Hemodynamic performance of the Fontan circulation compared with a normal biventricular circulation: a computational model study

Mathematical analysis of left ventricular elastance with respect to afterload change during ejection phase

Since the left ventricle (LV) has pressure (Plv) and volume (Vlv), we can define LV elastance from the ratio between Plv and Vlv, termed as "instantaneous elastance." On the other hand, end-systolic elastance (Emax) is known to be a good index of LV contractility, which is measured by the slope of several end-systolic Plv-Vlv points obtained by using different loads. The word Emax originates from the assumption that LV elastance increases during the ejection phase and attains its maximum at the end-systole. From this concept, we can define another elastance determined by the slope of isochronous Plv-Vlv points, that is Plv-Vlv points at a certain time after the ejection onset time by using different loads. We refer to this elastance as "load-dependent elastance." To reveal the relation between these two elastances, we used a hemodynamic model that included a detailed ventricular myocyte contraction model. From the simulation results, we found that the isochronous Plv-Vlv points lay in one line and that the line slope corresponding to the load-dependent elastance slightly decreased during the ejection phase, which is quite different from the instantaneous elastance. Subsequently, we analyzed the mechanism determining these elastances from the model equations. We found that instantaneous elastance is directly related to contraction force generated by the ventricular myocyte, but the load-dependent elastance is determined by two factors: one is the transient characteristics of the cardiac cell, i.e., the velocity-dependent force drops characteristics in instantaneous shortening. The other is the force-velocity relation of the cardiac cell. We also found that the linear isochronous pressure-volume relation is based on the approximately linear relation between the time derivative of the cellular contraction force and the cellular shortening velocity that results from the combined characteristics of LV and aortic compliances.

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

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

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.

Optimal Fenestration of the Fontan Circulation

In this paper, we develop a pulsatile compartmental model of the Fontan circulation and use it to explore the effects of a fenestration added to this physiology. A fenestration is a shunt between the systemic and pulmonary veins that is added either at the time of Fontan conversion or at a later time for the treatment of complications. This shunt increases cardiac output and decreases systemic venous pressure. However, these hemodynamic benefits are achieved at the expense of a decrease in the arterial oxygen saturation. The model developed in this paper incorporates fenestration size as a parameter and describes both blood flow and oxygen transport. It is calibrated to clinical data from Fontan patients, and we use it to study the impact of a fenestration on several hemodynamic variables, including systemic oxygen availability, effective oxygen availability, and systemic venous pressure. In certain scenarios corresponding to high-risk Fontan physiology, we demonstrate the existence of a range of fenestration sizes in which the systemic oxygen availability remains relatively constant while the systemic venous pressure decreases.

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

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

Comprehensive assessments of pulmonary circulation in children with pulmonary hypertension associated with congenital heart disease

Pulmonary hypertension associated with congenital heart disease (CHD-PH) encompasses different conditions confounded by the left-to-right shunt, left heart obstruction, ventricular dysfunction, hypoxia due to airway obstruction, dysplasia/hypoplasia of the pulmonary vasculature, pulmonary vascular obstructive disease, and genetic variations of vasoactive mediators. Pulmonary input impedance consists of the pulmonary vascular resistance (Rp) and capacitance (Cp). Rp is calculated as the transpulmonary pressure divided by the pulmonary cardiac output, whereas Cp is calculated as the pulmonary stroke volume divided by the pulmonary arterial pulse pressure. The plots of Rp and Cp demonstrate a unique hyperbolic relationship, namely, the resistor-capacitor coupling curve, which represents the pulmonary vascular condition. The product of Rp and Cp is the exponential pressure decay, which refers to the time constant. Alterations in Cp are more considerable in CHD patients at an early stage of developing pulmonary hypertension or with excessive pulmonary blood flow due to a left-to-right shunt. The importance of Cp has gained attention because recent reports have shown that low Cp potentially reflects poor prognosis in patients with CHD-PH and idiopathic pulmonary hypertension. It is also known that Cp levels decrease in specific populations, such as preterm infants and trisomy 21. Therefore, both Rp and Cp should be individually evaluated in the management of children with CHD-PH who have different disease conditions.

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan circulations.

Model-based analysis of the sensitivities and diagnostic implications of FFR and CFR under various pathological conditions

Although fractional flow reserve (FFR) and coronary flow reserve (CFR) are both frequently used to assess the functional severity of coronary artery stenosis, discordant results of diagnosis between FFR and CFR in some patient cohorts have been reported. In the present study, a computational model was employed to quantify the impacts of various pathophysiological factors on FFR and CFR. In addition, a hyperemic myocardial ischemic index (HMIx) was proposed as a reference for comparing the diagnostic performances of FFR and CFR. Obtained results showed that CFR was more susceptible than FFR to the influence of many pathophysiological factors unrelated to coronary artery stenosis. In particular, the numerical study proved that increasing hyperemic coronary microvascular resistance significantly elevated FFR while reducing CFR despite fixed severity of coronary artery stenosis, whereas introducing aortic valve disease only caused a significant decrease in CFR with little influence on FFR. These results provided theoretical evidence for explaining some clinical observations, such as the increased risk of discordant diagnostic results between FFR and CFR in patients with increased hyperemic microvascular resistance, and significant increase in CFR after surgical relief of severe aortic valve disease. When evaluated with respect to the predictive value for hyperemic myocardial ischemia, the performance of FFR was found to be considerably compromised in the presence of severe coronary vasodilation dysfunction or aortic valve disease, whereas the relationship between CFR and HMIx remained relatively stable, suggesting that CFR may be a more reliable indicator of myocardial ischemia under complex pathophysiological conditions.

Impact of Atrial Fibrillation on Fontan Circulation: Fontan Computational Model

BACKGROUND

Patients with Fontan circulation may develop heart failure resulting in atrial fibrillation during the late phase. Inotropic effects to ameliorate hemodynamics on the Fontan circulation are not well understood, especially when in atrial fibrillation. This study was performed to determine whether dobutamine therapy in patients with Fontan circulation has limited effects on improving hemodynamics.

METHODS

Lumped computational models (sinus and atrial fibrillation) were employed including biventricular, atriopulmonary connection (APC), and extracardiac total cavopulmonary connection (TCPC) Fontan models. The condition of atrial fibrillation including lack of atrial beat, irregular ventricular contraction, and time-varying elastance for the ventricle was introduced. A different dose of dobutamine was given by varying the elastance of the ventricle, heart rate, and peripheral resistance.

RESULTS

In all models, the cardiac output decreased by 22.5% to 25.8% in atrial fibrillation. At 10 μg/kg/min of dobutamine in sinus rhythm, the cardiac output increased by 32.3% in the biventricular model but by only 9.2% (p<0.001) and 9.1% (p<0.001) in the APC and TCPC Fontan models, respectively. At 10 μg/kg/min of dobutamine in atrial fibrillation, the percent increase in the cardiac output in the Fontan circulation [11.8% increase in APC (p<0.001) and 11.9% increase in TCPC (p<0.001)] was significantly less than that in the biventricular circulation (32.3% increase).

CONCLUSIONS

In the Fontan circulation, atrial fibrillation itself reduced the cardiac output by approximately 25%, and dobutamine had a limited effect on increasing the cardiac output, especially when in atrial fibrillation. Maintaining sinus rhythm in patients with Fontan circulation is very important.

Engineering Perspective on Cardiovascular Simulations of Fontan Hemodynamics: Where Do We Stand with a Look Towards Clinical Application

BACKGROUND

Cardiovascular simulations for patients with single ventricles undergoing the Fontan procedure can assess patient-specific hemodynamics, explore surgical advances, and develop personalized strategies for surgery and patient care. These simulations have not yet been broadly accepted as a routine clinical tool owing to a number of limitations. Numerous approaches have been explored to seek innovative solutions for improving methodologies and eliminating these limitations.

PURPOSE

This article first reviews the current state of cardiovascular simulations of Fontan hemodynamics. Then, it will discuss the technical progress of Fontan simulations with the emphasis of its clinical impact, noting that substantial improvements have been made in the considerations of patient-specific anatomy, flow, and blood rheology. The article concludes with insights into potential future directions involving clinical validation, uncertainty quantification, and computational efficiency. The advancements in these aspects could promote the clinical usage of Fontan simulations, facilitating its integration into routine clinical practice.

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.

Portosystemic shunt with hyperammonemia and high cardiac output as a complication after Fontan surgery

In the late phase after Fontan surgery, organ dysfunction due to high central venous pressure (CVP) is a major clinical problem. We have described the cases of two patients with portosystemic shunts who exhibited hyperammonemia and high cardiac output associated with peripheral vasodilatation after Fontan surgery. A high CVP in these patients may have resulted in the formation of a portosystemic shunt. We performed coil embolization and balloon-occluded retrograde transvenous obliteration for each case. The possibility of a portosystemic shunt as a postoperative complication of Fontan surgery should always be considered. Early detection and therapeutic intervention seem necessary from the viewpoint of stabilizing the Fontan circulation and delaying the progression of liver disorder. <Learning objectives: A portosystemic shunt may develop due to the high central venous pressure after Fontan surgery independent of hepatic disorder and should be considered as a potential cause of unexplained hyperammonemia and high cardiac output status. Transcatheter closure of the portosystemic shunt may improve the clinical status.>.

A female-specific cardiovascular lumped-parameter model

Historically, cardiovascular computational models have been developed considering the case of a 70 Kg male patient. However, hemodynamic quantities differ widely due to sex, age, and weight. In this study, we developed a female-specific model of the blood circulation of a young (18-40 y.o.) woman with BSA of 1.6 m². The lumped-parameter (0D) model, which includes the uterus, has been calibrated with female-specific parameters and validated with sex-specific literature data.

Cardiac and renal function interactions in heart failure with reduced ejection fraction: A mathematical modeling analysis

Congestive heart failure is characterized by suppressed cardiac output and arterial filling pressure, leading to renal retention of salt and water, contributing to further volume overload. Mathematical modeling provides a means to investigate the integrated function and dysfunction of heart and kidney in heart failure. This study updates our previously reported integrated model of cardiac and renal functions to account for the fluid exchange between the blood and interstitium across the capillary membrane, allowing the simulation of edema. A state of heart failure with reduced ejection fraction (HF-rEF) was then produced by altering cardiac parameters reflecting cardiac injury and cardiovascular disease, including heart contractility, myocyte hypertrophy, arterial stiffness, and systemic resistance. After matching baseline characteristics of the SOLVD clinical study, parameters governing rates of cardiac remodeling were calibrated to describe the progression of cardiac hemodynamic variables observed over one year in the placebo arm of the SOLVD clinical study. The model was then validated by reproducing improvements in cardiac function in the enalapril arm of SOLVD. The model was then applied to prospectively predict the response to the sodium-glucose co-transporter 2 (SGLT2) inhibitor dapagliflozin, which has been shown to reduce heart failure events in HF-rEF patients in the recent DAPAHF clinical trial by incompletely understood mechanisms. The simulations predict that dapagliflozin slows cardiac remodeling by reducing preload on the heart, and relieves congestion by clearing interstitial fluid without excessively reducing blood volume. This provides a quantitative mechanistic explanation for the observed benefits of SGLT2i in HF-rEF. The model also provides a tool for further investigation of heart failure drug therapies.

Comparison of Instantaneous Wave-Free Ratio (iFR) and Fractional Flow Reserve (FFR) with respect to Their Sensitivities to Cardiovascular Factors: A Computational Model-Based Study

While coronary revascularization strategies guided by instantaneous wave-free ratio (iFR) are, in general, noninferior to those guided by fractional flow reserve (FFR) with respect to the rate of major adverse cardiac events at one-year follow-up in patients with stable angina or an acute coronary syndrome, the overall accuracy of diagnosis with iFR in large patient cohorts is about 80% compared with the diagnosis with FFR. So far, it remains incompletely understood what factors contribute to the discordant diagnosis between iFR and FFR. In this study, a computational method was used to systemically investigate the respective effects of various cardiovascular factors on FFR and iFR. The results showed that deterioration in aortic valve disease (e.g., regurgitation or stenosis) led to a marked decrease in iFR and a mild increase in FFR given fixed severity of coronary artery stenosis and that increasing coronary microvascular resistance caused a considerable increase in both iFR and FFR, but the degree of increase in iFR was lower than that in FFR. These findings suggest that there is a high probability of discordant diagnosis between iFR and FFR in patients with severe aortic valve disease or coronary microcirculation dysfunction.

Hemodynamic Effects of A Simplified Venturi Conduit for Fontan Circulation: A Pilot, In Silico Analysis

Objectives: To study the effects of a self-powered Fontan circulation in both idealized Fontan models and patient-specific models. Methods: In silico, a conduit with a nozzle was introduced from ascending aorta into the anastomosis of superior vena cava and pulmonary artery. Computational fluid dynamics (CFD) simulation was applied to calculate the fluid fields of models. Three 3-dimentional idealized models with different offsets were reconstructed by computer-aided design to evaluate the effects of the self-powered conduit. Furthermore, to validate the effects in patient-specific models, the conduit was introduced to three reconstructed models with different offsets. Results: The pressures at superior venae cavae and inferior venae cavae were decreased in both idealized models (0.4 mmHg) and patient-specific models (0.7 mmHg). In idealized models, the flows to left lungs were decreased (70%) by the jets from the conduits. However, in patient-specific models, the reductions of blood to the left lungs were relatively limited (30%) comparing to idealized models. Conclusions: CFD simulation was applied to analyze the effectiveness of the Fontan self-powered conduit. This self-powered conduit may help to decrease the venae cavae pressures and increase the flow to pulmonary arteries.

Blood reservoir function in patients with Fontan circulation and asplenia syndrome

Splanchnic circulation constitutes a major portion of the vasculature capacitance and plays an important role in maintaining blood perfusion. Because patients with asplenia syndrome lack this vascular bed as a blood reservoir, they may have a unique blood volume and distribution, which may be related to their vulnerability to the haemodynamic changes often observed in clinical practice. During cardiac catheterisation, the mean circulatory filling pressure was calculated with the Valsalva manoeuvre in 19 patients with Fontan circulation, including 5 patients with asplenia syndrome. We also measured the cardiac output index and circulatory blood volume by using a dye dilution technique. The blood volume and the mean circulatory filling pressure and the venous capacitance in patients with asplenia syndrome were similar to those in the remaining patients with Fontan circulation (85 ± 14 versus 77 ± 18 ml/kg, p = 0.43, 31 ± 8 versus 27 ± 5 mmHg, p = 0.19, 2.8 ± 0.6 versus 2.9 ± 0.9 ml/kg/mmHg, p = 0.86). Unexpectedly, our data indicated that patients with asplenia syndrome, who lack splanchnic capacitance circulation, have blood volume and venous capacitance comparable to those in patients with splanchnic circulation. These data suggest that (1) there is a blood reservoir other than the spleen even in patients with asplenia; (2) considering the large blood pool of the spleen, the presence of a symmetrical liver may represent the possible organ functioning as a blood reservoir in asplenia syndrome; and (3) if this is indeed the case, there may be a higher risk of hepatic congestion in patients with Fontan circulation with asplenia syndrome than in those without.

Impact of the Fontan Operation on Organ Systems

In patients having undergone the Fontan operation, besides the well discussed changes in the cardiac, pulmonary and gastrointestinal system, alterations of further organ systems including the hematologic, immunologic, endocrinological and metabolic are reported. As a medical adjunct to Fontan surgery, the systematic study of the central role of the liver as a metabolizing and synthesizing organ should allow for a better understanding of the pathomechanism underlying the typical problems in Fontan patients, and in this context, the profiling of endocrinological and metabolic patterns might offer a tool for the optimization of Fontan follow-up, targeted monitoring and specific adjunct treatment.

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.

A regulated multiscale closed-loop cardiovascular model, with applications to hemorrhage and hypertension

A computational tool is developed for simulating the dynamic response of the human cardiovascular system to various stressors and injuries. The tool couples 0-dimensional models of the heart, pulmonary vasculature, and peripheral vasculature to 1-dimensional models of the major systemic arteries. To simulate autonomic response, this multiscale circulatory model is integrated with a feedback model of the baroreflex, allowing control of heart rate, cardiac contractility, and peripheral impedance. The performance of the tool is demonstrated in 2 scenarios: neurogenic hypertension by sustained stimulation of the sympathetic nervous system and an acute 10% hemorrhage from the left femoral artery.

Developing transmission line equations of oxygen transport for predicting oxygen distribution in the arterial system

The oxygen content in the arterial system plays a significant role in determining the physiological status of a human body. Understanding the oxygen concentration distribution in the arterial system is beneficial for the prevention and intervention of vascular disease. However, the oxygen concentration in the arteries could not be noninvasively monitored in clinical research. Although the oxygen concentration distribution in a vessel could be obtained from a three-dimensional (3D) numerical simulation of blood flow coupled with oxygen transport, a 3D numerical simulation of the systemic arterial tree is complicated and requires considerable computational resources and time. However, the lumped parameter model of oxygen transport derived from transmission line equations of oxygen transport requires fewer computational resources and less time to numerically predict the oxygen concentration distribution in the systemic arterial tree. In this study, transmission line equations of oxygen transport are developed according to the theory of oxygen transport in the vessel, and fluid transmission line equations are used as the theoretical reference for the development. The transmission line equations of oxygen transport could also be regarded as the theoretical basis for developing lumped parameter models of other substances in blood.

Importance of dynamic central venous pressure in Fontan circulation

We tested our hypotheses that central venous pressure (CVP) shows an excessive increase in response to volume overload in Fontan circulation according to the extent of the reduction in venous capacitance (Cv), and that the maximum CVP after volume loading is associated with hepatic congestion. Changes in CVP after angiography (volume loading) were examined in 40 patients with Fontan circulation and 29 controls with biventricular circulation. CVP significantly increased with angiography in both groups, but the changes were much more evident in the Fontan group than in controls (3.3 ± 2.0 vs. 0.9 ± 1.4 mmHg, p = 0.0003). Multivariate analysis demonstrated that reduced Cv was the only significant determinant of CVP increase, independent of the amount of injected contrast medium, blood volume, pulmonary resistance, and ventricular diastolic stiffness (p < 0.05). Importantly, the use of a venodilator was associated with increased Cv and the resultant suppression of CVP elevation with volume load. In addition, CVP levels both at baseline (p = 0.02) and after volume loading (p = 0.01) were weakly but significantly correlated with the plasma levels of γ-glutamyl transpeptidase, a marker of hepatic congestion; however, multivariate analysis revealed that the CVP level after volume loading was a more important determinant of hepatic congestion. The results of this study highlight the importance of assessing dynamic in addition to static CVP for a better understanding of Fontan circulation. The potential importance of Cv as a therapeutic target for improving Fontan physiology needs further elucidation.

Impact of the location of the fenestration on Fontan circulation haemodynamics: a three-dimensional, computational model study

OBJECTIVES

There is no consensus or theoretical explanation regarding the optimal location for the fenestration during the Fontan operation. We investigated the impact of the location of the fenestration on Fontan haemodynamics using a three-dimensional Fontan model in various physiological conditions.

METHODS

A three-dimensional Fontan model was constructed on the basis of CT images, and a 4-mm-diameter fenestration was located between the extracardiac Fontan conduit and the right atrium at three positions: superior, middle, and inferior part of the conduit. Haemodynamics in the Fontan route were analysed using a three-dimensional computational fluid dynamic model in realistic physiological conditions, which were predicted using a lumped parameter model of the cardiovascular system. The respiratory effect of the caval flow was taken into account. The flow rate through the fenestration, the effect of lowering the central venous pressure, and wall shear stress in the Fontan circuit were evaluated under central venous pressures of 10, 15, and 20 mmHg. The pulse power index and pulsatile energy loss index were calculated as energy loss indices.

RESULTS

Under all central venous pressures, the middle-part fenestration demonstrated the most significant effect on enhancing the flow rate through the fenestration while lowering the central venous pressure. The middle-part fenestration produced the highest time-averaged wall shear stress, pressure pulse index, and pulsatile energy loss index.

CONCLUSIONS

Despite slightly elevated energy loss, the middle-part fenestration most significantly increased cardiac output and lowered central venous pressure under respiration in the Fontan circulation.

A computational study of the Fontan circulation with fenestration or hepatic vein exclusion

Fontan patients may undergo additional surgical modifications to mitigate complications like protein-losing enteropathy, liver cirrhosis, and other issues in their splanchnic circulation. Recent case reports show promise for several types of modifications, but the subtle effects of these surgeries on the circulation are not well understood. In this paper, we employ mathematical modeling of blood flow to systematically quantify the impact of these surgical changes on extracardiac Fontan hemodynamics. We investigate two modifications: (1) the fenestrated Fontan and (2) the Fontan with hepatic vein exclusion. Closed-loop hemodynamic models are used, which consist of one-dimensional networks for the major vessels and zero-dimensional models for the heart and organ beds. Numerical results suggest the hepatic vein exclusion has the greatest overall impact on the hemodynamics, followed by the largest sized fenestration. In particular, the hepatic vein exclusion drastically lowers portal venous pressure while the fenestration decreases pulmonary artery pressure. Both modifications increase flow to the intestines, a finding consistent with their utility in clinical practice for combating complications in the splanchnic circulation.

Mechanical and physiological effect of partial pressure suit: Experiment and numerical study

BACKGROUND

During high-altitude flight, the protection of the pilot is vital. A partial pressure suit may affect human physiology, especially circulatory physiology.

OBJECTIVE

The purpose of this study was to investigate how a partial pressure suit works.

METHOD

Ten subjects took part in the flight simulation experiments. Counter pressure at the chest, abdomen, thigh and shank were detected, together with physiological parameters such as heart rate (HR), mean arterial pressure (MAP), stroke volume (SV), cardiac output (CO) and total peripheral resistance (TPR). A numerical model was also established to simulate hemo-physiological effects of the partial pressure suit.

RESULTS

The experiment's results show the non-uniform counter pressure distribution in different parts of the body. There is a linear, proportional relation between TPR and the pressurizing level. HR and MAP increase along with that of the pressure level. SV and CO decrease with the increase of the pressure level. The numerical model simulated the physiological effect of a partial pressure suit. The results were verified by experiment data. The simulation estimated the change of blood flow with the pressure level.

CONCLUSIONS

The numerical model provides a potential way to improve the protection of pilots.

Mathematical modelling of the maternal cardiovascular system in the three stages of pregnancy

In this study, a mathematical model of the female circulation during pregnancy is presented in order to investigate the hemodynamic response to the cardiovascular changes associated with each trimester of pregnancy. First, a preliminary lumped parameter model of the circulation of a non-pregnant female was developed, including the heart, the systemic circulation with a specific block for the uterine district and the pulmonary circulation. The model was first tested at rest; then heart rate and vascular resistances were individually varied to verify the correct response to parameter alterations characterising pregnancy. In order to simulate hemodynamics during pregnancy at each trimester, the main changes applied to the model consisted in reducing vascular resistances, and simultaneously increasing heart rate and ventricular wall volumes. Overall, reasonable agreement was found between model outputs and in vivo data, with the trends of the cardiac hemodynamic quantities suggesting correct response of the heart model throughout pregnancy. Results were reported for uterine hemodynamics, with flow tracings resembling typical Doppler velocity waveforms at each stage, including pulsatility indexes. Such a model may be used to explore the changes that happen during pregnancy in female with cardiovascular diseases.

Assessment of central venous physiology of Fontan circulation using peripheral venous pressure

OBJECTIVE

Elevated central venous pressure is a major cause of morbidity and mortality after the Fontan operation. The difference between mean circulatory filling pressure and central venous pressure, a driving force of venous return, is important in determining dynamic changes in central venous pressure in response to changes in ventricular properties or loading conditions. Thus, noninvasive central venous pressure and mean circulatory filling pressure estimation may contribute to optimal management in patients undergoing the Fontan operation. We tested the hypothesis that central venous pressure and mean circulatory filling pressure in those undergoing the Fontan operation can be simply estimated using peripheral venous pressure and arm equilibrium pressure, respectively.

METHODS

This study included 30 patients after the Fontan operation who underwent cardiac catheterization (median 8.6, 3.4-42 years). Peripheral venous pressure was measured at the peripheral vein in the upper extremities. Mean circulatory filling pressure was calculated by the changes of arterial pressure and central venous pressure during the Valsalva maneuver. Arm equilibrium pressure was measured as equilibrated venous pressure by rapidly inflating a blood pressure cuff to 200 mm Hg.

RESULTS

Central venous pressure and peripheral venous pressure were highly correlated (central venous pressure = 1.6 + 0.68 × peripheral venous pressure, R = 0.86, P < .0001). Stepwise multivariable regression analysis showed that only peripheral venous pressure was a significant determinant of central venous pressure. Central venous pressure was accurately estimated using regression after volume loading by contrast injection (R = 0.82, P < .0001). In addition, arm equilibrium pressure measurements were highly reproducible and robustly reflected invasively measured mean circulatory filling pressure (mean circulatory filling pressure = 9.1 + 0.63 × arm equilibrium pressure, R = 0.88, P < .0001).

CONCLUSIONS

Central venous pressure and mean circulatory filling pressure can be noninvasively estimated by peripheral venous pressure and arm equilibrium pressure, respectively. This should help clarify unidentified Fontan pathophysiology and the mechanisms of Fontan failure progression, thereby helping construct effective tailor-made approaches to prevent Fontan failure.

Cardiopulmonary Interactions

OBJECTIVES

The objectives of this review are to discuss the mechanisms by which respiration impacts cardiovascular function and vice versa, with an emphasis on the impact of these interactions in pediatric cardiac critical care.

DATA SOURCE

A search of MEDLINE was conducted using PubMed.

CONCLUSIONS

In the presence of underlying cardiac and respiratory disease, the interplay between these two systems is significant and plays a pivotal role in the pathophysiology of acute and chronic phases of a wide spectrum of diseases. An understanding of these relationships is essential to optimizing the care of critically ill patients.

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

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

Patient-Specific Surgical Planning, Where Do We Stand? The Example of the Fontan Procedure

The Fontan surgery for single ventricle heart defects is a typical example of a clinical intervention in which patient-specific computational modeling can improve patient outcome: with the functional heterogeneity of the presenting patients, which precludes generic solutions, and the clear influence of the surgically-created Fontan connection on hemodynamics, it is acknowledged that individualized computational optimization of the post-operative hemodynamics can be of clinical value. A large body of literature has thus emerged seeking to provide clinically relevant answers and innovative solutions, with an increasing emphasis on patient-specific approaches. In this review we discuss the benefits and challenges of patient-specific simulations for the Fontan surgery, reviewing state of the art solutions and avenues for future development. We first discuss the clinical impact of patient-specific simulations, notably how they have contributed to our understanding of the link between Fontan hemodynamics and patient outcome. This is followed by a survey of methodologies for capturing patient-specific hemodynamics, with an emphasis on the challenges of defining patient-specific boundary conditions and their extension for prediction of post-operative outcome. We conclude with insights into potential future directions, noting that one of the most pressing issues might be the validation of the predictive capabilities of the developed framework.