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

Guidelines for mechanistic modeling and analysis in cardiovascular research

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Investigation into the two-way interaction of coronary flow and heart function in coronary artery disease predicted by a computational model of autoregulation of coronary flow

This study presents a closed-loop computational model to investigate the interplay between heart function, coronary flow, and systemic circulation during exercise, with a specific focus on the impact of coronary artery stenosis. The model incorporates a lumped representation of the heart, main arteries, and coronary arteries, establishing a closed circulatory system. The simulation investigates the autoregulation of coronary flow in response to myocardial oxygen demands during physical exercise by incorporating sympathetic and parasympathetic functions. This study establishes a closed supply-demand loop and investigates the effect of coronary flow deficiency on heart function and systemic circulation in coronary artery diseases during exercise. In coronary artery diseases with low stenosis, heart function and systemic flow resemble those of a healthy person. However, as stenosis intensifies with physical exercise, an additional regulatory mechanism (reg2) is activated. This mechanism adjusts coronary flow by reducing myocardial contractility (E) and increasing heart rate (HR) while maintaining cardiac output (CO). The study results indicate that, at the highest exercise intensity for a healthy individual (HR = 150), the value of E increases from 6 to 8.65mmHg/ml. Meanwhile, for a patient with 85 % coronary artery stenosis in the same exercise intensity, the HR increases to 200, and the value of E decreases to 3.45mmHg/ml. The results also demonstrate that the initiation of the (reg2) mechanism at rest occurs at 83 % stenosis, while at the highest exercise intensity, this mechanism commences at 67 % stenosis.

A new synergistic model for simulating exercise incorporating control mechanisms at cellular and organ scales

The physiological response of the cardio-vascular system (CVS) to physical activity is of great importance to those working in sporting research and has profound consequences for the health and well-being of people. Coronary vasodilation and the physiological mechanisms involved in exercise have frequently been the focus of numerical models for simulating exercise. This is partly achieved using the time-varying-elastance (TVE) theory, which prescribes the pressure-volume relationship of the ventricle as a periodic function of time, tuned using empirical data. The empirical foundations of the TVE method however, and its suitability for CVS modelling are frequently questioned. To overcome this challenge, we adopt a different synergistic approach in which a model for the microscale heart muscle (myofibers) activity is embedded within a macro organ-scale CVS model. We developed such a synergistic model by including the coronary flow and various control mechanisms at the circulation level through feedback and feedforward means, and at the microscale (contractile) through the regulation of ATP availability and myofiber force depending on exercise intensity or heart rate. The coronary flow produced by the model displays the well-known 2-phase character of the flow, which is preserved under exercise. The model is tested by simulating reactive hyperemia, which is a transient occlusion of the coronary flow, successfully reproducing the additional coronary flow following the block removal. On-transient exercise results reveal a rise in both cardiac output and mean ventricle pressure as expected. The stroke volume increases initially, but then declines during the latter period of HR rise, corresponding with one of the main physiological responses to exercise. The pressure-volume loop expands during exercise, as systolic pressure rises. The Myocardial oxygen demand increases during exercise and the coronary blood supply increases in response, causing an excess of oxygen supply to the heart. Off-transient exercise recovery is largely a reverse of this response, although the behaviour is slightly more varied, with sudden spikes in coronary resistance. Different levels of fitness and exercise intensity are tested and reveal that the stroke volume rises until a level of myocardial oxygen demand is reached at which point it declines. This level of demand is independent of fitness or exercise intensity. An advantage of our model is demonstrated in the correspondence between the micro and organ scale mechanics so that cellular pathologies can be traced from exercise performance with relatively little computational or experimental expense.

Myocardial perfusion and flow reserve in the asynchronous heart: mechanistic insight from a computational model

The tight coupling between myocardial oxygen demand and supply has been recognized for decades, but it remains controversial whether this coupling persists under asynchronous activation, such as during left bundle branch block (LBBB). Furthermore, it is unclear whether the amount of local cardiac wall growth, following longer-lasting asynchronous activation, can explain differences in myocardial perfusion distribution between subjects. For a better understanding of these matters, we built upon our existing modeling framework for cardiac mechanics-to-perfusion coupling by incorporating coronary autoregulation. Regional coronary flow was regulated with a vasodilator signal based on regional demand, as estimated from regional fiber stress-strain area. Volume of left ventricular wall segments was adapted with chronic asynchronous activation toward a homogeneous distribution of myocardial oxygen demand per tissue weight. Modeling results show that 1) both myocardial oxygen demand and supply are decreased in early activated regions and increased in late-activated regions; 2) but that regional hyperemic flow remains unaffected; while 3) regional myocardial flow reserve (the ratio of hyperemic to resting myocardial flow) decreases with increases in absolute regional myocardial oxygen demand as well as with decreases in wall thickness. These findings suggest that septal hypoperfusion in LBBB represents an autoregulatory response to reduced myocardial oxygen demand. Furthermore, oxygen demand-driven remodeling of wall mass can explain asymmetric hypertrophy and the related homogenization of myocardial perfusion and flow reserve. Finally, the inconsistent observations of myocardial perfusion distribution can primarily be explained by the degree of dyssynchrony, the degree of asymmetric hypertrophy, and the imaging modality used.NEW & NOTEWORTHY This versatile modeling framework couples myocardial oxygen demand to oxygen supply and myocardial growth, enabling simulation of resting and hyperemic myocardial flow during acute and chronic asynchronous ventricular activation. Model-based findings suggest that reported inconsistencies in myocardial perfusion and flow reserve responses with asynchronous ventricular activation between patients can primarily be explained by the degree of dyssynchrony and wall mass remodeling, which together determine the heterogeneity in regional oxygen demand and, hence, supply with autoregulation.

A Computational Study of Dynamic Obstruction in Type B Aortic Dissection

A serious complication in aortic dissection is dynamic obstruction of the true lumen (TL). Dynamic obstruction results in malperfusion, a blockage of blood flow to a vital organ. Clinical data reveal that increases in central blood pressure promote dynamic obstruction. However, the mechanisms by which high pressures result in TL collapse are underexplored and poorly understood. Here, we developed a computational model to investigate biomechanical and hemodynamical factors involved in Dynamic obstruction. We hypothesize that relatively small pressure gradient between TL and false lumen (FL) are sufficient to displace the flap and induce obstruction. An idealized fluid-structure interaction model of type B aortic dissection was created. Simulations were performed under mean cardiac output while inducing dynamic changes in blood pressure by altering FL outflow resistance. As FL resistance increased, central aortic pressure increased from 95.7 to 115.3 mmHg. Concurrent with blood pressure increase, flap motion was observed, resulting in TL collapse, consistent with clinical findings. The maximum pressure gradient between TL and FL over the course of the dynamic obstruction was 4.5 mmHg, consistent with our hypothesis. Furthermore, the final stage of dynamic obstruction was very sudden in nature, occurring over a short time (<1 s) in our simulation, consistent with the clinical understanding of this dramatic event. Simulations also revealed sudden drops in flow and pressure in the TL in response to the flap motion, consistent with first stages of malperfusion. To our knowledge, this study represents the first computational analysis of potential mechanisms driving dynamic obstruction in aortic dissection.

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.

Data-driven computational models of ventricular-arterial hemodynamics in pediatric pulmonary arterial hypertension

Pulmonary arterial hypertension (PAH) is a complex disease involving increased resistance in the pulmonary arteries and subsequent right ventricular (RV) remodeling. Ventricular-arterial interactions are fundamental to PAH pathophysiology but are rarely captured in computational models. It is important to identify metrics that capture and quantify these interactions to inform our understanding of this disease as well as potentially facilitate patient stratification. Towards this end, we developed and calibrated two multi-scale high-resolution closed-loop computational models using open-source software: a high-resolution arterial model implemented using CRIMSON, and a high-resolution ventricular model implemented using FEniCS. Models were constructed with clinical data including non-invasive imaging and invasive hemodynamic measurements from a cohort of pediatric PAH patients. A contribution of this work is the discussion of inconsistencies in anatomical and hemodynamic data routinely acquired in PAH patients. We proposed and implemented strategies to mitigate these inconsistencies, and subsequently use this data to inform and calibrate computational models of the ventricles and large arteries. Computational models based on adjusted clinical data were calibrated until the simulated results for the high-resolution arterial models matched within 10% of adjusted data consisting of pressure and flow, whereas the high-resolution ventricular models were calibrated until simulation results matched adjusted data of volume and pressure waveforms within 10%. A statistical analysis was performed to correlate numerous data-derived and model-derived metrics with clinically assessed disease severity. Several model-derived metrics were strongly correlated with clinically assessed disease severity, suggesting that computational models may aid in assessing PAH severity.

A Combined Computational Fluid Dynamics and Arterial Spin Labeling MRI Modeling Strategy to Quantify Patient-Specific Cerebral Hemodynamics in Cerebrovascular Occlusive Disease

Cerebral hemodynamics in the presence of cerebrovascular occlusive disease (CVOD) are influenced by the anatomy of the intracranial arteries, the degree of stenosis, the patency of collateral pathways, and the condition of the cerebral microvasculature. Accurate characterization of cerebral hemodynamics is a challenging problem. In this work, we present a strategy to quantify cerebral hemodynamics using computational fluid dynamics (CFD) in combination with arterial spin labeling MRI (ASL). First, we calibrated patient-specific CFD outflow boundary conditions using ASL-derived flow splits in the Circle of Willis. Following, we validated the calibrated CFD model by evaluating the fractional blood supply from the main neck arteries to the vascular territories using Lagrangian particle tracking and comparing the results against vessel-selective ASL (VS-ASL). Finally, the feasibility and capability of our proposed method were demonstrated in two patients with CVOD and a healthy control subject. We showed that the calibrated CFD model accurately reproduced the fractional blood supply to the vascular territories, as obtained from VS-ASL. The two patients revealed significant differences in pressure drop over the stenosis, collateral flow, and resistance of the distal vasculature, despite similar degrees of clinical stenosis severity. Our results demonstrated the advantages of a patient-specific CFD analysis for assessing the hemodynamic impact of stenosis.

Branch flow distribution approach and its application in the calculation of fractional flow reserve in stenotic coronary artery

OBJECTIVE

To calculate fractional flow reserve (FFR) based on computed tomography angiography (i.e., FFRCT) by considering the branch flow distribution in the coronary arteries.

BACKGROUND

FFR is the gold standard to diagnose myocardial ischemia caused by coronary stenosis. An accurate and noninvasive method for obtaining total coronary blood flow is needed for the calculation of FFRCT.

METHODS

A mathematical model for estimating the coronary blood flow rate and two approaches for setting the patient-specific flow boundary condition were proposed. Coronary branch flow distribution methods based on a volume-flow approach and a diameter-flow approach were employed for the numerical simulation of FFRCT. The values of simulated FFRCT for 16 patients were compared with their clinically measured FFR.

RESULTS

The ratio of total coronary blood flow to cardiac output and the myocardial blood flow under the condition of hyperemia were 16.97% and 4.07 mL/min/g, respectively. The errors of FFRCT compared with clinical data under the volume-flow approach and diameter-flow approach were 10.47% and 11.76%, respectively, the diagnostic accuracies of FFRCT were 65% and 85%, and the consistencies were 95% and 90%.

CONCLUSIONS

The mathematical model for estimating the coronary blood flow rate and the coronary branch flow distribution method can be applied to calculate the value of clinical noninvasive FFRCT.

CRIMSON: An open-source software framework for cardiovascular integrated modelling and simulation

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) software environment. CRIMSON provides a powerful, customizable and user-friendly system for performing three-dimensional and reduced-order computational haemodynamics studies via a pipeline which involves: 1) segmenting vascular structures from medical images; 2) constructing analytic arterial and venous geometric models; 3) performing finite element mesh generation; 4) designing, and 5) applying boundary conditions; 6) running incompressible Navier-Stokes simulations of blood flow with fluid-structure interaction capabilities; and 7) post-processing and visualizing the results, including velocity, pressure and wall shear stress fields. A key aim of CRIMSON is to create a software environment that makes powerful computational haemodynamics tools accessible to a wide audience, including clinicians and students, both within our research laboratories and throughout the community. The overall philosophy is to leverage best-in-class open source standards for medical image processing, parallel flow computation, geometric solid modelling, data assimilation, and mesh generation. It is actively used by researchers in Europe, North and South America, Asia, and Australia. It has been applied to numerous clinical problems; we illustrate applications of CRIMSON to real-world problems using examples ranging from pre-operative surgical planning to medical device design optimization.

Preclinical techniques to investigate exercise training in vascular pathophysiology

Atherosclerosis is a dynamic process starting with endothelial dysfunction and inflammation and eventually leading to life-threatening arterial plaques. Exercise generally improves endothelial function in a dose-dependent manner by altering hemodynamics, specifically by increased arterial pressure, pulsatility, and shear stress. However, athletes who regularly participate in high-intensity training can develop arterial plaques, suggesting alternative mechanisms through which excessive exercise promotes vascular disease. Understanding the mechanisms that drive atherosclerosis in sedentary versus exercise states may lead to novel rehabilitative methods aimed at improving exercise compliance and physical activity. Preclinical tools, including in vitro cell assays, in vivo animal models, and in silico computational methods, broaden our capabilities to study the mechanisms through which exercise impacts atherogenesis, from molecular maladaptation to vascular remodeling. Here, we describe how preclinical research tools have and can be used to study exercise effects on atherosclerosis. We then propose how advanced bioengineering techniques can be used to address gaps in our current understanding of vascular pathophysiology, including integrating in vitro, in vivo, and in silico studies across multiple tissue systems and size scales. Improving our understanding of the antiatherogenic exercise effects will enable engaging, targeted, and individualized exercise recommendations to promote cardiovascular health rather than treating cardiovascular disease that results from a sedentary lifestyle.

A flexible framework for sequential estimation of model parameters in computational hemodynamics

A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A "Netlist" implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

Cardiac remodelling following thoracic endovascular aortic repair for descending aortic aneurysms

OBJECTIVES

Current endografts for thoracic endovascular aortic repair (TEVAR) are much stiffer than the aorta and have been shown to induce acute stiffening. In this study, we aimed to estimate the impact of TEVAR on left ventricular (LV) stroke work (SW) and mass using a non-invasive image-based workflow.

METHODS

The University of Michigan database was searched for patients treated with TEVAR for descending aortic pathologies (2013-2016). Patients with available pre-TEVAR and post-TEVAR computed tomography angiography and echocardiography data were selected. LV SW was estimated via patient-specific fluid-structure interaction analyses. LV remodelling was quantified through morphological measurements using echocardiography and electrocardiographic-gated computed tomography angiography data.

RESULTS

Eight subjects were included in this study, the mean age of the patients was 68 (73, 25) years, and 6 patients were women. All patients were prescribed antihypertensive drugs following TEVAR. The fluid-structure interaction simulations computed a 26% increase in LV SW post-TEVAR [0.94 (0.89, 0.34) J to 1.18 (1.11, 0.65) J, P = 0.012]. Morphological measurements revealed an increase in the LV mass index post-TEVAR of +26% in echocardiography [72 (73, 17)  g/m2 to 91 (87, 26)  g/m2, P = 0.017] and +15% in computed tomography angiography [52 (46, 29)  g/m2 to 60 (57, 22)  g/m2, P = 0.043]. The post- to pre-TEVAR LV mass index ratio was positively correlated with the post- to pre-TEVAR ratios of SW and the mean blood pressure (ρ = 0.690, P = 0.058 and ρ = 0.786, P = 0.021, respectively).

CONCLUSIONS

TEVAR was associated with increased LV SW and mass during follow-up. Medical device manufacturers should develop more compliant devices to reduce the stiffness mismatch with the aorta. Additionally, intensive antihypertensive management is needed to control blood pressure post-TEVAR.

Computational analysis of renal artery flow characteristics by modeling aortoplasty and aortic bypass interventions for abdominal aortic coarctation

OBJECTIVE

Suprarenal abdominal aortic coarctation (SAAC) alters flow and pressure patterns to the kidneys and is often associated with severe angiotensin-mediated hypertension refractory to drug therapy. SAAC is most often treated by a thoracoabdominal bypass (TAB) or patch aortoplasty (PA). It is currently unclear what effect these interventions have on renal flow and pressure waveforms. This study, using retrospective data from a patient with SAAC subjected to a TAB, undertook computational modeling to analyze aortorenal blood flow preoperatively as well as postoperatively after a variety of TAB and PA interventions.

METHODS

Patient-specific anatomic models were constructed from preoperative computed tomography angiograms of a 9-year-old child with an isolated SAAC. Fluid-structure interaction (FSI) simulations of hemodynamics were performed to analyze preoperative renal flow and pressure waveforms. A parametric study was then performed to examine the hemodynamic impact of different bypass diameters and patch oversizing.

RESULTS

Preoperative FSI results documented diastole-dominated renal perfusion with considerable high-frequency disturbances in blood flow and pressure. The postoperative TAB right and left kidney volumes increased by 58% and 79%, respectively, reflecting the increased renal artery blood flows calculated by the FSI analysis. Postoperative increases in systolic flow accompanied decreases in high-frequency disturbances, aortic pressure, and collateral flow after all surgical interventions. In general, lesser degrees of high-frequency disturbances followed PA interventions. High-frequency disturbances were eliminated with the 0% PA in contrast to the 30% and 50% PA oversizing and TAB interventions, in which these flow disturbances remained.

CONCLUSIONS

Both TAB and PA dramatically improved renal artery flow and pressure waveforms, although disturbed renal waveforms remained in many of the surgical scenarios. Importantly, only the 0% PA oversizing scenario eliminated all high-frequency disturbances, resulting in nearly normal aortorenal blood flow. The study also establishes the relevance of patient-specific computational modeling in planning interventions for the midaortic syndrome.

Computational Fluid Dynamics of Vascular Disease in Animal Models

Recent applications of computational fluid dynamics (CFD) applied to the cardiovascular system have demonstrated its power in investigating the impact of hemodynamics on disease initiation, progression, and treatment outcomes. Flow metrics such as pressure distributions, wall shear stresses (WSS), and blood velocity profiles can be quantified to provide insight into observed pathologies, assist with surgical planning, or even predict disease progression. While numerous studies have performed simulations on clinical human patient data, it often lacks prediagnosis information and can be subject to large intersubject variability, limiting the generalizability of findings. Thus, animal models are often used to identify and manipulate specific factors contributing to vascular disease because they provide a more controlled environment. In this review, we explore the use of CFD in animal models in recent studies to investigate the initiating mechanisms, progression, and intervention effects of various vascular diseases. The first section provides a brief overview of the CFD theory and tools that are commonly used to study blood flow. The following sections are separated by anatomical region, with the abdominal, thoracic, and cerebral areas specifically highlighted. We discuss the associated benefits and obstacles to performing CFD modeling in each location. Finally, we highlight animal CFD studies focusing on common surgical treatments, including arteriovenous fistulas (AVF) and pulmonary artery grafts. The studies included in this review demonstrate the value of combining CFD with animal imaging and should encourage further research to optimize and expand upon these techniques for the study of vascular disease.

Patient-specific modeling of right coronary circulation vulnerability post-liver transplant in Alagille's syndrome

OBJECTIVES

Cardiac output (CO) response to dobutamine can identify Alagille's syndrome (ALGS) patients at higher risk of cardiovascular complications during liver transplantation. We propose a novel patient-specific computational methodology to estimate the coronary autoregulatory responses during different hemodynamic conditions, including those experienced in a post-reperfusion syndrome (PRS), to aid cardiac risk-assessment.

MATERIAL AND METHODS

Data (pressure, flow, strain and ventricular volumes) from a 6-year-old ALGS patient undergoing catheter/dobutamine stress MRI (DSMRI) were used to parameterize a closed-loop coupled-multidomain (3D-0D) approach consisting of image-derived vascular models of pulmonary and systemic circulations and a series of 0D-lumped parameter networks (LPN) of the heart chambers and the distal arterial and venous circulations. A coronary microcirculation control model (CMCM) was designed to adjust the coronary resistance to match coronary blood flow (and thus oxygen delivery) with MVO2 requirements during Rest, Stress and a virtual PRS condition.

RESULTS

In all three simulated conditions, diastolic dominated right coronary artery (RCA) flow was observed, due to high right ventricle (RV) afterload. Despite a measured 45% increase in CO, impaired coronary flow reserve (CFR) (~1.4) at Stress was estimated by the CMCM. During modeled PRS, a marked vasodilatory response was insufficient to match RV myocardial oxygen requirements. Such exhaustion of the RCA autoregulatory response was not anticipated by the DSMRI study.

CONCLUSION

Impaired CFR undetected by DSMRI resulted in predicted myocardial ischemia in a computational model of PRS. This computational framework may identify ALGS patients at higher risk of complications during liver transplantation due to impaired coronary microvascular responses.

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.

Non-invasive instantaneous wave-free ratio using coronary CT angiography: diagnostic performance for evaluation of ischaemia-causing coronary stenosis confirmed by invasive fractional flow reserve

AIM

To determine the diagnostic performance of instantaneous wave-free ratio (iFR) derived from non-invasive coronary computed tomography angiography (CTA; iFR_CT) for ischaemia-causing coronary stenosis, and to compare the diagnostic efficacy of iFR_CT, CTA, and CTA plus iFR_CT.

METHODS AND MATERIALS

Thirty-nine patients (55 vessels) with known or suspected coronary artery disease were included. All patients underwent invasive coronary angiography and fractional flow reserve (FFR) according to CTA findings and clinical indicators. The same raw data used for CTA were used to build patient-specific computed flow dynamic models and to calculate iFR_CT.

RESULTS

On a vessel-based level, the correlation between iFR_CT and FFR was moderate (r=0.65, p<0.05); the optimal iFR_CT cut-off value was 0.85 based on an FFR cut-off value of 0.80, resulting in 85% sensitivity, 69% specificity, 61% positive predictive value (PPV), 89% negative predictive value (NPV), and 75% accuracy. The AUC showed significant differences between iFR_CT and CTA (vessel-based: 0.84 versus 0.68; patient-based: 0.84 versus 0.62; both p<0.01). The accuracy of CTA combined with iFR_CT was significantly increased compared to CTA alone for vessels with intermediate stenosis (83% versus 40%, p<0.01).

CONCLUSION

iFR_CT showed better diagnostic performance than CTA. iFR_CT may be a promising method for detection of ischaemia-causing coronary stenosis, even in vessels with intermediate stenosis.

The Use of Biophysical Flow Models in the Surgical Management of Patients Affected by Chronic Thromboembolic Pulmonary Hypertension

Introduction: Chronic Thromboembolic Pulmonary Hypertension (CTEPH) results from progressive thrombotic occlusion of the pulmonary arteries. It is treated by surgical removal of the occlusion, with success rates depending on the degree of microvascular remodeling. Surgical eligibility is influenced by the contributions of both the thrombus occlusion and microvasculature remodeling to the overall vascular resistance. Assessing this is challenging due to the high inter-individual variability in arterial morphology and physiology. We investigated the potential of patient-specific computational flow modeling to quantify pressure gradients in the pulmonary arteries of CTEPH patients to assist the decision-making process for surgical eligibility.

Methods: Detailed segmentations of the pulmonary arteries were created from postoperative chest Computed Tomography scans of three CTEPH patients. A focal stenosis was included in the original geometry to compare the pre- and post-surgical hemodynamics. Three-dimensional flow simulations were performed on each morphology to quantify velocity-dependent pressure changes using a finite element solver coupled to terminal 2-element Windkessel models. In addition to transient flow simulations, a parametric modeling approach based on constant flow simulations is also proposed as faster technique to estimate relative pressure drops through the proximal pulmonary vasculature.

Results: An asymmetrical flow split between left and right pulmonary arteries was observed in the stenosed models. Removing the proximal obstruction resulted in a reduction of the right-left pressure imbalance of up to 18%. Changes were also observed in the wall shear stresses and flow topology, where vortices developed in the stenosed model while the non-stenosed retained a helical flow. The predicted pressure gradients from constant flow simulations were consistent with the ones measured in the transient flow simulations.

Conclusion: This study provides a proof of concept that patient-specific computational modeling can be used as a noninvasive tool for assisting surgical decisions in CTEPH based on hemodynamics metrics. Our technique enables determination of the proximal relative pressure, which could subsequently be compared to the total pressure drop to determine the degree of distal and proximal vascular resistance. In the longer term this approach has the potential to form the basis for a more quantitative classification system of CTEPH types.

Patient-Specific Modeling of Hemodynamics: Supporting Surgical Planning in a Fontan Circulation Correction

Computational fluid dynamics (CFD) is a modeling technique that enables calculation of the behavior of fluid flows in complex geometries. In cardiovascular medicine, CFD methods are being used to calculate patient-specific hemodynamics for a variety of applications, such as disease research, noninvasive diagnostics, medical device evaluation, and surgical planning. This paper provides a concise overview of the methods to perform patient-specific computational analyses using clinical data, followed by a case study where CFD-supported surgical planning is presented in a patient with Fontan circulation complicated by unilateral pulmonary arteriovenous malformations. In closing, the challenges for implementation and adoption of CFD modeling in clinical practice are discussed.

Computational Fluid Dynamics and Additive Manufacturing to Diagnose and Treat Cardiovascular Disease

Noninvasive engineering models are now being used for diagnosing and planning the treatment of cardiovascular disease. Techniques in computational modeling and additive manufacturing have matured concurrently, and results from simulations can inform and enable the design and optimization of therapeutic devices and treatment strategies. The emerging synergy between large-scale simulations and 3D printing is having a two-fold benefit: first, 3D printing can be used to validate the complex simulations, and second, the flow models can be used to improve treatment planning for cardiovascular disease. In this review, we summarize and discuss recent methods and findings for leveraging advances in both additive manufacturing and patient-specific computational modeling, with an emphasis on new directions in these fields and remaining open questions.

Computational Fluid Dynamics and Aortic Thrombus Formation Following Thoracic Endovascular Aortic Repair

BACKGROUND

We present the possible utility of computational fluid dynamics in the assessment of thrombus formation and virtual surgical planning illustrated in a patient with aortic thrombus in a kinked ascending aortic graft following thoracic endovascular aortic repair.

METHODS

A patient-specific three-dimensional model was built from computed tomography. Additionally, we modeled 3 virtual aortic interventions to assess their effect on thrombosis potential: (1) open surgical repair, (2) conformable endografting, and (3) single-branched endografting. Flow waveforms were extracted from echocardiography and used for the simulations. We used the computational index termed platelet activation potential (PLAP) representing accumulated shear rates of fluid particles within a fluid domain to assess thrombosis potential.

RESULTS

The baseline model revealed high PLAP in the entire arch (119.8 ± 42.5), with significantly larger PLAP at the thrombus location (125.4 ± 41.2, p < 0.001). Surgical repair showed a 37% PLAP reduction at the thrombus location (78.6 ± 25.3, p < 0.001) and a 24% reduction in the arch (91.6 ± 28.9, p < 0.001). Single-branched endografting reduced PLAP in the thrombus region by 20% (99.7 ± 24.6, p < 0.001) and by 14% in the arch (103.8 ± 26.1, p < 0.001), whereas a more conformable endograft did not have a profound effect, resulting in a modest 4% PLAP increase (130.6 ± 43.7, p < 0.001) in the thrombus region relative to the baseline case.

CONCLUSIONS

Regions of high PLAP were associated with aortic thrombus. Aortic repair resolved pathologic flow patterns, reducing PLAP. Branched endografting also relieved complex flow patterns reducing PLAP. Computational fluid dynamics may assist in the prediction of aortic thrombus formation in hemodynamically complex cases and help guide repair strategies.

Reproducing Patient-Specific Hemodynamics in the Blalock-Taussig Circulation Using a Flexible Multi-Domain Simulation Framework: Applications for Optimal Shunt Design

For babies born with hypoplastic left heart syndrome, several open-heart surgeries are required. During Stage I, a Norwood procedure is performed to construct an appropriate circulation to both the systemic and the pulmonary arteries. The pulmonary arteries receive flow from the systemic circulation, often using a Blalock-Taussig (BT) shunt between the innominate artery and the right pulmonary artery. This procedure causes significantly disturbed flow in the pulmonary arteries. In this study, we use computational hemodynamic simulations to demonstrate its capacity for examining the properties of the flow through and near the BT shunt. Initially, we construct a computational model which produces blood flow and pressure measurements matching the clinical magnetic resonance imaging (MRI) and catheterization data. Achieving this required us to determine the level of BT shunt occlusion; because the occlusion is below the MRI resolution, this information is difficult to recover without the aid of computational simulations. We determined that the shunt had undergone an effective diameter reduction of 22% since the time of surgery. Using the resulting geometric model, we show that we can computationally reproduce the clinical data. We, then, replace the BT shunt with a hypothetical alternative shunt design with a flare at the distal end. Investigation of the impact of the shunt design reveals that the flare can increase pulmonary pressure by as much as 7% and flow by as much as 9% in the main pulmonary branches, which may be beneficial to the pulmonary circulation.