Both microscopic degradation in vascular tissues and hemodynamic (fluid-dynamic) forces play a crucial role in the initiation, growth and focal rupture of aneurysms (Sforza et al., 2009; Salman et al., 2019; Lipp et al., 2020; Wu et al., 2020). Aneurysms are vascular diseases characterized by excessive tissue degradation and chronic inflammation (Frösen, 2014). There are relations among aneurysmal geometry, intra-aneurysmal hemodynamics (flow), and aneurysm pathobiology (Meng et al., 2014): Geometry instantaneously alters flow conditions (short-term effect) (Wang et al., 2020, 2021a); abnormal-flow-induced hemodynamic-biomechanical triggers are transduced into biological signals and lead to the degradation, growth and/or remodeling of aneurysms via pathobiology (Meng et al., 2014); the interplay between the local flow environment and aneurysm pathobiology dominates the growth and geometric changes of the aneurysm (long-term effect) (Tarbell et al., 2014). Within an aneurysm wall, constructive (eutrophic) changes (cell proliferation and extracellular matrix production) and destructive (degradative) changes (cell death and extracellular matrix degradation) are ongoing concurrently (Frösen et al., 2012; Frösen, 2014; Meng et al., 2014). Wall shear stress (WSS), defined as the tangential stress component induced by the flowing blood and acting on endothelial cells, regulates the near-wall transport of chemicals and proteins (Kadirvel et al., 2007; Nixon et al., 2010; Meng et al., 2014). WSS, however, is usually calculated for a stationary/instantaneous blood flow and does not, per se, consider the pulsatility within a cardiac cycle. In order to better elucidate the mechanistic link between blood flow and vascular diseases (in particular, aneurysms), a number of WSS-related metrics have been proposed. Among these, the time-averaged wall shear stress (TAWSS) (He and Ku, 1996) and oscillatory shear index (OSI) (Ku et al., 1985) are the two most common candidates that are important for aneurysms' progression and rupture. TAWSS measures the average magnitude of WSS within a full cardiac cycle. OSI indicates the change in the direction along which WSS is acting on the vascular tissue. Abnormal WSS is a major cause of the imbalance between the constructive and destructive processes (Meng et al., 2014) and leads to vascular degradation and inflammation by activating inflammatory markers of endothelial cells (Franck et al., 2013; Meng et al., 2014), thereby causing the breakdown of the internal elastic lamina and loss of structural strength within the vessel wall (Kataoka et al., 1999). An aneurysm can grow and even rupture with continuous vascular injury, inflammation, and prolonged activation (Fisher and Demel, 2019).

On the one hand, although mechanisms underlying the effects of hemodynamic forces on aneurysm pathogenesis remain unclear, there is growing evidence that hemodynamic factors (in particular, TAWSS and OSI) act as crucial contributors to the progression and rupture of aneurysms. Low TAWSS and high OSI are commonly used risk factors for a rupture-prone phenotype (Xiang et al., 2011; Meng et al., 2014; Zhang et al., 2016; Liu et al., 2019a). Previous in vitro (Davies et al., 1984; Dai et al., 2004) and numerical (Sáez et al., 2015) studies have indicated that the remodeling of endothelial cells is dependent on the combined effects of TAWSS and OSI. Liu et al. (2019a) have recently suggested that low WSS and high OSI shall be considered as independent hemodynamic-morphological risk factors and proposed to use them as predictors for intra-operative aneurysm rupture. Low TAWSS and high OSI have also been shown to be significantly associated with thrombus formation in aneurysms (Les et al., 2010; Kelsey et al., 2017). In addition, Cebral et al. (2019) have argued that high WSS and low OSI, prevalent in the flow impingement region, may be also associated with the degradation and local thinning of aneurysmal walls. Both the TAWSS and OSI affect the endothelial mechanobiology locally. To localize regions exposed to both low TAWSS and high OSI, the so-called endothelial cell activation potential (ECAP) is used (Di Achille et al., 2014; Zambrano et al., 2016; Kelsey et al., 2017; Ong et al., 2019). It has been shown that low TAWSS, high OSI ang high ECAP correlate with regions of thrombus development in aneurysms (Zambrano et al., 2016; Kelsey et al., 2017; Ong et al., 2019). The effects of geometry on intra-aneurysmal hemodynamics have also been extensively studied (Hassan et al., 2005; Cebral et al., 2007; Baharoglu et al., 2010; Kawaguchi et al., 2012; Wang et al., 2020).

On the other hand, degradation-induced changes in mechanical properties of an aneurysmal wall may have an influence on hemodynamics inside the aneurysm, which is poorly studied though. Recently, we have developed a novel computational framework by combining a tissue degradation model and a finite element-based fluid-structure interaction (FSI) solver (Wang et al., 2021b). Using this model, we have shown that TAWSS increases near the flow-impingement region of idealized aneurysms and decreases away from it in the process of degradation (Wang et al., 2021b).

While several longitudinal studies (Arzani et al., 2014; Zambrano et al., 2016) have been conducted to understand the role of TAWSS and OSI in thrombus deposition in aneurysms, it remains unclear how degradation may affect the oscillatory shear index and its potential connection to TAWSS, and the endothelial cell activation potential. The present study aims at investigating this topic. To the best of our knowledge, this paper presents the first preliminary results uncovering qualitative trends and correlations of biomechanically important metrics upon degradation. Potential consequences of the central finding are discussed in the context of recent literature.

In this section, we investigate the effect of tissue degradation on two commonly used intra-aneurysmal hemodynamic quantities, TAWSS and OSI, and ECAP. Since the fluid is at rest at the beginning of our simulations, we wait for two full cardiac cycles before gathering the data on WSS and OSI. This way, we focus on cyclic dynamics, which regularly repeats itself.

In order to quantify the effects of tissue degradation on TAWSS, OSI and ECAP, we use Equation (4) and determine the tissue-degradation-induced relative changes of these hemodynamic quantities (Figure 3). Using this approach, a decrease or increase of TAWSS, OSI, and ECAP upon degradation shows itself in a negative or positive value and will be made visible by blue or red color, respectively.

As revealed by our simulations, degradation effects seem to be nearly homogeneous on wall stress (Figure 3C) and strain magnitude (Figure 3D) [in line with our previous study (Wang et al., 2021b)] but spatially heterogeneous on TAWSS (Figure 3E), OSI (Figure 3F) and ECAP (Figure 3H). Importantly, the degradation process appears to bring locally opposite influences on the TAWSS and OSI; a region with a decrease in TAWSS shows an increase in OSI (and thus an increase in ECAP as visualized by red color in Figure 3H), and vice versa.

To further highlight the enhancement of the inverse correlation between TAWSS and OSI in the progress of degradation, we quantify their correlation via

The degradation-induced local enhancement of the inverse correlation between TAWSS and OSI is indicated by negative C_{ΔTAWSS·ΔOSI} and is visualized by blue color in Figure 3G. The main advantage of introducing this quantity is that its negative value indicates opposite changes of TAWSS and OSI during degradation. When combined with the information contained in ECAP, one can then uniquely distinguish which of the two quantities has increased and which one has decreased. However, if TAWSS and OSI change in a similar manner (both increase or both decrease, leading to a positive correlation), ECAP will raise if (i) the percentage increase in OSI is larger than that of TAWSS but also if (ii) percentage decrease of OSI is lower than that of TAWSS. Similarly, two possibilities exist for a decrease of ECAP in the case of a positive correlation value.

In view of possible clinical consequences of an inverse correlation between TAWSS and OSI, we have examined the robustness of the observed behavior and have performed two new sets of simulations using patient-specific aneurysm geometries shown in Figures 1C,D. The data for these geometries are obtained from the Aneurisk repository (Aneurisk-Team, 2012).

We find that, at certain areas of each aneurysm sac investigated in this study, TAWSS and OSI are oppositely affected by degradation. This feature is stronger at places with low WSS (compare Figures 3A,G,H, 4A,C–F, 5A,C–F). In this study, a threshold value of 25 dyn/cm² is used to define the low and high TAWSS, also in agreement with reported values in the literature (Mendieta et al., 2020; Morbiducci et al., 2020; Tian et al., 2021). High OSI is considered to be larger than 0.15 (Xu et al., 2020).

As will be discussed in more detail below, this feature is robust and is confirmed in the case of both ideal and patient-specific geometries, and different degradation intensities, heart rates, and blood pressures.

Although mechanisms in aneurysm pathogenesis have not yet been fully elucidated, there is growing evidence that hemodynamic factors and tissue degradation act as crucial contributors to the progression of aneurysms (Kadirvel et al., 2007; Sforza et al., 2009; Nixon et al., 2010; Meng et al., 2014; Cebral et al., 2019; Salman et al., 2019). Abnormal flow-induced WSS often causes disruption and dysfunction of endothelial cells (Sorokin et al., 2020), initiating an aneurysm (Meng et al., 2014). Subsequently, a vascular wall may degrade due to inflammation-triggered biochemical reactions such as apoptosis and migration of smooth muscle cells, infiltration of inflammatory cells, and secretion of various cytokines (Pentimalli et al., 2004; Kwak et al., 2014; Meng et al., 2014; Liu et al., 2019b). Chronic hemodynamic stress and inflammation induce the structure change or damage in the endothelial cells and lead to the progression and eventual rupture of aneurysms (Frösen et al., 2012; Signorelli et al., 2018). Time-averaged wall shear stress and oscillatory shear index are commonly used to quantify changes in magnitude and direction of WSS.

Using computer simulations, we studied the effects of tissue degradation on these two hemodynamic stimuli, TAWSS and OSI, for the case of aneurysm geometry. The results obtained within this work revealed a strong heterogeneity in the effects arising from degradation on TAWSS and OSI.

Importantly, the degradation-induced variations of these two hemodynamic factors turned out to be opposite to each other. In places with decreased TAWSS due to tissue degradation, we found an increase in OSI and vice versa. For both the ideal and patient-specific aneurysm geometries investigated in this work, we observed that the degradation-related enhancement of this inverse correlation between TAWSS and OSI occurs predominantly at low-WSS regions.

Although intra-aneurysm flow patterns and hemodynamic quantities depend on the specific geometry (Varble et al., 2016; Wang et al., 2020, 2021a; Khan et al., 2021), effects of tissue degradation turn out to be qualitatively similar in all the investigated cases, i.e., for different geometries, degradation intensities, heart rates and blood pressures: at low-WSS sites, degradation leads to a lower TAWSS and at the same time a higher OSI.

Low TAWSS accompanied by high OSI has been associated with the thrombus accumulation in aneurysms (Frösen et al., 2012; Zambrano et al., 2016; Kelsey et al., 2017; Ong et al., 2019) via promoting a prothrombogenic phenotype (Chiu and Chien, 2011; Wolberg et al., 2012), and with the aneurysm's progression and a rupture-prone phenotype (Les et al., 2010; Xiang et al., 2011; Meng et al., 2014; Zhang et al., 2016; Liu et al., 2019a). Such hemodynamic characteristics also promote the formation of atherosclerotic plaques on aneurysms (Galis et al., 1999; Tateshima et al., 2008; Chiu and Chien, 2011; Yang et al., 2011; Frösen et al., 2012) and thus make the aneurysmal walls vulnerable to rupture. A number of molecules are involved in the formation and rupture of aneurysms. The combination of low WSS and high OSI is known to elicit the inflammatory response in the endothelium (Meng et al., 2014). When endothelial cells are exposed to low and oscillatory shear stress, they respond by producing reactive oxygen species (Galis et al., 1999; Chiu and Chien, 2011), recruiting more inflammatory cells (van Varik et al., 2012), upregulating vascular cell adhesion molecules and cytokines in the vessel wall (Aoki et al., 2011; van Varik et al., 2012), and increasing endothelial permeability (Malek et al., 1999; Bian et al., 2009; Chiu and Chien, 2011). Conway et al. (2010) have reported that low average shear stress and high OSI (or flow reversal) act as significant mechanical stimuli on the regulation of endothelial cell gene expression and monocyte adhesion, respectively. A “sticky” and “leaky” proinflammatory endothelium tends to promote leukocyte transmigration into the vascular wall during the progression of aneurysms (Chiu and Chien, 2011; Meng et al., 2014). Low WSS together with high OSI also causes smooth muscle cells to undergo phenotypic modulation and apoptosis (Hsu et al., 2011; Liu et al., 2019b), and facilitates inflammatory cell infiltration (Malek et al., 1999; Nixon et al., 2010; Soldozy et al., 2019). These inflammatory responses in vessel walls can produce matrix metalloproteinases to destroy internal elastic lamina and degrade the extracellular matrix (Galis et al., 1994), thereby leading to an imbalance between the constructive and destructive processes (Meng et al., 2014).

Importantly, if we combine our findings with prior observations, we obtain a ‘degradation loop': Degradation of an aneurysm wall leads to lower TAWSS and higher OSI which correspond to a favorable environment for pathological changes such as atherosclerosis and thrombus formation in the aneurysm; such flow environment, in turn, may induce further degradation. Hence, the present study suggests that degradation enhances this pathological process via a self-amplification mechanism: sites with a low TAWSS and at the same time a high OSI experience still lower TAWSS and higher OSI during degradation.

A degradation process may thus self-amplify/accelerate itself via enhancing the contrast between TAWSS and OSI. That is, tissue degradation may promote the aneurysm's pathological progression to rupture by accelerating the usually slow processes, which leads to enhanced vulnerability of the wall.

Several improvements can be added to the numerical approach used in this study. First, it assumes the blood to be a Newtonian fluid with constant viscosity. This is a good approximation at low flow rates but may need correction in large arteries, where shear rate varies over a wider range from the center toward the vessel wall. Second, active response and fatigue of the aneurysmal wall are not accounted for in the material model. Third, idealized fiber orientations are employed. Fourth, a uniform wall thickness is assumed in this study. Fifth, we assume a parabolic velocity profile at the inlet. The main reason for these simplifying assumptions is that the patient-specific data of the mechanical response of aneurysmal walls, the fiber architecture, the distribution of wall thickness and the boundary conditions are not yet available. This is presumably related to the complexity of the degradation phenomenon and difficulties associated with the measurements of these properties of the arterial wall during the degradation process. Indeed, the model can be easily improved if the corresponding experimental and clinical data become available.

This study is a first step to investigate the effects of tissue degradation on the hemodynamic factors and the potential evolution of an aneurysm. In the future, if clinical/experimental data of fiber orientations in an individual aneurysm becomes available, the current model could be used to predict if the aneurysm is susceptible to develop further damage and, if so, to estimate the regions where rupture is more likely to occur.

Using computer simulations with an idealized aneurysm and two patient-specific ones, we investigated the effects of tissue degradation on the mechanical stimuli, time-averaged wall shear stress and oscillatory shear index, which are commonly associated with aneurysms.

We found that the degradation-induced variations of TAWSS and OSI are opposite to each other: If in the course of degradation the time-averaged wall shear stress is decreased at a given site, we observed an increase in OSI at the same site and vice versa. This process is most prominent at sites that are already subject to a low TAWSS and at the same time a high OSI. This finding turned out to be robust and was confirmed in the case of all the three investigated aneurysm geometries and different degradation intensities, heart rates, and blood pressures.

Our findings are discussed in the light of the present state of understanding in the literature regarding biomechanical mechanisms responsible for aneurysm development and rupture. We argue that degradation is likely to enhance the existing contrast between these two hemodynamic factors (in particular, at sites subject to a low time-averaged wall shear stress and a high oscillatory shear index), and thereby pave the way for the next degradation step. This study thus underlines the importance of the inverse correlation between TAWSS and OSI as an independent risk factor for aneurysm degradation and rupture. Further investigations are warranted to examine these findings in a clinical setting.

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author/s.

HW and FV designed the details of the specific computational and analysis protocols including the study of patient-specific geometries. HW, VV, KU, and DB contributed to the algorithmic implementation. HW performed the simulations and analyses and wrote the first draft. HW and FV revised the manuscript. All authors contributed equally to the development of the original hypothesis of self-amplification and the design of suitable numerical analysis, read, and approved the final version of the manuscript.

This work was performed with support from the IMPRS-SurMat program and by the German Research Foundation (DFG) within SFB-TRR 287/1 (project A4).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.