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Mixing of inertial point particles in a turbulent channel flow at Re{\tau} = 950 is investigated by means of direct numerical simulations. We consider inertial particles, at varying Stokes number, released from pairs of sources located at different positions inside the channel and analyze the rate at which particles come into close proximity to each other. To do so, we employ a Lagrangian framework, which is suitable for the analysis of trajectories and in general for the study of mixing and dispersion problems. By varying the release position of particles along the wall-normal direction we obtain a thorough description of mixing in an anisotropic turbulent flow. Moreover, we analyze the effects of particle inertia and show that these are not univocal but also depend on the position and alignment of the sources, owing in particular to the dependence of the flow timescales on the distance from the wall., Comment: 19 pages, 7 figures

We study the transition to turbulence in a flat plate boundary layer by means of visibility analysis of velocity time-series extracted across the flow domain. By taking into account the mutual visibility of sampled values, visibility graphs are constructed from each time series. The latter are, thus, transformed into a geometrical object, whose main features can be explored using measures typical of network science that provide a reduced order representation of the underlying flow properties. Using these metrics, we observe the evolution of the flow from laminarity to turbulence and the effects exerted by the free-stream turbulence. Different from other methods requiring an extensive amount of spatiotemporal data (e.g., full velocity field) or a set of parameters and thresholds arbitrarily chosen by the user, the present network-based approach is able to identify the onset markers for transition by means of the streamwise velocity time-series alone., 11 pages, 5 figures

Dilatació aòrtica; Aneurisma de l'aorta ascendent; Anàlisi espai-temporal Dilatación aórtica; Aneurisma de la aorta ascendente; Análisis espacio-temporal Aortic dilation; Ascending aorta aneurysm; Spatiotemporal analysis Motivated by the evidence that the onset and progression of the aneurysm of the ascending aorta (AAo) is intertwined with an adverse hemodynamic environment, the present study characterized in vivo the hemodynamic spatiotemporal complexity and organization in human aortas, with and without dilated AAo, exploring the relations with clinically relevant hemodynamic and geometric parameters. The Complex Networks (CNs) theory was applied for the first time to 4D flow magnetic resonance imaging (MRI) velocity data of ten patients, five of them presenting with AAo dilation. The time-histories along the cardiac cycle of velocity-based quantities were used to build correlation-based CNs. The CNs approach succeeded in capturing large-scale coherent flow features, delimiting flow separation and recirculation regions. CNs metrics highlighted that an increasing AAo dilation (expressed in terms of the ratio between the maximum AAo and aortic root diameter) disrupts the correlation in forward flow reducing the correlation persistence length, while preserving the spatiotemporal homogeneity of secondary flows. The application of CNs to in vivo 4D MRI data holds promise for a mechanistic understanding of the spatiotemporal complexity and organization of aortic flows, opening possibilities for the integration of in vivo quantitative hemodynamic information into risk stratification and classification criteria. Open access funding provided by Politecnico di Torino within the CRUI-CARE Agreement.

The growing epidemiological burden of atrial fibrillation (AF) warrants urgent clarification of the mechanisms at the basis of the independent association between the arrhythmia and cognitive decline/dementia. Several mechanisms have been proposed, such as silent cerebral lesions (subclinical ischemia or micro-haemorrages), a chronic reduction in mean cerebral blood flow, AF-associated pro-inflammatory status and cerebral endothelial dysfunction. However, a new hypothesis based on computational da-ta has recently emerged, which claims that AF irregular rhythm itself may promote direct deleterious beat-to-beat effects, which translates into critical hemodynamic events in the distal cerebral circle. To overcome the limitations of the currently adopted techniques in the study of cerebral circle (transcranial Doppler and Arterial Spin Labeling MRI), we recently demonstrated that cerebral near-infrared spectroscopy (NIRS) with high sampling frequency (20 Hz) may provide beat-to-beat hemodynamic in-sights from the cerebral microcirculation, paving the way for the assessment of distal cerebral hemodynamics during AF. Should the computational findings be confirmed, it will be fundamental to evaluate whether the most aggressive rhythm control strate-gies (such as transcatether ablation) may contribute to reduce cognitive burden in AF patients.

Time irreversibility is a distinctive feature of non-equilibrium phenomena such as turbulent flows, where irreversibility is mainly associated with an energy cascade process. The connection between time irreversibility and coherent motions in wall turbulence, however, has not been investigated yet. An Eulerian, multiscale analysis of time irreversibility in wall-bounded turbulence is proposed in this study, which differs from previous works relying on a Lagrangian approach and mainly focusing on homogeneous turbulence. Outcomes reveal a strong connection between irreversibility levels and coherent structures in both turbulent channel and boundary layer flows. In the near-wall region, irreversibility is directly related to the inner spectral peak originating from small-scale turbulent structures in the buffer layer. Conversely, stronger irreversibility is found in correspondence to the outer spectral peak originating from larger turbulent flow scales far from the wall. Our results represent a first effort to characterize Eulerian TI in wall-bounded turbulent flows, thus paving the way for further developments in wall-turbulence modeling and control accounting for broken temporal symmetry.

Aims Atrial fibrillation (AF) patients may present ischaemic chest pain in the absence of classical obstructive coronary disease. Among the possible causes, the direct haemodynamic effect exerted by the irregular arrhythmia has not been studied in detail. Methods and results A computational fluid dynamics analysis was performed by means of a 1D-0D multiscale model of the entire human cardiovascular system, characterized by a detailed mathematical modelling of the coronary arteries and their downstream distal microcirculatory districts (subepicardial, midwall, and subendocardial layers). Three mean ventricular rates were simulated in both sinus rhythm (SR) and AF: 75, 100, 125 b.p.m. We conducted inter-layer and inter-frequency analysis of the ratio between mean beat-to-beat blood flow in AF compared to SR (Q¯AP/Q¯SR Inter-layer analysis showed that, for each simulated ventricular rate, Q¯AP/Q¯SR progressively decreased from the epicardial to the endocardial layer in the distal left coronary artery districts (P-values < 0.001 for both left anterior descending artery—LAD, and left circumflex artery—LCx), while this was not the case for the distal right coronary artery (RCA) district. Inter-frequency analysis showed that, focusing on each myocardial layer, Q¯AP/Q¯SR progressively worsened as the ventricular rates increased in all investigated microcirculatory districts (LAD, LCx, and RCA) (P-values < 0.001 for all layer-specific comparisons). Conclusions AF exerts direct haemodynamic consequences on the coronary microcirculation, causing a reduction in microvascular coronary flow particularly at higher ventricular rates; the most prominent reduction was seen in the subendocardial layers perfused by left coronary arteries (LAD and LCx).

In spite of cardiovascular system (CVS) response to posture changes have been widely studied, a number of mechanisms and their interplay in regulating central blood pressure and organs perfusion upon orthostatic stress are not yet clear. We propose a novel multiscale 1D-0D mathematical model of the human CVS to investigate the effects of passive (i.e., through head-up tilt without muscular intervention) posture changes. The model includes the main short-term regulation mechanisms and is carefully validated against literature data and

In spite of cardiovascular system (CVS) response to posture changes has been widely studied, a number of mechanisms and their interplay in regulating central blood pressure and organs perfusion upon orthostatic stress are not yet clear. We propose a novel multiscale 1D-0D mathematical model of the human CVS to investigate the effects of passive (i.e., through head-up tilt without muscular intervention) posture changes. The model includes the main short-term regulation mechanisms and is carefully validated against literature data and in-vivo measures here carried out. The model is used to study the transient and steady-state response of the CVS to tilting, the effects of the tilting rate, and the differences between tilt-up and tilt-down. Passive upright tilt led to an increase of mean arterial pressure and heart rate, and a decrease of stroke volume and cardiac output, in agreement with literature data and present in-vivo experiments. Pressure and flow rate waveform analysis along the arterial tree together with mechano-energetic and oxygen consumption parameters highlighted that the whole system approaches a less stressed condition at passive upright posture than supine, with a slight unbalance of the energy supply-demand ratio. The transient dynamics is not symmetric in tilt-up and tilt-down testing, and is non-linearly affected by the tilting rate, with stronger under- and overshoots of the hemodynamic parameters as the duration of tilt is reduced. By enriching the CVS response to posture changes, the present modeling approach shows promise in a number of applications, ranging from autonomic system disorders to spaceflight deconditioning., Supplementary Material

A temporal complex network-based approach is proposed as a novel formulation to investigate turbulent mixing from a Lagrangian viewpoint. By exploiting a spatial proximity criterion, the dynamics of a set of fluid particles is geometrized into a time-varying weighted network. Specifically, a numerically solved turbulent channel flow is employed as an exemplifying case. We show that the time-varying network is able to clearly describe the particle swarm dynamics, in a parametrically robust and computationally inexpensive way. The network formalism enables us to straightforwardly identify transient and long-term flow regimes, the interplay between turbulent mixing and mean flow advection and the occurrence of proximity events among particles. Thanks to their versatility and ability to highlight significant flow features, complex networks represent a suitable tool for Lagrangian investigations of turbulent mixing. The present application of complex networks offers a powerful resource for Lagrangian analysis of turbulent flows, thus providing a further step in building bridges between turbulence research and network science.

Patients with atrial fibrillation (AF) may present ischemic chest pain in the absence of classical obstructive coronary disease. Among the possible causes, the direct hemodynamic effect exerted by the irregular arrhythmia has not been studied in detail. We performed a computational fluid dynamics analysis by means of a 1D-0D multiscale model of the entire human cardiovascular system, enriched by a detailed mathematical modeling of the coronary arteries and their downstream distal microcirculatory districts (subepicardial, midwall and subendocardial layers). Three mean ventricular rates were simulated (75, 100, 125 bpm) in both sinus rhythm (SR) and atrial fibrillation, and an inter-layer and inter-frequency analysis was conducted focusing on the ratio between mean beat-to-beat blood flow in AF compared to SR. Our results show that AF exerts direct hemodynamic consequences on the coronary microcirculation, causing a reduction in microvascular coronary flow particularly at higher ventricular rates; the most prominent reduction was seen in the subendocardial layers perfused by left coronary arteries (left anterior descending and left circumflex arteries).

Scale interaction is studied in wall-bounded turbulence by focusing on the frequency modulation (FM) mechanism of large scales on small scale velocity fluctuations. Differently from amplitude modulation analysis, frequency modulation has been less investigated also due to the difficulty to develop robust tools for broadband signals. To face this issue, the natural visibility graph approach is proposed in this work to map the full velocity signals into complex networks. We show that the network degree centrality is able to capture the signal structure at local scales directly from the full signal, thereby quantifying FM. Velocity signals from numerically-simulated turbulent channel flows and an experimental turbulent boundary layer are investigated at different Reynolds numbers. A correction of Taylor's hypothesis for time-series is proposed to overcome the overprediction of near-wall frequency modulation obtained when local mean velocity is used as the convective velocity. Results provide network-based evidences of the large-to-small FM features for all the three velocity components in the near-wall region, with a reversal mechanism emerging far from the wall. Additionally, scaling arguments in the view of the quasi-steady quasi-homogeneous hypothesis are discussed, and a delay-time between large and small scales very close to the near-wall cycle characteristic time is detected. Results show that the visibility graph is a parameter-free tool that turns out to be effective and robust to detect FM in different configurations of wall-bounded turbulent flows. Based on present findings, the visibility network-based approach can represent a reliable tool to systematically investigate scale interaction mechanisms in wall-bounded turbulence.

Purpose: To show some preliminary results about the possibility to exploit a cardiovascular mathematical model - made patient-specific by noninvasive data routinely measured during ordinary clinical examinations - in order to obtain sufficiently accurate central blood pressure (BP) estimates. Methods: A closed-loop multiscale (0D and 1D) model of the cardiovascular system is made patient-specific by using as model inputs the individual mean heart rate and left-ventricular contraction time, weight, height, age, sex and mean/pulse brachial BPs. The resulting framework is used to determine central systolic, diastolic, mean and pulse pressures, which are compared with the beat-averaged invasive pressures of 12 patients aged 72$\pm$6.61 years. Results: Errors in central systolic, diastolic, mean and pulse pressures by the model are 4.26$\pm$2.81 mmHg, 5.86$\pm$4.38 mmHg, 4.98$\pm$3.95 mmHg and 3.51$\pm$2.38 mmHg, respectively. Conclusion: The proposed modeling approach shows a good patient-specific response and appears to be potentially useful in clinical practice. However, this approach needs to be evaluated in a larger cohort of patients and could possibly be improved through more accurate oscillometric BP measurement methods., 14 pages, 6 figures, 5 tables

Aims Atrial fibrillation (AFib) is associated with cognitive decline/dementia, independently from clinical strokes or transient ischaemic attacks (TIA). Recent in silico data suggested that AFib may induce transient critical haemodynamic events in the cerebral microcirculation. The aim of this study is to use non-invasive spatially resolved cerebral near-infrared spectroscopy (SRS-NIRS) to investigate in vivo beat-to-beat microcirculatory perfusion during AFib and after sinus rhythm (SR) restoration. Methods and results Cerebral SRS-NIRS with high-frequency sampling (20 Hz) and non-invasive systemic haemodynamic monitoring were recorded before and after elective electrical cardioversion (ECV) for AFib or atrial flutter (AFL). To assess beat-to-beat effects of the rhythm status, the frequency distribution of inter-beat differences in tissue haemoglobin index (THI), a proxy of microcirculatory cerebral perfusion, was compared before and after SR restoration. Fifty-three AFib/AFL patients (mean age 69 ± 8 years, 79% males) were ultimately enrolled. Cardioversion was successful in restoring SR in 51 (96%) patients. In front of a non-significant decrease in arterial blood pressure extreme events between pre- and post-ECV measurements, a significant decrease of both hypoperfusive and hyperperfusive/hypertensive microcirculatory events was observed after SR restoration (P Conclusion The present is the first in vivo demonstration that SR restoration by ECV significantly reduces the burden of extreme single-beat haemodynamic events in cerebral microcirculation. Future studies are needed to assess whether SR maintenance might slow long-term AFib-correlated cognitive decline/dementia.

The dispersion and mixing of passive particles in a turbulent channel flow is investigated by means of a network-based representation of their motion. We employ direct numerical simulations at five different Reynolds numbers, from $\mathrm{Re}_{\tau}$ = 180 up to $\mathrm{Re}_{\tau}$ = 950, and obtain sets of particle trajectories via numerical integration. By dividing the channel domain into wall-normal levels, the motion of particles across these levels is used to build a time-varying complex network, which is able to capture the transient phase of the wall-normal mixing process and its dependence on the Reynolds number, $\mathrm{Re}_{\tau}$. Using network metrics, we observe that the dispersion of clouds of tracers depends highly on both their wall-normal starting position and the time elapsed from their release. We identify two main mechanisms that contribute to the long lasting inhibition of the dispersion of particles released near the walls. We also show how the relative importance of these mechanisms varies with the Reynolds number. In particular, at low $\mathrm{Re}_{\tau}$ the weaker velocity fluctuations appear dominant in inhibiting dispersion, while at higher Reynolds numbers a larger role is played by cyclic patterns of motion. At the higher Reynolds numbers employed in this work, we find that most network properties are Reynolds-independent when scaled with outer flow variables. Instead, at lower $\mathrm{Re}_{\tau}$, the aforementioned scaling is not observed. We explore the meaning of the emergence of this scaling in relation to the features of dispersion and to the network definition., Comment: 18 pages, 7 figures

Computational hemodynamics is becoming an increasingly important tool in clinical applications and surgical procedures involving the cardiovascular system. Aim of this review is to provide a compact summary of state of the art 0D-1D multiscale models of the arterial coronary system, with particular attention to applications related to cardiac arrhythmias, whose effects on the coronary circulation remain so far poorly understood. The focus on 0D-1D models only is motivated by the competitive computational cost, the reliability of the outcomes for the whole cardiovascular system, and the ability to directly account for cardiac arrhythmias. The analyzed studies show that cardiac arrhythmias by their own are able to promote significant alterations of the coronary hemodynamics, with a worse scenario as the mean heart rate (HR) increases. The present review can stimulate future investigation, both in computational and clinical research, devoted to the hemodynamic effects induced by cardiac arrhythmias on the coronary circulation., Comment: 9 pages, 4 figures, 1 table

Turbulent mixing is studied in the Lagrangian framework with an approach based on the complex network formalism. We consider the motion of passive, noninertial particles inside a turbulent channel simulated at $Re_{\tau} = 950$. The time-dependent network is built to evaluate the transfer of tracers between thin wall-parallel layers which partition the channel in the wall-normal direction. By doing so, we are able to assess the spatial and temporal complexities arising from turbulence dynamics and their influence on the mixing process. This approach highlights the effects of small-scale features of turbulent flow structures and also the larger scale effects determined by wall-induced anisotropy. Complex networks, coupled to the Lagrangian description of turbulence, are effective in providing novel insights into inhomogeneous turbulence and mixing., Comment: 13 pages, 6 figures

Human spaceflight has been fascinating man for centuries, representing the intangible need to explore the unknown, challenge new frontiers, advance technology and push scientific boundaries further. A key area of importance is cardiovascular deconditioning, that is, the collection of hemodynamic changes - from blood volume shift and reduction to altered cardiac function - induced by sustained presence in microgravity. A thorough grasp of the 0G adjustment point per se is important from a physiological viewpoint and fundamental for astronauts' safety and physical capability on long spaceflights. However, hemodynamic details of cardiovascular deconditioning are incomplete, inconsistent and poorly measured to date; thus a computational approach can be quite valuable. We present a validated 1D-0D multiscale model to study the cardiovascular response to long-term 0G spaceflight in comparison to the 1G supine reference condition. Cardiac work, oxygen consumption and contractility indexes, as well as central mean and pulse pressures were reduced, augmenting the cardiac deconditioning scenario. Exercise tolerance of a spaceflight traveler was found to be comparable to an untrained person with a sedentary lifestyle. At the capillary-venous level significant waveform alterations were observed which can modify the regular perfusion and average nutrient supply at the cellular level. The present study suggests special attention should be paid to future long spaceflights which demand prompt physical capacity at the time of restoration of partial gravity (e.g., Moon/Mars landing). Since spaceflight deconditioning has features similar to accelerated aging understanding deconditioning mechanisms in microgravity are also relevant to the understanding of aging physiology on Earth., 14 pages, 5 tables, 5 figures

Background: Heart rate variability (HRV), defined as the variability between consecutive heartbeats, is a surrogate measure of cardiac vagal tone. It is widely accepted that a decreased HRV is associated to several risk factors and cardiovascular diseases. However, a possible association between HRV and altered cerebral hemodynamics is still debated, suffering from HRV short-term measures and the paucity of high-resolution deep cerebral data. We propose a computational approach to evaluate the deep cerebral and central hemodynamics subject to physiological alterations of HRV in an ideal young healthy patient at rest. Methods: The cardiovascular-cerebral model is composed by electrical components able to reproduce the response of the different cardiovascular regions and their features. The model was validated over more than thirty studies and recently exploited to understand the hemodynamic mechanisms between cardiac arrythmia and cognitive deficit. Three configurations (baseline, increased HRV, and decreased HRV) are built based on the standard deviation (SDNN) of RR beats. For each configuration, 5,000 RR beats are simulated to investigate the occurrence of extreme values, alteration of the regular hemodynamics pattern, and variation of mean perfusion/pressure levels. Results: In the cerebral circulation, our results show that HRV has overall a stronger impact on pressure than flow rate mean values but similarly alters pressure and flow rate in terms of extreme events. By comparing reduced and increased HRV, this latter induces a higher probability of altered mean and extreme values, and is therefore more detrimental at distal cerebral level. On the contrary, at central level a decreased HRV induces a higher cardiac effort without improving the mechano-contractile performance, thus overall reducing the heart efficiency. Conclusions: Present results suggest that: (i) the increase of HRV per se does not seem to be sufficient to trigger a better cerebral hemodynamic response; (ii) by accounting for both central and cerebral circulations, the optimal HRV configuration is found at baseline. Given the relation inversely linking HRV and HR, the presence of this optimal condition can contribute to explain why the mean HR of the general population settles around the baseline value (70 bpm).

Atrial fibrillation (AF) is the most common form of arrhythmia with accelerated and irregular heart rate (HR), leading to both heart failure and stroke and being responsible for an increase in cardiovascular morbidity and mortality. In spite of its importance, the direct effects of AF on the arterial hemodynamic patterns are not completely known to date. Based on a multiscale modelling approach, the proposed work investigates the effects of AF on the local arterial fluid dynamics. AF and normal sinus rhythm (NSR) conditions are simulated extracting 2000 $\mathrm{RR}$ heartbeats and comparing the most relevant cardiac and vascular parameters at the same HR (75 bpm). Present outcomes evidence that the arterial system is not able to completely absorb the AF-induced variability, which can be even amplified towards the peripheral circulation. AF is also able to locally alter the wave dynamics, by modifying the interplay between forward and backward signals. The sole heart rhythm variation (i.e., from NSR to AF) promotes an alteration of the regular dynamics at the arterial level which, in terms of pressure and peripheral perfusion, suggests a modification of the physiological phenomena ruled by periodicity (e.g., regular organ perfusion)and a possible vascular dysfunction due to the prolonged exposure to irregular and extreme values. The present study represents a first modeling approach to characterize the variability of arterial hemodynamics in presence of AF, which surely deserves further clinical investigation., Comment: 17 pages, 8 figures

A 1D description of the arterial tree is coupled to a lumped parameter model of the remaining circulatory system, resulting in a closed-loop multiscale model of the cardiovascular apparatus. The regulation of the arterial pressure is also implemented through a short-term baroreceptor model. The proposed framework reproduces well the physiological cardiovascular behaviour of an healthy young man and the modelled baroreflex mechanism is effective in adjusting the hemodynamic responses to both heart pacing and open-loop aortic-carotid sinus control.

Atherosclerosis at the early stage in coronary arteries has been associated with low cycle-average wall shear stress magnitude. However, parallel to the identification of an established active role for low wall shear stress in the onset/progression of the atherosclerotic disease, a weak association between lesions localization and low/oscillatory wall shear stress has been observed. In the attempt to fully identify the wall shear stress phenotype triggering early atherosclerosis in coronary arteries, this exploratory study aims at enriching the characterization of wall shear stress emerging features combining correlation-based analysis and complex networks theory with computational hemodynamics. The final goal is the characterization of the spatiotemporal and topological heterogeneity of wall shear stress waveforms along the cardiac cycle. In detail, here time-histories of wall shear stress magnitude and wall shear stress projection along the main flow direction and orthogonal to it (a measure of wall shear stress multidirectionality) are analyzed in a representative dataset of 10 left anterior descending pig coronary artery computational hemodynamics models. Among the main findings, we report that the proposed analysis quantitatively demonstrates that the model-specific inlet flow-rate shapes wall shear stress time-histories. Moreover, it emerges that a combined effect of low wall shear stress magnitude and of the shape of the wall shear stress–based descriptors time-histories could trigger atherosclerosis at its earliest stage. The findings of this work suggest for new experiments to provide a clearer determination of the wall shear stress phenotype which is at the basis of the so-called arterial hemodynamic risk hypothesis in coronary arteries.

Atrial fibrillation (AF), the most common cardiac arrhythmia leading to irregular and faster heartbeat, has been recently and independently associated to the risk of dementia. A constellation of hemodynamic mechanisms has been proposed to explain the possible link between the two pathologies. However, definitive data still miss, and it is unknown how heart rate (HR) influences the cerebral microcirculation. We propose a computational approach, based on a validated hemodynamic modeling, to compare the cerebral circulation during normal sinus rhythm (NSR) and AF at different HRs. AF is able to trigger a higher variability of the cerebral blood flow variables which grows towards the distal circulation. The alteration of the hemodynamic patterns, inducing the rupture of the signal periodicity and the consequent higher occurrence of extremely high/low values, increases with HR. Awaiting necessary clinical evidences, present findings highlight that a strict rate control strategy could be beneficial in terms of cognitive outcomes in patients with permanent AF.

International audience; The dynamics of a passive scalar plume in a turbulent boundary layer is experimentally investigated via vertical turbulent transport time series. Experimental data are acquired in a rough-wall turbulent boundary layer that develops in a recirculating wind tunnel setup. Two source sizes in an elevated position are considered in order to investigate the influence of the emission conditions on the plume dynamics. The analysis is focused on the effects of the meandering motion and the relative dispersion of the plume with respect to its center of mass. First, classical statistics are investigated. We found that (in accordance with previous studies) the meandering motion is the main factor responsible for differences in the variance and intermittency, as well as the kurtosis and power spectral density, between the two source sizes. On the contrary, the mean and the skewness are slightly affected by the emission conditions. With the aim to characterize the temporal structure of the turbulent transport series, the visibility algorithm is exploited to carry out a complex network-based analysis. In particular, two network metrics-the average peak occurrence and the assortativity coefficient-are analyzed, as they are able to capture the temporal occurrence of extreme events and their relative intensity in the series. The effects of the meandering motion and the relative dispersion of the plume are discussed in view of the network metrics, revealing that a stronger meandering motion is associated with higher values of both the average peak occurrence and the assortativity coefficient. The network-based analysis advances the level of information of classical statistics by characterizing the impact of the emission conditions on the temporal structure of the signals in terms of extreme events (namely, peaks and pits) and their relative intensity. In this way, complex networks provide-through the evaluation of network metrics-an effective tool for time-series analysis of experimental data.

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., 8 pages, 5 figures, 3 tables