Hemodynamic simulation of abdominal aortic aneurysm on idealised models: Investigation of stress parameters during disease progression

Highlights

• Hemodynamic and biomechanical stresses due to the progression of abdominal aortic aneurysms (AAA) are numerically simulated on idealized geometries.

• Coupled Fluid Structure Interaction (FSI) studies are performed by varying the shape index DHr (Dmax to height ratio).

• The shape index (DHr) was found to signify both hemodynamic and bio-mechanical indicators of fusiform aneurysm, at every growth stage. Inconsistent variation of these indicators exhibited by smaller aneurysms (low DHr) at different growth stages, demands routine monitoring (using scans), to prevent unexpected rupture.

Abstract

Background and Objective

Analysis and prediction of rupture risk of abdominal aortic aneurysms (AAA) facilitates planning for surgical interventions and assessment of plausible treatment modalities. Present approach of using maximum diameter criterion, is giving way to hemodynamic and bio-mechanical based predictors in conjunction with Computational fluid dynamic (CFD) simulations. Detailed studies on hemodynamic and bio-mechanical parameters at the stage of maximum growth/rupture is of practical importance to the clinical community. However, understanding the changes in these parameters at different stages of growth, will be useful for clinicians, in planning routine monitoring to reduce the risk of sudden rupture. This is particularly useful in medical resource starved nations. Present study investigates the hemodynamic and bio-mechanical changes occurring during the growth stages of aortic aneurysms using fluid structure interaction (FSI) studies.

Method

Six idealized fusiform aneurysm models spanning high (shorter) and low (longer) values of the shape index ($DHr$), have been analysed at three different stages of growth viz, a $D_{\max }$ of 3.5cm, 4.25cm, 5cm. Pulsatile Newtonian blood flow, passing through an elastic arterial vessel wall with uniform thickness is assumed. Two-way coupled fluid structure interaction have been employed for the numerical simulation of blood flow dynamics and arterial wall mechanics.

Results

Wall shear stress (WSS) parameters and vonmises stress indicators, co-relating rupture and thrombus formation, have been extracted and reported, at each growth stage. When the aneurysm progresses in diameter, the areas recording abnormally low TAWSS, as well as areas of high/low OSI were found to increase at different rates for shorter and longer aneurysms. Moreover, drastic increase in the maximum wall stresses (MWS) and wall displacement were observed as the aneurysm approached the critical diameter.

Conclusion

Hemodynamic predictors were found to be highly dependent on the shape index ($DHr$), when the aneurysm was small, whereas significant influence of $DHr$ on the wall stresses happens, as the aneurysm approaches the critical diameter. Inconsistent variation of these indicators exhibited by shorter aneurysms (high $DHr$) at different growth stages, demands routine monitoring (using scans), of such aneurysms, to prevent unexpected rupture.

Introduction

Aneurysms are the diseased segments of a blood vessel, with an unusual wall dilation, accentuated by fluid stresses. They are usually found in the abdominal and thoracic region of the aorta, as well as in the cerebral circulation of the brain. An abdominal aortic aneurysm (AAA) is the radial bulging of the aorta, along its axis, occurring in the abdominal region, near the iliac bifurcation, which is often accompanied by a thrombus growth. At an extremely dilated stage, the rupture of the diseased section may occur resulting in internal bleeding which could be fatal. Although the hemodynamic factors for the initiation of AAA are not fully understood, its growth is known to correlate well with the concentration variations of low density lipoprotein (LDL) close to the arterial walls [1]. In the current clinical practice, surgically repair of AAA is initiated, if the maximum diameter ($D_{\max }$) is greater than 5-6cm [2]. Relying on the diameter as the primary criterion, fails to take into consideration, smaller aneurysms that may rupture before reaching the critical size. Furthermore, the dynamic interactions with the flowing fluid and its mechano-biological activity in the vicinity of the arterial wall are not accounted in the diameter. The pulsatile nature of the flow further causes cyclic stresses resulting in weakening of the wall. This causes the attendant effect of dilatation and ultimately to rupture [3]. Vorp et al. [4] first argued that, from a bio-mechanical perspective, knowing the wall stresses in the lumen, can more accurately predict the rupture risk of AAA. Following this study, many bio-mechanical studies have focused on predicting rupture potential index (RPI) based on the peak wall stress (PWS) and the blood vessel tensile strength. They observed that the stress within the wall of an aneurysm and the potential for its rupture, are dependent on, maximum diameter (size) as well as its shape. Increase in wall stress level as well as decrease in wall tensile strength on AAA formation was observed by Raghavan et al. [5]. Subsequent studies inferred that the rupture potential based on bio-mechanical stresses on the arterial wall, is also influenced by geometric features like degree of asymmetry of the aneurysm, wall thickness, presence of intra-luminous thrombus (ILT), the illiac bifurcation angle etc [2], [6], [7]. It should be pointed out that, peak wall stress (PWS) is only a static parameter which fails to take into account the rupture occurring at normal aortic pressures. Hence prediction of rupture risk based on PWS alone, ignores the effect of hemodynamic factors like WSS, which is responsible for the cyclic loading of the arterial walls. Only in limited studies, using medical images of ruptured AAA tissues, bio-mechanical simulations could identify exact rupture locations as high wall stress regions [8]. Recent studies by Varshney et al. [9] have investigated the hemodynamics behind the non-invasive method of aneurysm treatment and found that moderate exercise exposed the aneurysmal wall and the distal end to high pressure, and mild exercise for prolonged duration can be an optimum approach for non-invasive aneurysmal treatment. Also, methodology for the prediction of annual risk of rupture of AAA, based on Bayesian statistics, mechanics and patient-specific blood pressure monitoring data was proposed for the first time by Polzer et al. [10], which upon clinical validation may optimize the surgical intervention criteria.

In view of the above studies, it is pertinent to analyse the flow features inside the diseased geometry, and develop a more consistent correlation between hemodynamic parameters and rupture characteristics of the aneurysms. The most commonly assessed parameters are wall shear stress (WSS) based, time-averaged wall shear stress (TAWSS), oscillatory shear stress (OSI), meanWSS, spacial and temporal gradients of WSS etc. All these hemodynamic parameters are reported to signify different factors like rupture location, thrombus growth, atherosclerosis sites etc. which are indirectly related to rupture risk. CFD simulations by Qiu et al. [11] using three ruptured and one unruptured patient-specific AAA models revealed that the rupture sites were found to be near the fluid stagnation regions which have nearly zero WSS with high WSS spatial gradient (WSSG). This is inline with the observation by Boyd et al. [12] which corroborate the occurrence of rupture in or near the flow re-circulation zones with low WSS and abundant thrombus deposition. Location of thrombus formation are found to match with the locations of low WSS, and high OSI in the studies by Les et al. [13] and Kelsey et al. [14]. Results reported by O’Rourke et al. [15] and Arzani et al. [16] have generated debate on this, as smaller aneurysms reported, high WSS and low OSI regions to be sites of high thrombus deposition and atherosclerosis. The influence of these hemodynamic parameters on the rupture characteristics is not fully understood and still needs further investigations. Similar to the bio-mechanical stresses all these hemodynamic parameters are also influenced by geometric features mentioned above [6], [17].

Meanwhile, aneurysm geometries are patient-specific and personalization of treatment methods is the need of modern times. However, grouping of patient specific aneurysms based on certain characterisation of its size and shape, and studies on the idealised geometries representing these groups, will help to generate sufficient statistical data, which can aid the clinical decision making process. Our earlier FSI studies on 2D model fusiform aneurysms, with various shape based indices have provided insights on the significance of the shape index $DHr$, which is the ratio of $D_{\max }$ to height ($H$) of the aneurysm, in predicting hemodynamics of aneurysm geometries. This study proposed $DHr$, as one of the primary shape index which can signify the hemodynamic behaviour and hypothesizes the use of $DHr$ along with $D_{\max }$ to ensure that, both the fluid stresses (dynamic), and its interactions with the wall mechanics as well as the static stress conditions are taken into account, on clinical interventions [18]. Significance of $DHr$ in the progression of aneurysm is studied in the experimental investigation by Salsac et al. [19] using symmetric aneurysms with different $DHr$ and the dilatation ratio $(D/d)$, ($d$ is the inner diameter of the parent vessel), using Particle Image Velocimetry (PIV).

However to the best of authors knowledge limited number of numerical studies, have focussed on bio-mechanical and hemodynamic stresses of smaller aneurysms and the variation of stresses during its growth. Also, none of the numerical studies so far, have investigated the influence of the shape index $DHr$ on the attendant stresses, as the aneurysm progresses to the critical diameter. Hence, the present study investigates hemodynamic and bio-mechanic stress indicators, of aneurysms with low (longer aneurysm) and high (shorter aneurysm) $DHr$, at three different stages of growth. This study is also expected to bring detailed understanding on the influence of shape of the fusiform section, on blood flow dynamics as well as wall mechanics during the initiation and progression of abdominal aortic aneurysm.