Arterial pressure and flow wave analysis using time-domain 1-D hemodynamics

Signatures of obstructions and expansions in the arterial frequency response

BACKGROUND AND OBJECTIVE

The blood pressure and flow waveforms carry valuable information about the condition of the cardiovascular system and a patient's health. Waveform analysis in health and pathological conditions can be performed in the time or frequency domains; the information to be emphasised defines the use of either domain. However, physicians are more familiar with the time domain, and the changes in the waveforms due to cardiovascular diseases and ageing are better characterised in such domain. On the other hand, the analysis of the vascular and geometrical variables determining the signatures in the frequency response of local vascular anomalies, such as aneurysms and stenoses, has not been thoroughly explored. This paper aims to characterise the signatures of obstructions (stenoses) and expansions (aneurysms) in the frequency response of tapered arteries.

METHODS

The first step in our methodology was to incorporate the viscous response of the arterial wall into a one-dimensional elastic formulation that solves the governing equations in the frequency domain. As a second step, we imposed a volumetric flow excitation in arteries simulating the aorta with increasing geometry complexity: from straight to tapered arteries with local expansions or obstructions; and we assessed the frequency response.

RESULTS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that are distinguishable from a health condition. The signatures of obstruction and expansions differ; the obstructions increase the magnitude of fundamental frequency and work as a close boundary condition. On the other hand, the expansions diminish the fundamental frequency and work as an open boundary condition. Furthermore, such signatures correlate to the distance between the artery's inlet and the anomaly's starting point and have the potential to pinpoint abnormalities non-invasively.

CONCLUSIONS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that have the potential to detect and follow up on the development of vascular abnormalities. For the latter purpose, constant monitoring may be required; despite this not being a common clinical practice, the new wearable technology offers the possibility of continuous monitoring of biophysical markers such as the pressure waveform.

Using the photoplethysmography method to monitor age-related changes in the cardiovascular system

Introduction: Aging is a physiological process characterized by progressive changes in all organ systems. In the last few decades, the elderly population has been growing, so the scientific community is focusing on the investigation of the aging process, all in order to improve the quality of life in elderly. One of the biggest challenges in studying the impact of the aging on the human body represents the monitoring of the changes that inevitably occur in arterial blood vessels. Therefore, the medical community has invested a great deal of effort in studying and discovering new methods and tools that could be used to monitor the changes in arterial blood vessels caused by the aging process. The goal of our research was to develop a new diagnostic method using a photoplethysmographic sensor and to examine the impact of the aging process on the cardiovascular system in adults. Long-term recorded arterial blood flow waveforms were analyzed using detrended fluctuation analysis. Materials and Methods: The study included 117 respondents, aged 20-70 years. The waveform of the arterial blood flow was recorded for 5 min, with an optical sensor placed above the left common carotid artery, simultaneously with a single-channel ECG. For each cardiac cycle, the blood flow amplitude was determined, and a new time series was formed, which was analyzed non-linearly (DFA method). The values of the scalar coefficients α 1 and α 2, particularly their ratio (α 1/α 2) were obtained, which were then monitored in relation to the age of the subjects. Result: The values of the scalar ratio (α 1/α 2) were significantly different between the subjects older and younger than 50 years. The value of the α 1/α 2 decreased exponentially with the aging. In the population of middle-aged adults, this ratio had a value around 1, in young adults the value was exclusively higher than 1 and in older adults the value was exclusively lower than 1. Conclusion: The results of this study indicated that the aging led to a decrease in the α 1/α 2 in the population of healthy subjects. With this non-invasive method, changes in the cardiovascular system due to aging can be detected and monitored.

An anatomically detailed arterial-venous network model. Cerebral and coronary circulation

In recent years, several works have addressed the problem of modeling blood flow phenomena in veins, as a response to increasing interest in modeling pathological conditions occurring in the venous network and their connection with the rest of the circulatory system. In this context, one-dimensional models have proven to be extremely efficient in delivering predictions in agreement with in-vivo observations. Pursuing the increase of anatomical accuracy and its connection to physiological principles in haemodynamics simulations, the main aim of this work is to describe a novel closed-loop Anatomically-Detailed Arterial-Venous Network (ADAVN) model. An extremely refined description of the arterial network consisting of 2,185 arterial vessels is coupled to a novel venous network featuring high level of anatomical detail in cerebral and coronary vascular territories. The entire venous network comprises 189 venous vessels, 79 of which drain the brain and 14 are coronary veins. Fundamental physiological mechanisms accounting for the interaction of brain blood flow with the cerebro-spinal fluid and of the coronary circulation with the cardiac mechanics are considered. Several issues related to the coupling of arterial and venous vessels at the microcirculation level are discussed in detail. Numerical simulations are compared to patient records published in the literature to show the descriptive capabilities of the model. Furthermore, a local sensitivity analysis is performed, evidencing the high impact of the venous circulation on main cardiovascular variables.

Novel Pressure Wave Separation Analysis for Cardiovascular Function Assessment Highlights Major Role of Aortic Root

Objective

A novel method was presented to separate the central blood pressure wave (CBPW) into five components with different biophysical and temporal origins. It includes a time-varying emission coefficient (γ) that quantifies pulse wave generation and reflection at the aortic root.

Methods

The method was applied to normotensive subjects with modulated physiology by inotropic/vasoactive drugs (n = 13), hypertensive subjects (n = 158), and virtual subjects (n = 4,374).

Results

γ is directly proportional to aortic flow throughout the cardiac cycle. Mean peak γ increased with increasing pulse pressure (from <30 to >70 mmHg) in the hypertensive (from 1.6 to 2.5, P < 0.001) and in silico (from 1.4 to 2.8, P < 0.001) groups, dobutamine dose (from baseline to 7.5 μg/kg/min) in the normotensive group (from 2.1 to 2.7, P < 0.05), and remained unchanged when peripheral wave reflections were suppressed in silico. This was accompanied by an increase in the percentage contribution of the cardiac-aortic-coupling component of CBPW in systole: from 11% to 23% (P < 0.001) in the hypertensive group, 9% to 21% (P < 0.001) in the in silico group, and 17% to 23% (P < 0.01) in the normotensive group.

Conclusion

These results suggest that the aortic root is a major reflection site in the systemic arterial network and ventricular-aortic coupling is the main determinant in the elevation of pulsatile pulse pressure.

Significance

Ventricular-aortic coupling is a prime therapeutic target for preventing/treating systolic hypertension.

Impact of tapering of arterial vessels on blood pressure, pulse wave velocity, and wave intensity analysis using one-dimensional computational model

The angle of arterial tapering increases with ageing, and the geometrical changes of the aorta may cause an increase in central arterial pressure and stiffness. The impact of tapering has been primarily studied using frequency-domain transmission line theories. In this work, we revisit the problem of tapering and investigate its effect on blood pressure and pulse wave velocity (PWV) using a time-domain analysis with a 1D computational model. First, tapering is modelled as a stepwise reduction in diameter and compared with results from a continuously tapered segment. Next, we studied wave reflections in a combination of stepwise diameter reduction of straight vessels and bifurcations, then repeated the experiments with decreasing the length to physiological values. As the model's segments became shorter in length, wave reflections and re-reflections resulted in waves overlapping in time. We extended our work by examining the effect of increasing the tapering angle on blood pressure and wave intensity in physiological models: a model of the thoracic aorta and a model of upper thoracic and descending aorta connected to the iliac bifurcation. Vessels tapering inherently changed the ratio between the inlet and outlet cross-sectional areas, increasing the vessel resistance and reducing the compliance compared with non-tapered vessels. These variables influence peak and pulse pressure. In addition, it is well established that pulse wave velocity increases in an ageing arterial tree. This work provides confirmation that tapering induces reflections and offers an additional explanation to the observation of increased peak pressure and decreased diastolic pressure distally in the arterial tree.

Hemodynamic modeling of the circle of Willis reveals unanticipated functions during cardiovascular stress

The circle of Willis (CW) allows blood to be redistributed throughout the brain during local ischemia; however, it is unlikely that the anatomic persistence of the CW across mammalian species is driven by natural selection of individuals with resistance to cerebrovascular disease typically occurring in elderly humans. To determine the effects of communicating arteries (CoAs) in the CW on cerebral pulse wave propagation and blood flow velocity, we simulated young, active adult humans undergoing different states of cardiovascular stress (i.e., fear and aerobic exercise) using discrete transmission line segments with stress-adjusted cardiac output, peripheral resistance, and arterial compliance. Phase delays between vertebrobasilar and carotid pulses allowed bidirectional shunting through CoAs: both posteroanterior shunting before the peak of the pulse waveform and anteroposterior shunting after internal carotid pressure exceeded posterior cerebral pressure. Relative to an absent CW without intact CoAs, the complete CW blunted anterior pulse waveforms, although limited to 3% and 6% reductions in peak pressure and pulse pressure, respectively. Systolic rate of change in pressure (i.e., ∂P/∂t) was reduced 15%-24% in the anterior vasculature and increased 23%-41% in the posterior vasculature. Bidirectional shunting through posterior CoAs was amplified during cardiovascular stress and increased peak velocity by 25%, diastolic-to-systolic velocity range by 44%, and blood velocity acceleration by 134% in the vertebrobasilar arteries. This effect may facilitate stress-related increases in blood flow to the cerebellum (improving motor coordination) and reticular-activating system (enhancing attention and focus) via a nitric oxide-dependent mechanism, thereby improving survival in fight-or-flight situations.NEW & NOTEWORTHY Hemodynamic modeling reveals potential evolutionary benefits of the intact circle of Willis (CW) during fear and aerobic exercise. The CW equalizes pulse waveforms due to bidirectional shunting of blood flow through communicating arteries, which boosts vertebrobasilar blood flow velocity and acceleration. These phenomena may enhance perfusion of the brainstem and cerebellum via nitric oxide-mediated vasodilation, improving performance of the reticular-activating system and motor coordination in survival situations.

Wave reflection: More than a round trip

Reflected pressure waves are key to the understanding of vascular ageing, a prominent factor in major cardiovascular events. Several different metrics have been proposed to index the effect of wave reflection on the pressure waveform and thereby serve as an indicator of vascular ageing. The extent to which these indices are influenced by factors other than vascular health remains a matter of concern. In this paper, we use transmission-line theory to derive a mathematical model for the reflection time (T_refl), and the augmentation index (AI), assuming a general extended model of the arterial system. Then, we test the proposed model against values reported in the literature. Finally, we discuss insights from the model to common observations in the literature such as age-related "shift" in the reflection site, the variation of AI with heart rate, and the flattening of T_refl in older participants.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

On the poro-elastic models for microvascular blood flow resistance: An in vitro validation

Nowadays, adequate and accurate representation of the microvascular flow resistance constitutes one of the major challenges in computational haemodynamic studies. In this work, a theoretical, porous media framework, ultimately designed for representing downstream resistance, is presented and compared against an in vitro experimental results. The resistor consists of a poro-elastic tube, with either a constant or variable porosity profile in space. The underlying physics, characterizing the fluid flow through the porous media, is analysed by considering flow variables at different network locations. Backward reflections, originated in the reservoir of the in vitro model, are accounted for through a reflection coefficient imposed as an outflow network condition. The simulation results are in good agreement with the measurements for both the homogenous and heterogeneous porosity conditions. In addition, the comparison allows identification of the range of values representing experimental reservoir reflection coefficients. The pressure drops across the heterogeneous porous media increases with respect to the simpler configuration, whilst flow remains almost unchanged. The effect of some fluid network features, such as tube Young's modulus and fluid viscosity, on the theoretical results is also elucidated, providing a reference for the invitro and insilico simulation of different microvascular conditions.

Dynamic Effects of Aortic Arch Stiffening on Pulsatile Energy Transmission to Cerebral Vasculature as A Determinant of Brain-Heart Coupling

Aortic stiffness increases with age and is a robust predictor of brain pathology including Alzheimer’s and other dementias. Aging causes disproportionate stiffening of the aorta compared with the carotid arteries, reducing protective impedance mismatches at their interface and affecting transmission of destructive pulsatile energy to the cerebral circulation. Recent clinical studies have measured regional stiffness within the aortic arch using pulse wave velocity (PWV) and have found a stronger association with cerebrovascular events than global stiffness measures. However, effects of aortic arch PWV on the transmission of harmful excessive pulsatile energy to the brain is not well-understood. In this study, we use an energy-based analysis of hemodynamic waves to quantify the effect of aortic arch stiffening on transmitted pulsatility to cerebral vasculature, employing a computational approach using a one-dimensional model of the human vascular network. Results show there exists an optimum wave condition—occurring near normal human heart rates—that minimizes pulsatile energy transmission to the brain. This indicates the important role of aortic arch biomechanics on heart-brain coupling. Our results also suggest that energy-based indices of pulsatility combining pressure and flow data are more sensitive to increased stiffness than using flow or pressure pulsatility indices in isolation.

The modified arterial reservoir: An update with consideration of asymptotic pressure (P∞) and zero-flow pressure (Pzf)

This article describes the modified arterial reservoir in detail. The modified arterial reservoir makes explicit the wave nature of both reservoir (P_res) and excess pressure (P_xs). The mathematical derivation and methods for estimating P_res in the absence of flow velocity data are described. There is also discussion of zero-flow pressure (P_zf), the pressure at which flow through the circulation ceases; its relationship to asymptotic pressure (P_∞) estimated by the reservoir model; and the physiological interpretation of P_zf . A systematic review and meta-analysis provides evidence that P_zf differs from mean circulatory filling pressure.

Assessment of Fractional-Order Arterial Windkessel as a Model of Aortic Input Impedance

Goal: Fractional-order Windkessel model is proposed to describe the aortic input impedance. Compared with the conventional arterial Windkessel, the main advantage of the proposed model is the consideration of the viscoelastic nature of the arterial wall using the fractional-order capacitor (FOC). Methods: The proposed model, along with the standard two-element Windkessel, three-element Windkessel, and the viscoelastic Windkessel models, are assessed and compared using in-silico data. Results: The results show that the fractional-order model fits better the moduli of the aortic input impedance and fairly approximates the phase angle. In addition, by its very nature, the pseudo-capacitance of FOC makes the proposed model's dynamic compliance complex and frequency-dependent. Conclusions: The analysis of the proposed fractional-order model indicates that fractional-order impedance yields a powerful tool for a flexible characterization of the arterial hemodynamics.

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.

A One-Dimensional Hemodynamic Model of the Coronary Arterial Tree

One-dimensional (1D) hemodynamic models of arteries have increasingly been applied to coronary circulation. In this study, we have adopted flow and pressure profiles in Olufsen's 1D structured tree as coronary boundary conditions, with terminals coupled to the dynamic pressure feedback resulting from the intra-myocardial stress because of ventricular contraction. We model a trifurcation structure of the example coronary tree as two adjacent bifurcations. The estimated results of blood pressure and flow rate from our simulation agree well with the clinical measurements and published data. Furthermore, the 1D model enables us to use wave intensity analysis to simulate blood flow in the developed coronary model. Six characteristic waves are observed in both left and right coronary flows, though the waves' magnitudes differ from each other. We study the effects of arterial wall stiffness on coronary blood flow in the left circumflex artery (LCX). Different diseased cases indicate that distinct pathological reactions of the cardiovascular system can be better distinguished through Wave Intensity analysis, which shows agreement with clinical observations. Finally, the feedback pressure in terminal vessels and measurement deviation are also investigated by changing parameters in the LCX. We find that larger feedback pressure increases the backward wave and decreases the forward one. Although simplified, this 1D model provides new insight into coronary hemodynamics in healthy and diseased conditions. We believe that this approach offers reference resources for studies on coronary circulation disease diagnosis, treatment and simulation.

Clinical assessment of a non-invasive wearable MEMS pressure sensor array for monitoring of arterial pulse waveform, heart rate and detection of atrial fibrillation

There is an unmet clinical need for a low cost and easy to use wearable devices for continuous cardiovascular health monitoring. A flexible and wearable wristband, based on microelectromechanical sensor (MEMS) elements array was developed to support this need. The performance of the device in cardiovascular monitoring was investigated by (i) comparing the arterial pressure waveform recordings to the gold standard, invasive catheter recording (n = 18), (ii) analyzing the ability to detect irregularities of the rhythm (n = 7), and (iii) measuring the heartrate monitoring accuracy (n = 31). Arterial waveforms carry important physiological information and the comparison study revealed that the recordings made with the wearable device and with the gold standard device resulted in almost identical (r = 0.9–0.99) pulse waveforms. The device can measure the heart rhythm and possible irregularities in it. A clustering analysis demonstrates a perfect classification accuracy between atrial fibrillation (AF) and sinus rhythm. The heartrate monitoring study showed near perfect beat-to-beat accuracy (sensitivity = 99.1%, precision = 100%) on healthy subjects. In contrast, beat-to-beat detection from coronary artery disease patients was challenging, but the averaged heartrate was extracted successfully (95% CI: −1.2 to 1.1 bpm). In conclusion, the results indicate that the device could be useful in remote monitoring of cardiovascular diseases and personalized medicine.

Wave intensity analysis in the internal carotid artery of hypertensive subjects using phase-contrast MR angiography and preliminary assessment of the effect of vessel morphology on wave dynamics

Objective: Hypertension is associated with reduced cerebral blood flow, but it is not known how this impacts on wave dynamics or potentially relates to arterial morphology. Given the location of the internal carotid artery (ICA) and risks associated with invasive measurements, wave dynamics in this artery have not been extensively assessed in vivo. This study explores the feasibility of studying wave dynamics in the internal carotid artery non-invasively. Approach: Normotensive, uncontrolled and controlled hypertensive participants were recruited (daytime ambulatory blood pressure  <135/85 mmHg and  >135/85 mmHg, respectively; n  =  38). Wave intensity, reservoir pressure and statistical shape analyses were performed on the right ICA and ascending aorta high-resolution phase-contrast magnetic resonance angiography data. Main results: Wave speed in the aorta was significantly lower in normotensive compared to hypertensive participants (6.7  ±  1.8 versus 11.2  ±  6.2 m s⁻¹ for uncontrolled and 11.8  ±  4.6 m s⁻¹ for controlled hypertensives, p  =  0.02), whilst there were no differences in wave speed in the ICA. There were no significant differences between the groups for the wave intensity or reservoir pressure. Interestingly, a significant association between the anatomy of the ICA and wave energy (FCW and size, r²  =  0.12, p  =  0.04) was found. Significance: This study shows it is feasible to study wave dynamics in the ICA non-invasively. Whilst changes in aortic wave speed confirmed an expected increase in arterial stiffness, this was not observed in the ICA. This might suggest a protective mechanism in the cerebral circulation, in conjunction with the effect of vessel tortuosity. Furthermore, it was observed that ICA shape correlated with wave energy but not wave speed.

Bayesian sensitivity analysis of a 1D vascular model with Gaussian process emulators

One-dimensional models of the cardiovascular system can capture the physics of pulse waves but involve many parameters. Since these may vary among individuals, patient-specific models are difficult to construct. Sensitivity analysis can be used to rank model parameters by their effect on outputs and to quantify how uncertainty in parameters influences output uncertainty. This type of analysis is often conducted with a Monte Carlo method, where large numbers of model runs are used to assess input-output relations. The aim of this study was to demonstrate the computational efficiency of variance-based sensitivity analysis of 1D vascular models using Gaussian process emulators, compared to a standard Monte Carlo approach. The methodology was tested on four vascular networks of increasing complexity to analyse its scalability. The computational time needed to perform the sensitivity analysis with an emulator was reduced by the 99.96% compared to a Monte Carlo approach. Despite the reduced computational time, sensitivity indices obtained using the two approaches were comparable. The scalability study showed that the number of mechanistic simulations needed to train a Gaussian process for sensitivity analysis was of the order O(d), rather than O(d×103) needed for Monte Carlo analysis (where d is the number of parameters in the model). The efficiency of this approach, combined with capacity to estimate the impact of uncertain parameters on model outputs, will enable development of patient-specific models of the vascular system, and has the potential to produce results with clinical relevance.

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.

Pulse Waveform Analysis: Is It Ready for Prime Time?

PURPOSE OF REVIEW

Arterial pulse waveform analysis has a long tradition but has not pervaded medical routine yet. This review aims to answer the question whether the methodology is ready for prime time use. The current methodological consensus is assessed, existing technologies for waveform measurement and pulse wave analysis are discussed, and further needs for a widespread use are proposed.

RECENT FINDINGS

A consensus document on the understanding and analysis of the pulse waveform was published recently. Although still some discrepancies remain, the analysis using both pressure and flow waves is favoured. However, devices which enable pulse wave measurement are limited, and the comparability between devices is not sufficiently given. Pulse waveform analysis has the potential for prime time. It is currently on a way towards broader use, but still needs to overcome challenges before settling its role in medical routine.

Relative contributions from the ventricle and arterial tree to arterial pressure and its amplification: an experimental study

The present study distinguishes contributions from cardiac and arterial parameters to elevated blood pressure and pressure amplification. Most importantly, it offers the first evidence that ventricular inotropy, an indicator of ventricular function, is an independent determinant of pressure amplification and could be measured with such established devices such as the SphygmoCor.

Arterial pressure is an important diagnostic parameter for cardiovascular disease. However, relative contributions of individual ventricular and arterial parameters in generating and augmenting pressure are not understood. Using a novel experimental arterial model, our aim was to characterize individual parameter contributions to arterial pressure and its amplification. A piston-driven ventricle provided programmable stroke profiles into various silicone arterial trees and a bovine aorta. Inotropy was varied in the ventricle, and arterial parameters modulated included wall thickness, taper and diameter, the presence of bifurcation, and a native aorta (bovine) versus silicone. Wave reflection at bifurcations was measured and compared with theory, varying parent-to-child tube diameter ratios, and branch angles. Intravascular pressure-tip wires and ultrasonic flow probes measured pressure and flow. Increasing ventricular inotropy independently augmented pressure amplification from 17% to 61% between the lower and higher systolic gradient stroke profiles in the silicone arterial network and from 10% to 32% in the bovine aorta. Amplification increased with presence of a bifurcation, decreasing wall thickness and vessel taper. Pulse pressure increased with increasing wall thickness (stiffness) and taper angle and decreasing diameter. Theoretical predictions of wave transmission through bifurcations werre similar to measurements (correlation: 0.91, R² = 0.94) but underestimated wave reflection (correlation: 0.75, R² = 0.94), indicating energy losses during mechanical wave reflection. This study offers the first comprehensive investigation of contributors to hypertensive pressure and its propagation throughout the arterial tree. Importantly, ventricular inotropy plays a crucial role in the amplification of peripheral pressure wave, which offers opportunity for noninvasive assessment of ventricular health.

NEW & NOTEWORTHY The present study distinguishes contributions from cardiac and arterial parameters to elevated blood pressure and pressure amplification. Most importantly, it offers the first evidence that ventricular inotropy, an indicator of ventricular function, is an independent determinant of pressure amplification and could be measured with such established devices such as the SphygmoCor.

Functional assessment of the stenotic carotid artery by CFD-based pressure gradient evaluation

The functional assessment of a hemodynamic significant stenosis base on blood pressure variation has been applied for evaluation of the myocardial ischemic event. This functional assessment shows great potential for improving the accuracy of the classification of the severity of carotid stenosis. To explore the value of grading the stenosis using a pressure gradient (PG)-we had reconstructed patient-specific carotid geometries based on MRI images-computational fluid dynamics were performed to analyze the PG in their stenotic arteries. Doppler ultrasound image data and the corresponding MRI image data of 19 patients with carotid stenosis were collected. Based on these, 31 stenotic carotid arterial geometries were reconstructed. A combinatorial boundary condition method was implemented for steady-state computer fluid dynamics simulations. Anatomic parameters, including tortuosity (T), the angle of bifurcation, and the cross-sectional area of the remaining lumen, were collected to investigate the effect on the pressure distribution. The PG is highly correlated with the severe stenosis (r = 0.902), whereas generally, the T and the angle of the bifurcation negatively correlate to the pressure drop of the internal carotid artery stenosis. The calculation required <10 min/case, which made it prepared for the fast diagnosis of the severe stenosis. According to the results, we had proposed a potential threshold value for distinguishing severe stenosis from mild-moderate stenosis (PG = 0.88). In conclusion, the PG could serve as the additional factor for improving the accuracy of grading the severity of the stenosis.

A Coupled Lumped-Parameter and Distributed Network Model for Cerebral Pulse-Wave Hemodynamics

The cerebral circulation is unique in its ability to maintain blood flow to the brain under widely varying physiologic conditions. Incorporating this autoregulatory response is necessary for cerebral blood flow (CBF) modeling, as well as investigations into pathological conditions. We discuss a one-dimensional (1D) nonlinear model of blood flow in the cerebral arteries coupled to autoregulatory lumped-parameter (LP) networks. The LP networks incorporate intracranial pressure (ICP), cerebrospinal fluid (CSF), and cortical collateral blood flow models. The overall model is used to evaluate changes in CBF due to occlusions in the middle cerebral artery (MCA) and common carotid artery (CCA). Velocity waveforms at the CCA and internal carotid artery (ICA) were examined prior and post MCA occlusion. Evident waveform changes due to the occlusion were observed, providing insight into cerebral vasospasm monitoring by morphological changes of the velocity or pressure waveforms. The role of modeling of collateral blood flows through cortical pathways and communicating arteries was also studied. When the MCA was occluded, the cortical collateral flow had an important compensatory role, whereas the communicating arteries in the circle of Willis (CoW) became more important when the CCA was occluded. To validate the model, simulations were conducted to reproduce a clinical test to assess dynamic autoregulatory function, and results demonstrated agreement with published measurements.

Novel wave power analysis linking pressure-flow waves, wave potential, and the forward and backward components of hydraulic power

Wave intensity analysis provides detailed insights into factors influencing hemodynamics. However, wave intensity is not a conserved quantity, so it is sensitive to diameter variations and is not distributed among branches of a junction. Moreover, the fundamental relation between waves and hydraulic power is unclear. We, therefore, propose an alternative to wave intensity called “wave power,” calculated via incremental changes in pressure and flow (dPdQ) and a novel time-domain separation of hydraulic pressure power and kinetic power into forward and backward wave-related components (ΠP± and ΠQ±). Wave power has several useful properties: 1) it is obtained directly from flow measurements, without requiring further calculation of velocity; 2) it is a quasi-conserved quantity that may be used to study the relative distribution of waves at junctions; and 3) it has the units of power (Watts). We also uncover a simple relationship between wave power and changes in ΠP± and show that wave reflection reduces transmitted power. Absolute values of ΠP± represent wave potential, a recently introduced concept that unifies steady and pulsatile aspects of hemodynamics. We show that wave potential represents the hydraulic energy potential stored in a compliant pressurized vessel, with spatial gradients producing waves that transfer this energy. These techniques and principles are verified numerically and also experimentally with pressure/flow measurements in all branches of a central bifurcation in sheep, under a wide range of hemodynamic conditions. The proposed “wave power analysis,” encompassing wave power, wave potential, and wave separation of hydraulic power provides a potent time-domain approach for analyzing hemodynamics.

Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model

One-dimensional (1D) modeling is a widely adopted approach for studying wave propagation phenomena in the arterial system. Despite the frequent use of the Windkessel (WK) model to prescribe outflow boundary conditions for 1D arterial tree models, it remains unclear to what extent the inherent limitation of the WK model in describing wave propagation in distal vasculatures affect hemodynamic variables simulated at the arterial level. In the present study, a 1D model of the arterial tree was coupled respectively with a WK boundary model and a structured-tree (ST) boundary model, yielding two types of arterial tree models. The effective resistances, compliances and inductances of the WK and ST boundary models were matched to facilitate quantitative comparisons. Obtained results showed that pressure/flow waves simulated by the two models were comparable in the aorta, whereas, their discrepancies increased towards the periphery. Wave analysis revealed that the differences in reflected waves generated by the boundary models were the major sources of pressure wave discrepancies observed in large arteries. Additional simulations performed under aging conditions demonstrated that arterial stiffening with age enlarged the discrepancies, but with the effects being partly counteracted by physiological aortic dilatation with age. These findings suggest that the method adopted for modeling the outflow boundary conditions has considerable influence on the performance of a 1D arterial tree model, with the extent of influence varying with the properties of the arterial system.

A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling

Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.

Measurement and modeling of coronary blood flow

Ischemic heart disease that comprises both coronary artery disease and microvascular disease is the single greatest cause of death globally. In this context, enhancing our understanding of the interaction of coronary structure and function is not only fundamental for advancing basic physiology but also crucial for identifying new targets for treating these diseases. A central challenge for understanding coronary blood flow is that coronary structure and function exhibit different behaviors across a range of spatial and temporal scales. While experimental studies have sought to understand this feature by isolating specific mechanisms, in tandem, computational modeling is increasingly also providing a unique framework to integrate mechanistic behaviors across different scales. In addition, clinical methods for assessing coronary disease severity are continuously being informed and updated by findings in basic physiology. Coupling these technologies, computational modeling of the coronary circulation is emerging as a bridge between the experimental and clinical domains, providing a framework to integrate imaging and measurements from multiple sources with mathematical descriptions of governing physical laws. State-of-the-art computational modeling is being used to combine mechanistic models with data to provide new insight into coronary physiology, optimization of medical technologies, and new applications to guide clinical practice.

Reducing the number of parameters in 1D arterial blood flow modeling: less is more for patient-specific simulations

Patient-specific one-dimensional (1D) blood flow modeling requires estimating model parameters from available clinical data, ideally acquired noninvasively. The larger the number of arterial segments in a distributed 1D model, the greater the number of input parameters that need to be estimated. We investigated the effect of a reduction in the number of arterial segments in a given distributed 1D model on the shape of the simulated pressure and flow waveforms. This is achieved by systematically lumping peripheral 1D model branches into windkessel models that preserve the net resistance and total compliance of the original model. We applied our methodology to a model of the 55 larger systemic arteries in the human and to an extended 67-artery model that contains the digital arteries that perfuse the fingers. Results show good agreement in the shape of the aortic and digital waveforms between the original 55-artery (67-artery) and reduced 21-artery (37-artery) models. Reducing the number of segments also enables us to investigate the effect of arterial network topology (and hence reflection sites) on the shape of waveforms. Results show that wave reflections in the thoracic aorta and renal arteries play an important role in shaping the aortic pressure and flow waves and in generating the second peak of the digital pressure and flow waves. Our novel methodology is important to simplify the computational domain while maintaining the precision of the numerical predictions and to assess the effect of wave reflections.