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

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.

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 in silico study of the effects of left ventricular assist device on right ventricular function and inter-ventricular interaction

BACKGROUND

Left ventricular assist device (LVAD) is associated with a high incidence of right ventricular (RV) failure, which is hypothesized to be caused by the occurring inter-ventricular interactions when the LV is unloaded. Factors contributing to these interactions are unknown.

METHODS

We used computer modeling to investigate the impact of the HeartMate 3 LVAD on RV functions. The model was first calibrated against pressure-volume (PV) loops associated with a heart failure (HF) patient and validated against measurements of inter-ventricular interactions in animal experiments. The model was then applied to investigate the effects of LVAD on (1) RV chamber contractility indexed byV 60 derived from its end-systolic PV relationship, and (2) RV diastolic function indexed byV 20 derived from its end-diastolic PV relationship. We also investigated how septal wall thickness and regional contractility affect the impact of LVAD on RV function.

RESULTS

The impact of LVAD on RV chamber contractility is small at a pump speed lower than 4k rpm. At a higher pump speed between 4k and 9k rpm, however, RV chamber contractility is reduced (by ~3% at 6k rpm and ~10% at 9k rpm). The reduction of RV chamber contractility is greater with a thinner septal wall or with a lower myocardial contractility at the LV free wall, septum, or RV free wall.

CONCLUSION

RV chamber contractility is reduced at a pump speed higher than 4k rpm, and this reduction is greater with a thinner septal wall or lower regional myocardial contractility. Findings here may have clinical implications in identifying LVAD patients who may suffer from RV failure.

Effect of pulmonary regurgitation on cardiac functions based on a human bi-ventricle model

BACKGROUND AND OBJECTIVE

Assessing the severity of pulmonary regurgitation (PR) and identifying optimal clinically relevant indicators for its treatment is crucial, yet standards for quantifying PR remain unclear in clinical practice. Computational modelling of the heart is in the process of providing valuable insights and information for cardiovascular physiology research. However, the advancements of finite element computational models have not been widely applied to simulate cardiac outputs in patients with PR. Furthermore, a computational model that incorporates both the left ventricle (LV) and right ventricle (RV) can be valuable in assessing the relationship between left and right ventricular morphometry and septal motion in PR patients. To enhance our understanding of the effect of PR on cardiac functions and mechanical behaviour, we developed a human bi-ventricle model to simulate five cases with varying degrees of PR severity.

METHODS

This bi-ventricle model was built using a patient-specific geometry and a widely used myofibre architecture. The myocardial material properties were described by a hyperelastic passive constitutive law and a modified time-varying elastance active tension model. To simulate realistic cardiac functions and the dysfunction of the pulmonary valve in PR disease cases, open-loop lumped parameter models representing systemic and pulmonary circulatory systems were designed.

RESULTS

In the baseline case, pressures in the aorta and main pulmonary artery and ejection fractions of both the LV and RV were within normal physiological ranges reported in the literature. The end-diastolic volume (EDV) of the RV under varying degrees of PR was comparable to the reported cardiac magnetic resonance imaging data. Moreover, RV dilation and interventricular septum motion from the baseline to the PR cases were clearly observed through the long-axis and short-axis views of the bi-ventricle geometry. The RV EDV in the severe PR case increased by 50.3% compared to the baseline case, while the LV EDV decreased by 18.1%. The motion of the interventricular septum was consistent with the literature. Furthermore, ejection fractions of both the LV and RV decreased as PR became severe, with LV ejection fraction decreasing from 60.5% at baseline to 56.3% in the severe case and RV ejection fraction decreasing from 51.8% to 46.8%. Additionally, the average myofibre stress of the RV wall at end-diastole significantly increased due to PR, from 2.7±12.1 kPa at baseline to 10.9±26.5 kPa in the severe case. The average myofibre stress of the LV wall at end-diastole increased from 3.7±18.1 kPa to 4.3±20.3 kPa.

CONCLUSIONS

This study established a foundation for the computational modelling of PR. The simulated results showed that severe PR leads to reduced cardiac outputs in both the LV and RV, clearly observable septum motion, and a significant increase in the average myofibre stress in the RV wall. These findings demonstrate the potential of the model for further exploration of PR.