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Acting upon clinical patient data, acquired in the pathway of percutaneous intervention, we deploy hierarchical, multi-stage, data-handling protocols and interacting low- and high-order mathematical models (chamber elastance, state-space system and CFD models), to establish and then validate a framework to quantify the burden of ischaemia. Our core tool is a compartmental, zero-dimensional model of the coupled circulation with four heart chambers, systemic and pulmonary circulations and an optimally adapted windkessel model of the coronary arteries that reflects the diastolic dominance of coronary flow. We guide the parallel development of protocols and models by appealing to foundational physiological principles of cardiac energetics and a parameterisation (stenotic Bernoulli resistance and micro-vascular resistance) of patients’ coronary flow. We validate our process first with results which substantiate our protocols and, second, we demonstrate good correspondence between model operation and patient data. We conclude that our core model is capable of representing (patho)physiological states and discuss how it can potentially be deployed, on clinical data, to provide a quantitative assessment of the impact, on the individual, of coronary artery disease.

This paper reviews the methodological aspects related to the patient-specific blood flow modeling of coronary artery disease, aiming to identify and quantify the main sources of errors and trying to minimize them but also accelerate the computational process. It is envisaged to extend these multiscale modeling techniques to multiple-branches arteries, in which case the computation time becomes critical. The possibility of replacing these 3D multiscale models with the much faster 0D models is suggested. First, the multiscale model of a single-branch coronary artery is presented. Then, the 0D and 3D multiscale model of a multiple-branches artery are presented. Finally, the simulation results of these models are compared with each-other and their errors analyzed.

SummaryBlood flow generates wall shear stress (WSS) which alters endothelial cell (EC) function. Low WSS promotes vascular inflammation and atherosclerosis whereas high uniform WSS is protective. Ivabradine decreases heart rate leading to altered haemodynamics. Besides its cardio-protective effects, ivabradine protects arteries from inflammation and atherosclerosis via unknown mechanisms. We hypothesised that ivabradine protects arteries by increasing WSS to reduce vascular inflammation. Hypercholesterolaemic mice were treated with ivabradine for seven weeks in drinking water or remained untreated as a control. En face immunostaining demonstrated that treatment with ivabradine reduced the expression of pro-inflammatory VCAM-1 (p

Pulmonary arterial hypertension (PAH) is a severe, low survival and rapidly progressive disease, characterised by an increase in the distal pulmonary vascular resistance and decrease in pulmonary compliance. The current standard procedure for PAH diagnosis and therapy response assessment is right heart catheterisation (RHC). Although if performed in a specialist centre, the severe complications associated with RHC are reduced, non-invasive alternatives are desirable. Windkessel models have been previously proposed[1], [2] to estimate the overall pulmonary system resistance and compliance.

Introduction: Pulmonary arterial hypertension (PAH) is a severe, low survival and rapidly progressive disease, characterised by an increase in the distal vascular resistance and decrease in the compliance. Right heart catheterisation (RHC) is the standard procedure for the PAH diagnosis and regular response to therapy assessment. Although the severe RHC associated risks are reduced, minimising the number of the interventions is highly desirable for improving patients9 life quality. Aim: The aim of the current study is to evaluate whether non-invasive measures of pulmonary vascular resistance and compliance can be used to assess the response to treatment in PAH patients. Methods: 93 patients diagnosed with PAH at RHC, underwent magnetic resonance imaging (MRI) of the main pulmonary artery at baseline and one year follow-up. At baseline, 56 patients were treatment naive and 37 on PAH therapy. A 3-element Windkessel model, using as input MRI flow and area waveforms, was implemented to compute the pulmonary resistance, R Wk and compliance, C Wk (Lungu et al., J Biomech 2014; 47:2941-7). R Wk and C Wk were compared at baseline with invasive pulmonary resistance, PVR, and vascular compliance, C SV computed as stroke volume to pulse pressure ratio. Results: At baseline, R Wk correlated with PVR (p Wk correlated with C SV (p Wk (p Wk (p Conclusion: The non-invasive proposed metrics have the potential to assess the response to PAH therapy, reducing the RHC interventions at follow-up.

Introduction: In contrast to the systemic arterial system, the association between age and compliance in the pulmonary circulation has to date not been investigated in vivo. The aim of this study was to evaluate the impact of age on pulmonary arterial compliance in health and in patients with pulmonary arterial hypertension (PAH). Methods: Consecutive patients with No PH (mPAP Results: 151 patients with PAH (57 underwent follow up RHC), 83 patients with No PH were identified and 34 healthy volunteers were included. Main pulmonary artery compliance correlated with age in patients with No PH (r=0.491, p Discussion: Advancing age is independently associated with pulmonary arterial compliance in health and disease. In contrast to younger patients, pulmonary arterial compliance does not increase in response to PAH therapy in older patients.

Purpose: An aortic valve stenosis is an abnormal narrowing of the aortic valve (AV). It impedes blood flow and is often quantified by the geometric orifice area of the AV (AVA) and the pressure drop (PD). Using the Bernoulli equation, a relation between the PD and the effective orifice area (EOA) represented by the area of the vena contracta (VC) downstream of the AV can be derived. We investigate the relation between the AVA and the EOA using patient anatomies derived from cardiac computed tomography (CT) angiography images and computational fluid dynamic (CFD) simulations. Methods: We developed a shape-constrained deformable model for segmenting the AV, the ascending aorta (AA) and the left ventricle (LV) in cardiac CT images. In particular, we designed a structured AV mesh model, trained the model on CT scans, and integrated it with an available model for heart segmentation. The planimetric AVA was determined from the cross-sectional slice with minimum AV opening area. In addition, the AVA was determined as the non-obstructed area along the AV axis by projecting the AV leaflet rims on a plane perpendicular to the AV axis. The flow rate was derived from the LV volume change. Steady-state CFD simulations were performed on the patient anatomies resulting from segmentation. Results: Heart and valve segmentation was used to retrospectively analyze 22 cardiac CT angiography image sequences of patients with non-calcified and (partially) severely calcified tricuspid AVs. Resulting AVAs were in the range of 1-4.5cm2 and ejection fractions (EFs) between 20-75%. AVA values computed by projection were smaller than those computed by planimetry, and both were strongly correlated (R2 = 0.995). EOA values computed via the Bernoulli equation from CFD-based PD results were strongly correlated to both AVA values (R2 = 0.97). EOA values were ˜ 10% smaller than planimetric AVA values. For EOA values < 2.0cm2, the EOA was up to ˜ 15% larger than the projected AVA. Conclusions: The presented segmentation algorithm allowed to construct detailed AV models for 22 patient cases. Because of the crown-like 3D structure of the AV, the planimetric AVA is larger than the projected AVA formed by the free edges of the AV leaflets. The AVA formed by the free edges of the AV leaflets was smaller than the EOA for EOA values < 2.0cm2. This contradiction with respect to previous studies that reported the EOA to be always smaller or equal to the geometric AVA is explained by the more detailed AV models used within this study.

Introduction: An MRI model derived from right ventricular (RV) measurements has been proposed for the evaluation of mean pulmonary arterial pressure (mPAP) with MRI has been proposed in the evaluation of patients with pulmonary hypertension (PH). The aim of this study was to estimate mPAP using MRI using metrics from both the RV and pulmonary artery (PA). Methods: A derivation cohort of 300 consecutive patients with suspected PH underwent RHC and MRI within 48 hours. An estimate of mPAP was derived using multivariate regression analysis of MRI measurements. The model was tested in an independent validation cohort of 140 patients with suspected PH. Comparative diagnostic accuracy of estimated mPAP derived from RV and PA indices, versus estimated mPAP derived from RV metrics alone was assessed. Results: The derivation cohort included 247 patients with PH and 53 patients with mPAP Conclusion: In addition to RV indices, PA diastolic area and relative area change measured by MRI, have incremental value for estimation of mPAP. A model using RV and PA metrics improves diagnostic accuracy over RV measurements alone.

Introduction: A cardiac MRI model has been proposed for estimation of mPAP in patients with suspected pulmonary hypertension (PH). The aim of this study was to evaluate the accuracy of MRI in PH subgroups compared to echocardiography. Methods: Patients with suspected PH between 2012 and 2014 who underwent MRI and right heart catheterisation (RHC) within 48hrs. MRI estimated mPAP (A) was defined as: -4.6 + (inter-ventricular septal angle x 0.23) + (ventricular mass index (diastolic right ventricular mass/left ventricular mass) x 16.3). Estimated mPAP was also derived using VMI measured in systole (B). Results: 440 patients with suspected PH were identified. RHC-mPAP correlated well with MRI estimated mPAP in pulmonary arterial hypertension (PAH) [r=0.70 (A) and r=0.78 (B)], patients with PH associated with respiratory disease (PH-RESP) [r=0.70 (A) and r=0.84 (B)] and patients with chronic thromboembolic PH (CTEPH) [r=0.63 (A) and r=0.74 (B)]. RHC-mPAP correlated weakly with MRI estimated mPAP (A and B) in patients with PH-left heart disease (LHD) [r=0.35 (A) and r=0.43 (B)]. MRI estimated mPAP was accurate for detecting PH in patients with PAH, PH-RESP and CTEPH (AUC 0.86-0.92), though inaccurate in patients with PH-LHD (AUC 0.68-0.73). Echocardiography had the strongest diagnostic accuracy in all subgroups (AUC 0.912-0.945). Conclusion: Echocardiography is more diagnostic than MRI in all patient subgroups. Except in patients with PH-LHD MRI derived mPAP tended to correlate more strongly with RHC-mPAP than echocardiography. This MRI model is not recommended for estimating mPAP in patients with PH-LHD, however may be a useful alternative to echocardiography in PAH, PH-RESP and CTEPH.

Introduction: Non-invasive diagnosis of pulmonary hypertension(PH) is highly desirable to eliminate right heart catheterisation(RHC) complications. Cardiopulmonary measurements of morphology and functions of the heart using MRI have shown promising results. Additional information is incorporated with MRI based mathematical models of pulse wave transmission and impedance of the pulmonary circulation. The aim of this study is to evaluate the added diagnostic value obtained by combining mathematical and cardiopulmonary metrics together with artificial intelligence(AI) classifiers. Methods: 72 patients suspected of PH, underwent RHC and MRI within 48hrs. 57 patients(mPAP≥25mmHg) were included in the PH group (44±14 mmHg) while 17 formed the control group (21±3 mmHg). A 0D and a 1D model(Lungu et.al,2014 Biomech 47:2941-2947) were applied to estimate: reflected (wasted) energy in the pulmonary circuit(W pb /W ptotal ), distal pulmonary resistance(R d ) and total pulmonary compliance(C). Cardiopulmonary MRI markers were also derived: MPA relative area change(RAC), right ventricular mass index(RVMI) and systolic septal angle. All metrics were passed to a random forest classifier and trained to decide between PH and NoPH individuals. Results: The classifier results, validated with leave-one-out-cross-validation, showed that 92% of patients were correctly classified, whereas the performance of the individual markers was∼75%, tested by maximisation of the Youden index. Conclusions: The findings support the hypothesis that combining PH biomarkers with AI classification algorithms increases the diagnostic power of these non-invasive measurements and models in PH.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards ‘digital patient’ or ‘virtual physiological human’ representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Atherosclerosis is influenced by blood flow whichS exert wall shear stress (WSS) on endothelial cells (EC). Low oscillatory WSS promotes atherosclerosis by inducing inflammatory molecules (e.g. VCAM-1), whereas high uniform WSS induces anti-inflammatory genes (e.g. eNOS). Ivabradine decreases heart rate by inhibiting the If current in the sinus node, without affecting blood pressure or cardiac contractility. Besides cardio-protection, ivabradine protects arteries from atherosclerosis via unknown mechanisms. We hypothesised that ivabradine reduces arterial inflammation by increasing blood flow-induced WSS. Mice (C57BL/6, male, aged 10 weeks) were treated with ivabradine for 1 week (162 mg/L in drinking water) or remained untreated. WSS was mapped at atherosusceptible (inner curvature) and protected (outer curvature) sites of the aorta by defining the geometry (CT angiography; Siemens) and flow characteristics (ultrasound; Visualsonics). Segmentation and smoothing were performed to reconstruct the volume of interest (Amira, VMTK) and a tetrahedral mesh with prismatic boundary layer was generated (IcemCFD). Fluid behavior was modeled over the cardiac cycle using Fluent 14.5 (ANSYS). Computational fluid dynamics revealed that WSS at the inner curvature of the aorta had lower magnitude and higher oscillatory index compared to the outer curvature. Ivabradine treatment reduced heart rate by 20% (p We conclude that ivabradine treatment altered hemodynamics in the murine aorta by increasing the magnitude and uniformity of shear stress. These changes were accompanied by induction of a mechanosensitive protective gene (eNOS) and suppression of inflammatory VCAM-1. Thus ivabradine may protect arteries by altering local mechanical conditions to trigger an anti-inflammatory response.

Pulmonary hypertension (PH), a disease with a high mortality rate, is currently diagnosed by invasive right heart catheterization (RHC). Quantification of wave reflections can offer information about the status of the pulmonary circulation in health and disease, and can be achieved by simultaneous measurement of flow and pressure at the same anatomical site. In practice such measurements are obtained using different acquisition techniques which needs to be synchronized in order to satisfy the simultaneity criterion. We hypothesis that combining the advantages of mathematical modelling with non-invasive Magnetic Resonance Imaging (MRI) measurements of flow and anatomy could offer totally non-invasive modalities for characterizing PH. Our preliminary work was focused on the development of automatic tools to determine accurately flow Q(t) and area A(t) measurements directly from MRI DICOM images, ultimately to support a novel characterisation protocol although the latter is beyond the scope of this paper.

The aortic valve area (AVA) and the pressure drop (PD) across the aortic valve are important quantities for characterizing an aortic valve stenosis. Using the Bernoulli equation and mass conservation, a relation between both quantities can be derived. We developed a simulation pipeline to assess the accuracy of this relation for realistic patient anatomies and blood flow rates. The key element of the pipeline is a shape-constrained deformable model (SCDM) for the segmentation of the aortic valve, the ascending aorta and the left ventricle over the cardiac cycle in cardiac CT images. Efficient segmentation enabled application of the simulation pipeline to cardiac CT image sequences of 22 patients. Planimetric AVA and Bernoulli-based PD estimates were computed from the same segmentation results. The resulting PD estimates show a high correlation (R = 0.97), but Bernoulli-based PD results are on average 25% smaller than the CFD-based results. The results contribute to a better understanding and interpretation of clinically used quantities such as the AVA and the PD.

To better understand the flow pattern and the mechanical environment induced by the single leaflet mechanical heart valves, both experimental and theoretical studies have been conducted. A pulse duplicator was used for driving two mechanical heart valves (Medtronic Hall and Omniscience) and a high speed video camera (500 frames per second) tracked their motion. Several tests, at different heart rates and cardiac outputs (stroke volumes) have been performed. Using a 2D image segmentation tool, developed in Matlab, the information about the instantaneous position of the valve was extracted from each frame of the video data. The pressure drop across the valve and the transvalvular flow has also been measured. The experimental results were in good agreement with the theoretical ones, previously obtained and reported by the authors.