Medical Engineering and Physics 38 (2016) 1505–1512

Contents lists available at ScienceDirect

Medical Engineering and Physics

journal homepage: www.elsevier.com/locate/medengphy

Technical note

Anisotropic abdominal aortic aneurysm replicas with biaxial material

characterization

Sergio Ruiz de Galarreta

a , Raúl Antón

a , ∗, Aitor Cazon

a , Gorka S. Larraona

a , Ender A. Finol b

a Department of Mechanical Engineering, Tecnun, University of Navarra, Paseo Manuel de Lardizabal, 13, 20018 San Sebastián, Spain b Department of Biomedical Engineering, The University of Texas at San Antonio, One UTSA Circle, AET 1.360, San Antonio, TX 78249-0669, United States

a r t i c l e i n f o

Article history:

Received 10 November 2015

Revised 16 August 2016

Accepted 23 September 2016

Keywords:

Anisotropy

AAA phantom

Biaxial

Stereovision

Vacuum casting

Additive manufacturing

a b s t r a c t

An Abdominal Aortic Aneurysm (AAA) is a permanent focal dilatation of the abdominal aorta at least

1.5 times its normal diameter. The criterion of maximum diameter is still used in clinical practice, al-

though numerical studies have demonstrated the importance of other biomechanical factors. Numerical

studies, however, must be validated experimentally before they can be clinically implemented. We have

developed a methodology for manufacturing anisotropic AAA replicas with non-uniform wall thickness.

Different com posites were fabricated and tested, and one was selected in order to manufacture a phan-

tom with the same properties. The composites and the phantom were characterized by biaxial tensile

tests and a material model was fit to the experimental data. The experimental results were compared

with data from the literature, and similar responses were obtained. The anisotropic AAA replicas with

non-uniform wall thickness can be used in benchtop experiments to validate deformations obtained with

numerical simulations or for pre-intervention testing of endovascular grafts. This is a significant step for-

ward considering the importance of anisotropy in numerical simulations.

© 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

1

t

c

I

t

a

t

g

s

v

c

t

[

t

r

g

n

1

p

a

r

l

f

t

p

a

a

t

r

2

2

S

b

d

h

1

. Introduction

An Abdominal Aortic Aneurysm (AAA) is a permanent dilata-

ion of the abdominal aorta, and its rupture remains a significant

ause of death in developed countries among men aged 65–85 [1] .

n clinical practice, uncertainty still remains about the correct time

o operate, but the criterion of maximum diameter is commonly

ccepted as a rupture prediction factor, meaning that medical doc-

ors recommend surgical interventions when AAA diameters are

reater than 55 mm [2] . When studying AAA rupture, numerical

imulations via Finite Element Analysis (FEA) have proved to be

ery useful in indicating that this rupture criterion needs to be

omplemented with AAA wall stress data [3–5] , meaning that fac-

ors such as geometry and biomechanics must also be considered

6,7] .

In vitro experiments with AAA phantoms have been shown

o be very useful in several applications [8–10] . These phantoms

anged from totally idealized geometries to real AAA geometries

enerally with uniform [11,12] but also with non-uniform thick-

ess [13] . However, the anisotropy found in the AAA tissue [14–

7] is an important property that was not considered in these

rojects. When using inverse analysis the mechanical properties

∗ Corresponding author. Fax: + 34 943 31 14 42.

E-mail address: ranton@tecnun.es (R. Antón).

f

w

j

p

ttp://dx.doi.org/10.1016/j.medengphy.2016.09.010

350-4533/© 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

re not critical [18,19] , but the consideration of the anisotropy pa-

ameter plays an important role in the results of numerical simu-

ations with a forward approach, and it must be taken into account

or further studies [20–22] . Within the context of physical replicas,

his consideration points to a step forward in the manufacturing of

hantoms with arterial anisotropic behavior.

The purpose of the present work is to describe and apply

new methodology for manufacturing AAA replicas that display

nisotropic behavior. To the best of the authors’ knowledge, this is

he first time that a methodology is reported for creating arterial

eplicas with non-uniform wall thickness and defined anisotropy.

. Materials and methods

.1. Uniaxial testing of isotropic specimens

Tensile tests were carried out following ASTM D412 Type B.

pecimens were manufactured via the vacuum casting technique

y using the bi-components PUR SLM 7140, 7160 and 7190 at seven

ifferent mixing ratios.

Tensile tests were performed on the specimens to generate

orce-extension data using an INSTRON MINI 44 (Instrom World-

ide, Norwood, MA) tensile test machine. Each specimen was sub-

ected to a cross-head speed of 3.4 mm/min until failure with

re-conditioning for 10 cycles to 7.5% of the gauge length. The

1506 S. Ruiz de Galarreta et al. / Medical Engineering and Physics 38 (2016) 1505–1512

Fig. 1. Complete process for creating composite specimens: (a) mold, (b) fibers, (c)

fibers placed in the mold before vacuum casting, (d) composite specimen.

Fig. 2. Complete biaxial testing system (left) and stereovision system (right).

b

s

c

t

i

s

v

p

T

p

t

∼

t

s

e

t

f

d

o

a

e

w

p

t

t

(

t

s

s

(

c

f

P

w

n

b

r

w

0

t

p

s

a

s

s

G

s

force-extension data from the uniaxial tests were converted to

strain and Cauchy stress ( Eqs. (1 ) and ( 2 )),

ε =

�l

l 0 (1)

σ =

F

A

∗ (2)

where �l is the change in specimen length at any time, l 0 is the

original length, F is the force required and A

∗ is the area at any

instant ( Eq. (3 ) assumes incompressibility).

A

∗ =

A 0 l 0 l 0 + �l

(3)

As the mechanical behavior of the components was quasi-

linear, a trend line for each material was fitted to the data

( R 2 = 0.96 ± 0.04) and stiffness was directly derived.

2.2. Biaxial testing of composite specimens

To reproduce the anisotropic behavior, various composite spec-

imens (3 mm-thick 25 × 25 mm

2 ) were fabricated, altering the fol-

lowing properties:

- f, proportion of fibers i.e. fiber volume/total volume ratio.

- Em , matrix elastic modulus.

- Ef , fiber elastic modulus.

Variations of f , Em and Ef were tested and the composite com-

bination with the properties closest to AAA tissue was selected. As

these properties were compared with Vande Geest’s data [16] , the

specimens’ geometries were the same, i.e. squares.

The procedure for obtaining the specimens with fibers inside

them was as follows. The specimen was modeled using CREO 2.0

and printed with an OBJET EDEN 330 Additive Manufacturing (AM)

printer. The specimen was used as a model for creating a silicone

mold that defined the external shape of the specimen ( Fig. 1 a). The

fibers were then attached to the mold ( Fig. 1 c), the PUR resin was

poured to fill the mold, and when cured the silicone mold was

opened and the specimen removed ( Fig. 1 d).

Tests on each specimen were conducted using a custom-made

planar biaxial testing system ( Fig. 2 ) similar to the one described

y Raghavan et al. [23] . Each sample was loaded with the help of

ixteen hooks (four at each side) that were connected to sixteen

ontainers able to hold weights. The load at each point was con-

rolled by gradually placing weights into the containers. Four load-

ng scenarios (240 g, 480 g, 720 g and 960 g) were considered. The

train measurement was calculated through the binocular stereo-

ision technique. Four small markers forming a 5 x 5 mm

2 were

laced in the center of the testing specimen for optical tracking.

his technique allows the markers’ 3D coordinates to be com-

uted by triangulation from a pair of images, which were cap-

ured by a pair of Logitech QuickCam E3500 webcams (resolution

0.03 mm/pixel) mounted at the top of the device. Before running

he biaxial tensile tests, the cameras were calibrated with an open-

ource code in MATLAB (Mathworks, Natick, MA, USA) language to

nsure accuracy [24] . To inspect the stereovision system’s accuracy,

he same template used for the calibration was recorded in 6 dif-

erent positions. For each position, 8 measurements were taken in

ifferent directions. The known distances were compared to the

nes calculated via stereovision and the errors were calculated as

percentage:

( % ) = | RD − MD | /RD (4)

here e is the error, RD is the real distance between selected

oints and MD is the distance measured by the stereovision sys-

em. The average error (SD) of the stereovision system was equal

o 0.58% (0.37%), i.e. a maximum error of 48 μm for 5 mm lengths

distance between markers).

Sample thickness was measured several times with a digi-

al caliper before testing, and the average thickness was used in

ubsequent stress calculations. The specimen was tested using a

tress-controlled protocol, where the first Piola–Kirchhoff stresses

i.e. the engineering stresses) served as a measure. The non-zero

omponents of the first Piola–Kirchhoff stress tensor P have the

orm:

θθ = f θ /T X L , P LL = f L /T X θ (5)

here f θ and f L denote the forces in each direction, T the thick-

ess in the unloaded configuration, and X θ and X L the dimensions

etween the hooks along the circumferential and longitudinal di-

ections of the square specimen, i.e. 20 mm. Each biaxial specimen

as tested in the following order: P θθ : P LL = 1:1, 0.75:1, 1:0.75,

.5:1, 1:0.5, 1:1, keeping the ratio P θθ : P LL constant for each pro-

ocol. The last equibiaxial tension protocol (i.e., P θθ : P LL = 1:1) was

erformed to confirm that no structural damage occurred in the

pecimen. Each specimen was preconditioned through six loading

nd unloading cycles, and the seventh cycle was used for the sub-

equent analysis.

From the recorded marker positions, deformation gradient ten-

or F was calculated at each measured value of imposed load [25] .

reen strain tensor E was calculated as denoted in Eq. (6 ). The

hear components of deformation gradient tensor F were found to

S. Ruiz de Galarreta et al. / Medical Engineering and Physics 38 (2016) 1505–1512 1507

b

d

E

E

w

u

V

a

W

w

d

(

S

S

S

1

a

I

t

A

w

2

t

f

c

fi

f

c

g

l

f

T

a

m

v

b

A

e

e

U

i

w

i

p

m

w

p

w

t

w

a

t

e

r

c

t

t

e

G

(

s

f

t

c

t

c

3

3

T

w

t

m

3

i

f

E

T

a

[

e

t

c

i

d

p

l

c

a

3

p

l

i

(

i

m

A

s

e negligible, so the in-plane Green strain tensor components were

etermined with Eq. (7 )

=

1

2

(F T F − 1

)(6)

θθ =

1

2

(λ2

θ − 1

), E LL =

1

2

(λ2

L − 1

)(7)

ith λθ and λL denoting the stretches in both directions.

Constitutive modeling

To model the mechanical response of the materials tested, we

sed strain energy function W ( Eq. (8 )), developed by Choi and

ito [26] and used by Vande Geest et al. [16] for both aneurysmal

nd non-aneurysmal abdominal aortic tissue:

= b 0 (e ( 1 / 2 ) b 1 E

2 θθ + e ( 1 / 2 ) b 2 E

2 LL + e b 3 E θθ E LL − 3

)(8)

here b 0 , b 1 , b 2 and b 3 are the material coefficients to be

etermined.

From Eq. (8 ) the in-plane second Piola–Kirchhoff stresses ( Eqs.

10 ) and ( 11 )) can be determined, applying Eq. (9 ).

=

∂W

∂E

(9)

θθ = b 0 (b 1 E θθ e ( 1 / 2 ) b 1 E

2 θθ + b 3 E LL e

b 3 E θθ E LL

)(10)

LL = b 0 (b 2 E LL e

( 1 / 2 ) b 2 E 2 LL + b 3 E θθ e b 3 E θθ E LL

)(11)

The data from the five biaxial protocols ( P θθ : P LL = 1:1, 0.75:1,

:0.75, 0.5:1, 1:0.5) for each specimen were fitted to this model

nd the material coefficients were derived for individual samples.

n order to derive a single constitutive model, data from each pro-

ocol was averaged to obtain a single dataset of the composite.

Additionally, the anisotropy parameter [16,26] :

I =

√

b 1 / b 2 (12)

as calculated.

.3. Anisotropic AAA phantom

The above process for creating anisotropic specimens was used

o manufacture an anisotropic AAA replica. Once the fiber volume

raction ( f ) is defined, the dimensions of the fibers need to be cal-

ulated. Due to the non-uniformity of the AAA wall thickness, the

ber dimensions should be variable in order to achieve the desired

along the whole AAA phantom. To that end the following pro-

ess was followed using MAGICS v16.02 (Materialise, Leuven, Bel-

ium). The AAA geometry was cut using nine planes normal to the

ongitudinal direction and spaced 10 mm apart. As a result, 8 dif-

erent cylindrical slices with non-uniform thickness were obtained.

hen each slice was divided into eight parts, and for each part the

verage thickness was measured. Finally the appropriate fiber di-

ensions for each slice were designed by considering the selected

alue of f .

Using these fibers, the process for creating the phantom was

ased on a previous work that describes how to build isotropic

AAs from medical images [13] . The patient-specific AAA geom-

try was obtained by segmenting CT images from Allegheny Gen-

ral Hospital (Pittsburgh, PA) using in-house software (AAAVASC,

niversity of Texas at San Antonio, San Antonio, TX) capable of

dentifying the boundaries of the lumen and the inner and outer

all surfaces [27,28] . Based on this virtual geometry, a rigid phys-

cal replica was created using an OBJET EDEN 330 AM printer. The

rinted artery was used as a model to create an outer silicone

old that defined the external shape of the artery and an inner

ax mold that defined its internal geometry. The wax mold was

laced inside the silicone mold, and the PUR 7140, 7160 or 7190

as poured to fill the gap between the inner and outer molds with

he help of a MCP 4/01 vacuum casting machine. When the gap

as filled, the vacuum was released and the mold was placed in

n oven at 45 °C to cure the resin. After 24 h of curing, the oven

emperature was increased to 85 °C to melt the inner wax. At the

nd of the melting process the silicone mold was opened and the

ubber-like artery removed.

To manufacture the anisotropic AAA, the abovementioned pro-

edure was slightly modified to add the fibers into the AAA prior

o the vacuum casting process with PUR resin. Each fiber was at-

ached to the external surface of the wax mold by gluing its two

nds with cyanoacrylate glue, i.e. Superglue 3 (Loctite, Düsseldorf,

ermany). Each fiber was fixed along the circumferential direction

Fig. 3 ). Next, the wax mold with its fibers was placed inside the

ilicone mold and the process mentioned above was subsequently

ollowed.

The AAA phantom was created with the same properties as the

ested composite. From this phantom, two square specimens were

ut for subsequent biaxial analysis. Before the tensile tests, sample

hickness was averaged by measuring it ten times with a digital

aliper. The same protocol was followed for the biaxial analysis.

. Results

.1. Uniaxial testing of isotropic specimens

A total of 42 specimens were uniaxially tested, six per material.

able 1 shows the average stiffness of each component, together

ith 95% confidence intervals. The stress–strain curves and the ul-

imate tensile strength of the materials are included in the Supple-

entary material.

.2. Biaxial testing of composite specimens

Considering the results of the uniaxial and biaxial tests (listed

n the Supplementary material), six composite specimens with the

ollowing parameters were fabricated and biaxially tested: f = 0.15,

m = 0.54 MPa (Component 7) and Ef = 1.64 MPa (Component 5).

he choice of this composite was made by comparing the over-

ll stiffness and the grade of anisotropy between the AAA tissue

16] and the different composites.

For all tested specimens, the results from the first and last

quibiaxial protocol coincided and thus suggested that no struc-

ural damage of the tissue occurred as a result of testing. The cir-

umferential and longitudinal experimental results for all the spec-

mens are shown in Tables 2 and 3 , respectively. The experimental

ata was averaged for this composite, and the representative S –E

lots are displayed in Fig. 4.

In addition, the ratio between the maximum Green strain in the

ongitudinal and the circumferential ( E LL,max /E θθ ,max ) directions was

alculated with an average (SD) equal to 1.77 (0.50). These values

re also shown in Table 4.

.3. Mathematical model of composite and phantom specimens

The material parameters for the composite specimens are re-

orted in Table 4 and shown graphically in Fig. 4 . As Fig. 4 il-

ustrates, the material model fit very well to the average compos-

te data ( R 2 = 0.98); it also fits the individual composite specimens

R 2 = 0.96) and AAA phantom specimens ( R 2 = 0.96) ( Table 4 ).

As a measure of overall stiffness, the strain energy at an equib-

axial nominal stress of 60 kPa was also calculated for each speci-

en and is reported in Table 4 together with the anisotropy factor

I .

The results derived from the AAA phantom specimens were

imilar and the model is shown in Fig. 4 , with the corresponding

1508 S. Ruiz de Galarreta et al. / Medical Engineering and Physics 38 (2016) 1505–1512

Fig. 3. PUR fibers attached to the wax inner mold (left) and as a part of the final anisotropic AAA physical replica (right).

Table 1

Stiffness average and stiffness extreme values (confidence interval 95%) of the seven components.

# Component SLM material A:B mixing ratio Stiffness mean [MPa] (95% C.I. n = 6)

1 7190 100:92 12.37 (11.50, 13.24)

2 7190 100:85 6.65 (5.81, 7.49)

3 7190 100:75 3.37 (2.62, 4.11)

4 7160 100:69 2.87 (2.75, 3.00)

5 7160 100:60 1.64 (1.49, 1.80)

6 7140 100:45 1.11 (1.07, 1.15)

7 7140 100:38 0.54 (0.45, 0.62)

Table 2

Nominal Stress–stretch response of specimens in the circumferential direction.

Protocol Nominal stress (kPa) Stretch Aver. stretch SD

V1 V2 V3 V4 V5 V6

1:1 39 .24 1.014 1.006 1.005 1.008 1.017 1.013 1.010 0.005

78 .48 1.028 1.008 1.014 1.028 1.025 1.023 1.021 0.008

117 .72 1.043 1.018 1.024 1.039 1.043 1.032 1.033 0.011

156 .96 1.059 1.031 1.036 1.053 1.067 1.040 1.048 0.014

1:0.75 39 .24 1.020 1.011 1.008 1.016 1.025 1.016 1.016 0.006

78 .48 1.036 1.018 1.018 1.028 1.044 1.029 1.029 0.010

117 .72 1.057 1.031 1.029 1.054 1.074 1.041 1.048 0.017

156 .96 1.075 1.045 1.043 1.072 1.094 1.061 1.065 0.020

1:0.5 39 .24 1.025 1.019 1.007 1.020 1.026 1.020 1.019 0.007

78 .48 1.051 1.032 1.023 1.045 1.055 1.032 1.040 0.013

117 .72 1.073 1.050 1.036 1.066 1.086 1.057 1.061 0.018

156 .96 1.098 1.067 1.056 1.090 1.110 1.074 1.082 0.020

0.75:1 29 .43 0.990 1.005 0.998 1.007 1.011 1.008 1.003 0.008

58 .86 1.002 1.002 1.002 1.013 1.018 1.010 1.008 0.007

88 .29 1.012 1.009 1.004 1.019 1.029 1.010 1.014 0.009

117 .72 1.020 1.008 1.010 1.025 1.036 1.020 1.020 0.010

0.5:1 19 .62 0.996 1.006 1.0 0 0 0.993 1.0 0 0 1.003 1.0 0 0 0.005

39 .24 0.990 1.0 0 0 0.998 0.998 0.999 1.004 0.998 0.005

58 .86 0.990 0.999 0.999 0.998 1.006 1.003 0.999 0.005

78 .48 0.984 0.992 0.991 1.0 0 0 0.999 0.994 0.993 0.006

S. Ruiz de Galarreta et al. / Medical Engineering and Physics 38 (2016) 1505–1512 1509

Table 3

Nominal Stress–stretch response of specimens in the longitudinal direction.

Protocol Nominal stress (kPa) Stretch Aver. stretch SD

V1 V2 V3 V4 V5 V6

1:1 39 .24 1.021 1.027 1.021 1.011 1.028 1.021 1.021 0.006

78 .48 1.047 1.049 1.041 1.028 1.051 1.031 1.041 0.010

117 .72 1.068 1.064 1.058 1.049 1.075 1.047 1.060 0.011

156 .96 1.101 1.079 1.074 1.065 1.101 1.057 1.080 0.018

1:0.75 29 .43 1.014 1.025 1.018 1.007 1.023 1.014 1.017 0.006

58 .86 1.024 1.034 1.026 1.015 1.037 1.022 1.026 0.008

88 .29 1.045 1.046 1.037 1.022 1.044 1.029 1.037 0.010

117 .72 1.061 1.054 1.041 1.030 1.056 1.033 1.046 0.013

1:0.5 19 .62 1.006 1.018 1.008 1.002 1.007 1.009 1.008 0.005

39 .24 1.005 1.018 1.011 1.004 1.012 1.009 1.010 0.005

58 .86 1.012 1.021 1.011 1.001 1.014 1.008 1.011 0.006

78 .48 1.016 1.021 1.013 1.002 1.019 1.006 1.013 0.008

0.75:1 39 .24 1.033 1.036 1.021 1.020 1.033 1.022 1.028 0.007

78 .48 1.069 1.052 1.049 1.037 1.058 1.040 1.051 0.012

117 .72 1.094 1.073 1.068 1.054 1.090 1.060 1.073 0.016

156 .96 1.127 1.098 1.09 1.082 1.124 1.072 1.100 0.022

0.5:1 39 .24 1.030 1.037 1.036 1.025 1.039 1.028 1.033 0.005

78 .48 1.068 1.060 1.055 1.046 1.071 1.047 1.058 0.010

117 .72 1.105 1.094 1.076 1.074 1.107 1.068 1.087 0.017

156 .96 1.156 1.113 1.105 1.098 1.151 1.093 1.119 0.028

Fig. 4. S –E plots of the composite average (top) and phantom specimen experimental data with the corresponding material model for the circumferential (left) and longitu-

dinal (right) direction.

1510 S. Ruiz de Galarreta et al. / Medical Engineering and Physics 38 (2016) 1505–1512

Table 4

Model parameters for average and individual specimen fits to Eqs. (8) –( 11 ), anisotropy factor ( AI ), peak

Green strain ratio and W values.

Specimen b 0 (kPa) b 1 b 2 b 3 AI E LLmax /E θθmax W 60 (kPa) R 2

V1 2787.43 0.48 0.35 0.24 1.18 1.76 1.91 0.98

V2 2482.89 0.83 0.50 0.34 1.29 2.62 1.48 0.92

V3 1278.27 1.96 1.10 0.74 1.33 2.06 1.31 0.97

V4 3205.90 0.51 0.47 0.27 1.04 1.25 1.41 0.98

V5 2590.61 0.45 0.36 0.21 1.12 1.54 2.13 0.97

V6 3784.70 0.51 0.42 0.25 1.09 1.43 1.29 0.97

Composite average 3716.25 0.45 0.33 0.21 1.17 1.77 1.58 0.98

P1 2696.18 0.45 0.35 0.19 1.14 1.81 2.15 0.96

P2 3906.77 0.33 0.21 0.12 1.24 1.98 2.29 0.96

Table 5

AI , Green strain ratio and W compared against Vande Geest’s data, composite specimens and AAA phantom specimens.

Vande Geest ( n = 26) Composite ( n = 6) AAA phantoms ( n = 2) Differences com posite Vande Geest (%) Differences phantom composite (%)

AI 1.13 ± 0.27 1.19 ± 0.07 1.29 ± 0.09 3 .54 1 .71

E LLmax /E θθmax 1.61 ± 1.08 1.77 ± 0.50 1.89 ± 0.12 9 .94 6 .78

W 60 1.25 ± 0.47 1.58 ± 0.35 2.22 ± 0.09 26 .40 40 .51

l

a

d

W

s

d

w

T

a

p

s

r

o

s

t

c

g

o

t

m

a

e

i

A

t

w

i

t

p

i

m

i

b

w

c

3

i

p

m

material coefficients illustrated in Table 4 . The differences in AI ,

E LL,max /E θθ ,max and W between the composite specimens and AAA

phantom specimens are not statistically significant, with p -values

equal to 0.871, 0.764 and 0.053, respectively.

4. Discussion and conclusions

The present work describes a methodology for manufacturing

patient-specific replicas of arteries with regionally varying wall

thickness and an overall anisotropic behavior. By varying the com-

posite parameters ( f, E m

and E f ), different mechanical properties

can be obtained for the AAA phantoms. It should be noted that

the fibers employed in this study are not intended to imitate the

wavy and dispersed distribution of collagen fibers nor their thick-

ness (0.8–2.4 μm); that cannot be achieved even with a 3D printer.

The purpose of including the fibers was to provide the AAA phan-

tom with anisotropic behavior at a macro scale, which was verified

by the experiments.

Two simplifications were made in this study. The first one was

the omission of the thrombus and calcifications, present in 75% of

AAAs [29,30] , as they are beyond the scope of this study. How-

ever, the inclusion of the thrombus in idealized AAA replicas was

studied by Corbett et al. [31] and could be implemented in this

methodology in an analogous way. The second simplification was

that we treated AAA tissue behavior as being quasi linear, while

several studies [16,17,32] have revealed the nonlinear behavior of

AAA tissue. However, the stress–strain curves reported in those

studies were obtained under a zero-stress condition, neglecting the

fact that in-vivo tissue is exposed to a stressed configuration [33] .

The residual strain [34] when tissue is excised was not contem-

plated either. Thus considering these factors, we believe that a re-

alistic AAA replica should mimic the second region of the curve,

which is why the material properties of the manufactured phan-

toms were contrasted with that region. Furthermore, small strain

ranges in a hyperelastic material can be considered linear since

the physiological strain ranges due to the pulsatile hemodynam-

ics are small; therefore mimicking the anisotropic range linearly is

a good first approach. In order to compare the grade of anisotropy

in the AAA tissue [16] and our composites, two parameters were

selected: AI and the mean peak Green strain ratio ( E LL,max /E θθ ,max ).

As a measure of overall stiffness, the strain energy at an equibiaxial

nominal stress of 60 kPa ( W 60 ) was also compared. As mentioned

above, in vivo the realistic material properties correspond to the

inear region of the stress–strain curves (we considered it to be

bove 10 kPa). Hence, in order to estimate W 60 from Vande Geest’s

ata, we used Eq. (13 ).

60 = ( W 70 − W 10 ) −∑

i = θ,L

[S i, P I =10

(E i, P i =70 − E i, P i =10

)](13)

The differences between the AAA samples and our data are

mall ( Table 5 ).

Comparing our tested composite with Vande Geest’s data, the

erived differences are relatively low ( Table 5 ) and acceptable,

ith a maximum difference equal to 26.40% in the W 60 parameter.

he differences in the factors measuring the grade of anisotropy

re lower than 10%. As the manufactured AAA phantom has the

atient-specific geometry and non-uniform wall thickness, it is not

urprizing that the difference between the composite and the AAA

eplica specimens exists because the experiments were not carried

ut under the same conditions. That is, while the composite

pecimens were completely planar and had a uniform thickness,

he AAA phantom specimens were not perfectly planar due to

urvature, and the thickness varied due to the patient-specific AAA

eometry. Both factors influenced the experimental results. An-

ther influential factor is the thickness error of the phantom due

o the manufacture process (average dimensional mismatch of 180

icrons, 11.14% [13] ), which changes the proportion of the fibers

nd thus the mechanical properties. This is why the main differ-

nce between the phantom and composite specimens ( p = 0.053)

s factor W 60 , with an average difference equal to 40.51%. However,

I index and Green strain ratio do not differ significantly between

he phantom and composite specimens ( p = 0.871 and p = 0.764),

ith differences lower than 7%. Apart from the composite shown

n this study, other composites have been tested and some of

hem are shown in Fig. 5 with the corresponding composite

arameters, material model, AI and W values. It is worth not-

ng that before the tensile tests, the specimens’ thickness was

easured by a digital caliper due to its simplicity, although it

s not devoid of measuring errors and a thickness gauge would

e a more accurate system [35] . The influence of fiber diameter

as also studied by manufacturing two specimens with the same

omposite parameters but a different number of fibers (2 and

). They were biaxially tested and similar results were obtained,

ndicating that fiber diameter is not as critical as the other com-

osite parameters. The results are included in the Supplementary

aterial.

S. Ruiz de Galarreta et al. / Medical Engineering and Physics 38 (2016) 1505–1512 1511

Fig. 5. S –E plots, AI and W 60 values for the two other tested composites.

t

n

t

p

n

fl

o

a

c

t

f

a

O

i

p

a

a

r

t

a

d

a

s

l

o

p

C

F

E

S

f

0

R

It must be noted that 3D printing is a promising alternative

echnology, and the considerable evolution over the last decade

ow makes multi-material 3D printing possible. However, the ini-

ial investment for 3D printers is high ($120,0 0 0), as is the case for

rinting flexible materials (approximately 300$/kg). Recently, Cloo-

an et al. [36] used this technology to manufacture AAAs with a

exible material. The development of the multi-material technol-

gy may allow anisotropic AAA phantoms to be printed, but to the

uthors’ knowledge it has not been done yet, possibly due to the

onsiderable effort and difficulties required to design the applica-

ion and set process parameters. The limitation in raw materials

or 3D printing is another drawback, which means there is a rel-

tively low variety in the mechanical properties of printed AAAs.

ther factors that may affect mechanical properties of the result-

ng AAAs are layering and multiple interfaces, which can cause im-

erfections in the phantom.

This study represents a step forward in manufacturing more re-

listic AAA models, presenting the development and application of

novel methodology for making AAA replicas with patient-specific,

egionally varying non-uniform wall thickness and anisotropic ma-

erial properties. However, one limitation should be noted: the

nisotropy attained in the AAA models is global, not local. This

rawback could be attenuated by increasing the number of fibers

nd reducing their size, but even using micro fibers would not re-

ult in a complete realistic in-vivo local anisotropy. Despite this

imitation, the global anisotropy yielded a more realistic behavior

f patient-specific AAA phantoms, which will have a positive im-

act on various clinical applications such as:

• The validation of numerical studies, medical image-based mod-

els and inverse characterization methods. • In vitro experiments (as an alternative to computational mod-

eling) for studying overall aneurysm mechanics coupled with

blood flow dynamics or for predicting rupture risk. • Pre-clinical testing of endovascular grafts where more realistic

in vitro models are needed. • Benchtop testing of endovascular grafts for the detection of

type III endoleaks.

• Experimental assessment of new or existing designs of catheter

devices in terms of trackability forces, the rigidity of catheter

guides, and the deployment of stent grafts.

ompeting interests

None declared.

unding

None.

thical approval

Not required.

upplementary materials

Supplementary material associated with this article can be

ound, in the online version, at doi:10.1016/j.medengphy.2016.09.

10 .

eferences

[1] Go AS, Mozaffarian D, Roger VL, Benjamin EJ, Berry JD, Borden WB, et al. Heartdisease and stroke statistics-2013 update: A report from the American heart

association. Circulation 2013;127:e124–7. doi: 10.1161/CIR.0b013e31828124ad . [2] Brewster DC, Cronenwett JL, Hallett JW, Johnston KW, Krupski WC, Mat-

sumura JS. Guidelines for the treatment of abdominal aortic aneurysms: Re-

port of a subcommittee of the joint council of the American association forvascular surgery and society for vascular surgery. J Vasc Surg 2003;37:1106–

17. doi: 10.1067/mva.2003.363 . [3] Doyle BJ, Callanan A, Walsh MT, Grace PA, McGloughlin TM. A finite ele-

ment analysis rupture index (FEARI) as an additional tool for abdominal aor-tic aneurysm rupture prediction. Vasc Dis Prev 2009;6:114–21. doi: 10.2174/

1567270 0 0 0906010114 . [4] Maier A, Gee MW, Reeps C, Pongratz J, Eckstein HH, WA W. A comparison

of diameter, wall stress, and rupture potential index for abdominal aortic

aneurysm rupture risk prediction. Ann Biomed Eng 2010;38:3124–34. doi: 10.1007/s10439-010-0067-6 .

[5] McGloughlin TM, Doyle BJ. New approaches to abdominal aortic aneurysmrupture risk assessment: Engineering insights with clinical gain. Arterioscler

Thromb Vasc Biol 2010;30:1687–94. doi: 10.1161/ATVBAHA.110.204529 .

1512 S. Ruiz de Galarreta et al. / Medical Engineering and Physics 38 (2016) 1505–1512

[

[

[

[

[

[

[6] Raut SS, Chandra S, Shum J, Finol EA. The role of geometric and biomechanicalfactors in abdominal aortic aneurysm rupture risk assessment. Ann Biomed

Eng 2013;41:1459–77. doi: 10.1007/s10439- 013- 0786- 6 . [7] Antón R, Chen C, Hung M, Finol E, Pekkan K. Experimental and computa-

tional investigation of the patient-specific abdominal aortic aneurysm pressurefield. Comput Methods Biomech Biomed Eng 2015;18:981–92. doi: 10.1080/

10255842.2013.865024 . [8] Ene F, Gachon C, Delassus P, Carroll R, Stefanov F, O’Flynn P, et al. In vitro eval-

uation of the effects of intraluminal thrombus on abdominal aortic aneurysm

wall dynamics. Med Eng Phys 2011;33:957–66. doi: 10.1016/j.medengphy.2011.03.005 .

[9] Morris L, Stefanov F, Hynes N, Diethrich EB, Sultan S. An experimental evalu-ation of device/arterial wall compliance mismatch for four stent-graft devices

and a multi-layer flow modulator device for the treatment of abdominal aorticaneurysms. Eur J Vasc Endovasc Surg 2015. doi: 10.1016/j.ejvs.2015.07.041 .

[10] Deplano V, Meyer C, Guivier-Curien C, Bertrand E. New insights into the

understanding of flow dynamics in an in vitro model for abdominal aorticaneurysms. Med Eng Phys 2012;35:800–9. doi: 10.1016/j.medengphy.2012.08.

010 . [11] Doyle BJ, Morris LG, Callanan A, Kelly P, Vorp DA, McGloughlin TM. 3D recon-

struction and manufacture of real abdominal aortic aneurysms: From CT scanto silicone model. J Biomech Eng 2008;130:034501. doi: 10.1115/1.2907765 .

[12] Doyle BJ, Corbett TJ, Cloonan AJ, O’Donnell MR, Walsh MT, Vorp DA, et al. Ex-

perimental modelling of aortic aneurysms: Novel applications of silicone rub-bers. Med Eng Phys 20 09;31:10 02–12. doi: 10.1016/j.medengphy.20 09.06.0 02 .

[13] Ruiz de Galarreta S, Cazón A, Antón R, Finol EA. Abdominal aortic aneurysm:From clinical imaging to realistic replicas. J Biomech Eng 2014;136:14502–5.

doi: 10.1115/1.4025883 . [14] Pasta S, Phillippi JA, Tsamis A, D’Amore A, Raffa GM, Pilato M, et al. Con-

stitutive modeling of ascending thoracic aortic aneurysms using microstruc-

tural parameters. Med Eng Phys 2015;0 0 0:1–10. doi: 10.1016/j.medengphy.2015.11.001 .

[15] Iliopoulos DC, Deveja RP, Kritharis EP, Perrea D, Sionis GD, Toutouzas K,et al. Regional and directional variations in the mechanical properties of as-

cending thoracic aortic aneurysms. Med Eng Phys 2009;31:1–9. doi: 10.1016/j.medengphy.20 08.03.0 02 .

[16] Vande Geest JP, Sacks MS, Vorp DA. The effects of aneurysm on the biaxial

mechanical behavior of human abdominal aorta. J Biomech 2006;39:1324–34.doi: 10.1016/j.jbiomech.20 05.03.0 03 .

[17] O’Leary SA, Healey DA, Kavanagh EG, Walsh MT, McGloughlin TM, Doyle BJ.The biaxial biomechanical behavior of abdominal aortic aneurysm tissue. Ann

Biomed Eng 2014;42:2440–50. doi: 10.1007/s10439- 014- 1106- 5 . [18] Miller K, Lu J. On the prospect of patient-specific biomechanics with-

out patient-specific properties of tissues. J Mech Behav Biomed Mater

2013;27:154–66. doi: 10.1016/j.jmbbm.2013.01.013 . [19] Joldes GR, Miller K, Wittek A, Doyle BJ. A simple, effective and clinically ap-

plicable method to compute abdominal aortic aneurysm wall stress. J MechBehav Biomed Mater 2015:1–10. doi: 10.1016/j.jmbbm.2015.07.029 .

[20] Rissland P , Alemu Y , Einav S , Ricotta JJ , Bluestein D . Abdominal aorticaneurysm risk of rupture: Patient-specific FSI simulations using anisotropic

model. J Biomech Eng 2009;131 .

[21] Rodríguez J, Martufi G, Doblaré M, Finol EA. The effect of material model for-mulation in the stress analysis of abdominal aortic aneurysms. Ann Biomed

Eng 2009;37:1–7. doi: 10.1007/s10439- 009- 9767- 1.THE . 22] Vande Geest JP, Schmidt DE, Sacks MS, Vorp DA. The effects of anisotropy

on the stress analyses of patient-specific abdominal aortic aneurysms. AnnBiomed Eng 2008;36:921–32. doi: 10.1007/s10439- 008- 9490- 3 .

23] Raghavan M , Lin K , Ramachandran M . Planar radial extension for constitu-tive modeling of anisotropic biological soft tissues. Int J Struct Change Solid

2011;3:23–31 .

[24] Bouguet J. Camera Calibration Toolbox for Matlab 2013. http://www.vision.caltech.edu/bouguetj/calib _ doc/index.html#ref

25] Sacks MS. Biaxial mechanical evaluation of planar biological materials. J Elast20 0 0;61:199–246. doi: 10.1023/A:1010917028671 .

26] Choi HS, Vito RP. Two-dimensional stress–strain relationship for canine peri-cardium. J Biomech Eng 1990;112. doi: 10.1115/1.2891166 .

[27] Martufi G, Di Martino ES, Amon CH, Muluk SC, Finol EA. Three-dimensional

geometrical characterization of abdominal aortic aneurysms: image-based wallthickness distribution. J Biomech Eng 2009;131:061015. doi: 10.1115/1.3127256 .

28] Shum J, Di Martino ES, Goldhammer A, Goldman DH, Acker LC, Patel G, et al.Semiautomatic vessel wall detection and quantification of wall thickness in

computed tomography images of human abdominal aortic aneurysms. MedPhys 2010;37:638–48. doi: http://dx.doi.org/10.1118/1.3284976 .

29] Harter L , Gross B , Callen P . Ultrasonic evaluation of abdominal aortic thrombus.

J Ultrasound Med 1982;1:315–18 . [30] Buijs RVC, Willems TP, Tio RA, Boersma HH, Tielliu IFJ, Slart RHJA, et al. Calci-

fication as a risk factor for rupture of abdominal aortic aneurysm. Eur J VascEndovasc Surg 2013;46:542–8. doi: 10.1016/j.ejvs.2013.09.006 .

[31] Corbett TJ, Doyle BJ, Callanan A, Walsh MT, McGloughlin TM. Engineering sili-cone rubbers for in vitro studies: Creating AAA models and ILT analogues with

physiological properties. J Biomech Eng 2009;132. doi: 10.1115/1.40 0 0156 .

[32] Martufi G, Satriano A, Moore RD, Vorp DA, Di Martino ES. Local quantificationof wall thickness and intraluminal thrombus offer insight into the mechan-

ical properties of the aneurysmal aorta. Ann Biomed Eng 2015. doi: 10.1007/s10439- 014- 1222- 2 .

[33] Speelman L, Bosboom EMH, Schurink GWH, Buth J, Breeuwer M, Jacobs MJ,et al. Initial stress and nonlinear material behavior in patient-specific AAA

wall stress analysis. J Biomech 2009;42:1713–19. doi: 10.1016/j.jbiomech.2009.

04.020 . [34] Polzer S, Bursa J, Gasser TC, Staffa R, Vlachovsky R. A numerical implementa-

tion to predict residual strains from the homogeneous stress hypothesis withapplication to abdominal aortic aneurysms. Ann Biomed Eng 2013;41:1516–27.

doi: 10.1007/s10439- 013- 0749- y . [35] O’Leary SA, Doyle BJ, McGloughlin TM. Comparison of methods used to mea-

sure the thickness of soft tissues and their influence on the evaluation of ten-

sile stress. J Biomech 2013;46:1955–60. doi: 10.1016/j.jbiomech.2013.05.003 . [36] Cloonan AJ, Shahmirzadi D, Li RX, Doyle BJ, Konofagou EE, McGloughlin TM.

3D-printed tissue-mimicking phantoms for medical imaging and computa-tional validation applications. 3D Print Addit Manuf 2014;1:14–23. doi: 10.

1089/3dp.2013.0010 .