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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 ISSN ISRN

HFL-0530 1654-1472 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 (FAD200647), 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 1921, Stockholm, Sweden, 2009.

Contents 1. INTRODUCTION 1.1. Background 1.2. Pathophysiology of AAA 1.3. Rupture criteria in a clinical setting 1.4. Biomechanical rupture risk assessment 1.5. AAA biomechanics

11 11 13

1.5.1. AAA wall histology 1.5.2. AAA wall mechanics 1.5.3. AAA wall expansion 1.5.4. AAA thrombus mechanics

16 17

14 15 16

18 20

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

23 23 23 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 5. CONCLUSIONS 6. REFERENCES

31 33 35

Paper A Paper B Paper C Paper D 9

Biomechanics of Abdominal Aortic Aneurysm

10

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 11


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: [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

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 halflife 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 13

Biomechanics of Abdominal Aortic Aneurysm 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

14

growth, and it cannot capture shape changes of potential interest for EVARrelated 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 nonruptured 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 15


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 patientspecific 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 16

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 17


descriptions

have

been

16,21,36,58,85,90,89,110,112

approaches

reported.

However,

the

phenomenological

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 18

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.

19

Biomechanics of Abdominal Aortic Aneurysm 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 nonlinear 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 20

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.

21


22

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, 23


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 tdesigns 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.

24

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.

25


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).

26

First Piola-Kirchhoff stress [MPa]

0.3 0.25

Mean pop. data circumferential Mean pop. data longitudinal FE model best fit

0.2

AAA biaxial tension

0.15 0.1 0.05 0 1

1.02

1.04

1.06

Stretch λ

1.08

1.1

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 meanpopulation 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 MPa 0.22

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 patientspecific 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.

28

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


30

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 multiscale 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. 31


32

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. 33


34

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