On the integration of the baroreflex control mechanism in a heterogeneous model of the cardiovascular system

One-Dimensional Blood Flow Modeling in the Cardiovascular System. From the Conventional Physiological Setting to Real-Life Hemodynamics

Research in the dynamics of blood flow is essential to the understanding of one of the major driving forces of human physiology. The hemodynamic conditions experienced within the cardiovascular system generate a highly variable mechanical environment that propels its function. Modeling this system is a challenging problem that must be addressed at the systemic scale to gain insight into the interplay between the different time and spatial scales of cardiovascular physiology processes. The vast majority of scientific contributions on systemic-scale distributed parameter-based blood flow modeling have approached the topic under relatively simple scenarios, defined by the resting state, the supine position, and, in some cases, by disease. However, the physiological states experienced by the cardiovascular system considerably deviate from such conditions throughout a significant part of our life. Moreover, these deviations are, in many cases, extremely beneficial for sustaining a healthy life. On top of this, inter-individual variability carries intrinsic complexities, requiring the modeling of patient-specific physiology. The impact of modeling hypotheses such as the effect of respiration, control mechanisms, and gravity, the consideration of other-than-resting physiological conditions, such as those encountered in exercise and sleeping, and the incorporation of organ-specific physiology and disease have been cursorily addressed in the specialized literature. In turn, patient-specific characterization of cardiovascular system models is in its early stages. As for models and methods, these conditions pose challenges regarding modeling the underlying phenomena and developing methodological tools to solve the associated equations. In fact, under certain conditions, the mathematical formulation becomes more intricate, model parameters suffer greater variability, and the overall uncertainty about the system's working point increases. This paper reviews current advances and opportunities to model and simulate blood flow in the cardiovascular system at the systemic scale in both the conventional resting setting and in situations experienced in everyday life.

Closed-loop baroreflex model with biophysically detailed afferent pathway

In this work, we couple a lumped-parameter closed-loop model of the cardiovascular system with a physiologically-detailed mathematical description of the baroreflex afferent pathway. The model features a classical Hodgkin-Huxley current-type model for the baroreflex afferent limb (primary neuron) and for the second-order neuron in the central nervous system. The pulsatile arterial wall distension triggers a frequency-modulated sequence of action potentials at the afferent neuron. This signal is then integrated at the brainstem neuron model. The efferent limb, representing the sympathetic and parasympathetic nervous system, is described as a transfer function acting on heart and blood vessel model parameters in order to control arterial pressure. Three in silico experiments are shown here: a step increase in the aortic pressure to evaluate the functionality of the reflex arch, a hemorrhagic episode and an infusion simulation. Through this model, it is possible to study the biophysical dynamics of the ionic currents proposed for the afferent limb components of the baroreflex during the cardiac cycle, and the way in which currents dynamics affect the cardiovascular function. Moreover, this system can be further developed to study in detail each baroreflex loop component, helping to unveil the mechanisms involved in the cardiovascular afferent information processing.

Modeling the impact of thoracic pressure on intracranial pressure

A potential contribution to the progression of Spaceflight Associated Neuro-ocular Syndrome is the thoracic-to-spinal dural sac transmural pressure relationship. In this study, we utilize a lumped-parameter computational model of human cerebrospinal fluid (CSF) systems to investigate mechanisms of CSF redistribution. We present two analyses to illustrate potential mechanisms for CSF pressure alterations similar to those observed in microgravity conditions. Our numerical evidence suggests that the compliant relationship between thoracic and CSF compartments is insufficient to solely explain the observed decrease in CSF pressure with respect to the supine position. Our analyses suggest that the interaction between thoracic pressure and the cardiovascular system, particularly the central veins, has greater influence on CSF pressure. These results indicate that future studies should focus on the holistic system, with the impact of cardiovascular changes to the CSF pressure emphasized over the sequestration of fluid in the spine.

Modeling essential hypertension with a closed-loop mathematical model for the entire human circulation

Arterial hypertension, defined as an increase in systemic arterial pressure, is a major risk factor for the development of diseases affecting the cardiovascular system. Every year, 9.4 million deaths worldwide are caused by complications arising from hypertension. Despite well-established approaches to diagnosis and treatment, fewer than half of all hypertensive patients have adequately controlled blood pressure. In this scenario, computational models of hypertension can be a practical approach for better quantifying the role played by different components of the cardiovascular system in the determination of this condition. In the present work we adopt a global closed-loop multi-scale mathematical model for the entire human circulation to reproduce a hypertensive scenario. In particular, we modify the model to reproduce alterations in the cardiovascular system that are cause and/or consequence of the hypertensive state. The adaptation does not only affect large systemic arteries and the heart but also the microcirculation, the pulmonary circulation and the venous system. Model outputs for the hypertensive scenario are validated through assessment of computational results against current knowledge on the impact of hypertension on the cardiovascular system.

A mathematical model for biomechanical behavior of the aortic arch

The aortic arch plays a significant role in homeostatic mechanisms to retain blood pressure at stable balance in the cardiovascular system. Therefore, the objective is to estimate and identify cardiovascular illness imposed by the abnormal blood hemodynamic domain. In this regard, hemodynamic forces are monitored by the baroreflex of the artery wall. Therefore, these receptors quickly detect the abnormal stress magnitudes in the aortic arterial wall. The present study presents a 3D aortic arch model extracted by a Computerized tomography scan. Also, the numerical solution was carried out by ANSYS 2020 R1 in view of Fluid-Structure Interaction After that, we found wall shear stress (WSS), pressure, and velocity in the fluid domain. Also, the normal stress was analyzed to determine the aortic arch baroreflex location in the solid range. In this regard, higher WSS values are measured at the supra-aortic branches going out the aortic arch that reached 42.5 Pa. Also, higher normal stress happened at the aortic root and the supra-aortic branches and reached approximately 200 kPa at peak systole.

Integrated cardiorespiratory system model with short timescale control mechanisms

A compartmental model of the cardiorespiratory system featuring pulsatile blood flow and gas transport, as well as closed loop mechanisms of cardiorespiratory regulation is presented. Short timescale regulatory action includes baroreflex, peripheral and central chemoreflex feedback. The cardiorespiratory model is composed by compartments to describe blood flow and gas exchange in the major systemic and pulmonic regions. The control systems include formulations to afferent activity of arterial baroreceptor and peripheral and central chemoreceptors. Simulations described here include situations of hypoxia, hypercapnia, and hemorrhage. The overall responses of our simulations agree with physiological (experimental) and theoretical data. Our results suggest that the present model could be used to further understand the interplay among major regulatory mechanisms in the functioning of the cardiovascular and respiratory systems in cases of normal and abnormal physiological conditions.

Total Effective Vascular Compliance of a Global Mathematical Model for the Cardiovascular System

In this work, we determined the total effective vascular compliance of a global closed-loop model for the cardiovascular system by performing an infusion test of 500 mL of blood in four minutes. Our mathematical model includes a network of arteries and veins where blood flow is described by means of a one-dimensional nonlinear hyperbolic PDE system and zero-dimensional models for other cardiovascular compartments. Some mathematical modifications were introduced to better capture the physiology of the infusion test: (1) a physiological distribution of vascular compliance and total blood volume was implemented, (2) a nonlinear representation of venous resistances and compliances was introduced, and (3) main regulatory mechanisms triggered by the infusion test where incorporated into the model. By means of presented in silico experiment, we show that effective total vascular compliance is the result of the interaction between the assigned constant physical vascular compliance and the capacity of the cardiovascular system to adapt to new situations via regulatory mechanisms.

Modeling individual differences in cardiovascular response to gravitational stress using a sensitivity analysis

The human cardiovascular (CV) system elicits a physiological response to gravitational environments, with significant variation between different individuals. Computational modeling can predict CV response, however model complexity and variation of physiological parameters in a normal population makes it challenging to capture individual responses. We conducted a sensitivity analysis on an existing 21-compartment lumped-parameter hemodynamic model in a range of gravitational conditions to 1) investigate the influence of model parameters on a tilt test CV response and 2) to determine the subset of those parameters with the most influence on systemic physiological outcomes. A supine virtual subject was tilted to upright under the influence of a constant gravitational field ranging from 0 g to 1 g. The sensitivity analysis was conducted using a Latin hypercube sampling/partial rank correlation coefficient methodology with subsets of model parameters varied across a normal physiological range. Sensitivity was determined by variation in outcome measures including heart rate, stroke volume, central venous pressure, systemic blood pressures, and cardiac output. Results showed that model parameters related to the length, resistance, and compliance of the large veins and parameters related to right ventricular function have the most influence on model outcomes. For most outcome measures considered, parameters related to the heart are dominant. Results highlight which model parameters to accurately value in simulations of individual subjects' CV response to gravitational stress, improving the accuracy of predictions. Influential parameters remain largely similar across gravity levels, highlighting that accurate model fitting in 1 g can increase the accuracy of predictive responses in reduced gravity.NEW & NOTEWORTHY Computational modeling is used to predict cardiovascular responses to altered gravitational environments. However, considerable variation between subjects and model complexity makes accurate parameter assignment for individuals challenging. This computational effort studies sensitivity in cardiovascular model outcomes due to varying parameters across a normal physiological range. This allows determination of which parameters have the largest influence on outcomes, i.e., which parameters must be most carefully selected to give accurate predictions of individual responses.

Influence of ageing on human body blood flow and heat transfer: A detailed computational modelling study

Ageing plays a fundamental role in arterial blood transport and heat transfer within a human body. The aim of this work is to provide a comprehensive methodology, based on biomechanical considerations, for modelling arterial flow and energy exchange mechanisms in the body accounting for age-induced changes. The study outlines a framework for age-related modifications within several interlinked subsystems, which include arterial stiffening, heart contractility variations, tissue volume and property changes, and thermoregulatory system deterioration. Some of the proposed age-dependent governing equations are directly extrapolated from experimental data sets. The computational framework is demonstrated through numerical experiments, which show the impact of such age-related changes on arterial blood pressure, local temperature distribution, and global body thermal response. The proposed numerical experiments show that the age-related changes in arterial convection do not significantly affect the tissue temperature distribution. Results also highlight age-related effects on the sweating mechanism, which lead to a significant reduction in heat dissipation and a subsequent rise in skin and core temperatures.

A regulated multiscale closed-loop cardiovascular model, with applications to hemorrhage and hypertension

A computational tool is developed for simulating the dynamic response of the human cardiovascular system to various stressors and injuries. The tool couples 0-dimensional models of the heart, pulmonary vasculature, and peripheral vasculature to 1-dimensional models of the major systemic arteries. To simulate autonomic response, this multiscale circulatory model is integrated with a feedback model of the baroreflex, allowing control of heart rate, cardiac contractility, and peripheral impedance. The performance of the tool is demonstrated in 2 scenarios: neurogenic hypertension by sustained stimulation of the sympathetic nervous system and an acute 10% hemorrhage from the left femoral artery.

A novel method for non-invasively detecting the severity and location of aortic aneurysms

The influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstrates the methods’ ability to detect the location and severity of an aortic aneurysm through the analysis of flow waveforms in clinically accessible locations. Therefore, the proposed methodology shows a high potential for non-invasive aneurysm detectors/monitors.

A high-order local time stepping finite volume solver for one-dimensional blood flow simulations: application to the ADAN model

In recent years, the complexity of vessel networks for one-dimensional blood flow models has significantly increased, because of enhanced anatomical detail or automatic peripheral vasculature generation, for example. This fact, along with the application of these models in uncertainty quantification and parameter estimation poses the need for extremely efficient numerical solvers. The aim of this work is to present a finite volume solver for one-dimensional blood flow simulations in networks of elastic and viscoelastic vessels, featuring high-order space-time accuracy and local time stepping (LTS). The solver is built on (i) a high-order finite volume type numerical scheme, (ii) a high-order treatment of the numerical solution at internal vertexes of the network, often called junctions, and (iii) an accurate LTS strategy. The accuracy of the proposed methodology is verified by empirical convergence tests. Then, the resulting LTS scheme is applied to arterial networks of increasing complexity and spatial scale heterogeneity, with a number of one-dimensional segments ranging from a few tens up to several thousands and vessel lengths ranging from less than a millimeter up to tens of centimeters, in order to evaluate its computational cost efficiency. The proposed methodology can be extended to any other hyperbolic system for which network applications are relevant. Copyright © 2016 John Wiley & Sons, Ltd.

Toward translating near-infrared spectroscopy oxygen saturation data for the non-invasive prediction of spatial and temporal hemodynamics during exercise

Image-based computational fluid dynamics (CFD) studies conducted at rest have shown that atherosclerotic plaque in the thoracic aorta (TA) correlates with adverse wall shear stress (WSS), but there is a paucity of such data under elevated flow conditions. We developed a pedaling exercise protocol to obtain phase contrast magnetic resonance imaging (PC-MRI) blood flow measurements in the TA and brachiocephalic arteries during three-tiered supine pedaling at 130, 150, and 170 % of resting heart rate (HR), and relate these measurements to non-invasive tissue oxygen saturation [Formula: see text] acquired by near-infrared spectroscopy (NIRS) while conducting the same protocol. Local quantification of WSS indices by CFD revealed low time-averaged WSS on the outer curvature of the ascending aorta and the inner curvature of the descending aorta (dAo) that progressively increased with exercise, but that remained low on the anterior surface of brachiocephalic arteries. High oscillatory WSS observed on the inner curvature of the aorta persisted during exercise as well. Results suggest locally continuous exposure to potentially deleterious indices of WSS despite benefits of exercise. Linear relationships between flow distributions and tissue oxygen extraction calculated from [Formula: see text] were found between the left common carotid versus cerebral tissue [Formula: see text] and the dAo versus leg tissue [Formula: see text]. A resulting six-step procedure is presented to use NIRS data as a surrogate for exercise PC-MRI when setting boundary conditions for future CFD studies of the TA under simulated exercise conditions. Relationships and ensemble-averaged PC-MRI inflow waveforms are provided in an online repository for this purpose.

Modelling and subject-specific validation of the heart-arterial tree system

A modeling approach integrated with a novel subject-specific characterization is here proposed for the assessment of hemodynamic values of the arterial tree. A 1D model is adopted to characterize large-to-medium arteries, while the left ventricle, aortic valve and distal micro-circulation sectors are described by lumped submodels. A new velocity profile and a new formulation of the non-linear viscoelastic constitutive relation suitable for the {Q, A} modeling are also proposed. The model is firstly verified semi-quantitatively against literature data. A simple but effective procedure for obtaining subject-specific model characterization from non-invasive measurements is then designed. A detailed subject-specific validation against in vivo measurements from a population of six healthy young men is also performed. Several key quantities of heart dynamics-mean ejected flow, ejection fraction, and left-ventricular end-diastolic, end-systolic and stroke volumes-and the pressure waveforms (at the central, radial, brachial, femoral, and posterior tibial sites) are compared with measured data. Mean errors around 5 and 8%, obtained for the heart and arterial quantities, respectively, testify the effectiveness of the model and its subject-specific characterization.

A global multiscale mathematical model for the human circulation with emphasis on the venous system

We present a global, closed-loop, multiscale mathematical model for the human circulation including the arterial system, the venous system, the heart, the pulmonary circulation and the microcirculation. A distinctive feature of our model is the detailed description of the venous system, particularly for intracranial and extracranial veins. Medium to large vessels are described by one-dimensional hyperbolic systems while the rest of the components are described by zero-dimensional models represented by differential-algebraic equations. Robust, high-order accurate numerical methodology is implemented for solving the hyperbolic equations, which are adopted from a recent reformulation that includes variable material properties. Because of the large intersubject variability of the venous system, we perform a patient-specific characterization of major veins of the head and neck using MRI data. Computational results are carefully validated using published data for the arterial system and most regions of the venous system. For head and neck veins, validation is carried out through a detailed comparison of simulation results against patient-specific phase-contrast MRI flow quantification data. A merit of our model is its global, closed-loop character; the imposition of highly artificial boundary conditions is avoided. Applications in mind include a vast range of medical conditions. Of particular interest is the study of some neurodegenerative diseases, whose venous haemodynamic connection has recently been identified by medical researchers.

Perspective on CFD studies of coronary artery disease lesions and hemodynamics: a review

Coronary artery disease (CAD) is the most common cardiovascular disease. Early diagnosis of CAD's physiological significance is of utmost importance for guiding individualized risk-tailored treatment strategies. In this paper, we first review the state-of-the-art clinical diagnostic indices to quantify the severity of CAD and the associated invasive and noninvasive imaging technologies in order to quantify the anatomical parameters of diameter stenosis, area stenosis, and hemodynamic indices of coronary flow reserve and fractional flow reserve. With the development of computational technologies and CFD methods, tremendous progress has been made in applying image-based CFD simulation techniques to elucidate the effects of hemodynamics in vascular pathophysiology toward the initialization and progression of CAD. So then, we review the advancements of CFD technologies in patient-specific modeling, involving the development of geometry reconstruction, boundary conditions, and fluid-structure interaction. Next, we review the applications of CFD to stenotic sites, in order to compute their hemodynamic parameters and study the relationship between the hemodynamic conditions and the clinical indices, to thereby assess the amount of viable myocardium and candidacy for percutaneous coronary intervention. Finally, we review the strengths and limitations of current researches of applying CFD to CAD studies.

Flow-induced ATP release in patient-specific arterial geometries--a comparative study of computational models

The importance of the endothelium in the local regulation of blood flow is reflected by its influence on vascular tone by means of vasodilatory responses to many physiological stimuli. Regulatory pathways are affected by mass transport and wall shear stress (WSS), via mechanotransduction mechanisms. In the present work, we review the most relevant computational models that have been proposed to date, and introduce a general framework for modelling the responses of the endothelium to alteration in the flow, with a view to understanding the biomechanical processes involved in the pathways to endothelial dysfunction. Simulations are performed on two different patient-specific stenosed carotid artery geometries to investigate the influence of WSS and mass transport phenomena upon the agonist coupling response at the endothelium. In particular, results presented for two different models of WSS-dependent adenosine-5'-triphosphate (ATP) release reveal that existing paradigms may not account for the conditions encountered in vivo and may therefore not be adequate to model the kinetics of ATP at the endothelium.

A black-box decomposition approach for coupling heterogeneous components in hemodynamics simulations

This work presents a generic and efficient black-box approach for the strong iterative coupling of dimensionally heterogeneous flow models in computational hemodynamics. A heterogeneous model of the cardiovascular system is formed by several vascular black-box components, which are connected through coupling equations. The associated system of equations is solved using the Broyden algorithm. In addition, a multiple time-stepping strategy is introduced to meet different component requirements. The proposed algorithm is employed to split a 3D-1D-0D closed-loop model of the cardiovascular system into corresponding black-box components standing for the 3D (specific vessels), 1D (systemic arteries/peripheral vessels), and 0D (venous/cardiac/pulmonary circulation) components. Examples of application are presented showing the robustness and suitability of this novel approach.

Modeling hemodynamics in vascular networks using a geometrical multiscale approach: numerical aspects

On the one hand the heterogeneity of the circulatory system requires the use of different models in its different compartments, featuring different assumptions on the spatial degrees of freedom. On the other hand, the mutual interactions between its compartments imply that these models should preferably not be considered separately. These requirements have led to the concept of geometrical multiscale modeling, where the main idea is to couple 3D models with reduced 1D and/or 0D models. As such detailed information on the flow field in a specific region of interest can be obtained while accounting for the global circulation. However, the combination of models with different mathematical features gives rise to many difficulties such as the assignment of boundary conditions at the interface between two models and the development of robust coupling algorithms, as the subproblems are usually solved in a partitioned way. This review aims to give an overview of the most important aspects concerning 3D-1D-0D coupled models. In addition, some applications are presented in order to illustrate the potentialities of these coupled models.