Predicting hemodynamic indices in coronary artery aneurysms using response surface method: An application in Kawasaki disease
Introduction
Coronary artery aneurysms (CAA) describe local dilatations of the coronary artery that exceed 1.5 times the neighboring artery diameter. The prevalence of CAA ranges from 0.3 to 5% [1]. The pathogenesis of CAA is not well understood. However, several factors come into play such as certain vasculitic and connective tissue diseases such as the Kawasaki disease (KD) [1]. KD is an inflammatory condition characterized by systemic inflammation and vasculitis of medium-sized arteries. Untreated, KD can result in coronary artery abnormalities in 20–25% of patients. Abnormalities can range from mild dilation and ectasia to fusiform or saccular aneurysm formation. Clinical symptoms appear due to the presence of concomitant atherosclerotic disease or local thrombosis in the large CAAs among others causes, leading to angina and myocardial infarction [1].
To date, the aneurysm size has been considered as the main criterion for CAA thrombosis risk evaluation, following the American Heart Association (AHA) and Japan's Ministry of Health guidelines [2,3]. The 2017 update to the AHA KD guidelines updated recommendations in children from using absolute dimension to the use of Z-scores to account for somatic growth in children, and better assess aneurysm severity relative to body size. Several datasets of coronary size measurements have been collected in healthy children and adults. Based on these datasets, multiple linear [4,5] and exponential [6,7] regression models have been developed for Z-score calculation in CAA, and their distribution stability and normality were tested. Recommendations for antithrombotic therapy from the AHA guidelines are based on these Z-scores, with at least 4 to 6 weeks of low dose aspirin recommended for normal and transitional CAAs (Z-score < 2.5), without any invasive cardiac test needed. In contrast, long-term antiplatelet therapy are suggested for small (2.5 < Z-score <5) and medium (5 < Z-score < 10) size CAAs respectively, besides periodic cardiac imaging and counseling [2]. Systemic anticoagulation is suggested for large or giant aneurysms (Z-score > 10), in addition to antiplatelet therapy.
In contrast to the aneurysms in other vessels that are prone to rupture, the main concern with the CAA is the risk of thrombus formation and myocardial infarction [8]. In addition to aneurysm diameter, many studies suggested that the thrombus risk can also be dependent to hemodynamic alterations in aneurysm region. Literature has shown that blood flow stagnation and sluggish flow are correlated with thrombosis and atherosclerosis [9]. Computational fluid dynamics (CFD) approach has been always of great interest in cardiovascular studies. CFD enables the computation of hemodynamic indicators like time averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT) with high accuracy, which is difficult to do in in-vitro and in-vivo tests [10], [11], [12]. High OSI and RRT are the main characteristics of oscillatory and circulatory flow. Many studies [13], [14], [15], [16] suggested that certain levels of these indicators can induce platelet activation and inflammatory responses, resulting in thrombosis and atherosclerosis. Generally speaking, low TAWSS and high OSI and RRT are correlated with an elevated risk of atherosclerosis and thrombosis.
Several patient-specific CFD and experimental investigations to analyze the flow and risk level of CAA cases based on hemodynamic indices were performed [17], [18], [19]. Sengupta et al. [18] showed that the wall shear stress at the aneurysm region, in a patient specific simulation of transient blood in KD patients, is approximately an order of magnitude lower than the normal coronary arteries. At the same time, there is an increase in wall shear stress gradient at the aneurysm neck. Moreover, due to the flow oscillations, the residence time of the blood particles at the aneurysm site was somewhat quadrupled compared to the normal cases. In another study, Gutierrez et al. [17] investigated the hemodynamic metrics in four KD patients. Blood flow simulations showed that the hemodynamic patterns could highly differ in cases with the same Z-score. However, the effect of different aneurysm shape indices and resulting flow parameters on local hemodynamics in CAAs has not been systematically investigated yet.
The goal of this study was to investigate the effect of CAA shape indices on local hemodynamics using the response surface method (RSM) through considering KD applications. CFD was performed on idealized controlled geometries where different CAA aspect ratios were considered. Regression models of TAWSS, OSI and RRT were developed. These models can be used as valuable tools to obtain a real-time assessment of CAA local hemodynamics and resulting risk stratification based on aneurysm shape indices.
Section snippets
Model development
An idealized fusiform aneurysm 3D model defined by a sinus curve (Eq. (1)) was designed based on three geometrical parameters, similar to the works of Martufi et al. [20] as shown in Fig. 1a.
After that, the maximum and minimum values of these parameters were set according to previous clinical measurements in KD patients [21] (Table 1). Since the parameters are not the same in range and units, they should be scaled for the regression analysis. A, B,
Hemodynamic indices and impact of geometrical parameters
The mean values of the three indices TAWSS, OSI, and RRT were calculated over the aneurysm area in all the 15 idealized cases. In order to understand the frequency distribution of these indices, the percentage of aneurysm area exposed to the threshold of each index was also calculated. The contours of TAWSS and RRT are plotted in Figs. 2 and 3 for all the cases. In both figures, we note that every combination of geometric parameters led to different distributions of TAWSS and RRT contours. To
Discussion
The combined effect of the shape ratios on hemodynamic indices were illustrated in this work through regression models based on CFD analysis of 15 different geometric scenarios.
The findings in Figs. 2, 3 and 8 along with the cases shown in Table 2 (A2 B2 C2, A2 B4 C2, A4 B2 C4 and A4 B4 C4) highlight the significant role of aneurysm diameter in hemodynamic alterations and induced thrombotic CAA. As shown in Fig. 8b, the red dots denote the cases with an aneurysm diameter of 8 mm or above,
Limitations
Regression models of hemodynamics indices were developed based on the CFD results of 15 idealized aneurysm cases determined by RSM-CCD of experiments approach that allows us to fully capture the curvature of the design space with the lowest possible number experiments. Although high R-squared values were achieved, the accuracy of these idealized models must be tested with more patient specific cases with non-uniform and irregular geometries. These models are full quadratic polynomials, which
Conclusions
In this study, simple quadratic regression models were developed for real-time risk evaluation of CAA based on hemodynamic indices. These models consider the geometrical ratios rather than just the diameter, which enhances the risk assessment by the Z-score. Here, it is shown that besides the aneurysm diameter, other geometrical parameters such as the length of the aneurysm can affect the local hemodynamics and the corresponding thrombotic risk. These models provide a quick and straightforward
Funding
This work is partially funded by Michigan Technological University's Research Excellence Fund. Alireza Asadbeygi is partly funded by the Blue Cross Blue Shield of Michigan Foundation. No other external funding was received.
Disclosures
Dr. Hatoum filed a patent application on computational predictive modeling of thrombosis in heart valves and on a novel implantable vascular shunt with real-time precise flow control. The other authors do not report any conflict of interest.
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