ASME Journal of Biomechanical Engineering

Abdominal aortic aneurysm endovascular repair: profiling post-implantation morphometry and hemodynamics with image-based computational fluid dynamics Paola Tasso Department of Mechanical and Aerospace Engineering Politecnico di Torino, Torino 10129, Italy [email protected] Anastasios Raptis Laboratory for Vascular Simulations Institute of Vascular Diseases, Ioannina 45500, Greece [email protected] Mitiadis Matsagkas Department of Vascular Surgery Faculty of Medicine, University of Thessaly, Larissa 41334, Greece [email protected] Maurizio Lodi Rizzini Department of Mechanical and Aerospace Engineering Politecnico di Torino, Torino 10129, Italy [email protected] Diego Gallo Department of Mechanical and Aerospace Engineering Politecnico di Torino, Torino 10129, Italy [email protected] Michalis Xenos Department of Mathematics University of Ioannina, Ioannina 45500, Greece [email protected] Umberto Morbiducci Department of Mechanical and Aerospace Engineering Politecnico di Torino, Torino 10129, Italy [email protected]

1

ASME Journal of Biomechanical Engineering

ABSTRACT Endovascular aneurysm repair (EVAR) has disseminated rapidly as an alternative to open surgical repair for the treatment of abdominal aortic aneurysms (AAAs), because of its reduced invasiveness, low mortality and morbidity rate. The effectiveness of the endovascular devices used in EVAR is always at question as postoperative adverse events can lead to re-intervention or to a possible fatal scenario for the circulatory system. Motivated by the assessment of the risks related to thrombus formation, here the impact of two different commercial endovascular grafts on local hemodynamics is explored through 20 image-based computational hemodynamic models of EVAR-treated patients (N=10 per each endograft model). Hemodynamic features, susceptible to promote thrombus formation, such as flow separation and recirculation, are quantitatively assessed and compared with the local hemodynamics established in image-based infrarenal abdominal aortic models of healthy subjects (N=10). Moreover, the durability of endovascular devices is investigated analyzing the displacement forces acting on them. The hemodynamic analysis is complemented by a geometrical characterization of the EVAR-induced reshaping of the infrarenal abdominal aortic vascular region. The findings of this study indicate that: (1) the clinically observed propensity to thrombus formation in devices used in EVAR strategies can be explained in terms of local hemodynamics by means of image-based computational hemodynamics approach; (2) reportedly pro-thrombotic hemodynamic structures are strongly associated with the geometry of the aortoiliac tract postoperatively; (3) displacement forces are associated with cross-sectional area of the aortoiliac tract postoperatively. In perspective, our study suggests that future clinical follow up studies could include a geometric analysis of the region of the implant, monitoring shape variations that can lead to hemodynamic disturbances of clinical significance.

2

ASME Journal of Biomechanical Engineering

1

INTRODUCTION

2

Abdominal aortic aneurysm (AAA) is a vascular disease characterized by an enlargement of the

3

abdominal aorta lumen due to the loss of collagen and elastin in the wall [1]. As very recently

4

reported by the guidelines of the Society for Vascular Surgery, several issues need to be

5

considered carefully in the clinical management of AAA patients, such as (1) varying risks of

6

aneurysm rupture, (2) patient-specific factors influencing life expectancy, (3) need for

7

intervention, and (4) related operative risks [2]. In case of intervention, the guidelines suggest

8

careful attention to the choice of AAA operative strategy, along with appropriate post-intervention

9

surveillance, in order to minimize subsequent aneurysm-related death or morbidity [2].

10

Focusing on AAA treatment, endovascular aneurysm repair (EVAR), adopted for the first time in

11

1991, has disseminated rapidly as an alternative to open surgical repair of AAA [3], because of its

12

reduced invasiveness, low mortality and low morbidity rate [3-9]. There is clear evidence that, in

13

the United States, EVAR is being used with increasing frequency, with a decrease in associated

14

mortality [10].

15

Notwithstanding the marked evolution in both the technology and the assessment of long-term

16

outcomes, debate still exists about EVAR effectiveness [2, 11]. In fact, EVAR is associated with

17

postoperative complications that arise with variable frequency among the commercial stent-graft

18

systems, suggesting that a device-specific analysis could be more insightful [2, 12, 13]. Clinical

19

studies

20

occlusion/thrombosis as the most usual adverse events with inherent biomechanical triggers, such

21

as ill-directional displacement forces acting on the device structure and sub-optimal postoperative

22

hemodynamic environment [14-17]. In particular, the altered hemodynamics establishing inside

23

the endograft are suspected to contribute to thrombus formation immediately after the

highlight

the

stent-graft

migration,

endoleaks

(mainly

type

I)

and

limb

3

ASME Journal of Biomechanical Engineering

24

implantation or after months, potentially increasing the risk of an ischemic episode [18]. Very

25

recently, the Society for Vascular Surgery practice guidelines on the care of AAA patients indicated

26

the study of thrombosis in endograft as an area in need of further research [2].

27

Here, the impact of two different commercial endovascular devices on local hemodynamics is

28

explored through image-based computational simulations of blood flow in EVAR-treated patients

29

one month after implantation. Several hemodynamic features are identified, quantitatively

30

assessed and compared between postoperative and healthy infrarenal lumen structures derived

31

from medical imaging data reconstructions. The study is completed with the analysis of the

32

displacement forces acting on the implanted endografts, which are considered a primary factor

33

responsible for implants migration [19-23].In fact, as observed elsewhere, “displacement forces

34

are arguably the most important factor in determining the risk of device migration and future

35

complications” [20].

36

As geometry shapes the flow, the hemodynamic analysis is complemented by the geometrical

37

characterization of the EVAR-induced reshaping of the infrarenal abdominal aortic vascular region,

38

to mark out the impact of different endograft design features on local arterial morphology. The

39

overall objective was the identification of unique post-implantation morphological and

40

hemodynamic features marking up the endografts under examination, based on a sample of AAA

41

patients and heathy subjects.

42

MATERIALS AND METHODS

43

The schematic of the workflow applied in this study is provided in Fig. 1 and its parts are detailed

44

in the following subsections.

45

Study Subjects and Image Acquisition

4

ASME Journal of Biomechanical Engineering

46

Clinical data for this study were acquired at the University Hospital of Ioannina (Ioannina, Greece).

47

Twenty subjects affected by infrarenal fusiform AAA without extension of the disease to the

48

common iliac arteries were selected for this study. Subjects affected by AAA were divided into two

49

subgroups: ten patients (males, age = 73.9±8.41 years) were treated with the Endurant

50

(Medtronic Vascular, Santa Rosa, CA) stent graft, and the other ten (males, age = 68.6±8.62 years)

51

with the Excluder (W.L. Gore & Associates, Flagstaff, AZ) stent graft; both devices are fixed just

52

below the renal bifurcation and below the iliac bifurcation. As detailed elsewhere [15] the two

53

patient subgroups were statistically homogeneous in terms of (1) age, and (2) preoperative AAA

54

morphological features (in detail: neck length, neck diameter, suprarenal angle, infrarenal angle,

55

aortic length, right iliac length, left iliac length, right iliac diameter, left iliac diameter, neck

56

diameter to right iliac diameter, neck diameter to left iliac diameter). Physiologic ranges of the

57

considered hemodynamic and geometric variables are defined by considering ten healthy subjects

58

(males, age = 57.3±15.7 years).

59

Clinical images of healthy and repaired abdominal aortas and common iliac arteries were

60

extracted from computer tomography angiography (CTA) scans (Fig. 1), as detailed elsewhere [15,

61

24]. In detail, CTA scans were obtained with a 16-slices CT system (Brilliance CT 16 slice, Philips

62

Healthcare, Best, The Netherlands) with intravenous injection of contrast agent. Imaging

63

parameters included: 0.75-2.00 mm slice thickness, 0.78125/0.78125 pixel spacing, 120 KVp, 366

64

mA. On the twenty subjects affected by AAA, images were acquired one month after stent-graft

65

implantation. Healthy subjects had no sign of AAA and underwent CTA for other reasons. The

66

protocol was approved by the Institutional Review Board of the University of Ioannina, Ioannina,

67

Greece, and all the subjects gave informed consent for the use of their screening data.

68

Image Segmentation and 3D reconstruction

5

ASME Journal of Biomechanical Engineering

69

The two-dimensional DICOM images from CT scans were segmented using a semi-automatic

70

approach minimizing user interactions, and converted into three-dimensional models using the

71

software Mimics (Materialise, Leuven, Belgium) [15, 24]. Segmentation was performed on vessel

72

lumen for healthy arteries, and on the stent internal graft surface for EVAR treated arteries,

73

neglecting vessels and devices wall thickness. An overview of the reconstructed three-dimensional

74

geometries, divided in the three groups (i.e., healthy, Endurant- and Excluder-treated subjects), is

75

presented in Fig. 2.

76

The region of interest (ROI) was selected based on the position of the aortic segment where the

77

endograft is located. In detail, the radiopaque markers located at the opposite ends of the

78

endograft were used as guidelines. For healthy subjects, the rationale behind the ROI selection

79

was to consider the same aortic region as in treated patients. In detail, the ROI was determined

80

based on the indications from the clinical practice for the endograft landing zone, i.e. below the

81

renal bifurcation and, at least, 1.5 cm below the iliac bifurcation [25, 26]. This results in different

82

branches length for healthy or treated subjects, due to the more proximal position of the device

83

bifurcation with respect to the native iliac bifurcation.

84

Morphometric analysis

85

On the 30 reconstructed geometries, a centerline-based morphometric analysis was carried out, as

86

proposed elsewhere [27-29]. Technically, centerlines were extracted as the geometrical locus of

87

the centers of the maximum inscribed spheres in the model, as given by the Vascular Modelling

88

Toolkit software (VMTK, Orobix, Bergamo, Italy). Free-knots regression splines were then adopted

89

[30] as a basis of representation for a vessel’s centerline to provide a continuous, noise free

90

analytical formulation C with continuous derivatives. By differentiation of the free-knots

91

regression spline centerline representation C, curvature and torsion were calculated [28, 31]. In 6

ASME Journal of Biomechanical Engineering

92

detail, local curvature κ is defined as the reciprocal of the radius of the circle lying on the

93

osculating plane (identified by the normal and tangent vectors to the curve at that point), to

94

measure the rate of change in the tangent vector orientation along the curve. Local torsion τ

95

measures the deviation of curve C from the osculating plane. Technically, the curvature κ and

96

torsion τ of a curve C along the curvilinear abscissa s can be defined as: = =

| × | | |

[′ × ′′] ∙ ′′′ |′ × ′′|

97

where C’(s), C’’(s) and C’’’(s) are, respectively, first, second and third derivative of curve C with the

98

respect to the curvilinear abscissa s. Both vessel’s curvature and torsion of are known to have an

99

influence on arterial hemodynamics [32].

100

Local cross-sectional area A(s) of the vessel and its variation rate r(s), defined as the derivative of

101

A(s) with respect to s along the centerline C, were also computed using Matlab (Mathworks,

102

Natick, MA) [27, 28].

103

The centerline-based morphometry analysis of the infrarenal abdominal aortic bifurcation region

104

was divided into three segments (Fig. 3): body (identified by the centerline segment upstream of

105

the bifurcation point), left branch, and right branch (identified by the centerline segments

106

downstream the bifurcation point). Over the whole infrarenal abdominal aortic bifurcation region

107

and over each segment, average values (τmean, κmean, Amean, rmean), peak values (τpeak, κpeak,

108

Apeak, rpeak) and peak-to-peak (intended as the difference between maximum and minimum

109

values) amplitudes (τpp, κpp, App, rpp) of each geometric descriptor were computed [28].

110

Computational hemodynamics 7

ASME Journal of Biomechanical Engineering

111

In this study, blood was assumed to be an incompressible, isothermal, homogeneous, Newtonian

112

fluid (ρ = 1050 kg/m3; μ = 0.0035 Pa∙s) [24]. The governing equations of fluid motion, in the form:

!"

+ " ∙ $" + $ ∙ %μ$" + $"' ( + ∇* = + , - ∇∙"=0

113

where is the density, . the dynamic viscosity, " the velocity, + the body force and * the

114

pressure, were numerically solved by applying the finite volume method. To do that, the general

115

purpose CFD code Fluent (ANSYS Inc., Canonsburg, PA) was used on fluid domains discretized by

116

using tetrahedrons (with near-wall refinement obtained implementing a radial meshing approach

117

with elements density higher near the wall). A preliminary analysis of the sensitivity of the

118

numerical solution to the cardinality of the mesh was carried out. Steady state simulations were

119

performed on one model with 13 different mesh densities (ranging from 1 to 14 million

120

tetrahedrons). The satisfactory compromise between solution accuracy and computational costs

121

resulted in a mesh grid with elements size between 0.58 and 0.63 mm in the bulk and between

122

0.19 and 0.22 mm for near-wall elements. Therefore, mesh cardinality in the 30 models ranges

123

from 3.5 to 12.5 million.

124

As for the applied numerical scheme, second order accuracy was prescribed to solve both the

125

momentum equation and pressure with the SIMPLE pressure-velocity coupling scheme. The

126

backward Euler implicit scheme was adopted for time integration, with a fixed 0.0035 s time

127

increment. Convergence was achieved when the maximum mass and momentum residuals fell

128

below 10-4.

129

The strategy applied to prescribe the conditions at inflow and outflow boundaries is detailed

130

elsewhere [33]. Briefly, a Neumann condition was prescribed at the inflow boundary in terms of

131

time-dependent pressure waveform available from the literature [33]. At the outflow sections, 8

ASME Journal of Biomechanical Engineering

132

flow rate waveforms available from the literature and scaled according to the outflow sections

133

area were prescribed in terms of fully developed velocity profiles [15, 33]. To minimize the

134

influence from boundary conditions, flow extensions were added to the inlet and outlet faces of all

135

CFD models. Arterial walls were assumed to be rigid, with no-slip condition.

136

Near-wall and intravascular hemodynamic descriptors

137

Near-wall hemodynamics was explored by using the Time Averaged Wall Shear Stress (TAWSS),

138

i.e., the average value of the magnitude of the wall shear stress (WSS) vector τw along the cardiac

139

cycle: 1 ' TAWSS2 = 5 |67 2, 8|98 ; 4 :

140

where T is the duration of cardiac cycle and s the generic location at the vessel wall [27, 34]. Here

141

TAWSS was applied to identify low WSS regions, which in general correspond to low velocity

142

regions of flow separation, more prone to thrombus formation. In this study, we also considered

143

the TAWSS value averaged over the luminal surface S of a healthy or treated model (AWSS):

AWSS =

1 5 TAWSS2 9< > < =

144

Hemodynamic-related thrombus formation risks was additionally assessed by considering

145

recirculating flow, which has been demonstrated to correlate with thrombotic markers. To

146

quantify it, a modified version of the descriptor proposed by Martorell et al. [35]. was adopted to

147

calculate the volume of recirculating flow. Technically, the volume of recirculating flow was

148

computed by projecting the velocity vector field along the local vessel centerlines (i.e., axial

149

direction), and then integrating all finite volumes containing a negative axial velocity component.

150

In detail, the axial component ("AC [email protected] ) of the cycle-average velocity vector ("[email protected] ) was calculated 9

ASME Journal of Biomechanical Engineering

151

according to the scheme proposed elsewhere [29]. Finite volume cells with negative "AC [email protected] value,

152

indicating average reverse flow, are markers of local recirculation. The Volume of Recirculation

153

(VolRec) was defined as the amount of fluid volume characterized a negative value of "AC [email protected] : L

DEFGHI = J δ KMN

1 if δk = 0 if

154

D O K K

(v ) (v ) ax

mean k ax

mean k

≤0 >0

155

Where Vk is the k-th finite volume cell, and N is the total number of finite volume cells of the fluid

156

domain. Here, the percentage VolRec value (%VolRec) for each model was calculated as follows: %DEFGHI =

DEFGHI ∙ 100 T 4E8QF DEFRSH

157

Eq. 7, allowed to use %VolRec for comparing the amount of blood recirculation among different

158

subjects, accounting for volumetric dimension intervariability of vascular segments.

159

Descriptors of the intravascular fluid structures such as helical flow were also applied, as it has

160

been observed that helical flow (1) has a physiological significance in arteries [36, 37], and (2)

161

smooths out WSS extremes [38-40]. The visualization of intravascular helical flow structures (for

162

the purposes of comparison) was performed by applying the Local Normalized Helicity (LNH): UVW =

"2, 8 ∙ X2, 8 = cos \ ] |"2, 8 ∙ X2, 8|

163

where ϕ is the angle between velocity and vorticity vectors [41]. By definition, the absolute value

164

of LNH ranges between one, when the flow is purely helical, and zero (in general) in presence of

165

reflectional symmetry in the flow. As reported elsewhere (see, e.g., [41]), LNH sign is an indicator 10

ASME Journal of Biomechanical Engineering

166

of the local right/left-handed direction of rotation of helical blood flow structures in the vessel.

167

Helical flow structures were characterized quantitatively by helicity-based hemodynamic

168

descriptors defined elsewhere [38, 39, 42], quantifying the (normalized to volume) average helicity

169

(h1), helicity intensity (h2), and helical flow topology (h3 and h4):

ℎN =

ℎ =

1 5 5 "2, 8 ∙ X2, 8 9D 98 a 4D ' `

1 5 5 |"2, 8 ∙ X2, 8| 9D 98 b 4D ' ` ℎ = ℎc =

ℎN

ℎ

|ℎN | ℎ

170

where T is the cardiac cycle, V is the vascular volume of interest, " the velocity vector, X the

171

vorticity vector and s the position in the fluid domain [38]. Briefly, eq. 9 and eq. 10 are non-

172

dimensional quantities and quantify the relative presence of counter-rotating helical structures. In

173

detail, h3 (-1 ≤ h3 ≤ 1) has by construction positive (negative) value when right-handed (left-

174

handed) helical structures are predominant in the fluid domain, while h4, defined as the absolute

175

value of h3, measures the strength of relative rotations of helical fluid structures in the fluid

176

domain, neglecting what is the major direction of rotation [38].

177

Displacement forces

178

The implanted endograft experiences a displacement force exerted by blood flow on its walls, and

179

its local value is given by the contribution of the pressure force and of the friction force. At each

180

time point along the cardiac cycle, the total displacement force (DF) acting over the entire wall of

11

ASME Journal of Biomechanical Engineering

181

the implanted device can be calculated by taking an area integral of the net pressure and of the

182

WSS vector [20]:

de8 = 5 * f 9< + 5 67 9< - =

=

183

where n is the unit vector locally normal to the wall and S is the surface area of the implanted

184

device. Here the quantity DFpeak, i.e., the magnitude of DF given by Eq. (13) calculated at peak

185

pressure time point at the inflow boundary, when the most elevated pressure and WSS values are

186

expected, was considered for the analysis.

187

Statistical analysis

188

To test for differences among healthy, Endurant or Excluder groups in quantities describing

189

geometric and hemodynamic features, the Mann-Whitney test was applied [43]. To identify

190

relationships among hemodynamic and geometric quantities, the Shapiro-Wilk test of normality

191

was preliminarily applied, due to the small sample investigated [44]. Pearson correlation

192

coefficients were then used if both variables were normally distributed, or Spearman correlation

193

coefficients in case one or both variables were not normally distributed. Regressions are reported

194

as the individual standardized correlation coefficient (β). For all analyses, significance was

195

assumed for p

Abdominal aortic aneurysm endovascular repair: profiling post-implantation morphometry and hemodynamics with image-based computational fluid dynamics Paola Tasso Department of Mechanical and Aerospace Engineering Politecnico di Torino, Torino 10129, Italy [email protected] Anastasios Raptis Laboratory for Vascular Simulations Institute of Vascular Diseases, Ioannina 45500, Greece [email protected] Mitiadis Matsagkas Department of Vascular Surgery Faculty of Medicine, University of Thessaly, Larissa 41334, Greece [email protected] Maurizio Lodi Rizzini Department of Mechanical and Aerospace Engineering Politecnico di Torino, Torino 10129, Italy [email protected] Diego Gallo Department of Mechanical and Aerospace Engineering Politecnico di Torino, Torino 10129, Italy [email protected] Michalis Xenos Department of Mathematics University of Ioannina, Ioannina 45500, Greece [email protected] Umberto Morbiducci Department of Mechanical and Aerospace Engineering Politecnico di Torino, Torino 10129, Italy [email protected]

1

ASME Journal of Biomechanical Engineering

ABSTRACT Endovascular aneurysm repair (EVAR) has disseminated rapidly as an alternative to open surgical repair for the treatment of abdominal aortic aneurysms (AAAs), because of its reduced invasiveness, low mortality and morbidity rate. The effectiveness of the endovascular devices used in EVAR is always at question as postoperative adverse events can lead to re-intervention or to a possible fatal scenario for the circulatory system. Motivated by the assessment of the risks related to thrombus formation, here the impact of two different commercial endovascular grafts on local hemodynamics is explored through 20 image-based computational hemodynamic models of EVAR-treated patients (N=10 per each endograft model). Hemodynamic features, susceptible to promote thrombus formation, such as flow separation and recirculation, are quantitatively assessed and compared with the local hemodynamics established in image-based infrarenal abdominal aortic models of healthy subjects (N=10). Moreover, the durability of endovascular devices is investigated analyzing the displacement forces acting on them. The hemodynamic analysis is complemented by a geometrical characterization of the EVAR-induced reshaping of the infrarenal abdominal aortic vascular region. The findings of this study indicate that: (1) the clinically observed propensity to thrombus formation in devices used in EVAR strategies can be explained in terms of local hemodynamics by means of image-based computational hemodynamics approach; (2) reportedly pro-thrombotic hemodynamic structures are strongly associated with the geometry of the aortoiliac tract postoperatively; (3) displacement forces are associated with cross-sectional area of the aortoiliac tract postoperatively. In perspective, our study suggests that future clinical follow up studies could include a geometric analysis of the region of the implant, monitoring shape variations that can lead to hemodynamic disturbances of clinical significance.

2

ASME Journal of Biomechanical Engineering

1

INTRODUCTION

2

Abdominal aortic aneurysm (AAA) is a vascular disease characterized by an enlargement of the

3

abdominal aorta lumen due to the loss of collagen and elastin in the wall [1]. As very recently

4

reported by the guidelines of the Society for Vascular Surgery, several issues need to be

5

considered carefully in the clinical management of AAA patients, such as (1) varying risks of

6

aneurysm rupture, (2) patient-specific factors influencing life expectancy, (3) need for

7

intervention, and (4) related operative risks [2]. In case of intervention, the guidelines suggest

8

careful attention to the choice of AAA operative strategy, along with appropriate post-intervention

9

surveillance, in order to minimize subsequent aneurysm-related death or morbidity [2].

10

Focusing on AAA treatment, endovascular aneurysm repair (EVAR), adopted for the first time in

11

1991, has disseminated rapidly as an alternative to open surgical repair of AAA [3], because of its

12

reduced invasiveness, low mortality and low morbidity rate [3-9]. There is clear evidence that, in

13

the United States, EVAR is being used with increasing frequency, with a decrease in associated

14

mortality [10].

15

Notwithstanding the marked evolution in both the technology and the assessment of long-term

16

outcomes, debate still exists about EVAR effectiveness [2, 11]. In fact, EVAR is associated with

17

postoperative complications that arise with variable frequency among the commercial stent-graft

18

systems, suggesting that a device-specific analysis could be more insightful [2, 12, 13]. Clinical

19

studies

20

occlusion/thrombosis as the most usual adverse events with inherent biomechanical triggers, such

21

as ill-directional displacement forces acting on the device structure and sub-optimal postoperative

22

hemodynamic environment [14-17]. In particular, the altered hemodynamics establishing inside

23

the endograft are suspected to contribute to thrombus formation immediately after the

highlight

the

stent-graft

migration,

endoleaks

(mainly

type

I)

and

limb

3

ASME Journal of Biomechanical Engineering

24

implantation or after months, potentially increasing the risk of an ischemic episode [18]. Very

25

recently, the Society for Vascular Surgery practice guidelines on the care of AAA patients indicated

26

the study of thrombosis in endograft as an area in need of further research [2].

27

Here, the impact of two different commercial endovascular devices on local hemodynamics is

28

explored through image-based computational simulations of blood flow in EVAR-treated patients

29

one month after implantation. Several hemodynamic features are identified, quantitatively

30

assessed and compared between postoperative and healthy infrarenal lumen structures derived

31

from medical imaging data reconstructions. The study is completed with the analysis of the

32

displacement forces acting on the implanted endografts, which are considered a primary factor

33

responsible for implants migration [19-23].In fact, as observed elsewhere, “displacement forces

34

are arguably the most important factor in determining the risk of device migration and future

35

complications” [20].

36

As geometry shapes the flow, the hemodynamic analysis is complemented by the geometrical

37

characterization of the EVAR-induced reshaping of the infrarenal abdominal aortic vascular region,

38

to mark out the impact of different endograft design features on local arterial morphology. The

39

overall objective was the identification of unique post-implantation morphological and

40

hemodynamic features marking up the endografts under examination, based on a sample of AAA

41

patients and heathy subjects.

42

MATERIALS AND METHODS

43

The schematic of the workflow applied in this study is provided in Fig. 1 and its parts are detailed

44

in the following subsections.

45

Study Subjects and Image Acquisition

4

ASME Journal of Biomechanical Engineering

46

Clinical data for this study were acquired at the University Hospital of Ioannina (Ioannina, Greece).

47

Twenty subjects affected by infrarenal fusiform AAA without extension of the disease to the

48

common iliac arteries were selected for this study. Subjects affected by AAA were divided into two

49

subgroups: ten patients (males, age = 73.9±8.41 years) were treated with the Endurant

50

(Medtronic Vascular, Santa Rosa, CA) stent graft, and the other ten (males, age = 68.6±8.62 years)

51

with the Excluder (W.L. Gore & Associates, Flagstaff, AZ) stent graft; both devices are fixed just

52

below the renal bifurcation and below the iliac bifurcation. As detailed elsewhere [15] the two

53

patient subgroups were statistically homogeneous in terms of (1) age, and (2) preoperative AAA

54

morphological features (in detail: neck length, neck diameter, suprarenal angle, infrarenal angle,

55

aortic length, right iliac length, left iliac length, right iliac diameter, left iliac diameter, neck

56

diameter to right iliac diameter, neck diameter to left iliac diameter). Physiologic ranges of the

57

considered hemodynamic and geometric variables are defined by considering ten healthy subjects

58

(males, age = 57.3±15.7 years).

59

Clinical images of healthy and repaired abdominal aortas and common iliac arteries were

60

extracted from computer tomography angiography (CTA) scans (Fig. 1), as detailed elsewhere [15,

61

24]. In detail, CTA scans were obtained with a 16-slices CT system (Brilliance CT 16 slice, Philips

62

Healthcare, Best, The Netherlands) with intravenous injection of contrast agent. Imaging

63

parameters included: 0.75-2.00 mm slice thickness, 0.78125/0.78125 pixel spacing, 120 KVp, 366

64

mA. On the twenty subjects affected by AAA, images were acquired one month after stent-graft

65

implantation. Healthy subjects had no sign of AAA and underwent CTA for other reasons. The

66

protocol was approved by the Institutional Review Board of the University of Ioannina, Ioannina,

67

Greece, and all the subjects gave informed consent for the use of their screening data.

68

Image Segmentation and 3D reconstruction

5

ASME Journal of Biomechanical Engineering

69

The two-dimensional DICOM images from CT scans were segmented using a semi-automatic

70

approach minimizing user interactions, and converted into three-dimensional models using the

71

software Mimics (Materialise, Leuven, Belgium) [15, 24]. Segmentation was performed on vessel

72

lumen for healthy arteries, and on the stent internal graft surface for EVAR treated arteries,

73

neglecting vessels and devices wall thickness. An overview of the reconstructed three-dimensional

74

geometries, divided in the three groups (i.e., healthy, Endurant- and Excluder-treated subjects), is

75

presented in Fig. 2.

76

The region of interest (ROI) was selected based on the position of the aortic segment where the

77

endograft is located. In detail, the radiopaque markers located at the opposite ends of the

78

endograft were used as guidelines. For healthy subjects, the rationale behind the ROI selection

79

was to consider the same aortic region as in treated patients. In detail, the ROI was determined

80

based on the indications from the clinical practice for the endograft landing zone, i.e. below the

81

renal bifurcation and, at least, 1.5 cm below the iliac bifurcation [25, 26]. This results in different

82

branches length for healthy or treated subjects, due to the more proximal position of the device

83

bifurcation with respect to the native iliac bifurcation.

84

Morphometric analysis

85

On the 30 reconstructed geometries, a centerline-based morphometric analysis was carried out, as

86

proposed elsewhere [27-29]. Technically, centerlines were extracted as the geometrical locus of

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the centers of the maximum inscribed spheres in the model, as given by the Vascular Modelling

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Toolkit software (VMTK, Orobix, Bergamo, Italy). Free-knots regression splines were then adopted

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[30] as a basis of representation for a vessel’s centerline to provide a continuous, noise free

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analytical formulation C with continuous derivatives. By differentiation of the free-knots

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regression spline centerline representation C, curvature and torsion were calculated [28, 31]. In 6

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detail, local curvature κ is defined as the reciprocal of the radius of the circle lying on the

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osculating plane (identified by the normal and tangent vectors to the curve at that point), to

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measure the rate of change in the tangent vector orientation along the curve. Local torsion τ

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measures the deviation of curve C from the osculating plane. Technically, the curvature κ and

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torsion τ of a curve C along the curvilinear abscissa s can be defined as: = =

| × | | |

[′ × ′′] ∙ ′′′ |′ × ′′|

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where C’(s), C’’(s) and C’’’(s) are, respectively, first, second and third derivative of curve C with the

98

respect to the curvilinear abscissa s. Both vessel’s curvature and torsion of are known to have an

99

influence on arterial hemodynamics [32].

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Local cross-sectional area A(s) of the vessel and its variation rate r(s), defined as the derivative of

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A(s) with respect to s along the centerline C, were also computed using Matlab (Mathworks,

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Natick, MA) [27, 28].

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The centerline-based morphometry analysis of the infrarenal abdominal aortic bifurcation region

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was divided into three segments (Fig. 3): body (identified by the centerline segment upstream of

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the bifurcation point), left branch, and right branch (identified by the centerline segments

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downstream the bifurcation point). Over the whole infrarenal abdominal aortic bifurcation region

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and over each segment, average values (τmean, κmean, Amean, rmean), peak values (τpeak, κpeak,

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Apeak, rpeak) and peak-to-peak (intended as the difference between maximum and minimum

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values) amplitudes (τpp, κpp, App, rpp) of each geometric descriptor were computed [28].

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Computational hemodynamics 7

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In this study, blood was assumed to be an incompressible, isothermal, homogeneous, Newtonian

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fluid (ρ = 1050 kg/m3; μ = 0.0035 Pa∙s) [24]. The governing equations of fluid motion, in the form:

!"

+ " ∙ $" + $ ∙ %μ$" + $"' ( + ∇* = + , - ∇∙"=0

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where is the density, . the dynamic viscosity, " the velocity, + the body force and * the

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pressure, were numerically solved by applying the finite volume method. To do that, the general

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purpose CFD code Fluent (ANSYS Inc., Canonsburg, PA) was used on fluid domains discretized by

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using tetrahedrons (with near-wall refinement obtained implementing a radial meshing approach

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with elements density higher near the wall). A preliminary analysis of the sensitivity of the

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numerical solution to the cardinality of the mesh was carried out. Steady state simulations were

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performed on one model with 13 different mesh densities (ranging from 1 to 14 million

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tetrahedrons). The satisfactory compromise between solution accuracy and computational costs

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resulted in a mesh grid with elements size between 0.58 and 0.63 mm in the bulk and between

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0.19 and 0.22 mm for near-wall elements. Therefore, mesh cardinality in the 30 models ranges

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from 3.5 to 12.5 million.

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As for the applied numerical scheme, second order accuracy was prescribed to solve both the

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momentum equation and pressure with the SIMPLE pressure-velocity coupling scheme. The

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backward Euler implicit scheme was adopted for time integration, with a fixed 0.0035 s time

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increment. Convergence was achieved when the maximum mass and momentum residuals fell

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below 10-4.

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The strategy applied to prescribe the conditions at inflow and outflow boundaries is detailed

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elsewhere [33]. Briefly, a Neumann condition was prescribed at the inflow boundary in terms of

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time-dependent pressure waveform available from the literature [33]. At the outflow sections, 8

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flow rate waveforms available from the literature and scaled according to the outflow sections

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area were prescribed in terms of fully developed velocity profiles [15, 33]. To minimize the

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influence from boundary conditions, flow extensions were added to the inlet and outlet faces of all

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CFD models. Arterial walls were assumed to be rigid, with no-slip condition.

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Near-wall and intravascular hemodynamic descriptors

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Near-wall hemodynamics was explored by using the Time Averaged Wall Shear Stress (TAWSS),

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i.e., the average value of the magnitude of the wall shear stress (WSS) vector τw along the cardiac

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cycle: 1 ' TAWSS2 = 5 |67 2, 8|98 ; 4 :

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where T is the duration of cardiac cycle and s the generic location at the vessel wall [27, 34]. Here

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TAWSS was applied to identify low WSS regions, which in general correspond to low velocity

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regions of flow separation, more prone to thrombus formation. In this study, we also considered

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the TAWSS value averaged over the luminal surface S of a healthy or treated model (AWSS):

AWSS =

1 5 TAWSS2 9< > < =

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Hemodynamic-related thrombus formation risks was additionally assessed by considering

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recirculating flow, which has been demonstrated to correlate with thrombotic markers. To

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quantify it, a modified version of the descriptor proposed by Martorell et al. [35]. was adopted to

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calculate the volume of recirculating flow. Technically, the volume of recirculating flow was

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computed by projecting the velocity vector field along the local vessel centerlines (i.e., axial

149

direction), and then integrating all finite volumes containing a negative axial velocity component.

150

In detail, the axial component ("AC [email protected] ) of the cycle-average velocity vector ("[email protected] ) was calculated 9

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according to the scheme proposed elsewhere [29]. Finite volume cells with negative "AC [email protected] value,

152

indicating average reverse flow, are markers of local recirculation. The Volume of Recirculation

153

(VolRec) was defined as the amount of fluid volume characterized a negative value of "AC [email protected] : L

DEFGHI = J δ KMN

1 if δk = 0 if

154

D O K K

(v ) (v ) ax

mean k ax

mean k

≤0 >0

155

Where Vk is the k-th finite volume cell, and N is the total number of finite volume cells of the fluid

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domain. Here, the percentage VolRec value (%VolRec) for each model was calculated as follows: %DEFGHI =

DEFGHI ∙ 100 T 4E8QF DEFRSH

157

Eq. 7, allowed to use %VolRec for comparing the amount of blood recirculation among different

158

subjects, accounting for volumetric dimension intervariability of vascular segments.

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Descriptors of the intravascular fluid structures such as helical flow were also applied, as it has

160

been observed that helical flow (1) has a physiological significance in arteries [36, 37], and (2)

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smooths out WSS extremes [38-40]. The visualization of intravascular helical flow structures (for

162

the purposes of comparison) was performed by applying the Local Normalized Helicity (LNH): UVW =

"2, 8 ∙ X2, 8 = cos \ ] |"2, 8 ∙ X2, 8|

163

where ϕ is the angle between velocity and vorticity vectors [41]. By definition, the absolute value

164

of LNH ranges between one, when the flow is purely helical, and zero (in general) in presence of

165

reflectional symmetry in the flow. As reported elsewhere (see, e.g., [41]), LNH sign is an indicator 10

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of the local right/left-handed direction of rotation of helical blood flow structures in the vessel.

167

Helical flow structures were characterized quantitatively by helicity-based hemodynamic

168

descriptors defined elsewhere [38, 39, 42], quantifying the (normalized to volume) average helicity

169

(h1), helicity intensity (h2), and helical flow topology (h3 and h4):

ℎN =

ℎ =

1 5 5 "2, 8 ∙ X2, 8 9D 98 a 4D ' `

1 5 5 |"2, 8 ∙ X2, 8| 9D 98 b 4D ' ` ℎ = ℎc =

ℎN

ℎ

|ℎN | ℎ

170

where T is the cardiac cycle, V is the vascular volume of interest, " the velocity vector, X the

171

vorticity vector and s the position in the fluid domain [38]. Briefly, eq. 9 and eq. 10 are non-

172

dimensional quantities and quantify the relative presence of counter-rotating helical structures. In

173

detail, h3 (-1 ≤ h3 ≤ 1) has by construction positive (negative) value when right-handed (left-

174

handed) helical structures are predominant in the fluid domain, while h4, defined as the absolute

175

value of h3, measures the strength of relative rotations of helical fluid structures in the fluid

176

domain, neglecting what is the major direction of rotation [38].

177

Displacement forces

178

The implanted endograft experiences a displacement force exerted by blood flow on its walls, and

179

its local value is given by the contribution of the pressure force and of the friction force. At each

180

time point along the cardiac cycle, the total displacement force (DF) acting over the entire wall of

11

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the implanted device can be calculated by taking an area integral of the net pressure and of the

182

WSS vector [20]:

de8 = 5 * f 9< + 5 67 9< - =

=

183

where n is the unit vector locally normal to the wall and S is the surface area of the implanted

184

device. Here the quantity DFpeak, i.e., the magnitude of DF given by Eq. (13) calculated at peak

185

pressure time point at the inflow boundary, when the most elevated pressure and WSS values are

186

expected, was considered for the analysis.

187

Statistical analysis

188

To test for differences among healthy, Endurant or Excluder groups in quantities describing

189

geometric and hemodynamic features, the Mann-Whitney test was applied [43]. To identify

190

relationships among hemodynamic and geometric quantities, the Shapiro-Wilk test of normality

191

was preliminarily applied, due to the small sample investigated [44]. Pearson correlation

192

coefficients were then used if both variables were normally distributed, or Spearman correlation

193

coefficients in case one or both variables were not normally distributed. Regressions are reported

194

as the individual standardized correlation coefficient (β). For all analyses, significance was

195

assumed for p