We present a continuum scale particle transport model for red blood cells following collision arguments, in a diffusive flux formulation. The model is implemented in FOAM, in a framework suitable for haemodynamics simulations and adapted to multi-scaling. Specifically, the framework we present is able to ingest transport coefficient models to be derived, prospectively, from complimentary but independent meso-scale simulations. For present purposes, we consider modern semi-mechanistic rheology models, which we implement and test as proxies for such data. The model is verified against a known analytical solution and shows excellent agreement for high quality meshes and good agreement for typical meshes as used in vascular flow simulations. Simulation results for different size and time scales show that migration of red blood cells does occur on physiologically relevany timescales on small vessels below 1 mm and that the haematocrit concentration modulates the non-Newtonian viscosity. This model forms part of a multi-scale approach to haemorheology and model parameters will be derived from meso-scale simulations using multi-component Lattice Boltzmann methods. The code, haemoFoam, is made available for interested researchers.

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.

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/) ( 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), ). Conclusions. MBF and MyoR can be quantified from 4D flow CMR. Resting MBF was reduced in patients with MI and MVO.

An advection-diffusion solver was applied to assess how stent strut shape and position impact the development of a pro-thrombotic region within the stented human artery. Presented here is a suitably parameterised advection-diffusion equation with a source term that is spatially uniform within a certain sub-domain of interest to compute a “time concentration”. The latter will serve as a surrogate quantity for the “age” of fluid parcels, i.e., the time the fluid parcel has spent in the sub-domain. This is a particularly useful concept in the context of coronary artery haemodynamics, where “stasis of blood” (or residence time) is recognized as the most important factor in thrombotic initiation. The novel method presented in this work has a very straightforward and convenient single lattice Boltzmann simulation framework encapsulation. A residence time surrogate is computed, presented and correlated with a range of traditional haemodynamic metrics (wall shear stress, shear rate and re-circulation region shapes) and finally, the role of these data to quantify the risk of thrombus formation is assessed.

We present computational fluid dynamics (CFD) results of virtual fractional flow reserve (vFFR) calculations, performed on reconstructed arterial geometries derived from a digital phantom (DP). The latter provides a convenient and parsimonious description of the main vessels of the left and right coronary arterial trees, which, crucially, is CFD-compatible. Using our DP, we investigate the reconstruction error in what we deem to be the most relevant way—by evaluating the change in the computed value of vFFR, which results from varying (within representative clinical bounds) the selection of the virtual angiogram pair (defined by their viewing angles) used to segment the artery, the eccentricity and severity of the stenosis, and thereby, the CFD simulation’s luminal boundary. The DP is used to quantify reconstruction and computed haemodynamic error within the VIRTUheart^TM software suite. However, our method and the associated digital phantom tool are readily transferable to equivalent, clinically oriented workflows. While we are able to conclude that error within the VIRTUheart^TM workflow is suitably controlled, the principal outcomes of the work reported here are the demonstration and provision of a practical tool along with an exemplar methodology for evaluating error in a coronary segmentation process.

Lack of available data, ease of clinical use and lack of evidence for prognostic benefit are arguably the key limitations to clinical uptake for any model. This paper reports the development of an image-based analysis protocol, coupling 0D left heart and systemic circulation components with a 3D aortic valve model to measure and to predict the pressure gradient across the aortic valve at rest. The model is personalized using routine clinical data available for aortic valve patients, augmented by additional image data (transesophageal echo and/or CT) to support valve characterization. Computed aortic pressure gradient both pre- and post-intervention was compared with clinical measurements based on Doppler ultrasound for a cohort of 21 patients with aortic valve disease. Correlation for the diseased state measures were adequate ($R^2= 0.81$) for those cases for which associated image data was deemed to be of acceptable quality for segmentation to support a 3D computational fluid dynamics analysis but poor otherwise. Post treatment correlation was reasonable ($R^2= 0.47$) for all cases. Importantly, the personalized model presented here describes the interaction between the patient’s cardiovascular system, including the heart and circulation, and the valve, rather than evaluating the valve in isolation.