Convergence, sampling and total order estimator effects on parameter orthogonality in global sensitivity analysis.

Dynamical system models typically involve numerous input parameters whose "effects" and orthogonality need to be quantified through sensitivity analysis, to identify inputs contributing the greatest uncertainty. Whilst prior art has compared total-order estimators' role in recovering "true" effects, assessing their ability to recover robust parameter orthogonality for use in identifiability metrics has not been investigated. In this paper, we perform: (i) an assessment using a different class of numerical models representing the cardiovascular system, (ii) a wider evaluation of sampling methodologies and their interactions with estimators, (iii) an investigation of the consequences of permuting estimators and sampling methodologies on input parameter orthogonality, (iv) a study of sample convergence through resampling, and (v) an assessment of whether positive outcomes are sustained when model input dimensionality increases. Our results indicate that Jansen or Janon estimators display efficient convergence with minimum uncertainty when coupled with Sobol and the lattice rule sampling methods, making them prime choices for calculating parameter orthogonality and influence. This study reveals that global sensitivity analysis is convergence driven. Unconverged indices are subject to error and therefore the true influence or orthogonality of the input parameters are not recovered. This investigation importantly clarifies the interactions of the estimator and the sampling methodology by reducing the associated ambiguities, defining novel practices for modelling in the life sciences.

Computational fluid dynamics investigation on aortic hemodynamics in double aortic arch before and after ligation surgery.

Double aortic arch (DAA) malformation is one of the reasons for symptomatic vascular rings, the hemodynamics of which is still poorly understood. This study aims to investigate the blood flow characteristics in patient-specific double aortic arches using computational fluid dynamics (CFD). Seven cases of infantile patients with DAA were collected and their computed tomography images were used to reconstruct 3D computational models. A modified Carreau model was used to consider the non-Newtonian effect of blood and a three-element Windkessel model taking the effect of the age of patients into account was applied to reproduce physiological pressure waveforms. Numerical results show that blood flow distribution and energy loss of DAA depends on relative sizes of the two aortic arches and their angles with the ascending aorta. Ligation of either aortic arch increases the energy loss of blood in the DAA, leading to the increase in cardiac workload. Generally, the rising rate of energy loss before and after the surgery is almost linear with the area ratio between the aortic arch without ligation and the ascending aorta.

Assessment of surface roughness and blood rheology on local coronary haemodynamics: a multi-scale computational fluid dynamics study.

The surface roughness of the coronary artery is associated with the onset of atherosclerosis. The study applies, for the first time, the micro-scale variation of the artery surface to a 3D coronary model, investigating the impact on haemodynamic parameters which are indicators for atherosclerosis. The surface roughness of porcine coronary arteries have been detailed based on optical microscopy and implemented into a cylindrical section of coronary artery. Several approaches to rheology are compared to determine the benefits/limitations of both single and multiphase models for multi-scale geometry. Haemodynamic parameters averaged over the rough/smooth sections are similar; however, the rough surface experiences a much wider range, with maximum wall shear stress greater than 6 Pa compared to the approximately 3 Pa on the smooth segment. This suggests the smooth-walled assumption may neglect important near-wall haemodynamics. While rheological models lack sufficient definition to truly encompass the micro-scale effects occurring over the rough surface, single-phase models (Newtonian and non-Newtonian) provide numerically stable and comparable results to other coronary simulations. Multiphase models allow for phase interactions between plasma and red blood cells which is more suited to such multi-scale models. These models require additional physical laws to govern advection/aggregation of particulates in the near-wall region.

Dietary Docosahexaenoic Acid Reduces Oscillatory Wall Shear Stress, Atherosclerosis, and Hypertension, Most Likely Mediated via an IL-1-Mediated Mechanism.

BACKGROUND: Hypertension is a complex condition and a common cardiovascular risk factor. Dietary docosahexaenoic acid (DHA) modulates atherosclerosis and hypertension, possibly via an inflammatory mechanism. IL-1 (interleukin 1) has an established role in atherosclerosis and inflammation, although whether IL-1 inhibition modulates blood pressure is unclear. METHODS AND RESULTS: Male apoE-/- (apolipoprotein E-null) mice were fed either a high fat diet or a high fat diet plus DHA (300 mg/kg per day) for 12 weeks. Blood pressure and cardiac function were assessed, and effects of DHA on wall shear stress and atherosclerosis were determined. DHA supplementation improved left ventricular function, reduced wall shear stress and oscillatory shear at ostia in the descending aorta, and significantly lowered blood pressure compared with controls (119.5±7 versus 159.7±3 mm Hg, P<0.001, n=4 per group). Analysis of atheroma following DHA feeding in mice demonstrated a 4-fold reduction in lesion burden in distal aortas and in brachiocephalic arteries (P<0.001, n=12 per group). In addition, DHA treatment selectively decreased plaque endothelial IL-1ß (P<0.01). CONCLUSIONS: Our findings revealed that raised blood pressure can be reduced by inhibiting IL-1 indirectly by administration of DHA in the diet through a mechanism that involves a reduction in wall shear stress and local expression of the proinflammatory cytokine IL-1ß.

Heart rate reduction with ivabradine promotes shear stress-dependent anti-inflammatory mechanisms in arteries.

Blood 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<0.01) and enhanced the expression of anti-inflammatory eNOS (p<0.01) at the inner curvature of the aorta. We concluded that ivabradine alters EC physiology indirectly via modulation of flow because treatment with ivabradine had no effect in ligated carotid arteries in vivo, and did not influence the basal or TNFα-induced expression of inflammatory (VCAM-1, MCP-1) or protective (eNOS, HMOX1, KLF2, KLF4) genes in cultured EC. We therefore considered whether ivabradine can alter WSS which is a regulator of EC inflammatory activation. Computational fluid dynamics demonstrated that ivabradine treatment reduced heart rate by 20 % and enhanced WSS in the aorta. In conclusion, ivabradine treatment altered haemodynamics in the murine aorta by increasing the magnitude of shear stress. This was accompanied by induction of eNOS and suppression of VCAM-1, whereas ivabradine did not alter EC that could not respond to flow. Thus ivabradine protects arteries by altering local mechanical conditions to trigger an anti-inflammatory response.

The progressive wave pump: numerical multiphysics investigation of a novel pump concept with potential to ventricular assist device application.

This article describes the numerical fluid-structure interaction (FSI) validation of a new pumping concept and the possibility for application of a further developed type, as an implantable ventricular assist device (VAD). The novel principle of the so-called progressive wave pump is based on the interaction of an elastic membrane actuated by forced excitation with a surrounding fluid and the pump housing. By applying forced vibrations to one end of the membrane, a transversal wave builds up and progresses to the far end generating both a positive pressure gradient and flow rate. Among others, two axisymmetric geometrical configurations are possible, namely the discoidal and the tubular design. The first one has been built as a physical prototype and is experimentally investigated. In addition, a corresponding numerical FSI model is set up and validated against the experimental findings. Based on this validated numerical method, further numerical investigations are conducted focusing on the development of a tubular progressive wave pump concept with regard to its potential for application as a VAD in the future. To address VAD-relevant issues such as size, hydraulic performance, and blood trauma, corresponding numerical simulations involving macroscopic blood trauma models have been performed. Although being still in an early phase of development, the results are promising and indicate that the wave pump concept in its present state is feasible and can be further developed and investigated as a new type of blood pump.

Partitioned fluid-solid coupling for cardiovascular blood flow: validation study of pressure-driven fluid-domain deformation.

The Karlsruhe Heart Model (KaHMo) is a patient-specific simulation tool for a three-dimensional blood flow evaluation inside the human heart. Whereas KaHMo MRT is based on geometry movement identified from MRT data, KaHMo FSI allows the consideration of structural properties and the analysis of FSI. Previous investigations by Oertel et al. have shown the ability of KaHMo to gain insight into different intra-ventricular fluid mechanics of both healthy and diseased hearts. However, the in vivo validation of the highly dynamic cavity flow pattern has been a challenging task in recent years. As a first step, the focus of this study is on an artificial ventricular experiment, derived from real heart anatomy. Fluid domain deformation and intra-ventricular flow dynamics are enforced by an outer surface pressure distribution. The pure geometrical representation of KaHMo MRT can now be complemented by constitutive properties, pressure forces, and interaction effects using KaHMo FSI's partitioned code-coupling approach. For the first time, fluid domain deformation and intra-ventricular flow of KaHMo FSI has been compared with experimental data. With a good overall agreement, the proof of KaHMo's validity represents an important step from feasibility study toward patient-specific analysis.

MRI-based CFD analysis of flow in a human left ventricle: methodology and application to a healthy heart.

A three-dimensional computational fluid dynamics (CFD) method has been developed to simulate the flow in a pumping left ventricle. The proposed method uses magnetic resonance imaging (MRI) technology to provide a patient specific, time dependent geometry of the ventricle to be simulated. Standard clinical imaging procedures were used in this study. A two-dimensional time-dependent orifice representation of the heart valves was used. The location and size of the valves is estimated based on additional long axis images through the valves. A semi-automatic grid generator was created to generate the calculation grid. Since the time resolution of the MR scans does not fit the requirements of the CFD calculations a third order bezier approximation scheme was developed to realize a smooth wall boundary and grid movement. The calculation was performed by a Navier-Stokes solver using the arbitrary Lagrange-Euler (ALE) formulation. Results show that during diastole, blood flow through the mitral valve forms an asymmetric jet, leading to an asymmetric development of the initial vortex ring. These flow features are in reasonable agreement with in vivo measurements but also show an extremely high sensitivity to the boundary conditions imposed at the inflow. Changes in the atrial representation severely alter the resulting flow field. These shortcomings will have to be addressed in further studies, possibly by inclusion of the real atrial geometry, and imply additional requirements for the clinical imaging processes.

Fluid-structure coupled CFD simulation of the left ventricular flow during filling phase.

The fluid-structure coupled simulation of the heart, though at its developing stage, has shown great prospect in heart function investigations and clinical applications. The purpose of this paper is to verify a commercial software based fluid-structure interaction scheme for the left ventricular filling. The scheme applies the finite volume method to discretize the arbitrary Lagrangian-Eulerian formulation of the Navier-Stokes equations for the fluid while using the nonlinear finite element method to model the structure. The coupling of the fluid and structure is implemented by combining the fluid and structure equations as a unified system and solving it simultaneously at every time step. The left ventricular filling flow in a three-dimensional ellipsoidal thin-wall model geometry of the human heart is simulated, based on a prescribed time-varying Young's modulus. The coupling converges smoothly though the deformation is very large. The pressure-volume relation of the model ventricle, the spatial and temporal distributions of pressure, transient velocity vectors as well as vortex patterns are analyzed, and they agree qualitatively and quantitatively well with the existing data. This preliminary study has verified the feasibility of the scheme and shown the possibility to simulate the left ventricular flow in a more realistic way by adding a myocardial constitutive law into the model and using a more realistic heart geometry.