Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries

The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congenital cardiovascular disease. The relevance of using boundary conditions that accommodate transient phenomena compared with boundary conditions that assume periodicity of the solution is discussed

On conditions of negativity of friction resistance for non-stationary modes of blood flow and possible mechanism of affecting of environmental factors on energy effectiveness of cardio-vascular system functioning

It is shown that initiated by action of molecular viscosity impulse flow, directed usually from the moving fluid to limiting it solid surface, can, under certain conditions, turn to zero and get negative values in the case of non-stationary flow caused by alternating in time longitudinal (along the pipe axis) pressure gradient. It is noted that this non-equilibrium mechanism of negative friction resistance in the similar case of pulsating blood flow in the blood vessels, in addition to the stable to turbulent disturbances swirled blood flow structure providing, can also constitute hydro-mechanical basis of the observed but not explained yet paradoxically high energy effectiveness of the normal functioning of the cardio-vascular system (CVS). We consider respective mechanism of affecting on the stability of the normal work of CVS by environmental variable factors using shifting of hydro-dynamic mode with negative resistance realization range boundaries and variation of linear hydro-dynamic instability leading to the structurally stable swirled blood flow organization

The haemodynamic effects of collateral donation to a chronic total occlusion : implications for patient management

Physiological lesion assessment in the form of Fractional Flow Reserve (FFR) is now well established for the purpose of guiding multi-vessel revascularization. Chronic total coronary occlusions are frequently associated with multi-vessel disease and the collateral dependent myocardium distal to the occlusion is often supplied by a collateral supply from another epicardial coronary artery. The haemodynamic effect of collateral donation upon collateral donor vessel flow may have important implications for the vessel's FFR; rendering it unreliable at predicting ischaemia should the CTO be revascularized. As a consequence, in the setting of multi-vessel disease, optimal revascularization strategy might be altered. There is a paucity of work in the medical literature directly examining this phenomenon. We endeavoured to review the existing literature related to it, to summarise from current knowledge of coronary physiology what is known about the potential effects of CTO revascularization on both collateral flow and collateral donor vessel physiology, and to highlight where further studies might inform practice

A delay recruitment model of the cardiovascular control system.

Copyright will be owned by Springer. We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigation of the rôles played by gain and delay, and the effects of ageing.

Impaired coronary blood flow at higher heart rates during atrial fibrillation: investigation via multiscale modelling

Background. Different mechanisms have been proposed to relate atrial fibrillation (AF) and coronary flow impairment, even in absence of relevant coronary artery disease (CAD). However, the underlying hemodynamics remains unclear. Aim of the present work is to computationally explore whether and to what extent ventricular rate during AF affects the coronary perfusion. Methods. AF is simulated at different ventricular rates (50, 70, 90, 110, 130 bpm) through a 0D-1D multiscale validated model, which combines the left heart-arterial tree together with the coronary circulation. Artificially-built RR stochastic extraction mimics the \emph{in vivo} beating features. All the hemodynamic parameters computed are based on the left anterior descending (LAD) artery and account for the waveform, amplitude and perfusion of the coronary blood flow. Results. Alterations of the coronary hemodynamics are found to be associated either to the heart rate increase, which strongly modifies waveform and amplitude of the LAD flow rate, and to the beat-to-beat variability. The latter is overall amplified in the coronary circulation as HR grows, even though the input RR variability is kept constant at all HRs. Conclusions. Higher ventricular rate during AF exerts an overall coronary blood flow impairment and imbalance of the myocardial oxygen supply-demand ratio. The combined increase of heart rate and higher AF-induced hemodynamic variability lead to a coronary perfusion impairment exceeding 90-110 bpm in AF. Moreover, it is found that coronary perfusion pressure (CPP) is no longer a good measure of the myocardial perfusion for HR higher than 90 bpm.Comment: 8 pages, 5 figures, 3 table

From time-series to complex networks: Application to the cerebrovascular flow patterns in atrial fibrillation

A network-based approach is presented to investigate the cerebrovascular flow patterns during atrial fibrillation (AF) with respect to normal sinus rhythm (NSR). AF, the most common cardiac arrhythmia with faster and irregular beating, has been recently and independently associated with the increased risk of dementia. However, the underlying hemodynamic mechanisms relating the two pathologies remain mainly undetermined so far; thus the contribution of modeling and refined statistical tools is valuable. Pressure and flow rate temporal series in NSR and AF are here evaluated along representative cerebral sites (from carotid arteries to capillary brain circulation), exploiting reliable artificially built signals recently obtained from an in silico approach. The complex network analysis evidences, in a synthetic and original way, a dramatic signal variation towards the distal/capillary cerebral regions during AF, which has no counterpart in NSR conditions. At the large artery level, networks obtained from both AF and NSR hemodynamic signals exhibit elongated and chained features, which are typical of pseudo-periodic series. These aspects are almost completely lost towards the microcirculation during AF, where the networks are topologically more circular and present random-like characteristics. As a consequence, all the physiological phenomena at microcerebral level ruled by periodicity - such as regular perfusion, mean pressure per beat, and average nutrient supply at cellular level - can be strongly compromised, since the AF hemodynamic signals assume irregular behaviour and random-like features. Through a powerful approach which is complementary to the classical statistical tools, the present findings further strengthen the potential link between AF hemodynamic and cognitive decline.Comment: 12 pages, 10 figure

Alteration of cerebrovascular haemodynamic patterns due to atrial fibrillation: an in silico investigation

There has recently been growing evidence that atrial fibrillation (AF), the most common cardiac arrhythmia, is independently associated with the risk of dementia. This represents a very recent frontier with high social impact for the number of individuals involved and for the expected increase in AF incidence in the next 40 years. Although a number of potential haemodynamic processes, such as microembolisms, altered cerebral blood flow, hypoperfusion and microbleeds, arise as connecting links between the two pathologies, the causal mechanisms are far from clear. An in silico approach is proposed that combines in sequence two lumped-parameter schemes, for the cardiovascular system and the cerebral circulation. The systemic arterial pressure is obtained from the cardiovascular system and used as the input for the cerebral circulation, with the aim of studying the role of AF on the cerebral haemodynamics with respect to normal sinus rhythm (NSR), over a 5000 beat recording. In particular, the alteration of the haemodynamic (pressure and flowrate) patterns in the microcirculation during AF is analysed by means of different statistical tools, from correlation coefficients to autocorrelation functions, crossing times, extreme values analysis and multivariate linear regression models. A remarkable signal alteration, such as a reduction in signal correlation (NSR, about 3 s; AF, less than 1 s) and increased probability (up to three to four times higher in AF than in NSR) of extreme value events, emerges for the peripheral brain circulation. The described scenario offers a number of plausible cause-effect mechanisms that might explain the occurrence of critical events and the haemodynamic links relating to AF and dementia.Comment: 13 pages, 9 Figures, 3 Table