Biomechanical characterization of ventricular–arterial coupling during aging: A multi-scale model study

In silico data-based comparison of the accuracy and error source of various methods for noninvasively estimating central aortic blood pressure

BACKGROUND AND OBJECTIVES

The higher clinical significance of central aortic blood pressure (CABP) compared to peripheral blood pressures has been extensively demonstrated. Accordingly, many methods for noninvasively estimating CABP have been proposed. However, there still lacks a systematic comparison of existing methods, especially in terms of how they differ in the ability to tolerate individual differences or measurement errors. The present study was designed to address this gap.

METHODS

A large-scale 'virtual subject' dataset (n = 600) was created using a computational model of the cardiovascular system, and applied to examine several classical CABP estimation methods, including the direct method, generalized transfer function (GTF) method, n-point moving average (NPMA) method, second systolic pressure of periphery (SBP2) method, physical model-based wave analysis (MBWA) method, and suprasystolic cuff-based waveform reconstruction (SCWR) method. The errors of CABP estimation were analyzed and compared among methods with respect to the magnitude/distribution, correlations with physiological/hemodynamic factors, and sensitivities to noninvasive measurement errors.

RESULTS

The errors of CABP estimation exhibited evident inter-method differences in terms of the mean and standard deviation (SD). Relatively, the estimation errors of the methods adopting pre-trained algorithms (i.e., the GTF and SCWR methods) were overall smaller and less sensitive to variations in physiological/hemodynamic conditions and random errors in noninvasive measurement of brachial arterial blood pressure (used for calibrating peripheral pulse wave). The performances of all the methods worsened following the introduction of random errors to peripheral pulse wave (used for deriving CABP), as characterized by the enlarged SD and/or increased mean of the estimation errors. Notably, the GTF and SCWR methods did not exhibit a better capability of tolerating pulse wave errors in comparison with other methods.

CONCLUSIONS

Classical noninvasive methods for estimating CABP were found to differ considerably in both the accuracy and error source, which provided theoretical evidence for understanding the specific advantages and disadvantages of each method. Knowledge about the method-specific error source and sensitivities of errors to different physiological/hemodynamic factors may contribute as theoretical references for interpreting clinical observations and exploring factors underlying large estimation errors, or provide guidance for optimizing existing methods or developing new methods.

Numerical study on the cerebral blood flow regulation in the circle of Willis with the vascular absence and internal carotid artery stenosis

Objectives

This study explores how vascular stenosis and absence affect the regulation of cerebral blood flow in the Circle of Willis (CoW) and the hemodynamic changes downstream of the stenosis.

Materials and Methods

Forty idealized CoW models were simulated to analyze the impact of vascular absence and internal carotid artery (ICA) stenosis on hemodynamics. Inlet conditions were set using a physiological pressure waveform, and outflow boundaries were modeled using three-element Windkessel models.

Results

The absence of vessels such as RP1, LP1, RA1, or LA1 had a comparable effect on total blood flow to a 40% stenosis of the left internal carotid artery (LICA) across the entire CoW. Specifically, when LP1 and RA1 were absent with a 50% LICA stenosis, the total blood flow closely resembled that of a complete CoW with 75% LICA stenosis. In cases of proximal ICA stenosis, downstream regions showed elevated oscillatory shear index (OSI >0.2) and reduced time-averaged wall shear stress (TAWSS <1 Pa). With increasing stenosis severity, areas of high OSI shifted, and regions of low TAWSS expanded notably. At 75% stenosis, the area with TAWSS <1 Pa downstream significantly increased. Until complete occlusion, the area of low TAWSS and high OSI were maximized.

Conclusion

This study underscores how anatomical variations in the CoW, combined with ICA stenosis, impact both total cerebral blood flow and its distribution among different outlets. Moreover, it highlights the potential for increased atherosclerosis development in affected areas. Particularly notable is the finding the absence of LP1 and RA1 vessels alongside 50% LICA stenosis results in blood flow patterns similar to those seen with 75% LICA stenosis in a complete CoW, emphasizing clinical implications for the patient. Hemodynamic changes, including TAWSS and OSI, are most pronounced downstream of the stenosis especially when the stenosis rate exceeds 75%.

Impact of Pressure Guidewire on Model-Based FFR Prediction

INTRODUCTION

Fractional Flow Reserve (FFR) is used to characterize the functional significance of coronary artery stenoses. FFR is assessed under hyperemic conditions by invasive measurements of trans-stenotic pressure thanks to the insertion of a pressure guidewire across the coronary stenosis during catheterization. In order to overcome the potential risk related to the invasive procedure and to reduce the associated high costs, three-dimensional blood flow simulations that incorporate clinical imaging and patient-specific characteristics have been proposed.

PURPOSE

Most CCTA-derived FFR models neglect the potential influence of the guidewire on computed flow and pressure. Here we aim to quantify the impact of taking into account the presence of the guidewire in model-based FFR prediction.

METHODS

We adopt a CCTA-derived FFR model and perform simulations with and without the guidewire for 18 patients with suspected stable CAD.

RESULTS

Presented results show that the presence of the guidewire leads to a tendency to predict a lower FFR value. The FFR reduction is prominent in cases of severe stenoses, while the influence of the guidewire is less pronounced in cases of moderate stenoses.

CONCLUSION

From a clinical decision-making point of view, including of the pressure guidewire is potentially relevant only for intermediate stenosis cases.

Optimization and validation of a suprasystolic brachial cuff-based method for noninvasively estimating central aortic blood pressure

Clinical studies have extensively demonstrated that central aortic blood pressure (CABP) has greater clinical significance in comparison with peripheral blood pressure. Despite the existence of various techniques for noninvasively measuring CABP, the clinical applications of most techniques are hampered by the unsatisfactory accuracy or large variability in measurement errors. In this study, we proposed a new method for noninvasively estimating CABP with improved accuracy and reduced uncertain errors. The main idea was to optimize the estimation of the pulse wave transit time from the aorta to the occluded lumen of the brachial artery under a suprasystolic cuff by identifying and utilizing the characteristic information of the cuff oscillation wave, thereby improving the accuracy and stability of the CABP estimation algorithms under various physiological conditions. The method was firstly developed and verified based on large-scale virtual subject data (n = 800) generated by a computational model of the cardiovascular system coupled to a brachial cuff, and then validated with small-scale in vivo data (n = 34). The estimation errors for the aortic systolic pressure were -0.05 ± 0.63 mmHg in the test group of the virtual subjects and -1.09 ± 3.70 mmHg in the test group of the patients, both demonstrating a good performance. In particular, the estimation errors were found to be insensitive to variations in hemodynamic conditions and cardiovascular properties, manifesting the high robustness of the method. The method may have promising clinical applicability, although further validation studies with larger-scale clinical data remain necessary.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Multi-Dimensional Modeling of Cerebral Hemodynamics: A Systematic Review

The Circle of Willis (CoW) describes the arterial system in the human brain enabling the neurovascular blood supply. Neurovascular diseases like intracranial aneurysms (IAs) can occur within the CoW and carry the risk of rupture, which can lead to subarachnoid hemorrhage. The assessment of hemodynamic information in these pathologies is crucial for their understanding regarding detection, diagnosis and treatment. Multi-dimensional in silico approaches exist to evaluate these hemodynamics based on patient-specific input data. The approaches comprise low-scale (zero-dimensional, one-dimensional) and high-scale (three-dimensional) models as well as multi-scale coupled models. The input data can be derived from medical imaging, numerical models, literature-based assumptions or from measurements within healthy subjects. Thus, the most realistic description of neurovascular hemodynamics is still controversial. Within this systematic review, first, the models of the three scales (0D, 1D, 3D) and second, the multi-scale models, which are coupled versions of the three scales, were discussed. Current best practices in describing neurovascular hemodynamics most realistically and their clinical applicablility were elucidated. The performance of 3D simulation entails high computational expenses, which could be reduced by analyzing solely the region of interest in detail. Medical imaging to establish patient-specific boundary conditions is usually rare, and thus, lower dimensional models provide a realistic mimicking of the surrounding hemodynamics. Multi-scale coupling, however, is computationally expensive as well, especially when taking all dimensions into account. In conclusion, the 0D-1D-3D multi-scale approach provides the most realistic outcome; nevertheless, it is least applicable. A 1D-3D multi-scale model can be considered regarding a beneficial trade-off between realistic results and applicable performance.

Validation of a Multiscale Computational Model Using a Mock Circulatory Loop to Simulate Cardiogenic Shock

The objectives of this study are to characterize the hemodynamics of cardiogenic shock (CS) through a computational model validated using a mock circulatory loop (MCL) and to perform sensitivity analysis and uncertainty propagation studies after the American Society of Mechanical Engineers (ASME) Validation and Verification (V&V) guidelines. The uncertainties in cardiac cycle time ( ), total resistance ( ), and total volume ( ) were quantified in the MCL and propagated in the computational model. Both models were used to quantify the pressure in the left atrium, aorta (Ao), and left ventricle (LV), along with the flow through the aortic valve, reaching a good agreement. The results suggest that 1) is the main source of uncertainty in the variables under study, 2) showed its greatest impact on the uncertainty of Ao hemodynamics, and 3) mostly affected the uncertainty of LV pressure and Ao flow at the late-systolic phase. Comparison of uncertainty levels in the computational and experimental results was used to infer the presence of additional contributing factors that were not captured and propagated during a first analysis. Future work will expand upon this study to analyze the impact of mechanical circulatory support devices, such as ventricular assist devices, under CS conditions.

Exergy destruction in atrial fibrillation and a new 'Exergy Age Index'

The concept of exergy in living organisms has been widely used to explore correlations between exergy and different physiological conditions. Atrial fibrillation (AF) is an abnormal physiological condition that takes place inside the heart and is recognised as a common supraventricular arrhythmia. AF can significantly undermine heart function and subsequently circulatory system. Thus, exergy analysis of cardiac flow during AF is a procedure to quantify the long-term impact of persistent AF. The present study adopts the lumped modelling approach for considering cardiovascular circulation and thermoregulation of the body to evaluate the exergy consumption and destruction of the heart in AF. In order to assess the impact of AF, four common AF-associated characteristics including lack of atrial kick, left atrial remodelling, left ventricular systolic dysfunction, and high-frequency fibrillation are examined. The results show that among AF deficiencies, high-frequency fibrillation is the main cause of exergy destruction of the heart during AF. Moreover, a novel 'exergy age index' is proposed which has shown that high fibrillatory conditions in AF can significantly accelerate the heart ageing process, which in turn substantiates AF's adverse impact on the heart.

Numerical coupling of 0D and 1D models in networks of vessels including transonic flow conditions. Application to short-term transient and stationary hemodynamic simulation of postural changes

When modeling complex fluid networks using one-dimensional (1D) approaches, boundary conditions can be imposed using zero-dimensional (0D) models. An application case is the modeling of the entire human circulation using closed-loop models. These models can be considered as a tool to investigate short-term transient and stationary hemodynamic responses to postural changes. The first shortcoming of existing 1D modeling methods in simulating these sudden maneuvers is their inability to deal with rapid variations in flow conditions, as they are limited to the subsonic case. On the other hand, numerical modeling of 0D models representing microvascular beds, venous valves or heart chambers is also currently modeled assuming subsonic flow conditions in 1D connecting vessels, failing when transonic and supersonic flow conditions appear. Therefore, if numerical simulation of sudden maneuvers is a goal in closed-loop models, it is necessary to reformulate the current methodologies used when coupling 0D and 1D models, allowing the correct handling of flow evolution for both subsonic and transonic conditions. This work focuses on the extension of the general methodology for the Junction Riemann Problem (JRP) when coupling 0D and 1D models. As an example of application, the short-term transient response to head-up tilt (HUT) from supine to upright position of a closed-loop model is shown, demonstrating the potential, capability and necessity of the presented numerical models when dealing with sudden maneuvers.

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.

Threshold values of brachial cuff-measured arterial stiffness indices determined by comparisons with the brachial-ankle pulse wave velocity: a cross-sectional study in the Chinese population

Background

Arterial Velocity-pulse Index (AVI) and Arterial Pressure-volume Index (API), measured by a brachial cuff, have been demonstrated to be indicative of arterial stiffness and correlated with the risk of cardiovascular events. However, the threshold values of AVI and API for screening increased arterial stiffness in the general population are yet to be established.

Methods

The study involved 860 subjects who underwent general physical examinations (M/F = 422/438, age 53.4 ± 12.7 years) and were considered to represent the general population in China. In addition to the measurements of AVI, API and brachial-ankle pulse wave velocity (baPWV), demographic information, arterial blood pressures, and data from blood and urine tests were collected. The threshold values of AVI and API were determined by receiver operating characteristic (ROC) analyses and covariate-adjusted ROC (AROC) analyses against baPWV, whose threshold for diagnosing high arterial stiffness was set at 18 m/s. Additional statistical analyses were performed to examine the correlations among AVI, API and baPWV and their correlations with other bio-indices.

Results

The area under the curve (AUC) values in ROC analysis for the diagnosis with AVI/API were 0.745/0.819, 0.788/0.837, and 0.772/0.825 (95% CI) in males, females, and all subjects, respectively. Setting the threshold values of AVI and API to 21 and 27 resulted in optimal diagnosis performance in the total cohort, whereas the threshold values should be increased to 24 and 29, respectively, in order to improve the accuracy of diagnosis in the female group. The AROC analyses revealed that the threshold values of AVI and API increased markedly with age and pulse pressure (PP), respectively.

Conclusions

With appropriate threshold values, AVI and API can be used to perform preliminary screening for individuals with increased arterial stiffness in the general population. On the other hand, the results of the AROC analyses imply that using threshold values adjusted for confounding factors may facilitate the refinement of diagnosis. Given the fact that the study is a cross-sectional one carried out in a single center, future multi-center or follow-up studies are required to further confirm the findings or examine the value of the threshold values for predicting cardiovascular events.

The Influence of Aortic Valve Disease on Coronary Hemodynamics: A Computational Model-Based Study

Aortic valve disease (AVD) often coexists with coronary artery disease (CAD), but whether and how the two diseases are correlated remains poorly understood. In this study, a zero-three dimensional (0-3D) multi-scale modeling method was developed to integrate coronary artery hemodynamics, aortic valve dynamics, coronary flow autoregulation mechanism, and systemic hemodynamics into a unique model system, thereby yielding a mathematical tool for quantifying the influences of aortic valve stenosis (AS) and aortic valve regurgitation (AR) on hemodynamics in large coronary arteries. The model was applied to simulate blood flows in six patient-specific left anterior descending coronary arteries (LADs) under various aortic valve conditions (i.e., control (free of AVD), AS, and AR). Obtained results showed that the space-averaged oscillatory shear index (SA-OSI) was significantly higher under the AS condition but lower under the AR condition in comparison with the control condition. Relatively, the overall magnitude of wall shear stress was less affected by AVD. Further data analysis revealed that AS induced the increase in OSI in LADs mainly through its role in augmenting the low-frequency components of coronary flow waveform. These findings imply that AS might increase the risk or progression of CAD by deteriorating the hemodynamic environment in coronary arteries.

Treatment strategy of different enhanced external counterpulsation frequencies for coronary heart disease and cerebral ischemic stroke: A hemodynamic numerical simulation study

BACKGROUND AND OBJECTIVES

Currently, enhanced external counterpulsation (EECP) devices mainly produce one counterpulsation per cardiac cycle. However, the effect of other frequencies of EECP on the hemodynamics of coronary and cerebral arteries is still unclear. It should be investigated whether one counterpulsation per cardiac cycle leads to the optimal therapeutic effect in patients with different clinical indications. Therefore, we measured the effects of different frequencies of EECP on the hemodynamics of coronary and cerebral arteries to determine the optimal counterpulsation frequency for the treatment of coronary heart disease and cerebral ischemic stroke.

METHODS

We established 0D/3D geometric multi-scale hemodynamics model of coronary and cerebral arteries in two healthy individuals, and performed clinical trials of EECP to verify the accuracy of the multi-scale hemodynamics model. The pressure amplitude (35 kPa) and pressurization duration (0.6 s) were fixed. The global and local hemodynamics of coronary and cerebral arteries were studied by changing counterpulsation frequency. Three frequency modes, including one counterpulsation in one, two and three cardiac cycles, were applied. Global hemodynamic indicators included diastolic / systolic blood pressure (D/S), mean arterial pressure (MAP), coronary artery flow (CAF), and cerebral blood flow (CBF), whereas local hemodynamic effects included area-time-averaged wall shear stress (ATAWSS) and oscillatory shear index (OSI). The optimal counterpulsation frequency was verified by analyzing the hemodynamic effects of different frequency modes of counterpulsation cycles and full cycles.

RESULTS

In the full cycle, CAF, CBF and ATAWSS of coronary and cerebral arteries were the highest when one counterpulsation per cardiac cycle was applied. However, in the counterpulsation cycle, the global and local hemodynamic indicators of coronary and cerebral artery reached the highest when one counterpulsation in one cardiac cycle or two cardiac cycles was applied.

CONCLUSIONS

For clinical application, the results of global hemodynamic indicators in the full cycle have more clinical practical significance. Combined with the comprehensive analysis of local hemodynamic indicators, it can be concluded that for coronary heart disease and cerebral ischemic stroke, applying one counterpulsation per cardiac cycle may provide the optimal benefit.

Remodeling of the cardiovascular hemodynamic environment by lower limb heat exposure: A computational fluid dynamic study

BACKGROUND

Lower limb heat exposure (LLHE) is a promising strategy for the daily management of cardiovascular health because of its non-pharmaceutical advantages. To support the application of this strategy in cardiovascular protection, we examined its impact on the global hemodynamic environment.

METHODS

Skin blood flow (SBF) of eight locations on the lower limbs was measured before and after LLHE (40 °C and 44 °C) in ten healthy subjects by using a laser Doppler flowmeter. A closed-loop model of circulation uses changes in SBF to quantify the influence of LLHE on the blood flow of the arterial trunk (from ascending aorta to the femoral artery) and visceral branches (coronary, celiac, renal, and mesenteric arteries).

RESULTS

The SBF in all locations tested on the lower limbs increased significantly (p<0.001) with LLHE and a 3.39-fold and 7.40-fold increase in mean SBF were observed under 40 °C and 44 °C conditions, respectively. In the model, the peak (3.9-25.1%), end-diastolic (13.7-107.3%), and mean blood flow (8.5-86.5%) in the arterial trunk increased with the increase in temperature, but the retrograde flow in the thoracic aorta and abdominal aorta Ⅰ increased at least twice in the diastolic period. Furthermore, LLHE also increased the blood flow of the visceral branches (2.5-20.7%).

CONCLUSION

These findings suggest that LLHE is expected to be a daily strategy for enhancing the functions of both the arterial trunk and visceral arteries, but the increased blood flow reversal in the thoracic and abdominal aortas warrants further investigation.

A numerical study of the hemodynamic behavior and gas transport in cardiovascular systems with severe cardiac or cardiopulmonary failure supported by venoarterial extracorporeal membrane oxygenation

Venoarterial extracorporeal membrane oxygenation (VA-ECMO) has been extensively demonstrated as an effective means of bridge-to-destination in the treatment of patients with severe ventricular failure or cardiopulmonary failure. However, appropriate selection of candidates and management of patients during Extracorporeal membrane oxygenation (ECMO) support remain challenging in clinical practice, due partly to insufficient understanding of the complex influences of extracorporeal membrane oxygenation support on the native cardiovascular system. In addition, questions remain as to how central and peripheral venoarterial extracorporeal membrane oxygenation modalities differ with respect to their hemodynamic impact and effectiveness of compensatory oxygen supply to end-organs. In this work, we developed a computational model to quantitatively address the hemodynamic interaction between the extracorporeal membrane oxygenation and cardiovascular systems and associated gas transport. Model-based numerical simulations were performed for cardiovascular systems with severe cardiac or cardiopulmonary failure and supported by central or peripheral venoarterial extracorporeal membrane oxygenation. Obtained results revealed that: 1) central and peripheral venoarterial extracorporeal membrane oxygenation modalities had a comparable capacity for elevating arterial blood pressure and delivering oxygenated blood to important organs/tissues, but induced differential changes of blood flow waveforms in some arteries; 2) increasing the rotation speed of extracorporeal membrane oxygenation pump (ω) could effectively improve arterial blood oxygenation, with the efficiency being especially high when ω was low and cardiopulmonary failure was severe; 3) blood oxygen indices (i.e., oxygen saturation and partial pressure) monitored at the right radial artery could be taken as surrogates for diagnosing potential hypoxemia in other arteries irrespective of the modality of extracorporeal membrane oxygenation; and 4) Left ventricular (LV) overloading could occur when ω was high, but the threshold of ω for inducing clinically significant left ventricular overloading depended strongly on the residual cardiac function. In summary, the study demonstrated the differential hemodynamic influences while comparable oxygen delivery performance of the central and peripheral venoarterial extracorporeal membrane oxygenation modalities in the management of patients with severe cardiac or cardiopulmonary failure and elucidated how the status of arterial blood oxygenation and severity of left ventricular overloading change in response to variations in ω. These model-based findings may serve as theoretical references for guiding the application of venoarterial extracorporeal membrane oxygenation or interpreting in vivo measurements in clinical practice.

A multiscale computational framework to evaluate flow alterations during mechanical thrombectomy for treatment of ischaemic stroke

The treatment of ischaemic stroke increasingly relies upon endovascular procedures known as mechanical thrombectomy (MT), which consists in capturing and removing the clot with a catheter-guided stent while at the same time applying external aspiration with the aim of reducing haemodynamic loads during retrieval. However, uniform consensus on procedural parameters such as the use of balloon guide catheters (BGC) to provide proximal flow control, or the position of the aspiration catheter is still lacking. Ultimately the decision is left to the clinician performing the operation, and it is difficult to predict how these treatment options might influence clinical outcome. In this study we present a multiscale computational framework to simulate MT procedures. The developed framework can provide quantitative assessment of clinically relevant quantities such as flow in the retrieval path and can be used to find the optimal procedural parameters that are most likely to result in a favorable clinical outcome. The results show the advantage of using BGC during MT and indicate small differences between positioning the aspiration catheter in proximal or distal locations. The framework has significant potential for future expansions and applications to other surgical treatments.

Relationship of Arterial Stiffness and Central Hemodynamics With Cardiovascular Risk In Hypertension

BACKGROUND

Hypertension is becoming a serious public health problem and noninvasive estimation of central hemodynamics and artery stiffness have been identified as important predictors of cardiovascular disease.

METHODS

The study included 4,311 participants, both sex and aged between 20 and 79 years. Arterial velocity pulse index, arterial pressure-volume index (AVI, API, and the index of artery stiffness), central systolic blood pressure, central artery pulse pressure (CSBP, CAPP, and estimated via oscillometric blood pressure monitor), and 10-year risk score of cardiovascular disease in China (China-PAR) and Framingham cardiovascular risk score (FCVRS) were assessed at baseline. Regression model was performed to identify factors associated with high cardiovascular disease risk stratification. The relationships between CSBP, CAPP and China-PAR, and FCVRS were analyzed by restrictive cubic spline functions.

RESULTS

The uncontrolled hypertension group showed the highest values of AVI, API, CSBP, and CAPP. In the regression analysis, CAPP and hypertension subtypes were identified as significant predictors of high cardiovascular risk stratification, and CAPP was strongly correlated with API in this cohort. Finally, CSBP and CAPP showed significant J-shaped relationships with China-PAR and FCVRS.

CONCLUSIONS

Subjects with uncontrolled hypertension present with elevated values of CAPP, CSBP, API, AVI, China-PAR, and FCVRS scores. CAPP was independently associated with high cardiovascular risk stratification, and there was a significant J-shaped relationship with China-PAR and FCVRS that may identify people with higher cardiovascular risk.

The effect of cardiac properties on arterial pulse waves: An in-silico study

This study investigated the effects of cardiac properties variability on arterial pulse wave morphology using blood flow modelling and pulse wave analysis. A lumped-parameter model of the left part of the heart was coupled to a one-dimensional model of the arterial network and validated using reference pulse waveforms in turn verified by comparison with in vivo measurements. A sensitivity analysis was performed to assess the effects of variations in cardiac parameters on central and peripheral pulse waveforms. Results showed that left ventricle contractility, stroke volume, cardiac cycle duration, and heart valves impairment are determinants of central waveforms morphology, pulse pressure and its amplification. Contractility of the left atrium has negligible effects on arterial pulse waves. Results also suggested that it might be possible to infer left ventricular dysfunction by analysing the timing of the dicrotic notch and cardiac function by analysing PPG signals. This study has identified cardiac properties that may be extracted from in vivo central and peripheral pulse waves to assess cardiac function.

Multiple blood flow surges during intermittent pneumatic compression: The origins and their implications

Intermittent pneumatic compression (IPC) therapy has been used to enhance peripheral blood flow for prevention and rehabilitation of ischemic-related vascular diseases. A novel phenomenon has been reported that multiple blood flow surges appeared in the skin blood flow signal during each compression, but its mechanism has not been fully revealed. This study aimed to gain insights into the origins of these blood flow surges through experiment and biomechanical modeling methods. Foot skin blood flow (SBF) signals of 13 healthy adults (23.8 ± 0.5 yr old, 7 males) and air cuff pressure signals were recorded during IPC. Lumped parameter modeling and wavelet analysis were adopted to investigate the multiple blood flow surges (named as Peak₁, Peak₂ and Peak₃). The results of the simulated Peak₁ and Peak₂ were in good agreements with the experiment results, suggesting that IPC could enhance foot SBF not only by deflation, but also by inflation. Statistical analysis demonstrated that high frequency compression with more frequent occurrence of Peak₁ and Peak₂ lead to significantly higher (Friedman test, p < 0.001) time-averaged SBF enhancement than the traditional mode. In addition, wavelet analysis showed that the major frequency component of the Peak₃ (0.059 Hz) was within the range of the vascular myogenic activity, suggesting a vascular regulation process triggered by intravascular pressure changes. Our study provide new insights into the mechanism of how IPC enhance foot SBF.

Uncertainty quantification in cerebral circulation simulations focusing on the collateral flow: Surrogate model approach with machine learning

Collateral circulation in the circle of Willis (CoW), closely associated with disease mechanisms and treatment outcomes, can be effectively investigated using one-dimensional–zero-dimensional hemodynamic simulations. As the entire cardiovascular system is considered in the simulation, it captures the systemic effects of local arterial changes, thus reproducing collateral circulation that reflects biological phenomena. The simulation facilitates rapid assessment of clinically relevant hemodynamic quantities under patient-specific conditions by incorporating clinical data. During patient-specific simulations, the impact of clinical data uncertainty on the simulated quantities should be quantified to obtain reliable results. However, as uncertainty quantification (UQ) is time-consuming and computationally expensive, its implementation in time-sensitive clinical applications is considered impractical. Therefore, we constructed a surrogate model based on machine learning using simulation data. The model accurately predicts the flow rate and pressure in the CoW in a few milliseconds. This reduced computation time enables the UQ execution with 100 000 predictions in a few minutes on a single CPU core and in less than a minute on a GPU. We performed UQ to predict the risk of cerebral hyperperfusion (CH), a life-threatening condition that can occur after carotid artery stenosis surgery if collateral circulation fails to function appropriately. We predicted the statistics of the postoperative flow rate increase in the CoW, which is a measure of CH, considering the uncertainties of arterial diameters, stenosis parameters, and flow rates measured using the patients’ clinical data. A sensitivity analysis was performed to clarify the impact of each uncertain parameter on the flow rate increase. Results indicated that CH occurred when two conditions were satisfied simultaneously: severe stenosis and when arteries of small diameter serve as the collateral pathway to the cerebral artery on the stenosis side. These findings elucidate the biological aspects of cerebral circulation in terms of the relationship between collateral flow and CH.

Reallocation of cutaneous and global blood circulation during sauna bathing through a closed-loop model

OBJECTIVE

Sauna bathing (SB) is an important strategy in cardiovascular protection, but there is no mathematical explanation for the reallocation of blood circulation during heat-induced superficial vasodilation. We sought to reveal such reallocation via a simulated hemodynamic model.

METHODS

A closed-loop cardiovascular model with a series of electrical parameters was constructed. The body surface was divided into seven blocks and each block was modeled by a lumped resistance. These resistances were adjusted to increase skin blood flow (SBF), with the aim of reflecting heat-induced vasodilation during SB. Finally, the blood pressure was compared before and after SB, and the blood flow inside the aorta and visceral arteries were also analyzed.

RESULTS

With increasing SBF in this model, the systolic, diastolic, and mean blood pressure in the arterial trunk decreased by 13-29, 18-36, and 19-37 mmHg, respectively. Despite the increase in the peak and mean blood flow in the arterial trunk, the diastolic blood flow reversal in the thoracic and abdominal aortas increased significantly. Nevertheless, the blood supply to the heart, liver, stomach, spleen, kidney, and intestine decreased by at least 25%. Moreover, the pulmonary blood flow increased significantly.

CONCLUSION

Simulated heat-induced cutaneous vasodilation in this model lowers blood pressure, induces visceral ischemia, and promotes pulmonary circulation, suggesting that the present closed-loop model may be able to describe the effect of sauna bathing on blood circulation. However, the increase of retrograde flow in the aortas found in this model deserves further examination.

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.

Model-based evaluation of local hemodynamic effects of enhanced external counterpulsation

BACKGROUND AND OBJECTIVES

The treatment benefits of enhanced external counterpulsation (EECP) heavily depends on hemodynamics. Global hemodynamics of EECP can cause blood flow redistribution in the circulatory system whereas local hemodynamic effects act on vascular endothelial cells (VECs). Local hemodynamic effects of EECP on VECs are important in the treatment of atherosclerosis, but currently cannot be not evaluated. Herein we aim to establish evaluation models of local hemodynamic effects based on the global hemodynamic indicators.

METHODS

We established 0D/3D geometric multi-scale hemodynamic models of the coronary and cerebral artery of two healthy individuals to calculate the global hemodynamic indicators and the local hemodynamic effects. Clinical EECP trials were performed to verify the accuracy of the multi-scale hemodynamic model. The global hemodynamic indicators included diastolic blood pressure/systolic blood pressure (Q = D/S), mean arterial pressure (MAP), internal carotid artery flow (ICAF) and cerebral blood flow (CBF), whereas local hemodynamic effects focused on time-averaged wall shear stress (TAWSS). The correlation between these indicators was analyzed via Pearson correlation coefficient. Significantly related indicators were selected for curve-fitting to establish evaluation models of the coronary and cerebral artery. Moreover, clinical data of a coronary heart disease patient and a cerebral ischemic stroke patient were collected to verify the effectiveness of the application of the established evaluation models to real patients.

RESULTS

For coronary artery, TAWSS was correlated to Q = D/S and ICAF (P < 0.05), whereas for cerebral artery, TAWSS was correlated to MAP and CBF (P < 0.05). The mean square error (MSE) between the evaluated values using evaluation model and the calculated values using 0D/3D model of TAWSS of the coronary and cerebral artery were 5.4% and 1.0%, respectively. The MSE of evaluation model applied to real patients was greater than that applied to healthy individuals, but within an acceptable range.

CONCLUSIONS

The presented error demonstrated validity and accuracy of the evaluation models in clinical patients. Based on the evaluation models, global hemodynamic indicators could be used to evaluate the local hemodynamic effects under the current counterpulsation mode. With TAWSS range of 4-7 Pa as the target range, EECP strategies can further be optimized.

An In Vivo Data-Based Computational Study on Sitting-Induced Hemodynamic Changes in the External Iliac Artery

Although sedentary behavior (characterized by prolonged sitting without otherwise being active in daily life) is widely regarded as a risk factor for peripheral artery disease (PAD), underlying biomechanical mechanisms remain insufficiently understood. In this study, geometrical models of ten external iliac arteries were reconstructed based on angiographic data acquired from five healthy young subjects resting in supine and sitting (mimicked by side lying with bent legs) positions, respectively, which were further combined with measured blood flow velocity waveforms in the common iliac arteries (with each body posture being maintained for 30 min) to build computational models for simulating intra-arterial hemodynamics. Morphological analyses showed that the external iliac arteries suffered from evident bending deformation upon the switch of body posture from supine to sitting. Measured blood flow velocity waveforms in the sitting position exhibited a marked decrease in mean flow velocity while increase in retrograde flow ratio compared with those in the supine position. Hemodynamic computations further revealed that sitting significantly altered blood flow patterns in the external iliac arteries, leading to a marked enlargement of atheroprone wall regions exposed to low and oscillatory wall shear stress (WSS), and enhanced multidirectional disturbance of WSS that may further impair endothelial function. In summary, our study demonstrates that prolonged sitting induces atheropromoting hemodynamic changes in the external iliac artery due to the combined effects of vascular bending deformation and changes in flow velocity waveform, which may provide important insights for understanding the involvement of biomechanical factors in sedentary behavior-related PAD.

Impact of Respiratory Fluctuation on Hemodynamics in Human Cardiovascular System: A 0-1D Multiscale Model

To explore hemodynamic interaction between the human respiratory system (RS) and cardiovascular system (CVS), here we propose an integrated computational model to predict the CVS hemodynamics with consideration of the respiratory fluctuation (RF). A submodule of the intrathoracic pressure (ITP) adjustment is developed and incorporated in a 0-1D multiscale hemodynamic model of the CVS specified for infant, adolescent, and adult individuals. The model is verified to enable reasonable estimation of the blood pressure waveforms accounting for the RF-induced pressure fluctuations in comparison with clinical data. The results show that the negative ITP caused by respiration increases the blood flow rates in superior and inferior vena cavae; the deep breathing improves the venous return in adolescents but has less influence on infants. It is found that a marked reduction in ITP under pathological conditions can excessively increase the flow rates in cavae independent of the individual ages, which may cause the hemodynamic instability and hence increase the risk of heart failure. Our results indicate that the present 0-1D multiscale CVS model incorporated with the RF effect is capable of providing a useful and effective tool to explore the physiological and pathological mechanisms in association with cardiopulmonary interactions and their clinical applications.

Cerebrospinal fluid dynamics coupled to the global circulation in holistic setting: Mathematical models, numerical methods and applications

This paper presents a mathematical model of the global, arterio-venous circulation in the entire human body, coupled to a refined description of the cerebrospinal fluid (CSF) dynamics in the craniospinal cavity. The present model represents a substantially revised version of the original Müller-Toro mathematical model. It includes one-dimensional (1D), non-linear systems of partial differential equations for 323 major blood vessels and 85 zero-dimensional, differential-algebraic systems for the remaining components. Highlights include the myogenic mechanism of cerebral blood regulation; refined vasculature for the inner ear, the brainstem and the cerebellum; and viscoelastic, rather than purely elastic, models for all blood vessels, arterial and venous. The derived 1D parabolic systems of partial differential equations for all major vessels are approximated by hyperbolic systems with stiff source terms following a relaxation approach. A major novelty of this paper is the coupling of the circulation, as described, to a refined description of the CSF dynamics in the craniospinal cavity, following Linninger et al. The numerical solution methodology employed to approximate the hyperbolic non-linear systems of partial differential equations with stiff source terms is based on the Arbitrary DERivative Riemann problem finite volume framework, supplemented with a well-balanced formulation, and a local time stepping procedure. The full model is validated through comparison of computational results against published data and bespoke MRI measurements. Then we present two medical applications: (i) transverse sinus stenoses and their relation to Idiopathic Intracranial Hypertension; and (ii) extra-cranial venous strictures and their impact in the inner ear circulation, and its implications for Ménière's disease.

Closed-Loop Multiscale Computational Model of Human Blood Circulation. Applications to Ballistocardiography

Cardiac mechanical activity leads to periodic changes in the distribution of blood throughout the body, which causes micro-oscillations of the body's center of mass and can be measured by ballistocardiography (BCG). However, many of the BCG findings are based on parameters whose origins are poorly understood. Here, we generate simulated multidimensional BCG signals based on a more exhaustive and accurate computational model of blood circulation than previous attempts. This model consists in a closed loop 0D-1D multiscale representation of the human blood circulation. The 0D elements include the cardiac chambers, cardiac valves, arterioles, capillaries, venules, and veins, while the 1D elements include 55 systemic and 57 pulmonary arteries. The simulated multidimensional BCG signal is computed based on the distribution of blood in the different compartments and their anatomical position given by whole-body magnetic resonance angiography on a healthy young subject. We use this model to analyze the elements affecting the BCG signal on its different axes, allowing a better interpretation of clinical records. We also evaluate the impact of filtering and healthy aging on the BCG signal. The results offer a better view of the physiological meaning of BCG, as compared to previous models considering mainly the contribution of the aorta and focusing on longitudinal acceleration BCG. The shape of experimental BCG signals can be reproduced, and their amplitudes are in the range of experimental records. The contributions of the cardiac chambers and the pulmonary circulation are non-negligible, especially on the lateral and transversal components of the velocity BCG signal. The shapes and amplitudes of the BCG waveforms are changing with age, and we propose a scaling law to estimate the pulse wave velocity based on the time intervals between the peaks of the acceleration BCG signal. We also suggest new formulas to estimate the stroke volume and its changes based on the BCG signal expressed in terms of acceleration and kinetic energy.

Impact of ductus arteriosus constriction and restrictive foramen ovale on global hemodynamics for term fetuses with d-TGA

The ductus arteriosus (DA) constriction and restrictive foramen ovale (FO) are known as the leading cause of compromise and death of fetuses with dextro-transposition of the great arteries (d-TGA). Although the d-TGA fetal hemodynamics is of great importance in making diagnosis and management of the congenital heart defect, it remains poorly understood, particularly in terms of abnormal DA and FO. In this study, we developed a closed-loop 0-1D multiscale model of the fetal cardiovascular system (CVS) specified for the d-TGA circulation and conducted a systematic study of the impact of the DA constriction and restrictive FO on fetal hemodynamics. We found that the DA constriction led to a pronounced increase in the pulmonary artery pressure, pulmonary and mitral valve (PV and MV) regurgitation as well as left heart volume; the restrictive FO was responsible for reducing MV E/A ratio, ie, the ratio of peak early filling and late diastolic filling velocities, and PV peak systolic flow (PSV) but could increase both aortic valve (AV) PSV and aortic isthmus systolic index (ISI). Moreover, the amount of blood flowing through the DA was observed equivalent to that through the FO; the influence of DA constriction on the cerebral and placental perfusions are larger than that of the FO. Our results demonstrate that the proposed fetal cardiovascular model may be a useful tool for studying the underlying mechanisms associated with d-TGA fetal circulation and providing insights into its complex physiology and pathology.

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.

Comparison of LBM and FVM in the estimation of LAD stenosis

The finite volume method (FVM)-based computational fluid dynamics (CFD) technology has been applied in the non-invasive diagnosis of coronary artery stenosis. Nonetheless, FVM is a time-consuming process. In addition to FVM, the lattice Boltzmann method (LBM) is used in fluid flow simulation. Unlike FVM solving the Navier-Stokes equations, LBM directly solves the simplified Boltzmann equation, thus saving computational time. In this study, 12 patients with left anterior descending (LAD) stenosis, diagnosed by CTA, are analysed using FVM and LBM. The velocities, pressures, and wall shear stress (WSS) predicted using FVM and LBM for each patient is compared. In particular, the ratio of the average and maximum speed at the stenotic part characterising the degree of stenosis is compared. Finally, the golden standard of LAD stenosis, invasive fractional flow reserve (FFR), is applied to justify the simulation results. Our results show that LBM and FVM are consistent in blood flow simulation. In the region with a high degree of stenosis, the local flow patterns in those two solvers are slightly different, resulting in minor differences in local WSS estimation and blood speed ratio estimation. Notably, these differences do not result in an inconsistent estimation. Comparison with invasive FFR shows that, in most cases, the non-invasive diagnosis is consistent with FFR measurements. However, in some cases, the non-invasive diagnosis either underestimates or overestimates the degree of stenosis. This deviation is caused by the difference between physiological and simulation conditions that remains the biggest challenge faced by all CFD-based non-invasive diagnostic methods.

Acute Hemodynamic Improvement by Thermal Vasodilation inside the Abdominal and Iliac Arterial Segments of Young Sedentary Individuals

OBJECTIVE

To study the hemodynamic response to lower leg heating intervention (LLHI) inside the abdominal and iliac arterial segments (AIAS) of young sedentary individuals.

METHODS

A Doppler measurement of blood flow was conducted for 5 young sedentary adults with LLHI. Heating durations of 0, 20, and 40 min were considered. A lumped parameter model (LPM) was used to ascertain the hemodynamic mechanism. The hemodynamics were determined via numerical approaches.

RESULTS

Ultrasonography revealed that the blood flow waveform shifted upwards under LLHI; in particular, the mean flow increased significantly (p < 0.05) with increasing heating duration. The LPM showed that its mechanism depends on the reduction in afterload resistance, not on the inertia of blood flow and arterial compliance. The time-averaged wall shear stress, time-averaged production rate of nitric oxide, and helicity in the external iliac arteries increased more significantly than in other segments as the heating duration increased, while the oscillation shear index (OSI) and relative residence time (RRT) in the AIAS declined with increasing heating duration. There was a more obvious helicity response in the bilateral external iliac arteries than the OSI and RRT responses.

CONCLUSION

LLHI can effectively induce a positive hemodynamic environment in the AIAS of young sedentary individuals.

Carotid Stump Pressure and Contralateral Internal Carotid Stenosis Ratio During Carotid Endarterectomies: 1D-0D Hemodynamic Simulation of Cerebral Perfusion

Objective: We selectively place carotid shunting when ipsilateral mean stump pressure is less than 40 mmHg during carotid endarterectomy (CEA). This study aimed to assess the validity of our selective shunting criterion by 1D-0D hemodynamic simulation technology.

Materials and Methods: We retrospectively reviewed 88 patients (95 cases) of CEA and divided them into two groups based on the degree of contralateral internal carotid artery (ICA) stenosis ratio, which was determined as severe when the peak systolic velocity ratio of the ICA to the common carotid artery was ≥4 by carotid duplex ultrasonography. Patients with severe stenosis or occlusion in contralateral ICA were classified as hypoperfusion group, and those without such contralateral ICA obstruction were classified as control group.

Results: Perioperatively, the mean carotid stump pressures were 33 mmHg in hypoperfusion group and 46 mmHg in the control group (P=0.006). We simulated changes in carotid stump pressure according to the changes in the contralateral ICA stenosis ratio. 1D-0D simulation indicated a sharp decline in carotid stump pressure when the contralateral stenosis ratio was >50%, while peripheral pressure of the middle cerebral arteries declined sharply at a ≥70% contralateral stenosis ratio. At this ratio, the direction of the ipsilateral cerebral arterial flow became inverted, the carotid stump pressure became dependent on the basilar artery circulation, and the ipsilateral middle cerebral artery became hypoperfused.

Conclusion: Our clinical and computer-simulated results confirmed the validation of our carotid shunting criterion and suggested that contralateral ICA stenosis ratio over 70% is a safe indication of selective shunting during CEA.

Retrograde branched extension limb assembling stent of pararenal abdominal aortic aneurysm: A longitudinal hemodynamic analysis for stent graft migration

PURPOSE

Pararenal abdominal aortic aneurysms (PRAAAs) are a life-threatening disease, and hemodynamic analysis may provide greater insight into the effectiveness and long-term outcomes of endovascular aneurysm repair (EVAR). However, the lack of patient-specific boundary conditions on the periphery compromises the accuracy. Windkessel (WK) boundary conditions coupled to hemodynamic follow-up models of a PRAAA patient, aims to provide insights into the link between hemodynamics and poor prognosis.

METHOD

One PRAAA patient underwent EVAR and reintervention after one branch of stent-graft (SG) had migrated. Totally five computational follow-up models were studied. Patient-specific flow data acquired via ultrasound were used to define the boundary conditions in the ascending aorta and the following three branches. Coupled zero-dimensional WK models representing the distal vasculature were used to define the outlet boundary conditions under the abdomen.

RESULTS

Flow divisions of the main SG branches were 40.7% and 24.7%, respectively. Time-averaged wall shear stress and oscillatory shear index (OSI) increased at the junction connected the SG branch and the stent leading to the right common iliac artery (RCIA) where the stent migrated. The OSI and relative residence time (RRT) value in superior mesenteric artery increased notably after the migration, the RRT continuously increased following the reintervention.

CONCLUSION

Unbalanced flow, resulting in locally high-speed flow, high WSS and OSI might significantly affect stent stability. Results suggest that diameters and interconnection design of stents in complex cases should take the flow division into consideration and computational simulations might be considered as a tool for intervention protocol design.

Personalized Hemodynamic Modeling of the Human Cardiovascular System: A Reduced-Order Computing Model

OBJECTIVE

Personalization of hemodynamic modeling plays a crucial role in functional prediction of the cardiovascular system (CVS). While reduced-order models of one-dimensional (1D) blood vessel models with zero-dimensional (0D) blood vessel and heart models have been widely recognized to be an effective tool for reasonably estimating the hemodynamic functions of the whole CVS, practical personalized models are still lacking. In this paper, we present a novel 0-1D coupled, personalized hemodynamic model of the CVS that can predict both pressure waveforms and flow velocities in arteries.

METHODS

We proposed a methodology by combining the multiscale CVS model with the Levenberg-Marquardt optimization algorithm for effectively solving an inverse problem based on measured blood pressure waveforms. Hemodynamic characteristics including brachial arterial pressure waveforms, artery diameters, stroke volumes, and flow velocities were measured noninvasively for 62 volunteers aged from 20 to 70 years for developing and validating the model.

RESULTS

The estimated arterial stiffness shows a physiologically realistic distribution. The model-fitted individual pressure waves have an averaged mean square error (MSE) of 7.1 mmHg²; simulated blood flow velocity waveforms in carotid artery match ultrasound measurements well, achieving an average correlation coefficient of 0.911.

CONCLUSION

The model is efficient, versatile, and capable of obtaining well-fitting individualized pressure waveforms while reasonably predicting flow waveforms.

SIGNIFICANCE

The proposed methodology of personalized hemodynamic modeling may therefore facilitate individualized patient-specific assessment of both physiological and pathological functions of the CVS.

Estimation of the Blood Pressure Waveform using Electrocardiography

This work presents a modelling approach to accurately predict the blood pressure (BP) waveform time series from a single input signal. A nonlinear autoregressive model with exogenous input (NARX) is implemented using artificial neural networks and trained on Electrocardiography (ECG) signals to predict the BP waveform. The efficacy of the model is demonstrated using the MIMIC II database. The proposed method can accurately estimate systolic and diastolic BP. The NARX model together with ECG measurement allows continuous monitoring of BP, enables the estimation of other physiological measurements, such as the cardiac output, and provides more insight on the patient health condition.

Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data

Mathematical models are widely recognized as a valuable tool for cardiovascular diagnosis and the study of circulatory diseases, especially to obtain data that require otherwise invasive measurements. To correctly simulate body hemodynamics, the viscoelastic properties of vessels walls are a key aspect to be taken into account as they play an essential role in cardiovascular behavior. The present work aims to apply the augmented fluid-structure interaction system of blood flow to real case studies to assess the validity of the model as a valuable resource to improve cardiovascular diagnostics and the treatment of pathologies. Main contributions of the paper include the evaluation of viscoelastic tube laws, estimation of viscoelastic parameters and comparison of models with literature results and in-vivo experiments. The ability of the model to correctly simulate pulse waveforms in single arterial segments is verified using literature benchmark test cases, designed taking into account a simple elastic behavior of the wall in the upper thoracic aorta and in the common carotid artery. Furthermore, in-vivo pressure waveforms, extracted from tonometric measurements performed on four human common carotid arteries and two common femoral arteries, are compared to numerical solutions. It is highlighted that the viscoelastic damping effect of arterial walls is required to avoid an overestimation of pressure peaks. Finally, an effective procedure to estimate the viscoelastic parameters of the model is herein proposed, which returns hysteresis curves of the common carotid arteries dissipating energy fractions in line with values calculated from literature hysteresis loops in the same vessel.

An In-Vitro Flow Study Using an Artificial Circle of Willis Model for Validation of an Existing One-Dimensional Numerical Model

A one-dimensional (1D) numerical model has been previously developed to investigate the hemodynamics of blood flow in the entire human vascular network. In the current work, an experimental study of water-glycerin mixture flow in a 3D-printed silicone model of an anatomically accurate, complete circle of Willis (CoW) was conducted to investigate the flow characteristics in comparison with the simulated results by the 1D numerical model. In the experiment, the transient flow and pressure waveforms were measured at 13 selected segments within the flow network for comparisons. In the 1D simulation, the initial parameters of the vessel network were obtained by a direct measurement of the tubes in the experimental setup. The results verified that the 1D numerical model is able to capture the main features of the experimental pressure and flow waveforms with good reliability. The mean flow rates measurement results agree with the predictions of the 1D model with an overall difference of less than 1%. Further experiment might be needed to validate the 1D model in capturing pressure waveforms.

Application of 0D model of blood flow to study vessel abnormalities in the human systemic circulation: An in-silico study

In this paper, a multi-compartment 0D model of the blood flow is considered to study the vessel abnormalities (stenoses and aneurysms) in the human systemic circulation (SC). In the complete SC, different levels of stenosis and aneurysms are artificially created by decreasing and increasing the vessel diameters respectively and their effects on pressure and flow are studied using sensitivity analysis (SA). Normalized local sensitivity analysis (LSA) is used to study the impact of stenosis and aneurysms on pressure and flow wave pattern. Furthermore, global sensitivity analysis (GSA), Sobol’s method is used to quantify the overall influence of stenoses and aneurysms in the complete SC.

The results of global sensitivity analysis revealed that the impact of both stenoses and aneurysms is strong within the individual structures (arm, legs, carotid bifurcation, aorta), while, aortic stenoses and aneurysms have effect on almost all downstream nodes. Moreover, the study could be useful for medical doctors, teachers and students to observe the hemodynamical changes in the SC with respect to vessel abnormalities, which could further help in making any clinical decision for patients having different levels of vessel abnormalities in any part or structure of the SC.

A multi-scale model of the coronary circulation applied to investigate transmural myocardial flow

Distribution of blood flow in myocardium is a key determinant of the localization and severity of myocardial ischemia under impaired coronary perfusion conditions. Previous studies have extensively demonstrated the transmural difference of ischemic vulnerability. However, it remains incompletely understood how transmural myocardial flow is regulated under in vivo conditions. In the present study, a computational model of the coronary circulation was developed to quantitatively evaluate the sensitivity of transmural flow distribution to various cardiovascular and hemodynamic factors. The model was further incorporated with the flow autoregulatory mechanism to simulate the regulation of myocardial flow in the presence of coronary artery stenosis. Numerical tests demonstrated that heart rate (HR), intramyocardial tissue pressure (P_im ), and coronary perfusion pressure (P_per ) were the major determinant factors for transmural flow distribution (evaluated by the subendocardial-to-subepicardial (endo/epi) flow ratio) and that the flow autoregulatory mechanism played an important compensatory role in preserving subendocardial perfusion against reduced P_per . Further analysis for HR variation-induced hemodynamic changes revealed that the rise in endo/epi flow ratio accompanying HR decrease was attributable not only to the prolongation of cardiac diastole relative to systole, but more predominantly to the fall in P_im . Moreover, it was found that P_im and P_per interfered with each other with respect to their influence on transmural flow distribution. These results demonstrate the interactive effects of various cardiovascular and hemodynamic factors on transmural myocardial flow, highlighting the importance of taking into account patient-specific conditions in the explanation of clinical observations.

Influence of aging-induced flow waveform variation on hemodynamics in aneurysms present at the internal carotid artery: A computational model-based study

The variation of blood flow waveform in the internal carotid artery (ICA) with age is a well-documented hemodynamic phenomenon, but little is known about how such variation affects the characteristics of blood flow in aneurysms present in the region. In the study, hemodynamic simulations were conducted for 26 ICA aneurysms, with flow waveforms measured in the ICAs of young and older adults being used respectively to set the inflow boundary conditions. Obtained results showed that replacing the young-adult flow waveform with the older-adult one led to little changes (<10%) in simulated time-averaged wall shear stress (WSS), transient maximum WSS, relative residence time and trans-aneurysm pressure loss coefficient, but resulted in a marked increase (32.36 ± 17.24%) in oscillatory shear index (OSI). Frequency-domain wave analysis revealed that the progressive enhancement of low-frequency harmonics dominated the observed flow waveform variation with age and was a major factor contributing to the increase in OSI. Cross-sectional comparisons among the aneurysms further revealed that the degree of increase in OSI correlated positively with some specific morphological features of aneurysm, such as aspect ratio and size ratio. In summary, the study demonstrates that the variation in flow waveform with age augments the oscillation of WSS in ICA aneurysms, which underlies the importance of setting patient-specific boundary conditions in hemodynamic studies on cerebral aneurysms, especially those involving long-term patient follow-up or cross-sectional comparison among patients of different ages.

A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh-Nagumo model for action potentials. The one-dimensional model for a deformable lymphatic vessel is a nonlinear system of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (circumferential stretch of the lymphatic wall and wall shear stress) and lymphatic vessel wall contractions. The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a stability analysis of the stationary state of the EFMC model. Contractions turn out to be triggered by the instability of the stationary state. Overall, the EFMC model allows emulating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled by extending an existing lumped-parameter model for blood vessels. Modern numerical methods are employed for the one-dimensional model (PDEs), for the EFMC model and valve dynamics (ODEs). Adopting the geometrical structure of collecting lymphatics from rat mesentery, we apply the full mathematical model to a carefully selected suite of test problems inspired by experiments. We analysed several indices of a single lymphangion for a wide range of upstream and downstream pressure combinations which included both favourable and adverse pressure gradients. The most influential model parameters were identified by performing two sensitivity analyses for favourable and adverse pressure gradients.

A mathematical model of human heart including the effects of heart contractility varying with heart rate changes

Incorporating the intrinsic variability of heart contractility varying with heart rate into the mathematical model of human heart would be useful for addressing the dynamical behaviors of human cardiovascular system, but models with such features were rarely reported. This study focused on the development and evaluation of a mathematical model of the whole heart, including the effects of heart contractility varying with heart rate changes. This model was developed based on a paradigm and model presented by Ottesen and Densielsen, which was used to model ventricular contraction. A piece-wise function together with expressions for time-related parameters were constructed for modeling atrial contraction. Atrial and ventricular parts of the whole heart model were evaluated by comparing with models from literature, and then the whole heart model were assessed through coupling with a simple model of the systemic circulation system and the pulmonary circulation system. The results indicated that both atrial and ventricular parts of the whole heart model could reasonably reflect their contractility varying with heart rate changes, and the whole heart model could exhibit major features of human heart. Results of the parameters variation studies revealed the correlations between the parameters in the whole heart model and performances (including the maximum pressure and the stroke volume) of every chamber. These results would be useful for helping users to adjust parameters in special applications.

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.

Determinant Factors for Arterial Hemodynamics in Hypertension: Theoretical Insights From a Computational Model-Based Study

Hypertension is a well-documented predictive factor for cardiovascular events. Clinical studies have extensively demonstrated the differential hemodynamic consequences of various antihypertensive drugs, but failed to clearly elucidate the underlying mechanisms due to the difficulty in performing a quantitative deterministic analysis based on clinical data that carry confounding information stemming from interpatient differences and the nonlinearity of cardiovascular hemodynamics. In the present study, a multiscale model of the cardiovascular system was developed to quantitatively investigate the relationships between hemodynamic variables and cardiovascular properties under hypertensive conditions, aiming to establish a theoretical basis for assisting in the interpretation of clinical observations or optimization of therapy. Results demonstrated that heart period, central arterial stiffness, and arteriolar radius were the major determinant factors for blood pressures and flow pulsatility indices both in large arteries and in the microcirculation. These factors differed in the degree and the way in which they affect hemodynamic variables due to their differential effects on wave reflections in the vascular system. In particular, it was found that the hemodynamic effects of varying arteriolar radius were considerably influenced by the state of central arterial stiffness, and vice versa, which implied the potential of optimizing antihypertensive treatment by selecting proper drugs based on patient-specific cardiovascular conditions. When analyzed in relation to clinical observations, the simulated results provided mechanistic explanations for the beneficial pressure-lowering effects of vasodilators as compared to β-blockers, and highlighted the significance of monitoring and normalizing arterial stiffness in the treatment of hypertension.

A computational model of the hepatic circulation applied to analyze the sensitivity of hepatic venous pressure gradient (HVPG) in liver cirrhosis

Measurement of hepatic venous pressure gradient (HVPG) is currently widely adopted to provide an estimate of portal pressure gradient (PPG) in the diagnosis and treatment of portal hypertension associated with liver cirrhosis. Despite the well-documented clinical utility of HVPG, it remains poorly understood how the relationship between HVPG and PPG is affected by factors involved in the pathogenesis and progression of cirrhosis. In the study, a computational model of the hepatic circulation calibrated to in vivo data was developed to simulate the procedure of HVPG measurement and quantitatively investigate the error of HVPG relative to PPG under various pathophysiological conditions. Obtained results confirmed the clinical consensus that HVPG is applicable to the assessment of portal hypertension caused by increased vascular resistance located primarily at the sinusoidal and postsinusoidal sites rather than at the presinusoidal site. On the other hand, our study demonstrated that the accuracy of HVPG measurement was influenced by many factors related to hepatic hemodynamics even in the case of sinusoidal portal hypertension. For instance, varying presinusoidal portal vascular resistance significantly altered the difference between HVPG and PPG, while an enhancement in portosystemic collateral flow tended to improve the accuracy of HVPG measurement. Moreover, it was found that presinusoidal and postsinusoidal vascular resistances interfered with each other with respect to their influence on HVPG measurement. These findings suggest that one should take into account patient-specific pathological conditions in order to achieve a better understanding and utilization of HVPG in the clinical practice.