In this work, we present a novel method for the derivation of the unloaded geometry of an abdominal aortic aneurysm (AAA) from a pressurized geometry in turn obtained by 3D reconstruction of computed tomography (CT) images. The approach was experimentally validated with an aneurysm phantom loaded with gauge pressures of 80, 120, and 140 mm Hg. The unloaded phantom geometries estimated from these pressurized states were compared to the actual unloaded phantom geometry, resulting in mean nodal surface distances of up to 3.9% of the maximum aneurysm diameter. An in-silico verification was also performed using a patient-specific AAA mesh, resulting in maximum nodal surface distances of 8 μm after running the algorithm for eight iterations. The methodology was then applied to 12 patient-specific AAA for which their corresponding unloaded geometries were generated in 5–8 iterations. The wall mechanics resulting from finite element analysis of the pressurized (CT image-based) and unloaded geometries were compared to quantify the relative importance of using an unloaded geometry for AAA biomechanics. The pressurized AAA models underestimate peak wall stress (quantified by the first principal stress component) on average by 15% compared to the unloaded AAA models. The validation and application of the method, readily compatible with any finite element solver, underscores the importance of generating the unloaded AAA volume mesh prior to using wall stress as a biomechanical marker for rupture risk assessment.

References

References
1.
Kent
,
K. C.
,
2014
, “
Abdominal Aortic Aneurysms
,”
N. Engl. J. Med.
,
371
(
22
), pp.
2101
2108
.
2.
Newman
,
A. B.
,
Arnold
,
A. M.
,
Burke
,
G. L.
,
O'Leary
,
D. H.
, and
Manolio
,
T. A.
, “
Cardiovascular Disease and Mortality in Older Adults With Small Abdominal Aortic Aneurysms Detected by Ultrasonography: The Cardiovascular Health Study
,”
Ann. Intern. Med.
,
134
(
3
), pp.
182
190
.
3.
Karkos
,
C.
,
Mukhopadhyay
,
U.
,
Papakostas
,
I.
,
Ghosh
,
J.
,
Thomson
,
G.
, and
Hughes
,
R.
,
2000
, “
Abdominal Aortic Aneurysm: The Role of Clinical Examination and Opportunistic Detection
,”
Eur. J. Vasc. Endovasc. Surg.
,
19
(
3
), pp.
299
303
.
4.
Brown
,
L. C.
, and
Powell
,
J. T.
,
1999
, “
Risk Factors for Aneurysm Rupture in Patients Kept Under Ultrasound Surveillance, UK Small Aneurysm Trial Participants
,”
Ann. Surg.
,
230
(
3
), pp.
289
296
; discussion 296–297.
5.
Limet
,
R.
,
Sakalihassan
,
N.
, and
Albert
,
A.
,
1991
, “
Determination of the Expansion Rate and Incidence of Rupture of Abdominal Aortic Aneurysms
,”
J. Vasc. Surg.
,
14
(
4
), pp.
540
548
.
6.
Fillinger
,
M. F.
,
Raghavan
,
M. L.
,
Marra
,
S. P.
,
Cronenwett
,
J. L.
, and
Kennedy
,
F. E.
,
2002
, “
In Vivo Analysis of Mechanical Wall Stress and Abdominal Aortic Aneurysm Rupture Risk
,”
J. Vasc. Surg.
,
36
(
3
), pp.
589
597
.
7.
Fillinger
,
M. F.
,
Marra
,
S. P.
,
Raghavan
,
M. L.
, and
Kennedy
,
F. E.
,
2003
, “
Prediction of Rupture Risk in Abdominal Aortic Aneurysm During Observation: Wall Stress Versus Diameter
,”
J. Vasc. Surg.
,
37
(
4
), pp.
724
732
.
8.
Raghavan
,
M. L.
, and
Vorp
,
D. A.
,
2000
, “
Toward a Biomechanical Tool to Evaluate Rupture Potential of Abdominal Aortic Aneurysm: Identification of a Finite Strain Constitutive Model and Evaluation of Its Applicability
,”
J. Biomech.
,
33
(
4
), pp.
475
482
.
9.
Thubrikar
,
M. J.
,
Al-Soudi
,
J.
, and
Robicsek
,
F.
,
2001
, “
Wall Stress Studies of Abdominal Aortic Aneurysm in a Clinical Model
,”
Ann. Vasc. Surg.
,
15
(
3
), pp.
355
366
.
10.
Truijers
,
M.
,
Pol
,
J. A.
,
Schultzekool
,
L. J.
,
van Sterkenburg
,
S. M.
,
Fillinger
,
M. F.
, and
Blankensteijn
,
J. D.
,
2007
, “
Wall Stress Analysis in Small Asymptomatic, Symptomatic and Ruptured Abdominal Aortic Aneurysms
,”
Eur. J. Vasc. Endovasc. Surg.
,
33
(
4
), pp.
401
407
.
11.
Di Martino
,
E. S.
,
Guadagni
,
G.
,
Fumero
,
A.
,
Ballerini
,
G.
,
Spirito
,
R.
,
Biglioli
,
P.
, and
Redaelli
,
A.
,
2001
, “
Fluid-Structure Interaction Within Realistic Three-Dimensional Models of the Aneurysmatic Aorta as a Guidance to Assess the Risk of Rupture of the Aneurysm
,”
Med. Eng. Phys.
,
23
(
9
), pp.
647
655
.
12.
Finol
,
E. A.
, and
Amon
,
C. H.
,
2002
, “
Flow-Induced Wall Shear Stress in Abdominal Aortic Aneurysms: Part II—Pulsatile Flow Hemodynamics
,”
Comput. Methods Biomech. Biomed. Eng.
,
5
(
4
), pp.
319
328
.
13.
Figueroa
,
A.
,
Vignon-Clementel
,
I.
,
Jansen
,
K.
,
Hughes
,
T. J. R.
, and
Taylor
,
C. A.
,
2005
, “
Simulation of Blood Flow and Vessel Deformation in Three-Dimensional, Patient-Specific Models of the Cardiovascular System Using a Novel Method for Fluid-Solid Interactions
,”
Fluid Structure Interaction and Moving Boundary Problems: No. 3
,
S.
Chakrabarti
,
S.
Hernandez
, and
C. A.
Brebbia
, eds.,
WIT Press
,
Ashurst, UK
, pp.
143
152
.
14.
Wolters
,
B. J.
,
Rutten
,
M. C.
,
Schurink
,
G. W.
,
Kose
,
U.
,
de Hart
,
J.
, and
van de Vosse
,
F. N.
,
2005
, “
A Patient-Specific Computational Model of Fluid-Structure Interaction in Abdominal Aortic Aneurysms
,”
Med. Eng. Phys.
,
27
(
10
), pp.
871
883
.
15.
Leung
,
J. H.
,
Wright
,
A. R.
,
Cheshire
,
N.
,
Crane
,
J.
,
Thom
,
S. A.
,
Hughes
,
A. D.
, and
Xu
,
X. Y.
,
2006
, “
Fluid Structure Interaction of Patient Specific Abdominal Aortic Aneurysms: A Comparison With Solid Stress Models
,”
Biomed. Eng. Online
,
5
, p.
33
.
16.
Papaharilaou
,
Y.
,
Ekaterinaris
,
J. A.
,
Manousaki
,
E.
, and
Katsamouris
,
A. N.
,
2007
, “
A Decoupled Fluid Structure Approach for Estimating Wall Stress in Abdominal Aortic Aneurysms
,”
J. Biomech.
,
40
(
2
), pp.
367
377
.
17.
Bluestein
,
D.
,
Dumont
,
K.
,
De Beule
,
M.
,
Ricotta
,
J.
,
Impellizzeri
,
P.
,
Verhegghe
,
B.
, and
Verdonck
,
P.
,
2009
, “
Intraluminal Thrombus and Risk of Rupture in Patient Specific Abdominal Aortic Aneurysm—FSI Modelling
,”
Comput. Methods Biomech. Biomed. Eng.
,
12
(
1
), pp.
73
81
.
18.
Rissland
,
P.
,
Alemu
,
Y.
,
Einav
,
S.
,
Ricotta
,
J.
, and
Bluestein
,
D.
,
2009
, “
Abdominal Aortic Aneurysm Risk of Rupture: Patient-Specific FSI Simulations Using Anisotropic Model
,”
ASME J. Biomech. Eng.
,
131
(
3
), p.
031001
.
19.
Scotti
,
C. M.
,
Jimenez
,
J.
,
Muluk
,
S. C.
, and
Finol
,
E. A.
,
2008
, “
Wall Stress and Flow Dynamics in Abdominal Aortic Aneurysms: Finite Element Analysis vs. Fluid-Structure Interaction
,”
Comput. Methods Biomech. Biomed. Eng.
,
11
(
3
), pp.
301
322
.
20.
Chandra
,
S. C.
,
Raut
,
S. S.
,
Jana
,
A.
,
Biederman
,
R. W.
,
Doyle
,
M.
,
Muluk
,
S. C.
, and
Finol
,
E. A.
,
2013
, “
Fluid Structure Interaction Modeling of Abdominal Aortic Aneurysms: The Impact of Patient Specific Inflow Conditions and Fluid/Solid Coupling
,”
ASME J. Biomech. Eng.
,
135
(
8
), p.
081001
.
21.
Vande Geest
,
J. P.
,
Sacks
,
M. S.
, and
Vorp
,
D. A.
,
2006
, “
A Planar Biaxial Constitutive Relation for the Luminal Layer of Intra-Luminal Thrombus in Abdominal Aortic Aneurysms
,”
J. Biomech.
,
39
(
13
), pp.
2347
2354
.
22.
Marra
,
S. P.
,
Raghavan
,
M. L.
,
Whittaker
,
D. R.
,
Fillinger
,
M. F.
,
Chen
,
D. T.
,
Dwyer
,
J. M.
,
Tsapakos
,
M. J.
, and
Kennedy
,
F. E.
,
2005
, “
Estimation of the Zero-Pressure Geometry of Abdominal Aortic Aneurysms From Dynamic Magnetic Resonance Imaging
,”
2005 Summer Bioengineering Conference
, Vail, CO, June 22–26, American Society of Mechanical Engineers, Abstract 298571.
23.
Raghavan
,
M. L.
,
Ma
,
B.
, and
Fillinger
,
M. F.
,
2006
, “
Non-Invasive Determination of Zero-Pressure Geometry of Arterial Aneurysms
,”
Ann. Biomed. Eng.
,
34
(
9
), pp.
1414
1419
.
24.
Lu
,
J.
,
Zhou
,
X.
, and
Raghavan
,
M. L.
,
2008
, “
Inverse Method of Stress Analysis for Cerebral Aneurysms
,”
Biomech. Model. Mechanobiol.
,
7
(
6
), pp.
477
486
.
25.
Lu
,
J.
,
Zhou
,
X.
, and
Raghavan
,
M. L.
,
2007
, “
Inverse Elastostatic Stress Analysis in Pre-Deformed Biological Structures: Demonstration Using Abdominal Aortic Aneurysms
,”
J. Biomech.
,
40
(
3
), pp.
693
696
.
26.
de Putter
,
S.
,
Wolters
,
B. J.
,
Rutten
,
M. C.
,
Breeuwer
,
M.
,
Gerritsen
,
F. A.
, and
van de Vosse
,
F. N.
,
2007
, “
Patient-Specific Initial Wall Stress in Abdominal Aortic Aneurysms With a Backward Incremental Method
,”
J. Biomech.
,
40
(
5
), pp.
1081
1090
.
27.
Riveros
,
F.
,
Chandra
,
S. C.
,
Finol
,
E. A.
,
Gasser
,
T. C.
, and
Rodriguez
,
J. F.
,
2013
, “
A Pull-Back Algorithm to Determine the Unloaded Vascular Geometry in Anisotropic Hyperelastic AAA Passive Mechanics
,”
Ann. Biomed. Eng.
,
41
(
4
), pp.
694
708
.
28.
Govindjee
,
S.
, and
Mihalic
,
P. A.
,
1996
, “
Computational Methods for Inverse Finite Elastostatics
,”
Comput. Methods Appl. Mech. Eng.
,
136
(
1–2
), pp.
47
57
.
29.
Shield
,
R. T.
,
1967
, “
Inverse Deformation Results in Finite Elasticity
,”
Z. Angew. Math. Phys.
,
18
(
4
), pp.
490
500
.
30.
Carlson
,
D. E.
,
1969
, “
Inverse Deformation Results for Elastic Materials
,”
Z. Angew. Math. Phys.
,
20
(
2
), pp.
261
263
.
31.
Shum
,
J.
,
Di Martino
,
E. S.
,
Goldhammer
,
A.
,
Goldman
,
D.
,
Acker
,
L.
,
Patel
,
G.
,
Ng
,
J. H.
,
Martufi
,
G.
, and
Finol
,
E. A.
,
2010
, “
Semi-Automatic Vessel Wall Detection and Quantification of Wall Thickness in Computed Tomography Images of Human Abdominal Aortic Aneurysms
,”
Med. Phys.
,
37
(
2
), pp.
638
648
.
32.
Shum
,
J.
,
Martufi
,
G.
,
Di Martino
,
E. S.
,
Washington
,
C. B.
,
Grisafi
,
J.
,
Muluk
,
S. C.
, and
Finol
,
E. A.
,
2011
, “
Quantitative Assessment of Abdominal Aortic Aneurysm Geometry
,”
Ann. Biomed. Eng.
,
39
(
1
), pp.
277
286
.
33.
Shum
,
J.
,
Xu
,
A.
,
Chatnuntawech
,
I.
, and
Finol
,
E. A.
,
2011
, “
A Framework for the Automatic Generation of Surface Topologies for Abdominal Aortic Aneurysm Models
,”
Ann. Biomed. Eng.
,
39
(
1
), pp.
249
259
.
34.
Raghavan
,
M. L.
,
Kratzberg
,
J.
,
Castro de Tolosa
,
E. M.
,
Hanaoka
,
M. M.
,
Walker
,
P.
, and
da Silva
,
E. S.
,
2006
, “
Regional Distribution of Wall Thickness and Failure Properties of Human Abdominal Aortic Aneurysm
,”
J. Biomech.
,
39
(
16
), pp.
3010
3016
.
35.
Bihari
,
P.
,
Shelke
,
A.
,
New
,
T. H.
,
Mularczyk
,
M.
,
Nelson
,
K.
,
Schmandra
,
T.
,
Knez
,
P.
, and
Schmitz-Rixen
,
T.
,
2013
, “
Strain Measurement of Abdominal Aortic Aneurysm With Real-Time 3D Ultrasound Speckle Tracking
,”
Eur. J. Vasc. Endovasc. Surg.
,
45
(
4
), pp.
315
323
.
36.
Goergen
,
C. J.
,
Azuma
,
J.
,
Barr
,
K. N.
,
Magdefessel
,
L.
,
Kallop
,
D. Y.
,
Gogineni
,
A.
,
Grewall
,
A.
,
Weimer
,
R. M.
,
Connolly
,
A. J.
,
Dalman
,
R. L.
,
Taylor
,
C. A.
,
Tsao
,
P. S.
, and
Greve
,
J. M.
,
2011
, “
Influences of Aortic Motion and Curvature on Vessel Expansion in Murine Experimental Aneurysms
,”
Arterioscler. Thromb. Vasc. Biol.
,
31
(
2
), pp.
270
279
.
37.
Seong
,
J.
,
Sadasivan
,
C.
,
Onizuka
,
M.
,
Gounis
,
M. J.
,
Christian
,
F.
,
Miskolczi
,
L.
,
Wakhloo
,
A. K.
, and
Lieber
,
B. B.
,
2005
, “
Morphology of Elastase-Induced Cerebral Aneurysm Model in Rabbit and Rapid Prototyping of Elastomeric Transparent Replicas
,”
Biorheology
,
42
(
5
), pp.
345
361
.
38.
Rodriguez
,
J. F.
,
Ruiz
,
C.
,
Doblare
,
M.
, and
Holzapfel
,
G. A.
,
2008
, “
Mechanical Stress in Abdominal Aortic Aneurysms: Influence of Diameter, Asymmetry, and Material Anisotropy
,”
ASME J. Biomech. Eng.
,
130
(
2
), p.
021023
.
39.
Speelman
,
L.
,
Bosboom
,
E. M.
,
Schurink
,
G. W.
,
Buth
,
J.
,
Breeuwer
,
M.
,
Jacobs
,
M. J.
, and
van de Vosse
,
F. N.
,
2009
, “
Initial Stress and Nonlinear Material Behavior in Patient-Specific AAA Wall Stress Analysis
,”
J. Biomech.
,
42
(
11
), pp.
1713
1719
.
40.
Gee
,
M. W.
,
Reeps
,
C.
,
Eckstein
,
H. H.
, and
Wall
,
W. A.
,
2009
, “
Prestressing in Finite Deformation Abdominal Aortic Aneurysm Simulation
,”
J. Biomech.
,
42
(
11
), pp.
1732
1739
.
41.
Gee
,
M. W.
,
Forster
,
C.
, and
Wall
,
W. A.
,
2010
, “
A Computational Strategy for Prestressing Patient-Specific Biomechanical Problems Under Finite Deformation
,”
Int. J. Numer. Methods Biomed. Eng.
,
26
(
1
), pp.
52
72
.
42.
Hsu
,
M. C.
, and
Bazilevs
,
Y.
,
2011
, “
Blood Vessel Tissue Prestress Modeling for Vascular Fluid-Structure Interaction Simulation
,”
Finite Elem. Anal. Des.
,
47
(
6
), pp.
593
599
.
43.
DiMartino
,
E. S.
,
Bohra
,
A.
,
VandeGeest
,
J. P.
,
Gupta
,
N. Y.
,
Makaroun
,
M. S.
, and
Vorp
,
D. A.
,
2006
, “
Biomechanical Properties of Ruptured Versus Electively Repaired Abdominal Aortic Aneurysm Wall Tissue
,”
J. Vasc. Surg.
,
43
(
3
), pp.
570
576
.
You do not currently have access to this content.