A review of multiscale 0D–1D computational modeling of coronary circulation with applications to cardiac arrhythmias

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

Reduced-order unscented Kalman filter in the frequency domain: Application to computational hemodynamics

Objective: The aim of this work is to assess the potential of the reduced order unscented Kalman filter (ROUKF) in the context of computational hemodynamics, in order to estimate cardiovascular model parameters when employing real patient-specific data. Methods: The approach combines an efficient blood flow solver for one-dimensional networks (for the forward problem) with the parameter estimation problem cast in the frequency space. Namely, the ROUKF is used to correct model parameter after each cardiac cycle, depending on the discrepancies of model outputs with respect to available observations properly mapped into the frequency space. Results: First we validate the filter in frequency domain applying it in the context of a set of experimental measurements for an in vitro model. Second, we perform different numerical experiments aiming at parameter estimation using patient-specific data. Conclusion: Our results demonstrate that the filter in frequency domain allows a faster and more robust parameter estimation, when compared to its time domain counterpart. Moreover, the proposed approach allows to estimate parameters that are not directly related to the network but are crucial for targeting inter-individual parameter variability (e.g., parameters that characterize the cardiac output). Significance: The ROUKF in frequency domain provides a robust and flexible tool for estimating parameters related to cardiovascular mathematical models using in vivo data

A model of blood flow in the mesenteric arterial system

<p>Abstract</p> <p>Background</p> <p>There are some early clinical indicators of cardiac ischemia, most notably a change in a person's electrocardiogram. Less well understood, but potentially just as dangerous, is ischemia that develops in the gastrointestinal system. Such ischemia is difficult to diagnose without angiography (an invasive and time-consuming procedure) mainly due to the highly unspecific nature of the disease.</p> <p>Understanding how perfusion is affected during ischemic conditions can be a useful clinical tool which can help clinicians during the diagnosis process. As a first step towards this final goal, a computational model of the gastrointestinal system has been developed and used to simulate realistic blood flow during normal conditions.</p> <p>Methods</p> <p>An anatomically and biophysically based model of the major mesenteric arteries has been developed to be used to simulate normal blood flows. The computational mesh used for the simulations has been generated using data from the Visible Human project. The 3D Navier-Stokes equations that govern flow within this mesh have been simplified to an efficient 1D scheme. This scheme, together with a constitutive pressure-radius relationship, has been solved numerically for pressure, vessel radius and velocity for the entire mesenteric arterial network.</p> <p>Results</p> <p>The computational model developed shows close agreement with physiologically realistic geometries other researchers have recorded <it>in vivo</it>. Using this model as a framework, results were analyzed for the four distinct phases of the cardiac cycle – diastole, isovolumic contraction, ejection and isovolumic relaxation. Profiles showing the temporally varying pressure and velocity for a periodic input varying between 10.2 kPa (77 mmHg) and 14.6 kPa (110 mmHg) at the abdominal aorta are presented. An analytical solution has been developed to model blood flow in tapering vessels and when compared with the numerical solution, showed excellent agreement.</p> <p>Conclusion</p> <p>An anatomically and physiologically realistic computational model of the major mesenteric arteries has been developed for the gastrointestinal system. Using this model, blood flow has been simulated which show physiologically realistic flow profiles.</p

Blood pressure gradients in cerebral arteries: A clue to pathogenesis of cerebral small vessel disease

Rationale: The role of hypertension in cerebral small vessel disease is poorly understood. At the base of the brain (the \u27vascular centrencephalon\u27), short straight arteries transmit blood pressure directly to small resistance vessels; the cerebral convexity is supplied by long arteries with many branches, resulting in a drop in blood pressure. Hypertensive small vessel disease (lipohyalinosis) causes the classically described lacunar infarctions at the base of the brain; however, periventricular white matter intensities (WMIs) seen on MRI and WMI in subcortical areas over the convexity, which are often also called \u27lacunes\u27, probably have different aetiologies. Objectives: We studied pressure gradients from proximal to distal regions of the cerebral vasculature by mathematical modelling. Methods and results: Blood flow/pressure equations were solved in an Anatomically Detailed Arterial Network (ADAN) model, considering a normotensive and a hypertensive case. Model parameters were suitably modified to account for structural changes in arterial vessels in the hypertensive scenario. Computations predict a marked drop in blood pressure from large and medium-sized cerebral vessels to cerebral peripheral beds. When blood pressure in the brachial artery is 192/113 mm Hg, the pressure in the small arterioles of the posterior parietal artery bed would be only 117/68 mm Hg. In the normotensive case, with blood pressure in the brachial artery of 117/75 mm Hg, the pressure in small parietal arterioles would be only 59/38 mm Hg. Conclusion: These findings have important implications for understanding small vessel disease. The marked pressure gradient across cerebral arteries should be taken into account when evaluating the pathogenesis of small WMIs on MRI. Hypertensive small vessel disease, affecting the arterioles at the base of the brain should be distinguished from small vessel disease in subcortical regions of the convexity and venous disease in the periventricular white matter

Mathematical modeling of local perfusion in large distensible microvascular networks

Microvessels -blood vessels with diameter less than 200 microns- form large, intricate networks organized into arterioles, capillaries and venules. In these networks, the distribution of flow and pressure drop is a highly interlaced function of single vessel resistances and mutual vessel interactions. In this paper we propose a mathematical and computational model to study the behavior of microcirculatory networks subjected to different conditions. The network geometry is composed of a graph of connected straight cylinders, each one representing a vessel. The blood flow and pressure drop across the single vessel, further split into smaller elements, are related through a generalized Ohm's law featuring a conductivity parameter, function of the vessel cross section area and geometry, which undergo deformations under pressure loads. The membrane theory is used to describe the deformation of vessel lumina, tailored to the structure of thick-walled arterioles and thin-walled venules. In addition, since venules can possibly experience negative transmural pressures, a buckling model is also included to represent vessel collapse. The complete model including arterioles, capillaries and venules represents a nonlinear system of PDEs, which is approached numerically by finite element discretization and linearization techniques. We use the model to simulate flow in the microcirculation of the human eye retina, a terminal system with a single inlet and outlet. After a phase of validation against experimental measurements, we simulate the network response to different interstitial pressure values. Such a study is carried out both for global and localized variations of the interstitial pressure. In both cases, significant redistributions of the blood flow in the network arise, highlighting the importance of considering the single vessel behavior along with its position and connectivity in the network

Computational simulation of intracoronary flow based on real coronary geometry

Objective: To assess the feasibility of computationally simulating intracoronary blood flow based on real coronary artery geometry and to graphically depict various mechanical characteristics of this flow. Methods: Explanted fresh pig hearts were fixed using a continuous perfusion of 4% formaldehyde at physiological pressures. Omnipaque dye added to lead rubber solution was titrated to an optimum proportion of 1:25, to cast the coronary arterial tree. The heart was stabilized in a phantom model so as to suspend the base and the apex without causing external deformation. High resolution computerized tomography scans of this model were utilized to reconstruct the three-dimensional coronary artery geometry, which in turn was used to generate several volumetric tetrahedral meshes of sufficient density needed for numerical accuracy. The transient equations of momentum and mass conservation were numerically solved by employing methods of computational fluid dynamics under realistic pulsatile inflow boundary conditions. Results: The simulations have yielded graphic distributions of intracoronary flow stream lines, static pressure drop, wall shear stress, bifurcation mass flow ratios and velocity profiles. The variability of these quantities within the cardiac cycle has been investigated at a temporal resolution of 1/100th of a second and a spatial resolution of about 10 μm. The areas of amplified variations in wall shear stress, mostly evident in the neighborhoods of arterial branching, seem to correlate well with clinically observed increased atherogenesis. The intracoronary flow lines showed stasis and extreme vorticity during the phase of minimum coronary flow in contrast to streamlined undisturbed flow during the phase of maximum flow. Conclusions: Computational tools of this kind along with a state-of-the-art multislice computerized tomography or magnetic resonance-based non-invasive coronary imaging, could enable realistic, repetitive, non-invasive and multidimensional quantifications of the effects of stenosis on distal hemodynamics, and thus help in precise surgical/interventional planning. It could also add insights into coronary and bypass graft atherogenesi

Left Ventricular Trabeculations Decrease the Wall Shear Stress and Increase the Intra-Ventricular Pressure Drop in CFD Simulations

The aim of the present study is to characterize the hemodynamics of left ventricular (LV) geometries to examine the impact of trabeculae and papillary muscles (PMs) on blood flow using high performance computing (HPC). Five pairs of detailed and smoothed LV endocardium models were reconstructed from high-resolution magnetic resonance images (MRI) of ex-vivo human hearts. The detailed model of one LV pair is characterized only by the PMs and few big trabeculae, to represent state of art level of endocardial detail. The other four detailed models obtained include instead endocardial structures measuring ≥1 mm2 in cross-sectional area. The geometrical characterizations were done using computational fluid dynamics (CFD) simulations with rigid walls and both constant and transient flow inputs on the detailed and smoothed models for comparison. These simulations do not represent a clinical or physiological scenario, but a characterization of the interaction of endocardial structures with blood flow. Steady flow simulations were employed to quantify the pressure drop between the inlet and the outlet of the LVs and the wall shear stress (WSS). Coherent structures were analyzed using the Q-criterion for both constant and transient flow inputs. Our results show that trabeculae and PMs increase the intra-ventricular pressure drop, reduce the WSS and disrupt the dominant single vortex, usually present in the smoothed-endocardium models, generating secondary small vortices. Given that obtaining high resolution anatomical detail is challenging in-vivo, we propose that the effect of trabeculations can be incorporated into smoothed ventricular geometries by adding a porous layer along the LV endocardial wall. Results show that a porous layer of a thickness of 1.2·10−2 m with a porosity of 20 kg/m2 on the smoothed-endocardium ventricle models approximates the pressure drops, vorticities and WSS observed in the detailed models.This paper has been partially funded by CompBioMed project, under H2020-EU.1.4.1.3 European Union’s Horizon 2020 research and innovation programme, grant agreement n◦ 675451. FS is supported by a grant from Severo Ochoa (n◦ SEV-2015-0493-16-4), Spain. CB is supported by a grant from the Fundació LaMarató de TV3 (n◦ 20154031), Spain. TI and PI are supported by the Institute of Engineering in Medicine, USA, and the Lillehei Heart Institute, USA.Peer ReviewedPostprint (published version

Multiscale Modeling of Hemodynamics in Human Vessel Network and Its Applications in Cerebral Aneurysms

Three-dimensional (3D) simulation of patient-specific morphological models has been widely used to provide the hemodynamic information of individual patients, such as wall shear stress (WSS), oscillatory shear index (OSI), and flow patterns, etc. Since patient-specific morphological segment was only restricted locally, boundary conditions (BCs) are required to implement the CFD simulation. Direct measurements of the flow and pressure waveforms were often required as input BCs for 3D CFD simulations of patient-specific models. However, as the morphology develops, the feedback from this topological deformation may lead to BCs being altered, and hence without this feedback, the flow characteristics of the morphology are only computed locally. A one-dimensional (1D) numerical model containing the entire human vessel network has been proposed to compute the global hemodynamics. In the meantime, experimental studies of blood flow in the patient-specific modeling of the circle of Willies (CoW) was conducted. The flow and pressure waveforms were quantified to validate the accuracy of the pure 1D model. This 1D model will be coupled with a 3D morphological model to account for the effects of the altered BCs. The proposed 1D-3D multi-scale modeling approach investigates how the global hemodynamic changes can be induced by the local morphological effects, and in consequence, may further result in altering of BCs to interfere with the solution of the 3D simulation. Validation of the proposed multi-scale model has also been made by comparing the solution of the flow rate and pressure waveforms with the experimental data and 3D numerical simulations reported in the literature. Moreover, the multi-scale model is extended to study a patient-specific cerebral aneurysm and a stenosis model. The proposed multi-scale model can be used as an alternative to current approaches to study intracranial vascular diseases such as an aneurysm, stenosis, and combined cases