On the relevance of boundary conditions and viscosity models in blood flow simulations in patient-specific aorto-coronary bypass models

Reliability of characterising coronary artery flow with the flow-split outflow strategy: Comparison against the multiscale approach

BACKGROUND

In computational modelling of coronary haemodynamics, imposing patient-specific flow conditions is paramount, yet often impractical due to resource and time constraints, limiting the ability to perform a large number of simulations particularly for diseased cases.

OBJECTIVE

To compare coronary haemodynamics quantified using a simplified flow-split strategy with varying exponents against the clinically verified but computationally intensive multiscale simulations under both resting and hyperaemic conditions in arteries with varying degrees of stenosis.

METHODS

Six patient-specific left coronary artery trees were segmented and reconstructed, including three with severe (>70 %) and three with mild (<50 %) focal stenoses. Simulations were performed for the entire coronary tree to account for the flow-limiting effects from epicardial artery stenoses. Both a 0D-3D coupled multiscale model and a flow-split approach with four different exponents (2.0, 2.27, 2.33, and 3.0) were used. The resulting prominent haemodynamic metrics were statistically compared between the two methods.

RESULTS

Flow-split and multiscale simulations did not significantly differ under resting conditions regardless of the stenosis severity. However, under hyperaemic conditions, the flow-split method significantly overestimated the time-averaged wall shear stress by up to 16.8 Pa (p = 0.031) and underestimate the fractional flow reserve by 0.327 (p = 0.043), with larger discrepancies observed in severe stenoses than in mild ones. Varying the exponent from 2.0 to 3.0 within the flow-split methods did not significantly affect the haemodynamic results (p > 0.141).

CONCLUSIONS

Flow-split strategies with exponents between 2.0 and 3.0 are appropriate for modelling stenosed coronaries under resting conditions. Multiscale simulations are recommended for accurate modelling of hyperaemic conditions, especially in severely stenosed arteries.(247/250 words).

Hemodynamics of asymmetrically stenotic vertebral arteries based on fluid-solid coupling

The study investigates the interaction between vertebral artery stenosis and pulsatile blood flow, with a focus on the mechanical properties and internal dynamics of blood flow. First, an asymmetrical stenosis mathematical model was established to reveal the relationship between the resistance ratio and shear stress ratio and their dependence on stenosis height and length. Next, various stenosis models were constructed using medical imaging data and analyzed through computational fluid dynamics (CFD) and fluid-structure interaction (FSI) methods. Finally, hemodynamic parameters, such as blood flow velocity and time-averaged wall shear stress (TAWSS), along with solid mechanics indicators, including total deformation and von Mises stress, were evaluated. The results indicate that changes in stenosis length and height significantly affect the resistance ratio and shear stress. Whole-segment stenosis in the vertebral artery may lead to thrombosis and intimal damage. In contrast, stenosis at the ostium of the vertebral artery increases the risk of platelet deposition on the vessel wall, potentially triggering atherosclerosis. This could ultimately lead to insufficient blood flow to the brain due to impaired vertebral artery circulation. FSI simulations revealed that elastic vessel walls are more sensitive to high-velocity flows, especially in stenotic and downstream regions. These findings provide critical insights into the effects of stenosis on blood flow and are crucial for developing effective clinical intervention strategies.

A review of computational methodologies to predict the fractional flow reserve in coronary arteries with stenosis

Computational methodologies for predicting the fractional flow reserve (FFR) in coronary arteries with stenosis have gained significant attention due to their potential impact on healthcare outcomes. Coronary artery disease is a leading cause of mortality worldwide, prompting the need for accurate diagnostic and treatment approaches. The use of medical image-based anatomical vascular geometries in computational fluid dynamics (CFD) simulations to evaluate the hemodynamics has emerged as a promising tool in the medical field. This comprehensive review aims to explore the state-of-the-art computational methodologies focusing on the possible considerations. Key aspects include the rheology of blood, boundary conditions, fluid-structure interaction (FSI) between blood and the arterial wall, and multiscale modelling (MM) of stenosis. Through an in-depth analysis of the literature, the goal is to obtain an overview of the major achievements regarding non-invasive methods to compute FFR and to identify existing gaps and challenges that inform further advances in the field. This research has the major objective of improving the current diagnostic capabilities and enhancing patient care in the context of cardiovascular diseases.

Effects of body posture on aortic valve hemodynamics and biomechanics using the fluid-structure interaction method

Bioprosthetic heart valve (BHV), the most widely and commonly used valves in clinical practice, are susceptible to fatigue damage. Biological valves are always in one or fewer body postures before sampling in pigs and bovines. Nevertheless, human body positions are far more than them. Variations in body position significantly affect the intrinsic environment of blood pressure (BP), heart rate (HR), and peripheral resistance (PR). Such boundary condition changes will inevitably affect the implanted biological valve. In this paper, the immersed boundary method was used to simulate the motion of the aortic valve during the entire cardiac cycle in five postural blood flow environments: upright, sitting, prone, supine and orthostatic hypotension (OH). Several hemodynamic and biomechanical parameters, including the transvalvular pressure gradient and valve displacement, were evaluated. The results showed that the OH group exhibited the worst performance of the valves, accompanied by the greatest regurgitation and high-frequency flutter, predisposing patients to thrombosis and fatigue calcification. For BHVs to serve longer, patients implanted with BHV should avoid OH in their daily routine.

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models

PURPOSE

The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model.

METHOD

The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation.

RESULTS

The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress.

CONCLUSION

Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.

Parametric analysis of an efficient boundary condition to control outlet flow rates in large arterial networks

Substantial effort is being invested in the creation of a virtual human-a model which will improve our understanding of human physiology and diseases and assist clinicians in the design of personalised medical treatments. A central challenge of achieving blood flow simulations at full-human scale is the development of an efficient and accurate approach to imposing boundary conditions on many outlets. A previous study proposed an efficient method for implementing the two-element Windkessel model to control the flow rate ratios at outlets. Here we clarify the general role of the resistance and capacitance in this approach and conduct a parametric sweep to examine how to choose their values for complex geometries. We show that the error of the flow rate ratios decreases exponentially as the resistance increases. The errors fall below 4% in a simple five-outlets model and 7% in a human artery model comprising ten outlets. Moreover, the flow rate ratios converge faster and suffer from weaker fluctuations as the capacitance decreases. Our findings also establish constraints on the parameters controlling the numerical stability of the simulations. The findings from this work are directly applicable to larger and more complex vascular domains encountered at full-human scale.

Structure (Epicardial Stenosis) and Function (Microvascular Dysfunction) That Influence Coronary Fractional Flow Reserve Estimation

Background. The treatment of coronary stenosis is decided by performing high risk invasive surgery to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerotic plaques. Non-invasive methods are a need of the times that necessitate the use of mathematical models of coronary hemodynamic physiology. This study proposes an extensible mathematical description of the coronary vasculature that provides an estimate of coronary fractional flow reserve. Methods. By adapting an existing computational model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simulations generated flow and pressure information, which was used to compute fractional flow reserve under several conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis was used to uncover the influence of model parameters on fractional flow reserve. The model was simulated as coupled non-linear ordinary differential equations and numerically solved using our implicit higher order method. Results. Large vessel stenosis affected fractional flow reserve. The model predicts that the presence, rather than severity, of microvascular disease affects coronary flow deleteriously. Conclusions. The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential to limit coronary flow. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index.