Non-dimensional modeling in flow simulation studies of coronary arteries including side-branches: a novel diagnostic tool in coronary artery disease

Measurement and modeling of coronary blood flow

Ischemic heart disease that comprises both coronary artery disease and microvascular disease is the single greatest cause of death globally. In this context, enhancing our understanding of the interaction of coronary structure and function is not only fundamental for advancing basic physiology but also crucial for identifying new targets for treating these diseases. A central challenge for understanding coronary blood flow is that coronary structure and function exhibit different behaviors across a range of spatial and temporal scales. While experimental studies have sought to understand this feature by isolating specific mechanisms, in tandem, computational modeling is increasingly also providing a unique framework to integrate mechanistic behaviors across different scales. In addition, clinical methods for assessing coronary disease severity are continuously being informed and updated by findings in basic physiology. Coupling these technologies, computational modeling of the coronary circulation is emerging as a bridge between the experimental and clinical domains, providing a framework to integrate imaging and measurements from multiple sources with mathematical descriptions of governing physical laws. State-of-the-art computational modeling is being used to combine mechanistic models with data to provide new insight into coronary physiology, optimization of medical technologies, and new applications to guide clinical practice.

A comparative study on the uniaxial mechanical properties of the umbilical vein and umbilical artery using different stress-strain definitions

The umbilical cord is part of the fetus and generally includes one umbilical vein (UV) and two umbilical arteries (UAs). As the saphenous vein and UV are the most commonly used veins for the coronary artery disease treatment as a coronary artery bypass graft (CABG), understating the mechanical properties of UV has a key asset in its performance for CABG. However, there is not only a lack of knowledge on the mechanical properties of UV and UA but there is no agreement as to which stress-strain definition should be implemented to measure their mechanical properties. In this study, the UV and UA samples were removed after caesarean from eight individuals and subjected to a series of tensile testing. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were employed to determine the linear mechanical properties of UVs and UAs. The nonlinear mechanical behavior of UV/UA was computationally investigated using hyperelastic material models, such as Ogden and Mooney-Rivlin. The results showed that the effect of varying the stress definition on the maximum stress measurements of the UV/UA is significant but not when calculating the elastic modulus. In the true stress-strain diagram, the maximum strain of UV was 92 % higher, while the elastic modulus and maximum stress were 162 and 42 % lower than that of UA. The Mooney-Rivlin material model was designated to represent the nonlinear mechanical behavior of the UV and UA under uniaxial loading.

Tortuosity of coronary bifurcation as a potential local risk factor for atherosclerosis: CFD steady state study based on in vivo dynamic CT measurements

The purpose of the present study was to determine whether in vivo bifurcation geometric factors would permit prediction of the risk of atherosclerosis. It is worldwide accepted that low or oscillatory wall shear stress (WSS) is a robust hemodynamic factor in the development of atherosclerotic plaque and has a strong correlation with the local site of plaque deposition. However, it still remains unclear how coronary bifurcation geometries are correlated with such hemodynamic forces. Computational fluid dynamics simulations were performed on left main (LM) coronary bifurcation geometries derived from CT of eight patients without significant atherosclerosis. WSS amplitudes were accurately quantified at two high risk zones of atherosclerosis, namely at proximal left anterior descending artery (LAD) and at proximal left circumflex artery (LCx), and also at three high WSS concentration sites near the bifurcation. Statistical analysis was used to highlight relationships between WSS amplitudes calculated at these five zones of interest and various geometric factors. The tortuosity index of the LM-LAD segment appears to be an emergent geometric factor in determining the low WSS amplitude at proximal LAD. Strong correlations were found between the high WSS amplitudes calculated at the endothelial regions close to the flow divider. This study not only demonstrated that CT imaging studies of local risk factor for atherosclerosis could be clinically performed, but also showed that tortuosity of LM-LAD coronary branch could be used as a surrogate marker for the onset of atherosclerosis.

A finite element investigation on plaque vulnerability in realistic healthy and atherosclerotic human coronary arteries

Atherosclerosis is the most common arterial disease. It has been shown that stresses that are induced during blood circulation can cause plaque rupture and, in turn, lead to thrombosis and stroke. In this study, finite element method is used to predict plaque vulnerability based on peak plaque stress using human samples. A total of 23 healthy and atherosclerotic human coronary arteries of 14 healthy and 9 atherosclerotic patients are excised within 5 h postmortem. The samples are mounted on an uniaxial tensile test machine, and the obtained mechanical properties are used in two-dimensional and three-dimensional finite element models. The results including the Neo-Hookean hyperelastic coefficients of the samples as well as peak plaque stresses are analyzed. The results indicate that the atherosclerotic human coronary arteries have significantly (p < 0.05) higher stiffness compared with the healthy ones. The hypocellular plaque also has the highest stress values and, as a result, is most likely (vulnerable) to rupture, while the calcified type has the lowest stress values and, consequently, is expected to remain stable. The results could be used in the plaque vulnerability anticipation and have clinical implications in interventions and surgeries, including balloon angioplasty, bypass, and stenting.

The use of shear stress for targeted drug delivery

Stenosed segments of arteries significantly alter the blood flow known from healthy vessels. In particular, the wall shear stress at critically stenosed arteries is at least an order of magnitude higher than in healthy situations. This alteration represents a change in physical force and might be used as a trigger signal for drug delivery. Mechano-sensitive drug delivery systems that preferentially release their payload under increased shear stress are discussed. Therefore, besides biological or chemical markers, physical triggers are a further principle approach for targeted drug delivery. We hypothesize that such a physical trigger is much more powerful to release drugs for vasodilation, plaque stabilization, or clot lysis at stenosed arteries than any known biological or chemical ones.

Measurement of the uniaxial mechanical properties of healthy and atherosclerotic human coronary arteries

Atherosclerosis is a common arterial disease which alters the stiffness of arterial wall. Arterial stiffness is related to many cardiovascular diseases. In this investigation, maximum stress and strain as well as physiological and maximum elastic modulus of 22 human coronary arteries are measured. In addition, the force-displacement diagram of human coronary artery is obtained to discern the alterations between the healthy and atherosclerotic arterial wall stiffness. The age of each specimen and its effect on the elastic modulus of human coronary arteries is also considered. Twenty-two human coronary arteries, including eight atherosclerotic and fourteen healthy arteries are excised within 5 hours post-mortem. Samples are mounted on a tensile-testing machine and force is applied until breakage occurs. Elastic modulus coefficient of each specimen is calculated to compare the stiffness of healthy and atherosclerotic coronary arteries. The results show that the atherosclerotic arteries bear 44.55% more stress and 34.61% less strain compared to the healthy ones. The physiological and maximum elastic moduli of healthy arteries are 2.53 and 2.91 times higher than that of atherosclerotic arteries, respectively. The age of specimens show no correlation with the arterial wall stiffness. A combination of biomechanics and mathematics is used to characterize the mechanical properties of human coronary arteries. These results could be utilized to understand the extension and rupture mechanism of coronary arteries and has implications for interventions and surgeries, including balloon-angioplasty, bypass, and stenting.

The multi-scale modelling of coronary blood flow

Coronary flow is governed by a number of determinants including network anatomy, systemic afterload and the mechanical interaction with the myocardium throughout the cardiac cycle. The range of spatial scales and multi-physics nature of coronary perfusion highlights a need for a multiscale framework that captures the relevant details at each level of the network. The goal of this review is to provide a compact and accessible introduction to the methodology and current state of the art application of the modelling frameworks that have been used to study the coronary circulation. We begin with a brief description of the seminal experimental observations that have motivated the development of mechanistic frameworks for understanding how myocardial mechanics influences coronary flow. These concepts are then linked to an overview of the lumped parameter models employed to test these hypotheses. We then outline the full and reduced-order (3D and 1D) continuum mechanics models based on the Navier–Stokes equations and highlight, with examples, their application regimes. At the smaller spatial scales the case for the importance of addressing the microcirculation is presented, with an emphasis on the poroelastic approach that is well-suited to bridge an existing gap in the development of an integrated whole heart model. Finally, the recent accomplishments of the wave intensity analysis and related approaches are presented and the clinical outlook for coronary flow modelling discussed.