Biomechanical changes during abdominal aortic aneurysm growth

The biomechanics-based Abdominal Aortic Aneurysm (AAA) rupture risk assessment has gained considerable scientific and clinical momentum. However, such studies have mainly focused on information at a single time point, and little is known about how AAA properties change over time. Consequently, the present study explored how geometry, wall stress-related and blood flow-related biomechanical properties change during AAA expansion. Four patients with a total of 23 Computed Tomography-Angiography (CT-A) scans at different time points were analyzed. At each time point, patient-specific properties were extracted from (i) the reconstructed geometry, (ii) the computed wall stress at Mean Arterial Pressure (MAP), and (iii) the computed blood flow velocity at standardized inflow and outflow conditions. Testing correlations between these parameters identified several nonintuitive dependencies. Most interestingly, the Peak Wall Rupture Index (PWRI) and the maximum Wall Shear Stress (WSS) independently predicted AAA volume growth. Similarly, Intra-luminal Thrombus (ILT) volume growth depended on both the maximum WSS and the ILT volume itself. In addition, ILT volume, ILT volume growth, and maximum ILT layer thickness correlated with PWRI as well as AAA volume growth. Consequently, a large ILT volume as well as fast increase of ILT volume over time may be a risk factor for AAA rupture. However, tailored clinical studies would be required to test this hypothesis and to clarify whether monitoring ILT development has any clinical benefit.


Introduction
Degradation of elastin, collagen and apoptosis of Smooth Muscle Cells (SMC) [1] may lead to Abdominal Aortic Aneurysm (AAA) formation in the infrarenal aorta, which in turn may result in aortic rupture. Elective surgical or endovascular AAA repair is offered to prevent such catastrophic events, and repair is indicated as soon as the risk of aortic rupture exceeds the interventional risks. While the risks of intervention are reasonably predictable, assessing AAA rupture risk remains challenging during clinical decision making. Present clinical guidelines recommend AAA repair as soon as the diameter reaches 55mm or grows faster than PLOS  10mm/year [2,3], and diameter remains the most important surrogate marker of AAA risk [4]. However, a considerable portion of AAAs rupture below the size of 55mm (especially in female patients and current smokers [5]), whereas many aneurysms larger than 55mm never rupture [6][7][8]. Consequently, a more robust AAA rupture risk assessment would be of great clinical value. The Biomechanical Rupture Risk Assessment (BRRA) quantitatively integrates many known risk factors for AAA rupture, allowing a more holistic risk assessment. The BRRA has gained considerable momentum [9][10][11][12][13][14][15][16][17][18], but the derived indices are essentially based on information at a single time point, and currently little is known about how AAA biomechanical parameters change over time.
Almost all clinically relevant AAAs contain an intra-luminal thrombus (ILT) [19] composed of fibrin and blood cells. The role of ILT is still contentious, but it is thought to play an important role in AAA progression. Despite ILT tissue being several times softer than the AAA wall, it may be large in volume, and thus having a significant structural impact on AAA biomechanics. Numerical [20,21] and in-vitro experimental [22] studies reported ILT's structural impact, and the location of Peak Wall Stress (PWS) has been associated with the site of smallest ILT layer thickness [23]. Consequently, a thrombus layer may protect the vessel wall from rupture by acting as a stress buffer [20,22], thus decreasing the rupture risk of the aneurysm. However, when growing too thick, the ILT layer can cause the wall to weaken, for example due to hypoxia [24]. The ILT also provides an ideal environment for proteolytic agents [25]. These chemicals can be conveyed through the porous ILT [26,27] and diminish wall strength by proteolytic degradation of elastin and collagen. Such a wall weakening mechanism could explain why a thick ILT layer [28] and fast increase in ILT volume [29] have been linked to AAA rupture risk. A recent CT-A-based study [30] reported some consequences for AAA growth that might be linked to both aforementioned (competing) ILT-based mechanisms. The study found slowest AAA wall expansion behind an about seven millimeter thick ILT layer, i.e. ILT-based stress buffering seems to be fully compensated by ILT-based wall weakening once the ILT layer reached this thickness.
The present study aims at investigating how geometry, wall stress-related and blood flowrelated biomechanical properties change during AAA expansion. Despite the fact that effects of blood flow on AAA growth have been reported [31], the interaction between these factors is still poorly understood. Knowledge about the time course of such parameters may lead to a better estimate of AAA rupture risk and improve monitoring protocols of AAA patients.

Patient cohort
The use of anonymized patient data was approved by the Karolinska Institute ethics committee. AAA patients from Karolinska University Hospital, Stockholm, Sweden with at least five high resolution Computed Tomography-Angiography (CT-A) scan recordings within the last 10 years were included. Most of the CT-A scans were performed for diagnostic purposes and AAA surveillance. Patient characteristics are listed in Table 1. To avoid temporal fluctuations, the blood pressure was averaged over all available measurements.

Geometrical analysis
The aorta was semi-automatically segmented between the renal arteries and the aortic bifurcation (A4clinics Research Edition, VASCOPS GmbH, Graz, Austria). Segmented geometries included luminal and exterior AAA surfaces and used a predefined wall thickness that accounted for the reported wall thinning behind the ILT [28]. Specifically, in order to account for a moderate wall thinning behind the ILT layer, the wall thickness was set to H WALL ¼ max 1:5 À 0: 17 25 H ILT Â Ã mm with H ILT denoting the local thickness of the ILT layer in millimeters. Such predefined value compares reasonably to 1.56mm, an average value reported in the literature, see Table 2 in another study [32]. The reproducibility of the applied method has been reported previously [33][34][35], and a typical AAA segmentation is shown in Fig 1A. The maximum diameter (d max ), the maximum ILT layer thickness (H ILT max ), and luminal (V lum ), thrombus (V ILT ) and total (V tot ) volumes were calculated for each aortic geometry. See Table 2 for further details.

Structural analysis
Non-linear Finite Element (FE) models were used to compute the stress in the AAA wall at Mean Arterial Pressure (MAP). Peak Wall Stress (PWS), i.e. the highest von Mises stress in the aneurysm wall, was extracted from each simulation (A4clinics Research Edition, VASCOPS GmbH, Graz, Austria). The FE model used hexahedral-dominated finite elements of Q1P0 formulation [38] to avoid volume locking of incompressible solids. The AAA was fixed at the Table 1. Patient characteristics and timeline of Computed Tomography-Angiography (CT-A) scans.  Table 2. Definition of geometrical and biomechanical parameters. Bold face notation denotes vector or tensor quantities, and the region of interest was (manually) specified between the lower level of the renal arteries and the upper level of the aortic bifurcation, respectively. Minimal, maximal and mean magnitude of the blood flow velocity. The mean blood flow velocity is derived by averaging the magnitude of the blood flow velocity v over the time T of the cardiac cycle, as well as the volume of the lumen

Notation Description Remark
Minimal and maximal scalar shear rates over the cardiac cycle. These quantities are derived from the spatial velocity gradient gradv, i.e. a quantity that denotes how fast the blood velocity changes in space.
Minimal and maximal magnitude of the Wall Shear Stress (WSS) vector WSS over the cardiac cycle. WSS denotes the mechanical stress induced by blood flow onto blood-tissue (wall or ILT) interface.

WSS min = min[|WSS|] WSS max = max[|WSS|]
OSI Oscillatory Shear Index. The OSI is computed from the averaged magnitude of WSS and its magnitude | WSS|. The OSI denotes oscillatory behavior of the flow caused by complex flow patterns. Specifically, the extreme cases OSI = 1 and OSI = 0 denote oscillating and uni-directional flows, respectively. renal arteries and at the aortic bifurcation, and no contact with surrounding organs was considered. Isotropic constitutive descriptions for the aneurysm wall [39] and the ILT [27] were assigned to each model with the ILT stiffness gradually decreasing from the luminal to the abluminal sites [27]. Specifically, the AAA wall was assumed to be homogenous and modeled by the two-parameter Yeoh strain energy function ψ = c 1 (I 1 − 3) + c 2 (I 1 − 3) 2 with I 1 = tr C denoting the first invariant of the right Cauchy-Green strain C. Here, the material parameters c 1 = 77 kPa and c 2 = 1881 kPa have been used, i.e. values identified from in-vitro AAA wall testing [39]. The ILT was modeled by an Ogden-type strain energy function c ¼ c P 3 i¼1 ðl 4 i À 1Þ with λ i , i = 1,2,3 denoting the principal stretches. The constitutive properties of the ILT are captured by c ¼ max 2:62 À 0:89 25 H ILT ; 1:73 Â Ã kPa with H ILT denoting the local thickness of the ILT layer in millimeters. This expression accounts for the gradual decrease of stiffness from the luminal to the abluminal layer, i.e. as reported from in-vitro testing of ILT tissue [27]. The wall-ILT interface was rigid, i.e. ILT and AAA wall displacements matched at their interface.
A wall rupture risk index was defined by locally dividing the von Mises wall stress to an estimate of wall strength. AAA wall strength was assigned inhomogeneously and estimated by a scaled version [18,34] of the strength model proposed previously [12]. Finally, the highest wall risk index, or Peak Wall Rupture Index (PWRI), was extracted. In order to avoid picking up PWRI artefacts, A4clinics Research Edition averages over a sufficiently large number of FE nodes, i.e. locations where the wall rupture risk index is computed. In addition, PWRI location is indicated in the software window, so that the user can disregard identified artefacts. Fig 1B  illustrates the typical distribution of the wall rupture risk index, and Table 2 details the investigated structural biomechanical parameters.

Hemodynamical analysis
Rigid wall Computational Fluid Dynamics (CFD) models (ANSYS CFX, ANSYS Inc. US) with reported inflow and outflow conditions [36,37] were used to predict the blood flow velocity. Specifically, at the inlet, a plug velocity profile was derived from the inflow volume rate, and at both outlets, the pre-defined pressure was used. Inflow volume rate and outlet pressure wave have been taken from the literature [37]. The no-slip boundary condition was prescribed all along the luminal surface. The AAA lumen was meshed with tetrahedral finite volume elements (about 2mm in size), and five layers of prism elements (layer thickness ranging from 0.1mm to 0.2mm) aimed at capture boundary layer flow. Estimates on the required mesh size were based on our previous CFD work [36]. Specifically, a mesh sensitivity analysis [40] compared velocity, pressure, and WSS at ten points, to assess the relation between discretization error and element size.
The continuity and momentum equation were solved within the segment of the vascular lumen that has been segmented from CT-A images; in total five cardiac cycles with blood of density r ¼ 1050 kg m 3 were simulated. In addition, blood's shear-thinning viscous properties were captured by the Carreau-Yasuda viscosity model a . Here, _ g denotes the scalar shear rate, and μ 0 = 0.16 Pa s and μ 1 = 0.0035 Pa s specified blood viscosity at low and high shear rates, respectively. In addition, the time constant λ = 8.2 s, the power law index n = 0.2128, and the Yasuda exponent a = 0.64 have been used. These parameters represent blood viscosity of blood at 37 degrees Celsius, and have been used previously [41,42]. Further details regarding the applied CFD, especially regarding verifying the plausibility of the predictions, are given elsewhere [43].
Hemodynamics parameters were extracted from the fifth calculated cardiac cycle and inside the aneurysmatic vessel domain (MATLAB, The MathWorks Inc., Natick, Massachusetts, USA). Specifically, the minimal (v min ), maximal (v max ) and mean (v mean ) blood flow velocities, minimal ( _ g min ) and maximal ( _ g max ) scalar shear rates, minimal (WSS min ) and maximal (WSS max ) Wall Shear Stresses (WSS), as well as the Oscillatory Shear Index (OSI) [28,44] were computed. The definition of these parameters is listed in

Data analysis
Data analysis of biomechanical parameters was carried out within the aneurysmatic portions of the aorta. The proximal border of the aneurysmatic domain was defined by the vessel section at which the aorta was at least 10% larger than the normal (non aneurysmatic) aorta. The distal border was set 2.0cm proximal to the aortic bifurcation.
The rates of change over time of the geometrical, structural and hemodynamical were also investigated. At given time point, such quantities were calculated as the arithmetic difference between two consecutive CT-A scans and divided by the time between the scans. The rate of change of parameter X was denoted by ΔX.
Pooled data from all patients were statistically analyzed (SPSS, IBM Corp. Released 2013. IBM SPSS Statistics, Armonk, USA). All parameters were tested for normality using the Shapiro-Wilk test (significance level: p < 0.05), and Pearson and Spearman's correlation tests (significance level: p < 0.05) were used to investigate simple correlation among normal and nonnormal distributed parameters, respectively. Analysis of variance (ANOVA) was used to assess the statistical significance of multivariate linear regressions.

Results
A complete analysis of a single case at one time point took about ten hours. Figs 2 and 3 illustrate the development of the wall rupture risk index and WSS over time for all four patients, respectively.  Diameter and biomechanical rupture risk index PWRI and d max varied considerably over time (Fig 4). AAA C is rather stable and slightly below the mean PWRI versus diameter curve. At baseline, AAA B has a slightly smaller diameter than AAA C (49mm versus 52mm) but a higher PWRI, and within 5.9 years its diameter grows up to 60mm. Interestingly, PWRI increases rapidly at first but slightly decreases later. Case D is rather small at baseline (42mm) at a PWRI between the cases B and C. After 3.5 years the diameter in case D reaches 48 mm, but subsequently both diameter and PWRI reduce. AAA A is already large at baseline (71 mm), and within 2.2 years its diameter grows to 82 mm, subsequently shrinking by about 4 mm.

Correlation analysis
Simple correlation analysis. Tables 3-6 summarize the results from the simple correlation analysis, and Fig 5A-5D illustrates key findings with respect to d max . Interestingly, d max  did not correlate with diameter growth Δd max (Fig 4A). Instead d max correlated with volume growth ΔV tot , wall shear stress WSS max , and the biomechanical risk index PWRI (Fig 5B-5D). Moreover, trivial correlations between the diameter and volumes (V lum , V tot and V ILT ) were found. The scalar shear rates _ g min and _ g mean as well as the wall shear stresses WSS max ( Fig 5E) and WSS mean correlated negatively with V ILT . In contrast, the biomechanical risk index PWRI ( Fig  5F) and the Oscillatory Shear Index OSI showed positive correlations with V ILT . In addition, the mean blood flow velocity v mean correlated negatively with V ILT .
With respect to growth parameters, the maximum ILT thickness H ILT max correlated with total volume growth ΔV tot (Fig 6C). In addition, PWRI (Fig 6B) and OSI correlated positively, while _ g min (Fig 6A) correlated negatively with ΔV tot . Finally, simple regression with respect to the ILT growth ΔV ILT , exhibited correlations with v max , PWRI (Fig 6D), H ILT max (Fig 6C) and _ g max (Table 3).
All identified correlations are given in the supporting information section.

Multiple correlation analysis.
Multiple linear regression showed that both WSS max (p = 0.004) and PWRI (p = 0.001) are independent predictors of vessel volume growth. Specifically, volume growth increased with low WSS max and high PWRI following the relation ΔV tot = a 0 + a 1 WSS max + a 2 PWRI with parameters a 0 = −47. Similarly, high WSS max (p = 0.023) and V ILT (p<0.001) independently predicted ILT volume growth according to ΔV ILT = b 0 + b 1 WSS max + b 2 V ILT with the parameters b 0 = −48.38

Discussion
Clinical and experimental observations have indicated that biomechanical conditions influence the progression of aneurysm disease [45,46]. Despite these observations, a fundamental understanding of these interactions is still missing, particularly the role of the ILT in AAA pathology [25] is controversially discussed. The ILT is an active biochemical entity [25] that influences wall strength [12,24] and AAA progression [30], but also mechanically unloads the stress in the wall [20][21][22]. Specifically, clinical studies have linked a thick ILT layer [28] and fast increase in ILT volume [29] to increased AAA rupture risk. The present biomechanical study supports these observations through a strong positive correlation of the biomechanical risk index PWRI with both ILT volume V ILT and its change over time ΔV ILT . Consequently, the suitability of monitoring ILT volume, and its change over time, as additional risk indicators should be explored in larger clinical studies. ILT formation requires platelet accumulation, and for platelets to be able to adhere to the vessel, platelets must spend sufficient time in the vicinity of thrombogenic surfaces. Therefore, the adhesion of platelets might be promoted at sites of low WSS [43], i.e. an inverse relationship between WSS and aneurysm expansion may exist. Such an inverse relationship is confirmed by our study through the negative correlation of ΔV tot with WSS. Similar conclusions have been drawn from clinical observations, experimental AAA models [46], and simulation studies [31] The present study found that PWRI and WSS max independently predicted the growth of total AAA volume ΔV tot . PWRI is strongly related to the stress in the wall, and our finding is supported by previous experimental studies [30] showing that the growth of small AAAs is especially sensitive to wall stress. Due to the lack of endothelial cells in AAAs [28], blood flow properties may only indirectly promote AAA growth through stimulation of the biochemical environment within the ILT. For example, a high OSI could support pumping proteolytic agents through the porous ILT, which in turn could promote AAA growth.
Contrary to intuition, our data showed that the biomechanical risk does not always increase in time. Wall stress is strongly linked to AAA shape parameters like its asymmetry [47] or, more generally, to the surface curvatures [41]. Consequently, if growth appears to reduce AAA asymmetry, the biomechanical risk for rupture also reduces, i.e. the aneurysm grows into a shape of lower risk for rupture. The fluctuations in PWRI could also be explained by releasing spots of high surface curvatures of the wall through "cracking" of wall calcifications during AAA expansion, for example. The present study has several limitations. First of all our study was based on a relatively small number of cases due to the requirement of analyzing at least five CT-A scans for each patient. CT-A exposes patients to ionizing radiation and nephrotoxic contrast agents and should not be performed frequently. However, CT-A is practically the only standard image modality providing images accurate enough to build robust computational AAA models. Another limitation is related to the quantification of aneurysm growth. AAA growth is complex, and single parameters like change in maximum diameter or aneurysm volume can only serve as surrogate growth parameters. Therefore, a more rigorous three-dimensional quantification of the changing geometry would have been advantageous. However, CT-A images do not provide enough tracers in the wall that can be correlated amongst the different time points for a robust extraction of local wall growth. Such approach requires always some algorithms that interpolate between a few tracers (like anatomical landmarks) [48], and the extracted growth would always be largely influenced by algorithmic parameters, i.e. how the wall motion is interpolated between such tracers.
Biomechanical models introduce numerous modeling assumptions and cannot (and should not) completely reflect biomechanics of the real aneurysm. The constitution of aneurysm tissue and blood was modelled using mean population data. Patient-specific tissue and blood properties would have likely increased the accuracy of the predictions. Using a predefined AAA wall thickness influences wall stress predictions as well as ILT thickness measurements, and prescribing an inflow velocity profile influences blood flow predictions. Despite some of this information could be measured in the individual patient, the need for doing so remains unclear, and more research would be required to explore the sensitivity of our study results to such modeling assumptions. However, as these assumptions were used consistently across all patients they might not influence our conclusions.