Evaluation of models of sequestration flow in coronary arteries-Physiology versus anatomy?

BACKGROUND: Myocardial ischaemia results from insufficient coronary blood flow. Computed virtual fractional flow reserve (vFFR) allows quantification of proportional flow loss without the need for invasive pressure-wire testing. In the current study, we describe a novel, conductivity model of side branch flow, referred to as 'leak'. This leak model is a function of taper and local pressure, the latter of which may change radically when focal disease is present. This builds upon previous techniques, which either ignore side branch flow, or rely purely on anatomical factors. This study aimed to describe a new, conductivity model of side branch flow and compare this with established anatomical models. METHODS AND RESULTS: The novel technique was used to quantify vFFR, distal absolute flow (Qd) and microvascular resistance (CMVR) in 325 idealised 1D models of coronary arteries, modelled from invasive clinical data. Outputs were compared to an established anatomical model of flow. The conductivity model correlated and agreed with the reference model for vFFR (r = 0.895, p < 0.0001; ＋0.02, 95% CI 0.00 to ＋ 0.22), Qd (r = 0.959, p < 0.0001; -5.2 mL/min, 95% CI -52.2 to ＋13.0) and CMVR (r = 0.624, p < 0.0001; ＋50 Woods Units, 95% CI -325 to ＋2549). CONCLUSION: Agreement between the two techniques was closest for vFFR, with greater proportional differences seen for Qd and CMVR. The conductivity function assumes vessel taper was optimised for the healthy state and that CMVR was not affected by local disease. The latter may be addressed with further refinement of the technique or inferred from complementary image data. The conductivity technique may represent a refinement of current techniques for modelling coronary side-branch flow. Further work is needed to validate the technique against invasive clinical data.

Rapid virtual fractional flow reserve using 3D computational fluid dynamics.

Aims: Over the last ten years, virtual Fractional Flow Reserve (vFFR) has improved the utility of Fractional Flow Reserve (FFR), a globally recommended assessment to guide coronary interventions. Although the speed of vFFR computation has accelerated, techniques utilising full 3D computational fluid dynamics (CFD) solutions rather than simplified analytical solutions still require significant time to compute. Methods and results: This study investigated the speed, accuracy and cost of a novel 3D-CFD software method based upon a graphic processing unit (GPU) computation, compared with the existing fastest central processing unit (CPU)-based 3D-CFD technique, on 40 angiographic cases. The novel GPU simulation was significantly faster than the CPU method (median 31.7 s (Interquartile Range (IQR) 24.0-44.4s) vs. 607.5 s (490-964 s), P < 0.0001). The novel GPU technique was 99.6% (IQR 99.3-99.9) accurate relative to the CPU method. The initial cost of the GPU hardware was greater than the CPU (£4080 vs. £2876), but the median energy consumption per case was significantly less using the GPU method (8.44 (6.80-13.39) Wh vs. 2.60 (2.16-3.12) Wh, P < 0.0001). Conclusion: This study demonstrates that vFFR can be computed using 3D-CFD with up to 28-fold acceleration than previous techniques with no clinically significant sacrifice in accuracy.

Sex differences in coronary microvascular resistance measured by a computational fluid dynamics model.

Background: Increased coronary microvascular resistance (CMVR) is associated with coronary microvascular dysfunction (CMD). Although CMD is more common in women, sex-specific differences in CMVR have not been demonstrated previously. Aim: To compare CMVR between men and women being investigated for chest pain. Methods and results: We used a computational fluid dynamics (CFD) model of human coronary physiology to calculate absolute CMVR based on invasive coronary angiographic images and pressures in 203 coronary arteries from 144 individual patients. CMVR was significantly higher in women than men (860 [650-1,205] vs. 680 [520-865] WU, Z = -2.24, p = 0.025). None of the other major subgroup comparisons yielded any differences in CMVR. Conclusion: CMVR was significantly higher in women compared with men. These sex-specific differences may help to explain the increased prevalence of CMD in women.

Wearable technology and the cardiovascular system: the future of patient assessment.

The past decade has seen a dramatic rise in consumer technologies able to monitor a variety of cardiovascular parameters. Such devices initially recorded markers of exercise, but now include physiological and health-care focused measurements. The public are keen to adopt these devices in the belief that they are useful to identify and monitor cardiovascular disease. Clinicians are therefore often presented with health app data accompanied by a diverse range of concerns and queries. Herein, we assess whether these devices are accurate, their outputs validated, and whether they are suitable for professionals to make management decisions. We review underpinning methods and technologies and explore the evidence supporting the use of these devices as diagnostic and monitoring tools in hypertension, arrhythmia, heart failure, coronary artery disease, pulmonary hypertension, and valvular heart disease. Used correctly, they might improve health care and support research.

Validation of a novel numerical model to predict regionalized blood flow in the coronary arteries.

Aims: Ischaemic heart disease results from insufficient coronary blood flow. Direct measurement of absolute flow (mL/min) is feasible, but has not entered routine clinical practice in most catheterization laboratories. Interventional cardiologists, therefore, rely on surrogate markers of flow. Recently, we described a computational fluid dynamics (CFD) method for predicting flow that differentiates inlet, side branch, and outlet flows during angiography. In the current study, we evaluate a new method that regionalizes flow along the length of the artery. Methods and results: Three-dimensional coronary anatomy was reconstructed from angiograms from 20 patients with chronic coronary syndrome. All flows were computed using CFD by applying the pressure gradient to the reconstructed geometry. Side branch flow was modelled as a porous wall boundary. Side branch flow magnitude was based on morphometric scaling laws with two models: a homogeneous model with flow loss along the entire arterial length; and a regionalized model with flow proportional to local taper. Flow results were validated against invasive measurements of flow by continuous infusion thermodilution (Coroventis™, Abbott). Both methods quantified flow relative to the invasive measures: homogeneous (r 0.47, P 0.006; zero bias; 95% CI -168 to +168 mL/min); regionalized method (r 0.43, P 0.013; zero bias; 95% CI -175 to +175 mL/min). Conclusion: During angiography and pressure wire assessment, coronary flow can now be regionalized and differentiated at the inlet, outlet, and side branches. The effect of epicardial disease on agreement suggests the model may be best targeted at cases with a stenosis close to side branches.

Quantifying Myocardial Blood Flow and Resistance Using 4D-Flow Cardiac Magnetic Resonance Imaging.

Background: Ischaemia with nonobstructive coronary arteries is most commonly caused by coronary microvascular dysfunction but remains difficult to diagnose without invasive testing. Myocardial blood flow (MBF) can be quantified noninvasively on stress perfusion cardiac magnetic resonance (CMR) or positron emission tomography but neither is routinely used in clinical practice due to practical and technical constraints. Quantification of coronary sinus (CS) flow may represent a simpler method for CMR MBF quantification. 4D flow CMR offers comprehensive intracardiac and transvalvular flow quantification. However, it is feasibility to quantify MBF remains unknown. Methods: Patients with acute myocardial infarction (MI) and healthy volunteers underwent CMR. The CS contours were traced from the 2-chamber view. A reformatted phase contrast plane was generated through the CS, and flow was quantified using 4D flow CMR over the cardiac cycle and normalised for myocardial mass. MBF and resistance (MyoR) was determined in ten healthy volunteers, ten patients with myocardial infarction (MI) without microvascular obstruction (MVO), and ten with known MVO. Results: MBF was quantified in all 30 subjects. MBF was highest in healthy controls (123.8 ± 48.4 mL/min), significantly lower in those with MI (85.7 ± 30.5 mL/min), and even lower in those with MI and MVO (67.9 ± 29.2 mL/min/) (P < 0.01 for both differences). Compared with healthy controls, MyoR was higher in those with MI and even higher in those with MI and MVO (0.79 (±0.35) versus 1.10 (±0.50) versus 1.50 (±0.69), P=0.02). Conclusions: MBF and MyoR can be quantified from 4D flow CMR. Resting MBF was reduced in patients with MI and MVO.

Refining Our Understanding of the Flow Through Coronary Artery Branches; Revisiting Murray's Law in Human Epicardial Coronary Arteries.

Background: Quantification of coronary blood flow is used to evaluate coronary artery disease, but our understanding of flow through branched systems is poor. Murray's law defines coronary morphometric scaling, the relationship between flow (Q) and vessel diameter (D) and is the basis for minimum lumen area targets when intervening on bifurcation lesions. Murray's original law (Q α DP) dictates that the exponent (P) is 3.0, whilst constant blood velocity throughout the system would suggest an exponent of 2.0. In human coronary arteries, the value of Murray's exponent remains unknown. Aim: To establish the exponent in Murray's power law relationship that best reproduces coronary blood flows (Q) and microvascular resistances (Rmicro) in a bifurcating coronary tree. Methods and Results: We screened 48 cases, and were able to evaluate inlet Q and Rmicro in 27 branched coronary arteries, taken from 20 patients, using a novel computational fluid dynamics (CFD) model which reconstructs 3D coronary anatomy from angiography and uses pressure-wire measurements to compute Q and Rmicro distribution in the main- and side-branches. Outputs were validated against invasive measurements using a Rayflow™ catheter. A Murray's power law exponent of 2.15 produced the strongest correlation and closest agreement with inlet Q (zero bias, r = 0.47, p = 0.006) and an exponent of 2.38 produced the strongest correlation and closest agreement with Rmicro (zero bias, r = 0.66, p = 0.0001). Conclusions: The optimal power law exponents for Q and Rmicro were not 3.0, as dictated by Murray's Law, but 2.15 and 2.38 respectively. These data will be useful in assessing patient-specific coronary physiology and tailoring revascularisation decisions.

The importance of three dimensional coronary artery reconstruction accuracy when computing virtual fractional flow reserve from invasive angiography.

Three dimensional (3D) coronary anatomy, reconstructed from coronary angiography (CA), is now being used as the basis to compute 'virtual' fractional flow reserve (vFFR), and thereby guide treatment decisions in patients with coronary artery disease (CAD). Reconstruction accuracy is therefore important. Yet the methods required remain poorly validated. Furthermore, the magnitude of vFFR error arising from reconstruction is unkown. We aimed to validate a method for 3D CA reconstruction and determine the effect this had upon the accuracy of vFFR. Clinically realistic coronary phantom models were created comprosing seven standard stenoses in aluminium and 15 patient-based 3D-printed, imaged with CA, three times, according to standard clinical protocols, yielding 66 datasets. Each was reconstructed using epipolar line projection and intersection. All reconstructions were compared against the real phantom models in terms of minimal lumen diameter, centreline and surface similarity. 3D-printed reconstructions (n = 45) and the reference files from which they were printed underwent vFFR computation, and the results were compared. The average error in reconstructing minimum lumen diameter (MLD) was 0.05 (± 0.03 mm) which was < 1% (95% CI 0.13-1.61%) compared with caliper measurement. Overall surface similarity was excellent (Hausdorff distance 0.65 mm). Errors in 3D CA reconstruction accounted for an error in vFFR of ± 0.06 (Bland Altman 95% limits of agreement). Errors arising from the epipolar line projection method used to reconstruct 3D coronary anatomy from CA are small but contribute to clinically relevant errors when used to compute vFFR.

Operator-dependent variability of angiography-derived fractional flow reserve and the implications for treatment.

AIMS: To extend the benefits of physiologically guided percutaneous coronary intervention to many more patients, angiography-derived, or 'virtual' fractional flow reserve (vFFR) has been developed, in which FFR is computed, based upon the images, instead of being measured invasively. The effect of operator experience with these methods upon vFFR accuracy remains unknown. We investigated variability in vFFR results based upon operator experience with image-based computational modelling techniques. METHODS AND RESULTS: Virtual fractional flow reserve was computed using a proprietary method (VIRTUheart) from the invasive angiograms of patients with coronary artery disease. Each case was processed by an expert (>100 vFFR cases) and a non-expert (<20 vFFR cases) operator and results were compared. The primary outcome was the variability in vFFR between experts and non-experts and the impact this had upon treatment strategy (PCI vs. conservative management). Two hundred and thirty-one vessels (199 patients) were processed. Mean non-expert and expert vFFRs were similar overall [0.76 (0.13) and 0.77 (0.16)] but there was significant variability between individual results (variability coefficient 12%, intraclass correlation coefficient 0.58), with only moderate agreement (κ = 0.46), and this led to a statistically significant change in management strategy in 27% of cases. Variability was significantly lower, and agreement higher, for expert operators; a change in their recommended management occurred in 10% of repeated expert measurements and 14% of inter-expert measurements. CONCLUSION: Virtual fractional flow reserve results are influenced by operator experience of vFFR processing. This had implications for treatment allocation. These results highlight the importance of training and quality assurance to ensure reliable, repeatable vFFR results.

The Impact of Virtual Fractional Flow Reserve and Virtual Coronary Intervention on Treatment Decisions in the Cardiac Catheter Laboratory.

BACKGROUND: Using fractional flow reserve (FFR) to guide percutaneous coronary intervention for patients with coronary artery disease (CAD) improves clinical decision making but remains underused. Virtual FFR (vFFR), computed from angiographic images, permits physiologic assessment without a pressure wire and can be extended to virtual coronary intervention (VCI) to facilitate treatment planning. This study investigated the effect of adding vFFR and VCI to angiography in patient assessment and management. METHODS: Two cardiologists independently reviewed clinical data and angiograms of 50 patients undergoing invasive management of coronary syndromes, and their management plans were recorded. The vFFRs were computed and disclosed, and the cardiologists submitted revised plans. Then, using VCI, the physiologic results of various interventional strategies were shown and further revision was invited. RESULTS: Disclosure of vFFR led to a change in strategy in 27%. VCI led to a change in stent size in 48%. Disclosure of vFFR and VCI resulted in an increase in operator confidence in their decision. Twelve cases were reviewed by 6 additional cardiologists. There was limited agreement in the management plans between cardiologists based on either angiography (kappa = 0.31) or vFFR (kappa = 0.39). CONCLUSIONS: vFFR has the potential to alter decision making, and VCI can guide stent sizing. However, variability in management strategy remains considerable between operators, even when presented with the same anatomic and physiologic data.

Comparison of stenosis models for usage in the estimation of pressure gradient across aortic coarctation.

Non-invasive estimation of the pressure gradient in cardiovascular stenosis has much clinical importance in assisting the diagnosis and treatment of stenotic diseases. In this research, a systematic comparison is conducted to investigate the accuracy of a group of stenosis models against the MRI- and catheter-measured patient data under the aortic coarctation condition. Eight analytical stenosis models, including six from the literature and two proposed in this study, are investigated to examine their prediction accuracy against the clinical data. The two improved models proposed in this study consider comprehensively the Poiseuille loss, the Bernoulli loss in its exact form, and the entrance effect, of the blood flow. Comparison of the results shows that one of the proposed models demonstrates a cycle-averaged mean prediction error of -0.15 ± 3.03 mmHg, a peak-to-peak prediction error of -1.8 ± 6.89 mmHg, which is the best among the models studied.

The new role of diagnostic angiography in coronary physiological assessment.

The role of 'stand-alone' coronary angiography (CAG) in the management of patients with chronic coronary syndromes is the subject of debate, with arguments for its replacement with CT angiography on the one hand and its confinement to the interventional cardiac catheter laboratory on the other. Nevertheless, it remains the standard of care in most centres. Recently, computational methods have been developed in which the laws of fluid dynamics can be applied to angiographic images to yield 'virtual' (computed) measures of blood flow, such as fractional flow reserve. Together with the CAG itself, this technology can provide an 'all-in-one' anatomical and functional investigation, which is particularly useful in the case of borderline lesions. It can add to the diagnostic value of CAG by providing increased precision and reduce the need for further non-invasive and functional tests of ischaemia, at minimal cost. In this paper, we place this technology in context, with emphasis on its potential to become established in the diagnostic workup of patients with suspected coronary artery disease, particularly in the non-interventional setting. We discuss the derivation and reliability of angiographically derived fractional flow reserve (CAG-FFR) as well as its limitations and how CAG-FFR could be integrated within existing national guidance. The assessment of coronary physiology may no longer be the preserve of the interventional cardiologist.

The relationship between coronary stenosis morphology and fractional flow reserve: a computational fluid dynamics modelling study.

Aims: International guidelines mandate the use of fractional flow reserve (FFR) and/or non-hyperaemic pressure ratios to assess the physiological significance of moderate coronary artery lesions to guide revascularization decisions. However, they remain underused such that visual estimation of lesion severity continues to be the predominant decision-making tool. It would be pragmatic to have an improved understanding of the relationship between lesion morphology and haemodynamics. The aim of this study was to compute virtual FFR (vFFR) in idealized coronary artery geometries with a variety of stenosis and vessel characteristics. Methods and results: Coronary artery geometries were modelled, based upon physiologically realistic branched arteries. Common stenosis characteristics were studied, including % narrowing, length, eccentricity, shape, number, position relative to branch, and distal (myocardial) resistance. Computational fluid dynamics modelling was used to calculate vFFRs using the VIRTUheart™ system. Percentage lesion severity had the greatest effect upon FFR. Any ≥80% diameter stenosis in two views (i.e. concentric) was physiologically significant (FFR ≤ 0.80), irrespective of length, shape, or vessel diameter. Almost all eccentric stenoses and all 50% concentric stenoses were physiologically non-significant, whilst 70% uniform concentric stenoses about 10 mm long straddled the ischaemic threshold (FFR 0.80). A low microvascular resistance (MVR) reduced FFR on average by 0.05, and a high MVR increased it by 0.03. Conclusion: Using computational modelling, we have produced an analysis of vFFR that relates stenosis characteristics to haemodynamic significance. The strongest predictor of a positive vFFR was a concentric, ≥80% diameter stenosis. The importance of MVR was quantified. Other lesion characteristics have a limited impact.

A novel method for measuring absolute coronary blood flow and microvascular resistance in patients with ischaemic heart disease.

AIMS: Ischaemic heart disease is the reduction of myocardial blood flow, caused by epicardial and/or microvascular disease. Both are common and prognostically important conditions, with distinct guideline-indicated management. Fractional flow reserve (FFR) is the current gold-standard assessment of epicardial coronary disease but is only a surrogate of flow and only predicts percentage flow changes. It cannot assess absolute (volumetric) flow or microvascular disease. The aim of this study was to develop and validate a novel method that predicts absolute coronary blood flow and microvascular resistance (MVR) in the catheter laboratory. METHODS AND RESULTS: A computational fluid dynamics (CFD) model was used to predict absolute coronary flow (QCFD) and coronary MVR using data from routine invasive angiography and pressure-wire assessment. QCFD was validated in an in vitro flow circuit which incorporated patient-specific, three-dimensional printed coronary arteries; and then in vivo, in patients with coronary disease. In vitro, QCFD agreed closely with the experimental flow over all flow rates [bias +2.08 mL/min; 95% confidence interval (error range) -4.7 to +8.8 mL/min; R2 = 0.999, P < 0.001; variability coefficient <1%]. In vivo, QCFD and MVR were successfully computed in all 40 patients under baseline and hyperaemic conditions, from which coronary flow reserve (CFR) was also calculated. QCFD-derived CFR correlated closely with pressure-derived CFR (R2 = 0.92, P < 0.001). This novel method was significantly more accurate than Doppler-wire-derived flow both in vitro (±6.7 vs. ±34 mL/min) and in vivo (±0.9 vs. ±24.4 mmHg). CONCLUSIONS: Absolute coronary flow and MVR can be determined alongside FFR, in absolute units, during routine catheter laboratory assessment, without the need for additional catheters, wires or drug infusions. Using this novel method, epicardial and microvascular disease can be discriminated and quantified. This comprehensive coronary physiological assessment may enable a new level of patient stratification and management.

The EurValve model execution environment.

The goal of this paper is to present a dedicated high-performance computing (HPC) infrastructure which is used in the development of a so-called reduced-order model (ROM) for simulating the outcomes of interventional procedures which are contemplated in the treatment of valvular heart conditions. Following a brief introduction to the problem, the paper presents the design of a model execution environment, in which representative cases can be simulated and the parameters of the ROM fine-tuned to enable subsequent deployment of a decision support system without further need for HPC. The presentation of the system is followed by information concerning its use in processing specific patient cases in the context of the EurValve international collaboration.

Correction: Role of growth arrest-specific gene 6-mer axis in multiple myeloma.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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 (1Dleaky) 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.

Subject-specific simulation for non-invasive assessment of aortic coarctation: Towards a translational approach.

We present a multi-scale CFD-based study conducted in a cohort of 11 patients with coarctation of the aorta (CoA). The study explores the potential for implementation of a workflow using non-invasive routinely collected medical imaging data and clinical measurements to provide a more detailed insight into local aortic haemodynamics in order to support clinical decision making. Our approach is multi-scale, using a reduced-order model (1D/0D) and an optimization process for the personalization of patient-specific boundary conditions and aortic vessel wall parameters from non-invasive measurements, to inform a more complex model (3D/0D) representing 3D aortic patient-specific anatomy. The reliability of the modelling approach is investigated by comparing 3D/0D model pressure drop estimation with measured peak gradients recorded during diagnostic cardiac catheterization and 2D PC-MRI flow rate measurements in the descending aorta. The current study demonstrated that the proposed approach requires low levels of user interaction, making it suitable for the clinical setting. The agreement between computed blood pressure drop and catheter measurements is 10  ±  8 mmHg at the coarctation site. The comparison between CFD derived and catheter measured pressure gradients indicated that the model has to be improved, suggesting the use of time varying pressure waveforms to further optimize the tuning process and modelling assumptions.

Cardiovascular models for personalised medicine: Where now and where next?

The aim of this position paper is to provide a brief overview of the current status of cardiovascular modelling and of the processes required and some of the challenges to be addressed to see wider exploitation in both personal health management and clinical practice. In most branches of engineering the concept of the digital twin, informed by extensive and continuous monitoring and coupled with robust data assimilation and simulation techniques, is gaining traction: the Gartner Group listed it as one of the top ten digital trends in 2018. The cardiovascular modelling community is starting to develop a much more systematic approach to the combination of physics, mathematics, control theory, artificial intelligence, machine learning, computer science and advanced engineering methodology, as well as working more closely with the clinical community to better understand and exploit physiological measurements, and indeed to develop jointly better measurement protocols informed by model-based understanding. Developments in physiological modelling, model personalisation, model outcome uncertainty, and the role of models in clinical decision support are addressed and 'where-next' steps and challenges discussed.

Estimation of valvular resistance of segmented aortic valves using computational fluid dynamics.

Aortic valve stenosis is associated with an elevated left ventricular pressure and transaortic pressure drop. Clinicians routinely use Doppler ultrasound to quantify aortic valve stenosis severity by estimating this pressure drop from blood velocity. However, this method approximates the peak pressure drop, and is unable to quantify the partial pressure recovery distal to the valve. As pressure drops are flow dependent, it remains difficult to assess the true significance of a stenosis for low-flow low-gradient patients. Recent advances in segmentation techniques enable patient-specific Computational Fluid Dynamics (CFD) simulations of flow through the aortic valve. In this work a simulation framework is presented and used to analyze data of 18 patients. The ventricle and valve are reconstructed from 4D Computed Tomography imaging data. Ventricular motion is extracted from the medical images and used to model ventricular contraction and corresponding blood flow through the valve. Simplifications of the framework are assessed by introducing two simplified CFD models: a truncated time-dependent and a steady-state model. Model simplifications are justified for cases where the simulated pressure drop is above 10 mmHg. Furthermore, we propose a valve resistance index to quantify stenosis severity from simulation results. This index is compared to established metrics for clinical decision making, i.e. blood velocity and valve area. It is found that velocity measurements alone do not adequately reflect stenosis severity. This work demonstrates that combining 4D imaging data and CFD has the potential to provide a physiologically relevant diagnostic metric to quantify aortic valve stenosis severity.