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

Non-invasive assessment of stroke volume and cardiovascular parameters based on peripheral pressure waveform

Cardiovascular diseases are the leading cause of death globally, making the development of non-invasive and simple-to-use tools that bring insights into the state of the cardiovascular system of utmost importance. We investigated the possibility of using peripheral pulse wave recordings to estimate stroke volume (SV) and subject-specific parameters describing the selected properties of the cardiovascular system. Peripheral pressure waveforms were recorded in the radial artery using applanation tonometry (SphygmoCor) in 35 hemodialysis (HD) patients and 14 healthy subjects. The pressure waveforms were then used to estimate subject-specific parameters of a mathematical model of pulse wave propagation coupled with the elastance-based model of the left ventricle. Bioimpedance cardiography measurements (PhysioFlow) were performed to validate the model-estimated SV. Mean absolute percentage error between the simulated and measured pressure waveforms was 4.0% and 2.8% for the HD and control group, respectively. We obtained a moderate correlation between the model-estimated and bioimpedance-based SV (r = 0.57, p<0.05, and r = 0.58, p<0.001, for the control group and HD patients, respectively). We also observed a correlation between the estimated end-systolic elastance of the left ventricle and the peripheral systolic pressure in both HD patients (r = 0.84, p<0.001) and the control group (r = 0.70, p<0.01). These preliminary results suggest that, after additional validation and possibly further refinement to increase accuracy, the proposed methodology could support non-invasive assessment of stroke volume and selected heart function parameters and vascular properties. Importantly, the proposed method could be potentially implemented in the existing devices measuring peripheral pressure waveforms.

Linking cerebral hemodynamics and ocular microgravity-induced alterations through an in silico-in vivo head-down tilt framework

Head-down tilt (HDT) has been widely proposed as a terrestrial analog of microgravity and used also to investigate the occurrence of spaceflight-associated neuro-ocular syndrome (SANS), which is currently considered one of the major health risks for human spaceflight. We propose here an in vivo validated numerical framework to simulate the acute ocular-cerebrovascular response to 6° HDT, to explore the etiology and pathophysiology of SANS. The model links cerebral and ocular posture-induced hemodynamics, simulating the response of the main cerebrovascular mechanisms, as well as the relationship between intracranial and intraocular pressure to HDT. Our results from short-term (10 min) 6° HDT show increased hemodynamic pulsatility in the proximal-to-distal/capillary-venous cerebral direction, a marked decrease (-43%) in ocular translaminar pressure, and an increase (+31%) in ocular perfusion pressure, suggesting a plausible explanation of the underlying mechanisms at the onset of ocular globe deformation and edema formation over longer time scales.

Arterial wave dynamics preservation upon orthostatic stress: a modelling perspective

Pressure-flow travelling waves are a key topic for understanding arterial haemodynamics. However, wave transmission and reflection processes induced by body posture changes have not been thoroughly explored yet. Current in vivo research has shown that the amount of wave reflection detected at a central level (ascending aorta, aortic arch) decreases during tilting to the upright position, despite the widely proved stiffening of the cardiovascular system. It is known that the arterial system is optimized when in the supine position, i.e. propagation of direct waves is enabled and reflected waves are trapped, protecting the heart; however, it is not known whether this is preserved with postural changes. To shed light on these aspects, we propose a multi-scale modelling approach to inquire into posture-induced arterial wave dynamics elicited by simulated head-up tilting. In spite of remarkable adaptation of the human vasculature following posture changes, our analysis shows that, upon tilting from supine to upright: (i) vessel lumens at arterial bifurcations remain well matched in the forward direction, (ii) wave reflection at central level is reduced due to the backward propagation of weakened pressure waves produced by cerebral autoregulation, and (iii) backward wave trapping is preserved.

Cardiovascular Response to Posture Changes: Multiscale Modeling and in vivo Validation During Head-Up Tilt

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 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.

A computational analysis of atrial fibrillation effects on coronary perfusion across the different myocardial layers

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).

Testing a Patient-Specific In-Silico Model to Noninvasively Estimate Central Blood Pressure

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 ± 6.61 years.

RESULTS

Errors in central systolic, diastolic, mean and pulse pressures by the model are 4.26 ± 2.81, 5.86 ± 4.38, 4.98 ± 3.95 and 3.51±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.

Cardiovascular deconditioning during long-term spaceflight through multiscale modeling

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 the Earth.

Fluid-structure interaction simulations outperform computational fluid dynamics in the description of thoracic aorta haemodynamics and in the differentiation of progressive dilation in Marfan syndrome patients

Abnormal fluid dynamics at the ascending aorta may be at the origin of aortic aneurysms. This study was aimed at comparing the performance of computational fluid dynamics (CFD) and fluid-structure interaction (FSI) simulations against four-dimensional (4D) flow magnetic resonance imaging (MRI) data; and to assess the capacity of advanced fluid dynamics markers to stratify aneurysm progression risk. Eight Marfan syndrome (MFS) patients, four with stable and four with dilating aneurysms of the proximal aorta, and four healthy controls were studied. FSI and CFD simulations were performed with MRI-derived geometry, inlet velocity field and Young's modulus. Flow displacement, jet angle and maximum velocity evaluated from FSI and CFD simulations were compared to 4D flow MRI data. A dimensionless parameter, the shear stress ratio (SSR), was evaluated from FSI and CFD simulations and assessed as potential correlate of aneurysm progression. FSI simulations successfully matched MRI data regarding descending to ascending aorta flow rates (R 2 = 0.92) and pulse wave velocity (R 2 = 0.99). Compared to CFD, FSI simulations showed significantly lower percentage errors in ascending and descending aorta in flow displacement (-46% ascending, -41% descending), jet angle (-28% ascending, -50% descending) and maximum velocity (-37% ascending, -34% descending) with respect to 4D flow MRI. FSI- but not CFD-derived SSR differentiated between stable and dilating MFS patients. Fluid dynamic simulations of the thoracic aorta require fluid-solid interaction to properly reproduce complex haemodynamics. FSI- but not CFD-derived SSR could help stratifying MFS patients.

Numerical Study of Atrial Fibrillation Effects on Flow Distribution in Aortic Circulation

Atrial fibrillation (AF) is the most common type of arrhythmia, which undermines cardiac function. Atrial fibrillation is a multi-facet malady and it may occur as a result of other diseases or it may trigger other problems. One of the main complications of AF is stroke due to the possibility of clot formation inside the atrium. However, the possibility of stroke occurrence due to the AF and the location from which an embolus dispatches are subject of debate. Another hypothesis about the embolus formation during AF is thrombus formation in aorta and carotid arteries, embolus detachment and its movement. To investigate the possibility of the latter postulation, the current work suggests a parametric study to quantify the sensitivity of aortic flow to four common AF traits including lack of atrial kick, atrial remodelling, left ventricle systolic dysfunction, and high frequency fibrillation. The simulation was carried out by coupling several in-house codes and ANSYS-CFX module. The results reveal that AF traits lower flow rate at left ventricular outflow tract, which in general lowers blood perfusion to systemic, cerebral and coronary circulations. Consequently, it leads to endothelial cell activation potential (ECAP) increase and variation of flow structure that both suggest predisposed areas to atherogenesis and thrombus formation in different regions in ascending aorta, aortic arch and descending thoracic aorta.

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 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.

Subject-specific pulse wave propagation modeling: Towards enhancement of cardiovascular assessment methods

Cardiovascular diseases are the leading cause of death worldwide. Pulse wave analysis (PWA) technique, which reconstructs and analyses aortic pressure waveform based on non-invasive peripheral pressure recording, became an important bioassay for cardiovascular assessment in a general population. The aim of our study was to establish a pulse wave propagation modeling framework capable of matching clinical PWA data from healthy individuals on a per-subject basis. Radial pressure profiles from 20 healthy individuals (10 males, 10 females), with mean age of 42 ± 10 years, were recorded using applanation tonometry (SphygmoCor, AtCor Medical, Australia) and used to estimate subject-specific parameters of mathematical model of blood flow in the system of fifty-five arteries. The model was able to describe recorded pressure profiles with high accuracy (mean absolute percentage error of 1.87 ± 0.75%) when estimating only 6 parameters for each subject. Cardiac output (CO) and stroke volume (SV) have been correctly identified by the model as lower in females than males (CO of 3.57 ± 0.54 vs. 4.18 ± 0.72 L/min with p-value < 0.05; SV of 49.5 ± 10.1 vs. 64.2 ± 16.8 ml with p-value = 0.076). Moreover, the model identified age related changes in the heart function, i.e. that the cardiac output at rest is maintained with age (r = 0.23; p-value = 0.32) despite the decreasing heart rate (r = −0.49; p-value < 0.05), because of the increase in stroke volume (r = 0.46; p-value < 0.05). Central PWA indices derived from recorded waveforms strongly correlated with those obtained using corresponding model-predicted radial waves (r > 0.99 and r > 0.97 for systolic (SP) and diastolic (DP) pressures, respectively; r > 0.77 for augmentation index (AI); all p—values < 0.01). Model-predicted central waveforms, however, had higher SP than those reconstructed by PWA using recorded radial waves (5.6 ± 3.3 mmHg on average). From all estimated subject-specific parameters only the time to the peak of heart ejection profile correlated with clinically measured AI. Our study suggests that the proposed model may serve as a tool to computationally investigate virtual patient scenarios mimicking different cardiovascular abnormalities. Such a framework can augment our understanding and help with the interpretation of PWA results.

Arterial pulse attenuation prediction using the decaying rate of a pressure wave in a viscoelastic material model

The present study examines the possibility of attenuating blood pulses by means of introducing prosthetic viscoelastic materials able to absorb energy and damp such pulses. Vascular prostheses made of polymeric materials modify the mechanical properties of blood vessels. The effect of these materials on the blood pulse propagation remains to be fully understood. Several materials for medical applications, such as medical polydimethylsiloxane or polytetrafluoroethylene, show viscoelastic behavior, modifying the original vessel stiffness and affecting the propagation of blood pulses. This study focuses on the propagation of pressure waves along a pipe with viscoelastic materials using the Maxwell and the Zener models. An expression of exponential decay has been obtained for the Maxwell material model and also for low viscous coefficient values in the Zener model. For relatively high values of the viscous term in the Zener model, the steepest part of the pulse can be damped quickly, leaving a smooth, slowly decaying wave. These mathematical models are critical to tailor those materials used in cardiovascular implants to the mechanical environment they are confronted with to repair or improve blood vessel function.

Non-invasive aortic systolic pressure and pulse wave velocity estimation in a primary care setting: An in silico study

Everyday clinical cardiovascular evaluation is still largely based on brachial systolic and diastolic pressures. However, several clinical studies have demonstrated the higher diagnostic capacities of the aortic pressure, as well as the need to assess the aortic mechanical properties (e.g., by measuring the aortic pulse wave velocity). In order to fill this gap, we propose to exploit a set of easy-to-obtain physical characteristics to estimate the aortic pressure and pulse wave velocity. To this aim, a large population of virtual subjects is created by a validated mathematical model of the cardiovascular system. Quadratic regressive models are then fitted and statistically selected in order to obtain reliable estimations of the aortic pressure and pulse wave velocity starting from the knowledge of the subject age, height, weight, brachial pressure, photoplethysmographic measures and either electrocardiogram or phonocardiogram. The results are very encouraging and foster clinical studies aiming to apply a similar technique to a real population.

In silico analysis of the anti-hypertensive drugs impact on myocardial oxygen balance

Hypertension is a very common pathology, and its clinical treatment largely relies on different drugs. Some of these drugs exhibit specific protective functions in addition to those resulting from blood pressure reduction. In this work, we study the impact of commonly used anti-hypertensive drugs (RAAS, [Formula: see text] and calcium channel blockers) on myocardial oxygen supply-consumption balance, which plays a crucial role in type 2 myocardial infarction. To this aim, 42 wash-out hypertensive patients were selected, a number of measured data were used to set a validated multi-scale cardiovascular model to subject-specific conditions, and the administration of different drugs was suitably simulated. Our results ascribe the well-known major cardioprotective efficiency of [Formula: see text] blockers compared to other drugs to a positive change of myocardial oxygen balance due to the concomitant: (1) reduction in aortic systolic, diastolic and pulse pressures, (2) decrease in left ventricular work, diastolic cavity pressure and oxygen consumption, (3) increase in coronary flow and (4) ejection efficiency improvement. RAAS blockers share several positive outcomes with [Formula: see text] blockers, although to a reduced extent. In contrast, calcium channel blockers seem to induce some potentially negative effects on the myocardial oxygen balance.

A LUMPED PARAMETER MODEL OF CARDIOVASCULAR SYSTEM WITH PULSATING HEART FOR DIAGNOSTIC STUDIES

Mathematical modeling of cardiovascular system provides an ability to study hemodynamics and to predict the results of treatment based on individual anatomical and physiological data of patients. However, the presently developed models of cardiovascular system have a limitation on use in clinical practice due to their physical and computational complexities. The aim of this study is to derive a lumped parameter model of cardiovascular system with pulsating heart in which all parameters have a physically based quantitative value and can be identified using clinical methods. For development of a cardiovascular system model the chamber analog was used which describes whole cardiovascular system as a set of elastic chambers. The proposed model consists of systemic and pulmonary circulation, four-chamber heart and four valves. The description of heart is based on a four-element representation of a cardiac muscle. The reverse blood flow via valves is considered. The accuracy of the derived model was evaluated by comparing the data of numerical simulation with experimental data. The limitations of the model were discussed as well as possible applications of the model were suggested. The proposed lumped parameter model can be used to support clinicians in their decisions in treating cardiovascular disorders.

Central Pressure Appraisal: Clinical Validation of a Subject-Specific Mathematical Model

Introduction

Current evidence suggests that aortic blood pressure has a superior prognostic value with respect to brachial pressure for cardiovascular events, but direct measurement is not feasible in daily clinical practice.

Aim

The aim of the present study is the clinical validation of a multiscale mathematical model for non-invasive appraisal of central blood pressure from subject-specific characteristics.

Methods

A total of 51 young male were selected for the present study. Aortic systolic and diastolic pressure were estimated with a mathematical model and were compared to the most-used non-invasive validated technique (SphygmoCor device, AtCor Medical, Australia). SphygmoCor was calibrated through diastolic and systolic brachial pressure obtained with a sphygmomanometer, while model inputs consist of brachial pressure, height, weight, age, left-ventricular end-systolic and end-diastolic volumes, and data from a pulse wave velocity study.

Results

Model-estimated systolic and diastolic central blood pressures resulted to be significantly related to SphygmoCor-assessed central systolic (r = 0.65 p <0.0001) and diastolic (r = 0.84 p<0.0001) blood pressures. The model showed a significant overestimation of systolic pressure (+7.8 (-2.2;14) mmHg, p = 0.0003) and a significant underestimation of diastolic values (-3.2(-7.5;1.6), p = 0.004), which imply a significant overestimation of central pulse pressure. Interestingly, model prediction errors mirror the mean errors reported in large meta-analysis characterizing the use of the SphygmoCor when non-invasive calibration is performed.

Conclusion

In conclusion, multi-scale mathematical model predictions result to be significantly related to SphygmoCor ones. Model-predicted systolic and diastolic aortic pressure resulted in difference of less than 10 mmHg in the 51% and 84% of the subjects, respectively, when compared with SphygmoCor-obtained pressures.

Compensatory Effect between Aortic Stiffening and Remodelling during Ageing

The arterial tree exhibits a complex spatio-temporal wave pattern, whose healthy behaviour depends on a subtle balance between mechanical and geometrical properties. Several clinical studies demonstrated that such a balance progressively breaks down during ageing, when the aorta stiffens and remodels by increasing its diameter. These two degenerative processes however, have different impacts on the arterial wave pattern. They both tend to compensate for each other, thus reducing the detrimental effect they would have had if they had arisen individually. This remarkable compensatory mechanism is investigated by a validated multi-scale model, with the aim to elucidate how aortic stiffening and remodelling quantitatively impact the complex interplay between forward and reflected backward waves in the arterial network. We focus on the aorta and on the pressure at the ventricular-aortic interface, which epidemiological studies demonstrate to play a key role in cardiovascular diseases.