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

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.

Simulation of coronary capillary transit time based on full vascular model of the heart

Capillary transit time (CTT) is a fundamental determinant of gas exchange between blood and tissues in the heart and other organs. Despite advances in experimental techniques, it remains difficult to measure coronary CTT in vivo. Here, we developed a novel computational framework that couples coronary microcirculation with cardiac mechanics in a closed-loop system that enables prediction of hemodynamics in the entire coronary network, including arteries, veins, and capillaries. We also developed a novel "particle-tracking" approach for computing CTT where "virtual tracers" are individually tracked as they traverse the capillary network. Model predictions compare well with blood pressure and flow rate distributions in the arterial network reported in previous studies. Model predictions of transit times in the capillaries (1.21 ± 1.5 s) and entire coronary network (11.8 ± 1.8 s) also agree with measurements. We show that, with increasing coronary artery stenosis (as quantified by fractional flow reserve, FFR), intravascular pressure and flow rate downstream are reduced but remain non-stationary even at 100 % stenosis because some flow (∼3 %) is redistributed from the non-occluded to the occluded territories. Importantly, the model predicts that occlusion of a large artery results in higher CTT. For moderate stenosis (FFR > 0.6), the increase in CTT (from 1.21 s without stenosis to 2.23 s at FFR=0.6) is caused by a decrease in capillary flow rate. In severe stenosis (FFR = 0.1), the increase in CTT to 14.2 s is due to both a decrease in flow rate and an increase in path length taken by "virtual tracers" in the capillary network.

Blood-wall fluttering instability as a physiomarker of the progression of thoracic aortic aneurysms

The diagnosis of aneurysms is informed by empirically tracking their size and growth rate. Here, by analysing the growth of aortic aneurysms from first principles via linear stability analysis of flow through an elastic blood vessel, we show that abnormal aortic dilatation is associated with a transition from stable flow to unstable aortic fluttering. This transition to instability can be described by the critical threshold for a dimensionless number that depends on blood pressure, the size of the aorta, and the shear stress and stiffness of the aortic wall. By analysing data from four-dimensional flow magnetic resonance imaging for 117 patients who had undergone cardiothoracic imaging and for 100 healthy volunteers, we show that the dimensionless number is a physiomarker for the growth of thoracic ascending aortic aneurysms and that it can be used to accurately discriminate abnormal versus natural growth. Further characterization of the transition to blood-wall fluttering instability may aid the understanding of the mechanisms underlying aneurysm progression in patients.

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.

Role of Electromechanical Dyssynchrony Assessment During Acute Circulatory Failure and Its Relation to Ventriculo-Arterial Coupling

Introduction

Two parallel paradigms of cardiovascular efficiency and haemodynamic optimisation coexist in haemodynamic research. Targeting ventriculo-arterial (VA) coupling [i.e., the ratio between arterial and ventricular elastance (E_V)] and electromechanical coupling are two promising approaches in acute circulatory failure. However, validation of the parameters of electromechanical coupling in critically ill patients is ongoing. Furthermore, a unifying link between VA and electromechanical coupling may exist, as E_V is correlated with different times of the cardiac cycle.

Materials and Methods

This study was a retrospective analysis of a prospectively collected observational database from one tertiary center ICU. We analyzed the relationship between electromechanical dyssynchrony and acute circulatory failure hemodynamics before and after treatment (i.e., fluid expansion, dobutamine, or norepinephrine infusion). The relationship between electromechanical coupling and VA coupling was also investigated. Adult patients with haemodynamic instability were included. Haemodynamic parameters, including arterial pressure, cardiac index, VA coupling, stroke work index/pressure–volume area (SWI/PVA), t-IVT, and Tei's index, were collected before and after treatment. A t-IVT of >12 s/min was classified as intraventricular dyssynchrony.

Results

We included 54 patients; 39 (72.2%) were classified as having intraventricular dyssynchrony at baseline. These patients with baseline dyssynchrony showed a statistically significant amelioration of t-IVT (from 18 ± 4 s to 14 ± 6 s, p = 0.001), left ventricular E_V [from 1.1 (0.72–1.52) to 1.33 (0.84–1.67) mmHg mL⁻¹, p = 0.001], VA coupling [from 2 (1.67–2.59) to 1.80 (1.40–2.21), p = 0.001], and SWI/PVA [from 0.58 (0.49–0.65) to 0.64 (0.51–0.68), p = 0.007]. Patients without baseline dyssynchrony showed no statistically significant results. The improvement in VA coupling was mediated by an amelioration of E_V. All patients improved their arterial pressure and cardiac index with treatment. The haemodynamic treatment group exhibited no effect on changing t-IVT.

Conclusion

Acute circulatory failure is associated with electromechanical dyssynchrony. Cardiac electromechanical coupling was improved by haemodynamic treatment only if altered at baseline. The improvement of cardiac electromechanical coupling was associated with the improvement of markers of cardiocirculatory efficacy and efficiency (i.e., SWI/PVA and VA coupling). This study was the first to demonstrate a possible link between cardiac electromechanical coupling and VA coupling in patients with acute circulatory failure.