Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

Flow-Based Coronary Artery Bypass Graft Patency Metrics: Uncertainty Quantification Simulations to Guide Development

PURPOSE

Over time, transit time flow measurement (TTFM) has proven itself as a simple and effective tool for intra-operative evaluation of coronary artery bypass grafts (CABGs). However, metrics used to screen for possible technical error show considerable spread, preventing the definition of sharp cut-off values to distinguish between patent, questionable, and failed grafts. The simulation study presented in this paper aims to quantify this uncertainty for commonly used patency metrics, and to identify the most important physiological parameters influencing it.

METHODS

Uncertainty quantification was performed on a realistic multiscale numerical model of the coronary circulation, guided by Morris screening sensitivity analysis of a simpler, lumped-parameter model. Simulation results were qualitatively verified against results of a recent clinical study.

RESULTS

Correspondence with clinical study data is reasonable, especially considering that the model was not fitted in any way. Stenosis severity was confirmed to be an influential parameter. However, also cardiac period and graft diameter were observed to be important, particularly for mean flow rate and pulsatility index.

CONCLUSION

Metrics quantifying the flow waveform's diastolic dominance show the highest sensitivity to graft stenosis, and seem to be least affected by autoregulation. Among these, the novel diastolic resistance index shows the strongest sensitivity to stenosis severity.

SIGNIFICANCE

The approach used in this study is expected to benefit the development of improved patency metrics, by allowing medical engineers to include sensitivity and uncertainty in assessing, in-silico, the potential of novel metrics, thus enabling them to provide better guidance in the design of clinical studies.

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

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

Simulation of coronary fractional flow reserve and whole-cycle flow based on optical coherence tomography in individual patients with coronary artery disease

Computer simulations of coronary fractional flow reserve (FFR) based on coronary imaging have emerged as an attractive alternative to invasive measurements. However, most methods are proprietary and employ non-physiological assumptions. Our aims were to develop and validate a physiologically realistic open-source simulation model for coronary flow, and to use this model to predict FFR based on intracoronary optical coherence tomography (OCT) data in individual patients. We included patients undergoing elective coronary angiography with angiographic borderline coronary stenosis. Invasive measurements of coronary hyperemic pressure and absolute flow and OCT imaging were performed. A computer model of coronary flow incorporating pulsatile flow and the effect of left ventricular contraction was developed and calibrated, and patient-specific flow simulation was performed. Forty-eight coronary arteries from 41 patients were included in the analysis. Average FFR was 0.79 ± 0.14, and 50% had FFR ≤ 0.80. Correlation between simulated and measured FFR was high (r = 0.83, p < 0.001). Average difference between simulated FFR and observed FFR in individual patients was - 0.009 ± 0.076. Overall diagnostic accuracy for simulated FFR ≤ 0.80 in predicting observed FFR ≤ 0.80 was 0.88 (0.75-0.95) with sensitivity 0.79 (0.58-0.93) and specificity 0.96 (0.79-1.00). The positive predictive value was 0.95 (0.75-1.00) and the negative predictive value was 0.82 (0.63-0.94). In conclusion, realistic simulations of whole-cycle coronary flow can be produced based on intracoronary OCT data with a new, computationally simple simulation model. Simulated FFR had moderate numerical agreement with observed FFR and a good diagnostic accuracy for predicting hemodynamic significance of coronary stenoses.

Integrated modeling and simulation of recruitment of myocardial perfusion and oxygen delivery in exercise

While exercise-mediated vasoregulation in the myocardium is understood to be governed by autonomic, myogenic, and metabolic-mediated mechanisms, we do not yet understand the spatial heterogeneity of vasodilation or its effects on microvascular flow patterns and oxygen delivery. This study uses a simulation and modeling approach to explore the mechanisms underlying the recruitment of myocardial perfusion and oxygen delivery in exercise. The simulation approach integrates model components representing: whole-body cardiovascular hemodynamics, cardiac mechanics and myocardial work; myocardial perfusion; and myocardial oxygen transport. Integrating these systems together, model simulations reveal: (1.) To match expected flow and transmural flow ratios at increasing levels of exercise, a greater degree of vasodilation must occur in the subendocardium compared to the subepicardium. (2.) Oxygen extraction and venous oxygenation are predicted to substantially decrease with increasing exercise level preferentially in the subendocardium, suggesting that an oxygen-dependent error signal driving metabolic mediated recruitment of flow would be operative only in the subendocardium. (3.) Under baseline physiological conditions approximately 4% of the oxygen delivered to the subendocardium may be supplied via retrograde flow from coronary veins.

Impact of Pressure Guidewire on Model-Based FFR Prediction

INTRODUCTION

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Modelling coronary flow and myocardial perfusion by integrating a structured-tree coronary flow model and a hyperelastic left ventricle model

BACKGROUND AND OBJECTIVE

There is an increasing demand to establish integrated computational models that facilitate the exploration of coronary circulation in physiological and pathological contexts, particularly concerning interactions between coronary flow dynamics and myocardial motion. The field of cardiology has also demonstrated a trend toward personalised medicine, where these integrated models can be instrumental in integrating patient-specific data to improve therapeutic outcomes. Notably, incorporating a structured-tree model into such integrated models is currently absent in the literature, which presents a promising prospect. Thus, the goal here is to develop a novel computational framework that combines a 1D structured-tree model of coronary flow in human coronary vasculature with a 3D left ventricle model utilising a hyperelastic constitutive law, enabling the physiologically accurate simulation of coronary flow dynamics.

METHODS

We adopted detailed geometric information from previous studies of both coronary vasculature and left ventricle to construct the coronary flow model and the left ventricle model. The structured-tree model for coronary flow was expanded to encompass the effect of time-varying intramyocardial pressure on intramyocardial blood vessels. Simultaneously, the left ventricle model served as a robust foundation for the calculation of intramyocardial pressure and subsequent quantitative evaluation of myocardial perfusion. A one-way coupling framework between the two models was established to enable the evaluation and examination of coronary flow dynamics and myocardial perfusion.

RESULTS

Our predicted coronary flow waveforms aligned well with published experimental data. Our model precisely captured the phasic pattern of coronary flow, including impeded or even reversed flow during systole. Moreover, our assessment of coronary flow, considering both globally and regionally averaged intramyocardial pressure, demonstrated that elevated intramyocardial pressure corresponds to increased impeding effects on coronary flow. Furthermore, myocardial blood flow simulated from our model was comparable with MRI perfusion data at rest, showcasing the capability of our model to predict myocardial perfusion.

CONCLUSIONS

The integrated model introduced in this study presents a novel approach to achieving physiologically accurate simulations of coronary flow and myocardial perfusion. It holds promise for its clinical applicability in diagnosing insufficient myocardial perfusion.

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.

Impact of TAVR on coronary artery hemodynamics using clinical measurements and image-based patient-specific in silico modeling

In recent years, transcatheter aortic valve replacement (TAVR) has become the leading method for treating aortic stenosis. While the procedure has improved dramatically in the past decade, there are still uncertainties about the impact of TAVR on coronary blood flow. Recent research has indicated that negative coronary events after TAVR may be partially driven by impaired coronary blood flow dynamics. Furthermore, the current technologies to rapidly obtain non-invasive coronary blood flow data are relatively limited. Herein, we present a lumped parameter computational model to simulate coronary blood flow in the main arteries as well as a series of cardiovascular hemodynamic metrics. The model was designed to only use a few inputs parameters from echocardiography, computed tomography and a sphygmomanometer. The novel computational model was then validated and applied to 19 patients undergoing TAVR to examine the impact of the procedure on coronary blood flow in the left anterior descending (LAD) artery, left circumflex (LCX) artery and right coronary artery (RCA) and various global hemodynamics metrics. Based on our findings, the changes in coronary blood flow after TAVR varied and were subject specific (37% had increased flow in all three coronary arteries, 32% had decreased flow in all coronary arteries, and 31% had both increased and decreased flow in different coronary arteries). Additionally, valvular pressure gradient, left ventricle (LV) workload and maximum LV pressure decreased by 61.5%, 4.5% and 13.0% respectively, while mean arterial pressure and cardiac output increased by 6.9% and 9.9% after TAVR. By applying this proof-of-concept computational model, a series of hemodynamic metrics were generated non-invasively which can help to better understand the individual relationships between TAVR and mean and peak coronary flow rates. In the future, tools such as these may play a vital role by providing clinicians with rapid insight into various cardiac and coronary metrics, rendering the planning for TAVR and other cardiovascular procedures more personalized.

Mechanism of exercise intolerance in heart diseases predicted by a computer model of myocardial demand-supply feedback system

BACKGROUND AND OBJECTIVE

The myocardial demand-supply feedback system plays an important role in augmenting blood supply in response to exercise-induced increased myocardial demand. During this feedback process, the myocardium and coronary blood flow interact bidirectionally at many different levels.

METHODS

To investigate these interactions, a novel computational framework that considers the closed myocardial demand-supply feedback system was developed. In the framework coupling the systemic circulation of the left ventricle and coronary perfusion with regulation, myocardial work affects coronary perfusion via flow regulation mechanisms (e.g., metabolic regulation) and myocardial-vessel interactions, whereas coronary perfusion affects myocardial contractility in a closed feedback system. The framework was calibrated based on the measurements from healthy subjects under graded exercise conditions, and then was applied to simulate the effects of graded exercise on myocardial demand-supply under different physiological and pathological conditions.

RESULTS

We found that the framework can recapitulate key features found during exercise in clinical and animal studies. We showed that myocardial blood flow is increased but maximum hyperemia is reduced during exercise, which led to a reduction in coronary flow reserve. For coronary stenosis and myocardial inefficiency, the model predicts that an increase in heart rate is necessary to maintain the baseline cardiac output. Correspondingly, the resting coronary flow reserve is exhausted and the range of heart rate before exhaustion of coronary flow reserve is reduced. In the presence of metabolic regulation dysfunction, the model predicts that the metabolic vasodilator signal is higher at rest, saturates faster during exercise, and as a result, causes quicker exhaustion of coronary flow reserve.

CONCLUSIONS

Model predictions showed that the coronary flow reserve deteriorates faster during graded exercise, which in turn, suggests a decrease in exercise tolerance for patients with stenosis, myocardial inefficiency and metabolic flow regulation dysfunction. The findings in this study may have clinical implications in diagnosing cardiovascular diseases.

A predictive patient-specific computational model of coronary artery bypass grafts for potential use by cardiac surgeons to guide selection of graft configurations

Cardiac surgeons face a significant degree of uncertainty when deciding upon coronary artery bypass graft configurations for patients with coronary artery disease. This leads to significant variation in preferred configuration between different surgeons for a particular patient. Additionally, for the majority of cases, there is no consensus regarding the optimal grafting strategy. This situation results in the tendency for individual surgeons to opt for a “one size fits all” approach and use the same grafting configuration for the majority of their patients neglecting the patient-specific nature of the diseased coronary circulation. Quantitative metrics to assess the adequacy of coronary bypass graft flows have recently been advocated for routine intraoperative use by cardiac surgeons. In this work, a novel patient-specific 1D-0D computational model called “COMCAB” is developed to provide the predictive haemodynamic parameters of functional graft performance that can aid surgeons to avoid configurations with grafts that have poor flow and thus poor patency. This model has significant potential for future expanded applications.

Simulating Stenotic Conditions of the Coronary Artery in a Lumped Parameter Model of the Cardiovascular System

Coronary flow control mechanisms maintain the average coronary blood flow (CBF) at 4% of the cardiac output (CO) in normal adults, with no prior diagnosis of coronary artery disease (CAD), under resting conditions. This paper explores a pulsatile sixth order lumped parameter (LP) model of the cardiovascular system (CVS) which utilizes the average CBF approximated from CO along with arterial blood pressure (ABP) waveform to estimate the coronary microvascular resistance using non-linear least square optimization technique. The CVS model includes a third order model of the coronary vascular bed and is shown to achieve phasic coronary flow. The coronary epicardial resistance is varied to emulate different degrees of stenosis and achieve realistic behavior of coronary microvascular resistance under these conditions.

Multiscale model of the physiological control of myocardial perfusion to delineate putative metabolic feedback mechanisms

Coronary blood flow is tightly regulated to ensure that myocardial oxygen delivery meets local metabolic demand via the concurrent action of myogenic, neural and metabolic mechanisms. Although several competing hypotheses exist, the specific nature of the local metabolic mechanism(s) remains poorly defined. To gain insights into the viability of putative metabolic feedback mechanisms and into the co-ordinated action of parallel regulatory mechanisms, we applied a multiscale modelling framework to analyse experimental data on coronary pressure, flow and myocardial oxygen delivery in the porcine heart in vivo. The modelling framework integrates a previously established lumped-parameter model of myocardial perfusion used to account for transmural haemodynamic variations and a simple vessel mechanics model used to simulate the vascular tone in each of three myocardial layers. Vascular tone in the resistance vessel mechanics model is governed by input stimuli from the myogenic, metabolic and autonomic control mechanisms. Seven competing formulations of the metabolic feedback mechanism are implemented in the modelling framework, and associated model simulations are compared with experimental data on coronary pressures and flows under a range of experimental conditions designed to interrogate the governing control mechanisms. Analysis identifies a maximally probable metabolic mechanism among the seven tested models, in which production of a metabolic signalling factor is proportional to myocardial oxygen consumption and delivery is proportional to flow. Finally, the identified model is validated based on comparisons of simulations with data on the myocardial perfusion response to conscious exercise that were not used for model identification. KEY POINTS: Although several competing hypotheses exist, we lack knowledge of specific nature of the metabolic mechanism(s) governing regional myocardial perfusion. Moreover, we lack an understanding of how parallel myogenic, adrenergic/autonomic and metabolic mechanisms work together to regulatory oxygen delivery in the beating heart. We have developed a multiscale modelling framework to test competing hypotheses against experimental data on coronary pressure, flow and myocardial oxygen delivery in the porcine heart in vivo. The analysis identifies a maximally probable metabolic mechanism among seven tested models, in which the production of a metabolic signalling factor is proportional to myocardial oxygen consumption and delivery is proportional to flow.

A Closed-Loop Modeling Framework for Cardiac-to-Coronary Coupling

The mechanisms by which cardiac mechanics effect coronary perfusion (cardiac-to-coronary coupling) remain incompletely understood. Several coronary models have been proposed to deepen our understanding of coronary hemodynamics, but possibilities for in-depth studies on cardiac-to-coronary coupling are limited as mechanical properties like myocardial stress and strain are most often neglected. To overcome this limitation, a mathematical model of coronary mechanics and hemodynamics was implemented in the previously published multi-scale CircAdapt model of the closed-loop cardiovascular system. The coronary model consisted of a relatively simple one-dimensional network of the major conduit arteries and veins as well as a lumped parameter model with three transmural layers for the microcirculation. Intramyocardial pressure was assumed to arise from transmission of ventricular cavity pressure into the myocardial wall as well as myocardial stiffness, based on global pump mechanics and local myofiber mechanics. Model-predicted waveforms of global epicardial flow velocity, as well as of intramyocardial flow and diameter were qualitatively and quantitatively compared with reported data. Versatility of the model was demonstrated in a case study of aortic valve stenosis. The reference simulation correctly described the phasic pattern of coronary flow velocity, arterial flow impediment, and intramyocardial differences in coronary flow and diameter. Predicted retrograde flow during early systole in aortic valve stenosis was in agreement with measurements obtained in patients. In conclusion, we presented a powerful multi-scale modeling framework that enables realistic simulation of coronary mechanics and hemodynamics. This modeling framework can be used as a research platform for in-depth studies of cardiac-to-coronary coupling, enabling study of the effect of abnormal myocardial tissue properties on coronary hemodynamics.

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

In spite of cardiovascular system (CVS) response to posture changes have been widely studied, a number of mechanisms and their interplay in regulating central blood pressure and organs perfusion upon orthostatic stress are not yet clear. We propose a novel multiscale 1D-0D mathematical model of the human CVS to investigate the effects of passive (i.e., through head-up tilt without muscular intervention) posture changes. The model includes the main short-term regulation mechanisms and is carefully validated against literature data and in vivo measures here carried out. The model is used to study the transient and steady-state response of the CVS to tilting, the effects of the tilting rate, and the differences between tilt-up and tilt-down. Passive upright tilt led to an increase of mean arterial pressure and heart rate, and a decrease of stroke volume and cardiac output, in agreement with literature data and present in vivo experiments. Pressure and flow rate waveform analysis along the arterial tree together with mechano-energetic and oxygen consumption parameters highlighted that the whole system approaches a less stressed condition at passive upright posture than supine, with a slight unbalance of the energy supply-demand ratio. The transient dynamics is not symmetric in tilt-up and tilt-down testing, and is non-linearly affected by the tilting rate, with stronger under- and overshoots of the hemodynamic parameters as the duration of tilt is reduced. By enriching the CVS response to posture changes, the present modeling approach shows promise in a number of applications, ranging from autonomic system disorders to spaceflight deconditioning.

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

Patients with atrial fibrillation (AF) may present ischemic chest pain in the absence of classical obstructive coronary disease. Among the possible causes, the direct hemodynamic effect exerted by the irregular arrhythmia has not been studied in detail. We performed a computational fluid dynamics analysis by means of a 1D-0D multiscale model of the entire human cardiovascular system, enriched by a detailed mathematical modeling of the coronary arteries and their downstream distal microcirculatory districts (subepicardial, midwall and subendocardial layers). Three mean ventricular rates were simulated (75, 100, 125 bpm) in both sinus rhythm (SR) and atrial fibrillation, and an inter-layer and inter-frequency analysis was conducted focusing on the ratio between mean beat-to-beat blood flow in AF compared to SR. Our results show that AF exerts direct hemodynamic consequences on the coronary microcirculation, causing a reduction in microvascular coronary flow particularly at higher ventricular rates; the most prominent reduction was seen in the subendocardial layers perfused by left coronary arteries (left anterior descending and left circumflex arteries).

Transmural Distribution of Coronary Perfusion and Myocardial Work Density Due to Alterations in Ventricular Loading, Geometry and Contractility

Myocardial supply changes to accommodate the variation of myocardial demand across the heart wall to maintain normal cardiac function. A computational framework that couples the systemic circulation of a left ventricular (LV) finite element model and coronary perfusion in a closed loop is developed to investigate the transmural distribution of the myocardial demand (work density) and supply (perfusion) ratio. Calibrated and validated against measurements of LV mechanics and coronary perfusion, the model is applied to investigate changes in the transmural distribution of passive coronary perfusion, myocardial work density, and their ratio in response to changes in LV contractility, preload, afterload, wall thickness, and cavity volume. The model predicts the following: (1) Total passive coronary flow varies from a minimum value at the endocardium to a maximum value at the epicardium transmurally that is consistent with the transmural distribution of IMP; (2) Total passive coronary flow at different transmural locations is increased with an increase in either contractility, afterload, or preload of the LV, whereas is reduced with an increase in wall thickness or cavity volume; (3) Myocardial work density at different transmural locations is increased transmurally with an increase in either contractility, afterload, preload or cavity volume of the LV, but is reduced with an increase in wall thickness; (4) Myocardial work density-perfusion mismatch ratio at different transmural locations is increased with an increase in contractility, preload, wall thickness or cavity volume of the LV, and the ratio is higher at the endocardium than the epicardium. These results suggest that an increase in either contractility, preload, wall thickness, or cavity volume of the LV can increase the vulnerability of the subendocardial region to ischemia.

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 relevance of boundary conditions and viscosity models in blood flow simulations in patient-specific aorto-coronary bypass models

Physiologically realistic results are the aim of every blood flow simulation. This is not different in aorto-coronary bypasses where the properties of the coronary circulation may significantly affect the relevance of the performed simulations. By considering three patient-specific bypass geometries, the present article focuses on two aspects of the coronary blood flow - its phasic flow pattern and its behaviour affected by blood rheology. For the phasic flow property, a multiscale modelling approach is chosen as a means to assess the ability of five different types of coronary boundary conditions (mean arterial pressure, Windkessel model and three lumped parameter models) to attain realistic coronary haemodynamics. From the analysed variants of boundary conditions, the best option in terms of physiological characteristics and its potential for use in patient-based simulations, is utilised to account for the effect of shear-dependent viscosity on the resulting haemodynamics and wall shear stress stimulation. Aside from the Newtonian model, the blood rheology is approximated by two non-Newtonian models in order to determine whether the choice of a viscosity model is important in simulations involving coronary circulation. A comprehensive analysis of obtained results demonstrated notable superiority of all lumped parameter models, especially in comparison to the constant outlet pressure, which regardless of bypass type gave overestimated and physiologically misleading results. In terms of rheology, it was noted that blood in undamaged coronary arteries behaves as a Newtonian fluid, whereas in vessels with atypical lumen geometry, such as that of anastomosis or stenosis, its shear-thinning behaviour should not be ignored.

Role of coronary flow regulation and cardiac-coronary coupling in mechanical dyssynchrony associated with right ventricular pacing

Mechanical dyssynchrony (MD) affects left ventricular (LV) mechanics and coronary perfusion. To understand the multifactorial effects of MD, we developed a computational model that bidirectionally couples the systemic circulation with the LV and coronary perfusion with flow regulation. In the model, coronary flow in the left anterior descending (LAD) and left circumflex (LCX) arteries affects the corresponding regional contractility based on a prescribed linear LV contractility-coronary flow relationship. The model is calibrated with experimental measurements of LV pressure and volume, as well as LAD and LCX flow rate waveforms acquired under regulated and fully dilated conditions from a swine under right atrial (RA) pacing. The calibrated model is applied to simulate MD. The model can simultaneously reproduce the reduction in mean LV pressure (39.3%), regulated flow (LAD: 7.9%; LCX: 1.9%), LAD passive flow (21.6%), and increase in LCX passive flow (15.9%). These changes are associated with right ventricular pacing compared with RA pacing measured in the same swine only when LV contractility is affected by flow alterations with a slope of 1.4 mmHg/mL² in a contractility-flow relationship. In sensitivity analyses, the model predicts that coronary flow reserve (CFR) decreases and increases in the LAD and LCX with increasing delay in LV free wall contraction. These findings suggest that asynchronous activation associated with MD impacts 1) the loading conditions that further affect the coronary flow, which may explain some of the changes in CFR, and 2) the coronary flow that reduces global contractility, which contributes to the reduction in LV pressure.NEW & NOTEWORTHY A computational model that couples the systemic circulation of the left ventricular (LV) and coronary perfusion with flow regulation is developed to study the effects of mechanical dyssynchrony. The delayed contraction in the LV free wall with respect to the septum has a significant effect on LV function and coronary flow reserve.

Diagnostic performance of virtual fractional flow reserve derived from routine coronary angiography using segmentation free reduced order (1-dimensional) flow modelling

Introduction

Fractional flow reserve (FFR) improves assessment of the physiological significance of coronary lesions compared with conventional angiography. However, it is an invasive investigation. We tested the performance of a virtual FFR (1D-vFFR) using routine angiographic images and a rapidly performed reduced order computational model.

Methods

Quantitative coronary angiography (QCA) was performed in 102 with coronary lesions assessed by invasive FFR. A 1D-vFFR for each lesion was created using reduced order (one-dimensional) computational flow modelling derived from conventional angiographic images and patient specific estimates of coronary flow. The diagnostic accuracy of 1D-vFFR and QCA derived stenosis was compared against the gold standard of invasive FFR using area under the receiver operator characteristic curve (AUC).

Results

QCA revealed the mean coronary stenosis diameter was 44% ± 12% and lesion length 13 ± 7 mm. Following angiography calculation of the 1DvFFR took less than one minute. Coronary stenosis (QCA) had a significant but weak correlation with FFR (r = -0.2, p = 0.04) and poor diagnostic performance to identify lesions with FFR <0.80 (AUC 0.39, p = 0.09), (sensitivity - 58% and specificity - 26% at a QCA stenosis of 50%). In contrast, 1D-vFFR had a better correlation with FFR (r = 0.32, p = 0.01) and significantly better diagnostic performance (AUC 0.67, p = 0.007), (sensitivity - 92% and specificity - 29% at a 1D-vFFR of 0.7).

Conclusions

1D-vFFR improves the determination of functionally significant coronary lesions compared with conventional angiography without requiring a pressure-wire or hyperaemia induction. It is fast enough to influence immediate clinical decision-making but requires further clinical evaluation.

Effects of Mechanical Dyssynchrony on Coronary Flow: Insights From a Computational Model of Coupled Coronary Perfusion With Systemic Circulation

Mechanical dyssynchrony affects left ventricular (LV) mechanics and coronary perfusion. Due to the confounding effects of their bi-directional interactions, the mechanisms behind these changes are difficult to isolate from experimental and clinical studies alone. Here, we develop and calibrate a closed-loop computational model that couples the systemic circulation, LV mechanics, and coronary perfusion. The model is applied to simulate the impact of mechanical dyssynchrony on coronary flow in the left anterior descending artery (LAD) and left circumflex artery (LCX) territories caused by regional alterations in perfusion pressure and intramyocardial pressure (IMP). We also investigate the effects of regional coronary flow alterations on regional LV contractility in mechanical dyssynchrony based on prescribed contractility-flow relationships without considering autoregulation. The model predicts that LCX and LAD flows are reduced by 7.2%, and increased by 17.1%, respectively, in mechanical dyssynchrony with a systolic dyssynchrony index of 10% when the LAD's IMP is synchronous with the arterial pressure. The LAD flow is reduced by 11.6% only when its IMP is delayed with respect to the arterial pressure by 0.07 s. When contractility is sensitive to coronary flow, mechanical dyssynchrony can affect global LV mechanics, IMPs and contractility that in turn, further affect the coronary flow in a feedback loop that results in a substantial reduction of dP_LV/dt, indicative of ischemia. Taken together, these findings imply that regional IMPs play a significant role in affecting regional coronary flows in mechanical dyssynchrony and the changes in regional coronary flow may produce ischemia when contractility is sensitive to the changes in coronary flow.

Artificial intelligence approaches to predict coronary stenosis severity using non-invasive fractional flow reserve

Fractional flow reserve is the current reference standard in the assessment of the functional impact of a stenosis in coronary heart disease. In this study, three models of artificial intelligence of varying degrees of complexity were compared to fractional flow reserve measurements. The three models are the multivariate polynomial regression, which is a statistical method used primarily for correlation; the feed-forward neural network; and the long short-term memory, which is a type of recurrent neural network that is suited to modelling sequences. The models were initially trained using a virtual patient database that was generated from a validated one-dimensional physics-based model. The feed-forward neural network performed the best for all test cases considered, which were a single vessel case from a virtual patient database, a multi-vessel network from a virtual patient database, and 25 clinically invasive fractional flow reserve measurements from real patients. The feed-forward neural network model achieved around 99% diagnostic accuracy in both tests involving virtual patients, and a respectable 72% diagnostic accuracy when compared to the invasive fractional flow reserve measurements. The multivariate polynomial regression model performed well in the single vessel case, but struggled on network cases as the variation of input features was much larger. The long short-term memory performed well for the single vessel cases, but tended to have a bias towards a positive fractional flow reserve prediction for the virtual multi-vessel case, and for the patient cases. Overall, the feed-forward neural network shows promise in successfully predicting fractional flow reserve in real patients, and could be a viable option if trained using a large enough data set of real patients.

Overview of mathematical modeling of myocardial blood flow regulation

The oxygen consumption by the heart and its extraction from the coronary arterial blood are the highest among all organs. Any increase in oxygen demand due to a change in heart metabolic activity requires an increase in coronary blood flow. This functional requirement of adjustment of coronary blood flow is mediated by coronary flow regulation to meet the oxygen demand without any discomfort, even under strenuous exercise conditions. The goal of this article is to provide an overview of the theoretical and computational models of coronary flow regulation and to reveal insights into the functioning of a complex physiological system that affects the perfusion requirements of the myocardium. Models for three major control mechanisms of myogenic, flow, and metabolic control are presented. These explain how the flow regulation mechanisms operating over multiple spatial scales from the precapillaries to the large coronary arteries yield the myocardial perfusion characteristics of flow reserve, autoregulation, flow dispersion, and self-similarity. The review not only introduces concepts of coronary blood flow regulation but also presents state-of-the-art advances and their potential to impact the assessment of coronary microvascular dysfunction (CMD), cardiac-coronary coupling in metabolic diseases, and therapies for angina and heart failure. Experimentalists and modelers not trained in these models will have exposure through this review such that the nonintuitive and highly nonlinear behavior of coronary physiology can be understood from a different perspective. This survey highlights knowledge gaps, key challenges, future research directions, and novel paradigms in the modeling of coronary flow regulation.

Effects of myocardial function and systemic circulation on regional coronary perfusion

Cardiac-coronary interaction and the effects of its pathophysiological variations on spatial heterogeneity of coronary perfusion and myocardial work are still poorly understood. This hypothesis-generating study predicts spatial heterogeneities in both regional cardiac work and perfusion that offer a new paradigm on the vulnerability of the subendocardium to ischemia, particularly at the apex. We propose a mathematical and computational modeling framework to simulate the interaction of left ventricular mechanics, systemic circulation, and coronary microcirculation. The computational simulations revealed that the relaxation rate of the myocardium has a significant effect whereas the contractility has a marginal effect on both the magnitude and transmural distribution of coronary perfusion. The ratio of subendocardial to subepicardial perfusion density (Q_endo/Q_epi) changed by -12 to +6% from a baseline value of 1.16 when myocardial contractility was varied by +25 and -10%, respectively; Q_endo/Q_epi changed by 37% when sarcomere relaxation rate, b, was faster and increased by 10% from the baseline value. The model predicts axial differences in regional myocardial work and perfusion density across the wall thickness. Regional myofiber work done at the apex is 30-50% lower than at the center region, whereas perfusion density in the apex is lower by only 18% compared with the center. There are large axial differences in coronary flow and myocardial work at the subendocardial locations, with the highest differences located at the apex region. A mismatch exists between perfusion density and regional work done at the subendocardium. This mismatch is speculated to be compensated by coronary autoregulation.NEW & NOTEWORTHY We present a model of left ventricle perfusion based on an anatomically realistic coronary tree structure that includes its interaction with the systemic circulation. Left ventricular relaxation rate has a significant effect on the regional distribution of coronary flow and myocardial work.

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.

Impaired coronary blood flow at higher heart rates during atrial fibrillation: Investigation via multiscale modelling

BACKGROUND

Different mechanisms have been proposed to relate atrial fibrillation (AF) and coronary flow impairment, even in absence of relevant coronary artery disease (CAD). However, the underlying hemodynamics remains unclear. Aim of the present work is to computationally explore whether and to what extent ventricular rate during AF affects the coronary perfusion.

METHODS

AF is simulated at different ventricular rates (50, 70, 90, 110, 130 bpm) through a 0D-1D multiscale validated model, which combines the left heart-arterial tree together with the coronary circulation. Artificially-built RR stochastic extraction mimics the in vivo beating features. All the hemodynamic parameters computed are based on the left anterior descending (LAD) artery and account for the waveform, amplitude and perfusion of the coronary blood flow.

RESULTS

Alterations of the coronary hemodynamics are found to be associated either to the heart rate increase, which strongly modifies waveform and amplitude of the LAD flow rate, and to the beat-to-beat variability. The latter is overall amplified in the coronary circulation as HR grows, even though the input RR variability is kept constant at all HRs.

CONCLUSIONS

Higher ventricular rate during AF exerts an overall coronary blood flow impairment and imbalance of the myocardial oxygen supply-demand ratio. The combined increase of heart rate and higher AF-induced hemodynamic variability lead to a coronary perfusion impairment exceeding 90-110 bpm in AF. Moreover, it is found that coronary perfusion pressure (CPP) is no longer a good measure of the myocardial perfusion for HR higher than 90 bpm.

A data-driven model to study utero-ovarian blood flow physiology during pregnancy

In this paper, we describe a mathematical model of the cardiovascular system in human pregnancy. An automated, closed-loop 1D-0D modelling framework was developed, and we demonstrate its efficacy in (1) reproducing measured multi-variate cardiovascular variables (pulse pressure, total peripheral resistance and cardiac output) and (2) providing automated estimates of variables that have not been measured (uterine arterial and venous blood flow, pulse wave velocity, pulsatility index). This is the first model capable of estimating volumetric blood flow to the uterus via the utero-ovarian communicating arteries. It is also the first model capable of capturing wave propagation phenomena in the utero-ovarian circulation, which are important for the accurate estimation of arterial stiffness in contemporary obstetric practice. The model will provide a basis for future studies aiming to elucidate the physiological mechanisms underlying the dynamic properties (changing shapes) of vascular flow waveforms that are observed with advancing gestation. This in turn will facilitate the development of methods for the earlier detection of pathologies that have an influence on vascular structure and behaviour.

Studying The Sensitivity Of Coronary Blood Flow Using Nondimensional Analysis

Nondimensional analysis was used to develop a novel model of coronary blood flow. In addition to general hemodynamics, the model was used to study the sensitivity of the arterial flow to variations in characteristic lumped parameters. Experimental hemodynamic data obtained from four normal healthy pigs were used in the current study. The results suggest that the mean coronary arterial flow is primarily sensitive to the flow and elasticity parameters of the coronary vasculature. Other flow features were also studied, and it was shown that the sensitivities of the general flow waveforms are influenced to different extents by the perturbations of these parameters. More specifically, the flow coefficient affects the systolic inflow more than the diastolic portion; conversely, the elasticity coefficient has more impact on the diastolic period.

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

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

Major influence of a 'smoke and mirrors' effect caused by wave reflection on early diastolic coronary arterial wave intensity

KEY POINTS

Coronary wave intensity analysis (WIA) is an emerging technique for assessing upstream and downstream influences on myocardial perfusion. It is thought that a dominant backward decompression wave (BDW_dia ) is generated by a distal suction effect, while early-diastolic forward decompression (FDW_dia ) and compression (FCW_dia ) waves originate in the aorta. We show that wave reflection also makes a substantial contribution to FDW_dia , FCW_dia and BDW_dia , as quantified by a novel method. In 18 sheep, wave reflection accounted for ∼70% of BDW_dia , whereas distal suction dominated in a computer model representing a hypertensive human. Non-linear addition/subtraction of mechanistically distinct waves (e.g. wave reflection and distal suction) obfuscates the true contribution of upstream and downstream forces on measured waves (the 'smoke and mirrors' effect). The mechanisms underlying coronary WIA are more complex than previously thought and the impact of wave reflection should be considered when interpreting clinical and experimental data.

ABSTRACT

Coronary arterial wave intensity analysis (WIA) is thought to provide clear insight into upstream and downstream forces on coronary flow, with a large early-diastolic surge in coronary flow accompanied by a prominent backward decompression wave (BDW_dia ), as well as a forward decompression wave (FDW_dia ) and forward compression wave (FCW_dia ). The BDW_dia is believed to arise from distal suction due to release of extravascular compression by relaxing myocardium, while FDW_dia and FCW_dia are thought to be transmitted from the aorta into the coronary arteries. Based on an established multi-scale computational model and high-fidelity measurements from the proximal circumflex artery (Cx) of 18 anaesthetized sheep, we present evidence that wave reflection has a major impact on each of these three waves, with a non-linear addition/subtraction of reflected waves obscuring the true influence of upstream and downstream forces through concealment and exaggeration, i.e. a 'smoke and mirrors' effect. We also describe methods, requiring additional measurement of aortic WIA, for unravelling the separate influences of wave reflection versus active upstream/downstream forces on coronary waves. Distal wave reflection accounted for ∼70% of the BDW_dia in sheep, but had a lesser influence (∼25%) in the computer model representing a hypertensive human. Negative reflection of the BDW_dia at the coronary-aortic junction attenuated the Cx FDW_dia (by ∼40% in sheep) and augmented Cx FCW_dia (∼5-fold), relative to the corresponding aortic waves. We conclude that wave reflection has a major influence on early-diastolic WIA, and thus needs to be considered when interpreting coronary WIA profiles.

A patient-specific lumped-parameter model of coronary circulation

A new lumped-parameter model for coronary hemodynamics is developed. This model is developed for the whole coronary network based on CT scans of a patient-specific geometry including the right coronary tree, which is absent in many previous mathematical models. The model adopts the structured tree model boundary conditions similar to the work of Olufsen et al., thus avoiding the necessity of invasive perfusion measurements. In addition, we also incorporated the effects of the head loss at the two inlets of the large coronary arteries for the first time. The head loss could explain the phenomenon of a sudden increase of the resistance at the inlet of coronary vessel. The estimated blood pressure and flow rate results from the model agree well with the clinical measurements. The computed impedances also match the experimental perfusion measurement. The effects of coronary arterial stenosis are considered and the fractional flow reserve and relative flow in the coronary vessels for a stenotic vessel computed in this model show good agreement with published experimental data. It is believed that the approach could be readily translated to clinical practice to facilitate real time clinical diagnosis.

Estimating the accuracy of a reduced-order model for the calculation of fractional flow reserve (FFR)

Image-based noninvasive fractional flow reserve (FFR) is an emergent approach to determine the functional relevance of coronary stenoses. The present work aimed to determine the feasibility of using a method based on coronary computed tomography angiography (CCTA) and reduced-order models (0D-1D) for the evaluation of coronary stenoses. The reduced-order methodology (cFFR_RO ) was kept as simple as possible and did not include pressure drop or stenosis models. The geometry definition was incorporated into the physical model used to solve coronary flow and pressure. cFFRRO was assessed on a virtual cohort of 30 coronary artery stenoses in 25 vessels and compared with a standard approach based on 3D computational fluid dynamics (cFFR_3D ). In this proof-of-concept study, we sought to investigate the influence of geometry and boundary conditions on the agreement between both methods. Performance on a per-vessel level showed a good correlation between both methods (Pearson's product-moment R=0.885, P<0.01), when using cFFR_3D  as the reference standard. The 95% limits of agreement were -0.116 and 0.08, and the mean bias was -0.018 (SD =0.05). Our results suggest no appreciable difference between cFFR_RO  and cFFR_3D with respect to lesion length and/or aspect ratio. At a fixed aspect ratio, however, stenosis severity and shape appeared to be the most critical factors accounting for differences in both methods. Despite the assumptions inherent to the 1D formulation, asymmetry did not seem to affect the agreement. The choice of boundary conditions is critical in obtaining a functionally significant drop in pressure. Our initial data suggest that this approach may be part of a broader risk assessment strategy aimed at increasing the diagnostic yield of cardiac catheterisation for in-hospital evaluation of haemodynamically significant stenoses.

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

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

Major contribution of central pulmonary reservoir discharge to increased pulmonary arterial diastolic blood flow after birth in near-term lambs

Recent fetal lamb data have suggested that the pulmonary trunk (PT) region displays a reservoir function and that a pharmacologically induced fall in pulmonary vascular resistance (PVR) increases and redistributes diastolic discharge from this central pulmonary reservoir toward the lungs, thereby producing a positive diastolic offset in the pulmonary arterial (PA) blood flow profile. As a similar offset in PA flow characteristically occurs after birth, this study tested the hypotheses that 1) central pulmonary reservoir discharge is both redistributed toward the lungs and increased in magnitude during the birth transition and 2) discharge from this reservoir constitutes a major component of increased PA diastolic blood flow after birth. Six anesthetized near-term fetal lambs were instrumented with PT, ductal and left PA transit-time flow probes, and aortic, PT and left atrial catheters. Hemodynamic data were recorded in fetuses and at regular intervals during 2-h mechanical ventilation following cesarean section delivery. Diastolic PA blood flow rose from near zero in fetuses to 468 ± 188 ml/min by 15 min ( P < 0.001). Central pulmonary reservoir discharge in fetuses (99 ± 44 ml/min) passed primarily right-to-left across the ductus. However, this reservoir discharge redistributed entirely to the lungs by 1 min after birth, and then doubled to a peak of 214 ± 167 ml/min at 15 min ( P < 0.001). Reservoir discharge subsequently stabilized at 151 ± 60 ml/min at 30–120 min, which comprised ∼50% of diastolic and ∼20% of mean PA blood flow. These findings suggest that enhanced diastolic central pulmonary reservoir discharge plays a major role in supporting an increased pulmonary perfusion after birth.

Impact of coronary bifurcation morphology on wave propagation

The branching pattern of the coronary vasculature is a key determinant of its function and plays a crucial role in shaping the pressure and velocity wave forms measured for clinical diagnosis. However, although multiple scaling laws have been proposed to characterize the branching pattern, the implications they have on wave propagation remain unassessed to date. To bridge this gap, we have developed a new theoretical framework by combining the mathematical formulation of scaling laws with the wave propagation theory in the pulsatile flow regime. This framework was then validated in multiple species using high-resolution cryomicrotome images of porcine, canine, and human coronary networks. Results demonstrate that the forward well-matchedness (no reflection for pressure/flow waves traveling from the coronary stem toward the microcirculation) is a salient feature in the coronary vasculature, and this result remains robust under many scenarios of the underlying pulse wave speed distribution assumed in the network. This result also implies a significant damping of the backward traveling waves, especially for smaller vessels (radius, <0.3 mm). Furthermore, the theoretical prediction of increasing area ratios (ratio between the area of the mother and daughter vessels) in more symmetric bifurcations found in the distal circulation was confirmed by experimental measurements. No differences were observed by clustering the vessel segments in terms of transmurality (from epicardium to endocardium) or perfusion territories (left anterior descending, left circumflex, and right coronary artery).

Influence of anatomical dominance and hypertension on coronary conduit arterial and microcirculatory flow patterns: a multiscale modeling study

Coronary hemodynamics are known to be affected by intravascular and extravascular factors that vary regionally and transmurally between the perfusion territories of left and right coronary arteries. However, despite clinical evidence that left coronary arterial dominance portends greater cardiovascular risk, relatively little is known about the effects of left or right dominance on regional conduit arterial and microcirculatory blood flow patterns, particularly in the presence of systemic or pulmonary hypertension. We addressed this issue using a multiscale numerical model of the human coronary circulation situated in a closed-loop cardiovascular model. The coronary model represented left or right dominant anatomies and accounted for transmural and regional differences in vascular properties and extravascular compression. Regional coronary flow dynamics of the two anatomical variants were compared under normotensive conditions, raised systemic or pulmonary pressures with maintained flow demand, and after accounting for adaptations known to occur in acute and chronic hypertensive states. Key findings were that 1) right coronary arterial flow patterns were strongly influenced by dominance and systemic/pulmonary hypertension; 2) dominance had minor effects on left coronary arterial and all microvascular flow patterns (aside from mean circumflex flow); 3) although systemic hypertension favorably increased perfusion pressure, this benefit varied regionally and transmurally and was offset by increased left ventricular and septal flow demands; and 4) pulmonary hypertension had a substantial negative effect on right ventricular and septal flows, which was exacerbated by greater metabolic demands. These findings highlight the importance of interactions between coronary arterial dominance and hypertension in modulating coronary hemodynamics.

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit.

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

Introduction

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

Aim

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

Methods

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

Results

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

Conclusion

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

In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.

A unified method for estimating pressure losses at vascular junctions

In reduced-order (0D/1D) blood or respiratory flow models, pressure losses at junctions are usually neglected. However, these may become important where velocities are high and significant flow redirection occurs. Current methods for estimating losses rely on relatively complex empirical equations that are only valid for specific junction geometries and flow regimes. In pulsatile multi-directional flows, switching between empirical equations upon reversing flow may introduce unrealistic discontinuities in simulated haemodynamic waveforms. Drawing from work by Bassett et al. (SAE Trans 112:565-583, 2003), we therefore developed a unified method (Unified0D) for estimating loss coefficients that can be applied to any junction (i.e. any number of branches at any angle) and any flow regime. Discontinuities in simulated waveforms were avoided by extending Bassett et al.'s control volume-based method to incorporate a 'pseudodatum' supplier branch, an imaginary effective vessel containing all inflow to the junction. Energy exchange between diverging flow streams was also accounted for empirically. The formulation was validated using high resolution computational fluid dynamics in a wide range flow conditions and junction configurations. In a pulsatile 1D simulation exhibiting transitions between four different flow regimes, the new formulation produced smooth transitions in calculated pressure losses.

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.