Biomechanics of abdominal aortic

aneurysm:Experimental evidence and multiscale constitutive modeling

Giampaolo Martufi

Doctoral thesis no. 80, 2012 KTH School of Engineering Sciences

Department of Solid Mechanics Royal Institute of Technology SE-100 44 Stockholm Sweden

TRITA HFL-0530 ISSN 1654-1472 ISRN KTH/HFL/R-12/0014-SE

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknisk doktorsexamen torsdagen den 20 september kl. 10.00 i sal L1, Kungliga Tekniska Högskolan, Drottning Kristinasvägen 30, Stockholm.

A mia madre

Abstract The reliable assessment of Abdominal Aortic Aneurysm (AAA) rupture risk is

critically important in reducing related mortality without unnecessarily increasing

the rate of elective repair. A multi-disciplinary approach including vascular

biomechanics and constitutive modeling is needed to better understand and more

effectively treat these diseases. AAAs are formed through irreversible

pathological remodeling of the vascular wall and integrating this biological

process in the constitutive description could improve the current understanding of

this disease as well as the predictability of biomechanical simulations.

First in this thesis, multiple centerline-based diameter measurements between

renal arteries and aortic bifurcation have been used to monitor aneurysm growth

of in total 51 patients from Computer Tomography-Angiography (CT-A) data.

Secondly, the thesis proposes a novel multi-scale constitutive model for the

vascular wall, where collagen fibers are assembled by proteoglycan cross-linked

collagen fibrils and reinforce an otherwise isotropic matrix (elastin). Collagen

fibrils are dynamically formed by a continuous stretch-mediated process,

deposited in the current configuration and removed by a constant degradation rate.

The micro-plane concept is then used for the Finite Element (FE) implementation

of the constitutive model. Finally, histological slices from intra-luminal thrombus

(ILT) tissue were analyzed using a sequence of automatic image processing steps.

Derived microstructural data were used to define Representative Volume

Elements (RVEs), which in turn allowed the estimation of microscopic material

properties using the non-linear FE.

The thesis showed that localized spots of fast diameter growth can be detected

through multiple centerline-based diameter measurements all over the AAA sac.

Consequently, this information might further reinforce the quality of aneurysm

surveillance programs. The novel constitutive model proposed in the thesis has a

strong biological motivation and provides an interface with biochemistry. Apart

from modeling the tissue’s passive response, the presented model is helpful to

predict saline feature of aneurysm growth and remodeling. Finally, the thesis

provided novel microstructural and micromechanical data of ILT tissue, which is

critically important to further explore the role of the ILT in aneurysm rupture.

Preface

The research presented in this doctoral thesis has been carried out at the

Department of Solid Mechanics, Royal Institute of Technology (KTH),

Stockholm between July 2008 and July 2012. The work was financially supported

by the Young Faculty Grant No. 2006-7568 provided by the Swedish Research

Council, VINNOVA and the Swedish Foundation for Strategic Research, and the

EC Seventh Framework Programme, fighting Aneurysmal Disease (FAD-

200647), which is sincerely acknowledged.

First of all I would like to express my sincere gratitude to my supervisor T.

Christian Gasser for giving me the opportunity to work with a very interesting and

challenging topic. I am thankful for his support, for the fruitful discussions and

excellent guidance through these four years at KTH. Further I would like to thank

Ender Finol for introducing me to the field of biomechanics and Elena Di Martino

for her valuable advices and knowledge in AAA biomechanics.

I would also like to thank my colleagues and friends at KTH Solid Mechanics for

making the working environment enjoyable.

Finally, I would like to extend my gratitude to my dad, my sister and my brother

in law for all the encouragement and support I received.

Stockholm, August 2012 Giampaolo Martufi

List of appended papers

Paper A: Growth of small abdominal aortic aneurysms: A multidimensional analysis

G. Martufi, M. Auer, J. Roy, J.Swedenborg, N. Sakalihasan, G. Panuccio and T.C. Gasser Report 529, Department of Solid Mechanics, KTH Engineering Sciences, Royal Institute of Technology, Stockholm, Sweden. Submitted to international journal for publication.

Paper B: A constitutive model for vascular tissue that integrates fibril, fiber and continuum levels with application to the isotropic and passive properties of the infrarenal aorta

G. Martufi and T.C. Gasser Journal of Biomechanics, 44(14):2544-2550, 2011.

Paper C: Turnover of fibrillar collagen in soft biological tissue with application to the expansion of abdominal aortic aneurysms

G. Martufi and T.C. Gasser Journal of the Royal Society Interface, published online, doi:10.1098/rsif.2012.0416, 2012.

Paper D: Micromechanical characterization of intra-luminal thrombus tissue from abdominal aortic aneurysms

T.C. Gasser, G. Martufi, M. Auer, M. Folkesson and J.Swedenborg Annals of Biomedical Engineering, 38(2):371-379, 2010.

In addition to the appended paper, the work has resulted in the following publications in conference proceedings fully reviewed prior to publication: Remodeling of fibrillar collagen applied to aneurysm growth G. Martufi and T.C. Gasser Proceedings of the Word Congress on Computational Mechanics, Sao Paulo, Brazil, July 8 – 13, 2012. Histo-mechanical modeling of the wall of abdominal aorta aneurysms G. Martufi and T.C. Gasser Proceedings of MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, Vienna, Austria, February 15-17, 2012. (6 pages paper) Remodeling of abdominal aortic aneurysm wall: A multi-scale structural approach G. Martufi and T.C. Gasser Proceedings of the 4th International Conference on the Mechanics of Biomaterials and Tissues, Hawaii, USA, December 11-15, 2011. A multi-scale collagen turn-over model for soft biological tissues with application to abdominal aortic aneurysms growth G. Martufi, T.C. Gasser and M. Auer Proceedings of ASME 2011 Summer Bioengineering Conference, Farmington, Pennsylvania, USA , June 22 - 25, 2011. Progression of abdominal aortic Aneurysm: Clinical evidence and multiscale modeling G. Martufi, T.C. Gasser, M. Labruto and J. Swedenborg Proceedings of the 6th International Symposium on Biomechanics in Vascular Biology and Cardiovascular Disease, Rotterdam, The Netherlands, April 14 – 15, 2011. A constitutive model for vascular tissue that integrates fibril, fiber and continuum levels T.C. Gasser, G. Martufi and M. Auer Proceedings of 2nd International Conference on Computational & Mathematical Biomedical Engineering, George Mason University, Washington D.C., USA March 30 - April 1, 2011. Abdominal aortic aneurysm development over time: Experimental evidence and constitutive modeling G. Martufi, T.C. Gasser, M. Auer, M. Labruto and J. Swedenborg Proceedings of the 6th World Congress on Biomechanics, Singapore, August 1 – 6, 2010.

A growth model for abdominal aortic aneurysms based on continuous collagen turn-over G. Martufi,T.C. Gasser and M. Auer Proceedings of the IV European Conference on Computational Mechanics, Paris, France, May 16 – 21, 2010. Micro-structural and micro-mechanical characterization of thrombus tissue from abdominal aortic aneurysms G. Martufi, T.C. Gasser, M. Folkesson and J. Swedenborg Proceedings of the 10th US National Congress on Computational Mechanics, Columbus, Ohio, US, July 16-19, 2009. Micro-structural and micro-mechanical analysis of thrombus tissue from abdominal aortic aneurysms G. Martufi, T.C. Gasser, M. Folkesson and J. Swedenborg Endovascular Surgery - Bringing Basic Science into Clinical Practice, March 19-21, Stockholm, Sweden, 2009.

Contents

1. INTRODUCTION 11 1.1. Background 11

13 1.2. Pathophysiology of AAA 1.3. Rupture criteria in a clinical setting 14 1.4. Biomechanical rupture risk assessment 15

16 1.5. AAA biomechanics 1.5.1. AAA wall histology 16 1.5.2. AAA wall mechanics 17 1.5.3. AAA wall expansion 18 1.5.4. AAA thrombus mechanics 20

2. METHODS 23 2.1. Experimental evidence of AAA growth 23 2.2. Multiscale constitutive modeling 23 2.3. Micromechanical characterization of ILT 24

3. RESULTS 25 3.1. Clinical study 25 3.2. Numerical predictions of the passive and active responses of the AAA

wall 26 3.3. Microstructural and micromechanical characterization of ILT 28

4. DISCUSSION 31

9

33 35

5. CONCLUSIONS 6. REFERENCES

Paper A

Paper B

Paper C

Paper D

Biomechanics of Abdominal Aortic Aneurysm

10

11

1. INTRODUCTION 1.1. Background

An aneurysm is defined as a local, permanent dilatation of an artery at least 1.5

times its normal diameter (Figure 1). Any artery can become aneurysmal yet the

infrarenal segment of the abdominal aorta is the most common site for

development of Abdominal Aortic Aneurysms (AAAs).

The prevalence of AAA is growing along with population age and according to

different studies AAA rupture is the 13th most common cause of death in the

United States81 causing an estimated 15.000 deaths per year. The incidence of

AAA is 2-4 per cent in the adult population, and it is growing with increase in the

average population age. Other risk factors include hypertension, atherosclerosis,

smoking and a positive family history. Although the etiology of AAA is still not

known, it is believed to be multi-factorial and mainly degenerative disease, arising

through a complex interaction among different biological factors.

If left untreated, all AAAs progress toward further enlargement and eventually

will rupture. There are no available indicators of how close the point of rupture is

and for selected patients rupture may not occur during their lifetime.

AAA rupture is a biomechanical phenomenon that occurs when the mechanical

stress acting on the aneurysm inner wall due to intraluminal pressure, exceeds the

failure strength of the degenerated aortic tissue121. The rupture of an AAA often

leads to severe disability and carries a mortality rate of up to 90 per cent111.

Aneurysms are seldom detected at early stages and for the most part they remain

latent until symptoms occur as their size increases, or they are found in incidental

exams. Once detected, one of the most challenging issues in clinical management

Biomechanics of Abdominal Aortic Aneurysm

of known aneurysm patients is the evaluation of the patient-specific risk of rupture

at any given time.

Due to the lack of knowledge of the role played by the different factors in the

enlargement process, there is currently no accurate technique to predict the

AAA’s expansion rate, or to determine its critical size at the point of rupture.

Figure 1. Normal aorta (A), thoracic aortic aneurysm (B) and abdominal aortic aneurysm (C). Aortic aneurysm. [image online] Available at: <http://vascular.surgery.ucsf.edu/conditions--procedures/abdominal-aortic-aneurysm.aspx > [Accessed 17 August 2012].

Based on the classic law of Laplace, the maximum transverse diameter of an

aneurysm is commonly used as main determinant in predicting its rupture risk, but

autopsy studies have demonstrated that small AAAs can rupture15,37 while some

12

13

of those considered large aneurysms remain quiescent for years15. In addition to

the diameter criterion, a high expansion rate is usually associated with an elevated

rupture risk. In particular, a maximum transverse diameter of 55 mm and an

expansion rate of 1 cm yr-1 are the most commonly used thresholds for elective

repair.

Traditional repair is via an open surgical treatment, which is associated with high

morbidity and a mortality rate ranging between 2 per cent and 4 per cent68,78. As

an alternative to surgical resection, the use of endovascular aneurysm repair

(EVAR) allows surgeons to repair aneurysms by delivering a bypass graft through

a small incision in the femoral artery.

1.2. Pathophysiology of AAA

AAAs are the end result of irreversible pathological remodeling of the

extracellular matrix (ECM)20. ECMs provide an essential mechanical environment

to which vascular tissue is continuously exposed, and mainly contain elastin,

collagen, and proteoglycans (PGs)13. While elastin is a stable protein having half-

life times of tens of years1, collagen is normally in a continual state of deposition

and degradation57. Specifically, vascular collagen has a normal half-life time of

60-70 days80, which decreases by up to 10-fold in case of disease and injury5.

The most prevalent features of later stage AAA wall are: degradation of the

protein elastin, compensatory increased collagen turnover and content, excessive

inflammatory infiltration and apoptosis of vascular smooth muscle cells. It is

generally accepted that loss of elastic fiber is thought to initiate arterial dilatation,

increase in collagen synthesis promotes enlargement, and localized weakening of

collagen by proteases leads to rupture. In particular, endstage AAA segments

show a negligible amount87 of fragmented62 elastin, as well as a severe decrease in

smooth muscle cells71.

An intraluminal thrombus (ILT) is found in nearly all formations of clinically

relevant size50 and contradictory hypotheses have been suggested in the role of the

ILT regarding aneurysm rupture. In particular, it is unclear if an ILT increases or

decreases the risk of aneurysm rupture, i.e. if it creates an environment for

Biomechanics of Abdominal Aortic Aneurysm

14

increased proteolytic activity14 (which weakens120 and/or thins62 the wall) or

buffers against wall stress69,119.

1.3. Rupture criteria in a clinical setting

The indication for elective repair is strongly related to the aneurysm’s risk of

rupture, and although maximum diameter is the current criteria for treatment, no

general consensus exists on the critical size beyond which elective repair is

recommended. In each case, the risk of rupture must be weighed against operation

morbidity. Therefore, a single threshold diameter is not appropriate for every

patient, hence the assessment of the risk of rupture should ideally be

individualized to better manage aneurysm patients.

Current clinical practice recommends to repair large AAA, with maximum

transverse diameter larger than 55 mm, or to regularly monitor smaller AAAs

(diameter less than 55 mm) with ultrasound. However, small aneurysms can also

rupture, with an associated mortality rate of up to 50 per cent113. Moreover, the

12-year follow-up of the UK Small Aneurysm Trial reported an overall mortality

of 67.3 per cent for the surveillance group83.

These findings question the ability of maximum diameter criterion to assess AAA

risk of rupture. Several reports demonstrated the existence of a risk of rupture of

AAA below 55 mm in diameter and showed that rapid aneurysm expansion is

associated with increased rupture risk independently of their size7,105,47.

In common clinical practice expansion rate of an AAA is generally defined as the

change in maximum aortic diameter over time.

Limet et al.70 associated the risk of rupture of AAAs with aneurysm expansion

rate and different studies reported an increased mean expansion rate in patients

with ruptured AAAs12,67.

Realistic AAAs have complex, tortuous, and asymmetric shapes with local

changes in surface curvature73,92,97 and the maximum-diameter measures at two

time points only provides limited information regarding aneurysm growth.

Specifically, it might miss regions of fast diameter growth, it cannot quantify axial

15

growth, and it cannot capture shape changes of potential interest for EVAR-

related decisions76.

Stenbaek et al.103 investigated the ILT growth as a potential rupture risk predictor

and concluded that a rapid increase in ILT area may be a better predictor of AAA

rupture than an increase in maximum transverse diameter.

Other factors that have been shown to have a positive correlation with AAA

expansions are blood pressure11,18,19,35,104,108, female sex11,66 and smoking72.

1.4. Biomechanical rupture risk assessment

Recent studies showed that peak wall stress (PWS) in AAAs is a more reliable

parameter than maximum transverse diameter for aneurysm rupture

prediction30,44,53,117. FE simulations of anatomically realistic AAA models were

performed to compare PWS between ruptured or symptomatic and unruptured

aneurysm cases30,31. These studies found a significant difference between the two

groups. The PWS for ruptured aneurysms is about 60 per cent higher than for non-

ruptured and the location of the PWS correlates with the site of rupture117.

However, it is necessary to underline that wall stress alone is not sufficient to

predict rupture risk; regional estimations of wall strength would also be

necessary115. It has previously been shown that wall strength differs significantly

from patient-to-patient and within the same aneurysmatic sac114,115,123. In addition,

Di Martino et al.22 found that the strength of the aneurysmatic wall from ruptured

AAA cases is considerably lower than that for electively repaired ones. In this

regard, Vande Geest and colleagues115 have proposed a statistical model to

noninvasively evaluate the wall strength distribution in AAA taking into account

factors such as gender, age, family history, AAA size and local ILT thickness.

However, based on the principles of material failure knowledge of both, AAA

wall stress distribution and wall tissue strength are necessary to assess rupture

potential, and different biomechanical rupture risk indicators have been suggested

in literature25,44,115.

Another factor of significant importance in AAA rupture risk prediction is the

non-uniformity of the wall thickness. In fact, AAA wall has considerable regional

Biomechanics of Abdominal Aortic Aneurysm

16

variation in wall thickness with a reduction in wall thickness near the rupture

site86. Moreover a significant difference in wall thickness was found between

ruptured and electively repaired aneurysms, as well as an inverse correlation

between wall thickness and local tissue strength22,34.

Due to the inability to measure wall thickness noninvasively, a uniform thickness

is typically assumed in biomechanics modeling of AAAs. Other significant

limitations of previous studies include the use of isotropic tissue constitutive law85

and of a load-free reference configuration. Although an ILT is known to be an

important solid structure40 that influences AAA wall stress distribution it has been

disregarded in many biomechanical AAA models.

Advances in medical imaging, provide good information to perform patient-

specific vascular geometries reconstructions3,99 and an accurate characterization of

the aneurysm shape with the variation of wall thickness73,98 need to be accounted

for the assessment of AAA rupture. In particular the assumption of constant

distribution of wall thickness causes an underestimation of the PWS93,94.

Moreover, accounting for the ILT and the non-homogeneous distribution of tissue

strength and wall thickness in AAA models, reinforced the predictability of FE

simulations, which allowed for a statistically significant discrimination between

ruptured and non-ruptured AAAs44.

1.5. AAA biomechanics

To obtain a reliable estimation of PWS, it is necessary to perform an accurate

three-dimensional reconstruction of the AAA geometry, describe the applied

loads/boundary conditions and identify an appropriate constitutive law for the

aneurysmal tissue. In addition to the mathematical description of mechanical

properties an efficient and implicit numerical implementation28,42,43,45,46 of

constitutive formulations is beneficial for analyzing clinically relevant problems.

1.5.1. AAA wall histology

The wall of later stage aneurysms shows a negligible amount87 of fragmented62

elastin, as well as a sever decrease of smooth muscle cells71. Specifically, collagen

fibers in the vascular wall have a major impact on the mechanical properties at

17

higher loads48,88, i.e. the condition experienced by the aneurysm wall. In addition

to the volume fraction of collagen, its spatial arrangement, including the spread in

orientations32, significantly affects the macroscopic mechanical properties39,46.

Collagen fibrils are regarded as one basic building block of ECMs and give

mechanical strength, stiffness and toughness to the vasculature. Collagen fibrils

are locally secreted by fibroblast and assembled into organized suprafibrillar

structures that, to a large extent, determine the macroscopic mechanical

behavior17. Consequently, understanding the development of hierarchical collagen

structures is crucial to understand the mechanical properties of the vascular wall.

It is well accepted that the collagen structure develops under the action of

mechanical loading and eventually leads to mechanically-optimized structures.

Physiological maintenance of these structures relies on a delicate (coupled)

balance between continual degradation and synthesis of collagen. The

maintenance of fibrillar collagen is realized by fibroblast cells, i.e. by synthesis of

new collagen and degradation by metalloproteinases (MMPs) of existing

collagen49. Mature fibroblasts perceive changes in the mechanical strains/stresses

and adjust their expression and synthesis of collagen molecules in order to

account for the changes in their micro-mechanical environment. While an

alteration of collagen turnover is essential in response to injury4,10,49,102,106, a

malfunction of collagen turnover could fail to result in homeostasis and

determines AAAs disease14. Specifically, at later stages of aneurysm disease the

collagen synthesis is insufficient to counteract higher mechanical wall stress14.

Consequently, the structural integrity of the wall is not ensured, such that wall

strength decreases and the risk for AAA rupture increases proportionally.

1.5.2. AAA wall mechanics

Physiologic and biomechanical studies showed that the AAA wall is a

heterogeneous material undergoing large strains prior to failure59and deforming in

an isochoric manner26. In addition to these observations, a recent study on the

biaxial mechanical behavior of human AAA tissue specimens116 demonstrated a

moderate anisotropic behavior for aneurysmal arterial tissue. Constitutive

modeling of vascular tissue is an active field of research and numerous

Biomechanics of Abdominal Aortic Aneurysm

18

descriptions have been reported. However, the phenomenological

approaches16,21,36,58,85,90,89,110,112 that have been successfully used to fit

experimental data cannot allocate stress to the different histological constituents in

the vascular wall. Structural constitutive models29,43,46,54,55,65,74,127,128 overcome

this limitation and integrate histological and mechanical information of the arterial

wall. Normally, biological tissues respond to their mechanical environment and

model predictions based on passive constitutive descriptions, i.e. suppressing

tissue remodeling and growth can only cover a limited time period. Vascular

tissue develops at its in-vivo loading state, which induces residual strains in its

(hypothetical) load-free configuration, i.e. in the setting that typically serves as a

reference for computations. Predicting realistic physiological stress states with

passive constitutive models requires residual strains in the load-free configuration,

which for complex geometries are unfortunately unknown. Consequently, the key

for improving biomechanical models is to understand the tissue’s inherent

property to adapt to mechanical environments, and in that respect computational

simulations can be potentially helpful. Specifically, multiscale models allow

considering biological process at the microscale, which in turn define the

development of the vascular wall’s macroscopic mechanical properties.

1.5.3. AAA wall expansion

Describing the growth of aneurysms is an active field of research and early work

by Skalak et al. (1981)101 followed by Rodrıguez27 and colleagues contributed

significantly to a continuum-mechanics based modeling of growth and introduced

the concept of kinematics growth; i.e. growth as change is size or shape. This

concept has been then extended to model aspect of arterial adaptations to altered

flow and pressure64,84,109.

In late 1990s Fung also suggested the concept of ‘mass-stress’ based relation of

growth. The second general approach to model growth was built from Fung’s

suggestion, that is, by incorporating evolving mass fractions for individual

constituents within constitutive relations for stress response employing the basic

concept of ‘constrained mixture’ formulations56. This type of approach has led to

different applications to model AAA growth and remodeling61,95,96,124,125, where

19

rule of mixture included contributions from elastin, fibrillar collagen and smooth

muscle. In addition, a focal loss of elastin initiates the process of arterial

dilatations, whereas collagen turnover is responsible for the continuum

expansions.

Although these models were able to predict some clinical observations they are

based on oversimplified assumptions. For example, they use a collagen structure

with two or four families of fiber that is not seen histologically. The collagen

organization in the AAA wall in fact, shows much dispersed orientations39.

In conclusion, these models require significant further development to be

launched clinically, i.e. to predict patient-individual aneurysm rupture in a clinical

setting.

A different approach adopts instead a multi-scale microsphere-based framework,

where the macroscopic mechanical tissue properties are derived through a

numerical integration of a one-dimensional constitutive formulation over the

domain of a unit sphere. Different investigations showed the efficient and robust

applicability and capability of this computational framework that allowed

simulating mechanically induced fiber reorientations and remodeling phenomena

typically observed in soft biological tissues75,77.

Most importantly, this multi-scale constitutive formulation provides an interface

to incorporate evolution equations for the fibrous micro-constituents, to study, for

example, the impact of collagen turnover on the macroscopic properties of the

tissue. This allowed first, to capture fiber alignment with more than one single

direction, then to predict collagen fiber orientation in the AAA wall under

physiological loading conditions, and finally to successfully capture the

enlargement of small AAAs75.

Other approaches to model AAA expansions included the use of isotropic linear

elasticity with prescribed reduction of Young’s modulus to simulate wall

weaking52 or the coupling of growth and failure of the abdominal aortic

aneurysm118.

Biomechanics of Abdominal Aortic Aneurysm

20

Although an ILT is known to be an important solid structure40 that increases the

predictability of AAA models44, it was disregarded in the above mentioned

studies. Beside the intra-luminal thrombus’ direct solid mechanical impact it must

also be seen as a dynamic structure that develops in time. Consequently, a

clinically relevant AAA growth model should also account for the flow of blood

through the aneurysm8 and its coagulation process to thrombus formation9.

Similarly, possible contact with surrounding organs was not considered through

all AAA models mentioned. Naturally, growth model could be improved by

considering the intra-luminal thrombus and possible contact of the AAA,

especially with the spine.

1.5.4. AAA thrombus mechanics

An ILT is found in most AAAs of clinically relevant size50. It has been suggested

that the presence of ILT could dramatically decrease the AAA wall strength;

hypoxia caused by ILT is the main reason for this reduction.

The ILT can be regarded as an incompressible elastic body40 that undergoes non-

linear strains122 in vivo and that influences mechanical stress of the underlying

vessel wall 23,69,79,122,123.

To fully investigate the effect of thrombus concerning rupture risk assessment, it

is important to evaluate its mechanical properties. Mechanical testing showed an

isotropic linear stress-stretch response for ILT tissue and Di Martino et al.23,24

suggested a Hook relation to capture its biomechanical behavior. More recently,

uniaxial40,123 and biaxial116 testing showed that ILT is moderately non-linear

elastic, inhomogeneous, and isotropic.

Multiple biochemical62,63,120 and biomechanical24,41,60,69,79,120 consequences of the

ILT on the AAA have been reported. Likewise, it has been hypothesized that in

vivo ILT failure might be related to aneurysm failure,91 and signs of ILT rupture

have been identified from evaluating CT-A data2,100,107.

Similarly, ILT reveals remarkable heterogeneous Magnetic Resonance (MR)

signal intensity indicating its complex heterogenous microstructure. Nevertheless,

current biomechanical AAA models assume either homogeneous24,60,69,79,120 or

radially changing41 mechanical properties for the ILT, and more realistic

21

distributions might impact the biomechanical assessment of AAA rupture risk.

Accounting for inhomogeneities such as fissures in the ILT can have a

pronounced impact on the stress in the aneurysm wall, and, consequently, the

influence of ILT’s inhomogeneous composition on the wall stress could be of

interest for further investigations82.

Biomechanics of Abdominal Aortic Aneurysm

22

23

2. METHODS

A brief review of the applied methods of the present thesis is given below. For

further details see the methods sections of the attached papers (Paper A-D).

2.1. Experimental evidence of AAA growth

Multiple centerline-based diameter measurements between renal arteries and

aortic bifurcation have been used in order to quantify AAA growth of in total 51

patients from CT-A data. Criteria for inclusion were at least one year patient

follow-up and the availability of at least two sufficiently high resolutions CT-A

scans that allowed an accurate three-dimensional reconstruction. Consequently,

124 CT-A scan were systematically analyzed with the diagnostic software

A4clinics (VASCOPS GmbH, Graz, Austria) and aneurysm growth was

monitored at 100 cross-sections perpendicular to the lumen centerline. Measuring

the expansion all along the aneurysm sac can uncover the site of fastest diameter

growth, quantifies the axial growth of the aneurysm, as well as the evolution of

the neck morphology.

2.2. Multiscale constitutive modeling

A novel multi-scale constitutive model for vascular tissue, where collagen fibers

are assembled by proteoglycan cross-linked collagen fibrils (CFPG-complex) and

reinforce an otherwise isotropic matrix (elastin), is presented. Multiplicative

kinematics account for the straightening and stretching of collagen fibrils, and an

orientation density function captures the spatial organization of collagen fibers in

the tissue. Mechanical and structural assumptions at the collagen fibril level

define a piece-wise analytical stress–stretch response of collagen fibers. Likewise,

Biomechanics of Abdominal Aortic Aneurysm

24

collagen fiber are dynamically formed by a continuous stretch-mediated process,

deposited in the current configuration and removed by a constant degradation rate.

Finally, similar to the micro-plane concept6, the macroscopic stress at the material

point is derived by integration over the unit sphere. Specifically, spherical t-

designs 28,51 are used to perform this integration and the constitutive law has been

implemented in a FE environment.

Finally, the model was calibrated to the growth of AAAs that were followed-up

with CT–A as illustrated in §2.1.

2.3. Micromechanical characterization of ILT

Histological slices from 7 ILTs were analyzed using a sequence of automatic

image processing and feature analyzing steps. Derived microstructural data was

used to define Representative Volume Elements (RVE), which in turn allowed the

estimation of microscopic material properties using the non-linear Finite Element

Method (FEM). To this end, constitutive properties at the microscale were

estimated by comparing homogenized FE results with macroscopic experimental

data derived earlier in our laboratory40.

25

3. RESULTS

The most essential results that were derived in this thesis are summarized below.

For further details see the results sections of the attached papers (Paper A-D).

3.1. Clinical study

The aneurysm diameter expanded all over the aneurysm sac in average by 5.6 per

cent per year and at the site of maximal growth of 16 per cent per year. The site of

maximum diameter growth did not coincide with the site of the maximum

diameter. The aneurysm sac expanded longitudinally by 3.7 per cent per year. The

neck length shortened in average by 6 per cent per year, which was accompanied

by a slight increase in neck angulations. The change of maximum aneurysm

diameter as well as volume over time correlated to the mean diameter expansion

of the aneurysm sac (r=0.69 and r=0.77) but not to its maximum diameter

expansion (r=0.43 and r=0.34). Figure 2 summarizes the main results.

Biomechanics of Abdominal Aortic Aneurysm

26

Figure 2: Box-and-Whisker plots of multiple centerline-based aneurysm expansions and global-based aneurysm expansions. : maximum diameter growth; : mean diameter growth, i.e. averaged between the renal arteries and the aortic bifurcation; : global maximum diameter-based expansion rate;

: global volume-based aneurysm expansion; : global longitudinal aneurysm expansion. + symbols denote outliers.

3.2. Numerical predictions of the passive and active responses of the AAA

wall

Although simple mechanical and kinematics assumptions define the collagen

fibril level, the passive model could capture the macroscopic complexity of

vascular tissue, i.e. it replicated the typical stiffening of vascular tissue at the

physiological strain level (Figure 3).

1 1.02 1.04 1.06 1.08 1.10

0.05

0.1

0.15

0.2

0.25

0.3

Stretch λ

Firs

t Pio

la-K

irchh

off s

tress

[MPa

]

Mean pop. data circumferentialMean pop. data longitudinalFE model best fit

AAA biaxial tension

Figure 3: Macroscopic constitutive response of the Abdominal Aortic Aneurysm (AAA) wall under biaxial tension. Best fit Finite Element (FE) results (points) according to the proposed multi-scale constitutive model were compared to mean-population data (lines) reported in the literature116.

Most importantly with regard to the active wall model, collagen turnover had a

remarkable impact on the macroscopic stress field. It avoided high stress gradients

across the vessel wall, thus predicted a physiologically reasonable stress field. It

was founded that the stretch spectrum, at which collagen fibrils are deposed, is the

most influential parameter. Specifically, it determines whether the vascular

geometry grows, shrinks or remains stable in time. See Figure 4 for the

development in time of a patient-specific AAA.

27

Biomechanics of Abdominal Aortic Aneurysm

28

0.22 MPa

0.01

(a) (b) (c) (d)

Figure 4: Stress and shape development of a patient-specific Abdominal Aortic Aneurysm (AAA) model. (a)-(c) Maximum principal Cauchy stress in a patient-specific Abdominal Aortic Aneurysm (AAA) model. (a) Maximum principal Cauchy stress prediction that neglected collagen turnover (passive model). (b) Maximum principal Cauchy stress prediction that accounted for collagen turnover leading to homeostasis. (c) Maximum principal Cauchy stress prediction after one year collagen turnover with parameters that matched the growth of small AAAs. (d) AAA shape difference between the homeostatic solution (b) (dashed line) and the prediction after one year growth (c) (solid line).

3.3. Microstructural and micromechanical characterization of ILT

ILT tissue exhibited complex microstructural arrangement with larger pores in the

abluminal layer than in the luminal layer. The microstructure was isotropic in the

abluminal layer, whereas pores started to orient along the circumferential

direction towards the luminal site. ILT’s macroscopic (reversible) deformability

was supported by large pores in the microstructure and the inhomogeneous

structure explains in part the radially changing macroscopic constitutive

properties of ILT. Its microscopic properties decreased just slightly from the

luminal to the abluminal layer. Moreover, ILT’s constitution was roughly two

times stiffer at the micro than at the macro-scale. See Figure 5 for the strain and

stress distribution at the micro-scale.

Figure 5: Maximum principal natural strain (left) and maximum principal Cauchy stress (right) at the microscale of ILT tissue. Quantities are considered in the ligament material of a particular luminal RVE under macroscopic uniaxial stretch of 6 per cent.

29

Biomechanics of Abdominal Aortic Aneurysm

30

31

4. DISCUSSION The results from this thesis showed that AAAs not necessarily grew fastest at the

site of the maximum diameter but randomly somewhere all along the

aneurysmatic sac. Consequently, monitoring the development of the maximum

diameter is not able to measure the maximum diameter growth of the aneurysm,

and hence may not be able to quantify the risk for rupture adequately. The

biomechanical model developed in this thesis was able to capture the non-linear

mechanics of the aortic wall and demonstrated good predictive capability.

Macroscopic stress predictions did not differ much from earlier proposed

constitutive models of the wall’s passive response; however, the multi-scale

approach followed in the present thesis provided information at different length

scales. The framework’s collagen fibril level allowed a sound integration of

vascular wall biology and the impact of collagen turnover on the macroscopic

properties of AAAs was studied. Although the model was able to successfully

capture the enlargement of small AAAs, a rigorous validation against

experimental data would be crucial to evaluate its descriptive and predictive

capabilities. Likewise, the constitutive concept renders a highly efficient multi-

scale structural approach that facilitates the numerical analysis of patient-specific

vascular geometries. Finally, the thesis provided novel structural and mechanical

data for a detailed biomechanical investigation of ILT tissue at the micro-scale.

As a demonstrative application the micro-stress distribution under macroscopic

uniaxial loading was predicted, which indicated micro-scale load transmission

pathways and possible failure scenarios. Similar investigations might be carried

out under general loading conditions to assist experimental testing and to derive

damage and failure surfaces for ILT tissue.

Biomechanics of Abdominal Aortic Aneurysm

32

33

5. CONCLUSIONS

This thesis contributed for a better understanding of AAA disease, which might

improve the clinical management of aneurysm patients. Specifically, it has been

shown that neither maximum diameter nor volume measurements over time are

able to measure the fastest diameter growth of the aneurysmatic sac, such that

expansion-related wall weakening might be inappropriately reflected by this type

of surveillance data. In contrast, localized spots of fast diameter growth can be

detected through multiple centerline-based diameter measurements all over the

aneurysmatic sac. Consequently, this information might further reinforce the

quality of aneurysm surveillance programs.

A better understanding of the risk of rupture critically depends on appropriate

constitutive models. The novel constitutive model proposed in the thesis has a

strong biological motivation and integrates the fibril and fiber levels of collagen

with the tissue’s macroscopic properties. Such a structural view is important to

understand the interplay of the tissue’s histology (internal architecture) and its

macroscopic mechanical properties. Apart from modeling the tissue’s passive

response, the presented model might be helpful to understand the impact of

collagen turnover on the macroscopic properties of tissue and to predict saline

feature of aneurysm growth and remodeling.

Finally, the thesis provided novel microstructural and micromechanical data of

ILT tissue, which is critically important to further explore the role of the ILT in

aneurysm rupture. Data provided in this study allow an integration of structural

information from medical imaging for example, to estimate non-invasively ILT’s

macroscopic mechanical properties.

Biomechanics of Abdominal Aortic Aneurysm

34

35

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