mathematical methodology adopted and in the physiological or pathological aspects described. Each model, in fact, mimics different aspects of cardiocirculatory physiology and pathophysiology to varying degrees: some of these models are geared to better understand the mechanisms of vascular hemodynamics, whereas others focus more on disease states so as to develop therapeutic standards of care or to test novel approaches. We will elucidate key issues involved in the modeling of cardiovascular system and its control by reviewing seven of these models developed to address these specific purposes.

From anatomy to function and then back to anatomy: invasive assessment of myocardial ischemia in the catheterization laboratory based on anatomy-derived indices of coronary physiology

For many decades, the severity of coronary artery disease (CAD) and the indication to proceed with either percutaneous coronary intervention (PCI) or surgical revascularization has been based on anatomically derived parameters of vessel stenosis, and typically on the percentage of lumen diameter stenosis (DS%) as determined by invasive coronary angiography (CA). However, it is currently a well-accepted concept that pre-specified thresholds of DS% have a weak correlation with the ischemic and functional potential of an epicardial coronary stenosis. In this regard, the introduction of fractional-flow reserve (FFR) has represented a paradigm-shift in the understanding, diagnosis, and treatment of CAD, but the adoption of FFR into the clinical practice remains surprisingly limited and sub-standard, probably because of the inherent drawbacks of pressure-wire-based technology such as additional costs, prolonged procedural time, invasive instrumentation of the target vessel, and use of vaso-dilatory agents causing side effects for patients. For this reason, new modalities are under development or validation to derive FFR from computational fluid dynamics (CFD) applied to a three-dimensional model (3D) of the target vessel obtained from CA, intravascular imaging, or coronary computed tomography angiography. The purpose of this review was to describe the technical details of these anatomy-derived indices of coronary physiology with a special focus on summarizing their workflow, available evidence, and future perspectives about their application in the clinical practice.

Application of physics-based flow models in cardiovascular medicine: Current practices and challenges

Personalized physics-based flow models are becoming increasingly important in cardiovascular medicine. They are a powerful complement to traditional methods of clinical decision-making and offer a wealth of physiological information beyond conventional anatomic viewing using medical imaging data. These models have been used to identify key hemodynamic biomarkers, such as pressure gradient and wall shear stress, which are associated with determining the functional severity of cardiovascular diseases. Importantly, simulation-driven diagnostics can help researchers understand the complex interplay between geometric and fluid dynamic parameters, which can ultimately improve patient outcomes and treatment planning. The possibility to compute and predict diagnostic variables and hemodynamics biomarkers can therefore play a pivotal role in reducing adverse treatment outcomes and accelerate development of novel strategies for cardiovascular disease management.

Multiscale modeling of blood flow to assess neurological complications in patients supported by venoarterial extracorporeal membrane oxygenation

Computational blood flow models in large arteries elucidate valuable relationships between cardiovascular diseases and hemodynamics, leading to improvements in treatment planning and clinical decision making. One such application with potential to benefit from simulation is venoarterial extracorporeal membrane oxygenation (VA-ECMO), a support system for patients with cardiopulmonary failure. VA-ECMO patients develop high rates of neurological complications, partially due to abnormal blood flow throughout the vasculature from the VA-ECMO system. To better understand these hemodynamic changes, it is important to resolve complex local flow parameters derived from three-dimensional (3D) fluid dynamics while also capturing the impact of VA-ECMO support throughout the systemic arterial system. As high-resolution 3D simulations of the arterial network remain computationally expensive and intractable for large studies, a validated, multiscale model is needed to compute both global effects and high-fidelity local hemodynamics. In this work, we developed and demonstrated a framework to model hemodynamics in VA-ECMO patients using coupled 3D and one-dimensional (1D) models (1D→3D). We demonstrated the ability of these multiscale models to simulate complex flow patterns in specific regions of interest while capturing bulk flow throughout the systemic arterial system. We compared 1D, 3D, and 1D→3D coupled models and found that multiscale models were able to sufficiently capture both global and local hemodynamics in the cerebral arteries and aorta in VA-ECMO patients. This study is the first to develop and compare 1D, 3D, and 1D→ 3D coupled models on the larger arterial system scale in VA-ECMO patients, with potential use for other large scale applications.

A zero-dimensional predictive model for the pressure drop in the stenotic coronary artery based on its geometric characteristics

The diameter- or area-reduction ratio measured from coronary angiography, commonly used in clinical practice, is not accurate enough to represent the functional significance of the stenosis, i.e., the pressure drop across the stenosis. We propose a new zero-dimensional model for the pressure drop across the stenosis considering its geometric characteristics and flow rate. To identify the geometric parameters affecting the pressure drop, we perform three-dimensional numerical simulations for thirty-three patient-specific coronary stenoses. From these numerical simulations, we show that the pressure drop is mostly determined by the curvature as well as the area-reduction ratio of the stenosis before the minimal luminal area (MLA), but heavily depends on the area-expansion ratio after the MLA due to flow separation. Based on this result, we divide the stenosis into the converging and diverging parts in the present zero-dimensional model. The converging part is segmented into a series of straight and curved pipes with curvatures, and the loss of each pipe is estimated by an empirical relation between the total pressure drop, flow rate, and pipe geometric parameters (length, diameter, and curvature). The loss in the diverging part is predicted by a relation among the total pressure drop, Reynolds number, and area expansion ratio with the coefficients determined by a machine learning method. The pressure drops across the stenoses predicted by the present zero-dimensional model agree very well with those obtained from three-dimensional numerical simulations.

Effect of side branch flow upon physiological indices in coronary artery disease

Recent efforts have demonstrated the ability of computational models to predict fractional flow reserve from coronary artery imaging without the need for invasive instrumentation. However, these models include only larger coronary arteries as smaller side branches cannot be resolved and are therefore neglected. The goal of this study was to evaluate the impact of neglecting the flow to these side branches when computing angiography-derived fractional flow reserve (vFFR) and indices of volumetric coronary artery blood flow. To compensate for the flow to side branches, a leakage function based upon vessel taper (Murray's Law) was added to a previously developed computational model of coronary blood flow. The augmented model with a leakage function (1D_leaky) and the original model (1D) were then applied to predict FFR as well as inlet and outlet flow in 146 arteries from 80 patients who underwent invasive coronary angiography and FFR measurement. The results show that the leakage function did not significantly change the vFFR but did significantly impact the estimated volumetric flow rate and predicted coronary flow reserve. As both procedures achieved similar predictive accuracy of vFFR despite large differences in coronary blood flow, these results suggest careful consideration of the application of this index for quantitatively assessing flow.

Fractional Flow Reserve Derived from CT: The State of Play in 2020

Fractional flow reserve derived from CT is a rapidly developing technique, with an increasing burden of literature supporting its potential role in the workup of patients suspected of having coronary artery disease.

Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis - A Mathematical Model Study

Introduction: Coronary arterial stenosis may impair myocardial perfusion with myocardial ischemia and associated morbidity and mortality as result. The myocardial fractional flow reserve (FFR) is clinically used as a stenosis-specific index. Aim: This study aims to identify the relation between the FFR and the degree of coronary arterial stenosis using a simple mathematical model of the coronary circulation. Methods: A mathematical model of the coronary circulation, including an arterial stenosis of variable degree, was developed. The relation between the FFR and the degree of stenosis (defined as the fractional cross sectional area narrowing) was investigated, including the influence of the aortic and venous pressures and the capillary resistance. An additional study concerning 22 patients with coronary artery disease permits comparison of clinical data and in silico findings. Results: The FFR shows an S-shaped relationship with the stenosis index. We found a marked influence of venous and aortic pressure and capillary resistance. The FFR is accompanied by a clinically relevant co-metric (FFR C ), defined by the Pythagorean sum of the two pressures in the definition formula for FFR. In the patient group the FFR C is strongly related to the post-stenotic pressure (R = 0.91). The FFR C requires establishment of a validated cut-off point using future trials. Conclusion: The S-shaped dependence of FFR on the severity of the stenosis makes the FFR a measure of the ordinal scale. The marked influences of the aortic and venous pressures and the capillary resistance on the FFR will be interpreted as significant variations in intra- and inter-individual clinical findings. These fluctuations are partly connected to the neglect of considering the FFR C . At otherwise identical conditions the FFR as measured at baseline differs from the value obtained during hyperemic conditions. This expected observation requires further investigation, as the current hyperemia based evaluation fails to take advantage of available baseline data.

Computational instantaneous wave-free ratio (IFR) for patient-specific coronary artery stenoses using 1D network models

In this work, we estimate the diagnostic threshold of the instantaneous wave-free ratio (iFR) through the use of a one-dimensional haemodynamic framework. To this end, we first compared the computed fractional flow reserve (cFFR) predicted from a 1D computational framework with invasive clinical measurements. The framework shows excellent promise and utilises minimal patient data from a cohort of 52 patients with a total of 66 stenoses. The diagnostic accuracy of the cFFR model was 75.76%, with a sensitivity of 71.43%, a specificity of 77.78%, a positive predictive value of 60%, and a negative predictive value of 85.37%. The validated model was then used to estimate the diagnostic threshold of iFR. The model determined a quadratic relationship between cFFR and the ciFR. The iFR diagnostic threshold was determined to be 0.8910 from a receiver operating characteristic curve that is in the range of 0.89 to 0.9 that is normally reported in clinical studies.

Non-invasive coronary CT angiography-derived fractional flow reserve: A benchmark study comparing the diagnostic performance of four different computational methodologies

Non-invasive coronary computed tomography (CT) angiography-derived fractional flow reserve (cFFR) is an emergent approach to determine the functional relevance of obstructive coronary lesions. Its feasibility and diagnostic performance has been reported in several studies. It is unclear if differences in sensitivity and specificity between these studies are due to study design, population, or "computational methodology." We evaluate the diagnostic performance of four different computational workflows for the prediction of cFFR using a limited data set of 10 patients, three based on reduced-order modelling and one based on a 3D rigid-wall model. The results for three of these methodologies yield similar accuracy of 6.5% to 10.5% mean absolute difference between computed and measured FFR. The main aspects of modelling which affected cFFR estimation were choice of inlet and outlet boundary conditions and estimation of flow distribution in the coronary network. One of the reduced-order models showed the lowest overall deviation from the clinical FFR measurements, indicating that reduced-order models are capable of a similar level of accuracy to a 3D model. In addition, this reduced-order model did not include a lumped pressure-drop model for a stenosis, which implies that the additional effort of isolating a stenosis and inserting a pressure-drop element in the spatial mesh may not be required for FFR estimation. The present benchmark study is the first of this kind, in which we attempt to homogenize the data required to compute FFR using mathematical models. The clinical data utilised in the cFFR workflows are made publicly available online.