Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements

Estimation of pulmonary vascular resistance for Glenn physiology

Children with single ventricle heart disease typically require a series of three operations, (1) Norwood, (2) Glenn, and (3) Fontan, which ultimately results in complete separation of the pulmonary and systemic circuits to improve pulmonary/systemic circulation. In the last stage, the Fontan operation, the inferior vena cava (IVC) is connected to the pulmonary arteries (PAs), allowing the remainder of deoxygenated blood to passively flow to the pulmonary circuit. It is hypothesized that optimizing the Fontan anatomy would lead to decreased power loss and more balanced hepatic flow distribution. One approach to optimizing the geometry is to create a patient-specific digital twin to simulate various configurations of the Fontan conduit, which requires a computational model of the proximal PA anatomy and resistance, as well as the distal Pulmonary Vascular Resistance (PVR), at the Glenn stage. To that end, an optimization pipeline was developed using 3D computational fluid dynamics (CFD) and 0D lumped parameter (LP) simulations to iteratively refine the PVR of each lung by minimizing the simulated flow and pressure error relative to patients' cardiac magnetic resonance (CMR) and catheterization (CATH) data. While the PVR can also be estimated directly by computing the ratio of pressure gradients and flow from CATH and CMR data, the computational approach can separately identify the different components of PVR along the Glenn pathway, allowing for a more detailed depiction of the Glenn vasculature. Results indicate good correlation between the optimized PVR of the CFD and LP models (n = 16), with an intraclass correlation coefficient (ICC) of 0.998 (p = 0.976) and 0.991 (p = 0.943) for the left and right lung, respectively. Furthermore, compared to CMR flow and CATH pressure data, the optimized PVR estimates result in mean outlet flow and pressure errors of less than 5%. The optimized PVR estimates also agree well with the computed PVR estimates from CATH pressure and CMR flow for both lungs, yielding a mean difference of less than 4%.

Age and sex-dependent sensitivity analysis of a common carotid artery model

The common carotid artery (CCA) is an accessible and informative site for assessing cardiovascular function which makes it a prime candidate for clinically relevant computational modelling. The interpretation of supplemental information possible through modelling is encumbered by measurement uncertainty and population variability in model parameters. The distribution of model parameters likely depends on the specific sub-population of interest and delineation based on sex, age or health status may correspond to distinct ranges of typical parameter values. To assess this impact in a 1D-CCA-model, we delineated specific sub-populations based on age, sex and health status and carried out uncertainty quantification and sensitivity analysis for each sub-population. We performed a structured literature review to characterize sub-population-specific variabilities for eight model parameters without consideration of health status; variations for a healthy sub-populations were based on previously established references values. The variabilities of diameter and distensibility found in the literature review differed from those previously established in a healthy population. Model diameter change and pulse pressure were most sensitive to variations in distensibility, while pressure was most sensitive to resistance in the Windkessel model for all groups. Uncertainties were lower when variabilities were based on a healthy sub-population; however, the qualitative distribution of sensitivity indices was largely similar between the healthy and general population. Average sensitivity of the pressure waveform showed a moderate dependence on age with decreasing sensitivity to distal resistance and increasing sensitivity to distensibility and diameter. The female population was less sensitive to variations in diameter but more sensitive to distensibility coefficient than the male population. Overall, as hypothesized input variabilities differed between sub-populations and resulted in distinct uncertainties and sensitivities of the 1D-CCA-model outputs, particularly over age for the pressure waveform and between males and females for pulse pressure.

Central arterial pressure estimation based on two peripheral pressure measurements using one-dimensional blood flow simulation

Aortic pressure can be estimated using one-dimensional arterial flow simulations. This study demonstrates that two peripheral pressure measurements can be used to acquire the central pressure curve through the patient-specific optimization of a set of system parameters. Radial and carotid pressure measurements and parameter optimization were performed in the case of 62 patients. The two calculated aortic curves were in good agreement, Systolic and Mean Blood Pressures differed on average by 0.5 and -0.5 mmHg, respectively. Good agreement was achieved with the transfer function method as well. The effect of carotid clamping is demonstrated using one resulting patient-specific arterial network.

An in silico study of the effects of cardiovascular aging on carotid flow waveforms and indexes in a virtual population

Cardiovascular aging is strongly associated with increased risk of cardiovascular disease and mortality. Moreover, health and lifestyle factors may accelerate age-induced alterations, such as increased arterial stiffness and wall dilation, beyond chronological age, making the clinical assessment of cardiovascular aging an important prompt for preventative action. Carotid flow waveforms contain information about age-dependent cardiovascular properties, and their ease of measurement via noninvasive Doppler ultrasound (US) makes their analysis a promising tool for the routine assessment of cardiovascular aging. In this work, the impact of different aging processes on carotid waveform morphology and derived indexes is studied in silico, with the aim of establishing the clinical potential of a carotid US-based assessment of cardiovascular aging. One-dimensional (1-D) hemodynamic modeling was employed to generate an age-specific virtual population (VP) of N = 5,160 realistic carotid hemodynamic waveforms. The resulting VP was statistically validated against in vivo aging trends in waveforms and indexes from the literature, and simulated waveforms were studied in relation to age and underlying cardiovascular parameters. In our study, the carotid flow augmentation index (FAI) significantly increased with age (with a median increase of 50% from the youngest to the oldest age group) and was strongly correlated to local arterial stiffening (r = 0.94). The carotid pulsatility index (PI), which showed less pronounced age variation, was inversely correlated with the reflection coefficient at the carotid branching (r = -0.88) and directly correlated with carotid net forward wave energy (r = 0.90), corroborating previous literature where it was linked to increased risk of cerebrovascular damage in the elderly. There was a high correlation between corrected carotid flow time (ccFT) and cardiac output (CO) (r = 0.99), which was not affected by vascular age. This study highlights the potential of carotid waveforms as a valuable tool for the assessment of cardiovascular aging.NEW & NOTEWORTHY An age-specific virtual population was generated based on a 1-D model of the arterial circulation, including newly defined literature-based specific age variations in carotid vessel properties. Simulated carotid flow/velocity waveforms, indexes, and age trends were statistically validated against in vivo data from the literature. A comprehensive study of the impact of aging on carotid flow waveform morphology was performed, and the mechanisms influencing different carotid indexes were elucidated. Notably, flow augmentation index (FAI) was found to be a strong indicator of local carotid stiffness.

Tube law parametrization using in vitro data for one-dimensional blood flow in arteries and veins: TUBE LAW PARAMETRIZATION IN ARTERIES AND VEINS

The deformability of blood vessels in one-dimensional blood flow models is typically described through a pressure-area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena. Here, we present a novel mathematical-property-preserving approach for the estimation of the parameters of the elastic and viscoelastic tube laws. Our goal was to estimate the parameters by using ovine and human in vitro data, while constraining them to meet prescribed mathematical properties. Results show that both elastic and viscoelastic tube laws accurately describe experimental pressure-area data concerning both quantitative and qualitative aspects. Additionally, the viscoelastic tube law can provide a qualitative explanation for the observed hysteresis cycles. The two models were evaluated using two approaches: (i) allowing all parameters to freely vary within their respective ranges and (ii) fixing some of the parameters. The former approach was found to be the most suitable for reproducing pressure-area curves.

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.

Central arterial pressure and patient-specific model parameter estimation based on radial pressure measurements

One-dimensional arterial flow simulations are suitable to estimate the aortic pressure from peripheral measurements in a patient-specific arterial network. This study introduces a reduction of the system parameters, and a novel calculation method to estimate the patient-specific set and the aortic curve based on radial applanation tonometry. Peripheral and aortic pressure curves were measured in patients, optimization were carried out. The aortic pressure curves were reproduced well, with an overestimation of the measured Systolic and Mean Blood Pressures on average by 0.6 and 0.5 mmHg respectively, and the Root Mean Square Difference of the curves was 3 mmHg on average.

An approach to study recruitment/derecruitment dynamics in a patient-specific computational model of an injured human lung

We present a new approach for physics-based computational modeling of diseased human lungs. Our main object is the development of a model that takes the novel step of incorporating the dynamics of airway recruitment/derecruitment into an anatomically accurate, spatially resolved model of respiratory system mechanics, and the relation of these dynamics to airway dimensions and the biophysical properties of the lining fluid. The importance of our approach is that it potentially allows for more accurate predictions of where mechanical stress foci arise in the lungs, since it is at these locations that injury is thought to arise and propagate from. We match the model to data from a patient with acute respiratory distress syndrome (ARDS) to demonstrate the potential of the model for revealing the underlying derangements in ARDS in a patient-specific manner. To achieve this, the specific geometry of the lung and its heterogeneous pattern of injury are extracted from medical CT images. The mechanical behavior of the model is tailored to the patient's respiratory mechanics using measured ventilation data. In retrospective simulations of various clinically performed, pressure-driven ventilation profiles, the model adequately reproduces clinical quantities measured in the patient such as tidal volume and change in pleural pressure. The model also exhibits physiologically reasonable lung recruitment dynamics and has the spatial resolution to allow the study of local mechanical quantities such as alveolar strains. This modeling approach advances our ability to perform patient-specific studies in silico, opening the way to personalized therapies that will optimize patient outcomes.

A review on the biomechanical behaviour of the aorta

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.

Modeling the effect of patient size on cerebral perfusion during veno-arterial extracorporeal membrane oxygenation

INTRODUCTION

A well-known complication of veno-arterial extracorporeal membrane oxygenation (VA ECMO) is differential hypoxia, in which poorly-oxygenated blood ejected from the left ventricle mixes with and displaces well-oxygenated blood from the circuit, thereby causing cerebral hypoxia and ischemia. We sought to characterize the impact of patient size and anatomy on cerebral perfusion under a range of different VA ECMO flow conditions.

METHODS

We use one-dimensional (1D) flow simulations to investigate mixing zone location and cerebral perfusion across 10 different levels of VA ECMO support in eight semi-idealized patient geometries, for a total of 80 scenarios. Measured outcomes included mixing zone location and cerebral blood flow (CBF).

RESULTS

Depending on patient anatomy, we found that a VA ECMO support ranging between 67-97% of a patient's ideal cardiac output was needed to perfuse the brain. In some cases, VA ECMO flows exceeding 90% of the patient's ideal cardiac output are needed for adequate cerebral perfusion.

CONCLUSIONS

Individual patient anatomy markedly affects mixing zone location and cerebral perfusion in VA ECMO. Future fluid simulations of VA ECMO physiology should incorporate varied patient sizes and geometries in order to best provide insights toward reducing neurologic injury and improved outcomes in this patient population.

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.

First blood: An efficient, hybrid one- and zero-dimensional, modular hemodynamic solver

Low-dimensional (1D or 0D) models can describe the whole human blood circulation, for example, 1D distributed parameter model for the arterial network and 0D concentrated models for the heart or other organs. This paper presents a combined 1D-0D solver, called first_blood, that solves the governing equations of fluid dynamics to model low-dimensional hemodynamic effects. An extended method of characteristics is applied here to solve the momentum, and mass conservation equations and the viscoelastic wall model equation, mimicking the material properties of arterial walls. The heart and the peripheral lumped models are solved with a general zero-dimensional (0D) nonlinear solver. The model topology can be modular, that is, first_blood can solve any 1D-0D hemodynamic model. To demonstrate the applicability of first_blood, the human arterial system, the heart and the peripherals are modelled using the solver. The simulation time of a heartbeat takes around 2 s, that is, first_blood requires only twice the real-time for the simulation using an average PC, which highlights the computational efficiency. The source code is available on GitHub, that is, it is open source. The model parameters are based on the literature suggestions and on the validation of output data to obtain physiologically relevant results.

One-dimensional analysis method of pulsatile blood flow in arterial network for REBOA operations

Based on the generalized Darcy model, here we develop a linear one-dimensional (1D) composite model to predict the effects of the inserted balloon under REBOA operations on the dynamic characteristics of blood flow in flexible arterial networks. We first consider the effect of the decrease of cardiac output under different degrees of blood loss through employing the fourth-order lumped parameter model of cardiovascular system. Then, the effect of the inserted balloon is included by developing the relation between flow resistance and occlusion ratio with the neural network approach. Finally, the accuracy of the developed 1D composite model for REBOA operations, which can be solved analytically in the frequency domain, is verified by comparing to computational fluid dynamics (CFD) simulations. It is demonstrated that the 1D model is able to reproduce main features of the systemic circulation under balloon occlusion of the aorta during REBOA surgery. The 1D composite model could substantially reduce the computational time, which makes it possible to give the instant prediction of the working parameters during RABOA operations.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

Wave reflection quantification analysis and personalized flow wave estimation based on the central aortic pressure waveform

Pulse wave reflections reflect cardiac afterload and perfusion, which yield valid indicators for monitoring cardiovascular status. Accurate quantification of pressure wave reflections requires the measurement of aortic flow wave. However, direct flow measurement involves extra equipment and well-trained operator. In this study, the personalized aortic flow waveform was estimated from the individual central aortic pressure waveform (CAPW) based on pressure-flow relations. The separated forward and backward pressure waves were used to calculate wave reflection indices such as reflection index (RI) and reflection magnitude (RM), as well as the central aortic pulse transit time (PTT). The effectiveness and feasibility of the method were validated by a set of clinical data (13 participants) and the Nektar1D Pulse Wave Database (4,374 subjects). The performance of the proposed personalized flow waveform method was compared with the traditional triangular flow waveform method and the recently proposed lognormal flow waveform method by statistical analyses. Results show that the root mean square error calculated by the personalized flow waveform approach is smaller than that of the typical triangular and lognormal flow methods, and the correlation coefficient with the measured flow waveform is higher. The estimated personalized flow waveform based on the characteristics of the CAPW can estimate wave reflection indices more accurately than the other two methods. The proposed personalized flow waveform method can be potentially used as a convenient alternative for the measurement of aortic flow waveform.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

Analysis identifying minimal governing parameters for clinically accurate in silico fractional flow reserve

Background

Personalized hemodynamic models can accurately compute fractional flow reserve (FFR) from coronary angiograms and clinical measurements (FFR baseline ), but obtaining patient-specific data could be challenging and sometimes not feasible. Understanding which measurements need to be patient-tuned vs. patient-generalized would inform models with minimal inputs that could expedite data collection and simulation pipelines.

Aims

To determine the minimum set of patient-specific inputs to compute FFR using invasive measurement of FFR (FFR invasive ) as gold standard.

Materials and Methods

Personalized coronary geometries ( N = 50 ) were derived from patient coronary angiograms. A computational fluid dynamics framework, FFR baseline , was parameterized with patient-specific inputs: coronary geometry, stenosis geometry, mean arterial pressure, cardiac output, heart rate, hematocrit, and distal pressure location. FFR baseline was validated against FFR invasive and used as the baseline to elucidate the impact of uncertainty on personalized inputs through global uncertainty analysis. FFR streamlined was created by only incorporating the most sensitive inputs and FFR semi-streamlined additionally included patient-specific distal location.

Results

FFR baseline was validated against FFR invasive via correlation ( r = 0.714 , p < 0.001 ), agreement (mean difference: 0.01 ± 0.09 ), and diagnostic performance (sensitivity: 89.5%, specificity: 93.6%, PPV: 89.5%, NPV: 93.6%, AUC: 0.95). FFR semi-streamlined provided identical diagnostic performance with FFR baseline . Compared to FFR baseline vs. FFR invasive , FFR streamlined vs. FFR invasive had decreased correlation ( r = 0.64 , p < 0.001 ), improved agreement (mean difference: 0.01 ± 0.08 ), and comparable diagnostic performance (sensitivity: 79.0%, specificity: 90.3%, PPV: 83.3%, NPV: 87.5%, AUC: 0.90).

Conclusion

Streamlined models could match the diagnostic performance of the baseline with a full gamut of patient-specific measurements. Capturing coronary hemodynamics depended most on accurate geometry reconstruction and cardiac output measurement.

Computational modelling and application of mechanical waves to detect arterial network anomalies: Diagnosis of common carotid stenosis

BACKGROUND AND OBJECTIVE

This paper proposes a novel strategy to localize anomalies in the arterial network based on its response to controlled transient waves. The idea is borrowed from system identification theories in which wave reflections can render significant information about a target system. Cardiovascular system studies often focus on the waves originating from the heart pulsations, which are of low bandwidth and, hence, can hardly carry information about the arteries with the desired resolution.

METHODS

Our strategy uses a relatively higher bandwidth transient signal to characterize healthy and unhealthy arterial networks through a frequency response function (FRF). We tested our novel approach on data simulated using a one-dimensional cardiovascular model that produced pulse waves in the larger arteries of the arterial network. Specifically, we excited the blood flow from the brachial artery with a relatively high bandwidth flow disturbance and collected the subsequent pressure waveform at peripheral positions. To better differentiate FRFs of healthy and unhealthy networks, we used a FRF that removes the effects of heart pulsations.

RESULTS

Results demonstrate the ability of the proposed FRF to detect and follow-up on the development of a common carotid artery (CCA) stenosis. We tested distinct geometrical variations of the stenosis (size, length and position) and observed differences between the FRFs of healthy and unhealthy networks in all cases; such differences were mainly due to geometrical variations determined by the stenosis.

CONCLUSIONS

We have provided a theoretical proof of concept that demonstrates the ability of our novel strategy to detect and track the development of CCA stenosis by using peripheral pressure waves that can be measured non-invasively in clinical practice.

A coupled atrioventricular-aortic setup for in-vitro hemodynamic study of the systemic circulation: Design, fabrication, and physiological relevancy

In-vitro models of the systemic circulation have gained a lot of interest for fundamental understanding of cardiovascular dynamics and for applied hemodynamic research. In this study, we introduce a physiologically accurate in-vitro hydraulic setup that models the hemodynamics of the coupled atrioventricular-aortic system. This unique experimental simulator has three major components: 1) an arterial system consisting of a human-scale artificial aorta along with the main branches, 2) an artificial left ventricle (LV) sac connected to a programmable piston-in-cylinder pump for simulating cardiac contraction and relaxation, and 3) an artificial left atrium (LA). The setup is designed in such a way that the basal LV is directly connected to the aortic root via an aortic valve, and to the LA via an artificial mitral valve. As a result, two-way hemodynamic couplings can be achieved for studying the effects that the LV, aorta, and LA have on each other. The collected pressure and flow measurements from this setup demonstrate a remarkable correspondence to clinical hemodynamics. We also investigate the physiological relevancies of isolated effects on cardiovascular hemodynamics of various major global parameters found in the circulatory system, including LV contractility, LV preload, heart rate, aortic compliance, and peripheral resistance. Subsequent control over such parameters ultimately captures physiological hemodynamic effects of LV systolic dysfunction, preload (cardiac) diseases, and afterload (arterial) diseases. The detailed design and fabrication of the proposed setup is also provided.

Automated generation of 0D and 1D reduced-order models of patient-specific blood flow

Three-dimensional (3D) cardiovascular fluid dynamics simulations typically require hours to days of computing time on a high-performance computing cluster. One-dimensional (1D) and lumped-parameter zero-dimensional (0D) models show great promise for accurately predicting blood bulk flow and pressure waveforms with only a fraction of the cost. They can also accelerate uncertainty quantification, optimization, and design parameterization studies. Despite several prior studies generating 1D and 0D models and comparing them to 3D solutions, these were typically limited to either 1D or 0D and a singular category of vascular anatomies. This work proposes a fully automated and openly available framework to generate and simulate 1D and 0D models from 3D patient-specific geometries, automatically detecting vessel junctions and stenosis segments. Our only input is the 3D geometry; we do not use any prior knowledge from 3D simulations. All computational tools presented in this work are implemented in the open-source software platform SimVascular. We demonstrate the reduced-order approximation quality against rigid-wall 3D solutions in a comprehensive comparison with N = 72 publicly available models from various anatomies, vessel types, and disease conditions. Relative average approximation errors of flows and pressures typically ranged from 1% to 10% for both 1D and 0D models, measured at the outlets of terminal vessel branches. In general, 0D model errors were only slightly higher than 1D model errors despite requiring only a third of the 1D runtime. Automatically generated ROMs can significantly speed up model development and shift the computational load from high-performance machines to personal computers.

Physics-Informed Neural Networks for Brain Hemodynamic Predictions Using Medical Imaging

Determining brain hemodynamics plays a critical role in the diagnosis and treatment of various cerebrovascular diseases. In this work, we put forth a physics-informed deep learning framework that augments sparse clinical measurements with one-dimensional (1D) reduced-order model (ROM) simulations to generate physically consistent brain hemodynamic parameters with high spatiotemporal resolution. Transcranial Doppler (TCD) ultrasound is one of the most common techniques in the current clinical workflow that enables noninvasive and instantaneous evaluation of blood flow velocity within the cerebral arteries. However, it is spatially limited to only a handful of locations across the cerebrovasculature due to the constrained accessibility through the skull's acoustic windows. Our deep learning framework uses in vivo real-time TCD velocity measurements at several locations in the brain combined with baseline vessel cross-sectional areas acquired from 3D angiography images and provides high-resolution maps of velocity, area, and pressure in the entire brain vasculature. We validate the predictions of our model against in vivo velocity measurements obtained via four-dimensional (4D) flow magnetic resonance imaging (MRI) scans. We then showcase the clinical significance of this technique in diagnosing cerebral vasospasm (CVS) by successfully predicting the changes in vasospastic local vessel diameters based on corresponding sparse velocity measurements. We show this capability by generating synthetic blood flow data after cerebral vasospasm at various levels of stenosis. Here, we demonstrate that the physics-based deep learning approach can estimate and quantify the subject-specific cerebral hemodynamic variables with high accuracy despite lacking knowledge of inlet and outlet boundary conditions, which is a significant limitation for the accuracy of the conventional purely physics-based computational models.

Personalized Pre- and Post-Operative Hemodynamic Assessment of Aortic Coarctation from 3D Rotational Angiography

PURPOSE

Coarctation of Aorta (CoA) is a congenital disease consisting of a narrowing that obstructs the systemic blood flow. This proof-of-concept study aimed to develop a framework for automatically and robustly personalizing aortic hemodynamic computations for the assessment of pre- and post-intervention CoA patients from 3D rotational angiography (3DRA) data.

METHODS

We propose a framework that combines hemodynamic modelling and machine learning (ML) based techniques, and rely on 3DRA data for non-invasive pressure computation in CoA patients. The key features of our framework are a parameter estimation method for calibrating inlet and outlet boundary conditions, and regional mechanical wall properties, to ensure that the computational results match the patient-specific measurements, and an improved ML based pressure drop model capable of predicting the instantaneous pressure drop for a wide range of flow conditions and anatomical CoA variations.

RESULTS

We evaluated the framework by investigating 6 patient datasets, under pre- and post-operative setting, and, since all calibration procedures converged successfully, the proposed approach is deemed robust. We compared the peak-to-peak and the cycle-averaged pressure drop computed using the reduced-order hemodynamic model with the catheter based measurements, before and after virtual and actual stenting. The mean absolute error for the peak-to-peak pressure drop, which is the most relevant measure for clinical decision making, was 2.98 mmHg for the pre- and 2.11 mmHg for the post-operative setting. Moreover, the proposed method is computationally efficient: the average execution time was of only [Formula: see text] minutes on a standard hardware configuration.

CONCLUSION

The use of 3DRA for hemodynamic modelling could allow for a complete hemodynamic assessment, as well as virtual interventions or surgeries and predictive modeling. However, before such an approach can be used routinely, significant advancements are required for automating the workflow.

Wave Intensity Analysis Combined With Machine Learning can Detect Impaired Stroke Volume in Simulations of Heart Failure

Heart failure is treatable, but in the United Kingdom, the 1-, 5- and 10-year mortality rates are 24.1, 54.5 and 75.5%, respectively. The poor prognosis reflects, in part, the lack of specific, simple and affordable diagnostic techniques; the disease is often advanced by the time a diagnosis is made. Previous studies have demonstrated that certain metrics derived from pressure-velocity-based wave intensity analysis are significantly altered in the presence of impaired heart performance when averaged over groups, but to date, no study has examined the diagnostic potential of wave intensity on an individual basis, and, additionally, the pressure waveform can only be obtained accurately using invasive methods, which has inhibited clinical adoption. Here, we investigate whether a new form of wave intensity based on noninvasive measurements of arterial diameter and velocity can detect impaired heart performance in an individual. To do so, we have generated a virtual population of two-thousand elderly subjects, modelling half as healthy controls and half with an impaired stroke volume. All metrics derived from the diameter-velocity-based wave intensity waveforms in the carotid, brachial and radial arteries showed significant crossover between groups-no one metric in any artery could reliably indicate whether a subject's stroke volume was normal or impaired. However, after applying machine learning to the metrics, we found that a support vector classifier could simultaneously achieve up to 99% recall and 95% precision. We conclude that noninvasive wave intensity analysis has significant potential to improve heart failure screening and diagnosis.

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.

A method of parameter estimation for cardiovascular hemodynamics based on deep learning and its application to personalize a reduced-order model

Precise model personalization is a key step towards the application of cardiovascular physical models. In this manuscript, we propose to use deep learning (DL) to solve the parameter estimation problem in cardiovascular hemodynamics. Based on the convolutional neural network (CNN) and fully connected neural network (FCNN), a multi-input deep neural network (DNN) model is developed to map the nonlinear relationship between measurements and the parameters to be estimated. In this model, two separate network structures are designed to extract the features of two types of measurement data, including pressure waveforms and a vector composed of heart rate (HR) and pulse transit time (PTT), and a shared structure is used to extract their combined dependencies on the parameters. Besides, we try to use the transfer learning (TL) technology to further strengthen the personalized characteristics of a trained-well network. For assessing the proposed method, we conducted the parameter estimation using synthetic data and in vitro data respectively, and in the test with synthetic data, we evaluated the performance of the TL algorithm through two individuals with different characteristics. A series of estimation results show that the estimated parameters are in good agreement with the true values. Furthermore, it is also found that the estimation accuracy can be significantly improved by a multicycle combination strategy. Therefore, we think that the proposed method has the potential to be used for parameter estimation in cardiovascular hemodynamics, which can provide an immediate, accurate, and sustainable personalization process, and deserves more attention in the future.

Pulsatility damping in the microcirculation: Basic pattern and modulating factors

Blood flow pulsatility is an important determinant of macro- and microvascular physiology. Pulsatility is damped largely in the microcirculation, but the characteristics of this damping and the factors that regulate it have not been fully elucidated yet. Applying computational approaches to real microvascular network geometry, we examined the pattern of pulsatility damping and the role of potential damping factors, including pulse frequency, vascular viscous resistance, vascular compliance, viscoelastic behavior of the vessel wall, and wave propagation and reflection. To this end, three full rat mesenteric vascular networks were reconstructed from intravital microscopic recordings, a one-dimensional (1D) model was used to reproduce pulsatile properties within the network, and potential damping factors were examined by sensitivity analysis. Results demonstrate that blood flow pulsatility is predominantly damped at the arteriolar side and remains at a low level at the venular side. Damping was sensitive to pulse frequency, vascular viscous resistance and vascular compliance, whereas viscoelasticity of the vessel wall or wave propagation and reflection contributed little to pulsatility damping. The present results contribute to our understanding of mechanical forces and their regulation in the microcirculation.

Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models

Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R² > .95) with experimental blood pressure data.

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.

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.

The effect of left ventricular contractility on arterial hemodynamics: A model-based investigation

Ventricular-arterial coupling is a major determinant of cardiovascular performance, however, there are still inherent difficulties in distinguishing ventricular from vascular effects on arterial pulse phenotypes. In the present study, we employed an extensive mathematical model of the cardiovascular system to investigate how sole changes in cardiac contractility might affect hemodynamics. We simulated two physiologically relevant cases of high and low contractility by altering the end-systolic elastance, E_es, (3 versus 1 mmHg/mL) under constant cardiac output and afterload, and subsequently performed pulse wave analysis and wave separation. The aortic forward pressure wave component was steeper for high E_es, which led to the change of the total pressure waveform from the characteristic Type A phenotype to Type C, and the decrease in augmentation index, AIx (-2.4% versus +18.1%). Additionally, the increase in E_es caused the pulse pressure amplification from the aorta to the radial artery to rise drastically (1.86 versus 1.39). Our results show that an increase in cardiac contractility alone, with no concomitant change in arterial properties, alters the shape of the forward pressure wave, which, consequently, changes central and peripheral pulse phenotypes. Indices based on the pressure waveform, like AIx, cannot be assumed to reflect only arterial properties.

Influence of cross-sectional velocity profile on flow characteristics of arterial wall modeled as elastic and viscoelastic material

In the present work, blood flow behavior in a single artery and in arterial network is studied using time domain based one-dimensional wave propagation model retaining the nonlinear convective force. 1-D Navier-Stokes equation is used to model the flow behavior of the blood, using three unknown parameters: flow rate (q), cross-sectional area of artery (A) and pressure (p) based formulation. Three different approximate velocity profile functions across the cross-section namely modified flat, parabolic and the one proposed by Bessems are used to calculate the nonlinear convective force and the frictional force. Two different constitutive models, linear elastic model and standard linear solid model (Zener model) are used to model the arterial wall mechanical behavior. The system of partial differential equations is discretized using finite element and Crank Nicolson methods in space and time domains, respectively. Based on the formulation, an in house finite element code is developed to simulate flow behavior in both a single artery as well as in arterial network consisting of 20 small and large size arteries. Simulations are performed by enforcing a flow rate at the inlet and Windkessel model at the outlet. The results for elastic arterial wall model are found to be in good agreement with the results available in the literature. The flow rate/pressure predictions using different velocity profile functions are found to be nearly the same, however the Bessems velocity profile predicts more closer to 3D results compared to modified flat and parabolic profiles. Whereas, significant difference is found in the results predicted using elastic and viscoelastic artery wall models.

Uncertainty quantification implementations in human hemodynamic flows

BACKGROUND AND OBJECTIVE

Human hemodynamic modeling is usually influenced by uncertainties occurring from a considerable unavailability of information linked to the boundary conditions and the physical properties used in the numerical models. Calculating the effect of these uncertainties on the numerical findings along the cardiovascular system is a demanding process due to the complexity of the morphology of the body and the area dynamics. To cope with all these difficulties, Uncertainty Quantification (UQ) methods seem to be an ideal tool.

RESULTS

This study focuses on analyzing and summarizing some of the recent research efforts and directions of implementing UQ in human hemodynamic flows by analyzing 139 research papers. Initially, the suitability of applying this approach is analyzed and demonstrated. Then, an overview of the most significant research work in various fields of biomedical hemodynamic engineering is presented. Finally, it is attempted to identify any possible forthcoming directions for research and methodological progress of UQ in biomedical sciences.

CONCLUSION

This review concludes that by finding the best statistical methods and parameters to represent the propagated uncertainties, while achieving a good interpretation of the interaction between input-output, is crucial for implementing UQ in biomedical sciences.

Localization of Arterial Bleeds Using Pulse Wave Reflections

INTRODUCTION

Localization of internal arterial bleeds is necessary for treatment in the battlefield. In this article, we describe a novel approach that utilizes pulse wave reflections generated by a bleed to locate it.

MATERIALS AND METHODS

To demonstrate our approach, velocity and diameter waveforms in the presence of bleeds were simulated using the 1D wave propagation equations in a straight-vessel model of the human thoracic aorta. The simulated waveforms were then decomposed into forward and backward components using wave intensity analysis. Reflections arising from the bleed were identified from the decomposed waveforms.

RESULTS

Reflection generated by the bleed introduced a new feature in the backward component, compared to the normal, no-bleed condition. The bleed location could be determined from the time delay between this reflection feature and the forward wave creating it, and the pulse wave velocity in the vessel.

CONCLUSIONS

The findings of this study could be utilized by ultrasound for hemorrhage localization.

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.

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.

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

Effects of local coronary blood flow dynamics on the predictions of a model of in-stent restenosis

Computational models are increasingly used to study cardiovascular disease. However, models of coronary vessel remodelling usually make some strong assumptions about the effects of a local narrowing on the flow through the narrowed vessel. Here, we test the effects of local flow dynamics on the predictions of an in-stent restenosis (ISR) model. A previously developed 2D model of ISR is coupled to a 1D model of coronary blood flow. Then, two different assumptions are tested. The first assumption is that the vasculature is always able to adapt, and the volumetric flow rate through the narrowed vessel is kept constant. The second, alternative, assumption is that the vasculature does not adapt at all, and the ratio of the pressure drop to the flow rate (hydrodynamic resistance) stays the same throughout the whole process for all vessels unaffected by the stenosis, and aortic or venous blood pressure does not change either. Then, the dynamics are compared for different locations in coronary tree for two different reendothelization scenarios. The assumptions of constant volumetric flow rate (absolute vascular adaptation) versus constant aortic pressure drop and no adaptation do not significantly affect the growth dynamics for most locations in the coronary tree, and the differences can only be observed at the locations where a strong alternative flow pathway is present. On the other hand, the difference between locations is significant, which is consistent with small vessel size being a risk factor for restenosis. These results suggest that the assumption of a constant flow is a good approximation for ISR models dealing with the typical progression of ISR in the most often stented locations such as the proximal parts of left anterior descending (LAD) and left circumflex (LCX) arteries.

Application of physics-based flow models in cardiovascular medicine: Current practices and challenges

Personalized physics-based flow models are becoming increasingly important in cardiovascular medicine. They are a powerful complement to traditional methods of clinical decision-making and offer a wealth of physiological information beyond conventional anatomic viewing using medical imaging data. These models have been used to identify key hemodynamic biomarkers, such as pressure gradient and wall shear stress, which are associated with determining the functional severity of cardiovascular diseases. Importantly, simulation-driven diagnostics can help researchers understand the complex interplay between geometric and fluid dynamic parameters, which can ultimately improve patient outcomes and treatment planning. The possibility to compute and predict diagnostic variables and hemodynamics biomarkers can therefore play a pivotal role in reducing adverse treatment outcomes and accelerate development of novel strategies for cardiovascular disease management.

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.

In vitro Biomodels in Stenotic Arteries to Perform Blood Analogues Flow Visualizations and Measurements: A Review

Cardiovascular diseases are one of the leading causes of death globally and the most common pathological process is atherosclerosis. Over the years, these cardiovascular complications have been extensively studied by applying in vivo, in vitro and numerical methods (in silico). In vivo studies represent more accurately the physiological conditions and provide the most realistic data. Nevertheless, these approaches are expensive, and it is complex to control several physiological variables. Hence, the continuous effort to find reliable alternative methods has been growing. In the last decades, numerical simulations have been widely used to assess the blood flow behavior in stenotic arteries and, consequently, providing insights into the cardiovascular disease condition, its progression and therapeutic optimization. However, it is necessary to ensure its accuracy and reliability by comparing the numerical simulations with clinical and experimental data. For this reason, with the progress of the in vitro flow measurement techniques and rapid prototyping, experimental investigation of hemodynamics has gained widespread attention. The present work reviews state-of-the-art in vitro macro-scale arterial stenotic biomodels for flow measurements, summarizing the different fabrication methods, blood analogues and highlighting advantages and limitations of the most used techniques.

Multiscale modeling of blood flow to assess neurological complications in patients supported by venoarterial extracorporeal membrane oxygenation

Computational blood flow models in large arteries elucidate valuable relationships between cardiovascular diseases and hemodynamics, leading to improvements in treatment planning and clinical decision making. One such application with potential to benefit from simulation is venoarterial extracorporeal membrane oxygenation (VA-ECMO), a support system for patients with cardiopulmonary failure. VA-ECMO patients develop high rates of neurological complications, partially due to abnormal blood flow throughout the vasculature from the VA-ECMO system. To better understand these hemodynamic changes, it is important to resolve complex local flow parameters derived from three-dimensional (3D) fluid dynamics while also capturing the impact of VA-ECMO support throughout the systemic arterial system. As high-resolution 3D simulations of the arterial network remain computationally expensive and intractable for large studies, a validated, multiscale model is needed to compute both global effects and high-fidelity local hemodynamics. In this work, we developed and demonstrated a framework to model hemodynamics in VA-ECMO patients using coupled 3D and one-dimensional (1D) models (1D→3D). We demonstrated the ability of these multiscale models to simulate complex flow patterns in specific regions of interest while capturing bulk flow throughout the systemic arterial system. We compared 1D, 3D, and 1D→3D coupled models and found that multiscale models were able to sufficiently capture both global and local hemodynamics in the cerebral arteries and aorta in VA-ECMO patients. This study is the first to develop and compare 1D, 3D, and 1D→ 3D coupled models on the larger arterial system scale in VA-ECMO patients, with potential use for other large scale applications.

Comparison of arterial wave intensity analysis by pressure-velocity and diameter-velocity methods in a virtual population of adult subjects

Pressure-velocity-based analysis of arterial wave intensity gives clinically relevant information about the performance of the heart and vessels, but its utility is limited because accurate pressure measurements can only be obtained invasively. Diameter-velocity-based wave intensity can be obtained noninvasively using ultrasound; however, due to the nonlinear relationship between blood pressure and arterial diameter, the two wave intensities might give disparate clinical indications. To test the magnitude of the disagreement, we have generated an age-stratified virtual population to investigate how the two dominant nonlinearities viscoelasticity and strain-stiffening cause the two formulations to differ. We found strong agreement between the pressure-velocity and diameter-velocity methods, particularly for the systolic wave energy, the ratio between systolic and diastolic wave heights, and older subjects. The results are promising regarding the introduction of noninvasive wave intensities in the clinic.

Measurement, Analysis and Interpretation of Pressure/Flow Waves in Blood Vessels

The optimal performance of the cardiovascular system, as well as the break-down of this performance with disease, both involve complex biomechanical interactions between the heart, conduit vascular networks and microvascular beds. ‘Wave analysis’ refers to a group of techniques that provide valuable insight into these interactions by scrutinizing the shape of blood pressure and flow/velocity waveforms. The aim of this review paper is to provide a comprehensive introduction to wave analysis, with a focus on key concepts and practical application rather than mathematical derivations. We begin with an overview of invasive and non-invasive measurement techniques that can be used to obtain the signals required for wave analysis. We then review the most widely used wave analysis techniques—pulse wave analysis, wave separation and wave intensity analysis—and associated methods for estimating local wave speed or characteristic impedance that are required for decomposing waveforms into forward and backward wave components. This is followed by a discussion of the biomechanical phenomena that generate waves and the processes that modulate wave amplitude, both of which are critical for interpreting measured wave patterns. Finally, we provide a brief update on several emerging techniques/concepts in the wave analysis field, namely wave potential and the reservoir-excess pressure approach.

Conduit arterial wave reflection promotes pressure transmission but impedes hydraulic energy transmission to the microvasculature

With aging, a reduction in the stiffness gradient between elastic and muscular arteries is thought to reduce wave reflection in conduit arteries, leading to increased pulsatile pressure transmission into the microvasculature. This assumes that wave reflection limits pressure transmission in arteries. However, using a computational model, we showed that wave reflection promotes pulsatile pressure transmission, although it does limit hydraulic energy transmission. Increased microvascular pulse pressure with aging is instead related to decreasing arterial compliance.

Accelerating massively parallel hemodynamic models of coarctation of the aorta using neural networks

Comorbidities such as anemia or hypertension and physiological factors related to exertion can influence a patient’s hemodynamics and increase the severity of many cardiovascular diseases. Observing and quantifying associations between these factors and hemodynamics can be difficult due to the multitude of co-existing conditions and blood flow parameters in real patient data. Machine learning-driven, physics-based simulations provide a means to understand how potentially correlated conditions may affect a particular patient. Here, we use a combination of machine learning and massively parallel computing to predict the effects of physiological factors on hemodynamics in patients with coarctation of the aorta. We first validated blood flow simulations against in vitro measurements in 3D-printed phantoms representing the patient’s vasculature. We then investigated the effects of varying the degree of stenosis, blood flow rate, and viscosity on two diagnostic metrics – pressure gradient across the stenosis (ΔP) and wall shear stress (WSS) - by performing the largest simulation study to date of coarctation of the aorta (over 70 million compute hours). Using machine learning models trained on data from the simulations and validated on two independent datasets, we developed a framework to identify the minimal training set required to build a predictive model on a per-patient basis. We then used this model to accurately predict ΔP (mean absolute error within 1.18 mmHg) and WSS (mean absolute error within 0.99 Pa) for patients with this disease.

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.

Effect of Viscoelasticity on Arterial-Like Pulsatile Flow Dynamics and Energy

Time-dependent arterial wall property is an important but difficult topic in vascular mechanics. Hysteresis, which appears during the measurement of arterial pressure-diameter relationship through a cardiac cycle, has been used to indicate time-dependent mechanics of arteries. However, the cause-effect relationship between viscoelastic (VE) properties of the arterial wall and hemodynamics, particularly the viscous contribution to hemodynamics, remains challenging. Herein, we show direct comparisons between elastic (E) (loss/storage < 0.1) and highly viscoelastic (loss/storage > 0.45) conduit structures with arterial-like compliance, in terms of their capability of altering pulsatile flow, wall shear, and energy level. Conduits were made from varying ratio of vinyl- and methyl-terminated poly(dimethylsiloxane) and were fit in a mimetic circulatory system measuring volumetric flow, pressure, and strain. Results indicated that when compared to elastic conduits, viscoelastic conduits attenuated lumen distension waveforms, producing an average of 11% greater cross-sectional area throughout a mimetic cardiac cycle. In response to such changes in lumen diameter strain, pressure and volumetric flow waves in viscoelastic conduits decreased by 3.9% and 6%, respectively, in the peak-to-peak amplitude. Importantly, the pulsatile waveforms for both diameter strain and volumetric flow demonstrated greater temporal alignment in viscoelastic conduits due to pulsation attenuation, resulting in 25% decrease in the oscillation of wall shear stress (WSS). We hope these findings may be used to further examine time-dependent arterial properties in disease prognosis and progression, as well as their use in vascular graft design.

Determining the impacts of venoarterial extracorporeal membrane oxygenation on cerebral oxygenation using a one-dimensional blood flow simulator

Venoarterial extracorporeal membrane oxygenation (VA-ECMO) is a mechanical system that provides rapid and short-term support for patients with cardiac failure. In many patients, pulmonary function is also impaired, resulting in poorly-oxygenated cardiac outflow competing against well-oxygenated VA-ECMO outflow, a condition known as North-South syndrome. North-South syndrome is a primary concern because of its potential to cause cerebral hypoxia, which has a critical influence on neurological complications often seen in this patient population. In order to reduce ischemic neurological complications, it is important to understand how clinical decisions regarding VA-ECMO parameters influence blood oxygenation. Here, we studied the impacts of flow rate and cannulation site on oxygenation using a one-dimensional (1D) model to simulate blood flow. Our model was initially tested by comparing blood flow results to those observed from experimental work in VA-ECMO patients. The 1D model was combined with a two-phase flow model to simulate oxygenation. Additionally, the influence of various other clinician-tunable parameters on oxygenation in the common carotid arteries (CCAs) were tested, including, blood viscosity, cannula position within the insertion artery, heart rate, and systemic vascular resistance (SVR), as well as geometrical changes such as arterial radius and length. Our results indicated that blood oxygenation to the brain strongly depended on the cannula insertion site and the VA-ECMO flow rate with a weaker but potentially significant dependence on arterial radius. During femoral cannulation, VA-ECMO flow rates greater than ~4.9L/min were needed to perfuse the CCAs. However, axillary and central cannulation began to perfuse the CCAs at significantly lower flow (~1L/min). These results may help explain the incidence of cerebral hypoxia in this patient population and the common need to change cannulation strategies during treatment to address this clinical problem. While this work describes patient-averaged results, determining these relationships between VA-ECMO parameters and cerebral hypoxia is an important step towards future work to develop patient-specific models that clinicians can use to improve outcomes.